Finite Group Databasebeta

← #30622578

Subgroups — #30622578

Order 15616.

922 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462346C211yesmaximal, characteristic
2#21462345C211yesmaximal, characteristic, complemented
3#21461909C211yesmaximal, characteristic, complemented
4#21461908C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461815C211yesmaximal, characteristic, complemented
8#21461812C211yesmaximal, characteristic, complemented
9#21461807C211yesmaximal, characteristic
10#21461805C211yesmaximal, characteristic, complemented
11#103×#6923C211yesmaximal, characteristic, complemented
12#102×#6923C211yesmaximal, characteristic, complemented
13C8×C22⋊#6923C211yesmaximal, characteristic, complemented
14#21461505C211yesmaximal, characteristic, complemented
15#465×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C2×#14519856C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24D61⋊(C22⋊C8)C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27(C2×#6923)⋊Q8C2211yescharacteristic
28#16840714—21no—
29#16840714C2211yescharacteristic
30#16840713C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840712—21no—
33#16840712—21no—
34#16840712—21no—
35#16840711—21no—
36#16840710—21no—
37C4⋊C4×#6923—21no—
38C4⋊C4×#6923C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C22⋊C4×#6923—21no—
41C4×C22⋊#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C22×C8×D61C2211yescharacteristic
54C22⋊Q8×D61C2211yescharacteristic
55#121×D61C2211yescharacteristic
56#16839994C411yescharacteristic, complemented
57#16839993C411yescharacteristic, complemented
58#16839992C411yescharacteristic, complemented
59#16839991C411yescharacteristic, complemented
60#16839990C411yescharacteristic, complemented
61#16839989C411yescharacteristic, complemented
62#16839988C411yescharacteristic, complemented
63#106×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#465C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—41no—
72D4×#6923—22no—
73D4×#6923—41no—
74#14519856—22no—
75#14519856—22no—
76#14519856—41no—
77#14519856—41no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923D411yescharacteristic
91C2×C22⋊#6923D411yescharacteristic
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#14519840—22no—
100#14519840—41no—
101#14519839—22no—
102#14519839—41no—
103#14519834—21no—
104C22⋊#92420—21no—
105C8×#6923—41no—
106C8×#6923—41no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C2×#11758190C2×C411yescharacteristic
120C2×#11758200C2×C411yescharacteristic
121C2×#11758201C2×C411yescharacteristic
122SD16×D61—41no—
123SD16×D61—41no—
124C22×#92418C2×C411yescharacteristic, complemented
125C2×C8×D61—41no—
126C2×C8×D61—41no—
127C2×C8×D61C2×C411yescharacteristic, complemented
128C2×C8×D61C2×C411yescharacteristic, complemented
129C2×C8×D61C2311yescharacteristic
130C2×C8×D61C2311yescharacteristic
131#14519757C2×C411yescharacteristic, complemented
132#14519756C2×C411yescharacteristic, complemented
133#14519755—21no—
134#14519754—21no—
135#14519753C2×C411yescharacteristic, complemented
136#14519752C2×C411yescharacteristic
137#14519751C2×C411yescharacteristic
138#14519750—21no—
139#14519749—21no—
140#14519748C2×C411yescharacteristic
141C4⋊C4×D61—21no—
142C4⋊C4×D61C2311yescharacteristic
143C4⋊C4×D61C2311yescharacteristic
144C22⋊C4×D61—21no—
145C22⋊C4×D61—21no—
146#14519709C2×C411yescharacteristic, complemented
147#14519708C2×C411yescharacteristic, complemented
148#14519708C2×C411yescharacteristic, complemented
149#14519702C2×C411yescharacteristic, complemented
150#14519701C2×C411yescharacteristic, complemented
151#14519700C2×C411yescharacteristic, complemented
152#14519699C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×SD16×C61C2×C411yescharacteristic
156C22×C8×C61C2×C411yescharacteristic, complemented
157C22⋊Q8×C61C2×C411yescharacteristic, complemented
158#121×C61C2×C411yescharacteristic
159#106×C61C2×C411yescharacteristic, complemented
160#103×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C23×D61C2×D411yescharacteristic
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—42no—
169C22×#6923—42no—
170C22×#6923—81no—
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C22×#6923C2×D411yescharacteristic
175C2×Q8×C61C22×C411yescharacteristic
176C2×D4×C61—21no—
177C2×D4×C61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C22×Dic61#4111yescharacteristic
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186Q8×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61—21no—
190D4×D61—21no—
191D4×D61—81no—
192D4×D61—81no—
193C2×D244—21no—
194C2×D244C22×C411yescharacteristic
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61C22×C411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61#4111yescharacteristic
205C2×C4×D61C2411yescharacteristic
206C2×Dic122—21no—
207C2×Dic122C22×C411yescharacteristic
208C22⋊#6923—22no—
209C22⋊#6923—22no—
210C22⋊#6923—42no—
211C22⋊#6923—42no—
212C22⋊#6923—42no—
213C22⋊#6923—42no—
214C22⋊#6923—81no—
215C2×#92420—21no—
216C2×#92420—21no—
217C4⋊#6923—21no—
218C4⋊#6923—21no—
219C4⋊#6923—21no—
220C4⋊#6923—21no—
221C4⋊#6923—21no—
222C4⋊#6923—21no—
223C4⋊#6923—42no—
224C4⋊#6923—42no—
225C4⋊#6923—81no—
226C4⋊#6923#4112yes—
227C4⋊#6923#4112yes—
228C4×#6923—21no—
229C4×#6923—21no—
230C4×#6923—21no—
231C4×#6923—21no—
232C4×#6923—42no—
233C4×#6923—42no—
234C4×#6923—42no—
235C4×#6923—42no—
236C4×#6923—81no—
237D61⋊C8—21no—
238D61⋊C8—21no—
239D61⋊C8—21no—
240D61⋊C8—21no—
241SD16×C61—41no—
242C2×C8×C61—41no—
243C2×C8×C61C22×C411yescharacteristic
244C2×C8×C61C22×C411yescharacteristic
245C4⋊C4×C61—21no—
246C4⋊C4×C61C22×C411yescharacteristic
247C4⋊C4×C61C22×C411yescharacteristic
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊Dic61—21no—
251C22⋊Dic61—21no—
252#11758201—41no—
253#11758200—41no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61C22×C411yescharacteristic
260C4⋊Dic61C22×C411yescharacteristic
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265C2×#92418—41no—
266C2×#92418C22×C411yescharacteristic
267C2×#92418C22×C411yescharacteristic
268#11758190—41no—
269C8×D61—21no—
270C8×D61—21no—
271C8×D61—21no—
272C8×D61—21no—
273C8×D61—41no—
274C8×D61—41no—
275C23×C61—21no—
276C23×C61C4×D411yescharacteristic
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61C4×D411yescharacteristic
291C22×D61C22×D411yescharacteristic
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—21no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—22no—
299C2×#6923—22no—
300C2×#6923—21no—
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—84no—
315C2×#6923#13512yes—
316C2×#6923#13512yes—
317Q8×C61—21no—
318Q8×C61—21no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—81no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61C4×D411yescharacteristic
328C2×C4×C61C23×C411yescharacteristic
329C22⋊D61—41no—
330C22⋊D61—41no—
331C22⋊D61—81no—
332C22⋊D61—81no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61C4×D411yescharacteristic
339C2×Dic61C2×#4111yescharacteristic
340D244—21no—
341D244—21no—
342D244—81no—
343C4×D61—21no—
344C4×D61—21no—
345C4×D61—21no—
346C4×D61—21no—
347C4×D61—21no—
348C4×D61—21no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61C2×#4111yescharacteristic
356C4×D61C2×#4111yescharacteristic
357C4×D61H(5,𝔽2)11yescharacteristic
358C4×D61H(5,𝔽2)11yescharacteristic
359Dic122—21no—
360Dic122—21no—
361Dic122—41no—
362Dic122—41no—
363#92420—41no—
364#92420—41no—
365C8×C61—21no—
366C8×C61—21no—
367#92418—21no—
368#92418—21no—
369#23131—611nomaximal, Sylow
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61C2×C4×D411yescharacteristic
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61#54611yescharacteristic
392C2×D61#54611yescharacteristic
393C2×D61C2×#13511yescharacteristic
394C2×D61C2×#13511yescharacteristic
395C2×D61#57711yescharacteristic
396C2×D61#57711yescharacteristic
397#6923—22no—
398#6923—22no—
399#6923—42no—
400#6923—41no—
401#6923—42no—
402#6923—41no—
403#6923—81no—
404#6923—81no—
405C4×C61—21no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61C4×#4111yescharacteristic
410C4×C61#51811yescharacteristic
411Dic61—21no—
412Dic61—41no—
413Dic61—41no—
414Dic61—41no—
415Dic61#55311yescharacteristic
416Dic61#55311yescharacteristic
417C2×#465—611no—
418#2363—611no—
419#2362—611no—
420#1934—611no—
421#1933—611no—
422#1920—611no—
423#1919—611no—
424#1880—611no—
425#1877—611no—
426#1875—611no—
427#1873—611no—
428C4×#103—611no—
429C4×#102—611no—
430C8×C22⋊C4—611no—
431#1735—611no—
432C2×C61—41no—
433C2×C61—81no—
434C2×C61#236411yescharacteristic
435C2×C61C4×#13511yescharacteristic
436C2×C61#294911yescharacteristic
437D61—41no—
438D61—81no—
439D61#329611yescharacteristic
440D61#330111yescharacteristic
441D61#330311yescharacteristic
442D61#330411yescharacteristic
443C22×SD16—611no—
444C23×C8—611no—
445C2×C22⋊Q8—611no—
446C2×#121—611no—
447C2×C4×Q8—611no—
448C2×C4×D4—611no—
449C2×#117—611no—
450C2×#117—611no—
451#465—611no—
452#465—611no—
453#465—611no—
454#465—611no—
455#465—611no—
456#465—611no—
457#465—611no—
458#465#692311yescharacteristic, complemented
459C2×#106—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×C22⋊C8—611no—
467C2×C4×C8—611no—
468C2×C4×C8—611no—
469#391—611no—
470#390—611no—
471#390—1221no—
472#389—611no—
473#389—611no—
474#388—1221no—
475#388—1221no—
476#388—1221no—
477#387—1221no—
478#386—1221no—
479C4×C4⋊C4—611no—
480C4×C4⋊C4—611no—
481C4×C4⋊C4—1221no—
482C4×C22⋊C4—611no—
483C4×C22⋊C4—1221no—
484#340—611no—
485#340—611no—
486#340—611no—
487#340—611no—
488#340—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#336—611no—
493#336—611no—
494C61#2313111yescharacteristic, complemented, Sylow
495C22×Q8—611no—
496C22×D4—611no—
497C22×D4—1221no—
498C23×C4—611no—
499C23×C4—1221no—
500C2×SD16—611no—
501C2×SD16—611no—
502C2×SD16—611no—
503C2×SD16—2441no—
504C2×SD16—2441no—
505C2×SD16C2×#692311yescharacteristic
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—611no—
509C22×C8—611no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—2441no—
514C22×C8—2441no—
515C22×C8C2×#692311yescharacteristic, complemented
516C22⋊Q8—611no—
517C22⋊Q8—611no—
518C22⋊Q8—611no—
519C22⋊Q8—1221no—
520C22⋊Q8—1221no—
521C22⋊Q8C2×#692311yescharacteristic, complemented
522#121—611no—
523#121—611no—
524#121—611no—
525#121—1221no—
526#121—1221no—
527#121C2×#692311yescharacteristic
528C4×Q8—1222no—
529C4×Q8—2441no—
530C4×D4—1222no—
531C4×D4—2441no—
532#117—1222no—
533#117—1222no—
534#117—2441no—
535#117—2441no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42—1221no—
562#106—611no—
563#106—611no—
564#106—611no—
565#106C2×#692311yescharacteristic, complemented
566#103—611no—
567#103—611no—
568#103—611no—
569#103—1222no—
570#103—2441no—
571#103C2×#692311yescharacteristic, complemented
572#102—611no—
573#102—611no—
574#102—611no—
575#102—1222no—
576#102—2441no—
577#102C2×#692311yescharacteristic
578C22⋊C8—1221no—
579C22⋊C8—1221no—
580C4×C8—2441no—
581C4×C8—2441no—
582#95—611no—
583#95—611no—
584#95—1221no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590C24—611no—
591C24—1221no—
592C2×Q8—611no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8C22×#692311yescharacteristic
599C2×D4—21no—
600C2×D4—611no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—4881no—
610C2×D4—4881no—
611C2×D4C22×#692311yescharacteristic
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—4881no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4C22×#692311yescharacteristic
636SD16—41no—
637SD16—2441no—
638SD16—2441no—
639SD16—2441no—
640C2×C8—41no—
641C2×C8—611no—
642C2×C8—611no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—2441no—
654C2×C8—2441no—
655C2×C8—2441no—
656C2×C8C22×#692311yescharacteristic
657C2×C8C22×#692311yescharacteristic
658C4⋊C4—21no—
659C4⋊C4—612no—
660C4⋊C4—612no—
661C4⋊C4—611no—
662C4⋊C4—611no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—4881no—
675C4⋊C4—2442no—
676C4⋊C4—2442no—
677C4⋊C4C22×#692311yescharacteristic
678C4⋊C4C22×#692311yescharacteristic
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—4881no—
690C22⋊C4—2442no—
691C22⋊C4—2442no—
692C22⋊C4—2442no—
693C22⋊C4—2442no—
694C42—1221no—
695C42—1221no—
696C42—1221no—
697C42—1221no—
698C42—4881no—
699C42—2442no—
700C42—2442no—
701C42—2442no—
702C42—2442no—
703C23—21no—
704C23—611no—
705C23—611no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23—2441no—
717C23—2441no—
718C23—2441no—
719C23D4×#692311yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—1221no—
723Q8—1221no—
724Q8—2441no—
725Q8—2441no—
726D4—21no—
727D4—21no—
728D4—81no—
729D4—1221no—
730D4—1221no—
731D4—4881no—
732D4—4881no—
733D4—4881no—
734D4—2441no—
735D4—2441no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—612no—
747C2×C4—612no—
748C2×C4—611no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—4884no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4D4×#692311yescharacteristic
790C2×C4C23×#692311yescharacteristic
791C8—21no—
792C8—21no—
793C8—1221no—
794C8—1221no—
795C8—2441no—
796C8—2441no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—611no—
804C22—611no—
805C22—611no—
806C22—611no—
807C22—611no—
808C22—611no—
809C22—1221no—
810C22—1221no—
811C22—1221no—
812C22—4881no—
813C22—4881no—
814C22—4881no—
815C22—4881no—
816C22—2441no—
817C22—2441no—
818C22—2441no—
819C22—2441no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22C2×D4×#692311yescharacteristic
824C4—21no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—611no—
829C4—611no—
830C4—1222no—
831C4—1222no—
832C4—1221no—
833C4—4881no—
834C4—4881no—
835C4—2441no—
836C4—2441no—
837C4—2442no—
838C4—2442no—
839C4—2441no—
840C4—2441no—
841C4—2441no—
842C4#41×#692311yescharacteristic
843C4#1684082911yescharacteristic
844C2—41no—
845C2—81no—
846C2—611no—
847C2—611no—
848C2—611no—
849C2—611no—
850C2—4881no—
851C2—2441no—
852C2#2146234711yescharacteristic
853C2#135×#692311yescharacteristic
854C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#465#6923
hypocenterC61#23131
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. #21462345C2semidirect
3. #21461909C2semidirect
4. #21461908C2semidirect
5. #21461882C2semidirect
6. #21461881C2semidirect
7. #21461815C2semidirect
8. #21461812C2semidirect
10. #21461805C2semidirect
11. #103×#6923C2semidirect
12. #102×#6923C2semidirect
13. C8×C22⋊#6923C2semidirect
14. #21461505C2semidirect
56. #16839994C4semidirect
57. #16839993C4semidirect
58. #16839992C4semidirect
59. #16839991C4semidirect
60. #16839990C4semidirect
61. #16839989C4semidirect
62. #16839988C4semidirect
66. C61×#465C4semidirect
124. C22×#92418C2×C4semidirect
127. C2×C8×D61C2×C4semidirect
128. C2×C8×D61C2×C4semidirect
131. #14519757C2×C4semidirect
132. #14519756C2×C4semidirect
135. #14519753C2×C4semidirect
146. #14519709C2×C4semidirect
147. #14519708C2×C4semidirect
148. #14519708C2×C4semidirect
149. #14519702C2×C4semidirect
150. #14519701C2×C4semidirect
151. #14519700C2×C4semidirect
156. C22×C8×C61C2×C4semidirect
157. C22⋊Q8×C61C2×C4semidirect
159. #106×C61C2×C4semidirect
160. #103×C61C2×C4semidirect
458. #465#6923semidirect
494. C61#23131semidirect
515. C22×C8C2×#6923semidirect
521. C22⋊Q8C2×#6923semidirect
565. #106C2×#6923semidirect
571. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623462
#214623452
#214619092
#214619082
#214618822
#214618812
#214618152
#214618122
#214618072
#214618052
#103×#69232
#102×#69232
C8×C22⋊#69232
#214615052
#465×D612
#2313161