Finite Group Databasebeta

← #29695434

Subgroups — #29695434

Order 15616.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840406C211yesmaximal, characteristic
2C2×#16839825C211yesmaximal, characteristic, complemented
3C2×#16839755C211yesmaximal, characteristic, complemented
4C22×#14519698C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446629C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446240C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21446124C211yesmaximal, characteristic, complemented
12#21445827C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic, complemented
19#16840406—24no—
20#16840406C418yescomplemented
21C2×#14519764C2211yescharacteristic
22C2×#14519758—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519746—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic, complemented
30C22×C4⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61—21no—
32#16839825—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839755—24no—
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519698—24no—
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519689C2211yescharacteristic, complemented
45C2×C8×Dic61C2211yescharacteristic, complemented
46#16839654—21no—
47#16839649—21no—
48#16839639—21no—
49#16839627C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52C22⋊C4×Dic61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yescomplemented
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C23×Dic61—21no—
76C23×Dic61—21no—
77C22×C4×D61C2311yescharacteristic
78C22×#92418—22no—
79C22×#92418—22no—
80C22×#92418—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—41no—
86#14519764—22no—
87#14519764C2×C414yescomplemented
88#14519758—28no—
89#14519756—22no—
90#14519756C2×C414yes—
91#14519749—28no—
92#14519748—22no—
93#14519748C2×C414yescomplemented
94#14519746—28no—
95D4×Dic61—22no—
96D4×Dic61C2×C414yescomplemented
97C4×C22⋊D61C2×C414yes—
98C4×C22⋊D61D414yes—
99#14519735—22no—
100#14519735—41no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—41no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—28no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519706—22no—
123#14519702—22no—
124#14519702—41no—
125#14519700—22no—
126#14519700—41no—
127#14519698—22no—
128#14519698—22no—
129#14519698—22no—
130#14519698D414yescomplemented
131#14519689—22no—
132C8×Dic61—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C25×C61—21no—
138C22×D4×C61—22no—
139C22×D4×C61—22no—
140C22×D4×C61—21no—
141C22×D4×C61—22no—
142C22×D4×C61—41no—
143C22×D4×C61—41no—
144C22×D4×C61C2×C414yes—
145C22×D4×C61C2311yescharacteristic
146C22×D4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—41no—
156#102×C61—41no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—24no—
162C24×C61—42no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—81no—
167C24×C61—81no—
168C24×C61C2×D411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C2×D4×C61—28no—
171C2×D4×C61—24no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—44no—
181C2×D4×C61—44no—
182C2×D4×C61—44no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61C22×C412yes—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C2×D412yes—
188C2×D4×C61#4112yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61C22⋊C414yes—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—21no—
214C22×Dic61—42no—
215C22×Dic61—42no—
216C22×Dic61—42no—
217C22×Dic61—42no—
218C22×Dic61—81no—
219C22×Dic61—81no—
220C22×Dic61—81no—
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224#11758224—28no—
225#11758224—44no—
226#11758224—44no—
227#11758224—44no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C2×D412yes—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C22⋊C4×C61—42no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61C22⋊C414yes—
257#11758198—42no—
258#11758198—81no—
259#11758198C22⋊C414yes—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—42no—
265C4⋊Dic61C22×C412yes—
266C4⋊Dic61C2×D412yes—
267#11758196—24no—
268#11758196C22⋊C414yes—
269C4×Dic61—42no—
270C4×Dic61—81no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—44no—
279C2×#92418C2×D412yes—
280C8×D61—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—48no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—48no—
301C23×C61—84no—
302C23×C61—84no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61C2×C22⋊C412yes—
307C23×C61#13512yes—
308C23×C61#13512yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—48no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61C4×D414yes—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61C2×C22⋊C412yes—
339C2×C4×C61C23×C411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C22⋊D61—28no—
346C22⋊D61—48no—
347C22⋊D61—84no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—48no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—84no—
368C2×Dic61—84no—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371C2×Dic61C2×C22⋊C412yes—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#22414—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—24no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—816no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61#41614yescomplemented
407C22×C61C22×C22⋊C411yescharacteristic
408C22×C61D4211yescharacteristic
409C22×C61#54611yescharacteristic
410C22×C61C2×#13511yescharacteristic
411C22×C61C2×#13511yescharacteristic
412C22×C61#57611yescharacteristic
413C22×C61#57711yescharacteristic
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C4×C61—22no—
422C4×C61—81no—
423C4×C61—81no—
424C4×C61C2×C4×D411yescharacteristic
425C4×C61#51811yescharacteristic
426C4×C61D4211yescharacteristic
427C4×C61#54611yescharacteristic
428Dic61—22no—
429Dic61—22no—
430Dic61—22no—
431Dic61—42no—
432Dic61—42no—
433Dic61—42no—
434Dic61—81no—
435C2×#546—611no—
436C2×C8×D4—611no—
437C2×#416—611no—
438C22×#102—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1893—611no—
443#1892—611no—
444#1875—611no—
445#1872—611no—
446#1804—611no—
447#1788—611no—
448#1786D6111yescharacteristic, complemented
449C4×#102—611no—
450C2×C61—24no—
451C2×C61—44no—
452C2×C61—82no—
453C2×C61D4×C22⋊C411yescharacteristic
454C2×C61C2×#41611yescharacteristic
455C2×C61#289711yescharacteristic
456C2×C61#328011yescharacteristic
457C2×C61#328211yescharacteristic
458C2×C61#329611yescharacteristic
459C2×C61#329711yescharacteristic
460D61—42no—
461C22×#41—611no—
462C23×D4C2×D6111yescharacteristic
463C23×C8—611no—
464C23×C8—611no—
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
470C2×#121—611no—
471C2×#121—1221no—
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4—611no—
475C2×#117—611no—
476C22×C4⋊C4—611no—
477C22×C22⋊C4—1221no—
478C8×D4—1224no—
479C2×C4⋊C8—611no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—1224no—
490C2×#102C2×D6111yescharacteristic
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×#102C2×D6111yescharacteristic
494C2×C22⋊C8—611no—
495C2×C22⋊C8C2×D6111yescharacteristic
496C2×C4×C8—611no—
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380C2×D6111yescharacteristic
503C4×C4⋊C4—611no—
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509C61#2241411yescharacteristic, complemented, Sylow
510C25—21no—
511C2×#41—614no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—611no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4C4×D6114yes—
528C22×D4C22×D6111yescharacteristic
529C22×D4C22×D6111yescharacteristic
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—1222no—
538C22×C8—1222no—
539C22×C8—1222no—
540C22×C8—1222no—
541C22×C8—2441no—
542C22×C8—2441no—
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—614no—
549C22⋊Q8—1222no—
550#121—614no—
551#121—1228no—
552#121—1222no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—1222no—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—2441no—
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C4⋊C8—1222no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#102—22no—
590#102—22no—
591#102—41no—
592#102—41no—
593#102—614no—
594#102—1222no—
595#102—1222no—
596#102—1222no—
597C22⋊C8—22no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—21no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24—611no—
615C24D4×D6111yescharacteristic
616#41—1228no—
617#41—2444no—
618#41—2444no—
619#41—2444no—
620C2×Q8—612no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×D4—28no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—24no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—614no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—1224no—
645C2×D4—1224no—
646C2×D4—4881no—
647C2×D4—4881no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6112yes—
651C2×D4C2×C4×D6112yes—
652C2×D4D4×D6112yes—
653C2×D4#1175822412yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1224no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—4881no—
676C22×C4—4881no—
677C22×C4—4881no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6112yes—
683C22×C4D4×D6112yes—
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—612no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—2444no—
699C2×C8—2444no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—614no—
705C4⋊C4—612no—
706C4⋊C4—612no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1224no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—2442no—
713C22⋊C4—42no—
714C22⋊C4—614no—
715C22⋊C4—614no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—4881no—
722C22⋊C4—2442no—
723C42—612no—
724C42—612no—
725C42—4881no—
726C42—2442no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—48no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—48no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—84no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—612no—
753C23—1221no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23C22⋊C4×D6112yes—
760C23#1451979612yes—
761C23#1451979812yes—
762C23C2×D4×D6111yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4—1228no—
776D4—4884no—
777D4—2448no—
778D4#1451973714yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—612no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—4884no—
808C2×C4—4884no—
809C2×C4—2448no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22⋊C4×D6112yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×#1175822411yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982211yescharacteristic
826C8—41no—
827C8—41no—
828C8—1222no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—816no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22#1683975514yescomplemented
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039411yescharacteristic
861C22#1684039911yescharacteristic
862C22C2×#1451979611yescharacteristic
863C22C2×#1451979811yescharacteristic
864C22#1684056611yescharacteristic
865C22#1684057211yescharacteristic
866C4—22no—
867C4—81no—
868C4—81no—
869C4—1222no—
870C4—1222no—
871C4—1222no—
872C4—4881no—
873C4—2442no—
874C4—2442no—
875C4—2442no—
876C4C2×#1451973711yescharacteristic
877C4#1684023511yescharacteristic
878C4#1684039411yescharacteristic
879C4#1684039911yescharacteristic
880C2—24no—
881C2—44no—
882C2—82no—
883C2—2442no—
884C2#2144863511yescharacteristic
885C2C2×#1683975511yescharacteristic
886C2#2145434411yescharacteristic
887C2#2145749711yescharacteristic
888C2#2145753011yescharacteristic
889C2#2145765811yescharacteristic
890C2#2145767311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC2×#16840406C2
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#22414
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#16839825C2semidirect
3. C2×#16839755C2semidirect
4. C22×#14519698C2semidirect
5. #21448750C2semidirect
6. #21446750C2semidirect
7. #21446629C2semidirect
8. #21446244C2semidirect
9. #21446240C2semidirect
10. #21446138C2semidirect
11. #21446124C2semidirect
12. #21445827C2semidirect
13. #21445756C2semidirect
14. #102×Dic61C2semidirect
15. C61×#1786C2semidirect
18. C22×C8×D61C22semidirect
20. #16840406C4semidirect
29. C2×#14519735C22semidirect
33. C2×#14519706C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
44. C2×#14519689C22semidirect
45. C2×C8×Dic61C22semidirect
49. #16839627C22semidirect
50. #16839619C22semidirect
51. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
69. C2×#11758224C2×C4semidirect
87. #14519764C2×C4semidirect
93. #14519748C2×C4semidirect
96. D4×Dic61C2×C4semidirect
130. #14519698D4semidirect
406. C22×C61#416semidirect
448. #1786D61semidirect
509. C61#22414semidirect
858. C22#16839755semidirect

Maximal subgroups

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

subgroupindex
C2×#168404062
C2×#168398252
C2×#168397552
C22×#145196982
#214487502
#214467502
#214466292
#214462442
#214462402
#214461382
#214461242
#214458272
#214457562
#102×Dic612
C61×#17862
#2241461