Finite Group Databasebeta

← #29887092

Subgroups — #29887092

Order 15616.

2644 conjugacy classes of subgroups.

The subgroup lattice has 1818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840345C211yesmaximal, characteristic, complemented
2#21454111C211yesmaximal, characteristic, complemented
3#21454101C211yesmaximal, characteristic, complemented
4#21452488C211yesmaximal, characteristic, complemented
5#21452443C211yesmaximal, characteristic, complemented
6#21452413C211yesmaximal, characteristic, complemented
7#21452402C211yesmaximal, characteristic, complemented
8#21452234C211yesmaximal, characteristic, complemented
9#21452184C211yesmaximal, characteristic, complemented
10#21452174C211yesmaximal, characteristic, complemented
11#21452167C211yesmaximal, characteristic, complemented
12#21452153C211yesmaximal, characteristic, complemented
13#21452147C211yesmaximal, characteristic, complemented
14#21452144C211yesmaximal, characteristic, complemented
15#21452138C211yesmaximal, characteristic, complemented
16#21452064C211yesmaximal, characteristic, complemented
17#21452041C211yesmaximal, characteristic, complemented
18#21452033C211yesmaximal, characteristic, complemented
19#21452031C211yesmaximal, characteristic, complemented
20#21451703C211yesmaximal, characteristic, complemented
21#21451656C211yesmaximal, characteristic, complemented
22#21451506C211yesmaximal, characteristic, complemented
23#21451440C211yesmaximal, characteristic, complemented
24#21451416C211yesmaximal, characteristic, complemented
25#21451401C211yesmaximal, characteristic, complemented
26#21450786C211yesmaximal, characteristic, complemented
27#21450705C211yesmaximal, characteristic, complemented
28#21449158C211yesmaximal, characteristic, complemented
29#21449134C211yesmaximal, characteristic, complemented
30#21448462C211yesmaximal, characteristic, complemented
31C2×C61×#525C211yesmaximal, characteristic, complemented
32#16840345—28no—
33C2×#14519773C2211yescharacteristic
34C2×#14519772C2211yescharacteristic, complemented
35C2×#14519771C2211yescharacteristic, complemented
36C2×#14519765C2211yescharacteristic, complemented
37C2×#14519764C2211yescharacteristic, complemented
38C2×#14519763C2211yescharacteristic
39C2×#14519762C2211yescharacteristic, complemented
40C2×#14519760C2211yescharacteristic
41C2×#14519760C2211yescharacteristic
42C2×#14519758C2211yescharacteristic
43C2×#14519754C2211yescharacteristic, complemented
44C2×#14519753C2211yescharacteristic, complemented
45C2×#14519751C2211yescharacteristic
46C2×#14519751C2211yescharacteristic
47C2×#14519751C2211yescharacteristic
48C2×#14519750C2211yescharacteristic
49C2×#14519749C2211yescharacteristic
50C2×#14519748C2211yescharacteristic, complemented
51C2×#14519747C2211yescharacteristic, complemented
52C2×#14519746C2211yescharacteristic
53C2×#14519746C2211yescharacteristic
54C2×#14519746C2211yescharacteristic, complemented
55C2×#14519745C2211yescharacteristic
56C2×#14519745C2211yescharacteristic
57C2×#14519745C2211yescharacteristic
58C2×#14519745C2211yescharacteristic, complemented
59C2×C4×C22⋊D61C2211yescharacteristic, complemented
60C22×#11758198C2211yescharacteristic, complemented
61#16839701C2211yescharacteristic, complemented
62#16839698C2211yescharacteristic, complemented
63#16839695C2211yescharacteristic, complemented
64#16839695C2211yescharacteristic, complemented
65#16839693C2211yescharacteristic, complemented
66#16839690C2211yescharacteristic, complemented
67#16839690C2211yescharacteristic, complemented
68#16839688C2211yescharacteristic, complemented
69#16839685C2211yescharacteristic, complemented
70#16839685C2211yescharacteristic, complemented
71#16839684C2211yescharacteristic, complemented
72#16839684C2211yescharacteristic, complemented
73#16839684C2211yescharacteristic, complemented
74#16839684C2211yescharacteristic, complemented
75#16839682C2211yescharacteristic, complemented
76#16839679C2211yescharacteristic, complemented
77#16839679C2211yescharacteristic, complemented
78#16839678C2211yescharacteristic
79#16839678C2211yescharacteristic
80#16839678C2211yescharacteristic
81#16839678C2211yescharacteristic
82#16839678C2211yescharacteristic, complemented
83#16839678C2211yescharacteristic, complemented
84#16839678C2211yescharacteristic, complemented
85#16839678C2211yescharacteristic, complemented
86#16839677C2211yescharacteristic
87#16839677C2211yescharacteristic
88#16839677C2211yescharacteristic, complemented
89#16839677C2211yescharacteristic, complemented
90#16839676C2211yescharacteristic
91#16839676C2211yescharacteristic
92#16839676C2211yescharacteristic, complemented
93#16839676C2211yescharacteristic, complemented
94#16839676C2211yescharacteristic, complemented
95#16839674C2211yescharacteristic, complemented
96#16839673C2211yescharacteristic, complemented
97#16839673C2211yescharacteristic, complemented
98#16839671C2211yescharacteristic
99#16839671C2211yescharacteristic, complemented
100#16839670C2211yescharacteristic
101#16839670C2211yescharacteristic
102#16839670C2211yescharacteristic
103#16839670C2211yescharacteristic
104#16839670C2211yescharacteristic
105#16839670C2211yescharacteristic
106#16839670C2211yescharacteristic
107#16839670C2211yescharacteristic, complemented
108#16839670C2211yescharacteristic, complemented
109#16839669C2211yescharacteristic, complemented
110#16839667C2211yescharacteristic, complemented
111#16839665C2211yescharacteristic
112#16839665C2211yescharacteristic
113#16839665C2211yescharacteristic, complemented
114#16839663C2211yescharacteristic, complemented
115#16839662C2211yescharacteristic
116#16839662C2211yescharacteristic
117#16839662C2211yescharacteristic
118#16839662C2211yescharacteristic, complemented
119#16839662C2211yescharacteristic, complemented
120#16839661C2211yescharacteristic, complemented
121#16839661C2211yescharacteristic, complemented
122#16839657C2211yescharacteristic, complemented
123#16839656C2211yescharacteristic, complemented
124#16839656C2211yescharacteristic, complemented
125#16839656C2211yescharacteristic, complemented
126#16839655C2211yescharacteristic, complemented
127#16839655C2211yescharacteristic, complemented
128#16839655C2211yescharacteristic, complemented
129#16839655C2211yescharacteristic, complemented
130#16839653C2211yescharacteristic, complemented
131#16839653C2211yescharacteristic, complemented
132#16839653C2211yescharacteristic, complemented
133#16839652C2211yescharacteristic, complemented
134#16839652C2211yescharacteristic, complemented
135#16839652C2211yescharacteristic, complemented
136#16839650C2211yescharacteristic, complemented
137#16839646C2211yescharacteristic, complemented
138#16839643C2211yescharacteristic, complemented
139#16839642C2211yescharacteristic
140#16839642C2211yescharacteristic, complemented
141#16839641C2211yescharacteristic
142#16839641C2211yescharacteristic
143#16839641C2211yescharacteristic
144#16839641C2211yescharacteristic
145#16839641C2211yescharacteristic
146#16839641C2211yescharacteristic
147#16839641C2211yescharacteristic
148#16839641C2211yescharacteristic, complemented
149#16839641C2211yescharacteristic, complemented
150#16839641C2211yescharacteristic, complemented
151#16839641C2211yescharacteristic, complemented
152#16839641C2211yescharacteristic, complemented
153#16839641C2211yescharacteristic, complemented
154#16839638C2211yescharacteristic, complemented
155#16839635C2211yescharacteristic, complemented
156#16839635C2211yescharacteristic, complemented
157#16839635C2211yescharacteristic, complemented
158#16839635C2211yescharacteristic, complemented
159#16839635C2211yescharacteristic, complemented
160#16839633C2211yescharacteristic, complemented
161#16839625C2211yescharacteristic, complemented
162#16839625C2211yescharacteristic, complemented
163#16839625C2211yescharacteristic, complemented
164#16839623C2211yescharacteristic, complemented
165#16839622C2211yescharacteristic, complemented
166#16839622C2211yescharacteristic, complemented
167#16839622C2211yescharacteristic, complemented
168#16839622C2211yescharacteristic, complemented
169#16839618C2211yescharacteristic, complemented
170#16839617C2211yescharacteristic, complemented
171C4×C4⋊Dic61C2211yescharacteristic, complemented
172#16839608C2211yescharacteristic, complemented
173C22×#41×C61C2211yescharacteristic
174C24×C4×C61C2211yescharacteristic, complemented
175C61×#525—28no—
176C2×#123×C61C2211yescharacteristic
177C2×#123×C61C2211yescharacteristic, complemented
178C2×C22⋊Q8×C61C2211yescharacteristic, complemented
179C2×C22⋊Q8×C61C2211yescharacteristic, complemented
180C2×#121×C61C2211yescharacteristic
181C2×#121×C61C2211yescharacteristic
182C2×#120×C61C2211yescharacteristic
183C2×#120×C61C2211yescharacteristic, complemented
184C2×C4×D4×C61C2211yescharacteristic
185C2×C4×D4×C61C2211yescharacteristic
186C2×C4×D4×C61C2211yescharacteristic, complemented
187C2×C4×D4×C61C2211yescharacteristic, complemented
188C2×#117×C61C2211yescharacteristic, complemented
189C24×D61C2311yescharacteristic
190C22×Dic122C2311yescharacteristic
191C22×D244C2311yescharacteristic
192C22×D244C2311yescharacteristic
193C22×C22⋊D61C2311yescharacteristic
194C22×C22⋊D61C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C22×C22⋊D61C2311yescharacteristic
197C22×C22⋊D61C2311yescharacteristic
198C22×C22⋊D61C2311yescharacteristic
199C22×C22⋊D61C2311yescharacteristic
200C22×C22⋊D61C2311yescharacteristic
201C22×C22⋊D61C2311yescharacteristic
202C22×C22⋊D61C2311yescharacteristic
203C22×C22⋊D61C2311yescharacteristic
204C22×C22⋊D61C2311yescharacteristic
205C22×C22⋊D61C2311yescharacteristic
206C23×Dic61C2311yescharacteristic
207C22×C4×D61C2311yescharacteristic
208#14519773—42no—
209#14519772—24no—
210#14519771—24no—
211#14519765—24no—
212#14519764—42no—
213#14519763—24no—
214#14519762—24no—
215#14519760—24no—
216#14519760—42no—
217#14519758—42no—
218#14519754—24no—
219#14519753—42no—
220#14519751—24no—
221#14519751—42no—
222#14519751—42no—
223#14519750—24no—
224#14519749—24no—
225#14519748—42no—
226#14519747—24no—
227#14519746—42no—
228#14519746—42no—
229#14519746—42no—
230#14519745—24no—
231#14519745—42no—
232#14519745—42no—
233#14519745—42no—
234C4×C22⋊D61—24no—
235C2×C4⋊Dic61C2311yescharacteristic
236C2×C4⋊Dic61C2311yescharacteristic
237C2×C4⋊Dic61C2311yescharacteristic
238C2×C4⋊Dic61C2311yescharacteristic
239C2×C4⋊Dic61C2311yescharacteristic
240C2×C4⋊Dic61C2311yescharacteristic
241C2×C4⋊Dic61C2311yescharacteristic
242C2×#11758196C2311yescharacteristic
243C2×#11758196C2311yescharacteristic
244C2×#11758196C2311yescharacteristic
245C2×#11758196C2311yescharacteristic
246C2×#11758196C2311yescharacteristic
247C2×#11758196C2311yescharacteristic
248C2×#11758196C2311yescharacteristic
249C2×#11758196C2311yescharacteristic
250C2×#11758196C2311yescharacteristic
251C2×#11758196C2311yescharacteristic
252C2×#11758196C2311yescharacteristic
253C2×C22⋊Dic61C2311yescharacteristic
254C2×C22⋊Dic61C2311yescharacteristic
255C2×C22⋊Dic61C2311yescharacteristic
256C2×C22⋊Dic61C2311yescharacteristic
257C2×C22⋊Dic61C2311yescharacteristic
258C2×C22⋊Dic61C2311yescharacteristic
259C2×C22⋊Dic61C2311yescharacteristic
260C2×C22⋊Dic61C2311yescharacteristic
261C2×C22⋊Dic61C2311yescharacteristic
262C2×C22⋊Dic61C2311yescharacteristic
263C2×C22⋊Dic61C2311yescharacteristic
264C2×C22⋊Dic61C2311yescharacteristic
265C2×C22⋊Dic61C2311yescharacteristic
266C2×C22⋊Dic61C2311yescharacteristic
267C2×C22⋊Dic61C2311yescharacteristic
268C2×C22⋊Dic61C2311yescharacteristic
269C2×C22⋊Dic61C2311yescharacteristic
270C2×C22⋊Dic61C2311yescharacteristic
271C2×C22⋊Dic61C2311yescharacteristic
272C2×C22⋊Dic61C2311yescharacteristic
273C2×C22⋊Dic61C2311yescharacteristic
274C2×C22⋊Dic61C2311yescharacteristic
275C2×C22⋊Dic61C2311yescharacteristic
276C2×C22⋊Dic61C2311yescharacteristic
277C2×C22⋊Dic61C2311yescharacteristic
278C2×#11758198—24no—
279C2×#11758198C2311yescharacteristic
280C2×#11758198C2311yescharacteristic
281C2×#11758198C2311yescharacteristic
282C2×#11758198C2311yescharacteristic
283C2×#11758198C2311yescharacteristic
284C2×#11758198C2311yescharacteristic
285C2×#11758198C2311yescharacteristic
286C2×#11758198C2311yescharacteristic
287C2×#11758198C2311yescharacteristic
288C2×#11758198C2311yescharacteristic
289C2×#11758198C2311yescharacteristic
290C2×#11758198C2311yescharacteristic
291C2×#11758198C2311yescharacteristic
292C2×#11758198C2311yescharacteristic
293C2×#11758198C2311yescharacteristic
294C2×#11758198C2311yescharacteristic
295C2×#11758198C2311yescharacteristic
296C2×#11758198C2311yescharacteristic
297C2×#11758198C2311yescharacteristic
298C2×#11758198C2311yescharacteristic
299C2×#11758198C2311yescharacteristic
300C2×#11758198C2311yescharacteristic
301C2×#11758198C2311yescharacteristic
302C2×#11758198C2311yescharacteristic
303C2×#11758198C2311yescharacteristic
304C2×C4×Dic61C2311yescharacteristic
305C2×C4×Dic61C2311yescharacteristic
306C2×C4×Dic61C2311yescharacteristic
307C2×C4×Dic61C2311yescharacteristic
308C2×C4×Dic61C2311yescharacteristic
309#14519684C2311yescharacteristic
310#14519684C2311yescharacteristic
311#14519684C2311yescharacteristic
312#14519684C2311yescharacteristic
313#14519684C2311yescharacteristic
314#14519684C2311yescharacteristic
315#14519684C2311yescharacteristic
316#14519684C2311yescharacteristic
317#14519684C2311yescharacteristic
318#14519684C2311yescharacteristic
319#14519684C2311yescharacteristic
320#14519684C2311yescharacteristic
321#14519684C2311yescharacteristic
322#14519684C2311yescharacteristic
323#14519684C2311yescharacteristic
324#14519684C2311yescharacteristic
325#14519684C2311yescharacteristic
326#14519684C2311yescharacteristic
327#14519684C2311yescharacteristic
328#14519684C2311yescharacteristic
329#14519684C2311yescharacteristic
330#14519684C2311yescharacteristic
331#14519684C2311yescharacteristic
332#14519684C2311yescharacteristic
333#14519684C2311yescharacteristic
334#14519684C2311yescharacteristic
335#14519684C2311yescharacteristic
336#14519684C2311yescharacteristic
337C25×C61C2311yescharacteristic
338C2×#41×C61—24no—
339C2×#41×C61—42no—
340C2×#41×C61—42no—
341C22×Q8×C61C2311yescharacteristic
342C22×D4×C61C2311yescharacteristic
343C22×D4×C61C2311yescharacteristic
344C22×D4×C61C2311yescharacteristic
345C22×D4×C61C2311yescharacteristic
346C22×D4×C61C2311yescharacteristic
347C22×D4×C61C2311yescharacteristic
348C22×D4×C61C2311yescharacteristic
349C23×C4×C61—24no—
350C23×C4×C61—42no—
351C23×C4×C61—42no—
352C23×C4×C61C2311yescharacteristic
353C23×C4×C61C2311yescharacteristic
354C23×C4×C61C2311yescharacteristic
355C23×C4×C61C2311yescharacteristic
356C23×C4×C61C2311yescharacteristic
357C23×C4×C61C2311yescharacteristic
358C23×C4×C61C2311yescharacteristic
359C23×C4×C61C2311yescharacteristic
360#123×C61—24no—
361#123×C61—24no—
362C22⋊Q8×C61—24no—
363C22⋊Q8×C61—24no—
364#121×C61—24no—
365#121×C61—24no—
366#120×C61—24no—
367#120×C61—24no—
368C4×D4×C61—24no—
369C4×D4×C61—24no—
370C4×D4×C61—24no—
371C4×D4×C61D418yescomplemented
372#117×C61—24no—
373C2×C4⋊C4×C61C2311yescharacteristic
374C2×C4⋊C4×C61C2311yescharacteristic
375C2×C4⋊C4×C61C2311yescharacteristic
376C2×C4⋊C4×C61C2311yescharacteristic
377C2×C4⋊C4×C61C2311yescharacteristic
378C2×C4⋊C4×C61C2311yescharacteristic
379C2×C22⋊C4×C61C2311yescharacteristic
380C2×C22⋊C4×C61C2311yescharacteristic
381C2×C22⋊C4×C61C2311yescharacteristic
382C2×C22⋊C4×C61C2311yescharacteristic
383C2×C22⋊C4×C61C2311yescharacteristic
384C2×C22⋊C4×C61C2311yescharacteristic
385C2×C22⋊C4×C61C2311yescharacteristic
386C2×C22⋊C4×C61C2311yescharacteristic
387C2×C22⋊C4×C61C2311yescharacteristic
388C2×C22⋊C4×C61C2311yescharacteristic
389C2×C42×C61C2311yescharacteristic
390C2×C42×C61C2311yescharacteristic
391C24×C61—22no—
392C24×C61—22no—
393C24×C61—22no—
394C24×C61—41no—
395C24×C61—41no—
396C24×C61—41no—
397C24×C61—41no—
398C24×C61C2411yescharacteristic
399C24×C61C2411yescharacteristic
400C24×C61C2411yescharacteristic
401C24×C61C2411yescharacteristic
402C24×C61C2411yescharacteristic
403C23×D61—22no—
404C23×D61—41no—
405C23×D61—41no—
406C23×D61—41no—
407C23×D61—41no—
408C23×D61—41no—
409C23×D61—41no—
410C23×D61C2411yescharacteristic
411C23×D61C2411yescharacteristic
412C23×D61C2411yescharacteristic
413#41×C61—416no—
414C2×Q8×C61—22no—
415C2×Q8×C61—22no—
416C2×Q8×C61—41no—
417C2×D4×C61—22no—
418C2×D4×C61—22no—
419C2×D4×C61—22no—
420C2×D4×C61—22no—
421C2×D4×C61—22no—
422C2×D4×C61—22no—
423C2×D4×C61—22no—
424C2×D4×C61—22no—
425C2×D4×C61—22no—
426C2×D4×C61—22no—
427C2×D4×C61—22no—
428C2×D4×C61—41no—
429C2×D4×C61—41no—
430C2×D4×C61—41no—
431C2×D4×C61—41no—
432C2×D4×C61—41no—
433C2×D4×C61—41no—
434C2×D4×C61—41no—
435C2×D4×C61—41no—
436C2×D4×C61—41no—
437C2×D4×C61C2×D414yes—
438C22×C4×C61—22no—
439C22×C4×C61—22no—
440C22×C4×C61—22no—
441C22×C4×C61—22no—
442C22×C4×C61—22no—
443C22×C4×C61—22no—
444C22×C4×C61—22no—
445C22×C4×C61—22no—
446C22×C4×C61—22no—
447C22×C4×C61—22no—
448C22×C4×C61—22no—
449C22×C4×C61—41no—
450C22×C4×C61—41no—
451C22×C4×C61—41no—
452C22×C4×C61—41no—
453C22×C4×C61—41no—
454C22×C4×C61—41no—
455C22×C4×C61—41no—
456C22×C4×C61—41no—
457C22×C4×C61—41no—
458C22×C4×C61—41no—
459C22×C4×C61—41no—
460C22×C4×C61—416no—
461C22×C4×C61C2×D414yes—
462C22×C4×C61C2×D414yes—
463C22×C4×C61C2411yescharacteristic
464C22×C4×C61C2411yescharacteristic
465C22×C4×C61C2411yescharacteristic
466C22×C4×C61C2411yescharacteristic
467C22×C4×C61C2411yescharacteristic
468C22×C4×C61C2411yescharacteristic
469C22×C4×C61C2411yescharacteristic
470C22×C4×C61C2411yescharacteristic
471C22×C4×C61C2411yescharacteristic
472C22×C4×C61C2411yescharacteristic
473C2×C22⋊D61—22no—
474C2×C22⋊D61—22no—
475C2×C22⋊D61—22no—
476C2×C22⋊D61—22no—
477C2×C22⋊D61—22no—
478C2×C22⋊D61—22no—
479C2×C22⋊D61—22no—
480C2×C22⋊D61—22no—
481C2×C22⋊D61—22no—
482C2×C22⋊D61—22no—
483C2×C22⋊D61—41no—
484C2×C22⋊D61—41no—
485C2×C22⋊D61—41no—
486C2×C22⋊D61—41no—
487C2×C22⋊D61—41no—
488C2×C22⋊D61—41no—
489C2×C22⋊D61—41no—
490C2×C22⋊D61—41no—
491C2×C22⋊D61—41no—
492C2×C22⋊D61—41no—
493C2×C22⋊D61—41no—
494C2×C22⋊D61—41no—
495C2×C22⋊D61—41no—
496C2×C22⋊D61—41no—
497C2×C22⋊D61—41no—
498C2×C22⋊D61—41no—
499C2×C22⋊D61—41no—
500C2×C22⋊D61—41no—
501C2×C22⋊D61—41no—
502C2×C22⋊D61—41no—
503C2×C22⋊D61—41no—
504C2×C22⋊D61—41no—
505C2×C22⋊D61—41no—
506C2×C22⋊D61—41no—
507C2×C22⋊D61—41no—
508C2×C22⋊D61—41no—
509C2×C22⋊D61—41no—
510C2×C22⋊D61—41no—
511C2×C22⋊D61—41no—
512C22×Dic61—22no—
513C22×Dic61—41no—
514C22×Dic61—41no—
515C22×Dic61C2411yescharacteristic
516C22×Dic61C2411yescharacteristic
517C22×Dic61C2411yescharacteristic
518C22×Dic61C2411yescharacteristic
519C22×Dic61C2411yescharacteristic
520C22×Dic61C2411yescharacteristic
521C22×Dic61C2411yescharacteristic
522C22×Dic61C2411yescharacteristic
523C22×Dic61C2411yescharacteristic
524C22×Dic61C2411yescharacteristic
525C22×Dic61C2411yescharacteristic
526C22×Dic61C2411yescharacteristic
527C22×Dic61C2411yescharacteristic
528C2×D244—22no—
529C2×D244—22no—
530C2×D244—41no—
531C2×D244—41no—
532C2×D244—41no—
533C2×D244—41no—
534C2×C4×D61—22no—
535C2×C4×D61—41no—
536C2×C4×D61—41no—
537C2×Dic122—22no—
538C2×Dic122—41no—
539C2×Dic122—41no—
540C4⋊C4×C61—22no—
541C4⋊C4×C61—22no—
542C4⋊C4×C61—22no—
543C4⋊C4×C61—22no—
544C4⋊C4×C61—22no—
545C4⋊C4×C61C2×D414yes—
546C22⋊C4×C61—22no—
547C22⋊C4×C61—22no—
548C22⋊C4×C61—22no—
549C22⋊C4×C61—22no—
550C22⋊C4×C61—22no—
551C22⋊C4×C61—22no—
552C22⋊C4×C61—22no—
553C22⋊C4×C61—22no—
554C22⋊C4×C61C2×D414yes—
555C22⋊C4×C61C2×D414yes—
556C42×C61—22no—
557C42×C61C2×D414yes—
558C22⋊Dic61—22no—
559C22⋊Dic61—22no—
560C22⋊Dic61—22no—
561C22⋊Dic61—22no—
562C22⋊Dic61—22no—
563C22⋊Dic61—22no—
564C22⋊Dic61—41no—
565C22⋊Dic61—41no—
566C22⋊Dic61—41no—
567C22⋊Dic61—41no—
568C22⋊Dic61—41no—
569C22⋊Dic61—41no—
570C22⋊Dic61—41no—
571C22⋊Dic61—41no—
572C22⋊Dic61—41no—
573C22⋊Dic61—41no—
574C22⋊Dic61—41no—
575C22⋊Dic61—41no—
576C22⋊Dic61—41no—
577C22⋊Dic61—41no—
578C22⋊Dic61—41no—
579C22⋊Dic61—41no—
580C22⋊Dic61—41no—
581C22⋊Dic61—41no—
582C22⋊Dic61—41no—
583#11758198—22no—
584#11758198—22no—
585#11758198—22no—
586#11758198—22no—
587#11758198—22no—
588#11758198—22no—
589#11758198—22no—
590#11758198—22no—
591#11758198—22no—
592#11758198—22no—
593#11758198—22no—
594#11758198—22no—
595#11758198—22no—
596#11758198—41no—
597#11758198—41no—
598#11758198—41no—
599#11758198—41no—
600#11758198—41no—
601#11758198—41no—
602#11758198—41no—
603#11758198—41no—
604#11758198—41no—
605#11758198—41no—
606#11758198—41no—
607#11758198—41no—
608C4⋊Dic61—22no—
609C4⋊Dic61—41no—
610C4⋊Dic61—41no—
611C4⋊Dic61—41no—
612C4⋊Dic61—41no—
613C4⋊Dic61—41no—
614C4⋊Dic61—41no—
615#11758196—22no—
616#11758196—22no—
617#11758196—22no—
618#11758196—22no—
619#11758196—22no—
620#11758196—41no—
621#11758196—41no—
622#11758196—41no—
623#11758196—41no—
624#11758196—41no—
625#11758196—41no—
626C4×Dic61—22no—
627C4×Dic61—41no—
628C4×Dic61—41no—
629C4×Dic61—41no—
630C4×Dic61—41no—
631C23×C61—21no—
632C23×C61—21no—
633C23×C61—21no—
634C23×C61—21no—
635C23×C61—21no—
636C23×C61—21no—
637C23×C61—21no—
638C23×C61—21no—
639C23×C61—21no—
640C23×C61—21no—
641C23×C61—21no—
642C23×C61—21no—
643C23×C61—21no—
644C23×C61—21no—
645C23×C61—21no—
646C23×C61—21no—
647C23×C61—21no—
648C23×C61—21no—
649C23×C61—21no—
650C23×C61—21no—
651C23×C61—21no—
652C23×C61—21no—
653C23×C61—21no—
654C23×C61—21no—
655C23×C61—21no—
656C23×C61—21no—
657C23×C61—21no—
658C23×C61—21no—
659C23×C61—21no—
660C23×C61—21no—
661C23×C61—21no—
662C23×C61—44no—
663C23×C61—44no—
664C23×C61—44no—
665C23×C61—44no—
666C23×C61—44no—
667C23×C61—44no—
668C23×C61—44no—
669C23×C61C22×D412yes—
670C23×C61C22×D412yes—
671C23×C61H(5,𝔽2)12yes—
672C23×C61H(5,𝔽2)12yes—
673C23×C61C2511yescharacteristic
674C22×D61—21no—
675C22×D61—21no—
676C22×D61—21no—
677C22×D61—21no—
678C22×D61—21no—
679C22×D61—21no—
680C22×D61—21no—
681C22×D61—21no—
682C22×D61—21no—
683C22×D61—21no—
684C22×D61—21no—
685C22×D61—21no—
686C22×D61—21no—
687C22×D61—21no—
688C22×D61—21no—
689C22×D61—21no—
690C22×D61—21no—
691C22×D61—21no—
692C22×D61—21no—
693C22×D61—21no—
694C22×D61—21no—
695C22×D61—44no—
696C22×D61—82no—
697C22×D61—82no—
698C22×D61—82no—
699C22×D61—82no—
700C22×D61—82no—
701C22×D61—82no—
702Q8×C61—44no—
703D4×C61—44no—
704D4×C61—44no—
705D4×C61—44no—
706D4×C61—44no—
707D4×C61—44no—
708D4×C61—44no—
709D4×C61—44no—
710C2×C4×C61—28no—
711C2×C4×C61—21no—
712C2×C4×C61—21no—
713C2×C4×C61—21no—
714C2×C4×C61—21no—
715C2×C4×C61—21no—
716C2×C4×C61—21no—
717C2×C4×C61—21no—
718C2×C4×C61—21no—
719C2×C4×C61—21no—
720C2×C4×C61—21no—
721C2×C4×C61—21no—
722C2×C4×C61—21no—
723C2×C4×C61—21no—
724C2×C4×C61—21no—
725C2×C4×C61—21no—
726C2×C4×C61—21no—
727C2×C4×C61—21no—
728C2×C4×C61—21no—
729C2×C4×C61—21no—
730C2×C4×C61—21no—
731C2×C4×C61—21no—
732C2×C4×C61—21no—
733C2×C4×C61—21no—
734C2×C4×C61—21no—
735C2×C4×C61—44no—
736C2×C4×C61—44no—
737C2×C4×C61—44no—
738C2×C4×C61—44no—
739C2×C4×C61—44no—
740C2×C4×C61—44no—
741C2×C4×C61—44no—
742C2×C4×C61C22×D412yes—
743C2×C4×C61C22×D412yes—
744C2×C4×C61C22×D412yes—
745C2×C4×C61C22×D412yes—
746C2×C4×C61C22×D412yes—
747C2×C4×C61H(5,𝔽2)12yes—
748C22⋊D61—44no—
749C22⋊D61—82no—
750C22⋊D61—82no—
751C22⋊D61—82no—
752C22⋊D61—82no—
753C22⋊D61—82no—
754C22⋊D61—82no—
755C22⋊D61—82no—
756C22⋊D61—82no—
757C22⋊D61—82no—
758C22⋊D61—82no—
759C22⋊D61—82no—
760C22⋊D61—82no—
761C2×Dic61—21no—
762C2×Dic61—21no—
763C2×Dic61—21no—
764C2×Dic61—21no—
765C2×Dic61—21no—
766C2×Dic61—21no—
767C2×Dic61—21no—
768C2×Dic61—21no—
769C2×Dic61—21no—
770C2×Dic61—21no—
771C2×Dic61—21no—
772C2×Dic61—21no—
773C2×Dic61—21no—
774C2×Dic61—21no—
775C2×Dic61—21no—
776C2×Dic61—21no—
777C2×Dic61—21no—
778C2×Dic61—21no—
779C2×Dic61—21no—
780C2×Dic61—21no—
781C2×Dic61—21no—
782C2×Dic61—21no—
783C2×Dic61—21no—
784C2×Dic61—21no—
785C2×Dic61—21no—
786C2×Dic61—21no—
787C2×Dic61—21no—
788C2×Dic61—21no—
789C2×Dic61—21no—
790C2×Dic61—21no—
791C2×Dic61—21no—
792C2×Dic61—21no—
793C2×Dic61—21no—
794C2×Dic61—21no—
795C2×Dic61—21no—
796C2×Dic61—21no—
797C2×Dic61—21no—
798C2×Dic61—21no—
799C2×Dic61—21no—
800C2×Dic61—82no—
801D244—82no—
802D244—82no—
803C4×D61—82no—
804Dic122—82no—
805#36724—611nomaximal, Sylow
806C22×C61—22no—
807C22×C61—22no—
808C22×C61—22no—
809C22×C61—22no—
810C22×C61—22no—
811C22×C61—22no—
812C22×C61—22no—
813C22×C61—22no—
814C22×C61—22no—
815C22×C61—22no—
816C22×C61—22no—
817C22×C61—22no—
818C22×C61—416no—
819C22×C61—41no—
820C22×C61—41no—
821C22×C61—41no—
822C22×C61—41no—
823C22×C61—41no—
824C22×C61—41no—
825C22×C61—41no—
826C22×C61—41no—
827C22×C61—41no—
828C22×C61—41no—
829C22×C61—41no—
830C22×C61—41no—
831C22×C61—41no—
832C22×C61—41no—
833C22×C61—41no—
834C22×C61—41no—
835C22×C61—41no—
836C22×C61—41no—
837C22×C61—41no—
838C22×C61—41no—
839C22×C61—41no—
840C22×C61—41no—
841C22×C61—41no—
842C22×C61C23×D411yescharacteristic
843C22×C61C2×H(5,𝔽2)11yescharacteristic
844C22×C61C2×H(5,𝔽2)11yescharacteristic
845C22×C61C2×H(5,𝔽2)11yescharacteristic
846C22×C61#58511yescharacteristic
847C22×C61#58511yescharacteristic
848C22×C61#58511yescharacteristic
849C2×D61—41no—
850C2×D61—41no—
851C2×D61—41no—
852C2×D61—41no—
853C2×D61—41no—
854C2×D61—41no—
855C2×D61—41no—
856C2×D61—41no—
857C2×D61—41no—
858C2×D61—41no—
859C2×D61—41no—
860C2×D61—41no—
861C2×D61—41no—
862C2×D61—41no—
863C2×D61—41no—
864C2×D61—41no—
865C2×D61—41no—
866C2×D61—41no—
867C2×D61—41no—
868C2×D61—41no—
869C2×D61—41no—
870C2×D61—88no—
871C4×C61—22no—
872C4×C61—22no—
873C4×C61—22no—
874C4×C61—22no—
875C4×C61—22no—
876C4×C61—22no—
877C4×C61—41no—
878C4×C61—41no—
879C4×C61—41no—
880C4×C61—41no—
881Dic61—41no—
882Dic61—41no—
883Dic61—41no—
884Dic61—41no—
885Dic61—41no—
886Dic61—41no—
887Dic61—41no—
888Dic61—41no—
889Dic61—41no—
890Dic61—41no—
891Dic61—41no—
892Dic61—41no—
893Dic61—41no—
894C2×#538—611no—
895C2×#525D6111yescharacteristic, complemented
896#2849—611no—
897#2847—611no—
898#2705—611no—
899#2702—611no—
900#2700—611no—
901#2699—611no—
902#2687—611no—
903#2682—611no—
904#2681—611no—
905#2681—611no—
906#2679—611no—
907#2678—611no—
908#2678—611no—
909#2678—611no—
910#2672—611no—
911#2670—611no—
912#2669—611no—
913#2669—611no—
914#2635—611no—
915#2630—611no—
916#2610—611no—
917#2603—611no—
918#2601—611no—
919#2600—611no—
920#2544—611no—
921#2534—611no—
922#2407—611no—
923#2404—611no—
924#2319—611no—
925C2×C61—42no—
926C2×C61—42no—
927C2×C61—42no—
928C2×C61—42no—
929C2×C61—81no—
930C2×C61#344911yescharacteristic
931C2×C61#348411yescharacteristic
932C2×C61#348811yescharacteristic
933C2×C61#353311yescharacteristic
934C2×C61#353411yescharacteristic
935C2×C61#354011yescharacteristic
936C2×C61#354211yescharacteristic
937D61—81no—
938D61—81no—
939D61—81no—
940C22×#41C2×D6111yescharacteristic
941C24×C4C2×D6111yescharacteristic, complemented
942#538—1228no—
943C2×#127—611no—
944C2×#126—611no—
945C2×#126—611no—
946C2×#124—611no—
947C2×#124—611no—
948C2×#124—611no—
949#525—28no—
950C2×#123—611no—
951C2×#123—611no—
952C2×#123—611no—
953C2×#123—611no—
954C2×#123C2×D6111yescharacteristic
955C2×#123C2×D6111yescharacteristic, complemented
956C2×C22⋊Q8—611no—
957C2×C22⋊Q8—611no—
958C2×C22⋊Q8C2×D6111yescharacteristic, complemented
959C2×C22⋊Q8C2×D6111yescharacteristic, complemented
960C2×#121—611no—
961C2×#121—611no—
962C2×#121—611no—
963C2×#121—611no—
964C2×#121—611no—
965C2×#121—611no—
966C2×#121C2×D6111yescharacteristic
967C2×#121C2×D6111yescharacteristic
968C2×#120—611no—
969C2×#120—611no—
970C2×#120—611no—
971C2×#120—611no—
972C2×#120—611no—
973C2×#120—611no—
974C2×#120—611no—
975C2×#120—611no—
976C2×#120C2×D6111yescharacteristic
977C2×#120C2×D6111yescharacteristic, complemented
978C2×C4×D4—611no—
979C2×C4×D4C2×D6111yescharacteristic
980C2×C4×D4C2×D6111yescharacteristic
981C2×C4×D4C2×D6111yescharacteristic, complemented
982C2×C4×D4C2×D6111yescharacteristic, complemented
983C2×#117C2×D6111yescharacteristic, complemented
984C22×C22⋊C4—611no—
985#400—611no—
986#399—611no—
987#398—611no—
988#398—611no—
989#398—611no—
990#397—611no—
991#397—611no—
992#397—611no—
993#396—611no—
994#396—611no—
995#396—611no—
996#396—611no—
997#396—611no—
998#396—611no—
999#395—611no—
1000#394—611no—
1001#394—611no—
1002#394—611no—
1003#394—611no—
1004#394—611no—
1005#394—611no—
1006#394—611no—
1007#394—611no—
1008#394—611no—
1009#394—611no—
1010#394—611no—
1011#394—611no—
1012#394—611no—
1013#394—611no—
1014#394—611no—
1015#394—611no—
1016#394—611no—
1017#394—611no—
1018#394—611no—
1019#393—611no—
1020#393—611no—
1021#393—611no—
1022#392—611no—
1023#392—611no—
1024#392—611no—
1025#392—611no—
1026#392—611no—
1027#392—611no—
1028#392—611no—
1029#392—611no—
1030#392—611no—
1031#392—611no—
1032#392—611no—
1033#391—611no—
1034#391—611no—
1035#390—611no—
1036#390—611no—
1037#390—611no—
1038#390—611no—
1039#390—611no—
1040#390—611no—
1041#390—611no—
1042#390—611no—
1043#390—611no—
1044#389—611no—
1045#389—611no—
1046#389—611no—
1047#388—611no—
1048#388—611no—
1049#388—611no—
1050#388—611no—
1051#388—611no—
1052#388—611no—
1053#388—611no—
1054#388—611no—
1055#388—611no—
1056#388—611no—
1057#388—611no—
1058#388—611no—
1059#388—611no—
1060#388—611no—
1061#387—611no—
1062#387—611no—
1063#386—611no—
1064#386—611no—
1065#386—611no—
1066#386—611no—
1067#386—611no—
1068#386—611no—
1069#386—611no—
1070#386—611no—
1071#386—611no—
1072#386—611no—
1073#386—611no—
1074#386—611no—
1075#386—611no—
1076#386—611no—
1077#386—611no—
1078#386—611no—
1079#385—611no—
1080#385—611no—
1081#385—611no—
1082#385—611no—
1083#385—611no—
1084#385—611no—
1085#381—611no—
1086#381—611no—
1087#381—611no—
1088#381—611no—
1089#380—611no—
1090#380—611no—
1091#380—611no—
1092#380—611no—
1093#379—611no—
1094#379—611no—
1095C4×C4⋊C4—611no—
1096#376—611no—
1097C61#3672411yescharacteristic, complemented, Sylow
1098C25—611no—
1099C25C22×D6111yescharacteristic
1100C2×#41—24no—
1101C2×#41—42no—
1102C2×#41—42no—
1103C22×Q8—611no—
1104C22×Q8C22×D6111yescharacteristic
1105C22×D4—611no—
1106C22×D4—611no—
1107C22×D4—611no—
1108C22×D4—611no—
1109C22×D4—611no—
1110C22×D4—611no—
1111C22×D4—611no—
1112C22×D4—611no—
1113C22×D4—611no—
1114C22×D4—611no—
1115C22×D4—611no—
1116C22×D4—611no—
1117C22×D4—611no—
1118C22×D4—611no—
1119C22×D4—611no—
1120C22×D4C22×D6111yescharacteristic
1121C22×D4C22×D6111yescharacteristic
1122C22×D4C22×D6111yescharacteristic
1123C22×D4C22×D6111yescharacteristic
1124C22×D4C22×D6111yescharacteristic
1125C22×D4C22×D6111yescharacteristic
1126C22×D4C22×D6111yescharacteristic
1127C23×C4—24no—
1128C23×C4—42no—
1129C23×C4—42no—
1130C23×C4—611no—
1131C23×C4—611no—
1132C23×C4C22×D6111yescharacteristic
1133C23×C4C22×D6111yescharacteristic
1134C23×C4C22×D6111yescharacteristic
1135C23×C4C22×D6111yescharacteristic
1136C23×C4C22×D6111yescharacteristic
1137C23×C4C22×D6111yescharacteristic
1138C23×C4C22×D6111yescharacteristic
1139C23×C4C22×D6111yescharacteristic
1140#127—2442no—
1141#126—1224no—
1142#126—1224no—
1143#124—1224no—
1144#124—1224no—
1145#124—2442no—
1146#123—24no—
1147#123—24no—
1148#123—1224no—
1149#123—1224no—
1150#123—2442no—
1151#123—2442no—
1152C22⋊Q8—24no—
1153C22⋊Q8—24no—
1154C22⋊Q8—1224no—
1155C22⋊Q8—2442no—
1156#121—24no—
1157#121—24no—
1158#121—1224no—
1159#121—1224no—
1160#121—1224no—
1161#121—2442no—
1162#121—2442no—
1163#121—2442no—
1164#120—24no—
1165#120—24no—
1166#120—1224no—
1167#120—1224no—
1168#120—2442no—
1169#120—2442no—
1170#120—2442no—
1171#120—2442no—
1172#120—2442no—
1173#120—2442no—
1174C4×D4—24no—
1175C4×D4—24no—
1176C4×D4—24no—
1177C4×D4—1224no—
1178C4×D4C22⋊D6118yescomplemented
1179#117—24no—
1180C2×C4⋊C4—611no—
1181C2×C4⋊C4—611no—
1182C2×C4⋊C4—611no—
1183C2×C4⋊C4—611no—
1184C2×C4⋊C4—611no—
1185C2×C4⋊C4—611no—
1186C2×C4⋊C4—611no—
1187C2×C4⋊C4—611no—
1188C2×C4⋊C4—611no—
1189C2×C4⋊C4—611no—
1190C2×C4⋊C4—611no—
1191C2×C4⋊C4—611no—
1192C2×C4⋊C4—611no—
1193C2×C4⋊C4—611no—
1194C2×C4⋊C4—611no—
1195C2×C4⋊C4—611no—
1196C2×C4⋊C4—611no—
1197C2×C4⋊C4—611no—
1198C2×C4⋊C4C22×D6111yescharacteristic
1199C2×C4⋊C4C22×D6111yescharacteristic
1200C2×C4⋊C4C22×D6111yescharacteristic
1201C2×C4⋊C4C22×D6111yescharacteristic
1202C2×C4⋊C4C22×D6111yescharacteristic
1203C2×C4⋊C4C22×D6111yescharacteristic
1204C2×C22⋊C4—611no—
1205C2×C22⋊C4—611no—
1206C2×C22⋊C4—611no—
1207C2×C22⋊C4—611no—
1208C2×C22⋊C4—611no—
1209C2×C22⋊C4—611no—
1210C2×C22⋊C4—611no—
1211C2×C22⋊C4—611no—
1212C2×C22⋊C4—611no—
1213C2×C22⋊C4—611no—
1214C2×C22⋊C4—611no—
1215C2×C22⋊C4—611no—
1216C2×C22⋊C4—611no—
1217C2×C22⋊C4—611no—
1218C2×C22⋊C4—611no—
1219C2×C22⋊C4—611no—
1220C2×C22⋊C4—611no—
1221C2×C22⋊C4—611no—
1222C2×C22⋊C4—611no—
1223C2×C22⋊C4—611no—
1224C2×C22⋊C4—611no—
1225C2×C22⋊C4—611no—
1226C2×C22⋊C4—611no—
1227C2×C22⋊C4—611no—
1228C2×C22⋊C4—611no—
1229C2×C22⋊C4—611no—
1230C2×C22⋊C4—611no—
1231C2×C22⋊C4—611no—
1232C2×C22⋊C4—611no—
1233C2×C22⋊C4—611no—
1234C2×C22⋊C4—611no—
1235C2×C22⋊C4—611no—
1236C2×C22⋊C4—611no—
1237C2×C22⋊C4—611no—
1238C2×C22⋊C4—611no—
1239C2×C22⋊C4—611no—
1240C2×C22⋊C4—611no—
1241C2×C22⋊C4—611no—
1242C2×C22⋊C4—611no—
1243C2×C22⋊C4—611no—
1244C2×C22⋊C4—611no—
1245C2×C22⋊C4—611no—
1246C2×C22⋊C4—611no—
1247C2×C22⋊C4—611no—
1248C2×C22⋊C4—611no—
1249C2×C22⋊C4—611no—
1250C2×C22⋊C4—611no—
1251C2×C22⋊C4—611no—
1252C2×C22⋊C4—611no—
1253C2×C22⋊C4—611no—
1254C2×C22⋊C4—1224no—
1255C2×C22⋊C4C22×D6111yescharacteristic
1256C2×C22⋊C4C22×D6111yescharacteristic
1257C2×C22⋊C4C22×D6111yescharacteristic
1258C2×C22⋊C4C22×D6111yescharacteristic
1259C2×C22⋊C4C22×D6111yescharacteristic
1260C2×C22⋊C4C22×D6111yescharacteristic
1261C2×C22⋊C4C22×D6111yescharacteristic
1262C2×C22⋊C4C22×D6111yescharacteristic
1263C2×C22⋊C4C22×D6111yescharacteristic
1264C2×C22⋊C4C22×D6111yescharacteristic
1265C2×C42—611no—
1266C2×C42—611no—
1267C2×C42—611no—
1268C2×C42—611no—
1269C2×C42—611no—
1270C2×C42C22×D6111yescharacteristic
1271C2×C42C22×D6111yescharacteristic
1272#95—611no—
1273#95—611no—
1274#95—611no—
1275#95—611no—
1276#95—611no—
1277#95—611no—
1278#95—611no—
1279#95—611no—
1280#95—611no—
1281#95—611no—
1282#95—611no—
1283#95—611no—
1284#95—611no—
1285#95—611no—
1286#95—611no—
1287#95—611no—
1288#95—611no—
1289#95—611no—
1290#95—611no—
1291#95—611no—
1292#95—611no—
1293#95—611no—
1294#95—611no—
1295#95—611no—
1296#95—611no—
1297#95—611no—
1298#95—611no—
1299#95—611no—
1300C24—22no—
1301C24—22no—
1302C24—22no—
1303C24—41no—
1304C24—41no—
1305C24—41no—
1306C24—41no—
1307C24—611no—
1308C24—611no—
1309C24—611no—
1310C24—1222no—
1311C24—2441no—
1312C24—2441no—
1313C24—2441no—
1314C24—2441no—
1315C24—2441no—
1316C24—2441no—
1317C24C23×D6111yescharacteristic
1318C24C23×D6111yescharacteristic
1319C24C23×D6111yescharacteristic
1320C24C23×D6111yescharacteristic
1321C24C23×D6111yescharacteristic
1322#41—416no—
1323C2×Q8—22no—
1324C2×Q8—22no—
1325C2×Q8—41no—
1326C2×Q8—1222no—
1327C2×Q8—2441no—
1328C2×Q8—2441no—
1329C2×D4—22no—
1330C2×D4—22no—
1331C2×D4—22no—
1332C2×D4—22no—
1333C2×D4—22no—
1334C2×D4—22no—
1335C2×D4—22no—
1336C2×D4—22no—
1337C2×D4—22no—
1338C2×D4—22no—
1339C2×D4—22no—
1340C2×D4—41no—
1341C2×D4—41no—
1342C2×D4—41no—
1343C2×D4—41no—
1344C2×D4—41no—
1345C2×D4—41no—
1346C2×D4—41no—
1347C2×D4—41no—
1348C2×D4—41no—
1349C2×D4—1222no—
1350C2×D4—1222no—
1351C2×D4—1222no—
1352C2×D4—1222no—
1353C2×D4—1222no—
1354C2×D4—1222no—
1355C2×D4—1222no—
1356C2×D4—1222no—
1357C2×D4—1222no—
1358C2×D4—1222no—
1359C2×D4—1222no—
1360C2×D4—1222no—
1361C2×D4—2441no—
1362C2×D4—2441no—
1363C2×D4—2441no—
1364C2×D4—2441no—
1365C2×D4—2441no—
1366C2×D4—2441no—
1367C2×D4—2441no—
1368C2×D4—2441no—
1369C2×D4—2441no—
1370C2×D4—2441no—
1371C2×D4—2441no—
1372C2×D4—2441no—
1373C2×D4—2441no—
1374C2×D4—2441no—
1375C2×D4—2441no—
1376C2×D4—2441no—
1377C2×D4—2441no—
1378C2×D4—2441no—
1379C2×D4—2441no—
1380C2×D4—2441no—
1381C2×D4—2441no—
1382C2×D4—2441no—
1383C2×D4—2441no—
1384C2×D4—2441no—
1385C2×D4—2441no—
1386C2×D4—2441no—
1387C2×D4—2441no—
1388C2×D4—2441no—
1389C2×D4—2441no—
1390C2×D4—2441no—
1391C2×D4—2441no—
1392C2×D4—2441no—
1393C2×D4—2441no—
1394C2×D4C2×C22⋊D6114yes—
1395C22×C4—22no—
1396C22×C4—22no—
1397C22×C4—22no—
1398C22×C4—22no—
1399C22×C4—22no—
1400C22×C4—22no—
1401C22×C4—22no—
1402C22×C4—22no—
1403C22×C4—22no—
1404C22×C4—22no—
1405C22×C4—22no—
1406C22×C4—41no—
1407C22×C4—41no—
1408C22×C4—41no—
1409C22×C4—41no—
1410C22×C4—41no—
1411C22×C4—41no—
1412C22×C4—41no—
1413C22×C4—41no—
1414C22×C4—41no—
1415C22×C4—41no—
1416C22×C4—41no—
1417C22×C4—416no—
1418C22×C4—611no—
1419C22×C4—611no—
1420C22×C4—611no—
1421C22×C4—611no—
1422C22×C4—611no—
1423C22×C4—611no—
1424C22×C4—611no—
1425C22×C4—611no—
1426C22×C4—611no—
1427C22×C4—611no—
1428C22×C4—611no—
1429C22×C4—611no—
1430C22×C4—611no—
1431C22×C4—1222no—
1432C22×C4—1222no—
1433C22×C4—2441no—
1434C22×C4—2441no—
1435C22×C4—2441no—
1436C22×C4—2441no—
1437C22×C4C2×C22⋊D6114yes—
1438C22×C4C2×C22⋊D6114yes—
1439C22×C4C23×D6111yescharacteristic
1440C22×C4C23×D6111yescharacteristic
1441C22×C4C23×D6111yescharacteristic
1442C22×C4C23×D6111yescharacteristic
1443C22×C4C23×D6111yescharacteristic
1444C22×C4C23×D6111yescharacteristic
1445C22×C4C23×D6111yescharacteristic
1446C22×C4C23×D6111yescharacteristic
1447C22×C4C23×D6111yescharacteristic
1448C22×C4C23×D6111yescharacteristic
1449C4⋊C4—22no—
1450C4⋊C4—22no—
1451C4⋊C4—22no—
1452C4⋊C4—22no—
1453C4⋊C4—22no—
1454C4⋊C4—1222no—
1455C4⋊C4—1222no—
1456C4⋊C4—1222no—
1457C4⋊C4—1222no—
1458C4⋊C4—1222no—
1459C4⋊C4—1222no—
1460C4⋊C4—2441no—
1461C4⋊C4—2441no—
1462C4⋊C4—2441no—
1463C4⋊C4—2441no—
1464C4⋊C4—2441no—
1465C4⋊C4—2441no—
1466C4⋊C4—2441no—
1467C4⋊C4—2441no—
1468C4⋊C4—2441no—
1469C4⋊C4—2441no—
1470C4⋊C4—2441no—
1471C4⋊C4—2441no—
1472C4⋊C4C2×C22⋊D6114yes—
1473C22⋊C4—22no—
1474C22⋊C4—22no—
1475C22⋊C4—22no—
1476C22⋊C4—22no—
1477C22⋊C4—22no—
1478C22⋊C4—22no—
1479C22⋊C4—22no—
1480C22⋊C4—22no—
1481C22⋊C4—1222no—
1482C22⋊C4—1222no—
1483C22⋊C4—1222no—
1484C22⋊C4—1222no—
1485C22⋊C4—1222no—
1486C22⋊C4—1222no—
1487C22⋊C4—1222no—
1488C22⋊C4—1222no—
1489C22⋊C4—1222no—
1490C22⋊C4—1222no—
1491C22⋊C4—1222no—
1492C22⋊C4—1222no—
1493C22⋊C4—1222no—
1494C22⋊C4—1222no—
1495C22⋊C4—1222no—
1496C22⋊C4—1222no—
1497C22⋊C4—1222no—
1498C22⋊C4—1222no—
1499C22⋊C4—1222no—
1500C22⋊C4—2441no—
1501C22⋊C4—2441no—
1502C22⋊C4—2441no—
1503C22⋊C4—2441no—
1504C22⋊C4—2441no—
1505C22⋊C4—2441no—
1506C22⋊C4—2441no—
1507C22⋊C4—2441no—
1508C22⋊C4—2441no—
1509C22⋊C4—2441no—
1510C22⋊C4—2441no—
1511C22⋊C4—2441no—
1512C22⋊C4—2441no—
1513C22⋊C4—2441no—
1514C22⋊C4—2441no—
1515C22⋊C4—2441no—
1516C22⋊C4—2441no—
1517C22⋊C4—2441no—
1518C22⋊C4—2441no—
1519C22⋊C4—2441no—
1520C22⋊C4—2441no—
1521C22⋊C4—2441no—
1522C22⋊C4—2441no—
1523C22⋊C4—2441no—
1524C22⋊C4—2441no—
1525C22⋊C4—2441no—
1526C22⋊C4—2441no—
1527C22⋊C4—2441no—
1528C22⋊C4—2441no—
1529C22⋊C4—2441no—
1530C22⋊C4—2441no—
1531C22⋊C4C2×C22⋊D6114yes—
1532C22⋊C4C2×C22⋊D6114yes—
1533C42—22no—
1534C42—1222no—
1535C42—2441no—
1536C42—2441no—
1537C42—2441no—
1538C42—2441no—
1539C42C2×C22⋊D6114yes—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—21no—
1558C23—21no—
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—21no—
1563C23—21no—
1564C23—21no—
1565C23—21no—
1566C23—21no—
1567C23—21no—
1568C23—21no—
1569C23—21no—
1570C23—21no—
1571C23—44no—
1572C23—44no—
1573C23—44no—
1574C23—44no—
1575C23—44no—
1576C23—44no—
1577C23—44no—
1578C23—1221no—
1579C23—1221no—
1580C23—1221no—
1581C23—1221no—
1582C23—1221no—
1583C23—1221no—
1584C23—1221no—
1585C23—1221no—
1586C23—1221no—
1587C23—1221no—
1588C23—1221no—
1589C23—1221no—
1590C23—1221no—
1591C23—1221no—
1592C23—1221no—
1593C23—1221no—
1594C23—1221no—
1595C23—1221no—
1596C23—1221no—
1597C23—1221no—
1598C23—1221no—
1599C23—4882no—
1600C23—4882no—
1601C23—4882no—
1602C23—4882no—
1603C23—4882no—
1604C23—4882no—
1605C23—2444no—
1606C23C22×C22⋊D6112yes—
1607C23C22×C22⋊D6112yes—
1608C23#1451982212yes—
1609C23#1451982312yes—
1610C23C24×D6111yescharacteristic
1611Q8—44no—
1612Q8—4882no—
1613D4—44no—
1614D4—44no—
1615D4—44no—
1616D4—44no—
1617D4—44no—
1618D4—44no—
1619D4—44no—
1620D4—4882no—
1621D4—4882no—
1622D4—4882no—
1623D4—4882no—
1624D4—4882no—
1625D4—4882no—
1626D4—4882no—
1627D4—4882no—
1628D4—4882no—
1629D4—4882no—
1630D4—4882no—
1631D4—4882no—
1632D4—4882no—
1633D4—4882no—
1634D4—2444no—
1635C2×C4—28no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—44no—
1661C2×C4—44no—
1662C2×C4—44no—
1663C2×C4—44no—
1664C2×C4—44no—
1665C2×C4—44no—
1666C2×C4—44no—
1667C2×C4—1221no—
1668C2×C4—1221no—
1669C2×C4—1221no—
1670C2×C4—1221no—
1671C2×C4—1221no—
1672C2×C4—1221no—
1673C2×C4—1221no—
1674C2×C4—1221no—
1675C2×C4—1221no—
1676C2×C4—1221no—
1677C2×C4—1221no—
1678C2×C4—1221no—
1679C2×C4—1221no—
1680C2×C4—1221no—
1681C2×C4—1221no—
1682C2×C4—1221no—
1683C2×C4—1221no—
1684C2×C4—1221no—
1685C2×C4—1221no—
1686C2×C4—1221no—
1687C2×C4—1221no—
1688C2×C4—1221no—
1689C2×C4—1221no—
1690C2×C4—1221no—
1691C2×C4—1221no—
1692C2×C4—1221no—
1693C2×C4—1221no—
1694C2×C4—1221no—
1695C2×C4—1221no—
1696C2×C4—1221no—
1697C2×C4—1221no—
1698C2×C4—1221no—
1699C2×C4—1221no—
1700C2×C4—1221no—
1701C2×C4—1221no—
1702C2×C4—1221no—
1703C2×C4—1221no—
1704C2×C4—1221no—
1705C2×C4—1221no—
1706C2×C4—4882no—
1707C2×C4—4882no—
1708C2×C4C22×C22⋊D6112yes—
1709C2×C4C22×C22⋊D6112yes—
1710C2×C4C22×C22⋊D6112yes—
1711C2×C4C22×C22⋊D6112yes—
1712C2×C4C22×C22⋊D6112yes—
1713C2×C4#1451982212yes—
1714C22—22no—
1715C22—22no—
1716C22—22no—
1717C22—22no—
1718C22—22no—
1719C22—22no—
1720C22—22no—
1721C22—22no—
1722C22—22no—
1723C22—22no—
1724C22—22no—
1725C22—22no—
1726C22—416no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—41no—
1736C22—41no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—41no—
1741C22—41no—
1742C22—41no—
1743C22—41no—
1744C22—41no—
1745C22—41no—
1746C22—41no—
1747C22—41no—
1748C22—41no—
1749C22—41no—
1750C22—4888no—
1751C22—2441no—
1752C22—2441no—
1753C22—2441no—
1754C22—2441no—
1755C22—2441no—
1756C22—2441no—
1757C22—2441no—
1758C22—2441no—
1759C22—2441no—
1760C22—2441no—
1761C22—2441no—
1762C22—2441no—
1763C22—2441no—
1764C22—2441no—
1765C22—2441no—
1766C22—2441no—
1767C22—2441no—
1768C22—2441no—
1769C22—2441no—
1770C22—2441no—
1771C22—2441no—
1772C22C23×C22⋊D6111yescharacteristic
1773C22C2×#1451982211yescharacteristic
1774C22C2×#1451982211yescharacteristic
1775C22C2×#1451982311yescharacteristic
1776C22#1684059811yescharacteristic
1777C22#1684059811yescharacteristic
1778C22#1684059811yescharacteristic
1779C4—22no—
1780C4—22no—
1781C4—22no—
1782C4—22no—
1783C4—22no—
1784C4—22no—
1785C4—41no—
1786C4—41no—
1787C4—41no—
1788C4—41no—
1789C4—2441no—
1790C4—2441no—
1791C4—2441no—
1792C4—2441no—
1793C4—2441no—
1794C4—2441no—
1795C4—2441no—
1796C4—2441no—
1797C4—2441no—
1798C4—2441no—
1799C4—2441no—
1800C4—2441no—
1801C4—2441no—
1802C2—42no—
1803C2—42no—
1804C2—42no—
1805C2—42no—
1806C2—81no—
1807C2—4881no—
1808C2—4881no—
1809C2—4881no—
1810C2#2145914811yescharacteristic
1811C2#2145945411yescharacteristic
1812C2#2145948811yescharacteristic
1813C2#2145998311yescharacteristic
1814C2#2146000311yescharacteristic
1815C2#2146008711yescharacteristic
1816C2#2146012711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC2×C61×#525C2
hypercenterC2×#525D61
hypocenterC61#36724
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#525

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840345C2semidirect
2. #21454111C2semidirect
3. #21454101C2semidirect
4. #21452488C2semidirect
5. #21452443C2semidirect
6. #21452413C2semidirect
7. #21452402C2semidirect
8. #21452234C2semidirect
9. #21452184C2semidirect
10. #21452174C2semidirect
11. #21452167C2semidirect
12. #21452153C2semidirect
13. #21452147C2semidirect
14. #21452144C2semidirect
15. #21452138C2semidirect
16. #21452064C2semidirect
17. #21452041C2semidirect
18. #21452033C2semidirect
19. #21452031C2semidirect
20. #21451703C2semidirect
21. #21451656C2semidirect
22. #21451506C2semidirect
23. #21451440C2semidirect
24. #21451416C2semidirect
25. #21451401C2semidirect
26. #21450786C2semidirect
27. #21450705C2semidirect
28. #21449158C2semidirect
29. #21449134C2semidirect
30. #21448462C2semidirect
31. C2×C61×#525C2semidirect
34. C2×#14519772C22semidirect
35. C2×#14519771C22semidirect
36. C2×#14519765C22semidirect
37. C2×#14519764C22semidirect
39. C2×#14519762C22semidirect
43. C2×#14519754C22semidirect
44. C2×#14519753C22semidirect
50. C2×#14519748C22semidirect
51. C2×#14519747C22semidirect
54. C2×#14519746C22semidirect
58. C2×#14519745C22semidirect
59. C2×C4×C22⋊D61C22semidirect
60. C22×#11758198C22semidirect
61. #16839701C22semidirect
62. #16839698C22semidirect
63. #16839695C22semidirect
64. #16839695C22semidirect
65. #16839693C22semidirect
66. #16839690C22semidirect
67. #16839690C22semidirect
68. #16839688C22semidirect
69. #16839685C22semidirect
70. #16839685C22semidirect
71. #16839684C22semidirect
72. #16839684C22semidirect
73. #16839684C22semidirect
74. #16839684C22semidirect
75. #16839682C22semidirect
76. #16839679C22semidirect
77. #16839679C22semidirect
82. #16839678C22semidirect
83. #16839678C22semidirect
84. #16839678C22semidirect
85. #16839678C22semidirect
88. #16839677C22semidirect
89. #16839677C22semidirect
92. #16839676C22semidirect
93. #16839676C22semidirect
94. #16839676C22semidirect
95. #16839674C22semidirect
96. #16839673C22semidirect
97. #16839673C22semidirect
99. #16839671C22semidirect
107. #16839670C22semidirect
108. #16839670C22semidirect
109. #16839669C22semidirect
110. #16839667C22semidirect
113. #16839665C22semidirect
114. #16839663C22semidirect
118. #16839662C22semidirect
119. #16839662C22semidirect
120. #16839661C22semidirect
121. #16839661C22semidirect
122. #16839657C22semidirect
123. #16839656C22semidirect
124. #16839656C22semidirect
125. #16839656C22semidirect
126. #16839655C22semidirect
127. #16839655C22semidirect
128. #16839655C22semidirect
129. #16839655C22semidirect
130. #16839653C22semidirect
131. #16839653C22semidirect
132. #16839653C22semidirect
133. #16839652C22semidirect
134. #16839652C22semidirect
135. #16839652C22semidirect
136. #16839650C22semidirect
137. #16839646C22semidirect
138. #16839643C22semidirect
140. #16839642C22semidirect
148. #16839641C22semidirect
149. #16839641C22semidirect
150. #16839641C22semidirect
151. #16839641C22semidirect
152. #16839641C22semidirect
153. #16839641C22semidirect
154. #16839638C22semidirect
155. #16839635C22semidirect
156. #16839635C22semidirect
157. #16839635C22semidirect
158. #16839635C22semidirect
159. #16839635C22semidirect
160. #16839633C22semidirect
161. #16839625C22semidirect
162. #16839625C22semidirect
163. #16839625C22semidirect
164. #16839623C22semidirect
165. #16839622C22semidirect
166. #16839622C22semidirect
167. #16839622C22semidirect
168. #16839622C22semidirect
169. #16839618C22semidirect
170. #16839617C22semidirect
171. C4×C4⋊Dic61C22semidirect
172. #16839608C22semidirect
174. C24×C4×C61C22semidirect
177. C2×#123×C61C22semidirect
178. C2×C22⋊Q8×C61C22semidirect
179. C2×C22⋊Q8×C61C22semidirect
183. C2×#120×C61C22semidirect
186. C2×C4×D4×C61C22semidirect
187. C2×C4×D4×C61C22semidirect
188. C2×#117×C61C22semidirect
371. C4×D4×C61D4semidirect
895. C2×#525D61semidirect
941. C24×C4C2×D61semidirect
955. C2×#123C2×D61semidirect
958. C2×C22⋊Q8C2×D61semidirect
959. C2×C22⋊Q8C2×D61semidirect
977. C2×#120C2×D61semidirect
981. C2×C4×D4C2×D61semidirect
982. C2×C4×D4C2×D61semidirect
983. C2×#117C2×D61semidirect
1097. C61#36724semidirect
1178. C4×D4C22⋊D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168403452
#214541112
#214541012
#214524882
#214524432
#214524132
#214524022
#214522342
#214521842
#214521742
#214521672
#214521532
#214521472
#214521442
#214521382
#214520642
#214520412
#214520332
#214520312
#214517032
#214516562
#214515062
#214514402
#214514162
#214514012
#214507862
#214507052
#214491582
#214491342
#214484622
C2×C61×#5252
#3672461