Finite Group Databasebeta

← #30552765

Subgroups — #30552765

Order 15616.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459631C211yesmaximal, characteristic, complemented
2#21459235C211yesmaximal, characteristic
3#21457124C214yesmaximal, complemented
4#21457077C214yesmaximal, complemented
5#21457044C212yesmaximal, complemented
6#21457016C212yesmaximal, complemented
7#21457002C212yesmaximal, complemented
8#21456946C212yesmaximal, complemented
9#21456351C212yesmaximal, complemented
10#21456177C212yesmaximal, complemented
11#21455806C212yesmaximal, complemented
12#21455780C212yesmaximal, complemented
13#21455634C211yesmaximal, characteristic, complemented
14#21455612C211yesmaximal, characteristic, complemented
15C2×#16840053C211yesmaximal, characteristic, complemented
16#21454484C211yesmaximal, characteristic, complemented
17C61×#3076C211yesmaximal, characteristic, complemented
18Q8×Dic122—21no—
19#16840490—21no—
20#16840472—21no—
21#16840470—22no—
22Q8×D244—21no—
23#16840425—22no—
24#16840392C2214yescomplemented
25#16840390C2211yescharacteristic
26#16840390C2212yes—
27#16840384C2212yes—
28#16840383—21no—
29#16840367—21no—
30#16840363C2212yes—
31#16840345—22no—
32#16840340C2211yescharacteristic
33#16840331C2211yescharacteristic
34#16840326C2211yescharacteristic
35#16840317C2212yescomplemented
36#16840312—21no—
37#16840309C2212yes—
38C2×#14519777C2211yescharacteristic
39C4⋊Q8×D61C2212yescomplemented
40#16840299C2212yes—
41#16840296—21no—
42#16840271—22no—
43#16840242C2212yes—
44C4×#11758222C2211yescharacteristic
45C2×C4×D244C2211yescharacteristic
46#16840170C2214yescomplemented
47#16840170C2214yescomplemented
48#16840162C2214yescomplemented
49#16840159C2214yescomplemented
50#16840125C2214yes—
51#16840123C2214yes—
52#16840118C2214yes—
53#16840107C2214yes—
54#16840101C2214yescomplemented
55#16840091C2214yescomplemented
56#16840089C2214yes—
57#16840088C2214yes—
58#16840085C2214yescomplemented
59#16840082C2214yes—
60#16840079C2214yescomplemented
61#16840077C2214yes—
62#16840059C2214yes—
63#16840057C2212yescomplemented
64#16840053C2212yes—
65#16840053C2212yes—
66#16840053C2214yes—
67#16840052C2212yescomplemented
68#16840049C2212yes—
69#16840047C2212yescomplemented
70#16840042C2212yescomplemented
71#16840039C2212yes—
72#16839822C2214yescomplemented
73#16839818C2212yescomplemented
74#16839814C2212yescomplemented
75#16839805C2212yes—
76#16839805C2212yes—
77C2×#14519709C2212yes—
78#16839786C2211yescharacteristic
79#16839766C2212yes—
80#16839763C2212yes—
81C2×#14519699C2212yes—
82#16839728C2212yes—
83#16839717C2212yes—
84C61×#533C2211yescharacteristic
85C4×#41×C61C2211yescharacteristic
86C61×#479C2212yescomplemented
87C61×#478C2212yescomplemented
88C61×#477C2211yescharacteristic, complemented
89C61×#476C2211yescharacteristic, complemented
90C61×#475C2211yescharacteristic, complemented
91C61×#474C2211yescharacteristic, complemented
92C61×#427C2212yes—
93C2×C4⋊C8×C61C2211yescharacteristic
94C61×#416C2212yes—
95C2×#11758222—22no—
96C2×#11758222C2311yescharacteristic
97C22×Dic122—21no—
98C2×Q8×D61—22no—
99C22×D244C2311yescharacteristic
100C22×C4×D61—21no—
101C2×#11758194C2312yes—
102#14519777—21no—
103#14519777—21no—
104#14519777—22no—
105#14519777—21no—
106#14519777C2312yes—
107#14519777C2312yes—
108#14519776—24no—
109#14519776—22no—
110#14519776C2314yes—
111#14519776C2312yes—
112#14519775—22no—
113#14519774—21no—
114#14519773C2312yes—
115#14519772—22no—
116#14519771—22no—
117#14519769—22no—
118#14519769—21no—
119#14519768C2312yes—
120#14519768C2314yes—
121#14519767—24no—
122#14519766C2312yes—
123#14519765—21no—
124#14519765—22no—
125#14519763—22no—
126#14519762—22no—
127#14519762—22no—
128#14519760—22no—
129#14519759—22no—
130#14519757—22no—
131#14519757—24no—
132#14519756—21no—
133#14519755—24no—
134#14519755—22no—
135#14519754—24no—
136#14519754—22no—
137#14519753—22no—
138#14519753C2312yes—
139#14519752C2312yes—
140#14519752C2312yes—
141#14519751—21no—
142#14519751—22no—
143#14519751—21no—
144#14519751—21no—
145#14519750—22no—
146#14519750—22no—
147#14519749—22no—
148#14519748C2312yes—
149#14519747—22no—
150#14519745—22no—
151Q8×Dic61—22no—
152C4×Dic122—22no—
153C4×Dic122D411yescharacteristic
154C4×Dic122D411yescharacteristic
155#14519742—22no—
156C4×D244—22no—
157C4×D244—22no—
158C4×D244—21no—
159C4×D244—21no—
160C4×D244D411yescharacteristic
161C4×D244D411yescharacteristic
162C4×D244C2312yes—
163C4×D244C2312yes—
164C4×C22⋊D61—22no—
165C4×C22⋊D61D412yes—
166C4×C22⋊D61D412yes—
167#14519737—24no—
168#14519736C2311yescharacteristic
169#14519735C2314yes—
170#14519734—22no—
171#14519734C2312yes—
172C2×C4⋊Dic61—21no—
173C2×C4⋊Dic61C2311yescharacteristic
174C2×C4⋊Dic61C2312yes—
175C4⋊C4×D61—22no—
176C4⋊C4×D61C2314yes—
177C2×#11758198—21no—
178C42×D61C2312yes—
179#14519710C2314yes—
180#14519710C2314yes—
181#14519709C2314yes—
182#14519709C2314yes—
183#14519708C2314yes—
184#14519708C2314yes—
185C4⋊#92418C2312yes—
186C4⋊#92418C2312yes—
187#14519701C2314yes—
188#14519699C2314yes—
189#14519699C2314yes—
190#14519698C2314yes—
191#14519697C2314yes—
192#14519697C2314yes—
193#14519689C2314yes—
194#14519689C2314yes—
195#14519687C2314yes—
196C8×Dic61C2314yes—
197C2×#41×C61C2311yescharacteristic
198C22×C8×C61C2312yes—
199C4⋊Q8×C61C2311yescharacteristic
200C4⋊Q8×C61C2311yescharacteristic
201#125×C61C2312yes—
202C22⋊Q8×C61—21no—
203C22⋊Q8×C61—21no—
204C4×Q8×C61—21no—
205C4×Q8×C61—21no—
206C4×Q8×C61C2311yescharacteristic
207C4×Q8×C61C2311yescharacteristic
208C4×D4×C61—21no—
209C4×D4×C61—21no—
210C4×D4×C61C2311yescharacteristic
211C4×D4×C61C2311yescharacteristic
212#117×C61—21no—
213#117×C61C2312yes—
214#117×C61C2311yescharacteristic
215C2×C42×C61—21no—
216C2×C42×C61C2311yescharacteristic
217#107×C61C2312yes—
218#107×C61C2312yes—
219#106×C61C2312yes—
220#106×C61C2312yes—
221C4⋊C8×C61C2311yescharacteristic
222C4⋊C8×C61C2311yescharacteristic
223C4⋊C8×C61C2312yes—
224#103×C61C2312yes—
225#103×C61C2312yes—
226#102×C61C2312yes—
227#102×C61C2312yes—
228C23×D61—21no—
229#41×C61—22no—
230#41×C61—22no—
231C2×Q8×C61—21no—
232C2×Q8×C61—21no—
233C2×Q8×C61C2411yescharacteristic
234C2×D4×C61—21no—
235C2×D4×C61C2411yescharacteristic
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2411yescharacteristic
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—22no—
245C2×C22⋊D61C2×D412yes—
246C22×Dic61—21no—
247C22×Dic61—22no—
248Q8×D61—84no—
249#11758222—22no—
250#11758222—22no—
251#11758222—84no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—21no—
255C2×D244—22no—
256C2×D244—22no—
257C2×D244C2×D411yescharacteristic
258C2×D244C2412yes—
259C2×C4×D61—22no—
260C2×C4×D61—24no—
261C2×C4×D61—22no—
262C2×C4×D61—82no—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2×D412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—24no—
269C2×Dic122—22no—
270C2×Dic122—82no—
271C2×Dic122C2×D411yescharacteristic
272C2×C8×C61—24no—
273C2×C8×C61C2412yes—
274C2×C8×C61C2412yes—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—22no—
278C4⋊C4×C61—22no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C2412yes—
282C4⋊C4×C61C2412yes—
283C4⋊C4×C61C2411yescharacteristic
284C4⋊C4×C61C2411yescharacteristic
285C22⋊C4×C61—21no—
286C22⋊C4×C61—22no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C42×C61—21no—
290C42×C61—21no—
291C42×C61—21no—
292C42×C61—22no—
293C42×C61C2×D411yescharacteristic
294C42×C61C2×D411yescharacteristic
295C42×C61C2411yescharacteristic
296C42×C61C2411yescharacteristic
297C22⋊Dic61—22no—
298C22⋊Dic61C2×D412yes—
299#11758198—24no—
300#11758198—22no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—22no—
306#11758198—22no—
307#11758198C2×D412yes—
308#11758198C2×D412yes—
309C4⋊Dic61—22no—
310C4⋊Dic61—22no—
311C4⋊Dic61—21no—
312C4⋊Dic61—22no—
313C4⋊Dic61—22no—
314C4⋊Dic61—24no—
315C4⋊Dic61C2×D411yescharacteristic
316C4⋊Dic61C2×D411yescharacteristic
317C4⋊Dic61C2414yes—
318C4⋊Dic61C2412yes—
319#11758196—24no—
320#11758196—24no—
321#11758196—22no—
322#11758196—22no—
323#11758196—22no—
324#11758196—24no—
325#11758196C2×D412yes—
326#11758196C2×D412yes—
327C4×Dic61—24no—
328C4×Dic61C2×D412yes—
329C4×Dic61C2×D412yes—
330C4×Dic61C2412yes—
331#11758194—24no—
332C2×#92418C2414yes—
333C23×C61—21no—
334C23×C61C22×D411yescharacteristic
335C22×D61—22no—
336C22×D61—42no—
337C22×D61—81no—
338C22×D61—81no—
339C22×D61C22×D412yes—
340Q8×C61—21no—
341Q8×C61—21no—
342Q8×C61—42no—
343Q8×C61—42no—
344D4×C61—21no—
345D4×C61—21no—
346D4×C61—42no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—41no—
354C2×C4×C61—42no—
355C2×C4×C61—42no—
356C2×C4×C61—81no—
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C612−1+412yes—
363C2×C4×C612−1+412yes—
364C2×C4×C61C2511yescharacteristic
365C22⋊D61—24no—
366C22⋊D61—82no—
367C22⋊D61—82no—
368C22⋊D61—82no—
369C2×Dic61—24no—
370C2×Dic61—22no—
371C2×Dic61—82no—
372C2×Dic61—81no—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376D244—22no—
377D244—22no—
378D244—22no—
379D244—42no—
380D244—82no—
381D244—82no—
382C4×D61—24no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—42no—
386C4×D61—44no—
387C4×D61—82no—
388C4×D61—84no—
389Dic122—22no—
390Dic122—44no—
391Dic122—82no—
392Dic122—84no—
393Dic122—82no—
394C8×C61—22no—
395C8×C61—22no—
396#92418—24no—
397#60892—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61#53612yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—84no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—42no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61—42no—
420C4×C61#53612yes—
421C4×C61#57712yes—
422C4×C61C2×2−1+411yescharacteristic
423C4×C61C2×2−1+411yescharacteristic
424Dic61—22no—
425Dic61—22no—
426Dic61—22no—
427Dic61—44no—
428Dic61—42no—
429#3503—611no—
430#3460—611no—
431#3244—614no—
432#3241—614no—
433#3238—612no—
434#3235—612no—
435#3233—612no—
436#3227—612no—
437#3163—612no—
438#3136—612no—
439#3099—612no—
440#3096—612no—
441#3079—611no—
442#3077—611no—
443#3076D6111yescharacteristic, complemented
444C2×#476—611no—
445#2925—611no—
446C2×C61—22no—
447C2×C61—81no—
448C2×C61C2×#53611yescharacteristic
449C2×C61C2×#57711yescharacteristic
450C2×C61#358511yescharacteristic
451D61—42no—
452D61—82no—
453Q82—1221no—
454#557—1221no—
455#554—1221no—
456#554—1222no—
457D4×Q8—1221no—
458D4×Q8—1222no—
459#544—614no—
460#544—612no—
461#544—611no—
462#542—612no—
463#542—1221no—
464#540—612no—
465#540—1221no—
466#538—1222no—
467#537—611no—
468#535—611no—
469#535—611no—
470#533—612no—
471#533C2×D6111yescharacteristic
472#532—612no—
473#532—1221no—
474C2×C4⋊Q8—612no—
475C2×C4⋊Q8—611no—
476#529—612no—
477#529—1221no—
478#525—1222no—
479#520—612no—
480C4×#41—611no—
481C4×#41C2×D6111yescharacteristic
482C2×C4×D4—611no—
483#501—614no—
484#501—614no—
485#499—614no—
486#498—614no—
487#490—614no—
488#489—614no—
489#488—614no—
490#486—614no—
491#485—614no—
492#483—614no—
493#482—614no—
494#482—614no—
495#482—614no—
496#481—614no—
497#481—614no—
498#480—614no—
499#479C2×D6112yescomplemented
500#478—614no—
501#478C2×D6112yescomplemented
502#477—612no—
503#477C2×D6111yescharacteristic, complemented
504#476—612no—
505#476—612no—
506#476—612no—
507#476—612no—
508#476—614no—
509#476C2×D6111yescharacteristic, complemented
510#475—612no—
511#475C2×D6111yescharacteristic, complemented
512#474—612no—
513#474—612no—
514#474C2×D6111yescharacteristic, complemented
515#433—614no—
516#432—612no—
517#431—612no—
518#428—612no—
519#428—612no—
520#427C2×D6112yes—
521C2×#106—612no—
522#423—611no—
523C2×C4⋊C8C2×D6111yescharacteristic
524#418—612no—
525#417—612no—
526#416C2×D6112yes—
527C2×#102—612no—
528#408—612no—
529#405—612no—
530C61#6089211yescharacteristic, complemented, Sylow
531C2×#41—611no—
532C2×#41—1222no—
533C2×#41C22×D6111yescharacteristic
534C22×Q8—1222no—
535C22×Q8—1221no—
536C22×D4—611no—
537C23×C4—1221no—
538C2×M16—612no—
539C22×C8C22×D6112yes—
540C4⋊Q8—614no—
541C4⋊Q8—612no—
542C4⋊Q8—612no—
543C4⋊Q8—612no—
544C4⋊Q8—1221no—
545C4⋊Q8—1222no—
546C4⋊Q8—1222no—
547C4⋊Q8—1222no—
548C4⋊Q8—1224no—
549C4⋊Q8—1221no—
550C4⋊Q8—1221no—
551C4⋊Q8C22×D6111yescharacteristic
552C4⋊Q8C22×D6111yescharacteristic
553#127—612no—
554#127—1221no—
555#126—1222no—
556#126—1222no—
557#125—612no—
558#125—614no—
559#125—1221no—
560#125—1222no—
561#125—1224no—
562#125C22×D6112yes—
563#124—612no—
564#124—1222no—
565#124—1221no—
566#124—1222no—
567#123—1222no—
568#123—1222no—
569#123—1222no—
570#123—1222no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—612no—
574C22⋊Q8—1222no—
575C22⋊Q8—1224no—
576C22⋊Q8—1224no—
577C22⋊Q8—1224no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580C22⋊Q8—1221no—
581C22⋊Q8—1222no—
582#121—612no—
583#121—612no—
584#121—612no—
585#121—1222no—
586#121—1222no—
587#121—1222no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1222no—
592#120—1222no—
593#120—1222no—
594C4×Q8—21no—
595C4×Q8—21no—
596C4×Q8—611no—
597C4×Q8—611no—
598C4×Q8—1222no—
599C4×Q8—1222no—
600C4×Q8—1222no—
601C4×Q8C22×D6111yescharacteristic
602C4×Q8C22×D6111yescharacteristic
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—612no—
606C4×D4—612no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—612no—
610C4×D4—612no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C4×D4—1224no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4C22×D6111yescharacteristic
618C4×D4C22×D6111yescharacteristic
619#117—21no—
620#117—611no—
621#117—612no—
622#117—614no—
623#117—1222no—
624#117C22×D6111yescharacteristic
625#117C22×D6112yes—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—614no—
629C2×C4⋊C4—1222no—
630C2×C4⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C42—21no—
633C2×C42—612no—
634C2×C42C22×D6111yescharacteristic
635#107—614no—
636#107—614no—
637#107C22×D6112yes—
638#107C22×D6112yes—
639#106—614no—
640#106—614no—
641#106—614no—
642#106—614no—
643#106C22×D6112yes—
644#106C22×D6112yes—
645C4⋊C8—612no—
646C4⋊C8—612no—
647C4⋊C8C22×D6111yescharacteristic
648C4⋊C8C22×D6111yescharacteristic
649C4⋊C8C22×D6112yes—
650#103—614no—
651#103C22×D6112yes—
652#103C22×D6112yes—
653#102—614no—
654#102—614no—
655#102—614no—
656#102—614no—
657#102—614no—
658#102C22×D6112yes—
659#102C22×D6112yes—
660C22⋊C8—614no—
661C22⋊C8—614no—
662#97—614no—
663C4×C8—614no—
664C24—1221no—
665#41—22no—
666#41—22no—
667#41—1222no—
668#41—1222no—
669#41—4884no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—611no—
673C2×Q8—1222no—
674C2×Q8—1224no—
675C2×Q8—1222no—
676C2×Q8—1222no—
677C2×Q8—4882no—
678C2×Q8—4884no—
679C2×Q8C23×D6111yescharacteristic
680C2×D4—21no—
681C2×D4—612no—
682C2×D4—611no—
683C2×D4—612no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1221no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4C23×D6111yescharacteristic
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—612no—
697C22×C4—612no—
698C22×C4—612no—
699C22×C4—1224no—
700C22×C4—1221no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—4882no—
705C22×C4D4×D6111yescharacteristic
706C22×C4D4×D6111yescharacteristic
707C22×C4C23×D6111yescharacteristic
708M16—1224no—
709C2×C8—24no—
710C2×C8—614no—
711C2×C8C23×D6112yes—
712C2×C8C23×D6112yes—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—612no—
720C4⋊C4—612no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—614no—
724C4⋊C4—612no—
725C4⋊C4—1224no—
726C4⋊C4—1224no—
727C4⋊C4—1222no—
728C4⋊C4—1222no—
729C4⋊C4—1222no—
730C4⋊C4—1224no—
731C4⋊C4—1222no—
732C4⋊C4—1224no—
733C4⋊C4—1221no—
734C4⋊C4—1222no—
735C4⋊C4—1222no—
736C4⋊C4—1222no—
737C4⋊C4C23×D6112yes—
738C4⋊C4C23×D6112yes—
739C4⋊C4C23×D6111yescharacteristic
740C4⋊C4C23×D6111yescharacteristic
741C22⋊C4—21no—
742C22⋊C4—22no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—612no—
746C22⋊C4—612no—
747C22⋊C4—612no—
748C22⋊C4—1222no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C22⋊C4—1222no—
752C22⋊C4—1224no—
753C22⋊C4—1222no—
754C22⋊C4—1222no—
755C22⋊C4—1222no—
756C22⋊C4—1222no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—22no—
761C42—612no—
762C42—612no—
763C42—612no—
764C42—1224no—
765C42D4×D6111yescharacteristic
766C42D4×D6111yescharacteristic
767C42C23×D6111yescharacteristic
768C42C23×D6111yescharacteristic
769C23—21no—
770C23—612no—
771C23—1222no—
772C23—4881no—
773C23—4881no—
774C23—2442no—
775C23C2×D4×D6111yescharacteristic
776Q8—21no—
777Q8—21no—
778Q8—42no—
779Q8—42no—
780Q8—1222no—
781Q8—4882no—
782Q8—4884no—
783Q8—4882no—
784Q8—2444no—
785D4—21no—
786D4—21no—
787D4—42no—
788D4—1224no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—4882no—
793D4—4882no—
794D4—4882no—
795D4—4882no—
796D4—4882no—
797D4—2442no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—612no—
809C2×C4—612no—
810C2×C4—612no—
811C2×C4—1224no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1224no—
815C2×C4—1222no—
816C2×C4—4882no—
817C2×C4—4884no—
818C2×C4—4881no—
819C2×C4—4882no—
820C2×C4—2442no—
821C2×C4—2444no—
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4#1451982412yes—
828C2×C4#1451982512yes—
829C2×C4C24×D6111yescharacteristic
830C8—22no—
831C8—22no—
832C8—1224no—
833C22—21no—
834C22—21no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—4884no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22#1684033512yes—
846C22C22×D4×D6111yescharacteristic
847C4—21no—
848C4—21no—
849C4—21no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—41no—
855C4—1222no—
856C4—1222no—
857C4—1222no—
858C4—2442no—
859C4—2444no—
860C4#1684033512yes—
861C4#1684056912yes—
862C4C2×#1451982411yescharacteristic
863C4C2×#1451982511yescharacteristic
864C2—22no—
865C2—81no—
866C2—4882no—
867C2—2442no—
868C2C2×#1684033511yescharacteristic
869C2C2×#1684056911yescharacteristic
870C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3076C2
socleC22×C61C23×D4
prime radical#21459235C2
hypercenter#3076D61
hypocenterC61#60892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #21459631C2semidirect
3. #21457124C2semidirect
4. #21457077C2semidirect
5. #21457044C2semidirect
6. #21457016C2semidirect
7. #21457002C2semidirect
8. #21456946C2semidirect
9. #21456351C2semidirect
10. #21456177C2semidirect
11. #21455806C2semidirect
12. #21455780C2semidirect
13. #21455634C2semidirect
14. #21455612C2semidirect
15. C2×#16840053C2semidirect
16. #21454484C2semidirect
17. C61×#3076C2semidirect
24. #16840392C22semidirect
35. #16840317C22semidirect
39. C4⋊Q8×D61C22semidirect
46. #16840170C22semidirect
47. #16840170C22semidirect
48. #16840162C22semidirect
49. #16840159C22semidirect
54. #16840101C22semidirect
55. #16840091C22semidirect
58. #16840085C22semidirect
60. #16840079C22semidirect
63. #16840057C22semidirect
67. #16840052C22semidirect
69. #16840047C22semidirect
70. #16840042C22semidirect
72. #16839822C22semidirect
73. #16839818C22semidirect
74. #16839814C22semidirect
86. C61×#479C22semidirect
87. C61×#478C22semidirect
88. C61×#477C22semidirect
89. C61×#476C22semidirect
90. C61×#475C22semidirect
91. C61×#474C22semidirect
443. #3076D61semidirect
499. #479C2×D61semidirect
501. #478C2×D61semidirect
503. #477C2×D61semidirect
509. #476C2×D61semidirect
511. #475C2×D61semidirect
514. #474C2×D61semidirect
530. C61#60892semidirect

Maximal subgroups

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

subgroupindex
#214596312
#214592352
#214571242
#214570772
#214570442
#214570162
#214570022
#214569462
#214563512
#214561772
#214558062
#214557802
#214556342
#214556122
C2×#168400532
#214544842
C61×#30762
#6089261