Finite Group Databasebeta

← #30552420

Subgroups — #30552420

Order 15616.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459565C211yesmaximal, characteristic
2C2×#16840390C211yesmaximal, characteristic, complemented
3#21457123C214yesmaximal, complemented
4#21457085C214yesmaximal, complemented
5#21457043C212yesmaximal, complemented
6#21457024C212yesmaximal, complemented
7#21456992C212yesmaximal, complemented
8#21456961C212yesmaximal, complemented
9#21456349C212yesmaximal, complemented
10#21456180C212yesmaximal, complemented
11#21455744C211yesmaximal, characteristic
12#21455732C211yesmaximal, characteristic
13C2×#16840090C211yesmaximal, characteristic, complemented
14#21455680C212yesmaximal, complemented
15#21455663C212yesmaximal, complemented
16#21454479C211yesmaximal, characteristic, complemented
17C61×#3095C211yesmaximal, characteristic, complemented
18#16840483—21no—
19#16840470—21no—
20#16840454—21no—
21#16840447—22no—
22#16840446—21no—
23#16840438—22no—
24#16840393C2211yescharacteristic
25#16840390—21no—
26#16840390—21no—
27#16840390—22no—
28#16840390C2212yes—
29#16840390C2212yes—
30#16840390C2214yes—
31#16840385C2212yes—
32#16840372C2212yes—
33#16840336C2211yescharacteristic
34#16840314C2212yes—
35C2×#14519777—21no—
36C2×#14519776C2212yes—
37#16840298C2212yes—
38C2×#14519769—21no—
39C2×#14519768C2212yes—
40#16840273C2211yescharacteristic
41C2×#14519754—22no—
42#16840243C2211yescharacteristic
43#16840240C2211yescharacteristic
44C2×#14519736C2211yescharacteristic
45C22×C4⋊Dic61C2211yescharacteristic
46#16840170C2214yescomplemented
47#16840169C2214yescomplemented
48#16840163C2214yescomplemented
49#16840159C2214yescomplemented
50#16840129C2214yescomplemented
51#16840123C2214yescomplemented
52#16840118C2214yescomplemented
53#16840111C2214yescomplemented
54#16840103C2212yes—
55#16840098C2212yes—
56#16840097C2211yescharacteristic
57#16840093C2212yes—
58#16840092C2211yescharacteristic
59#16840090C2212yes—
60#16840090C2212yes—
61#16840090C2214yes—
62#16840086C2212yes—
63#16840081C2212yes—
64#16840080C2211yescharacteristic
65#16840076C2212yes—
66#16840075C2211yescharacteristic
67#16840071C2214yescomplemented
68#16840068C2214yescomplemented
69#16840067C2214yescomplemented
70#16840065C2214yescomplemented
71#16840055C2214yescomplemented
72#16840051C2214yescomplemented
73#16840046C2214yescomplemented
74#16840045C2214yescomplemented
75#16839820C2214yes—
76#16839816C2212yes—
77#16839812C2212yes—
78#16839804C2212yes—
79#16839798C2212yes—
80C2×#14519708C2212yes—
81#16839790C2212yes—
82#16839764C2212yes—
83#16839756C2212yes—
84C2×#14519701C2212yes—
85C2×C22⋊#92418C2211yescharacteristic
86#16839720C2212yes—
87C2×C22⋊Q8×C61C2211yescharacteristic
88C2×#117×C61C2211yescharacteristic
89C61×#485C2214yes—
90C61×#484C2212yes—
91C61×#483C2212yes—
92C61×#428C2212yes—
93C61×#419C2212yes—
94C61×#407C2211yescharacteristic
95C2×#11758222C2311yescharacteristic
96C22×Dic122—22no—
97C23×Dic61—21no—
98C22×#92418C2312yes—
99#14519777—22no—
100#14519777—22no—
101#14519777—24no—
102#14519776—21no—
103#14519776—22no—
104#14519776—22no—
105#14519776C2314yes—
106#14519776C2314yes—
107#14519776C2312yes—
108#14519775C2312yes—
109#14519772—22no—
110#14519772—22no—
111#14519770—22no—
112#14519770—22no—
113#14519769—22no—
114#14519769—22no—
115#14519769—24no—
116#14519768—22no—
117#14519768—21no—
118#14519768—22no—
119#14519768—22no—
120#14519768C2314yes—
121#14519768C2314yes—
122#14519768C2312yes—
123#14519767—22no—
124#14519767—22no—
125#14519766C2312yes—
126#14519763—22no—
127#14519761—22no—
128#14519760—21no—
129#14519760—22no—
130#14519759—22no—
131#14519757—22no—
132#14519756—22no—
133#14519756C2311yescharacteristic
134#14519756C2311yescharacteristic
135#14519754—22no—
136#14519754—24no—
137#14519754—24no—
138#14519754—24no—
139#14519754—24no—
140#14519753—21no—
141#14519753—21no—
142#14519751C2311yescharacteristic
143#14519751C2311yescharacteristic
144#14519746—21no—
145Q8×Dic61—21no—
146Q8×Dic61—21no—
147Q8×Dic61C2312yes—
148Q8×Dic61C2312yes—
149#14519742—22no—
150#14519742C2312yes—
151#14519739C2312yes—
152C4×C22⋊D61—21no—
153C4×C22⋊D61—21no—
154C4×C22⋊D61—22no—
155#14519737—22no—
156#14519736—22no—
157#14519736D411yescharacteristic
158#14519736D411yescharacteristic
159#14519736D412yes—
160#14519736C2311yescharacteristic
161#14519736C2311yescharacteristic
162#14519736C2311yescharacteristic
163#14519736C2312yes—
164#14519735—21no—
165#14519735—22no—
166#14519733—22no—
167C2×C4⋊Dic61—21no—
168C2×C4⋊Dic61—21no—
169C2×C4⋊Dic61—21no—
170C2×C4⋊Dic61—22no—
171C2×C4⋊Dic61D411yescharacteristic
172C2×C4⋊Dic61D411yescharacteristic
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2312yes—
175C2×C4⋊Dic61C2312yes—
176C2×#11758196—22no—
177C2×#11758196—22no—
178C4⋊C4×D61—21no—
179C2×C22⋊Dic61D412yes—
180C2×C4×Dic61C2312yes—
181#14519711C2314yes—
182#14519710C2312yes—
183#14519710C2312yes—
184#14519709C2314yes—
185#14519708C2312yes—
186#14519708C2314yes—
187#14519708C2314yes—
188#14519708C2312yes—
189#14519706C2314yes—
190#14519706C2314yes—
191#14519702C2314yes—
192#14519701C2314yes—
193#14519701C2314yes—
194#14519700C2312yes—
195#14519700C2312yes—
196#14519699C2314yes—
197#14519697C2312yes—
198#14519697C2312yes—
199C22⋊#92418C2311yescharacteristic
200C22⋊#92418C2311yescharacteristic
201C22⋊#92418C2312yes—
202#14519687C2314yes—
203C8×Dic61C2314yes—
204C22×Q8×C61C2311yescharacteristic
205C23×C4×C61C2311yescharacteristic
206C2×M16×C61C2312yes—
207C22⋊Q8×C61—21no—
208C22⋊Q8×C61—21no—
209C22⋊Q8×C61C2312yes—
210C22⋊Q8×C61C2312yes—
211#117×C61—21no—
212#117×C61—21no—
213#117×C61C2312yes—
214#117×C61C2312yes—
215C2×C4⋊C4×C61—21no—
216C2×C4⋊C4×C61C2311yescharacteristic
217C2×C4⋊C4×C61C2311yescharacteristic
218C2×C4⋊C4×C61C2311yescharacteristic
219C2×C22⋊C4×C61—21no—
220C2×C22⋊C4×C61—21no—
221C2×C42×C61—21no—
222#107×C61C2314yes—
223#106×C61C2314yes—
224#103×C61C2314yes—
225#103×C61C2314yes—
226C22⋊C8×C61C2312yes—
227C22⋊C8×C61C2312yes—
228C24×C61C2×D411yescharacteristic
229C2×Q8×C61—21no—
230C2×Q8×C61—24no—
231C2×Q8×C61C2412yes—
232C22×C4×C61—24no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2411yescharacteristic
241C22×C4×C61C2411yescharacteristic
242C22×C4×C61C2411yescharacteristic
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C22×Dic61—22no—
247C22×Dic61—22no—
248C22×Dic61—22no—
249C22×Dic61—82no—
250C22×Dic61C2×D412yes—
251C22×Dic61C2×D412yes—
252#11758222—24no—
253C2×D244C2411yescharacteristic
254C2×C4×D61—21no—
255C2×C4×D61—22no—
256C2×Dic122—24no—
257C2×Dic122—24no—
258C2×Dic122—22no—
259C2×Dic122—84no—
260C2×Dic122C2411yescharacteristic
261M16×C61—24no—
262C2×C8×C61C2414yes—
263C4⋊C4×C61—22no—
264C4⋊C4×C61—22no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C2412yes—
269C4⋊C4×C61C2412yes—
270C4⋊C4×C61C2412yes—
271C22⋊C4×C61—22no—
272C22⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—22no—
275C42×C61—22no—
276C42×C61—22no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61C2×D412yes—
281C22⋊Dic61C2×D412yes—
282C22⋊Dic61C2×D412yes—
283C22⋊Dic61C2×D412yes—
284#11758198—21no—
285#11758198—21no—
286#11758198—22no—
287#11758198—22no—
288#11758198—22no—
289C4⋊Dic61—22no—
290C4⋊Dic61—22no—
291C4⋊Dic61—22no—
292C4⋊Dic61—24no—
293C4⋊Dic61—24no—
294C4⋊Dic61—22no—
295C4⋊Dic61—22no—
296C4⋊Dic61—22no—
297C4⋊Dic61C2×D411yescharacteristic
298C4⋊Dic61C2×D411yescharacteristic
299C4⋊Dic61C2×D411yescharacteristic
300C4⋊Dic61C2×D411yescharacteristic
301C4⋊Dic61C2×D412yes—
302C4⋊Dic61C2×D412yes—
303C4⋊Dic61C2414yes—
304C4⋊Dic61C2411yescharacteristic
305C4⋊Dic61C2411yescharacteristic
306#11758196—21no—
307#11758196—21no—
308#11758196—22no—
309#11758196—24no—
310#11758196—24no—
311#11758196—24no—
312#11758196—24no—
313#11758196—22no—
314#11758196—22no—
315#11758196—22no—
316#11758196—22no—
317C4×Dic61—21no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C4×Dic61C2×D412yes—
322C4×Dic61C2×D412yes—
323C4×Dic61C2412yes—
324C4×Dic61C2412yes—
325C2×#92418—24no—
326C2×#92418C2412yes—
327C2×#92418C2412yes—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—41no—
331C23×C61C22×D411yescharacteristic
332C23×C61C22×D411yescharacteristic
333C23×C61C22×D411yescharacteristic
334C22×D61—21no—
335Q8×C61—24no—
336Q8×C61—42no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—81no—
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C612−1+414yes—
354C2×C4×C61C2511yescharacteristic
355C22⋊D61—42no—
356C22⋊D61—42no—
357C22⋊D61—81no—
358C2×Dic61—24no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—24no—
363C2×Dic61—42no—
364C2×Dic61—44no—
365C2×Dic61—82no—
366C2×Dic61—82no—
367C2×Dic61C22×D412yes—
368C2×Dic61C22×D412yes—
369C2×Dic61C22×D412yes—
370C2×Dic61C22×D412yes—
371D244—22no—
372C4×D61—42no—
373C4×D61—82no—
374Dic122—22no—
375Dic122—82no—
376Dic122—84no—
377Dic122—84no—
378C8×C61—24no—
379#92418—22no—
380#92418—22no—
381#60872—611nomaximal, Sylow
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—44no—
390C22×C61#53612yes—
391C22×C61#57712yes—
392C22×C61C23×D411yescharacteristic
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—42no—
399C4×C61—42no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61#53612yes—
403C4×C61C2×2−1+412yes—
404Dic61—22no—
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61—41no—
409Dic61—41no—
410Dic61—44no—
411Dic61—41no—
412#3495—611no—
413C2×#544—611no—
414#3244—614no—
415#3242—614no—
416#3238—612no—
417#3236—612no—
418#3232—612no—
419#3229—612no—
420#3163—612no—
421#3137—612no—
422#3095D6111yescharacteristic, complemented
423#3092—611no—
424#3091—611no—
425C2×#483—611no—
426#3084—612no—
427#3082—612no—
428#2924—611no—
429C2×C61—22no—
430C2×C61—22no—
431C2×C61—41no—
432C2×C61C2×#53611yescharacteristic
433C2×C61C2×#57711yescharacteristic
434C2×C61#358611yescharacteristic
435D61—81no—
436#556—1221no—
437#554—1221no—
438#552—1222no—
439#552—1221no—
440#552—1221no—
441#551—1222no—
442#544—612no—
443#544—612no—
444#544—614no—
445#544—611no—
446#544—1222no—
447#544—1221no—
448#544—1221no—
449#542—612no—
450#541—612no—
451#536—611no—
452#533—612no—
453C2×C4⋊Q8—612no—
454C2×C4⋊Q8—1221no—
455#529—612no—
456C2×#125—612no—
457C2×#125—1221no—
458#525—611no—
459C2×C22⋊Q8—1222no—
460C2×C22⋊Q8C2×D6111yescharacteristic
461#520—611no—
462#519—611no—
463C2×#117—611no—
464C2×#117C2×D6111yescharacteristic
465C22×C4⋊C4—611no—
466#501—614no—
467#501—614no—
468#499—614no—
469#498—614no—
470#491—614no—
471#489—614no—
472#488—614no—
473#487—614no—
474#485—612no—
475#485C2×D6114yes—
476#484—611no—
477#484—612no—
478#484C2×D6112yes—
479#483—612no—
480#483—612no—
481#483—614no—
482#483—611no—
483#483—612no—
484#483C2×D6112yes—
485#482—612no—
486#481—611no—
487#481—612no—
488#480—611no—
489#480—612no—
490#479—614no—
491#479—614no—
492#479—614no—
493#478—614no—
494#477—614no—
495#476—614no—
496#475—614no—
497#475—614no—
498#433—614no—
499#432—612no—
500#431—612no—
501#428—612no—
502#428C2×D6112yes—
503#427—612no—
504C2×#106—612no—
505#424—612no—
506#419C2×D6112yes—
507#417—612no—
508#416—612no—
509C2×#103—612no—
510#407C2×D6111yescharacteristic
511C2×C22⋊C8—611no—
512#405—612no—
513C61#6087211yescharacteristic, complemented, Sylow
514C2×#41—611no—
515C22×Q8—1222no—
516C22×Q8C22×D6111yescharacteristic
517C23×C4—1221no—
518C23×C4C22×D6111yescharacteristic
519C2×M16C22×D6112yes—
520C22×C8—612no—
521C4⋊Q8—614no—
522C4⋊Q8—614no—
523C4⋊Q8—612no—
524C4⋊Q8—612no—
525C4⋊Q8—1222no—
526C4⋊Q8—1222no—
527C4⋊Q8—1224no—
528C4⋊Q8—1222no—
529C4⋊Q8—1222no—
530C4⋊Q8—1221no—
531#126—1222no—
532#126—1222no—
533#126—1222no—
534#126—1222no—
535#125—614no—
536#125—614no—
537#125—612no—
538#125—1222no—
539#125—1224no—
540#125—1222no—
541#125—1222no—
542#125—1222no—
543#125—1222no—
544#125—1222no—
545#125—1222no—
546#125—1221no—
547#124—612no—
548#124—1222no—
549#123—1222no—
550#123—1222no—
551#123—1222no—
552#123—1221no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—611no—
556C22⋊Q8—611no—
557C22⋊Q8—1224no—
558C22⋊Q8—1224no—
559C22⋊Q8—1224no—
560C22⋊Q8—1224no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8C22×D6112yes—
567C22⋊Q8C22×D6112yes—
568#121—611no—
569#121—611no—
570#120—1221no—
571C4×Q8—612no—
572C4×Q8—612no—
573C4×Q8—612no—
574C4×Q8—1222no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×D4—612no—
578C4×D4—1222no—
579C4×D4—1222no—
580C4×D4—1221no—
581C4×D4—1221no—
582#117—21no—
583#117—21no—
584#117—611no—
585#117—612no—
586#117—611no—
587#117—611no—
588#117—611no—
589#117—612no—
590#117—611no—
591#117—1222no—
592#117—1222no—
593#117—1222no—
594#117—1221no—
595#117C22×D6112yes—
596#117C22×D6112yes—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—611no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—612no—
601C2×C4⋊C4—612no—
602C2×C4⋊C4—612no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4C22×D6111yescharacteristic
611C2×C4⋊C4C22×D6111yescharacteristic
612C2×C4⋊C4C22×D6111yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—612no—
616C2×C42—21no—
617C2×C42—612no—
618#107—614no—
619#107—612no—
620#107—612no—
621#107C22×D6114yes—
622#106—614no—
623#106—614no—
624#106—614no—
625#106—612no—
626#106—612no—
627#106C22×D6114yes—
628C4⋊C8—614no—
629C4⋊C8—614no—
630#103—614no—
631#103—614no—
632#103—614no—
633#103—612no—
634#103—612no—
635#103C22×D6114yes—
636#103C22×D6114yes—
637#102—614no—
638#102—612no—
639#102—612no—
640C22⋊C8—611no—
641C22⋊C8—611no—
642C22⋊C8—612no—
643C22⋊C8C22×D6112yes—
644C22⋊C8C22×D6112yes—
645#97—614no—
646C4×C8—614no—
647C24D4×D6111yescharacteristic
648#41—1224no—
649C2×Q8—21no—
650C2×Q8—24no—
651C2×Q8—611no—
652C2×Q8—1222no—
653C2×Q8—1224no—
654C2×Q8—1224no—
655C2×Q8—4884no—
656C2×Q8C23×D6112yes—
657C2×D4—611no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C22×C4—24no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1221no—
673C22×C4—4882no—
674C22×C4D4×D6111yescharacteristic
675C22×C4D4×D6111yescharacteristic
676C22×C4D4×D6111yescharacteristic
677C22×C4C23×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680M16—24no—
681C2×C8—612no—
682C2×C8—612no—
683C2×C8—1224no—
684C2×C8C23×D6114yes—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—612no—
693C4⋊C4—611no—
694C4⋊C4—611no—
695C4⋊C4—612no—
696C4⋊C4—614no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—1222no—
700C4⋊C4—1224no—
701C4⋊C4—1224no—
702C4⋊C4—1224no—
703C4⋊C4—1224no—
704C4⋊C4—1224no—
705C4⋊C4—1224no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1222no—
709C4⋊C4—1222no—
710C4⋊C4—1222no—
711C4⋊C4—1222no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C4⋊C4—1222no—
715C4⋊C4—1222no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4C23×D6112yes—
719C4⋊C4C23×D6112yes—
720C4⋊C4C23×D6112yes—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—612no—
726C22⋊C4—612no—
727C22⋊C4—612no—
728C22⋊C4—612no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1222no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C42—22no—
738C42—22no—
739C42—612no—
740C42—612no—
741C42—612no—
742C42—612no—
743C42—1222no—
744C42—1222no—
745C42—1222no—
746C42—1221no—
747C23—22no—
748C23—22no—
749C23—41no—
750C23—1221no—
751C23C2×D4×D6111yescharacteristic
752C23C2×D4×D6111yescharacteristic
753C23C2×D4×D6111yescharacteristic
754Q8—24no—
755Q8—42no—
756Q8—1222no—
757Q8—4882no—
758Q8—4884no—
759Q8—4884no—
760D4—1222no—
761D4—4881no—
762D4—2442no—
763D4—2442no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—81no—
777C2×C4—612no—
778C2×C4—612no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—1224no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1224no—
786C2×C4—4882no—
787C2×C4—4882no—
788C2×C4—4882no—
789C2×C4—2442no—
790C2×C4—2444no—
791C2×C4—2442no—
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4#1451982414yes—
796C2×C4C24×D6111yescharacteristic
797C8—24no—
798C8—1222no—
799C8—1222no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—44no—
808C22—2441no—
809C22—2441no—
810C22—2441no—
811C22#1684033412yes—
812C22#1684057112yes—
813C22C22×D4×D6111yescharacteristic
814C4—21no—
815C4—21no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4—1222no—
824C4—2444no—
825C4—2441no—
826C4—2441no—
827C4—2441no—
828C4#1684033412yes—
829C4C2×#1451982412yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—4881no—
834C2C2×#1684033411yescharacteristic
835C2C2×#1684057111yescharacteristic
836C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3095C2
socleC22×C61C23×D4
prime radical#16840273C22
hypercenter#3095D61
hypocenterC61#60872
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
2. C2×#16840390C2semidirect
3. #21457123C2semidirect
4. #21457085C2semidirect
5. #21457043C2semidirect
6. #21457024C2semidirect
7. #21456992C2semidirect
8. #21456961C2semidirect
9. #21456349C2semidirect
10. #21456180C2semidirect
13. C2×#16840090C2semidirect
14. #21455680C2semidirect
15. #21455663C2semidirect
16. #21454479C2semidirect
17. C61×#3095C2semidirect
46. #16840170C22semidirect
47. #16840169C22semidirect
48. #16840163C22semidirect
49. #16840159C22semidirect
50. #16840129C22semidirect
51. #16840123C22semidirect
52. #16840118C22semidirect
53. #16840111C22semidirect
67. #16840071C22semidirect
68. #16840068C22semidirect
69. #16840067C22semidirect
70. #16840065C22semidirect
71. #16840055C22semidirect
72. #16840051C22semidirect
73. #16840046C22semidirect
74. #16840045C22semidirect
422. #3095D61semidirect
513. C61#60872semidirect

Maximal subgroups

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

subgroupindex
#214595652
C2×#168403902
#214571232
#214570852
#214570432
#214570242
#214569922
#214569612
#214563492
#214561802
#214557442
#214557322
C2×#168400902
#214556802
#214556632
#214544792
C61×#30952
#6087261