Finite Group Databasebeta

← #29850198

Subgroups — #29850198

Order 15616.

2804 conjugacy classes of subgroups.

The subgroup lattice has 1708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840293C211yesmaximal, characteristic, complemented
2C2×#16840272C211yesmaximal, characteristic, complemented
3#21450962C211yesmaximal, characteristic, complemented
4#21450947C211yesmaximal, characteristic, complemented
5#21450932C211yesmaximal, characteristic, complemented
6#21450917C211yesmaximal, characteristic, complemented
7#21450898C211yesmaximal, characteristic, complemented
8#21450889C211yesmaximal, characteristic, complemented
9#21450874C211yesmaximal, characteristic, complemented
10#21450859C211yesmaximal, characteristic, complemented
11#21450830C211yesmaximal, characteristic, complemented
12#21450751C211yesmaximal, characteristic, complemented
13#21450705C211yesmaximal, characteristic, complemented
14#21450143C211yesmaximal, characteristic, complemented
15#21449950C211yesmaximal, characteristic, complemented
16#21449376C211yesmaximal, characteristic, complemented
17#21449361C211yesmaximal, characteristic, complemented
18#21449096C211yesmaximal, characteristic, complemented
19#21449077C211yesmaximal, characteristic, complemented
20#21449062C211yesmaximal, characteristic, complemented
21#21449031C211yesmaximal, characteristic, complemented
22#21448360C211yesmaximal, characteristic, complemented
23#21448344C211yesmaximal, characteristic, complemented
24#121×Dic61C211yesmaximal, characteristic, complemented
25#21448329C211yesmaximal, characteristic, complemented
26#21448324C211yesmaximal, characteristic, complemented
27#21448304C211yesmaximal, characteristic, complemented
28#21448279C211yesmaximal, characteristic, complemented
29C4×D4×Dic61C211yesmaximal, characteristic, complemented
30C2×#16839609C211yesmaximal, characteristic, complemented
31C61×#2543C211yesmaximal, characteristic, complemented
32C22×#11758224C2211yescharacteristic
33C23×C4×D61C2211yescharacteristic
34#16840293—28no—
35C2×#14519770C2211yescharacteristic, complemented
36C2×#14519770C2211yescharacteristic, complemented
37C2×#14519768C2211yescharacteristic, complemented
38C2×#14519764C2211yescharacteristic, complemented
39C2×#14519763C2211yescharacteristic
40#16840272—28no—
41C2×#14519759C2211yescharacteristic
42C2×#14519759C2211yescharacteristic
43C2×#14519758C2211yescharacteristic
44C2×#14519758C2211yescharacteristic
45C2×#14519758C2211yescharacteristic
46C2×#14519757C2211yescharacteristic
47C2×#14519756C2211yescharacteristic
48C2×#14519756C2211yescharacteristic
49C2×#14519749C2211yescharacteristic
50C2×#14519748C2211yescharacteristic
51C2×#14519745C2211yescharacteristic
52C2×#14519745C2211yescharacteristic
53C2×#14519745C2211yescharacteristic
54C2×#14519742C2211yescharacteristic, complemented
55C2×D4×Dic61C2211yescharacteristic
56C2×D4×Dic61C2211yescharacteristic
57C2×D4×Dic61C2211yescharacteristic
58C2×D4×Dic61C2211yescharacteristic
59C2×D4×Dic61C2211yescharacteristic, complemented
60C2×D4×Dic61C2211yescharacteristic, complemented
61C2×#14519737C2211yescharacteristic
62C2×#14519737C2211yescharacteristic
63C2×#14519737C2211yescharacteristic
64C2×#14519737C2211yescharacteristic
65C2×#14519735C2211yescharacteristic
66C2×#14519733C2211yescharacteristic, complemented
67C2×#14519733C2211yescharacteristic, complemented
68C22×#11758198C2211yescharacteristic
69C22×#11758198C2211yescharacteristic
70C22×C4×Dic61C2211yescharacteristic
71C22×C4×Dic61C2211yescharacteristic
72C22×C4×Dic61C2211yescharacteristic, complemented
73#16839704C2211yescharacteristic, complemented
74#16839703C2211yescharacteristic, complemented
75#16839697C2211yescharacteristic
76#16839697C2211yescharacteristic
77#16839696C2211yescharacteristic, complemented
78#16839696C2211yescharacteristic, complemented
79#16839695C2211yescharacteristic, complemented
80#16839691C2211yescharacteristic
81#16839690C2211yescharacteristic, complemented
82#16839690C2211yescharacteristic, complemented
83#16839685C2211yescharacteristic, complemented
84#16839684C2211yescharacteristic
85#16839684C2211yescharacteristic
86#16839684C2211yescharacteristic
87#16839683C2211yescharacteristic, complemented
88#16839683C2211yescharacteristic, complemented
89#16839678C2211yescharacteristic
90#16839678C2211yescharacteristic
91#16839678C2211yescharacteristic
92#16839678C2211yescharacteristic
93#16839677C2211yescharacteristic
94#16839677C2211yescharacteristic
95#16839676C2211yescharacteristic, complemented
96#16839675C2211yescharacteristic
97#16839674C2211yescharacteristic, complemented
98#16839670C2211yescharacteristic
99#16839670C2211yescharacteristic
100#16839670C2211yescharacteristic
101#16839666C2211yescharacteristic, complemented
102#16839666C2211yescharacteristic, complemented
103#16839666C2211yescharacteristic, complemented
104#16839665C2211yescharacteristic, complemented
105#16839662C2211yescharacteristic
106#16839662C2211yescharacteristic
107#16839662C2211yescharacteristic
108#16839662C2211yescharacteristic
109#16839662C2211yescharacteristic
110#16839662C2211yescharacteristic
111#16839661C2211yescharacteristic, complemented
112#16839659C2211yescharacteristic, complemented
113#16839659C2211yescharacteristic, complemented
114#16839657C2211yescharacteristic, complemented
115#16839656C2211yescharacteristic, complemented
116#16839656C2211yescharacteristic, complemented
117#16839656C2211yescharacteristic, complemented
118#16839655C2211yescharacteristic, complemented
119#16839655C2211yescharacteristic, complemented
120#16839655C2211yescharacteristic, complemented
121#16839654C2211yescharacteristic
122#16839653C2211yescharacteristic
123#16839653C2211yescharacteristic
124#16839652C2211yescharacteristic
125#16839651C2211yescharacteristic
126#16839650C2211yescharacteristic, complemented
127#16839649C2211yescharacteristic, complemented
128#16839649C2211yescharacteristic, complemented
129#16839642C2211yescharacteristic
130#16839642C2211yescharacteristic
131#16839642C2211yescharacteristic, complemented
132#16839641C2211yescharacteristic
133#16839641C2211yescharacteristic
134#16839639C2211yescharacteristic
135#16839638C2211yescharacteristic
136#16839638C2211yescharacteristic
137#16839636C2211yescharacteristic
138#16839636C2211yescharacteristic
139#16839635C2211yescharacteristic
140#16839635C2211yescharacteristic
141#16839626C2211yescharacteristic, complemented
142#16839623C2211yescharacteristic
143#16839622C2211yescharacteristic
144#16839620C2211yescharacteristic, complemented
145#16839617C2211yescharacteristic
146C4⋊C4×Dic61C2211yescharacteristic, complemented
147C4⋊C4×Dic61C2211yescharacteristic, complemented
148C4⋊C4×Dic61C2211yescharacteristic, complemented
149C4×C4⋊Dic61C2211yescharacteristic, complemented
150#16839613C2211yescharacteristic, complemented
151#16839613C2211yescharacteristic, complemented
152C22⋊C4×Dic61C2211yescharacteristic
153C22⋊C4×Dic61C2211yescharacteristic
154C22⋊C4×Dic61C2211yescharacteristic, complemented
155C22⋊C4×Dic61C2211yescharacteristic, complemented
156C22⋊C4×Dic61C2211yescharacteristic, complemented
157C22⋊C4×Dic61C2211yescharacteristic, complemented
158C22⋊C4×Dic61C2211yescharacteristic, complemented
159C22⋊C4×Dic61C2211yescharacteristic, complemented
160C4×C22⋊Dic61C2211yescharacteristic
161C4×C22⋊Dic61C2211yescharacteristic, complemented
162#16839609C2211yescharacteristic
163#16839609C2211yescharacteristic
164#16839609C2211yescharacteristic
165#16839609C2211yescharacteristic
166#16839609C2211yescharacteristic
167#16839609C2211yescharacteristic
168#16839609C2211yescharacteristic
169#16839609C2211yescharacteristic
170#16839609C2211yescharacteristic
171#16839609C2211yescharacteristic
172C2×#14519684C2211yescharacteristic
173C42×Dic61C2211yescharacteristic, complemented
174C2×#121×C61C2211yescharacteristic
175C2×#121×C61C2211yescharacteristic
176C2×#121×C61C2211yescharacteristic
177C2×C4×D4×C61C2211yescharacteristic
178C61×#398C2211yescharacteristic, complemented
179C61×#397C2211yescharacteristic, complemented
180C61×#394C2211yescharacteristic, complemented
181C61×#392C2211yescharacteristic, complemented
182C61×#388C2211yescharacteristic, complemented
183C61×#388C2211yescharacteristic, complemented
184C61×#386C2211yescharacteristic
185C61×#386C2211yescharacteristic
186C61×#386C2211yescharacteristic, complemented
187C61×#386C2211yescharacteristic, complemented
188C2×#95×C61C2211yescharacteristic
189C24×D61C2311yescharacteristic
190C2×#11758224—24no—
191C2×#11758224—24no—
192C2×#11758224—42no—
193C22×Dic122C2311yescharacteristic
194C22×Dic122C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C22×C22⋊D61C2311yescharacteristic
197C22×C22⋊D61C2311yescharacteristic
198C22×C22⋊D61C2311yescharacteristic
199C22×C22⋊D61C2311yescharacteristic
200C22×C22⋊D61C2311yescharacteristic
201C23×Dic61C2311yescharacteristic
202C23×Dic61C2311yescharacteristic
203C23×Dic61C2311yescharacteristic
204C23×Dic61C2311yescharacteristic
205C23×Dic61C2311yescharacteristic
206C23×Dic61C2311yescharacteristic
207C23×Dic61C2311yescharacteristic
208C22×C4×D61—24no—
209C22×C4×D61—24no—
210C22×C4×D61—42no—
211C22×C4×D61C2311yescharacteristic
212C22×C4×D61C2311yescharacteristic
213C22×C4×D61C2311yescharacteristic
214C22×C4×D61C2311yescharacteristic
215#14519770—24no—
216#14519770—24no—
217#14519768—24no—
218#14519764—24no—
219#14519763—24no—
220#14519759—24no—
221#14519759—24no—
222#14519758—24no—
223#14519758—24no—
224#14519758—24no—
225#14519757—24no—
226#14519756—24no—
227#14519756—24no—
228#14519749—24no—
229#14519748—24no—
230#14519745—24no—
231#14519745—24no—
232#14519745—24no—
233#14519742—24no—
234D4×Dic61—24no—
235D4×Dic61—24no—
236D4×Dic61—24no—
237D4×Dic61—24no—
238D4×Dic61—42no—
239D4×Dic61D418yescomplemented
240#14519737—24no—
241#14519737—24no—
242#14519737—24no—
243#14519737—42no—
244#14519735—24no—
245#14519733—24no—
246#14519733—24no—
247C2×C4⋊Dic61C2311yescharacteristic
248C2×C4⋊Dic61C2311yescharacteristic
249C2×C4⋊Dic61C2311yescharacteristic
250C2×C4⋊Dic61C2311yescharacteristic
251C2×C4⋊Dic61C2311yescharacteristic
252C2×C4⋊Dic61C2311yescharacteristic
253C2×C4⋊Dic61C2311yescharacteristic
254C2×C4⋊Dic61C2311yescharacteristic
255C2×#11758196C2311yescharacteristic
256C2×#11758196C2311yescharacteristic
257C2×#11758196C2311yescharacteristic
258C2×#11758196C2311yescharacteristic
259C2×#11758196C2311yescharacteristic
260C2×#11758196C2311yescharacteristic
261C2×#11758196C2311yescharacteristic
262C2×#11758196C2311yescharacteristic
263C2×#11758196C2311yescharacteristic
264C2×#11758196C2311yescharacteristic
265C2×#11758196C2311yescharacteristic
266C2×#11758196C2311yescharacteristic
267C2×#11758196C2311yescharacteristic
268C2×#11758196C2311yescharacteristic
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×C22⋊Dic61C2311yescharacteristic
279C2×C22⋊Dic61C2311yescharacteristic
280C2×C22⋊Dic61C2311yescharacteristic
281C2×C22⋊Dic61C2311yescharacteristic
282C2×C22⋊Dic61C2311yescharacteristic
283C2×C22⋊Dic61C2311yescharacteristic
284C2×C22⋊Dic61C2311yescharacteristic
285C2×C22⋊Dic61C2311yescharacteristic
286C2×C22⋊Dic61C2311yescharacteristic
287C2×#11758198—24no—
288C2×#11758198—24no—
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×#11758198C2311yescharacteristic
305C2×#11758198C2311yescharacteristic
306C2×#11758198C2311yescharacteristic
307C2×C4×Dic61—24no—
308C2×C4×Dic61—42no—
309C2×C4×Dic61—42no—
310C2×C4×Dic61C2311yescharacteristic
311C2×C4×Dic61C2311yescharacteristic
312C2×C4×Dic61C2311yescharacteristic
313C2×C4×Dic61C2311yescharacteristic
314C2×C4×Dic61C2311yescharacteristic
315C2×C4×Dic61C2311yescharacteristic
316C2×C4×Dic61C2311yescharacteristic
317C2×C4×Dic61C2311yescharacteristic
318C2×C4×Dic61C2311yescharacteristic
319C2×C4×Dic61C2311yescharacteristic
320C2×C4×Dic61C2311yescharacteristic
321C2×C4×Dic61C2311yescharacteristic
322C2×C4×Dic61C2311yescharacteristic
323C2×C4×Dic61C2311yescharacteristic
324C2×C4×Dic61C2311yescharacteristic
325C2×C4×Dic61C2311yescharacteristic
326C2×C4×Dic61C2311yescharacteristic
327C2×C4×Dic61C2311yescharacteristic
328#14519684C2311yescharacteristic
329#14519684C2311yescharacteristic
330#14519684C2311yescharacteristic
331#14519684C2311yescharacteristic
332#14519684C2311yescharacteristic
333#14519684C2311yescharacteristic
334#14519684C2311yescharacteristic
335#14519684C2311yescharacteristic
336#14519684C2311yescharacteristic
337#14519684C2311yescharacteristic
338#14519684C2311yescharacteristic
339#14519684C2311yescharacteristic
340#14519684C2311yescharacteristic
341#14519684C2311yescharacteristic
342#14519684C2311yescharacteristic
343#14519684C2311yescharacteristic
344#14519684C2311yescharacteristic
345#14519684C2311yescharacteristic
346#14519684C2311yescharacteristic
347#14519684C2311yescharacteristic
348#14519684C2311yescharacteristic
349#14519684C2311yescharacteristic
350#14519684C2311yescharacteristic
351#14519684C2311yescharacteristic
352C22×D4×C61C2311yescharacteristic
353C22×D4×C61C2311yescharacteristic
354C22×D4×C61C2311yescharacteristic
355C22×D4×C61C2311yescharacteristic
356C22×D4×C61C2311yescharacteristic
357C22×D4×C61C2311yescharacteristic
358C23×C4×C61C2311yescharacteristic
359C23×C4×C61C2311yescharacteristic
360C23×C4×C61C2311yescharacteristic
361C23×C4×C61C2311yescharacteristic
362#121×C61—24no—
363#121×C61—24no—
364#121×C61—24no—
365C4×D4×C61—24no—
366C2×C4⋊C4×C61C2311yescharacteristic
367C2×C4⋊C4×C61C2311yescharacteristic
368C2×C4⋊C4×C61C2311yescharacteristic
369C2×C4⋊C4×C61C2311yescharacteristic
370C2×C22⋊C4×C61C2311yescharacteristic
371C2×C22⋊C4×C61C2311yescharacteristic
372C2×C22⋊C4×C61C2311yescharacteristic
373C2×C22⋊C4×C61C2311yescharacteristic
374C2×C22⋊C4×C61C2311yescharacteristic
375C2×C22⋊C4×C61C2311yescharacteristic
376C2×C22⋊C4×C61C2311yescharacteristic
377C2×C22⋊C4×C61C2311yescharacteristic
378C2×C22⋊C4×C61C2311yescharacteristic
379C2×C22⋊C4×C61C2311yescharacteristic
380C2×C22⋊C4×C61C2311yescharacteristic
381C2×C22⋊C4×C61C2311yescharacteristic
382C2×C42×C61C2311yescharacteristic
383#95×C61C2311yescharacteristic
384#95×C61C2311yescharacteristic
385#95×C61C2311yescharacteristic
386#95×C61C2311yescharacteristic
387#95×C61C2311yescharacteristic
388#95×C61C2311yescharacteristic
389#95×C61C2311yescharacteristic
390#95×C61C2311yescharacteristic
391C24×C61C2411yescharacteristic
392C24×C61C2411yescharacteristic
393C24×C61C2411yescharacteristic
394C24×C61C2411yescharacteristic
395C23×D61—22no—
396C23×D61—22no—
397C23×D61—22no—
398C23×D61—22no—
399C23×D61—22no—
400C23×D61—41no—
401C23×D61—41no—
402C23×D61C2411yescharacteristic
403C23×D61C2411yescharacteristic
404C2×D4×C61—22no—
405C2×D4×C61—22no—
406C2×D4×C61—22no—
407C2×D4×C61—22no—
408C2×D4×C61—22no—
409C2×D4×C61—22no—
410C2×D4×C61—22no—
411C2×D4×C61—22no—
412C2×D4×C61—22no—
413C2×D4×C61—22no—
414C2×D4×C61—22no—
415C2×D4×C61—22no—
416C2×D4×C61—22no—
417C2×D4×C61—41no—
418C2×D4×C61—41no—
419C2×D4×C61—41no—
420C2×D4×C61—41no—
421C2×D4×C61C2×D414yes—
422C22×C4×C61—22no—
423C22×C4×C61—22no—
424C22×C4×C61—22no—
425C22×C4×C61—22no—
426C22×C4×C61—22no—
427C22×C4×C61—41no—
428C22×C4×C61—41no—
429C22×C4×C61—41no—
430C22×C4×C61—41no—
431C22×C4×C61—41no—
432C22×C4×C61—41no—
433C22×C4×C61#4114yescomplemented
434C22×C4×C61C2411yescharacteristic
435C22×C4×C61C2411yescharacteristic
436C22×C4×C61C2411yescharacteristic
437C22×C4×C61C2411yescharacteristic
438C22×C4×C61C2411yescharacteristic
439C22×C4×C61C2411yescharacteristic
440C22×C4×C61C2411yescharacteristic
441C22×C4×C61C2411yescharacteristic
442C22×C4×C61C2411yescharacteristic
443C22×C4×C61C2411yescharacteristic
444C22×C4×C61C2411yescharacteristic
445C2×C22⋊D61—22no—
446C2×C22⋊D61—22no—
447C2×C22⋊D61—22no—
448C2×C22⋊D61—22no—
449C2×C22⋊D61—22no—
450C2×C22⋊D61—22no—
451C2×C22⋊D61—22no—
452C2×C22⋊D61—22no—
453C2×C22⋊D61—22no—
454C2×C22⋊D61—22no—
455C2×C22⋊D61—22no—
456C2×C22⋊D61—22no—
457C2×C22⋊D61—41no—
458C2×C22⋊D61—41no—
459C2×C22⋊D61—41no—
460C2×C22⋊D61—41no—
461C2×C22⋊D61—41no—
462C2×C22⋊D61—41no—
463C22×Dic61—22no—
464C22×Dic61—22no—
465C22×Dic61—22no—
466C22×Dic61—22no—
467C22×Dic61—22no—
468C22×Dic61—22no—
469C22×Dic61—22no—
470C22×Dic61—22no—
471C22×Dic61—22no—
472C22×Dic61—22no—
473C22×Dic61—22no—
474C22×Dic61—22no—
475C22×Dic61—22no—
476C22×Dic61—22no—
477C22×Dic61—22no—
478C22×Dic61—22no—
479C22×Dic61—22no—
480C22×Dic61—41no—
481C22×Dic61—41no—
482C22×Dic61C2×D414yes—
483C22×Dic61C2×D414yes—
484C22×Dic61C2411yescharacteristic
485C22×Dic61C2411yescharacteristic
486C22×Dic61C2411yescharacteristic
487C22×Dic61C2411yescharacteristic
488C22×Dic61C2411yescharacteristic
489C22×Dic61C2411yescharacteristic
490C22×Dic61C2411yescharacteristic
491C22×Dic61C2411yescharacteristic
492C22×Dic61C2411yescharacteristic
493C22×Dic61C2411yescharacteristic
494C22×Dic61C2411yescharacteristic
495C22×Dic61C2411yescharacteristic
496C22×Dic61C2411yescharacteristic
497C22×Dic61C2411yescharacteristic
498#11758224—416no—
499C2×C4×D61—22no—
500C2×C4×D61—22no—
501C2×C4×D61—22no—
502C2×C4×D61—22no—
503C2×C4×D61—22no—
504C2×C4×D61—22no—
505C2×C4×D61—22no—
506C2×C4×D61—22no—
507C2×C4×D61—22no—
508C2×C4×D61—416no—
509C2×C4×D61—41no—
510C2×C4×D61—41no—
511C2×C4×D61#4114yes—
512C2×Dic122—22no—
513C2×Dic122—22no—
514C2×Dic122—22no—
515C2×Dic122—22no—
516C2×Dic122—41no—
517C2×Dic122—41no—
518C4⋊C4×C61—22no—
519C4⋊C4×C61—22no—
520C4⋊C4×C61—22no—
521C4⋊C4×C61—22no—
522C22⋊C4×C61—22no—
523C22⋊C4×C61—22no—
524C22⋊C4×C61—22no—
525C22⋊C4×C61—22no—
526C22⋊C4×C61—22no—
527C22⋊C4×C61—22no—
528C22⋊C4×C61—22no—
529C22⋊C4×C61—22no—
530C22⋊C4×C61—22no—
531C22⋊C4×C61—22no—
532C22⋊C4×C61—41no—
533C22⋊C4×C61—41no—
534C42×C61—22no—
535C22⋊Dic61—22no—
536C22⋊Dic61—22no—
537C22⋊Dic61—22no—
538C22⋊Dic61—22no—
539C22⋊Dic61—22no—
540C22⋊Dic61—22no—
541C22⋊Dic61—22no—
542C22⋊Dic61—22no—
543C22⋊Dic61—22no—
544C22⋊Dic61—22no—
545C22⋊Dic61—22no—
546C22⋊Dic61—22no—
547C22⋊Dic61—22no—
548C22⋊Dic61—41no—
549C22⋊Dic61—41no—
550C22⋊Dic61C2×D414yes—
551C22⋊Dic61C2×D414yes—
552C22⋊Dic61#4114yescomplemented
553#11758198—22no—
554#11758198—22no—
555#11758198—22no—
556#11758198—22no—
557#11758198—22no—
558#11758198—22no—
559#11758198—22no—
560#11758198—22no—
561#11758198—22no—
562#11758198—22no—
563#11758198—22no—
564#11758198—22no—
565#11758198—22no—
566#11758198—22no—
567#11758198—22no—
568#11758198—41no—
569#11758198—41no—
570#11758198#4114yescomplemented
571C4⋊Dic61—22no—
572C4⋊Dic61—22no—
573C4⋊Dic61—22no—
574C4⋊Dic61—22no—
575C4⋊Dic61—22no—
576C4⋊Dic61—41no—
577C4⋊Dic61—41no—
578C4⋊Dic61C2×D414yes—
579#11758196—22no—
580#11758196—22no—
581#11758196—22no—
582#11758196—22no—
583#11758196—22no—
584#11758196—22no—
585#11758196—22no—
586#11758196—22no—
587#11758196—22no—
588#11758196—22no—
589#11758196—22no—
590#11758196—22no—
591#11758196—41no—
592#11758196—41no—
593C4×Dic61—22no—
594C4×Dic61—22no—
595C4×Dic61—22no—
596C4×Dic61—22no—
597C4×Dic61—22no—
598C4×Dic61—22no—
599C4×Dic61—22no—
600C4×Dic61—22no—
601C4×Dic61—22no—
602C4×Dic61—22no—
603C4×Dic61—22no—
604C4×Dic61—22no—
605C4×Dic61—41no—
606C4×Dic61—41no—
607C4×Dic61—41no—
608C4×Dic61—41no—
609C4×Dic61—41no—
610C4×Dic61C2×D414yes—
611C23×C61—21no—
612C23×C61—21no—
613C23×C61—21no—
614C23×C61—21no—
615C23×C61—21no—
616C23×C61—21no—
617C23×C61—21no—
618C23×C61—21no—
619C23×C61—21no—
620C23×C61—21no—
621C23×C61—21no—
622C23×C61—21no—
623C23×C61—21no—
624C23×C61—21no—
625C23×C61—21no—
626C23×C61—21no—
627C23×C61—21no—
628C23×C61—21no—
629C23×C61—21no—
630C23×C61—21no—
631C23×C61—21no—
632C23×C61—21no—
633C23×C61—21no—
634C23×C61—21no—
635C23×C61C22×D412yes—
636C23×C61C22×D412yes—
637C23×C61C2×#4112yes—
638C23×C61C2×#4112yes—
639C23×C61C2511yescharacteristic
640C22×D61—28no—
641C22×D61—21no—
642C22×D61—21no—
643C22×D61—21no—
644C22×D61—21no—
645C22×D61—21no—
646C22×D61—21no—
647C22×D61—21no—
648C22×D61—21no—
649C22×D61—21no—
650C22×D61—21no—
651C22×D61—21no—
652C22×D61—21no—
653C22×D61—44no—
654C22×D61—44no—
655C22×D61—44no—
656C22×D61—44no—
657C22×D61—44no—
658C22×D61—44no—
659C22×D61C2×#4112yes—
660C22×D61C2×#4112yes—
661D4×C61—28no—
662D4×C61—44no—
663D4×C61—44no—
664D4×C61—44no—
665D4×C61—44no—
666D4×C61—44no—
667C2×C4×C61—21no—
668C2×C4×C61—21no—
669C2×C4×C61—21no—
670C2×C4×C61—21no—
671C2×C4×C61—21no—
672C2×C4×C61—21no—
673C2×C4×C61—21no—
674C2×C4×C61—21no—
675C2×C4×C61—21no—
676C2×C4×C61—21no—
677C2×C4×C61—21no—
678C2×C4×C61—21no—
679C2×C4×C61—21no—
680C2×C4×C61—21no—
681C2×C4×C61—21no—
682C2×C4×C61—21no—
683C2×C4×C61—21no—
684C2×C4×C61—21no—
685C2×C4×C61—21no—
686C2×C4×C61—21no—
687C2×C4×C61—21no—
688C2×C4×C61—21no—
689C2×C4×C61—21no—
690C2×C4×C61—21no—
691C2×C4×C61—21no—
692C2×C4×C61—21no—
693C2×C4×C61—21no—
694C2×C4×C61—21no—
695C2×C4×C61—44no—
696C2×C4×C61—44no—
697C2×C4×C61—44no—
698C2×C4×C61—44no—
699C2×C4×C61C22×D412yes—
700C2×C4×C61C2×#4112yes—
701C2×C4×C61C2×#4112yes—
702C2×C4×C61C2×#4112yes—
703C2×C4×C61C2×#4112yes—
704C22⋊D61—44no—
705C22⋊D61—44no—
706C22⋊D61—44no—
707C22⋊D61—44no—
708C22⋊D61—44no—
709C22⋊D61—44no—
710C2×Dic61—21no—
711C2×Dic61—21no—
712C2×Dic61—21no—
713C2×Dic61—21no—
714C2×Dic61—21no—
715C2×Dic61—21no—
716C2×Dic61—21no—
717C2×Dic61—21no—
718C2×Dic61—21no—
719C2×Dic61—21no—
720C2×Dic61—21no—
721C2×Dic61—21no—
722C2×Dic61—28no—
723C2×Dic61—28no—
724C2×Dic61—21no—
725C2×Dic61—21no—
726C2×Dic61—21no—
727C2×Dic61—21no—
728C2×Dic61—21no—
729C2×Dic61—21no—
730C2×Dic61—21no—
731C2×Dic61—21no—
732C2×Dic61—21no—
733C2×Dic61—21no—
734C2×Dic61—21no—
735C2×Dic61—21no—
736C2×Dic61—21no—
737C2×Dic61—21no—
738C2×Dic61—21no—
739C2×Dic61—21no—
740C2×Dic61—21no—
741C2×Dic61—21no—
742C2×Dic61—21no—
743C2×Dic61—21no—
744C2×Dic61—21no—
745C2×Dic61—44no—
746C2×Dic61—44no—
747C2×Dic61—44no—
748C2×Dic61—44no—
749C2×Dic61—44no—
750C2×Dic61C22×D412yes—
751C2×Dic61C22×D412yes—
752C2×Dic61C22×D412yes—
753C2×Dic61C22×D412yes—
754C2×Dic61C2×#4112yes—
755C2×Dic61C2×#4112yes—
756C2×Dic61C2×#4112yes—
757C2×Dic61C2×#4112yes—
758C2×Dic61H(5,𝔽2)12yes—
759C4×D61—28no—
760C4×D61—44no—
761C4×D61—44no—
762C4×D61—44no—
763Dic122—44no—
764Dic122—44no—
765#34829—611nomaximal, Sylow
766C22×C61—22no—
767C22×C61—22no—
768C22×C61—22no—
769C22×C61—22no—
770C22×C61—22no—
771C22×C61—22no—
772C22×C61—22no—
773C22×C61—22no—
774C22×C61—22no—
775C22×C61—41no—
776C22×C61—41no—
777C22×C61—41no—
778C22×C61—41no—
779C22×C61—41no—
780C22×C61—41no—
781C22×C61—41no—
782C22×C61—41no—
783C22×C61—41no—
784C22×C61—41no—
785C22×C61—41no—
786C22×C61—41no—
787C22×C61—41no—
788C22×C61—41no—
789C22×C61—41no—
790C22×C61—41no—
791C22×C61—41no—
792C22×C61—41no—
793C22×C61#53214yes—
794C22×C61C23×D411yescharacteristic
795C22×C61C22×#4111yescharacteristic
796C22×C61C22×#4111yescharacteristic
797C22×C61C22×#4111yescharacteristic
798C22×C61C22×#4111yescharacteristic
799C22×C61C2×H(5,𝔽2)11yescharacteristic
800C22×C61#58511yescharacteristic
801C2×D61—22no—
802C2×D61—22no—
803C2×D61—22no—
804C2×D61—22no—
805C2×D61—22no—
806C2×D61—22no—
807C2×D61—416no—
808C2×D61—41no—
809C2×D61—41no—
810C2×D61—41no—
811C2×D61—41no—
812C2×D61—41no—
813C2×D61—41no—
814C2×D61—41no—
815C2×D61—41no—
816C4×C61—22no—
817C4×C61—22no—
818C4×C61—22no—
819C4×C61—22no—
820C4×C61—22no—
821C4×C61—41no—
822C4×C61—41no—
823C4×C61—41no—
824C4×C61—41no—
825C4×C61—41no—
826C4×C61—41no—
827Dic61—22no—
828Dic61—22no—
829Dic61—22no—
830Dic61—22no—
831Dic61—22no—
832Dic61—22no—
833Dic61—41no—
834Dic61—41no—
835Dic61—41no—
836Dic61—41no—
837Dic61—41no—
838Dic61—41no—
839Dic61—41no—
840Dic61#54614yes—
841C2×#529—611no—
842C2×#525—611no—
843#2560—611no—
844#2559—611no—
845#2558—611no—
846#2557—611no—
847#2556—611no—
848#2555—611no—
849#2554—611no—
850#2553—611no—
851#2549—611no—
852#2543D6111yescharacteristic, complemented
853#2539—611no—
854#2534—611no—
855#2488—611no—
856#2472—611no—
857#2425—611no—
858#2424—611no—
859#2396—611no—
860#2395—611no—
861#2392—611no—
862#2388—611no—
863C4×#124—611no—
864C4×#123—611no—
865C4×#121—611no—
866C4×#121—611no—
867C4×#120—611no—
868#2297—611no—
869#2293—611no—
870C42×D4—611no—
871C2×C4×C22⋊C4—611no—
872C2×C61—24no—
873C2×C61—42no—
874C2×C61—81no—
875C2×C61—81no—
876C2×C61C2×#53211yescharacteristic
877C2×C61#344411yescharacteristic
878C2×C61#345911yescharacteristic
879C2×C61C2×#54611yescharacteristic
880C2×C61D4×#4111yescharacteristic
881C2×C61#347511yescharacteristic
882C2×C61#348111yescharacteristic
883D61—42no—
884D61—42no—
885C22×#41—611no—
886C24×C4—611no—
887#529—1228no—
888C2×#126—611no—
889C2×#126—611no—
890C2×#125—611no—
891C2×#124—611no—
892C2×#124—611no—
893#525—1228no—
894C2×#123—611no—
895C2×#123—611no—
896C2×#123—611no—
897C2×#123—611no—
898C2×#123—611no—
899C2×C22⋊Q8—611no—
900C2×C22⋊Q8—611no—
901C2×C22⋊Q8—611no—
902C2×#121—611no—
903C2×#121—611no—
904C2×#121C2×D6111yescharacteristic
905C2×#121C2×D6111yescharacteristic
906C2×#121C2×D6111yescharacteristic
907C2×#120—611no—
908C2×#120—611no—
909C2×#120—611no—
910C2×C4×Q8—611no—
911C2×C4×D4—611no—
912C2×C4×D4—611no—
913C2×C4×D4—611no—
914C2×C4×D4—611no—
915C2×C4×D4—611no—
916C2×C4×D4—611no—
917C2×C4×D4—611no—
918C2×C4×D4—611no—
919C2×C4×D4—611no—
920C2×C4×D4—611no—
921C2×C4×D4C2×D6111yescharacteristic
922C2×#117—611no—
923C2×#117—611no—
924C2×#117—611no—
925C22×C22⋊C4—611no—
926C22×C22⋊C4—611no—
927C22×C42—611no—
928C22×C42—611no—
929C22×C42—611no—
930#400—611no—
931#400—611no—
932#399—611no—
933#399—611no—
934#398—611no—
935#398—611no—
936#398—611no—
937#398C2×D6111yescharacteristic, complemented
938#397—611no—
939#397—611no—
940#397—611no—
941#397C2×D6111yescharacteristic, complemented
942#396—611no—
943#396—611no—
944#396—611no—
945#396—611no—
946#395—611no—
947#395—611no—
948#394—611no—
949#394—611no—
950#394—611no—
951#394—611no—
952#394—611no—
953#394—611no—
954#394—611no—
955#394C2×D6111yescharacteristic, complemented
956#393—611no—
957#393—611no—
958#392—611no—
959#392—611no—
960#392—611no—
961#392C2×D6111yescharacteristic, complemented
962#391—611no—
963#391—611no—
964#391—611no—
965#390—611no—
966#390—611no—
967#390—611no—
968#390—611no—
969#390—611no—
970#390—611no—
971#390—611no—
972#389—611no—
973#389—611no—
974#389—611no—
975#389—611no—
976#388—611no—
977#388—611no—
978#388—611no—
979#388—611no—
980#388—611no—
981#388—611no—
982#388—611no—
983#388—611no—
984#388—611no—
985#388—611no—
986#388—611no—
987#388—611no—
988#388C2×D6111yescharacteristic, complemented
989#388C2×D6111yescharacteristic, complemented
990#387—611no—
991#387—611no—
992#386—611no—
993#386—611no—
994#386—611no—
995#386—611no—
996#386—611no—
997#386—611no—
998#386—611no—
999#386—611no—
1000#386C2×D6111yescharacteristic
1001#386C2×D6111yescharacteristic
1002#386C2×D6111yescharacteristic, complemented
1003#386C2×D6111yescharacteristic, complemented
1004#385—611no—
1005#385—611no—
1006#385—611no—
1007#385—611no—
1008#382—611no—
1009#381—611no—
1010#380—611no—
1011#380—611no—
1012#379—611no—
1013C4×C4⋊C4—611no—
1014C4×C4⋊C4—611no—
1015C4×C4⋊C4—611no—
1016C4×C4⋊C4—611no—
1017C4×C4⋊C4—611no—
1018C4×C4⋊C4—611no—
1019C4×C22⋊C4—611no—
1020C4×C22⋊C4—611no—
1021C4×C22⋊C4—611no—
1022C4×C22⋊C4—611no—
1023C4×C22⋊C4—611no—
1024C4×C22⋊C4—611no—
1025C4×C22⋊C4—611no—
1026C4×C22⋊C4—611no—
1027C4×C22⋊C4—611no—
1028C4×C22⋊C4—611no—
1029C4×C22⋊C4—611no—
1030C4×C22⋊C4—611no—
1031C4×C22⋊C4—611no—
1032C4×C22⋊C4—611no—
1033C4×C22⋊C4—611no—
1034C4×C22⋊C4—611no—
1035C4×C22⋊C4—611no—
1036C4×C22⋊C4—611no—
1037C4×C22⋊C4—611no—
1038C4×C22⋊C4—611no—
1039C2×#95—611no—
1040C2×#95C2×D6111yescharacteristic
1041C43—611no—
1042C61#3482911yescharacteristic, complemented, Sylow
1043C25—611no—
1044C2×#41—1224no—
1045C2×#41—1224no—
1046C2×#41—2442no—
1047C22×Q8—611no—
1048C22×Q8—611no—
1049C22×D4—611no—
1050C22×D4—611no—
1051C22×D4—611no—
1052C22×D4—611no—
1053C22×D4—611no—
1054C22×D4—611no—
1055C22×D4C22×D6111yescharacteristic
1056C22×D4C22×D6111yescharacteristic
1057C22×D4C22×D6111yescharacteristic
1058C22×D4C22×D6111yescharacteristic
1059C22×D4C22×D6111yescharacteristic
1060C22×D4C22×D6111yescharacteristic
1061C23×C4—611no—
1062C23×C4—611no—
1063C23×C4—611no—
1064C23×C4—611no—
1065C23×C4—611no—
1066C23×C4—611no—
1067C23×C4—611no—
1068C23×C4—611no—
1069C23×C4—611no—
1070C23×C4—611no—
1071C23×C4—611no—
1072C23×C4—1224no—
1073C23×C4—1224no—
1074C23×C4—2442no—
1075C23×C4C22×D6111yescharacteristic
1076C23×C4C22×D6111yescharacteristic
1077C23×C4C22×D6111yescharacteristic
1078C23×C4C22×D6111yescharacteristic
1079#126—1224no—
1080#126—1224no—
1081#125—1224no—
1082#124—1224no—
1083#124—1224no—
1084#123—1224no—
1085#123—1224no—
1086#123—1224no—
1087#123—1224no—
1088#123—1224no—
1089C22⋊Q8—1224no—
1090C22⋊Q8—1224no—
1091C22⋊Q8—1224no—
1092#121—24no—
1093#121—24no—
1094#121—24no—
1095#121—1224no—
1096#121—1224no—
1097#120—1224no—
1098#120—1224no—
1099#120—1224no—
1100C4×Q8—1224no—
1101C4×D4—24no—
1102C4×D4—618no—
1103C4×D4—1224no—
1104C4×D4—1224no—
1105C4×D4—1224no—
1106C4×D4—1224no—
1107C4×D4—1224no—
1108C4×D4—1224no—
1109C4×D4—1224no—
1110C4×D4—2442no—
1111C4×D4—2442no—
1112#117—1224no—
1113#117—1224no—
1114#117—1224no—
1115C2×C4⋊C4—611no—
1116C2×C4⋊C4—611no—
1117C2×C4⋊C4—611no—
1118C2×C4⋊C4—611no—
1119C2×C4⋊C4—611no—
1120C2×C4⋊C4—611no—
1121C2×C4⋊C4—611no—
1122C2×C4⋊C4—611no—
1123C2×C4⋊C4—611no—
1124C2×C4⋊C4—611no—
1125C2×C4⋊C4—611no—
1126C2×C4⋊C4—611no—
1127C2×C4⋊C4—611no—
1128C2×C4⋊C4—611no—
1129C2×C4⋊C4—611no—
1130C2×C4⋊C4—611no—
1131C2×C4⋊C4—611no—
1132C2×C4⋊C4—611no—
1133C2×C4⋊C4—611no—
1134C2×C4⋊C4—611no—
1135C2×C4⋊C4—611no—
1136C2×C4⋊C4—611no—
1137C2×C4⋊C4C22×D6111yescharacteristic
1138C2×C4⋊C4C22×D6111yescharacteristic
1139C2×C4⋊C4C22×D6111yescharacteristic
1140C2×C4⋊C4C22×D6111yescharacteristic
1141C2×C22⋊C4—611no—
1142C2×C22⋊C4—611no—
1143C2×C22⋊C4—611no—
1144C2×C22⋊C4—611no—
1145C2×C22⋊C4—611no—
1146C2×C22⋊C4—611no—
1147C2×C22⋊C4—611no—
1148C2×C22⋊C4—611no—
1149C2×C22⋊C4—611no—
1150C2×C22⋊C4—611no—
1151C2×C22⋊C4—611no—
1152C2×C22⋊C4—611no—
1153C2×C22⋊C4—611no—
1154C2×C22⋊C4—611no—
1155C2×C22⋊C4—611no—
1156C2×C22⋊C4—611no—
1157C2×C22⋊C4—611no—
1158C2×C22⋊C4—611no—
1159C2×C22⋊C4—611no—
1160C2×C22⋊C4—611no—
1161C2×C22⋊C4—611no—
1162C2×C22⋊C4—611no—
1163C2×C22⋊C4—611no—
1164C2×C22⋊C4—611no—
1165C2×C22⋊C4—611no—
1166C2×C22⋊C4—611no—
1167C2×C22⋊C4—611no—
1168C2×C22⋊C4—611no—
1169C2×C22⋊C4—611no—
1170C2×C22⋊C4—611no—
1171C2×C22⋊C4—611no—
1172C2×C22⋊C4—611no—
1173C2×C22⋊C4—611no—
1174C2×C22⋊C4—611no—
1175C2×C22⋊C4—611no—
1176C2×C22⋊C4—611no—
1177C2×C22⋊C4—1224no—
1178C2×C22⋊C4—1224no—
1179C2×C22⋊C4C22×D6111yescharacteristic
1180C2×C22⋊C4C22×D6111yescharacteristic
1181C2×C22⋊C4C22×D6111yescharacteristic
1182C2×C22⋊C4C22×D6111yescharacteristic
1183C2×C22⋊C4C22×D6111yescharacteristic
1184C2×C22⋊C4C22×D6111yescharacteristic
1185C2×C22⋊C4C22×D6111yescharacteristic
1186C2×C22⋊C4C22×D6111yescharacteristic
1187C2×C22⋊C4C22×D6111yescharacteristic
1188C2×C22⋊C4C22×D6111yescharacteristic
1189C2×C22⋊C4C22×D6111yescharacteristic
1190C2×C22⋊C4C22×D6111yescharacteristic
1191C2×C42—611no—
1192C2×C42—611no—
1193C2×C42—611no—
1194C2×C42—611no—
1195C2×C42—611no—
1196C2×C42—611no—
1197C2×C42—611no—
1198C2×C42—611no—
1199C2×C42—611no—
1200C2×C42—611no—
1201C2×C42—611no—
1202C2×C42—611no—
1203C2×C42—611no—
1204C2×C42—611no—
1205C2×C42—611no—
1206C2×C42—611no—
1207C2×C42—611no—
1208C2×C42—611no—
1209C2×C42—1224no—
1210C2×C42—2442no—
1211C2×C42—2442no—
1212C2×C42C22×D6111yescharacteristic
1213#95—611no—
1214#95—611no—
1215#95—611no—
1216#95—611no—
1217#95—611no—
1218#95—611no—
1219#95—611no—
1220#95—611no—
1221#95—611no—
1222#95—611no—
1223#95—611no—
1224#95—611no—
1225#95—611no—
1226#95—611no—
1227#95—611no—
1228#95—611no—
1229#95—611no—
1230#95—611no—
1231#95—611no—
1232#95—611no—
1233#95—611no—
1234#95—611no—
1235#95—611no—
1236#95—611no—
1237#95C22×D6111yescharacteristic
1238#95C22×D6111yescharacteristic
1239#95C22×D6111yescharacteristic
1240#95C22×D6111yescharacteristic
1241#95C22×D6111yescharacteristic
1242#95C22×D6111yescharacteristic
1243#95C22×D6111yescharacteristic
1244#95C22×D6111yescharacteristic
1245C24—611no—
1246C24—611no—
1247C24—1222no—
1248C24—1222no—
1249C24—1222no—
1250C24—1222no—
1251C24—1222no—
1252C24—2441no—
1253C24—2441no—
1254C24C23×D6111yescharacteristic
1255C24C23×D6111yescharacteristic
1256C24C23×D6111yescharacteristic
1257C24C23×D6111yescharacteristic
1258#41—24416no—
1259C2×Q8—1222no—
1260C2×Q8—1222no—
1261C2×Q8—1222no—
1262C2×Q8—1222no—
1263C2×Q8—2441no—
1264C2×Q8—2441no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—22no—
1275C2×D4—22no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—41no—
1279C2×D4—41no—
1280C2×D4—41no—
1281C2×D4—41no—
1282C2×D4—1222no—
1283C2×D4—1222no—
1284C2×D4—1222no—
1285C2×D4—1222no—
1286C2×D4—1222no—
1287C2×D4—1222no—
1288C2×D4—1222no—
1289C2×D4—1222no—
1290C2×D4—1222no—
1291C2×D4—1222no—
1292C2×D4—1222no—
1293C2×D4—1222no—
1294C2×D4—2441no—
1295C2×D4—2441no—
1296C2×D4—2441no—
1297C2×D4—2441no—
1298C2×D4—2441no—
1299C2×D4—2441no—
1300C2×D4D4×D6114yes—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—41no—
1307C22×C4—41no—
1308C22×C4—41no—
1309C22×C4—41no—
1310C22×C4—41no—
1311C22×C4—41no—
1312C22×C4—611no—
1313C22×C4—614no—
1314C22×C4—614no—
1315C22×C4—611no—
1316C22×C4—611no—
1317C22×C4—611no—
1318C22×C4—611no—
1319C22×C4—611no—
1320C22×C4—611no—
1321C22×C4—614no—
1322C22×C4—611no—
1323C22×C4—611no—
1324C22×C4—611no—
1325C22×C4—611no—
1326C22×C4—611no—
1327C22×C4—611no—
1328C22×C4—611no—
1329C22×C4—1222no—
1330C22×C4—1222no—
1331C22×C4—1222no—
1332C22×C4—1222no—
1333C22×C4—1222no—
1334C22×C4—1222no—
1335C22×C4—1222no—
1336C22×C4—1222no—
1337C22×C4—1222no—
1338C22×C4—1222no—
1339C22×C4—1222no—
1340C22×C4—1222no—
1341C22×C4—1222no—
1342C22×C4—1222no—
1343C22×C4—1222no—
1344C22×C4—1222no—
1345C22×C4—1222no—
1346C22×C4—1222no—
1347C22×C4—1222no—
1348C22×C4—1222no—
1349C22×C4—1222no—
1350C22×C4—1222no—
1351C22×C4—1222no—
1352C22×C4—1222no—
1353C22×C4—1222no—
1354C22×C4—1222no—
1355C22×C4—2441no—
1356C22×C4—2441no—
1357C22×C4—24416no—
1358C22×C4—2441no—
1359C22×C4—2441no—
1360C22×C4#1175822414yescomplemented
1361C22×C4C23×D6111yescharacteristic
1362C22×C4C23×D6111yescharacteristic
1363C22×C4C23×D6111yescharacteristic
1364C22×C4C23×D6111yescharacteristic
1365C22×C4C23×D6111yescharacteristic
1366C22×C4C23×D6111yescharacteristic
1367C22×C4C23×D6111yescharacteristic
1368C22×C4C23×D6111yescharacteristic
1369C22×C4C23×D6111yescharacteristic
1370C22×C4C23×D6111yescharacteristic
1371C22×C4C23×D6111yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—614no—
1377C4⋊C4—1222no—
1378C4⋊C4—1222no—
1379C4⋊C4—1222no—
1380C4⋊C4—1222no—
1381C4⋊C4—1222no—
1382C4⋊C4—1222no—
1383C4⋊C4—1222no—
1384C4⋊C4—1222no—
1385C4⋊C4—1222no—
1386C4⋊C4—1222no—
1387C4⋊C4—1222no—
1388C4⋊C4—1222no—
1389C4⋊C4—1222no—
1390C4⋊C4—1222no—
1391C4⋊C4—1222no—
1392C4⋊C4—1222no—
1393C4⋊C4—1222no—
1394C4⋊C4—2441no—
1395C4⋊C4—2441no—
1396C4⋊C4—2441no—
1397C4⋊C4—2441no—
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—22no—
1407C22⋊C4—22no—
1408C22⋊C4—41no—
1409C22⋊C4—41no—
1410C22⋊C4—614no—
1411C22⋊C4—614no—
1412C22⋊C4—614no—
1413C22⋊C4—614no—
1414C22⋊C4—1222no—
1415C22⋊C4—1222no—
1416C22⋊C4—1222no—
1417C22⋊C4—1222no—
1418C22⋊C4—1222no—
1419C22⋊C4—1222no—
1420C22⋊C4—1222no—
1421C22⋊C4—1222no—
1422C22⋊C4—1222no—
1423C22⋊C4—1222no—
1424C22⋊C4—1222no—
1425C22⋊C4—1222no—
1426C22⋊C4—1222no—
1427C22⋊C4—1222no—
1428C22⋊C4—1222no—
1429C22⋊C4—1222no—
1430C22⋊C4—1222no—
1431C22⋊C4—1222no—
1432C22⋊C4—1222no—
1433C22⋊C4—1222no—
1434C22⋊C4—1222no—
1435C22⋊C4—1222no—
1436C22⋊C4—1222no—
1437C22⋊C4—1222no—
1438C22⋊C4—1222no—
1439C22⋊C4—1222no—
1440C22⋊C4—1222no—
1441C22⋊C4—1222no—
1442C22⋊C4—2441no—
1443C22⋊C4—2441no—
1444C22⋊C4—2441no—
1445C22⋊C4—2441no—
1446C42—22no—
1447C42—614no—
1448C42—1222no—
1449C42—1222no—
1450C42—1222no—
1451C42—1222no—
1452C42—1222no—
1453C42—1222no—
1454C42—1222no—
1455C42—1222no—
1456C42—1222no—
1457C42—1222no—
1458C42—1222no—
1459C42—1222no—
1460C42—2441no—
1461C42—2441no—
1462C42—2441no—
1463C42—2441no—
1464C42—2441no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—612no—
1490C23—612no—
1491C23—1228no—
1492C23—1221no—
1493C23—1221no—
1494C23—1221no—
1495C23—1221no—
1496C23—1221no—
1497C23—1221no—
1498C23—1221no—
1499C23—1221no—
1500C23—1221no—
1501C23—1221no—
1502C23—1221no—
1503C23—1221no—
1504C23—2444no—
1505C23—2444no—
1506C23—2444no—
1507C23—2444no—
1508C23—2444no—
1509C23—2444no—
1510C23C2×D4×D6112yes—
1511C23C2×D4×D6112yes—
1512C23#41×D6112yes—
1513C23C2×#1175822412yes—
1514C23C24×D6111yescharacteristic
1515Q8—2444no—
1516Q8—2444no—
1517D4—28no—
1518D4—44no—
1519D4—44no—
1520D4—44no—
1521D4—44no—
1522D4—44no—
1523D4—2444no—
1524D4—2444no—
1525D4—2444no—
1526D4—2444no—
1527D4—2444no—
1528D4—2444no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—44no—
1558C2×C4—44no—
1559C2×C4—44no—
1560C2×C4—44no—
1561C2×C4—612no—
1562C2×C4—612no—
1563C2×C4—612no—
1564C2×C4—612no—
1565C2×C4—612no—
1566C2×C4—612no—
1567C2×C4—612no—
1568C2×C4—612no—
1569C2×C4—612no—
1570C2×C4—1228no—
1571C2×C4—1228no—
1572C2×C4—1228no—
1573C2×C4—1221no—
1574C2×C4—1221no—
1575C2×C4—1221no—
1576C2×C4—1221no—
1577C2×C4—1221no—
1578C2×C4—1221no—
1579C2×C4—1221no—
1580C2×C4—1221no—
1581C2×C4—1221no—
1582C2×C4—1221no—
1583C2×C4—1221no—
1584C2×C4—1221no—
1585C2×C4—1221no—
1586C2×C4—1221no—
1587C2×C4—1221no—
1588C2×C4—1221no—
1589C2×C4—1221no—
1590C2×C4—1221no—
1591C2×C4—1221no—
1592C2×C4—1221no—
1593C2×C4—1221no—
1594C2×C4—1221no—
1595C2×C4—1221no—
1596C2×C4—1221no—
1597C2×C4—1221no—
1598C2×C4—1221no—
1599C2×C4—1221no—
1600C2×C4—1221no—
1601C2×C4—1221no—
1602C2×C4—1221no—
1603C2×C4—1221no—
1604C2×C4—1221no—
1605C2×C4—1221no—
1606C2×C4—2444no—
1607C2×C4—2444no—
1608C2×C4—2444no—
1609C2×C4—2444no—
1610C2×C4—2444no—
1611C2×C4—2444no—
1612C2×C4—2444no—
1613C2×C4—2444no—
1614C2×C4C2×D4×D6112yes—
1615C2×C4#41×D6112yes—
1616C2×C4#41×D6112yes—
1617C2×C4C2×#1175822412yes—
1618C2×C4C2×#1175822412yes—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—41no—
1629C22—41no—
1630C22—41no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—1222no—
1647C22—1222no—
1648C22—1222no—
1649C22—1222no—
1650C22—1222no—
1651C22—1222no—
1652C22—24416no—
1653C22—2441no—
1654C22—2441no—
1655C22—2441no—
1656C22—2441no—
1657C22—2441no—
1658C22—2441no—
1659C22—2441no—
1660C22—2441no—
1661C22#1684030714yes—
1662C22C22×D4×D6111yescharacteristic
1663C22C2×#41×D6111yescharacteristic
1664C22C2×#41×D6111yescharacteristic
1665C22C2×#41×D6111yescharacteristic
1666C22C22×#1175822411yescharacteristic
1667C22H(5,𝔽2)×D6111yescharacteristic
1668C22#1684059711yescharacteristic
1669C4—22no—
1670C4—22no—
1671C4—22no—
1672C4—22no—
1673C4—22no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—614no—
1681C4—1222no—
1682C4—1222no—
1683C4—1222no—
1684C4—1222no—
1685C4—1222no—
1686C4—1222no—
1687C4—2441no—
1688C4—2441no—
1689C4—2441no—
1690C4—2441no—
1691C4—2441no—
1692C4—2441no—
1693C4—2441no—
1694C2—24no—
1695C2—42no—
1696C2—81no—
1697C2—81no—
1698C2—2442no—
1699C2—2442no—
1700C2C2×#1684030711yescharacteristic
1701C2#2145911411yescharacteristic
1702C2#2145922511yescharacteristic
1703C2#546×D6111yescharacteristic
1704C2#2145930311yescharacteristic
1705C2#2145937811yescharacteristic
1706C2#2145942611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2543C2
hypercenter#2543D61
hypocenterC61#34829
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. C2×#16840293C2semidirect
2. C2×#16840272C2semidirect
3. #21450962C2semidirect
4. #21450947C2semidirect
5. #21450932C2semidirect
6. #21450917C2semidirect
7. #21450898C2semidirect
8. #21450889C2semidirect
9. #21450874C2semidirect
10. #21450859C2semidirect
11. #21450830C2semidirect
12. #21450751C2semidirect
13. #21450705C2semidirect
14. #21450143C2semidirect
15. #21449950C2semidirect
16. #21449376C2semidirect
17. #21449361C2semidirect
18. #21449096C2semidirect
19. #21449077C2semidirect
20. #21449062C2semidirect
21. #21449031C2semidirect
22. #21448360C2semidirect
23. #21448344C2semidirect
24. #121×Dic61C2semidirect
25. #21448329C2semidirect
26. #21448324C2semidirect
27. #21448304C2semidirect
28. #21448279C2semidirect
29. C4×D4×Dic61C2semidirect
30. C2×#16839609C2semidirect
31. C61×#2543C2semidirect
35. C2×#14519770C22semidirect
36. C2×#14519770C22semidirect
37. C2×#14519768C22semidirect
38. C2×#14519764C22semidirect
54. C2×#14519742C22semidirect
59. C2×D4×Dic61C22semidirect
60. C2×D4×Dic61C22semidirect
66. C2×#14519733C22semidirect
67. C2×#14519733C22semidirect
72. C22×C4×Dic61C22semidirect
73. #16839704C22semidirect
74. #16839703C22semidirect
77. #16839696C22semidirect
78. #16839696C22semidirect
79. #16839695C22semidirect
81. #16839690C22semidirect
82. #16839690C22semidirect
83. #16839685C22semidirect
87. #16839683C22semidirect
88. #16839683C22semidirect
95. #16839676C22semidirect
97. #16839674C22semidirect
101. #16839666C22semidirect
102. #16839666C22semidirect
103. #16839666C22semidirect
104. #16839665C22semidirect
111. #16839661C22semidirect
112. #16839659C22semidirect
113. #16839659C22semidirect
114. #16839657C22semidirect
115. #16839656C22semidirect
116. #16839656C22semidirect
117. #16839656C22semidirect
118. #16839655C22semidirect
119. #16839655C22semidirect
120. #16839655C22semidirect
126. #16839650C22semidirect
127. #16839649C22semidirect
128. #16839649C22semidirect
131. #16839642C22semidirect
141. #16839626C22semidirect
144. #16839620C22semidirect
146. C4⋊C4×Dic61C22semidirect
147. C4⋊C4×Dic61C22semidirect
148. C4⋊C4×Dic61C22semidirect
149. C4×C4⋊Dic61C22semidirect
150. #16839613C22semidirect
151. #16839613C22semidirect
154. C22⋊C4×Dic61C22semidirect
155. C22⋊C4×Dic61C22semidirect
156. C22⋊C4×Dic61C22semidirect
157. C22⋊C4×Dic61C22semidirect
158. C22⋊C4×Dic61C22semidirect
159. C22⋊C4×Dic61C22semidirect
161. C4×C22⋊Dic61C22semidirect
173. C42×Dic61C22semidirect
178. C61×#398C22semidirect
179. C61×#397C22semidirect
180. C61×#394C22semidirect
181. C61×#392C22semidirect
182. C61×#388C22semidirect
183. C61×#388C22semidirect
186. C61×#386C22semidirect
187. C61×#386C22semidirect
239. D4×Dic61D4semidirect
433. C22×C4×C61#41semidirect
552. C22⋊Dic61#41semidirect
570. #11758198#41semidirect
852. #2543D61semidirect
937. #398C2×D61semidirect
941. #397C2×D61semidirect
955. #394C2×D61semidirect
961. #392C2×D61semidirect
988. #388C2×D61semidirect
989. #388C2×D61semidirect
1002. #386C2×D61semidirect
1003. #386C2×D61semidirect
1042. C61#34829semidirect
1360. C22×C4#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168402932
C2×#168402722
#214509622
#214509472
#214509322
#214509172
#214508982
#214508892
#214508742
#214508592
#214508302
#214507512
#214507052
#214501432
#214499502
#214493762
#214493612
#214490962
#214490772
#214490622
#214490312
#214483602
#214483442
#121×Dic612
#214483292
#214483242
#214483042
#214482792
C4×D4×Dic612
C2×#168396092
C61×#25432
#3482961