Finite Group Databasebeta

← #29695617

Subgroups — #29695617

Order 15616.

1606 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×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839767C211yesmaximal, characteristic, complemented
5#21448741C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446629C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446250C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21446129C211yesmaximal, characteristic, complemented
12#21445827C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, 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×#14519736C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic, complemented
31C22×C22⋊Dic61—21no—
32#16839837—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839767—24no—
35#16839760—24no—
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519689C2211yescharacteristic, complemented
45C2×C8×Dic61C2211yescharacteristic, complemented
46#16839650—21no—
47#16839644—21no—
48#16839638—21no—
49#16839627C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52#16839609—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×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C23×Dic61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758194—22no—
79C2×#11758194—22no—
80C2×#11758194—41no—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—41no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519764—22no—
87#14519764C2×C414yescomplemented
88#14519758—28no—
89#14519756—22no—
90#14519756C2×C414yescomplemented
91#14519749—28no—
92#14519748—22no—
93#14519748C2×C414yes—
94#14519746—28no—
95D4×Dic61—22no—
96D4×Dic61C2×C414yescomplemented
97C4×C22⋊D61C2×C414yes—
98C4×C22⋊D61D414yes—
99#14519736—22no—
100#14519736—41no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196D411yescharacteristic
107C4⋊C4×D61—22no—
108C4⋊C4×D61—41no—
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⋊Dic61—21no—
116C2×C22⋊Dic61D411yescharacteristic
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×C414yescomplemented
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—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
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—81no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758224—28no—
222#11758224—44no—
223#11758224—44no—
224#11758224—44no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—81no—
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—81no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—42no—
257C22⋊Dic61C22⋊C414yes—
258#11758198—42no—
259#11758198C22⋊C414yes—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C412yes—
265C4⋊Dic61C2×D412yes—
266#11758196—24no—
267#11758196—42no—
268#11758196C22⋊C414yes—
269C4×Dic61—42no—
270C4×Dic61—81no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273#11758194—44no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C2×D412yes—
280#11758189—44no—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—48no—
292C23×C61—48no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61C2×C22⋊C412yes—
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—44no—
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×Dic61C2×C22⋊C412yes—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—24no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—41no—
392C22×C61—42no—
393C22×C61—41no—
394C22×C61—42no—
395C22×C61—41no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—816no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61C22×C22⋊C411yescharacteristic
408C22×C61D4211yescharacteristic
409C22×C61#54611yescharacteristic
410C22×C61#57511yescharacteristic
411C22×C61#57511yescharacteristic
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×#436—611no—
437C2×#417—611no—
438C2×#418—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1895—611no—
443#1894—611no—
444#1874—611no—
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786D6111yescharacteristic, complemented
449C4×#102—611no—
450C2×C61—42no—
451C2×C61—44no—
452C2×C61—82no—
453C2×C61D4×C22⋊C411yescharacteristic
454C2×C61#289611yescharacteristic
455C2×C61#289711yescharacteristic
456C2×C61#327311yescharacteristic
457C2×C61#327511yescharacteristic
458C2×C61#332211yescharacteristic
459C2×C61#332311yescharacteristic
460D61—42no—
461C22×#41—611no—
462C23×D4C2×D6111yescharacteristic
463C22×M16—611no—
464C22×M16—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—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
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#2242711yescharacteristic, 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×D6114yescomplemented
528C22×D4C22×D6111yescharacteristic
529C22×D4C22×D6111yescharacteristic
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535C2×M16—1222no—
536C2×M16—1222no—
537C2×M16—1222no—
538C2×M16—1222no—
539C2×M16—2441no—
540C2×M16—2441no—
541C22×C8—611no—
542C22×C8—611no—
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—1224no—
643C2×D4—1224no—
644C2×D4—4881no—
645C2×D4—4881no—
646C2×D4—2441no—
647C2×D4—2441no—
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
686M16—2444no—
687M16—2444no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—612no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
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—81no—
714C22⋊C4—614no—
715C22⋊C4—614no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—2442no—
722C22⋊C4—2442no—
723C42—612no—
724C42—612no—
725C42—4881no—
726C42—2442no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—22no—
737C23—48no—
738C23—48no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—612no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23—1221no—
761C23C22⋊C4×D6112yes—
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—4884no—
776D4—2444no—
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—24no—
833C22—22no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—816no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22—2441no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039411yescharacteristic
861C22#1684039911yescharacteristic
862C22#1684055811yescharacteristic
863C22#1684055811yescharacteristic
864C22#1684056311yescharacteristic
865C22#1684056811yescharacteristic
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—42no—
881C2—44no—
882C2—82no—
883C2—2442no—
884C2#2144863511yescharacteristic
885C2#2145433311yescharacteristic
886C2#2145434011yescharacteristic
887C2#2145743011yescharacteristic
888C2#2145745411yescharacteristic
889C2#2145802411yescharacteristic
890C2#2145803911yescharacteristic
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#22427
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×#16839837C2semidirect
3. C2×#16839760C2semidirect
4. C2×#16839767C2semidirect
5. #21448741C2semidirect
6. #21446750C2semidirect
7. #21446629C2semidirect
8. #21446254C2semidirect
9. #21446250C2semidirect
10. #21446133C2semidirect
11. #21446129C2semidirect
12. #21445827C2semidirect
13. #21445756C2semidirect
14. #102×Dic61C2semidirect
15. C61×#1786C2semidirect
18. C22×#11758189C22semidirect
20. #16840406C4semidirect
30. C2×C4⋊C4×D61C22semidirect
33. C2×#14519706C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519700C22semidirect
39. 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
87. #14519764C2×C4semidirect
90. #14519756C2×C4semidirect
96. D4×Dic61C2×C4semidirect
130. #14519698D4semidirect
144. C22×D4×C61C2×C4semidirect
448. #1786D61semidirect
509. C61#22427semidirect
527. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404062
C2×#168398372
C2×#168397602
C2×#168397672
#214487412
#214467502
#214466292
#214462542
#214462502
#214461332
#214461292
#214458272
#214457562
#102×Dic612
C61×#17862
#2242761