Finite Group Databasebeta

← #29848675

Subgroups — #29848675

Order 15616.

2938 conjugacy classes of subgroups.

The subgroup lattice has 1714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic, complemented
2C2×#41×Dic61C211yesmaximal, characteristic, complemented
3#21450019C211yesmaximal, characteristic, complemented
4#21450004C211yesmaximal, characteristic, complemented
5#21449929C211yesmaximal, characteristic, complemented
6#21449914C211yesmaximal, characteristic, complemented
7#21449835C211yesmaximal, characteristic, complemented
8#21449820C211yesmaximal, characteristic, complemented
9#21449736C211yesmaximal, characteristic, complemented
10#21449721C211yesmaximal, characteristic, complemented
11#21449647C211yesmaximal, characteristic, complemented
12#21449565C211yesmaximal, characteristic, complemented
13#21449495C211yesmaximal, characteristic, complemented
14#21449361C211yesmaximal, characteristic, complemented
15#21449279C211yesmaximal, characteristic, complemented
16#21449205C211yesmaximal, characteristic, complemented
17#21449134C211yesmaximal, characteristic, complemented
18#21449101C211yesmaximal, characteristic, complemented
19#21449090C211yesmaximal, characteristic, complemented
20#21449062C211yesmaximal, characteristic, complemented
21#21449031C211yesmaximal, characteristic, complemented
22#123×Dic61C211yesmaximal, characteristic, complemented
23#21448338C211yesmaximal, characteristic, complemented
24#121×Dic61C211yesmaximal, characteristic, complemented
25#21448329C211yesmaximal, characteristic, complemented
26#21448324C211yesmaximal, characteristic, complemented
27#21448304C211yesmaximal, characteristic, complemented
28#21448259C211yesmaximal, characteristic, complemented
29#21448255C211yesmaximal, characteristic, complemented
30C2×#16839609C211yesmaximal, characteristic, complemented
31C61×#2430C211yesmaximal, characteristic, complemented
32C22×#11758224C2211yescharacteristic
33C23×C4×D61C2211yescharacteristic
34#16840272—28no—
35C2×#14519761C2211yescharacteristic
36C2×#14519759C2211yescharacteristic
37C2×#14519759C2211yescharacteristic
38C2×#14519757C2211yescharacteristic
39C2×#14519756C2211yescharacteristic
40C2×#14519749C2211yescharacteristic
41C2×#14519748C2211yescharacteristic
42C2×#14519745C2211yescharacteristic
43C2×#14519745C2211yescharacteristic
44C2×#14519745C2211yescharacteristic
45#41×Dic61—28no—
46C2×Q8×Dic61C2211yescharacteristic, complemented
47C2×Q8×Dic61C2211yescharacteristic, complemented
48C2×D4×Dic61C2211yescharacteristic
49C2×D4×Dic61C2211yescharacteristic
50C2×D4×Dic61C2211yescharacteristic
51C2×D4×Dic61C2211yescharacteristic
52C2×D4×Dic61C2211yescharacteristic
53C2×D4×Dic61C2211yescharacteristic, complemented
54C2×D4×Dic61C2211yescharacteristic, complemented
55C2×D4×Dic61C2211yescharacteristic, complemented
56C2×#14519737C2211yescharacteristic
57C2×#14519737C2211yescharacteristic
58C2×#14519737C2211yescharacteristic
59C2×#14519737C2211yescharacteristic
60C2×#14519736C2211yescharacteristic
61C2×#14519736C2211yescharacteristic, complemented
62C2×#14519736C2211yescharacteristic, complemented
63C2×#14519735C2211yescharacteristic
64C2×#14519733C2211yescharacteristic, complemented
65C22×#11758198C2211yescharacteristic
66C22×#11758198C2211yescharacteristic
67C22×C4×Dic61C2211yescharacteristic
68C22×C4×Dic61C2211yescharacteristic
69C22×C4×Dic61C2211yescharacteristic, complemented
70C22×C4×Dic61C2211yescharacteristic, complemented
71#16839704C2211yescharacteristic, complemented
72#16839704C2211yescharacteristic, complemented
73#16839701C2211yescharacteristic, complemented
74#16839699C2211yescharacteristic
75#16839696C2211yescharacteristic, complemented
76#16839694C2211yescharacteristic, complemented
77#16839694C2211yescharacteristic, complemented
78#16839690C2211yescharacteristic, complemented
79#16839689C2211yescharacteristic
80#16839687C2211yescharacteristic, complemented
81#16839685C2211yescharacteristic, complemented
82#16839684C2211yescharacteristic
83#16839684C2211yescharacteristic
84#16839684C2211yescharacteristic
85#16839683C2211yescharacteristic, complemented
86#16839678C2211yescharacteristic
87#16839678C2211yescharacteristic
88#16839678C2211yescharacteristic
89#16839678C2211yescharacteristic
90#16839678C2211yescharacteristic
91#16839677C2211yescharacteristic
92#16839676C2211yescharacteristic, complemented
93#16839674C2211yescharacteristic, complemented
94#16839673C2211yescharacteristic
95#16839673C2211yescharacteristic
96#16839670C2211yescharacteristic
97#16839670C2211yescharacteristic
98#16839670C2211yescharacteristic
99#16839666C2211yescharacteristic, complemented
100#16839666C2211yescharacteristic, complemented
101#16839665C2211yescharacteristic, complemented
102#16839662C2211yescharacteristic
103#16839662C2211yescharacteristic
104#16839662C2211yescharacteristic
105#16839661C2211yescharacteristic, complemented
106#16839659C2211yescharacteristic, complemented
107#16839656C2211yescharacteristic, complemented
108#16839655C2211yescharacteristic, complemented
109#16839655C2211yescharacteristic, complemented
110#16839655C2211yescharacteristic, complemented
111#16839655C2211yescharacteristic, complemented
112#16839654C2211yescharacteristic
113#16839654C2211yescharacteristic
114#16839652C2211yescharacteristic
115#16839652C2211yescharacteristic
116#16839652C2211yescharacteristic
117#16839650C2211yescharacteristic, complemented
118#16839650C2211yescharacteristic, complemented
119#16839649C2211yescharacteristic, complemented
120#16839648C2211yescharacteristic, complemented
121#16839648C2211yescharacteristic, complemented
122#16839647C2211yescharacteristic, complemented
123#16839645C2211yescharacteristic, complemented
124#16839645C2211yescharacteristic, complemented
125#16839645C2211yescharacteristic, complemented
126#16839643C2211yescharacteristic, complemented
127#16839642C2211yescharacteristic
128#16839642C2211yescharacteristic
129#16839642C2211yescharacteristic
130#16839642C2211yescharacteristic
131#16839642C2211yescharacteristic, complemented
132#16839641C2211yescharacteristic
133#16839641C2211yescharacteristic
134#16839641C2211yescharacteristic
135#16839641C2211yescharacteristic
136#16839639C2211yescharacteristic
137#16839639C2211yescharacteristic
138#16839638C2211yescharacteristic
139#16839638C2211yescharacteristic
140#16839637C2211yescharacteristic
141#16839637C2211yescharacteristic, complemented
142#16839636C2211yescharacteristic
143#16839636C2211yescharacteristic
144#16839635C2211yescharacteristic
145#16839635C2211yescharacteristic
146#16839634C2211yescharacteristic
147#16839625C2211yescharacteristic
148#16839623C2211yescharacteristic, complemented
149#16839622C2211yescharacteristic
150#16839620C2211yescharacteristic, complemented
151#16839617C2211yescharacteristic
152C4⋊C4×Dic61C2211yescharacteristic, complemented
153C4⋊C4×Dic61C2211yescharacteristic, complemented
154C4⋊C4×Dic61C2211yescharacteristic, complemented
155#16839613C2211yescharacteristic, complemented
156C22⋊C4×Dic61C2211yescharacteristic
157C22⋊C4×Dic61C2211yescharacteristic, complemented
158C22⋊C4×Dic61C2211yescharacteristic, complemented
159C22⋊C4×Dic61C2211yescharacteristic, complemented
160C22⋊C4×Dic61C2211yescharacteristic, complemented
161C22⋊C4×Dic61C2211yescharacteristic, complemented
162#16839609C2211yescharacteristic
163#16839609C2211yescharacteristic
164#16839609C2211yescharacteristic
165#16839609C2211yescharacteristic
166#16839609C2211yescharacteristic
167#16839609C2211yescharacteristic
168#16839609C2211yescharacteristic
169#16839609C2211yescharacteristic
170#16839609C2211yescharacteristic
171#16839609C2211yescharacteristic
172#16839607C2211yescharacteristic, complemented
173C2×#14519684C2211yescharacteristic
174C22×#41×C61C2211yescharacteristic
175C2×#123×C61C2211yescharacteristic
176C2×#121×C61C2211yescharacteristic
177C2×#121×C61C2211yescharacteristic
178C61×#395C2211yescharacteristic, complemented
179C61×#394C2211yescharacteristic, complemented
180C61×#393C2211yescharacteristic, complemented
181C61×#392C2211yescharacteristic, complemented
182C61×#386C2211yescharacteristic
183C61×#386C2211yescharacteristic
184C61×#386C2211yescharacteristic, complemented
185C61×#386C2211yescharacteristic, complemented
186C61×#385C2211yescharacteristic, complemented
187C61×#385C2211yescharacteristic, complemented
188C2×#95×C61C2211yescharacteristic
189C24×D61C2311yescharacteristic
190C2×#11758224—24no—
191C2×#11758224—24no—
192C2×#11758224—42no—
193C22×Dic122C2311yescharacteristic
194C22×C22⋊D61C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C22×C22⋊D61C2311yescharacteristic
197C22×C22⋊D61C2311yescharacteristic
198C22×C22⋊D61C2311yescharacteristic
199C22×C22⋊D61C2311yescharacteristic
200C23×Dic61C2311yescharacteristic
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#14519761—24no—
216#14519759—24no—
217#14519759—24no—
218#14519757—24no—
219#14519756—24no—
220#14519749—24no—
221#14519748—24no—
222#14519745—24no—
223#14519745—24no—
224#14519745—24no—
225Q8×Dic61—24no—
226Q8×Dic61—24no—
227D4×Dic61—24no—
228D4×Dic61—24no—
229D4×Dic61—24no—
230D4×Dic61—24no—
231D4×Dic61—24no—
232D4×Dic61—24no—
233D4×Dic61—42no—
234D4×Dic61D418yescomplemented
235#14519737—24no—
236#14519737—24no—
237#14519737—24no—
238#14519737—42no—
239#14519736—24no—
240#14519736—24no—
241#14519736—24no—
242#14519735—24no—
243#14519733—42no—
244C2×C4⋊Dic61C2311yescharacteristic
245C2×C4⋊Dic61C2311yescharacteristic
246C2×C4⋊Dic61C2311yescharacteristic
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×C4⋊Dic61C2311yescharacteristic
256C2×#11758196C2311yescharacteristic
257C2×#11758196C2311yescharacteristic
258C2×#11758196C2311yescharacteristic
259C2×#11758196C2311yescharacteristic
260C2×#11758196C2311yescharacteristic
261C2×#11758196C2311yescharacteristic
262C2×#11758196C2311yescharacteristic
263C2×#11758196C2311yescharacteristic
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×C22⋊Dic61C2311yescharacteristic
279C2×C22⋊Dic61C2311yescharacteristic
280C2×C22⋊Dic61C2311yescharacteristic
281C2×#11758198—24no—
282C2×#11758198—24no—
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×C4×Dic61—24no—
302C2×C4×Dic61—24no—
303C2×C4×Dic61—24no—
304C2×C4×Dic61—42no—
305C2×C4×Dic61C2311yescharacteristic
306C2×C4×Dic61C2311yescharacteristic
307C2×C4×Dic61C2311yescharacteristic
308C2×C4×Dic61C2311yescharacteristic
309C2×C4×Dic61C2311yescharacteristic
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
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
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
350C2×#41×C61—24no—
351C2×#41×C61—24no—
352C2×#41×C61—24no—
353C22×Q8×C61C2311yescharacteristic
354C22×D4×C61C2311yescharacteristic
355C22×D4×C61C2311yescharacteristic
356C22×D4×C61C2311yescharacteristic
357C22×D4×C61C2311yescharacteristic
358C22×D4×C61C2311yescharacteristic
359C22×D4×C61C2311yescharacteristic
360C23×C4×C61C2311yescharacteristic
361C23×C4×C61C2311yescharacteristic
362C23×C4×C61C2311yescharacteristic
363C23×C4×C61C2311yescharacteristic
364C23×C4×C61C2311yescharacteristic
365#123×C61—24no—
366#121×C61—24no—
367#121×C61—24no—
368C2×C4⋊C4×C61C2311yescharacteristic
369C2×C4⋊C4×C61C2311yescharacteristic
370C2×C4⋊C4×C61C2311yescharacteristic
371C2×C4⋊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×C22⋊C4×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
404#41×C61—232no—
405C2×Q8×C61—22no—
406C2×Q8×C61—22no—
407C2×Q8×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—22no—
418C2×D4×C61—22no—
419C2×D4×C61—22no—
420C2×D4×C61—22no—
421C2×D4×C61—22no—
422C2×D4×C61—41no—
423C2×D4×C61—41no—
424C2×D4×C61C2×D414yes—
425C2×D4×C61#4114yescomplemented
426C22×C4×C61—22no—
427C22×C4×C61—22no—
428C22×C4×C61—22no—
429C22×C4×C61—22no—
430C22×C4×C61—22no—
431C22×C4×C61—22no—
432C22×C4×C61—22no—
433C22×C4×C61—22no—
434C22×C4×C61—22no—
435C22×C4×C61—22no—
436C22×C4×C61—22no—
437C22×C4×C61—22no—
438C22×C4×C61—41no—
439C22×C4×C61—41no—
440C22×C4×C61#4114yescomplemented
441C22×C4×C61C2411yescharacteristic
442C22×C4×C61C2411yescharacteristic
443C22×C4×C61C2411yescharacteristic
444C22×C4×C61C2411yescharacteristic
445C22×C4×C61C2411yescharacteristic
446C22×C4×C61C2411yescharacteristic
447C22×C4×C61C2411yescharacteristic
448C22×C4×C61C2411yescharacteristic
449C22×C4×C61C2411yescharacteristic
450C22×C4×C61C2411yescharacteristic
451C22×C4×C61C2411yescharacteristic
452C2×C22⋊D61—22no—
453C2×C22⋊D61—22no—
454C2×C22⋊D61—22no—
455C2×C22⋊D61—22no—
456C2×C22⋊D61—22no—
457C2×C22⋊D61—22no—
458C2×C22⋊D61—22no—
459C2×C22⋊D61—22no—
460C2×C22⋊D61—22no—
461C2×C22⋊D61—22no—
462C2×C22⋊D61—22no—
463C2×C22⋊D61—22no—
464C2×C22⋊D61—41no—
465C2×C22⋊D61—41no—
466C2×C22⋊D61—41no—
467C2×C22⋊D61—41no—
468C2×C22⋊D61—41no—
469C2×C22⋊D61—41no—
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—22no—
481C22×Dic61—22no—
482C22×Dic61—22no—
483C22×Dic61—22no—
484C22×Dic61—22no—
485C22×Dic61—22no—
486C22×Dic61—22no—
487C22×Dic61—41no—
488C22×Dic61—41no—
489C22×Dic61—41no—
490C22×Dic61—41no—
491C22×Dic61—41no—
492C22×Dic61C2×D414yes—
493C22×Dic61C2×D414yes—
494C22×Dic61C2411yescharacteristic
495C22×Dic61C2411yescharacteristic
496C22×Dic61C2411yescharacteristic
497C22×Dic61C2411yescharacteristic
498C22×Dic61C2411yescharacteristic
499C22×Dic61C2411yescharacteristic
500C22×Dic61C2411yescharacteristic
501C22×Dic61C2411yescharacteristic
502C22×Dic61C2411yescharacteristic
503C22×Dic61C2411yescharacteristic
504C22×Dic61C2411yescharacteristic
505C22×Dic61C2411yescharacteristic
506C22×Dic61C2411yescharacteristic
507C22×Dic61C2411yescharacteristic
508#11758224—416no—
509C2×C4×D61—22no—
510C2×C4×D61—22no—
511C2×C4×D61—22no—
512C2×C4×D61—22no—
513C2×C4×D61—22no—
514C2×C4×D61—22no—
515C2×C4×D61—22no—
516C2×C4×D61—22no—
517C2×C4×D61—22no—
518C2×C4×D61—416no—
519C2×C4×D61—41no—
520C2×C4×D61—41no—
521C2×C4×D61#4114yescomplemented
522C2×Dic122—22no—
523C2×Dic122—22no—
524C2×Dic122—41no—
525C4⋊C4×C61—22no—
526C4⋊C4×C61—22no—
527C4⋊C4×C61—22no—
528C4⋊C4×C61—22no—
529C22⋊C4×C61—22no—
530C22⋊C4×C61—22no—
531C22⋊C4×C61—22no—
532C22⋊C4×C61—22no—
533C22⋊C4×C61—22no—
534C22⋊C4×C61—22no—
535C22⋊C4×C61—22no—
536C22⋊C4×C61—22no—
537C22⋊C4×C61—22no—
538C22⋊C4×C61—41no—
539C22⋊C4×C61—41no—
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⋊Dic61—41no—
551C22⋊Dic61—41no—
552C22⋊Dic61—41no—
553C22⋊Dic61—41no—
554C22⋊Dic61—41no—
555C22⋊Dic61C2×D414yes—
556C22⋊Dic61C2×D414yes—
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—22no—
569#11758198—22no—
570#11758198—22no—
571#11758198—22no—
572#11758198—41no—
573#11758198—41no—
574#11758198#4114yescomplemented
575C4⋊Dic61—22no—
576C4⋊Dic61—22no—
577C4⋊Dic61—22no—
578C4⋊Dic61—22no—
579C4⋊Dic61—22no—
580C4⋊Dic61—22no—
581C4⋊Dic61—22no—
582C4⋊Dic61—22no—
583C4⋊Dic61—22no—
584C4⋊Dic61—41no—
585C4⋊Dic61—41no—
586C4⋊Dic61C2×D414yes—
587#11758196—22no—
588#11758196—22no—
589#11758196—22no—
590#11758196—22no—
591#11758196—41no—
592#11758196—41no—
593#11758196—41no—
594#11758196—41no—
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—22no—
606C4×Dic61—22no—
607C4×Dic61—22no—
608C4×Dic61—22no—
609C4×Dic61—41no—
610C4×Dic61—41no—
611C4×Dic61C2×D414yes—
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×C61C2×#4112yes—
640C23×C61C2511yescharacteristic
641C22×D61—28no—
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—21no—
654C22×D61—44no—
655C22×D61—44no—
656C22×D61—44no—
657C22×D61—44no—
658C22×D61—44no—
659C22×D61—44no—
660C22×D61C2×#4112yes—
661C22×D61C2×#4112yes—
662Q8×C61—28no—
663D4×C61—28no—
664D4×C61—28no—
665D4×C61—28no—
666D4×C61—44no—
667D4×C61—44no—
668D4×C61—44no—
669C2×C4×C61—28no—
670C2×C4×C61—28no—
671C2×C4×C61—28no—
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—21no—
696C2×C4×C61—21no—
697C2×C4×C61—21no—
698C2×C4×C61—21no—
699C2×C4×C61—44no—
700C2×C4×C61—44no—
701C2×C4×C61C22×D412yes—
702C2×C4×C61C2×#4112yes—
703C2×C4×C61C2×#4112yes—
704C2×C4×C61C2×#4112yes—
705C2×C4×C61C2×#4112yes—
706C2×C4×C61C2×#4112yes—
707C22⋊D61—44no—
708C22⋊D61—44no—
709C22⋊D61—44no—
710C22⋊D61—44no—
711C22⋊D61—44no—
712C22⋊D61—44no—
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—28no—
722C2×Dic61—28no—
723C2×Dic61—21no—
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—21no—
746C2×Dic61—21no—
747C2×Dic61—21no—
748C2×Dic61—21no—
749C2×Dic61—21no—
750C2×Dic61—44no—
751C2×Dic61—44no—
752C2×Dic61—44no—
753C2×Dic61—44no—
754C2×Dic61—44no—
755C2×Dic61—44no—
756C2×Dic61C22×D412yes—
757C2×Dic61C22×D412yes—
758C2×Dic61C22×D412yes—
759C2×Dic61C22×D412yes—
760C2×Dic61C2×#4112yes—
761C2×Dic61C2×#4112yes—
762C2×Dic61H(5,𝔽2)12yes—
763C4×D61—28no—
764C4×D61—44no—
765C4×D61—44no—
766C4×D61—44no—
767Dic122—44no—
768#34732—611nomaximal, Sylow
769C22×C61—22no—
770C22×C61—22no—
771C22×C61—22no—
772C22×C61—22no—
773C22×C61—22no—
774C22×C61—22no—
775C22×C61—22no—
776C22×C61—22no—
777C22×C61—22no—
778C22×C61—22no—
779C22×C61—22no—
780C22×C61—22no—
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—41no—
794C22×C61—41no—
795C22×C61—41no—
796C22×C61#52514yes—
797C22×C61C23×D411yescharacteristic
798C22×C61C22×#4111yescharacteristic
799C22×C61C22×#4111yescharacteristic
800C22×C61C22×#4111yescharacteristic
801C22×C61C22×#4111yescharacteristic
802C22×C61C2×H(5,𝔽2)11yescharacteristic
803C22×C61#58511yescharacteristic
804C2×D61—22no—
805C2×D61—22no—
806C2×D61—22no—
807C2×D61—22no—
808C2×D61—22no—
809C2×D61—22no—
810C2×D61—416no—
811C2×D61—41no—
812C2×D61—41no—
813C2×D61—41no—
814C2×D61—41no—
815C2×D61—41no—
816C2×D61—41no—
817C2×D61—41no—
818C2×D61—41no—
819C4×C61—22no—
820C4×C61—22no—
821C4×C61—22no—
822C4×C61—22no—
823C4×C61—22no—
824C4×C61—22no—
825C4×C61—41no—
826C4×C61—41no—
827C4×C61—41no—
828C4×C61—41no—
829C4×C61—41no—
830Dic61—22no—
831Dic61—22no—
832Dic61—22no—
833Dic61—22no—
834Dic61—41no—
835Dic61—41no—
836Dic61—41no—
837Dic61—41no—
838Dic61—41no—
839Dic61—41no—
840Dic61—41no—
841Dic61—41no—
842Dic61—41no—
843Dic61#54614yes—
844C2×#525—611no—
845C2×C4×#41—611no—
846#2477—611no—
847#2476—611no—
848#2471—611no—
849#2470—611no—
850#2465—611no—
851#2464—611no—
852#2458—611no—
853#2457—611no—
854#2450—611no—
855#2444—611no—
856#2438—611no—
857#2430D6111yescharacteristic, complemented
858#2424—611no—
859#2418—611no—
860#2411—611no—
861#2404—611no—
862#2398—611no—
863#2396—611no—
864#2392—611no—
865#2388—611no—
866C4×#123—611no—
867C4×#123—611no—
868C4×#121—611no—
869C4×#121—611no—
870C4×#120—611no—
871#2297—611no—
872#2290—611no—
873#2290—611no—
874C2×C4×C22⋊C4—611no—
875C2×C61—24no—
876C2×C61—42no—
877C2×C61—42no—
878C2×C61—81no—
879C2×C61C2×#52511yescharacteristic
880C2×C61#344411yescharacteristic
881C2×C61#346011yescharacteristic
882C2×C61C2×#54611yescharacteristic
883C2×C61D4×#4111yescharacteristic
884C2×C61#347511yescharacteristic
885C2×C61#348111yescharacteristic
886D61—42no—
887D61—42no—
888C22×#41—611no—
889C22×#41C2×D6111yescharacteristic
890C24×C4—611no—
891#525—1228no—
892C2×#123—611no—
893C2×#123—611no—
894C2×#123—611no—
895C2×#123C2×D6111yescharacteristic
896C2×C22⋊Q8—611no—
897C2×C22⋊Q8—611no—
898C2×#121—611no—
899C2×#121—611no—
900C2×#121C2×D6111yescharacteristic
901C2×#121C2×D6111yescharacteristic
902C2×#120—611no—
903C2×#120—611no—
904C2×#120—611no—
905C4×#41—1228no—
906C2×C4×Q8—611no—
907C2×C4×Q8—611no—
908C2×C4×D4—611no—
909C2×C4×D4—611no—
910C2×C4×D4—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×#117—611no—
921C2×#117—611no—
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—
930C22×C42—611no—
931#400—611no—
932#400—611no—
933#400—611no—
934#399—611no—
935#398—611no—
936#398—611no—
937#398—611no—
938#397—611no—
939#397—611no—
940#397—611no—
941#396—611no—
942#396—611no—
943#396—611no—
944#396—611no—
945#395—611no—
946#395C2×D6111yescharacteristic, complemented
947#394—611no—
948#394—611no—
949#394—611no—
950#394—611no—
951#394—611no—
952#394—611no—
953#394—611no—
954#394C2×D6111yescharacteristic, complemented
955#393—611no—
956#393—611no—
957#393—611no—
958#393C2×D6111yescharacteristic, complemented
959#392—611no—
960#392—611no—
961#392—611no—
962#392C2×D6111yescharacteristic, complemented
963#391—611no—
964#391—611no—
965#390—611no—
966#390—611no—
967#390—611no—
968#390—611no—
969#389—611no—
970#389—611no—
971#388—611no—
972#388—611no—
973#388—611no—
974#388—611no—
975#388—611no—
976#388—611no—
977#388—611no—
978#388—611no—
979#388—611no—
980#388—611no—
981#388—611no—
982#388—611no—
983#387—611no—
984#387—611no—
985#387—611no—
986#387—611no—
987#387—611no—
988#387—611no—
989#387—611no—
990#387—611no—
991#386—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#386—611no—
1001#386—611no—
1002#386—611no—
1003#386—611no—
1004#386C2×D6111yescharacteristic
1005#386C2×D6111yescharacteristic
1006#386C2×D6111yescharacteristic, complemented
1007#386C2×D6111yescharacteristic, complemented
1008#385—611no—
1009#385—611no—
1010#385—611no—
1011#385—611no—
1012#385—611no—
1013#385—611no—
1014#385—611no—
1015#385C2×D6111yescharacteristic, complemented
1016#385C2×D6111yescharacteristic, complemented
1017#381—611no—
1018#381—611no—
1019#380—611no—
1020#380—611no—
1021#379—611no—
1022C4×C4⋊C4—611no—
1023C4×C4⋊C4—611no—
1024C4×C4⋊C4—611no—
1025C4×C4⋊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—
1039C4×C22⋊C4—611no—
1040C4×C22⋊C4—611no—
1041C4×C22⋊C4—611no—
1042#376—611no—
1043C2×#95—611no—
1044C2×#95C2×D6111yescharacteristic
1045C61#3473211yescharacteristic, complemented, Sylow
1046C25—611no—
1047C2×#41—24no—
1048C2×#41—24no—
1049C2×#41—24no—
1050C2×#41—1224no—
1051C2×#41—1224no—
1052C2×#41—2442no—
1053C22×Q8—611no—
1054C22×Q8C22×D6111yescharacteristic
1055C22×D4—611no—
1056C22×D4—611no—
1057C22×D4—611no—
1058C22×D4—611no—
1059C22×D4—611no—
1060C22×D4—611no—
1061C22×D4C22×D6111yescharacteristic
1062C22×D4C22×D6111yescharacteristic
1063C22×D4C22×D6111yescharacteristic
1064C22×D4C22×D6111yescharacteristic
1065C22×D4C22×D6111yescharacteristic
1066C22×D4C22×D6111yescharacteristic
1067C23×C4—611no—
1068C23×C4—611no—
1069C23×C4—611no—
1070C23×C4—611no—
1071C23×C4—611no—
1072C23×C4—611no—
1073C23×C4—611no—
1074C23×C4—611no—
1075C23×C4—611no—
1076C23×C4—611no—
1077C23×C4—611no—
1078C23×C4—611no—
1079C23×C4—1224no—
1080C23×C4—1224no—
1081C23×C4—2442no—
1082C23×C4C22×D6111yescharacteristic
1083C23×C4C22×D6111yescharacteristic
1084C23×C4C22×D6111yescharacteristic
1085C23×C4C22×D6111yescharacteristic
1086C23×C4C22×D6111yescharacteristic
1087#123—24no—
1088#123—1224no—
1089#123—1224no—
1090#123—1224no—
1091C22⋊Q8—1224no—
1092C22⋊Q8—1224no—
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×Q8—1224no—
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—1224no—
1111C4×D4—1224no—
1112C4×D4—2442no—
1113C4×D4—2442no—
1114#117—1224no—
1115#117—1224no—
1116#117—1224no—
1117#117—1224no—
1118#117—2442no—
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⋊C4—611no—
1138C2×C4⋊C4—611no—
1139C2×C4⋊C4C22×D6111yescharacteristic
1140C2×C4⋊C4C22×D6111yescharacteristic
1141C2×C4⋊C4C22×D6111yescharacteristic
1142C2×C4⋊C4C22×D6111yescharacteristic
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—611no—
1178C2×C22⋊C4—1224no—
1179C2×C22⋊C4—1224no—
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—1224no—
1209C2×C42—1224no—
1210C2×C42—1224no—
1211C2×C42—2442no—
1212#95—611no—
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#95—611no—
1238#95—611no—
1239#95—611no—
1240#95C22×D6111yescharacteristic
1241#95C22×D6111yescharacteristic
1242#95C22×D6111yescharacteristic
1243#95C22×D6111yescharacteristic
1244#95C22×D6111yescharacteristic
1245#95C22×D6111yescharacteristic
1246#95C22×D6111yescharacteristic
1247#95C22×D6111yescharacteristic
1248C24—611no—
1249C24—611no—
1250C24—1222no—
1251C24—1222no—
1252C24—1222no—
1253C24—1222no—
1254C24—1222no—
1255C24—2441no—
1256C24—2441no—
1257C24C23×D6111yescharacteristic
1258C24C23×D6111yescharacteristic
1259C24C23×D6111yescharacteristic
1260C24C23×D6111yescharacteristic
1261#41—232no—
1262#41—24416no—
1263C2×Q8—22no—
1264C2×Q8—22no—
1265C2×Q8—22no—
1266C2×Q8—1222no—
1267C2×Q8—1222no—
1268C2×Q8—2441no—
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—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—41no—
1284C2×D4—41no—
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—1222no—
1295C2×D4—1222no—
1296C2×D4—1222no—
1297C2×D4—2441no—
1298C2×D4—2441no—
1299C2×D4—2441no—
1300C2×D4—2441no—
1301C2×D4—2441no—
1302C2×D4—2441no—
1303C2×D4D4×D6114yes—
1304C2×D4#1175822414yescomplemented
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—41no—
1318C22×C4—41no—
1319C22×C4—611no—
1320C22×C4—614no—
1321C22×C4—614no—
1322C22×C4—611no—
1323C22×C4—611no—
1324C22×C4—611no—
1325C22×C4—611no—
1326C22×C4—614no—
1327C22×C4—611no—
1328C22×C4—611no—
1329C22×C4—611no—
1330C22×C4—611no—
1331C22×C4—611no—
1332C22×C4—611no—
1333C22×C4—611no—
1334C22×C4—611no—
1335C22×C4—611no—
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—1222no—
1356C22×C4—1222no—
1357C22×C4—1222no—
1358C22×C4—1222no—
1359C22×C4—1222no—
1360C22×C4—1222no—
1361C22×C4—1222no—
1362C22×C4—2441no—
1363C22×C4—2441no—
1364C22×C4—24416no—
1365C22×C4—2441no—
1366C22×C4—2441no—
1367C22×C4—2441no—
1368C22×C4—2441no—
1369C22×C4—2441no—
1370C22×C4#1175822414yescomplemented
1371C22×C4C23×D6111yescharacteristic
1372C22×C4C23×D6111yescharacteristic
1373C22×C4C23×D6111yescharacteristic
1374C22×C4C23×D6111yescharacteristic
1375C22×C4C23×D6111yescharacteristic
1376C22×C4C23×D6111yescharacteristic
1377C22×C4C23×D6111yescharacteristic
1378C22×C4C23×D6111yescharacteristic
1379C22×C4C23×D6111yescharacteristic
1380C22×C4C23×D6111yescharacteristic
1381C22×C4C23×D6111yescharacteristic
1382C4⋊C4—22no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—614no—
1387C4⋊C4—1222no—
1388C4⋊C4—1222no—
1389C4⋊C4—1222no—
1390C4⋊C4—1222no—
1391C4⋊C4—1222no—
1392C4⋊C4—1222no—
1393C4⋊C4—1222no—
1394C4⋊C4—1222no—
1395C4⋊C4—1222no—
1396C4⋊C4—1222no—
1397C4⋊C4—1222no—
1398C4⋊C4—1222no—
1399C4⋊C4—1222no—
1400C4⋊C4—2441no—
1401C4⋊C4—2441no—
1402C4⋊C4—2441no—
1403C4⋊C4—2441no—
1404C4⋊C4—2441no—
1405C4⋊C4—2441no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—41no—
1416C22⋊C4—41no—
1417C22⋊C4—614no—
1418C22⋊C4—614no—
1419C22⋊C4—614no—
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—1222no—
1443C22⋊C4—2441no—
1444C22⋊C4—2441no—
1445C22⋊C4—2441no—
1446C22⋊C4—2441no—
1447C22⋊C4—2441no—
1448C22⋊C4—2441no—
1449C22⋊C4—2441no—
1450C22⋊C4—2441no—
1451C22⋊C4—2441no—
1452C42—614no—
1453C42—1222no—
1454C42—1222no—
1455C42—1222no—
1456C42—1222no—
1457C42—1222no—
1458C42—1222no—
1459C42—1222no—
1460C42—1222no—
1461C42—1222no—
1462C42—1222no—
1463C42—1222no—
1464C42—1222no—
1465C42—1222no—
1466C42—1222no—
1467C42—2441no—
1468C42—2441no—
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—21no—
1490C23—21no—
1491C23—21no—
1492C23—612no—
1493C23—612no—
1494C23—1228no—
1495C23—1221no—
1496C23—1221no—
1497C23—1221no—
1498C23—1221no—
1499C23—1221no—
1500C23—1221no—
1501C23—1221no—
1502C23—1221no—
1503C23—1221no—
1504C23—1221no—
1505C23—1221no—
1506C23—1221no—
1507C23—2444no—
1508C23—2444no—
1509C23—2444no—
1510C23—2444no—
1511C23—2444no—
1512C23—2444no—
1513C23C2×D4×D6112yes—
1514C23C2×D4×D6112yes—
1515C23C2×#1175822412yes—
1516C23C2×#1175822412yes—
1517C23C2×#1175822412yes—
1518C23C24×D6111yescharacteristic
1519Q8—28no—
1520Q8—2444no—
1521D4—28no—
1522D4—28no—
1523D4—28no—
1524D4—44no—
1525D4—44no—
1526D4—44no—
1527D4—2444no—
1528D4—2444no—
1529D4—2444no—
1530D4—2444no—
1531D4—2444no—
1532D4—2444no—
1533C2×C4—28no—
1534C2×C4—28no—
1535C2×C4—28no—
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—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—44no—
1564C2×C4—44no—
1565C2×C4—612no—
1566C2×C4—612no—
1567C2×C4—612no—
1568C2×C4—612no—
1569C2×C4—612no—
1570C2×C4—612no—
1571C2×C4—612no—
1572C2×C4—1228no—
1573C2×C4—1228no—
1574C2×C4—1228no—
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—1221no—
1607C2×C4—1221no—
1608C2×C4—1221no—
1609C2×C4—1221no—
1610C2×C4—2444no—
1611C2×C4—2444no—
1612C2×C4—2444no—
1613C2×C4—2444no—
1614C2×C4—2444no—
1615C2×C4—2444no—
1616C2×C4—2444no—
1617C2×C4—2444no—
1618C2×C4—2444no—
1619C2×C4C2×D4×D6112yes—
1620C2×C4#41×D6112yes—
1621C2×C4#41×D6112yes—
1622C2×C4C2×#1175822412yes—
1623C2×C4C2×#1175822412yes—
1624C2×C4C2×#1175822412yes—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—1222no—
1653C22—1222no—
1654C22—1222no—
1655C22—1222no—
1656C22—1222no—
1657C22—1222no—
1658C22—24416no—
1659C22—2441no—
1660C22—2441no—
1661C22—2441no—
1662C22—2441no—
1663C22—2441no—
1664C22—2441no—
1665C22—2441no—
1666C22—2441no—
1667C22#1684026814yes—
1668C22C22×D4×D6111yescharacteristic
1669C22C2×#41×D6111yescharacteristic
1670C22C2×#41×D6111yescharacteristic
1671C22C22×#1175822411yescharacteristic
1672C22C22×#1175822411yescharacteristic
1673C22H(5,𝔽2)×D6111yescharacteristic
1674C22#1684059911yescharacteristic
1675C4—22no—
1676C4—22no—
1677C4—22no—
1678C4—22no—
1679C4—22no—
1680C4—22no—
1681C4—41no—
1682C4—41no—
1683C4—41no—
1684C4—41no—
1685C4—41no—
1686C4—614no—
1687C4—1222no—
1688C4—1222no—
1689C4—1222no—
1690C4—1222no—
1691C4—2441no—
1692C4—2441no—
1693C4—2441no—
1694C4—2441no—
1695C4—2441no—
1696C4—2441no—
1697C4—2441no—
1698C4—2441no—
1699C4—2441no—
1700C2—24no—
1701C2—42no—
1702C2—42no—
1703C2—81no—
1704C2—2442no—
1705C2—2442no—
1706C2C2×#1684026811yescharacteristic
1707C2#2145911411yescharacteristic
1708C2#2145923611yescharacteristic
1709C2#546×D6111yescharacteristic
1710C2#2145930611yescharacteristic
1711C2#2145938211yescharacteristic
1712C2#2145942411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2430C2
hypercenter#2430D61
hypocenterC61#34732
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2430

Complements

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

NH ≅ G/Ntype
1. C2×#16840272C2semidirect
2. C2×#41×Dic61C2semidirect
3. #21450019C2semidirect
4. #21450004C2semidirect
5. #21449929C2semidirect
6. #21449914C2semidirect
7. #21449835C2semidirect
8. #21449820C2semidirect
9. #21449736C2semidirect
10. #21449721C2semidirect
11. #21449647C2semidirect
12. #21449565C2semidirect
13. #21449495C2semidirect
14. #21449361C2semidirect
15. #21449279C2semidirect
16. #21449205C2semidirect
17. #21449134C2semidirect
18. #21449101C2semidirect
19. #21449090C2semidirect
20. #21449062C2semidirect
21. #21449031C2semidirect
22. #123×Dic61C2semidirect
23. #21448338C2semidirect
24. #121×Dic61C2semidirect
25. #21448329C2semidirect
26. #21448324C2semidirect
27. #21448304C2semidirect
28. #21448259C2semidirect
29. #21448255C2semidirect
30. C2×#16839609C2semidirect
31. C61×#2430C2semidirect
46. C2×Q8×Dic61C22semidirect
47. C2×Q8×Dic61C22semidirect
53. C2×D4×Dic61C22semidirect
54. C2×D4×Dic61C22semidirect
55. C2×D4×Dic61C22semidirect
61. C2×#14519736C22semidirect
62. C2×#14519736C22semidirect
64. C2×#14519733C22semidirect
69. C22×C4×Dic61C22semidirect
70. C22×C4×Dic61C22semidirect
71. #16839704C22semidirect
72. #16839704C22semidirect
73. #16839701C22semidirect
75. #16839696C22semidirect
76. #16839694C22semidirect
77. #16839694C22semidirect
78. #16839690C22semidirect
80. #16839687C22semidirect
81. #16839685C22semidirect
85. #16839683C22semidirect
92. #16839676C22semidirect
93. #16839674C22semidirect
99. #16839666C22semidirect
100. #16839666C22semidirect
101. #16839665C22semidirect
105. #16839661C22semidirect
106. #16839659C22semidirect
107. #16839656C22semidirect
108. #16839655C22semidirect
109. #16839655C22semidirect
110. #16839655C22semidirect
111. #16839655C22semidirect
117. #16839650C22semidirect
118. #16839650C22semidirect
119. #16839649C22semidirect
120. #16839648C22semidirect
121. #16839648C22semidirect
122. #16839647C22semidirect
123. #16839645C22semidirect
124. #16839645C22semidirect
125. #16839645C22semidirect
126. #16839643C22semidirect
131. #16839642C22semidirect
141. #16839637C22semidirect
148. #16839623C22semidirect
150. #16839620C22semidirect
152. C4⋊C4×Dic61C22semidirect
153. C4⋊C4×Dic61C22semidirect
154. C4⋊C4×Dic61C22semidirect
155. #16839613C22semidirect
157. C22⋊C4×Dic61C22semidirect
158. C22⋊C4×Dic61C22semidirect
159. C22⋊C4×Dic61C22semidirect
160. C22⋊C4×Dic61C22semidirect
161. C22⋊C4×Dic61C22semidirect
172. #16839607C22semidirect
178. C61×#395C22semidirect
179. C61×#394C22semidirect
180. C61×#393C22semidirect
181. C61×#392C22semidirect
184. C61×#386C22semidirect
185. C61×#386C22semidirect
186. C61×#385C22semidirect
187. C61×#385C22semidirect
234. D4×Dic61D4semidirect
425. C2×D4×C61#41semidirect
440. C22×C4×C61#41semidirect
521. C2×C4×D61#41semidirect
574. #11758198#41semidirect
857. #2430D61semidirect
946. #395C2×D61semidirect
954. #394C2×D61semidirect
958. #393C2×D61semidirect
962. #392C2×D61semidirect
1006. #386C2×D61semidirect
1007. #386C2×D61semidirect
1015. #385C2×D61semidirect
1016. #385C2×D61semidirect
1045. C61#34732semidirect
1304. C2×D4#11758224semidirect
1370. C22×C4#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
C2×#41×Dic612
#214500192
#214500042
#214499292
#214499142
#214498352
#214498202
#214497362
#214497212
#214496472
#214495652
#214494952
#214493612
#214492792
#214492052
#214491342
#214491012
#214490902
#214490622
#214490312
#123×Dic612
#214483382
#121×Dic612
#214483292
#214483242
#214483042
#214482592
#214482552
C2×#168396092
C61×#24302
#3473261