Finite Group Databasebeta

← #30620612

Subgroups — #30620612

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462328C211yesmaximal, characteristic, complemented
2#21462324C211yesmaximal, characteristic
3#21461911C211yesmaximal, characteristic, complemented
4#21461909C211yesmaximal, characteristic, complemented
5#21461897C211yesmaximal, characteristic, complemented
6#21461896C211yesmaximal, characteristic, complemented
7#21461785C211yesmaximal, characteristic, complemented
8#21461783C211yesmaximal, characteristic, complemented
9#21461722C211yesmaximal, characteristic, complemented
10#21461697C211yesmaximal, characteristic, complemented
11#21461659C211yesmaximal, characteristic
12#21461592C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#417×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24D61⋊(C22⋊C8)C2211yescharacteristic
25C2×#14519831C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27#16840714—21no—
28#16840714—21no—
29#16840714C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840711—21no—
34#16840711—21no—
35#16840704—21no—
36#16840704—21no—
37#16840704C2211yescharacteristic
38#16840704C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4×C22⋊#6923—21no—
42C4×C22⋊#6923—21no—
43C4×C22⋊#6923C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×#41×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54C2×C4⋊C4×D61C2211yescharacteristic
55#16839764C411yescharacteristic, complemented
56#16839763C411yescharacteristic, complemented
57#16839762C411yescharacteristic, complemented
58#16839762C411yescharacteristic, complemented
59#16839761C411yescharacteristic, complemented
60#16839760C411yescharacteristic, complemented
61#16839760C411yescharacteristic, complemented
62#103×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#417C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71Q8×#6923—41no—
72Q8×#6923—41no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923D411yescharacteristic
88C2×C22⋊#6923D411yescharacteristic
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923C2311yescharacteristic
94C2×C4×#6923C2311yescharacteristic
95#14519846—41no—
96#14519845—41no—
97#14519840—22no—
98#14519840—22no—
99#14519839—41no—
100#14519839—41no—
101#14519834—21no—
102C22⋊#92420—21no—
103#14519831—41no—
104C8×#6923—41no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4D411yescharacteristic
112(C2×#6923)⋊C4D411yescharacteristic
113C2×#11758226C2×C411yescharacteristic
114C2×#11758222—21no—
115C2×#11758222C2×C411yescharacteristic
116C2×#11758224—21no—
117C2×#11758224C2×C411yescharacteristic
118#41×D61—22no—
119#41×D61—22no—
120#41×D61—41no—
121#41×D61—41no—
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61—21no—
124C2×D4×D61C2311yescharacteristic
125C22×C4×D61—21no—
126C22×C4×D61—21no—
127C22×C4×D61C2311yescharacteristic
128C2×#11758194C2×C411yescharacteristic
129C2×#11758189C2×C411yescharacteristic
130C2×#11758189C2×C411yescharacteristic
131M16×D61—41no—
132M16×D61—41no—
133C2×C8×D61C2311yescharacteristic
134C2×C8×D61C2311yescharacteristic
135C2×C4⋊Dic61C2×C411yescharacteristic
136C2×#11758196—21no—
137C4⋊C4×D61—21no—
138C4⋊C4×D61—21no—
139C4⋊C4×D61C2×C411yescharacteristic
140C4⋊C4×D61C2×C411yescharacteristic
141C4⋊C4×D61C2311yescharacteristic
142C4⋊C4×D61C2311yescharacteristic
143#14519702C2×C411yescharacteristic
144#14519702C2×C411yescharacteristic
145#14519701C2×C411yescharacteristic
146#14519701C2×C411yescharacteristic
147#14519700C2×C411yescharacteristic
148#14519700C2×C411yescharacteristic
149#14519699C2×C411yescharacteristic
150#14519699C2×C411yescharacteristic
151#14519698C2×C411yescharacteristic
152#14519698C2×C411yescharacteristic
153#14519697C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×#41×C61C2×C411yescharacteristic
156C2×M16×C61C2×C411yescharacteristic
157C2×C4⋊C4×C61C2×C411yescharacteristic
158#103×C61C2×C411yescharacteristic
159#103×C61C2×C411yescharacteristic
160#102×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C23×D61C2×D411yescharacteristic
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172#41×C61—22no—
173#41×C61—41no—
174C2×Q8×C61C22×C411yescharacteristic
175C2×D4×C61—21no—
176C2×D4×C61C22×C411yescharacteristic
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61C22×C411yescharacteristic
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61#4111yescharacteristic
186#11758226—22no—
187#11758226—41no—
188Q8×D61—21no—
189Q8×D61—21no—
190Q8×D61#4112yes—
191Q8×D61#4112yes—
192#11758224—22no—
193#11758224—41no—
194#11758224—42no—
195#11758224—42no—
196D4×D61—21no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61—21no—
200D4×D61—42no—
201D4×D61—42no—
202#11758222—22no—
203#11758222—42no—
204#11758222—42no—
205#11758222—41no—
206C2×D244—21no—
207C2×D244C22×C411yescharacteristic
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—81no—
222C2×C4×D61—81no—
223C2×C4×D61C22×C411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61#4111yescharacteristic
226C2×C4×D61C2411yescharacteristic
227C2×Dic122—21no—
228C2×Dic122C22×C411yescharacteristic
229C22⋊#6923—22no—
230C22⋊#6923—41no—
231C22⋊#6923—42no—
232C22⋊#6923—42no—
233C22⋊#6923—42no—
234C22⋊#6923—81no—
235C22⋊#6923—81no—
236C22⋊#6923—81no—
237C2×#92420—21no—
238C2×#92420—21no—
239C4⋊#6923—21no—
240C4⋊#6923—21no—
241C4⋊#6923—21no—
242C4⋊#6923—21no—
243C4⋊#6923—21no—
244C4⋊#6923—21no—
245C4⋊#6923—21no—
246C4⋊#6923—21no—
247C4⋊#6923—42no—
248C4⋊#6923—42no—
249C4⋊#6923—81no—
250C4⋊#6923—81no—
251C4×#6923—21no—
252C4×#6923—21no—
253C4×#6923—21no—
254C4×#6923—21no—
255C4×#6923—42no—
256C4×#6923—42no—
257C4×#6923—81no—
258C4×#6923—81no—
259D61⋊C8—21no—
260D61⋊C8—21no—
261D61⋊C8—21no—
262D61⋊C8—21no—
263M16×C61—41no—
264C2×C8×C61C22×C411yescharacteristic
265C2×C8×C61C22×C411yescharacteristic
266C4⋊C4×C61—21no—
267C4⋊C4×C61C22×C411yescharacteristic
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊Dic61—21no—
270C4⋊Dic61C22×C411yescharacteristic
271C4⋊Dic61C22×C411yescharacteristic
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758194—41no—
277C2×#92418C22×C411yescharacteristic
278C2×#92418C22×C411yescharacteristic
279#11758189—41no—
280#11758189—41no—
281C8×D61—21no—
282C8×D61—21no—
283C8×D61—21no—
284C8×D61—21no—
285C23×C61—21no—
286C23×C61C4×D411yescharacteristic
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61C4×D411yescharacteristic
301C22×D61C22×D411yescharacteristic
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
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#13712yes—
326Q8×C61—21no—
327Q8×C61#11712yes—
328D4×C61—21no—
329D4×C61—21no—
330D4×C61—42no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—42no—
337C2×C4×C61—81no—
338C2×C4×C61C4×D411yescharacteristic
339C2×C4×C61C23×C411yescharacteristic
340C22⋊D61—42no—
341C22⋊D61—42no—
342C22⋊D61—41no—
343C22⋊D61—41no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—42no—
350C2×Dic61—81no—
351C2×Dic61C4×D411yescharacteristic
352C2×Dic61C2×#4111yescharacteristic
353D244—21no—
354D244—21no—
355D244—42no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—42no—
365C4×D61—42no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—81no—
371C4×D61—81no—
372C4×D61C2×#4111yescharacteristic
373C4×D61C2×#4111yescharacteristic
374C4×D61H(5,𝔽2)11yescharacteristic
375C4×D61H(5,𝔽2)11yescharacteristic
376Dic122—21no—
377Dic122—22no—
378Dic122—22no—
379Dic122#11712yes—
380#92420—41no—
381#92420—41no—
382C8×C61—21no—
383C8×C61—21no—
384#92418—21no—
385#92418—21no—
386#22579—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61C2×C4×D411yescharacteristic
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—81no—
405C2×D61—81no—
406C2×D61—81no—
407C2×D61—81no—
408C2×D61#54611yescharacteristic
409C2×D61#54611yescharacteristic
410C2×D61C2×#13711yescharacteristic
411C2×D61#57511yescharacteristic
412C2×D61#57611yescharacteristic
413C2×D61#57711yescharacteristic
414#6923—22no—
415#6923—41no—
416#6923—41no—
417#6923—41no—
418#6923—81no—
419#6923—81no—
420#6923—81no—
421#6923—81no—
422C4×C61—22no—
423C4×C61—21no—
424C4×C61—41no—
425C4×C61—41no—
426C4×C61C2×#11711yescharacteristic
427C4×C61#51811yescharacteristic
428Dic61—22no—
429Dic61—21no—
430Dic61—41no—
431Dic61—41no—
432Dic61#55111yescharacteristic
433Dic61#55111yescharacteristic
434C2×#417—611no—
435#2345—611no—
436#2341—611no—
437#1936—611no—
438#1934—611no—
439#1926—611no—
440#1925—611no—
441#1865—611no—
442#1863—611no—
443#1823—611no—
444#1809—611no—
445#1788—611no—
446#1763—611no—
447C4×#103—611no—
448#1753—611no—
449C2×C61—41no—
450C2×C61—81no—
451C2×C61#234211yescharacteristic
452C2×C61C4×#13711yescharacteristic
453C2×C61#294611yescharacteristic
454D61—41no—
455D61—81no—
456D61#330911yescharacteristic
457D61#331611yescharacteristic
458D61#332611yescharacteristic
459D61#333311yescharacteristic
460C22×#41—611no—
461C22×M16—611no—
462C2×C4×Q8—611no—
463C2×C4×Q8—611no—
464C22×C4⋊C4—611no—
465C2×#107—611no—
466C2×#106—611no—
467#417—611no—
468#417—611no—
469#417—611no—
470#417—611no—
471#417—611no—
472#417—611no—
473#417—611no—
474#417#692311yescharacteristic, complemented
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×C22⋊C8—611no—
484C2×#97—611no—
485C2×C4×C8—611no—
486#390—611no—
487#390—611no—
488#390—1221no—
489#390—1221no—
490#389—611no—
491#389—611no—
492#387—1221no—
493#387—1221no—
494#380—611no—
495#380—611no—
496#380—1221no—
497#380—1221no—
498C4×C4⋊C4—611no—
499C4×C4⋊C4—611no—
500C4×C22⋊C4—611no—
501C4×C22⋊C4—1221no—
502C4×C22⋊C4—1221no—
503#340—611no—
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509#336—611no—
510#336—611no—
511C61#2257911yescharacteristic, complemented, Sylow
512C2×#41—611no—
513C2×#41—611no—
514C2×#41—611no—
515C2×#41—1221no—
516C2×#41—1221no—
517C2×#41—1222no—
518C2×#41—1222no—
519C2×#41—2441no—
520C2×#41—2441no—
521C2×#41C2×#692311yescharacteristic
522C22×Q8—611no—
523C22×D4—611no—
524C22×D4—1221no—
525C23×C4—611no—
526C23×C4—1221no—
527C23×C4—1221no—
528C2×M16—611no—
529C2×M16—611no—
530C2×M16—611no—
531C2×M16—2441no—
532C2×M16—2441no—
533C2×M16C2×#692311yescharacteristic
534C22×C8—611no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—611no—
538C4×Q8—1222no—
539C4×Q8—1222no—
540C4×Q8—2441no—
541C4×Q8—2441no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4C2×#692311yescharacteristic
559C2×C22⋊C4—611no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—1221no—
570C2×C42—1221no—
571C2×C42—1221no—
572C2×C42—1221no—
573#107—2441no—
574#106—2441no—
575#103—611no—
576#103—611no—
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#103—1222no—
582#103—1222no—
583#103C2×#692311yescharacteristic
584#103C2×#692311yescharacteristic
585#102—611no—
586#102—611no—
587#102—611no—
588#102—611no—
589#102—611no—
590#102—611no—
591#102—2441no—
592#102—2441no—
593#102C2×#692311yescharacteristic
594#102C2×#692311yescharacteristic
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597#97—2441no—
598C4×C8—2441no—
599#95—611no—
600#95—611no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607C24—611no—
608C24—1221no—
609#41—22no—
610#41—41no—
611#41—1222no—
612#41—1222no—
613#41—1222no—
614#41—2441no—
615#41—2442no—
616#41—2442no—
617#41—2441no—
618#41—2442no—
619#41—2442no—
620#41—2441no—
621C2×Q8—612no—
622C2×Q8—612no—
623C2×Q8—611no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8C22×#692311yescharacteristic
628C2×D4—21no—
629C2×D4—611no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—2442no—
639C2×D4—2442no—
640C2×D4C22×#692311yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—4881no—
670C22×C4—4881no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4C22×#692311yescharacteristic
674M16—41no—
675M16—2441no—
676M16—2441no—
677M16—2441no—
678C2×C8—611no—
679C2×C8—611no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8C22×#692311yescharacteristic
691C2×C8C22×#692311yescharacteristic
692C4⋊C4—21no—
693C4⋊C4—611no—
694C4⋊C4—611no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—4881no—
709C4⋊C4—4881no—
710C4⋊C4—2442no—
711C4⋊C4—2442no—
712C4⋊C4C22×#692311yescharacteristic
713C4⋊C4C22×#692311yescharacteristic
714C22⋊C4—1222no—
715C22⋊C4—4881no—
716C22⋊C4—4881no—
717C22⋊C4—4881no—
718C22⋊C4—2442no—
719C22⋊C4—2441no—
720C22⋊C4—2442no—
721C22⋊C4—2442no—
722C42—1221no—
723C42—1221no—
724C42—1221no—
725C42—1221no—
726C42—4881no—
727C42—4881no—
728C42—2442no—
729C42—2442no—
730C23—21no—
731C23—611no—
732C23—611no—
733C23—1221no—
734C23—1221no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23D4×#692311yescharacteristic
747Q8—21no—
748Q8—612no—
749Q8—1222no—
750Q8—1222no—
751Q8—1221no—
752Q8#1451985612yes—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—1221no—
757D4—1221no—
758D4—2442no—
759D4—2441no—
760D4—2441no—
761D4—2442no—
762D4—2442no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—42no—
769C2×C4—81no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—612no—
776C2×C4—611no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
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—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—4881no—
802C2×C4—4881no—
803C2×C4—4881no—
804C2×C4—2442no—
805C2×C4—2442no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2442no—
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×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4D4×#692311yescharacteristic
824C2×C4C23×#692311yescharacteristic
825C8—21no—
826C8—21no—
827C8—1221no—
828C8—1221no—
829C8—2441no—
830C8—2441no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—611no—
838C22—611no—
839C22—611no—
840C22—611no—
841C22—611no—
842C22—611no—
843C22—1221no—
844C22—1221no—
845C22—1221no—
846C22—4881no—
847C22—4881no—
848C22—4881no—
849C22—4881no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22C2×D4×#692311yescharacteristic
858C4—21no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—611no—
863C4—611no—
864C4—1222no—
865C4—1221no—
866C4—1222no—
867C4—4881no—
868C4—4881no—
869C4—4881no—
870C4—4881no—
871C4—2441no—
872C4—2441no—
873C4—2441no—
874C4—2441no—
875C4—2441no—
876C4C2×#1451985611yescharacteristic
877C4#1684082911yescharacteristic
878C2—41no—
879C2—81no—
880C2—611no—
881C2—611no—
882C2—611no—
883C2—611no—
884C2—4881no—
885C2—2441no—
886C2#2146232511yescharacteristic
887C2#137×#692311yescharacteristic
888C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#417C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#417#6923
hypocenterC61#22579
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #21462328C2semidirect
3. #21461911C2semidirect
4. #21461909C2semidirect
5. #21461897C2semidirect
6. #21461896C2semidirect
7. #21461785C2semidirect
8. #21461783C2semidirect
9. #21461722C2semidirect
10. #21461697C2semidirect
12. #21461592C2semidirect
13. #103×#6923C2semidirect
14. #21461559C2semidirect
55. #16839764C4semidirect
56. #16839763C4semidirect
57. #16839762C4semidirect
58. #16839762C4semidirect
59. #16839761C4semidirect
60. #16839760C4semidirect
61. #16839760C4semidirect
66. C61×#417C4semidirect
474. #417#6923semidirect
511. C61#22579semidirect

Maximal subgroups

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

subgroupindex
#214623282
#214623242
#214619112
#214619092
#214618972
#214618962
#214617852
#214617832
#214617222
#214616972
#214616592
#214615922
#103×#69232
#214615592
#417×D612
#2257961