Finite Group Databasebeta

← #30622742

Subgroups — #30622742

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic
2C2×Q16×#6923C211yesmaximal, characteristic, complemented
3#21462350C211yesmaximal, characteristic
4#21462348C211yesmaximal, characteristic, complemented
5#21461987C211yesmaximal, characteristic
6#21461985C211yesmaximal, characteristic, complemented
7#21461967C211yesmaximal, characteristic, complemented
8#21461964C211yesmaximal, characteristic
9#21461815C211yesmaximal, characteristic
10#21461813C211yesmaximal, characteristic, complemented
11#21461813C211yesmaximal, characteristic, complemented
12#21461812C211yesmaximal, characteristic
13#21461633C211yesmaximal, characteristic, complemented
14#21461617C211yesmaximal, characteristic, complemented
15#497×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840801—24no—
21Q16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519840C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×#14519839C2211yescharacteristic
33C2×#14519831C2211yescharacteristic
34C2×C8×#6923C2211yescharacteristic
35(C2×#6923)⋊Q8C2211yescharacteristic
36(C2×#6923)⋊Q8C2211yescharacteristic
37(C2×#6923)⋊Q8C2211yescharacteristic
38#16840714C2211yescharacteristic
39#16840713—21no—
40#16840712—21no—
41#16840712—21no—
42#16840711—21no—
43#16840711—21no—
44#16840709—21no—
45C4⋊C4×#6923—21no—
46C4×C4⋊#6923C2211yescharacteristic
47C4×C4⋊#6923C2211yescharacteristic
48C4×C4⋊#6923C2211yescharacteristic
49C22⋊C4×#6923—21no—
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×Q16×D61C2211yescharacteristic
55C2×Q16×D61C2211yescharacteristic
56C2×SD16×D61C2211yescharacteristic
57C2×SD16×D61C2211yescharacteristic
58C4⋊Q8×D61C2211yescharacteristic
59#124×D61C2211yescharacteristic
60#16840157C411yescharacteristic, complemented
61#16840156C411yescharacteristic, complemented
62#16840155C411yescharacteristic, complemented
63#16840155C411yescharacteristic, complemented
64#16840154C411yescharacteristic, complemented
65#16840153C411yescharacteristic, complemented
66#16840153C411yescharacteristic, complemented
67#97×D61C2211yescharacteristic
68C61×#497C411yescharacteristic, complemented
69C23×#6923—21no—
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72Q8×#6923—22no—
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—41no—
76Q8×#6923—41no—
77Q8×#6923—41no—
78D4×#6923—22no—
79D4×#6923—41no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923D411yescharacteristic
84C2×C4⋊#6923D411yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923C2311yescharacteristic
98C2×C4×#6923C2311yescharacteristic
99#14519846D414yes—
100#14519845—22no—
101#14519844—21no—
102C4⋊#92420—21no—
103#14519840—22no—
104#14519840—22no—
105#14519840—22no—
106#14519840—41no—
107#14519840—41no—
108#14519840—41no—
109#14519839—22no—
110#14519839—41no—
111#14519831—22no—
112C8×#6923—22no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4D411yescharacteristic
122(C2×#6923)⋊C4D411yescharacteristic
123C2×Q8×D61C2311yescharacteristic
124C2×Q8×D61C2311yescharacteristic
125C2×Q8×D61C2311yescharacteristic
126C2×D4×D61C2311yescharacteristic
127C2×Dic244C2×C411yescharacteristic, complemented
128C2×Dic244C2×C411yescharacteristic, complemented
129C2×#11758202C2×C411yescharacteristic, complemented
130C2×#11758202C2×C411yescharacteristic, complemented
131C2×#11758202C2×C411yescharacteristic, complemented
132C2×#11758202C2×C411yescharacteristic, complemented
133Q16×D61—22no—
134Q16×D61—22no—
135Q16×D61—41no—
136Q16×D61—41no—
137C2×#11758190C2×C411yescharacteristic
138C2×#11758190C2×C411yescharacteristic
139C2×#11758200C2×C411yescharacteristic
140C2×#11758200C2×C411yescharacteristic
141C2×#11758201C2×C411yescharacteristic
142C2×#11758201C2×C411yescharacteristic
143SD16×D61—22no—
144SD16×D61—22no—
145SD16×D61—41no—
146SD16×D61—41no—
147C2×C8×D61C2311yescharacteristic
148C2×C8×D61C2311yescharacteristic
149#14519777C2×C411yescharacteristic, complemented
150#14519776—21no—
151#14519776—21no—
152#14519775C2×C411yescharacteristic, complemented
153#14519775C2×C411yescharacteristic, complemented
154#14519766C2×C411yescharacteristic
155#14519765C2×C411yescharacteristic
156#14519764C2×C411yescharacteristic
157#14519763—21no—
158#14519763—21no—
159C4⋊C4×D61—21no—
160C4⋊C4×D61—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C42×D61C2311yescharacteristic
164#14519688C2×C411yescharacteristic, complemented
165#14519687C2×C411yescharacteristic, complemented
166#14519687C2×C411yescharacteristic, complemented
167C2×Q16×C61C2×C411yescharacteristic, complemented
168C2×Q16×C61C2×C411yescharacteristic, complemented
169C2×SD16×C61C2×C411yescharacteristic
170C2×SD16×C61C2×C411yescharacteristic
171C4⋊Q8×C61C2×C411yescharacteristic, complemented
172#124×C61C2×C411yescharacteristic
173#97×C61C2×C411yescharacteristic, complemented
174C23×D61—21no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—42no—
180C22×#6923—42no—
181C22×#6923—81no—
182C22×#6923C2×D411yescharacteristic
183C22×#6923C2×D411yescharacteristic
184C22×#6923C2×D411yescharacteristic
185C22×#6923C2×D411yescharacteristic
186C2×Q8×C61C22×C411yescharacteristic
187C2×Q8×C61C22×C411yescharacteristic
188C2×Q8×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C2×C22⋊D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193Q8×D61—21no—
194Q8×D61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197Q8×D61—21no—
198Q8×D61—21no—
199Q8×D61—21no—
200Q8×D61—21no—
201Q8×D61—21no—
202Q8×D61—21no—
203D4×D61—21no—
204D4×D61—21no—
205D4×D61—21no—
206D4×D61—21no—
207C2×D244C22×C411yescharacteristic
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2411yescharacteristic
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122C22×C411yescharacteristic
218C2×Dic122C22×C411yescharacteristic
219C2×Dic122C22×C411yescharacteristic
220C22⋊#6923—42no—
221C22⋊#6923—42no—
222C22⋊#6923—81no—
223C2×#92420—21no—
224C2×#92420—21no—
225C4⋊#6923—22no—
226C4⋊#6923—21no—
227C4⋊#6923—21no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—41no—
233C4⋊#6923—42no—
234C4⋊#6923—42no—
235C4⋊#6923—42no—
236C4⋊#6923C2×D412yes—
237C4⋊#6923C2×D412yes—
238C4×#6923—21no—
239C4×#6923—21no—
240C4×#6923—21no—
241C4×#6923—21no—
242C4×#6923—42no—
243C4×#6923—42no—
244C4×#6923—42no—
245C4×#6923—42no—
246C4×#6923—81no—
247D61⋊C8—21no—
248D61⋊C8—21no—
249D61⋊C8—21no—
250D61⋊C8—21no—
251Q16×C61—22no—
252Q16×C61—41no—
253SD16×C61—22no—
254SD16×C61—41no—
255C2×C8×C61C22×C411yescharacteristic
256C2×C8×C61C22×C411yescharacteristic
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C42×C61C22×C411yescharacteristic
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264#11758202—22no—
265#11758202—22no—
266#11758202—41no—
267#11758202—41no—
268#11758201—22no—
269#11758201—41no—
270#11758200—22no—
271#11758200—41no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—21no—
281#11758196—21no—
282C4×Dic61C22×C411yescharacteristic
283C4×Dic61#4111yescharacteristic
284C4×Dic61#4111yescharacteristic
285C2×#92418C22×C411yescharacteristic
286C2×#92418C22×C411yescharacteristic
287Dic244—22no—
288Dic244—41no—
289#11758190—22no—
290#11758190—41no—
291C8×D61—21no—
292C8×D61—21no—
293C8×D61C2×D412yes—
294C8×D61#4112yes—
295C23×C61—21no—
296C22×D61—21no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61C22×D411yescharacteristic
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—22no—
310C2×#6923—22no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—21no—
314C2×#6923—21no—
315C2×#6923—21no—
316C2×#6923—21no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—84no—
328C2×#6923#13712yes—
329Q8×C61—21no—
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—21no—
333Q8×C61—21no—
334Q8×C61—21no—
335D4×C61—21no—
336D4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61C4×D411yescharacteristic
342C2×C4×C61C23×C411yescharacteristic
343C22⋊D61—41no—
344C22⋊D61—41no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61C4×D411yescharacteristic
349C2×Dic61C4×D411yescharacteristic
350C2×Dic61C2×#4111yescharacteristic
351D244—21no—
352D244—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61C22×D411yescharacteristic
364C4×D61C2×#4111yescharacteristic
365C4×D61H(5,𝔽2)11yescharacteristic
366C4×D61H(5,𝔽2)11yescharacteristic
367Dic122—21no—
368Dic122—21no—
369Dic122—21no—
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—41no—
374Dic122—41no—
375Dic122—41no—
376Dic122—41no—
377Dic122—41no—
378Dic122—41no—
379#92420—41no—
380#92420—41no—
381C8×C61—21no—
382C8×C61C4×D412yes—
383#92418—21no—
384#92418C4×D412yes—
385#23194—611nomaximal, Sylow
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61C2×C4×D411yescharacteristic
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61—81no—
396C2×D61—81no—
397C2×D61D4211yescharacteristic
398C2×D61#55011yescharacteristic
399C2×D61C2×#13711yescharacteristic
400C2×D61#57511yescharacteristic
401C2×D61#57711yescharacteristic
402C2×D61#57811yescharacteristic
403#6923—22no—
404#6923—41no—
405#6923—41no—
406#6923—42no—
407#6923—42no—
408#6923—41no—
409#6923—81no—
410#6923—81no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61C2×C4×D411yescharacteristic
417C4×C61#51811yescharacteristic
418Dic61—21no—
419Dic61—21no—
420Dic61—41no—
421Dic61—41no—
422Dic61—41no—
423Dic61#55011yescharacteristic
424Dic61#55911yescharacteristic
425C2×#497—611no—
426C2×#440—611no—
427C2×C4×Q16—611no—
428#2367—611no—
429#2365—611no—
430#1983—611no—
431#1981—611no—
432#1971—611no—
433#1968—611no—
434#1880—611no—
435#1878—611no—
436#1878—611no—
437#1877—611no—
438#1776—611no—
439#1771—611no—
440C2×C61—81no—
441C2×C61#236611yescharacteristic
442C2×C61C4×#13711yescharacteristic
443C2×C61#294711yescharacteristic
444D61—81no—
445D61#326711yescharacteristic
446D61#327011yescharacteristic
447D61#340011yescharacteristic
448D61#340211yescharacteristic
449C22×Q16—611no—
450C22×Q16—611no—
451C22×SD16—611no—
452C22×SD16—611no—
453C2×C4⋊Q8—611no—
454C2×#124—611no—
455C2×C4×Q8—611no—
456C2×C4×Q8—611no—
457C2×C4×Q8—611no—
458C2×C4×D4—611no—
459#497—611no—
460#497—611no—
461#497—611no—
462#497—611no—
463#497—611no—
464#497—611no—
465#497—611no—
466#497#692311yescharacteristic, complemented
467#440—1224no—
468C4×Q16—1224no—
469C2×#107—611no—
470C2×#106—611no—
471C2×C4⋊C8—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#97—611no—
481C2×#97—611no—
482C2×C4×C8—611no—
483#391—611no—
484#391—611no—
485#391—611no—
486#390—611no—
487#389—1221no—
488#388—1221no—
489#388—1221no—
490#387—1221no—
491#387—1221no—
492#385—1221no—
493C4×C4⋊C4—611no—
494C4×C4⋊C4—611no—
495C4×C4⋊C4—611no—
496C4×C4⋊C4—1221no—
497C4×C22⋊C4—1221no—
498#340—611no—
499#340—611no—
500#336—611no—
501#336—611no—
502C61#2319411yescharacteristic, complemented, Sylow
503C22×Q8—611no—
504C22×Q8—611no—
505C22×Q8—611no—
506C22×D4—611no—
507C23×C4—1221no—
508C2×Q16—611no—
509C2×Q16—611no—
510C2×Q16—611no—
511C2×Q16—611no—
512C2×Q16—611no—
513C2×Q16—611no—
514C2×Q16—1222no—
515C2×Q16—1222no—
516C2×Q16—2441no—
517C2×Q16—2441no—
518C2×Q16C2×#692311yescharacteristic, complemented
519C2×Q16C2×#692311yescharacteristic, complemented
520C2×SD16—611no—
521C2×SD16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—611no—
526C2×SD16—1222no—
527C2×SD16—1222no—
528C2×SD16—2441no—
529C2×SD16—2441no—
530C2×SD16C2×#692311yescharacteristic
531C2×SD16C2×#692311yescharacteristic
532C22×C8—611no—
533C22×C8—611no—
534C22×C8—611no—
535C22×C8—611no—
536C4⋊Q8—611no—
537C4⋊Q8—611no—
538C4⋊Q8—611no—
539C4⋊Q8—1221no—
540C4⋊Q8—1221no—
541C4⋊Q8C2×#692311yescharacteristic, complemented
542#124—611no—
543#124—611no—
544#124—611no—
545#124—1221no—
546#124—1221no—
547#124C2×#692311yescharacteristic
548C4×Q8—1222no—
549C4×Q8—1222no—
550C4×Q8—1222no—
551C4×Q8—2441no—
552C4×Q8—2441no—
553C4×Q8—2441no—
554C4×D4—1222no—
555C4×D4—2441no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—1221no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579C2×C42—1221no—
580#107—614no—
581#106—1222no—
582C4⋊C8—1221no—
583C4⋊C8—1221no—
584#103—1222no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#103—2441no—
590#102—1222no—
591#102—2441no—
592#97—611no—
593#97—611no—
594#97—611no—
595#97—1222no—
596#97C2×#692311yescharacteristic, complemented
597C4×C8—1222no—
598#95—611no—
599#95—611no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608C24—1221no—
609C2×Q8—611no—
610C2×Q8—611no—
611C2×Q8—611no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8C22×#692311yescharacteristic
628C2×Q8C22×#692311yescharacteristic
629C2×Q8C22×#692311yescharacteristic
630C2×D4—611no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4C22×#692311yescharacteristic
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—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—4881no—
652C22×C4—2442no—
653C22×C4—2442no—
654Q16—22no—
655Q16—41no—
656Q16—1222no—
657Q16—1222no—
658Q16—1222no—
659Q16—2441no—
660Q16—2441no—
661Q16—2441no—
662SD16—22no—
663SD16—41no—
664SD16—1222no—
665SD16—1222no—
666SD16—1222no—
667SD16—2441no—
668SD16—2441no—
669SD16—2441no—
670C2×C8—611no—
671C2×C8—612no—
672C2×C8—612no—
673C2×C8—611no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8C22×#692311yescharacteristic
683C2×C8C22×#692311yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—612no—
687C4⋊C4—612no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1222no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—2441no—
702C4⋊C4—2442no—
703C4⋊C4—2442no—
704C4⋊C4—2442no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—1221no—
708C22⋊C4—1221no—
709C22⋊C4—1221no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—4881no—
714C22⋊C4—2442no—
715C22⋊C4—2442no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—1221no—
720C42—1221no—
721C42—1221no—
722C42—1221no—
723C42—4881no—
724C42—2442no—
725C42—2442no—
726C42—2442no—
727C42—2442no—
728C42C22×#692311yescharacteristic
729C23—21no—
730C23—611no—
731C23—1221no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738Q8—21no—
739Q8—21no—
740Q8—21no—
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—1221no—
745Q8—1221no—
746Q8—1221no—
747Q8—1221no—
748Q8—1221no—
749Q8—1221no—
750Q8—2441no—
751Q8—2441no—
752Q8—2441no—
753Q8—2441no—
754Q8—2441no—
755Q8—2441no—
756D4—21no—
757D4—21no—
758D4—1221no—
759D4—1221no—
760D4—2441no—
761D4—2441no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—612no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—4884no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4D4×#692311yescharacteristic
811C2×C4D4×#692311yescharacteristic
812C2×C4C23×#692311yescharacteristic
813C8—21no—
814C8—612no—
815C8—1221no—
816C8—2441no—
817C8—2441no—
818C8D4×#692312yes—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—611no—
823C22—611no—
824C22—611no—
825C22—611no—
826C22—611no—
827C22—611no—
828C22—4881no—
829C22—4881no—
830C22—4881no—
831C22—4881no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C2×D4×#692311yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—611no—
842C4—611no—
843C4—1222no—
844C4—1221no—
845C4—1221no—
846C4—4881no—
847C4—4881no—
848C4—2441no—
849C4—2441no—
850C4—2441no—
851C4—2442no—
852C4—2442no—
853C4—2441no—
854C4—2441no—
855C4—2441no—
856C4C2×D4×#692311yescharacteristic
857C4#1684082911yescharacteristic
858C2—81no—
859C2—611no—
860C2—611no—
861C2—611no—
862C2—611no—
863C2—4881no—
864C2#2146234911yescharacteristic
865C2#137×#692311yescharacteristic
866C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#497C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#497#6923
hypocenterC61#23194
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. C2×Q16×#6923C2semidirect
4. #21462348C2semidirect
6. #21461985C2semidirect
7. #21461967C2semidirect
10. #21461813C2semidirect
11. #21461813C2semidirect
13. #21461633C2semidirect
14. #21461617C2semidirect
60. #16840157C4semidirect
61. #16840156C4semidirect
62. #16840155C4semidirect
63. #16840155C4semidirect
64. #16840154C4semidirect
65. #16840153C4semidirect
66. #16840153C4semidirect
68. C61×#497C4semidirect
127. C2×Dic244C2×C4semidirect
128. C2×Dic244C2×C4semidirect
129. C2×#11758202C2×C4semidirect
130. C2×#11758202C2×C4semidirect
131. C2×#11758202C2×C4semidirect
132. C2×#11758202C2×C4semidirect
149. #14519777C2×C4semidirect
152. #14519775C2×C4semidirect
153. #14519775C2×C4semidirect
164. #14519688C2×C4semidirect
165. #14519687C2×C4semidirect
166. #14519687C2×C4semidirect
167. C2×Q16×C61C2×C4semidirect
168. C2×Q16×C61C2×C4semidirect
171. C4⋊Q8×C61C2×C4semidirect
173. #97×C61C2×C4semidirect
466. #497#6923semidirect
502. C61#23194semidirect
518. C2×Q16C2×#6923semidirect
519. C2×Q16C2×#6923semidirect
541. C4⋊Q8C2×#6923semidirect
596. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×Q16×#69232
#214623502
#214623482
#214619872
#214619852
#214619672
#214619642
#214618152
#214618132
#214618122
#214616332
#214616172
#497×D612
#2319461