Finite Group Databasebeta

← #29697388

Subgroups — #29697388

Order 15616.

888 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#21454479C211yesmaximal, characteristic, complemented
2#21454338C211yesmaximal, characteristic
3#21454268C211yesmaximal, characteristic
4#21446527C211yesmaximal, characteristic, complemented
5#21446520C211yesmaximal, characteristic, complemented
6#21446470C211yesmaximal, characteristic, complemented
7#21446470C211yesmaximal, characteristic, complemented
8#21446092C211yesmaximal, characteristic, complemented
9#21446092C211yesmaximal, characteristic, complemented
10#21445919C211yesmaximal, characteristic, complemented
11#21445859C211yesmaximal, characteristic, complemented
12#21445664C211yesmaximal, characteristic, complemented
13#21445657C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#1789C211yesmaximal, characteristic
16C2×#14519784C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839820—21no—
21#16839820—21no—
22#16839816—21no—
23#16839812—21no—
24C2×#14519712C2211yescharacteristic, complemented
25C2×#14519712C2211yescharacteristic, complemented
26#16839790C2211yescharacteristic, complemented
27#16839790C2211yescharacteristic, complemented
28#16839771C411yescharacteristic, complemented
29#16839771C411yescharacteristic, complemented
30#16839767C411yescharacteristic, complemented
31#16839767C411yescharacteristic, complemented
32#16839763C411yescharacteristic, complemented
33#16839763C411yescharacteristic, complemented
34#16839763C411yescharacteristic, complemented
35#16839763C411yescharacteristic, complemented
36#16839758C2211yescharacteristic
37#16839758C2211yescharacteristic
38#16839758C2211yescharacteristic
39#16839758C2211yescharacteristic
40#16839729—21no—
41#16839729—21no—
42#16839729C2211yescharacteristic
43#16839729C2211yescharacteristic
44#16839726—21no—
45#16839726C2211yescharacteristic
46C2×C22⋊#92418—21no—
47C2×C22⋊#92418C2211yescharacteristic
48#16839720C2211yescharacteristic, complemented
49#16839720C2211yescharacteristic, complemented
50C2×#14519688C2211yescharacteristic, complemented
51C2×C4×#92418C2211yescharacteristic, complemented
52#16839526C2211yescharacteristic, complemented
53#16839526C2211yescharacteristic, complemented
54#16839522C2211yescharacteristic, complemented
55#16839522C2211yescharacteristic, complemented
56#16839522C2211yescharacteristic, complemented
57#16839522C2211yescharacteristic, complemented
58#16839517C2211yescharacteristic, complemented
59#16839517C2211yescharacteristic, complemented
60C22×#41×C61C2211yescharacteristic
61C2×#104×C61C2211yescharacteristic
62C2×#104×C61C2211yescharacteristic
63C2×#104×C61C2211yescharacteristic
64C2×#104×C61C2211yescharacteristic
65C61×#407C2211yescharacteristic
66C4×C22⋊C4×C61C2211yescharacteristic
67#14519784—22no—
68#14519784—22no—
69#14519784—41no—
70#14519784—41no—
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194—41no—
74C2×#11758194—41no—
75C2×#11758194C2×C411yescharacteristic
76C2×#11758194C2×C411yescharacteristic
77C2×#11758194C2×C411yescharacteristic
78C2×#11758194C2×C411yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C22×#92418—21no—
82C22×#92418—21no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87#14519736—21no—
88#14519736—21no—
89#14519736C2×C411yescharacteristic
90#14519736C2×C411yescharacteristic
91#14519736C2311yescharacteristic
92#14519736C2311yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61—21no—
96C2×C4×Dic61—21no—
97#14519712—41no—
98#14519712—41no—
99#14519706—21no—
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519701C2×C411yescharacteristic
104#14519701C2×C411yescharacteristic
105#14519701C2×C411yescharacteristic
106#14519701C2×C411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519701C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519701C2×C411yescharacteristic
111#14519698C2×C411yescharacteristic
112#14519698C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115#14519698C2×C411yescharacteristic
116#14519698C2×C411yescharacteristic
117#14519698C2×C411yescharacteristic
118#14519698C2×C411yescharacteristic
119C22⋊#92418—21no—
120C22⋊#92418—21no—
121C22⋊#92418—21no—
122C22⋊#92418—21no—
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125C22⋊#92418D411yescharacteristic
126C22⋊#92418D411yescharacteristic
127C22⋊#92418D411yescharacteristic
128C22⋊#92418D411yescharacteristic
129#14519688—41no—
130#14519687—21no—
131#14519687—21no—
132C4×#92418—41no—
133C8×Dic61—21no—
134C8×Dic61—21no—
135C2×#41×C61—21no—
136C2×#41×C61—21no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—41no—
140C2×#41×C61—41no—
141C2×#41×C61C2×C411yescharacteristic
142C2×#41×C61C2×C411yescharacteristic
143C2×#41×C61C2311yescharacteristic
144C2×#41×C61C2311yescharacteristic
145C22×Q8×C61C2×C411yescharacteristic
146C22×D4×C61—21no—
147C22×D4×C61C2×C411yescharacteristic
148C23×C4×C61—21no—
149C23×C4×C61C2311yescharacteristic
150C2×M16×C61C2311yescharacteristic
151C2×M16×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C2×C42×C61C2311yescharacteristic
155#104×C61—22no—
156#104×C61—22no—
157#104×C61—41no—
158#104×C61—41no—
159C22⋊C8×C61—21no—
160C22⋊C8×C61—21no—
161#95×C61—21no—
162C24×C61—21no—
163C24×C61#4111yescharacteristic
164#41×C61—21no—
165#41×C61—21no—
166#41×C61—22no—
167#41×C61—22no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—42no—
173#41×C61—42no—
174#41×C61—41no—
175#41×C61—41no—
176#41×C61—42no—
177#41×C61—42no—
178#41×C61#4112yes—
179#41×C61#4112yes—
180C2×Q8×C61—21no—
181C2×Q8×C61—22no—
182C2×Q8×C61—41no—
183C2×Q8×C61C22×C411yescharacteristic
184C2×Q8×C61C22×C411yescharacteristic
185C2×D4×C61—21no—
186C2×D4×C61—22no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—41no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61C22×C411yescharacteristic
195C2×D4×C61C22×C411yescharacteristic
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61#4111yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C22×Dic61—21no—
216C22×Dic61—21no—
217M16×C61—21no—
218M16×C61—21no—
219M16×C61—21no—
220M16×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C22⋊C4×C61—42no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C22⋊Dic61—21no—
229C22⋊Dic61—21no—
230C22⋊Dic61—21no—
231C22⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61C22×C411yescharacteristic
235C4⋊Dic61C22×C411yescharacteristic
236C4⋊Dic61C22×C411yescharacteristic
237C4⋊Dic61C22×C411yescharacteristic
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242#11758194—21no—
243#11758194—21no—
244#11758194—21no—
245#11758194—21no—
246#11758194—41no—
247#11758194—41no—
248#11758194—41no—
249#11758194—41no—
250#11758194—42no—
251#11758194—42no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—42no—
263C2×#92418—42no—
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266C2×#92418C22×C411yescharacteristic
267C2×#92418C22×C411yescharacteristic
268C2×#92418C2×D411yescharacteristic
269C2×#92418C2×D411yescharacteristic
270C2×#92418C2×D411yescharacteristic
271C2×#92418C2×D411yescharacteristic
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—81no—
281C23×C61C4×D411yescharacteristic
282C23×C61C4×D411yescharacteristic
283C23×C61C2×#4111yescharacteristic
284Q8×C61—21no—
285Q8×C61—21no—
286Q8×C61—21no—
287Q8×C61—42no—
288Q8×C61#11712yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61#11712yes—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—42no—
338C2×Dic61—81no—
339C8×C61—41no—
340C8×C61—41no—
341#92418—21no—
342#92418—21no—
343#92418—21no—
344#92418—21no—
345#92418—21no—
346#92418—21no—
347#92418—21no—
348#92418—21no—
349#92418—41no—
350#92418—41no—
351#22588—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—22no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—84no—
369C22×C61C2×C4×D411yescharacteristic
370C22×C61#55111yescharacteristic
371C22×C61#55111yescharacteristic
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—22no—
375C4×C61—42no—
376C4×C61—41no—
377C4×C61—81no—
378C4×C61C2×#11711yescharacteristic
379C4×C61#51811yescharacteristic
380C4×C61#54611yescharacteristic
381C4×C61#54611yescharacteristic
382Dic61—41no—
383Dic61—41no—
384Dic61—41no—
385Dic61—41no—
386#2924—611no—
387#2896—611no—
388#2880—611no—
389#1938—611no—
390#1937—611no—
391#1929—611no—
392#1929—611no—
393#1866—611no—
394#1866—611no—
395#1826—611no—
396#1811—611no—
397#1789D6111yescharacteristic
398#1765—611no—
399#1764—611no—
400#1753—611no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—41no—
404C2×C61—41no—
405C2×C61—42no—
406C2×C61—81no—
407C2×C61#234211yescharacteristic
408C2×C61#295511yescharacteristic
409C2×C61#295611yescharacteristic
410C22×#41C2×D6111yescharacteristic
411C2×#131—611no—
412C2×#131—611no—
413C22×M16—611no—
414C2×#117—611no—
415#433—1221no—
416#433—1221no—
417#432—1221no—
418#431—1221no—
419C2×#108—611no—
420C2×#108—611no—
421#424—611no—
422#424—611no—
423C2×#104C2×D6111yescharacteristic
424C2×#104C2×D6111yescharacteristic
425C2×#104C2×D6111yescharacteristic
426C2×#104C2×D6111yescharacteristic
427#419—611no—
428#419—611no—
429#418—611no—
430#418—611no—
431#417—611no—
432#417—611no—
433#417—611no—
434#417—611no—
435#416—611no—
436#416—611no—
437#416—611no—
438#416—611no—
439#408—611no—
440#408—611no—
441#408—1221no—
442#408—1221no—
443#407—611no—
444#407—1221no—
445#407C2×D6111yescharacteristic
446C2×C22⋊C8—611no—
447C2×C22⋊C8—1221no—
448#405—611no—
449#405—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452C4×C22⋊C4C2×D6111yescharacteristic
453#341—611no—
454#341—611no—
455#339—611no—
456#339—611no—
457#339—611no—
458#339—611no—
459#336—611no—
460#336—611no—
461C61#2258811yescharacteristic, complemented, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C4×D6111yescharacteristic
469C2×#41C4×D6111yescharacteristic
470C2×#41C22×D6111yescharacteristic
471C2×#41C22×D6111yescharacteristic
472C22×Q8C4×D6111yescharacteristic
473C22×D4—21no—
474C22×D4C4×D6111yescharacteristic
475C23×C4—21no—
476C23×C4C22×D6111yescharacteristic
477#131—1222no—
478#131—1222no—
479#131—2441no—
480#131—2441no—
481C2×M16—611no—
482C2×M16—611no—
483C2×M16—611no—
484C2×M16—611no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—2441no—
490C2×M16—2441no—
491C2×M16C22×D6111yescharacteristic
492C2×M16C22×D6111yescharacteristic
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—611no—
496C22×C8—611no—
497C22×C8—1221no—
498C22×C8—1221no—
499#117—611no—
500#117—611no—
501#117—611no—
502#117—611no—
503#117—1221no—
504#117—1221no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1221no—
509C2×C42—1221no—
510C2×C42C22×D6111yescharacteristic
511C2×C42C22×D6111yescharacteristic
512#108—2441no—
513#108—2441no—
514C4⋊C8—1221no—
515C4⋊C8—1221no—
516C4⋊C8—1221no—
517C4⋊C8—1221no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
522#103—611no—
523#103—611no—
524#103—611no—
525#103—611no—
526#103—611no—
527#103—611no—
528#103—611no—
529#103—611no—
530#102—611no—
531#102—611no—
532#102—611no—
533#102—611no—
534#102—611no—
535#102—611no—
536#102—611no—
537#102—611no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—611no—
541C22⋊C8—611no—
542C22⋊C8—611no—
543C22⋊C8—611no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550#97—1221no—
551#97—1221no—
552#97—2441no—
553C4×C8—1221no—
554C4×C8—1221no—
555C4×C8—2441no—
556#95—21no—
557C24—21no—
558C24#1175822411yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1175822412yes—
574#41#1175822412yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C2×C4×D6111yescharacteristic
579C2×Q8C2×C4×D6111yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C2×C4×D6111yescharacteristic
590C2×D4C2×C4×D6111yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610C22×C4#1175822411yescharacteristic
611C22×C4C23×D6111yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1221no—
617M16—1221no—
618M16—1221no—
619M16—1221no—
620M16—2441no—
621M16—2441no—
622M16—2441no—
623M16—2441no—
624M16—2442no—
625M16—2442no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—611no—
629C2×C8—611no—
630C2×C8—611no—
631C2×C8—611no—
632C2×C8—611no—
633C2×C8—611no—
634C2×C8—611no—
635C2×C8—611no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—2442no—
647C2×C8—2442no—
648C4⋊C4—611no—
649C4⋊C4—611no—
650C4⋊C4—611no—
651C4⋊C4—611no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C22⋊C4—42no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—1221no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23#1451973711yescharacteristic
677C23#1451973711yescharacteristic
678C23C2×#1175822411yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1451973312yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1451973312yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—4881no—
725C2×C4—2442no—
726C2×C4#1451973711yescharacteristic
727C2×C4#1451973711yescharacteristic
728C2×C4C22×C4×D6111yescharacteristic
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4C2×#1175822411yescharacteristic
731C2×C4C2×#1175822411yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982211yescharacteristic
734C8—41no—
735C8—41no—
736C8—1221no—
737C8—1221no—
738C8—1221no—
739C8—1221no—
740C8—1221no—
741C8—1221no—
742C8—1221no—
743C8—1221no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×#1451973711yescharacteristic
764C22#1684044311yescharacteristic
765C22#1684044311yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—81no—
772C4—2441no—
773C4—2441no—
774C4—2441no—
775C4—2441no—
776C4C2×#1451973311yescharacteristic
777C4#1684023511yescharacteristic
778C4#1684039911yescharacteristic
779C4#1684039911yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2144867011yescharacteristic
787C2#2145471811yescharacteristic
788C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1789C2
socleC22×C61C2×C4×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenter#1789D61
hypocenterC61#22588
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #21454479C2semidirect
4. #21446527C2semidirect
5. #21446520C2semidirect
6. #21446470C2semidirect
7. #21446470C2semidirect
8. #21446092C2semidirect
9. #21446092C2semidirect
10. #21445919C2semidirect
11. #21445859C2semidirect
12. #21445664C2semidirect
13. #21445657C2semidirect
14. #21445603C2semidirect
24. C2×#14519712C22semidirect
25. C2×#14519712C22semidirect
26. #16839790C22semidirect
27. #16839790C22semidirect
28. #16839771C4semidirect
29. #16839771C4semidirect
30. #16839767C4semidirect
31. #16839767C4semidirect
32. #16839763C4semidirect
33. #16839763C4semidirect
34. #16839763C4semidirect
35. #16839763C4semidirect
48. #16839720C22semidirect
49. #16839720C22semidirect
50. C2×#14519688C22semidirect
51. C2×C4×#92418C22semidirect
52. #16839526C22semidirect
53. #16839526C22semidirect
54. #16839522C22semidirect
55. #16839522C22semidirect
56. #16839522C22semidirect
57. #16839522C22semidirect
58. #16839517C22semidirect
59. #16839517C22semidirect
461. C61#22588semidirect

Maximal subgroups

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

subgroupindex
#214544792
#214543382
#214542682
#214465272
#214465202
#214464702
#214460922
#214459192
#214458592
#214456642
#214456572
#214456032
C61×#17892
#2258861