Finite Group Databasebeta

← #30615228

Subgroups — #30615228

Order 15616.

1428 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461727C212yesmaximal, complemented
4#21461694C212yesmaximal, complemented
5#21461693C212yesmaximal, complemented
6#21461661C212yesmaximal
7C4×#14519842C212yesmaximal, complemented
8C4×#14519841C212yesmaximal, complemented
9C4×#41×D61C211yesmaximal, characteristic
10C2×#14519856—21no—
11#16840785—21no—
12#16840782—21no—
13#16840780—21no—
14#16840779—21no—
15#16840767C2212yescomplemented
16C2×#14519842C2214yes—
17C2×#14519841C2214yes—
18#16840733C2212yes—
19C4×#11758213C2212yescomplemented
20C4×C4⋊#6923—21no—
21C4×C4⋊#6923C2212yescomplemented
22C4×C22⋊#6923—21no—
23C4×C22⋊#6923C2212yes—
24#16840698—21no—
25C42×#6923C2212yescomplemented
26#16840632C2214yescomplemented
27#16840632C2214yescomplemented
28C2×#41×D61C2211yescharacteristic
29#41×Dic61C411yescharacteristic, complemented
30C4×#11758226C2211yescharacteristic
31C4×#11758226C2211yescharacteristic
32C4×#11758222—21no—
33C4×#11758222C411yescharacteristic, complemented
34#16840230—21no—
35#16840230C411yescharacteristic, complemented
36C4×#11758224—21no—
37C4×#11758224—21no—
38C4×#11758224C2211yescharacteristic
39C4×#11758224C2211yescharacteristic
40C4×Q8×D61C411yescharacteristic, complemented
41C4×Q8×D61C411yescharacteristic, complemented
42C4×D4×D61—21no—
43C4×D4×D61—21no—
44C4×D4×D61C411yescharacteristic, complemented
45C4×D4×D61C411yescharacteristic, complemented
46#117×D61—21no—
47#117×D61C2211yescharacteristic
48C2×C42×D61—21no—
49C2×C42×D61C2211yescharacteristic
50C4×#41×C61C411yescharacteristic, complemented
51C2×#11758213C2314yes—
52#14519856—28no—
53C2×C4⋊#6923—22no—
54C2×C22⋊#6923—22no—
55C2×C4×#6923—22no—
56C2×C4×#6923—22no—
57C2×C4×#6923C2314yes—
58#14519844—22no—
59#14519844—22no—
60#14519842—28no—
61#14519841—28no—
62#14519834—22no—
63C22⋊#92420—22no—
64#14519832—22no—
65C4×#92420—22no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68C2×#11758226C2311yescharacteristic
69C2×#11758222—21no—
70C2×#11758222C2×C411yescharacteristic
71C2×#11758224—21no—
72C2×#11758224C2311yescharacteristic
73#41×D61—24no—
74#41×D61—24no—
75C2×Q8×D61C2×C411yescharacteristic
76C2×D4×D61—21no—
77C2×D4×D61C2×C411yescharacteristic
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84Q8×Dic61C2×C411yescharacteristic
85Q8×Dic61C2×C411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122C2×C411yescharacteristic
89C4×Dic122C2×C411yescharacteristic
90#14519742—21no—
91#14519742—21no—
92#14519742C2×C411yescharacteristic
93#14519742C2×C411yescharacteristic
94C4×D244—21no—
95C4×D244—21no—
96C4×D244C2×C411yescharacteristic
97C4×D244C2×C411yescharacteristic
98D4×Dic61—21no—
99D4×Dic61—21no—
100D4×Dic61C2×C411yescharacteristic
101D4×Dic61C2×C411yescharacteristic
102#14519739—21no—
103#14519739—21no—
104#14519739C2×C411yescharacteristic
105#14519739C2×C411yescharacteristic
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111C4×C22⋊D61—21no—
112#14519737—21no—
113#14519737—21no—
114#14519737—21no—
115#14519737—21no—
116#14519737—21no—
117#14519737—21no—
118#14519736—21no—
119#14519736C2×C411yescharacteristic
120#14519735—21no—
121#14519735—21no—
122#14519735C2311yescharacteristic
123#14519735C2311yescharacteristic
124#14519734—21no—
125#14519734—21no—
126#14519734—21no—
127#14519733—21no—
128#14519733—21no—
129#14519733—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61C2×C411yescharacteristic
133C4⋊C4×D61C2×C411yescharacteristic
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C42×D61—21no—
144C42×D61—21no—
145C42×D61—21no—
146C42×D61—21no—
147C42×D61—21no—
148C42×D61—21no—
149C42×D61—21no—
150C42×D61C2×C411yescharacteristic
151C42×D61C2×C411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C42×D61C2311yescharacteristic
157C42×D61C2311yescharacteristic
158C2×#41×C61C2×C411yescharacteristic
159C4×Q8×C61C2×C411yescharacteristic
160C4×Q8×C61C2×C411yescharacteristic
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61C2×C411yescharacteristic
164C4×D4×C61C2×C411yescharacteristic
165#117×C61—21no—
166#117×C61C2×C411yescharacteristic
167C2×C42×C61—21no—
168C2×C42×C61C2×C411yescharacteristic
169C23×D61—21no—
170C23×D61C2×D411yescharacteristic
171C22×#6923—24no—
172#41×C61—22no—
173#41×C61—22no—
174C2×Q8×C61C22×C411yescharacteristic
175C2×D4×C61—21no—
176C2×D4×C61C22×C411yescharacteristic
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61C22⋊C411yescharacteristic
181C22×C4×C61C22⋊C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61C22⋊C411yescharacteristic
190C22×Dic61C22⋊C411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192#11758226—22no—
193#11758226#4114yes—
194Q8×D61—22no—
195Q8×D61—22no—
196#11758224—28no—
197#11758224—22no—
198#11758224#4114yes—
199D4×D61—28no—
200D4×D61—22no—
201D4×D61—22no—
202#11758222—28no—
203#11758222—22no—
204#11758222—22no—
205C2×D244—21no—
206C2×D244C22×C411yescharacteristic
207C2×C4×D61—28no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—24no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—42no—
221C2×C4×D61—44no—
222C2×C4×D61—44no—
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122C22×C411yescharacteristic
237C22⋊#6923—28no—
238C2×#92420—24no—
239C4⋊#6923—28no—
240C4×#6923—28no—
241C4×#6923—24no—
242C4×#6923—24no—
243C4×#6923—44no—
244#11758213—24no—
245#11758213—24no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C22×C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61C22⋊C411yescharacteristic
257C42×C61C22⋊C411yescharacteristic
258C42×C61C22×C411yescharacteristic
259C42×C61C22×C411yescharacteristic
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C22×C411yescharacteristic
272C4⋊Dic61C22×C411yescharacteristic
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758196—21no—
278#11758196—21no—
279C4×Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—21no—
286C4×Dic61—21no—
287C4×Dic61—21no—
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22⋊C411yescharacteristic
291C4×Dic61C22⋊C411yescharacteristic
292C4×Dic61C22⋊C411yescharacteristic
293C4×Dic61C22⋊C411yescharacteristic
294C4×Dic61C22×C411yescharacteristic
295C4×Dic61C22×C411yescharacteristic
296C4×Dic61C2×D411yescharacteristic
297C4×Dic61C2×D411yescharacteristic
298C4×Dic61C2×D411yescharacteristic
299C4×Dic61C2×D411yescharacteristic
300C23×C61—21no—
301C23×C61C2×C22⋊C411yescharacteristic
302C22×D61—24no—
303C22×D61—21no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—41no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61C2×C22⋊C411yescharacteristic
310C22×D61C22×D411yescharacteristic
311C2×#6923—28no—
312C2×#6923—44no—
313C2×#6923—44no—
314Q8×C61—21no—
315Q8×C61#11712yescomplemented
316D4×C61—24no—
317D4×C61—21no—
318D4×C61#11712yescomplemented
319C2×C4×C61—24no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—41no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61C2×C22⋊C411yescharacteristic
330C2×C4×C61C2×C22⋊C411yescharacteristic
331C2×C4×C61C2×C22⋊C411yescharacteristic
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C23×C411yescharacteristic
335C22⋊D61—24no—
336C22⋊D61—24no—
337C22⋊D61—24no—
338C2×Dic61—21no—
339C2×Dic61—22no—
340C2×Dic61—24no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C22×D411yescharacteristic
353D244—24no—
354D244—21no—
355D244#11712yescomplemented
356C4×D61—24no—
357C4×D61—24no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—24no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—42no—
371C4×D61—42no—
372C4×D61—42no—
373C4×D61—42no—
374C4×D61—42no—
375C4×D61—42no—
376C4×D61#10414yescomplemented
377C4×D61C2×#4112yes—
378C4×D61C2×#4112yes—
379Dic122—24no—
380Dic122—21no—
381Dic122#11712yescomplemented
382#92420—44no—
383#20747—611nomaximal, Sylow
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61C22×C22⋊C411yescharacteristic
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—22no—
396C2×D61—44no—
397C2×D61—48no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61C2×#10412yes—
401C2×D61#52512yes—
402#6923—48no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—22no—
407C4×C61—21no—
408C4×C61—41no—
409C4×C61—41no—
410C4×C61C2×#10412yes—
411C4×C61C2×#11711yescharacteristic
412C4×C61C2×#11711yescharacteristic
413Dic61—21no—
414Dic61—21no—
415Dic61—21no—
416Dic61—22no—
417Dic61—41no—
418Dic61—41no—
419Dic61C2×#10412yes—
420Dic61#42112yes—
421Dic61#52512yes—
422C2×C4×#41—611no—
423#2920—611no—
424C4×#117—611no—
425#1826—612no—
426#1806—612no—
427#1806—612no—
428#1789—612no—
429C4×#104—612no—
430C4×#104—612no—
431C2×C61—41no—
432C2×C61—42no—
433C2×C61#228011yescharacteristic
434C2×C61C22×#10411yescharacteristic
435C2×C61C2×#42111yescharacteristic
436D61—22no—
437D61—22no—
438D61—42no—
439C22×#41—611no—
440C4×#41—611no—
441C4×#41—611no—
442C4×#41—611no—
443C4×#41—611no—
444C4×#41—611no—
445C4×#41—611no—
446C4×#41—611no—
447C4×#41—1221no—
448C4×#41—1221no—
449C4×#41—1221no—
450C4×#41—1221no—
451C4×#41#692311yescharacteristic, complemented
452C2×C4×Q8—611no—
453C2×C4×Q8—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C2×#117—611no—
459C2×#117—1221no—
460C2×#117—1221no—
461C22×C42—611no—
462C22×C42—1221no—
463#432—1221no—
464#432—1221no—
465#431—1221no—
466#431—1221no—
467#423—612no—
468C2×#104—614no—
469C2×#104—614no—
470#407—612no—
471C4×M16—612no—
472C4×C4⋊C4—612no—
473C4×C4⋊C4—1221no—
474C4×C22⋊C4—612no—
475C4×C22⋊C4—1221no—
476#376—1221no—
477C43—612no—
478#339—614no—
479#339—614no—
480C61#2074711yescharacteristic, complemented, Sylow
481C2×#41—611no—
482C2×#41—611no—
483C2×#41—611no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1224no—
487C2×#41—1224no—
488C2×#41C2×#692311yescharacteristic
489C22×Q8—611no—
490C22×D4—611no—
491C22×D4—1221no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4—1221no—
498C2×M16—614no—
499C4×Q8—611no—
500C4×Q8—611no—
501C4×Q8—611no—
502C4×Q8—611no—
503C4×Q8—611no—
504C4×Q8—611no—
505C4×Q8—1221no—
506C4×Q8—1221no—
507C4×Q8—1221no—
508C4×Q8—1221no—
509C4×Q8C2×#692311yescharacteristic
510C4×Q8C2×#692311yescharacteristic
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—611no—
514C4×D4—611no—
515C4×D4—611no—
516C4×D4—611no—
517C4×D4—611no—
518C4×D4—611no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4C2×#692311yescharacteristic
538C4×D4C2×#692311yescharacteristic
539#117—21no—
540#117—611no—
541#117—611no—
542#117—611no—
543#117—1221no—
544#117—1221no—
545#117—1221no—
546#117—1221no—
547#117—1221no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551#117—1228no—
552#117—1221no—
553#117C2×#692311yescharacteristic
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1222no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1222no—
563C2×C42—21no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—614no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579C2×C42—1221no—
580C2×C42—1221no—
581C2×C42—1221no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42—1221no—
585C2×C42—1222no—
586C2×C42—1221no—
587C2×C42—1222no—
588C2×C42C2×#692311yescharacteristic
589C4⋊C8—1222no—
590C4⋊C8—1222no—
591#104—1228no—
592#104—1228no—
593C22⋊C8—1222no—
594C22⋊C8—1222no—
595#97—1222no—
596C4×C8—1222no—
597#95—1222no—
598#95—1222no—
599C24—611no—
600C24—1221no—
601#41—22no—
602#41—22no—
603#41—614no—
604#41—614no—
605#41—1222no—
606#41—1222no—
607#41—1228no—
608#41—1222no—
609#41—1222no—
610#41—1228no—
611C2×Q8—611no—
612C2×Q8—1221no—
613C2×Q8—1222no—
614C2×Q8—1222no—
615C2×Q8C22×#692311yescharacteristic
616C2×D4—21no—
617C2×D4—611no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1222no—
621C2×D4—1228no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1222no—
625C2×D4C22×#692311yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—1221no—
645C22×C4—1224no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1228no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1224no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—2444no—
662C22×C4—2442no—
663C22×C4—2444no—
664C22×C4C22⋊#692311yescharacteristic
665C22×C4C22⋊#692311yescharacteristic
666C22×C4C22×#692311yescharacteristic
667M16—1224no—
668M16—1224no—
669C2×C8—1224no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—611no—
673C4⋊C4—611no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1228no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4C22×#692311yescharacteristic
684C4⋊C4C22×#692311yescharacteristic
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1228no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—1221no—
714C42—1221no—
715C42—1221no—
716C42—1221no—
717C42—1221no—
718C42—1221no—
719C42—1224no—
720C42—1224no—
721C42—1228no—
722C42—1221no—
723C42—1221no—
724C42—1221no—
725C42—2444no—
726C42C22⋊#692311yescharacteristic
727C42C22⋊#692311yescharacteristic
728C42C22×#692311yescharacteristic
729C42C22×#692311yescharacteristic
730C23—21no—
731C23—611no—
732C23—611no—
733C23—1222no—
734C23—1222no—
735C23—1224no—
736C23—1221no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23C2×C22⋊#692311yescharacteristic
741Q8—21no—
742Q8—612no—
743Q8—1224no—
744Q8—1221no—
745Q8#1451985612yescomplemented
746D4—24no—
747D4—21no—
748D4—612no—
749D4—1224no—
750D4—1224no—
751D4—1224no—
752D4—1224no—
753D4—1221no—
754D4#1451985612yescomplemented
755C2×C4—24no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—614no—
769C2×C4—612no—
770C2×C4—612no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1224no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1224no—
782C2×C4—1224no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1224no—
787C2×C4—1221no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1228no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4—2442no—
802C2×C4—2442no—
803C2×C4—2444no—
804C2×C4—2444no—
805C2×C4—2442no—
806C2×C4C2×C22⋊#692311yescharacteristic
807C2×C4C2×C22⋊#692311yescharacteristic
808C2×C4C2×C22⋊#692311yescharacteristic
809C2×C4C2×C22⋊#692311yescharacteristic
810C2×C4C2×C22⋊#692311yescharacteristic
811C2×C4C23×#692311yescharacteristic
812C8—2444no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22—612no—
820C22—612no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—1221no—
825C22—1222no—
826C22—2444no—
827C22—2448no—
828C22—2441no—
829C22—2441no—
830C22C22×C22⋊#692311yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—22no—
836C4—41no—
837C4—41no—
838C4—612no—
839C4—612no—
840C4—612no—
841C4—1221no—
842C4—1221no—
843C4—1221no—
844C4—1222no—
845C4—2448no—
846C4—2441no—
847C4—2441no—
848C4D61⋊#10412yes—
849C4C2×#1451985611yescharacteristic
850C4C2×#1451985611yescharacteristic
851C2—41no—
852C2—42no—
853C2—1222no—
854C2—1222no—
855C2—2442no—
856C2#2146226311yescharacteristic
857C2C2×D61⋊#10411yescharacteristic
858C2D61⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61#20747
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #21462498C2semidirect
2. C4×#14519856C2semidirect
3. #21461727C2semidirect
4. #21461694C2semidirect
5. #21461693C2semidirect
7. C4×#14519842C2semidirect
8. C4×#14519841C2semidirect
15. #16840767C22semidirect
19. C4×#11758213C22semidirect
21. C4×C4⋊#6923C22semidirect
25. C42×#6923C22semidirect
26. #16840632C22semidirect
27. #16840632C22semidirect
29. #41×Dic61C4semidirect
33. C4×#11758222C4semidirect
35. #16840230C4semidirect
40. C4×Q8×D61C4semidirect
41. C4×Q8×D61C4semidirect
44. C4×D4×D61C4semidirect
45. C4×D4×D61C4semidirect
50. C4×#41×C61C4semidirect
315. Q8×C61#117semidirect
318. D4×C61#117semidirect
355. D244#117semidirect
376. C4×D61#104semidirect
381. Dic122#117semidirect
451. C4×#41#6923semidirect
480. C61#20747semidirect
745. Q8#14519856semidirect
754. D4#14519856semidirect

Maximal subgroups

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

subgroupindex
#214624982
C4×#145198562
#214617272
#214616942
#214616932
#214616612
C4×#145198422
C4×#145198412
C4×#41×D612
#2074761