Finite Group Databasebeta

← #29697371

Subgroups — #29697371

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454476C211yesmaximal, characteristic, complemented
2#416×D61C211yesmaximal, characteristic
3#21454266C211yesmaximal, characteristic
4#21446524C211yesmaximal, characteristic, complemented
5#21446522C211yesmaximal, characteristic, complemented
6#21446468C211yesmaximal, characteristic, complemented
7#21446466C211yesmaximal, characteristic, complemented
8#21446096C211yesmaximal, characteristic, complemented
9#21445917C211yesmaximal, characteristic, complemented
10#21445854C211yesmaximal, characteristic, complemented
11#21445761C211yesmaximal, characteristic
12#21445657C211yesmaximal, characteristic, complemented
13#21445654C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#117×D61C2211yescharacteristic
20#16839822—21no—
21#16839822—21no—
22#16839818—21no—
23#16839814—21no—
24C2×#14519713C2211yescharacteristic, complemented
25#16839789C2211yescharacteristic, complemented
26C2×#14519705C2211yescharacteristic
27C2×#14519704C2211yescharacteristic
28C2×#14519703C2211yescharacteristic
29#16839759C2211yescharacteristic
30#16839758C2211yescharacteristic
31#16839757C411yescharacteristic, complemented
32#16839757C411yescharacteristic, complemented
33#16839756C2211yescharacteristic
34#16839755C411yescharacteristic, complemented
35#16839755C411yescharacteristic, complemented
36#103×D61C411yescharacteristic, complemented
37#103×D61C411yescharacteristic, complemented
38#102×D61C411yescharacteristic, complemented
39#102×D61C411yescharacteristic, complemented
40#16839730—21no—
41#16839730C2211yescharacteristic
42#16839728—21no—
43#16839728C2211yescharacteristic
44#16839725—21no—
45#16839725C2211yescharacteristic
46#16839725C2211yescharacteristic
47C2×#14519689—21no—
48C2×#14519689C2211yescharacteristic
49#16839720C2211yescharacteristic, complemented
50#16839717C2211yescharacteristic, complemented
51C2×C4×#92418C2211yescharacteristic, complemented
52C2×C8×Dic61C2211yescharacteristic, complemented
53C4×#11758198C2211yescharacteristic
54#16839526C2211yescharacteristic, complemented
55#16839526C2211yescharacteristic, complemented
56#16839523C2211yescharacteristic, complemented
57#16839522C2211yescharacteristic, complemented
58#16839521C2211yescharacteristic, complemented
59#16839516C2211yescharacteristic, complemented
60C2×#131×C61C2211yescharacteristic
61C2×#108×C61C2211yescharacteristic, complemented
62C61×#424C2211yescharacteristic, complemented
63C2×#104×C61C2211yescharacteristic
64C61×#416C2211yescharacteristic
65C61×#339C2211yescharacteristic, complemented
66C61×#336C2211yescharacteristic, complemented
67C2×#11758226C2×C411yescharacteristic
68C2×#11758222—21no—
69C2×#11758222C2311yescharacteristic
70C2×#11758224—21no—
71C2×#11758224C2×C411yescharacteristic
72#41×D61—22no—
73#41×D61—22no—
74#41×D61—41no—
75#41×D61—41no—
76C2×Q8×D61C2×C411yescharacteristic
77C2×D4×D61—21no—
78C2×D4×D61C2×C411yescharacteristic
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81#14519784—22no—
82#14519784—41no—
83C2×#11758194—21no—
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C22×#92418—21no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—41no—
90C2×C8×D61—41no—
91C2×C8×D61C2×C411yescharacteristic
92C2×C8×D61C2×C411yescharacteristic
93C2×C8×D61C2×C411yescharacteristic
94C2×C8×D61C2×C411yescharacteristic
95#14519736C2311yescharacteristic
96#14519735C2×C411yescharacteristic
97#14519735C2×C411yescharacteristic
98#14519734—21no—
99#14519733—21no—
100C4⋊C4×D61C2×C411yescharacteristic
101C4⋊C4×D61C2×C411yescharacteristic
102C2×#11758198—21no—
103C22⋊C4×D61—21no—
104C2×C4×Dic61C2311yescharacteristic
105C42×D61—21no—
106#14519713—41no—
107C4⋊#92418—21no—
108C4⋊#92418—21no—
109#14519705—41no—
110#14519704—22no—
111#14519703—41no—
112#14519702C2×C411yescharacteristic
113#14519702C2×C411yescharacteristic
114#14519701C2×C411yescharacteristic
115#14519701C2×C411yescharacteristic
116#14519700C2×C411yescharacteristic
117#14519700C2×C411yescharacteristic
118#14519699C2×C411yescharacteristic
119#14519699C2×C411yescharacteristic
120#14519698C2×C411yescharacteristic
121#14519698C2×C411yescharacteristic
122#14519697C2×C411yescharacteristic
123#14519697C2×C411yescharacteristic
124#14519689—21no—
125#14519689—21no—
126#14519689—21no—
127#14519689—21no—
128#14519689—21no—
129#14519689—21no—
130#14519689—21no—
131#14519689—21no—
132#14519689D411yescharacteristic
133#14519689D411yescharacteristic
134#14519689D411yescharacteristic
135#14519689D411yescharacteristic
136#14519687—21no—
137#14519687—21no—
138C4×#92418—41no—
139C8×Dic61—21no—
140C8×Dic61—21no—
141C8×Dic61—41no—
142#14519684—21no—
143C2×#41×C61C2311yescharacteristic
144#131×C61—22no—
145#131×C61—41no—
146C2×M16×C61—21no—
147C2×M16×C61C2311yescharacteristic
148C2×M16×C61C2311yescharacteristic
149C22×C8×C61—21no—
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152#117×C61C2311yescharacteristic
153C2×C42×C61C2311yescharacteristic
154#108×C61—41no—
155C4⋊C8×C61—21no—
156C4⋊C8×C61—21no—
157#104×C61—22no—
158#103×C61C2×C411yescharacteristic
159#103×C61C2×C411yescharacteristic
160#102×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C23×D61#4111yescharacteristic
164#41×C61—21no—
165#41×C61—21no—
166#41×C61#4112yes—
167#41×C61#4112yes—
168C2×Q8×C61C22×C411yescharacteristic
169C2×D4×C61—21no—
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C2×C22⋊D61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61#4111yescharacteristic
180#11758226—22no—
181#11758226—41no—
182Q8×D61—22no—
183Q8×D61—41no—
184#11758224—22no—
185#11758224—41no—
186#11758224—42no—
187#11758224—42no—
188D4×D61—22no—
189D4×D61—41no—
190D4×D61—42no—
191D4×D61—42no—
192#11758222—21no—
193#11758222—21no—
194#11758222—21no—
195#11758222—21no—
196#11758222—42no—
197#11758222—42no—
198C2×D244—21no—
199C2×D244C22×C411yescharacteristic
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61C22×C411yescharacteristic
212C2×C4×D61C22×C411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×Dic122—21no—
216C2×Dic122C22×C411yescharacteristic
217M16×C61—21no—
218M16×C61—21no—
219M16×C61—21no—
220M16×C61—21no—
221M16×C61—42no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—42no—
229C2×C8×C61C22×C411yescharacteristic
230C2×C8×C61C22×C411yescharacteristic
231C2×C8×C61C2×D411yescharacteristic
232C2×C8×C61C2×D411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C4⋊C4×C61C22×C411yescharacteristic
235C22⋊C4×C61—21no—
236C42×C61—21no—
237C42×C61—21no—
238C42×C61—21no—
239C22⋊Dic61—21no—
240#11758198—24no—
241#11758198—21no—
242#11758198—21no—
243C4⋊Dic61C22×C411yescharacteristic
244C4⋊Dic61C22×C411yescharacteristic
245#11758196—21no—
246#11758196—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252#11758194—21no—
253#11758194—21no—
254#11758194—21no—
255#11758194—21no—
256#11758194—42no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—42no—
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266C2×#92418C2×D411yescharacteristic
267C2×#92418C2×D411yescharacteristic
268C8×D61—41no—
269C8×D61—41no—
270C8×D61—41no—
271C8×D61—41no—
272C23×C61—21no—
273C23×C61C2×#4111yescharacteristic
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—22no—
277C22×D61—21no—
278C22×D61—41no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—81no—
282C22×D61C4×D411yescharacteristic
283C22×D61C4×D411yescharacteristic
284Q8×C61—21no—
285Q8×C61#11712yes—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—21no—
289D4×C61#11712yes—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61C23×C411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C22⋊D61—42no—
305C22⋊D61—42no—
306C22⋊D61—41no—
307C22⋊D61—41no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—42no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61C4×D411yescharacteristic
318C2×Dic61C4×D411yescharacteristic
319D244—21no—
320D244—21no—
321D244—42no—
322C4×D61—21no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—21no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—42no—
331C4×D61—42no—
332C4×D61—42no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—81no—
336Dic122—21no—
337Dic122—21no—
338Dic122—42no—
339C8×C61—21no—
340C8×C61—21no—
341C8×C61—21no—
342C8×C61—21no—
343C8×C61—41no—
344C8×C61—41no—
345#92418—21no—
346#92418—21no—
347#92418—21no—
348#92418—21no—
349#92418—41no—
350#92418—41no—
351#22587—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—22no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61C2×C4×D411yescharacteristic
358C22×C61#55111yescharacteristic
359C22×C61#55111yescharacteristic
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—84no—
371C2×D61#44312yes—
372C4×C61—22no—
373C4×C61—42no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61C2×#11711yescharacteristic
377C4×C61#51811yescharacteristic
378C4×C61#54611yescharacteristic
379C4×C61#54611yescharacteristic
380Dic61—21no—
381Dic61—21no—
382Dic61—42no—
383Dic61—41no—
384Dic61—41no—
385Dic61—41no—
386#2924—611no—
387C2×#416—611no—
388#2880—611no—
389#1937—611no—
390#1937—611no—
391#1929—611no—
392#1929—611no—
393#1866—611no—
394#1866D6111yescharacteristic, complemented
395#1826—611no—
396#1810—611no—
397#1789—611no—
398#1764—611no—
399#1764—611no—
400C8×C22⋊C4—611no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—42no—
404C2×C61#234211yescharacteristic
405C2×C61C2×#44311yescharacteristic
406C2×C61#295711yescharacteristic
407D61—22no—
408D61—41no—
409D61—81no—
410C22×#41—611no—
411C2×#131—611no—
412C2×#131C2×D6111yescharacteristic
413C23×C8—611no—
414C2×#117—611no—
415#433—1221no—
416#433—1221no—
417#432—1221no—
418#431—1221no—
419C2×#108—611no—
420C2×#108C2×D6111yescharacteristic, complemented
421#424—611no—
422#424C2×D6111yescharacteristic, complemented
423C2×#104—611no—
424C2×#104—611no—
425C2×#104—611no—
426C2×#104C2×D6111yescharacteristic
427#416—611no—
428#416—611no—
429#416—611no—
430#416—611no—
431#416—611no—
432#416—611no—
433#416—611no—
434#416C2×D6111yescharacteristic
435C2×#103—611no—
436C2×#103—611no—
437C2×#102—611no—
438C2×#102—611no—
439#408—611no—
440#408—611no—
441#408—1221no—
442#408—1221no—
443#407—611no—
444#407—611no—
445#407—1221no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—1221no—
448#405—611no—
449#405—611no—
450C2×C4×C8—611no—
451C2×C4×C8—611no—
452C4×C22⋊C4—611no—
453#341—611no—
454#341—611no—
455#339—611no—
456#339—611no—
457#339—611no—
458#339C2×D6111yescharacteristic, complemented
459#336—611no—
460#336C2×D6111yescharacteristic, complemented
461C61#2258711yescharacteristic, complemented, Sylow
462C2×#41—611no—
463C2×#41—611no—
464C2×#41—611no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1222no—
468C2×#41—1222no—
469C2×#41—2441no—
470C2×#41—2441no—
471C2×#41C22×D6111yescharacteristic
472C22×Q8—611no—
473C22×D4—611no—
474C22×D4—1221no—
475C23×C4—611no—
476C23×C4—1221no—
477#131—22no—
478#131—41no—
479#131—1222no—
480#131—2441no—
481C2×M16—21no—
482C2×M16—611no—
483C2×M16—611no—
484C2×M16—1221no—
485C2×M16C22×D6111yescharacteristic
486C2×M16C22×D6111yescharacteristic
487C22×C8—21no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—1221no—
495C22×C8—2441no—
496C22×C8—2441no—
497C22×C8C22×D6111yescharacteristic
498C22×C8C22×D6111yescharacteristic
499#117—611no—
500#117—611no—
501#117—611no—
502#117—1221no—
503#117—1221no—
504#117C22×D6111yescharacteristic
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C42—611no—
510C2×C42—1221no—
511C2×C42C22×D6111yescharacteristic
512#108—41no—
513#108—2441no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—1221no—
517C4⋊C8—1221no—
518#104—22no—
519#104—1222no—
520#104—2441no—
521#104—2441no—
522#103—611no—
523#103—611no—
524#103—611no—
525#103—611no—
526#103—611no—
527#103—611no—
528#103C4×D6111yescharacteristic
529#103C4×D6111yescharacteristic
530#102—611no—
531#102—611no—
532#102—611no—
533#102—611no—
534#102—611no—
535#102—611no—
536#102C4×D6111yescharacteristic
537#102C4×D6111yescharacteristic
538C22⋊C8—611no—
539C22⋊C8—611no—
540C22⋊C8—611no—
541C22⋊C8—611no—
542C22⋊C8—1221no—
543C22⋊C8—1221no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550#97—1221no—
551#97—1221no—
552C4×C8—1221no—
553C4×C8—1221no—
554C4×C8—2441no—
555C4×C8—2441no—
556#95—1221no—
557C24—611no—
558C24—1221no—
559#41—21no—
560#41—21no—
561#41—1222no—
562#41—1222no—
563#41—1221no—
564#41—1221no—
565#41—1221no—
566#41—1221no—
567#41—2442no—
568#41—2442no—
569#41—2441no—
570#41—2442no—
571#41—2442no—
572#41—2441no—
573#41#1175822412yes—
574#41#1175822612yes—
575C2×Q8—611no—
576C2×Q8—1221no—
577C2×Q8—1222no—
578C2×Q8—2441no—
579C2×Q8C2×C4×D6111yescharacteristic
580C2×D4—21no—
581C2×D4—611no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—2441no—
588C2×D4—2442no—
589C2×D4—2442no—
590C2×D4C2×C4×D6111yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4C23×D6111yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—42no—
617M16—1221no—
618M16—1221no—
619M16—1221no—
620M16—1221no—
621M16—2442no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8—611no—
630C2×C8—611no—
631C2×C8—611no—
632C2×C8—611no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—2441no—
640C2×C8—2441no—
641C2×C8—2441no—
642C2×C8—2441no—
643C2×C8—2442no—
644C2×C8C2×C4×D6111yescharacteristic
645C2×C8C2×C4×D6111yescharacteristic
646C2×C8D4×D6111yescharacteristic
647C2×C8D4×D6111yescharacteristic
648C4⋊C4—611no—
649C4⋊C4—611no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4C2×C4×D6111yescharacteristic
653C4⋊C4C2×C4×D6111yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1224no—
658C22⋊C4—1221no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—1221no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C23—21no—
668C23—611no—
669C23—611no—
670C23—1222no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—4881no—
675C23—2441no—
676C23—2442no—
677C23—2442no—
678C23#41×D6111yescharacteristic
679Q8—21no—
680Q8—1221no—
681Q8—1221no—
682Q8—2442no—
683Q8#1451973512yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—1221no—
688D4—1221no—
689D4—2442no—
690D4—2442no—
691D4—2442no—
692D4—2441no—
693D4—2441no—
694D4#1451973512yes—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1222no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—4881no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4C22×C4×D6111yescharacteristic
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4C2×#1175822411yescharacteristic
731C2×C4C2×#1175822611yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—1221no—
741C8—1221no—
742C8—1221no—
743C8—1221no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—21no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—612no—
752C22—1221no—
753C22—1221no—
754C22—1221no—
755C22—1221no—
756C22—1221no—
757C22—4884no—
758C22—2442no—
759C22—2442no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22C4×D4×D6111yescharacteristic
764C22#1684043511yescharacteristic
765C22#1684043911yescharacteristic
766C4—22no—
767C4—42no—
768C4—41no—
769C4—41no—
770C4—1221no—
771C4—1221no—
772C4—2442no—
773C4—2441no—
774C4—2441no—
775C4—2441no—
776C4C2×#1451973511yescharacteristic
777C4#1684023411yescharacteristic
778C4#1684039911yescharacteristic
779C4#1684040311yescharacteristic
780C2—21no—
781C2—21no—
782C2—42no—
783C2—1222no—
784C2—4881no—
785C2—2441no—
786C2#2144866611yescharacteristic
787C2#443×D6111yescharacteristic
788C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1866C2
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1866D61
hypocenterC61#22587
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
1. #21454476C2semidirect
4. #21446524C2semidirect
5. #21446522C2semidirect
6. #21446468C2semidirect
7. #21446466C2semidirect
8. #21446096C2semidirect
9. #21445917C2semidirect
10. #21445854C2semidirect
12. #21445657C2semidirect
13. #21445654C2semidirect
14. #21445589C2semidirect
15. C61×#1866C2semidirect
24. C2×#14519713C22semidirect
25. #16839789C22semidirect
31. #16839757C4semidirect
32. #16839757C4semidirect
34. #16839755C4semidirect
35. #16839755C4semidirect
36. #103×D61C4semidirect
37. #103×D61C4semidirect
38. #102×D61C4semidirect
39. #102×D61C4semidirect
49. #16839720C22semidirect
50. #16839717C22semidirect
51. C2×C4×#92418C22semidirect
52. C2×C8×Dic61C22semidirect
54. #16839526C22semidirect
55. #16839526C22semidirect
56. #16839523C22semidirect
57. #16839522C22semidirect
58. #16839521C22semidirect
59. #16839516C22semidirect
61. C2×#108×C61C22semidirect
62. C61×#424C22semidirect
65. C61×#339C22semidirect
66. C61×#336C22semidirect
394. #1866D61semidirect
420. C2×#108C2×D61semidirect
422. #424C2×D61semidirect
458. #339C2×D61semidirect
460. #336C2×D61semidirect
461. C61#22587semidirect

Maximal subgroups

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

subgroupindex
#214544762
#416×D612
#214542662
#214465242
#214465222
#214464682
#214464662
#214460962
#214459172
#214458542
#214457612
#214456572
#214456542
#214455892
C61×#18662
#2258761