Finite Group Databasebeta

← #29697380

Subgroups — #29697380

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#21454473C211yesmaximal, characteristic, complemented
2#21454338C211yesmaximal, characteristic
3#21446533C211yesmaximal, characteristic, complemented
4#21446526C211yesmaximal, characteristic, complemented
5#21446464C211yesmaximal, characteristic, complemented
6#21446464C211yesmaximal, characteristic, complemented
7#21446094C211yesmaximal, characteristic, complemented
8#21446094C211yesmaximal, characteristic, complemented
9#21445916C211yesmaximal, characteristic, complemented
10#21445859C211yesmaximal, characteristic, complemented
11#21445763C211yesmaximal, characteristic
12#21445661C211yesmaximal, characteristic, complemented
13#21445654C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C61×#2880C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16839820—21no—
19#16839820—21no—
20#16839816—21no—
21#16839812—21no—
22C2×#14519712C2211yescharacteristic, complemented
23C2×#14519712C2211yescharacteristic, complemented
24#16839788C2211yescharacteristic, complemented
25#16839788C2211yescharacteristic, complemented
26C2×#14519704C2211yescharacteristic
27C2×#14519704C2211yescharacteristic
28C2×#14519704C2211yescharacteristic
29C2×#14519704C2211yescharacteristic
30#16839771C411yescharacteristic, complemented
31#16839771C411yescharacteristic, complemented
32#16839767C411yescharacteristic, complemented
33#16839767C411yescharacteristic, complemented
34#16839763C411yescharacteristic, complemented
35#16839763C411yescharacteristic, complemented
36#16839763C411yescharacteristic, complemented
37#16839763C411yescharacteristic, complemented
38#16839758C2211yescharacteristic
39#16839758C2211yescharacteristic
40#16839758C2211yescharacteristic
41#16839758C2211yescharacteristic
42#16839726C2211yescharacteristic
43#16839717C2211yescharacteristic, complemented
44#16839717C2211yescharacteristic, complemented
45C2×#14519687C2211yescharacteristic, complemented
46C2×C8×Dic61C2211yescharacteristic, complemented
47C4×C22⋊Dic61C2211yescharacteristic
48#16839526C2211yescharacteristic, complemented
49#16839526C2211yescharacteristic, complemented
50#16839523C2211yescharacteristic, complemented
51#16839523C2211yescharacteristic, complemented
52#16839523C2211yescharacteristic, complemented
53#16839523C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C22×#41×C61C2211yescharacteristic
57C2×#131×C61C2211yescharacteristic
58C2×#131×C61C2211yescharacteristic
59C61×#408—21no—
60C61×#408—21no—
61C61×#408C2211yescharacteristic
62C61×#408C2211yescharacteristic
63C61×#407—21no—
64C61×#407C2211yescharacteristic
65C2×C22⋊C8×C61—21no—
66C2×C22⋊C8×C61C2211yescharacteristic
67C2×#11758194—41no—
68C2×#11758194—41no—
69C2×#11758194C2×C411yescharacteristic
70C2×#11758194C2×C411yescharacteristic
71C2×#11758194C2×C411yescharacteristic
72C2×#11758194C2×C411yescharacteristic
73C2×#11758194C2311yescharacteristic
74C2×#11758194C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519736—21no—
78#14519736—21no—
79#14519736C2×C411yescharacteristic
80#14519736C2×C411yescharacteristic
81#14519736C2311yescharacteristic
82#14519736C2311yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90#14519712—41no—
91#14519712—41no—
92#14519706—21no—
93#14519706—21no—
94#14519706—21no—
95#14519706—21no—
96#14519704—22no—
97#14519704—22no—
98#14519704—41no—
99#14519704—41no—
100#14519701C2×C411yescharacteristic
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519701C2×C411yescharacteristic
104#14519701C2×C411yescharacteristic
105#14519701C2×C411yescharacteristic
106#14519701C2×C411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic
109#14519698C2×C411yescharacteristic
110#14519698C2×C411yescharacteristic
111#14519698C2×C411yescharacteristic
112#14519698C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115#14519698C2×C411yescharacteristic
116C22⋊#92418—21no—
117C22⋊#92418—21no—
118#14519687—21no—
119#14519687—21no—
120#14519687—41no—
121C8×Dic61—21no—
122C8×Dic61—21no—
123C8×Dic61—41no—
124#14519684—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—22no—
128C2×#41×C61—22no—
129C2×#41×C61—41no—
130C2×#41×C61—41no—
131C2×#41×C61C2×C411yescharacteristic
132C2×#41×C61C2×C411yescharacteristic
133C2×#41×C61C2311yescharacteristic
134C2×#41×C61C2311yescharacteristic
135C22×Q8×C61C2×C411yescharacteristic
136C22×D4×C61—21no—
137C22×D4×C61C2×C411yescharacteristic
138C23×C4×C61—21no—
139C23×C4×C61C2311yescharacteristic
140#131×C61—22no—
141#131×C61—22no—
142#131×C61—41no—
143#131×C61—41no—
144C2×M16×C61—21no—
145C2×M16×C61—21no—
146C2×M16×C61C2311yescharacteristic
147C2×M16×C61C2311yescharacteristic
148C22×C8×C61—21no—
149C22×C8×C61—21no—
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C22⋊C8×C61—21no—
153C22⋊C8×C61—21no—
154C22⋊C8×C61—21no—
155C22⋊C8×C61—21no—
156C22⋊C8×C61—21no—
157C22⋊C8×C61—21no—
158C22⋊C8×C61D411yescharacteristic
159C22⋊C8×C61D411yescharacteristic
160C22⋊C8×C61D411yescharacteristic
161C22⋊C8×C61D411yescharacteristic
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—42no—
206C22×C4×C61—42no—
207C22×C4×C61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61#4111yescharacteristic
212C22×C4×C61C2411yescharacteristic
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217M16×C61—21no—
218M16×C61—21no—
219M16×C61—21no—
220M16×C61—21no—
221M16×C61—42no—
222M16×C61—42no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—42no—
230C2×C8×C61—42no—
231C2×C8×C61C2×D411yescharacteristic
232C2×C8×C61C2×D411yescharacteristic
233C2×C8×C61C2×D411yescharacteristic
234C2×C8×C61C2×D411yescharacteristic
235C22⋊Dic61—21no—
236C22⋊Dic61—21no—
237C22⋊Dic61—21no—
238C22⋊Dic61—21no—
239C22⋊Dic61—42no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61C22×C411yescharacteristic
243C4⋊Dic61C22×C411yescharacteristic
244C4⋊Dic61C22×C411yescharacteristic
245C4⋊Dic61C22×C411yescharacteristic
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—21no—
254#11758194—21no—
255#11758194—21no—
256#11758194—21no—
257#11758194—21no—
258#11758194—41no—
259#11758194—41no—
260#11758194—41no—
261#11758194—41no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418C22×C411yescharacteristic
269C2×#92418C22×C411yescharacteristic
270C2×#92418C22×C411yescharacteristic
271C2×#92418C22×C411yescharacteristic
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—21no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61C4×D411yescharacteristic
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61C23×C411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61H(5,𝔽2)11yescharacteristic
326C2×C4×C61H(5,𝔽2)11yescharacteristic
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—41no—
333C2×Dic61—42no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—81no—
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#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—41no—
376C4×C61C2×#11711yescharacteristic
377C4×C61#51811yescharacteristic
378C4×C61#54611yescharacteristic
379C4×C61#54611yescharacteristic
380Dic61—42no—
381Dic61—41no—
382Dic61—41no—
383Dic61—41no—
384Dic61—41no—
385Dic61—81no—
386#2924—611no—
387#2896—611no—
388#2880D6111yescharacteristic
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#1789—611no—
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×#131C2×D6111yescharacteristic
412C2×#131C2×D6111yescharacteristic
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×#104—611no—
424C2×#104—611no—
425C2×#104—611no—
426C2×#104—611no—
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—21no—
440#408—21no—
441#408C2×D6111yescharacteristic
442#408C2×D6111yescharacteristic
443#407—21no—
444#407—611no—
445#407C2×D6111yescharacteristic
446C2×C22⋊C8—21no—
447C2×C22⋊C8C2×D6111yescharacteristic
448#405—611no—
449#405—611no—
450C2×#97—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#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—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—611no—
484C2×M16—611no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—611no—
488C2×M16—611no—
489C2×M16—2441no—
490C2×M16—2441no—
491C2×M16C22×D6111yescharacteristic
492C2×M16C22×D6111yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—611no—
496C22×C8—611no—
497C22×C8C22×D6111yescharacteristic
498C22×C8C22×D6111yescharacteristic
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—1221no—
508C2×C22⋊C4—1221no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—1221no—
512#108—2441no—
513#108—2441no—
514C4⋊C8—1221no—
515C4⋊C8—1221no—
516C4⋊C8—1221no—
517C4⋊C8—1221no—
518#104—1222no—
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#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—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8C22⋊D6111yescharacteristic
547C22⋊C8C22⋊D6111yescharacteristic
548C22⋊C8C22⋊D6111yescharacteristic
549C22⋊C8C22⋊D6111yescharacteristic
550#97—1221no—
551#97—1221no—
552#97—2441no—
553C4×C8—1221no—
554C4×C8—1221no—
555C4×C8—2441no—
556#95—1221no—
557C24—21no—
558C24#1175822211yescharacteristic
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—42no—
601C22×C4—42no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4#1175822211yescharacteristic
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C23×D6111yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—42no—
617M16—42no—
618M16—1221no—
619M16—1221no—
620M16—1221no—
621M16—1221no—
622M16—2441no—
623M16—2441no—
624M16—2441no—
625M16—2441no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—42no—
633C2×C8—42no—
634C2×C8—611no—
635C2×C8—611no—
636C2×C8—611no—
637C2×C8—611no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8C2×C22⋊D6111yescharacteristic
645C2×C8C2×C22⋊D6111yescharacteristic
646C2×C8C2×C22⋊D6111yescharacteristic
647C2×C8C2×C22⋊D6111yescharacteristic
648C4⋊C4—611no—
649C4⋊C4—611no—
650C4⋊C4—611no—
651C4⋊C4—611no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—2442no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
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—
676C23C4×C22⋊D6111yescharacteristic
677C23C4×C22⋊D6111yescharacteristic
678C23C2×#1175822211yescharacteristic
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—21no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—1222no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—4881no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2442no—
725C2×C4—2441no—
726C2×C4C4×C22⋊D6111yescharacteristic
727C2×C4C4×C22⋊D6111yescharacteristic
728C2×C4C22×C4×D6111yescharacteristic
729C2×C4C22×C22⋊D6111yescharacteristic
730C2×C4C2×#1175822411yescharacteristic
731C2×C4C2×#1175822411yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982211yescharacteristic
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—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×C4×C22⋊D6111yescharacteristic
764C22#1684043811yescharacteristic
765C22#1684043811yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—4881no—
771C4—2442no—
772C4—2441no—
773C4—2441no—
774C4—2441no—
775C4—2441no—
776C4C2×#1451973311yescharacteristic
777C4#1684023511yescharacteristic
778C4#1684040611yescharacteristic
779C4#1684040611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2144866411yescharacteristic
787C2#2145472011yescharacteristic
788C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2880C2
socleC22×C61C2×C4×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenter#2880D61
hypocenterC61#22588
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. #21454473C2semidirect
3. #21446533C2semidirect
4. #21446526C2semidirect
5. #21446464C2semidirect
6. #21446464C2semidirect
7. #21446094C2semidirect
8. #21446094C2semidirect
9. #21445916C2semidirect
10. #21445859C2semidirect
12. #21445661C2semidirect
13. #21445654C2semidirect
14. #21445605C2semidirect
22. C2×#14519712C22semidirect
23. C2×#14519712C22semidirect
24. #16839788C22semidirect
25. #16839788C22semidirect
30. #16839771C4semidirect
31. #16839771C4semidirect
32. #16839767C4semidirect
33. #16839767C4semidirect
34. #16839763C4semidirect
35. #16839763C4semidirect
36. #16839763C4semidirect
37. #16839763C4semidirect
43. #16839717C22semidirect
44. #16839717C22semidirect
45. C2×#14519687C22semidirect
46. C2×C8×Dic61C22semidirect
48. #16839526C22semidirect
49. #16839526C22semidirect
50. #16839523C22semidirect
51. #16839523C22semidirect
52. #16839523C22semidirect
53. #16839523C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
461. C61#22588semidirect

Maximal subgroups

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

subgroupindex
#214544732
#214543382
#214465332
#214465262
#214464642
#214460942
#214459162
#214458592
#214457632
#214456612
#214456542
#214456052
C61×#28802
#2258861