Finite Group Databasebeta

← #30560048

Subgroups — #30560048

Order 15616.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459705C211yesmaximal, characteristic, complemented
2#21459635C211yesmaximal, characteristic, complemented
3#21458621C212yesmaximal, complemented
4#21458599C212yesmaximal, complemented
5#21458558C212yesmaximal, complemented
6#21458536C212yesmaximal, complemented
7#21458503C212yesmaximal, complemented
8#21458496C212yesmaximal, complemented
9#21458467C212yesmaximal, complemented
10#21458460C212yesmaximal, complemented
11#21456187C212yesmaximal, complemented
12C2×#16840114C211yesmaximal, characteristic, complemented
13#21455659C212yesmaximal, complemented
14#21455368C212yesmaximal
15#21455307C211yesmaximal, characteristic, complemented
16#21454749C211yesmaximal, characteristic, complemented
17#21454660C212yesmaximal, complemented
18C4×#14519797C211yesmaximal, characteristic
19C61×#3079C211yesmaximal, characteristic, complemented
20C2×#14519810C2212yes—
21C2×#14519797C2211yescharacteristic
22#16840492C2212yes—
23#16840490C2212yes—
24#16840490C2212yes—
25#16840487C2212yes—
26#16840482C2212yes—
27#16840482C2212yes—
28#16840473C2212yes—
29#16840467—22no—
30#16840452—22no—
31#16840452—22no—
32#16840427C2212yes—
33Q8×C22⋊D61—22no—
34#16840393C2212yes—
35#16840389—22no—
36#16840374—22no—
37#16840333C2212yes—
38#16840319—21no—
39#16840319—21no—
40#16840319C2211yescharacteristic
41#16840317—21no—
42C2×#14519777C2211yescharacteristic
43C4⋊Q8×D61—21no—
44#16840243C2212yes—
45#16840239C2212yes—
46C4×#11758222C2211yescharacteristic
47#16840129C2214yes—
48#16840120C2214yes—
49#16840115C2214yes—
50#16840114C2212yes—
51#16840114C2212yes—
52#16840114C2212yes—
53#16840114C2212yes—
54#16840111C2214yes—
55#16840072C2214yes—
56#16840068C2214yes—
57#16840056C2214yes—
58#16840046C2214yes—
59#16839983C2214yes—
60#16839976C2214yes—
61#16839973C2212yes—
62#16839973C2212yes—
63#16839971C2214yes—
64#16839968C2212yes—
65#16839968C2212yes—
66#16839966C2214yes—
67#16839889C2212yes—
68#16839889C2212yes—
69#16839886C2212yes—
70#16839886C2212yes—
71#16839868C2214yes—
72#16839861C2214yes—
73#16839856C2214yes—
74C4×#11758202C2211yescharacteristic
75C4×#11758202C2211yescharacteristic
76C4×#11758201C2211yescharacteristic
77C4×#11758201C2211yescharacteristic
78#16839849C2214yes—
79C4×#11758200C2211yescharacteristic
80C4×#11758200C2211yescharacteristic
81C4×#11758199C2211yescharacteristic
82C4×#11758199C2211yescharacteristic
83#16839798C2211yescharacteristic
84#16839790C2212yes—
85#16839772C2212yes—
86#16839758C2211yescharacteristic
87#16839756C2211yescharacteristic
88C2×#14519700C2212yes—
89C2×#14519700C2212yes—
90#16839720C2212yes—
91C2×C4×#92418C2211yescharacteristic
92C2×C4⋊Q8×C61C2211yescharacteristic
93C4×#41×C61C2211yescharacteristic
94C61×#477C2212yes—
95C61×#476C2212yes—
96C61×#475C2212yes—
97C61×#474C2212yes—
98C61×#428C2212yes—
99C61×#423C2211yescharacteristic
100C61×#417C2212yes—
101C2×#11758222C2311yescharacteristic
102C22×Dic122C2312yes—
103C2×Q8×D61—22no—
104#14519810—28no—
105#14519797—24no—
106C2×Dic244C2314yes—
107C2×#11758202C2311yescharacteristic
108C2×#11758190C2314yes—
109C2×#11758200C2311yescharacteristic
110C2×#11758201C2311yescharacteristic
111C2×#11758199C2311yescharacteristic
112C22×#92418C2311yescharacteristic
113C22×#92418C2311yescharacteristic
114#14519777—21no—
115#14519777—21no—
116#14519777D411yescharacteristic
117#14519777D411yescharacteristic
118#14519777C2312yes—
119#14519777C2312yes—
120#14519776—22no—
121#14519776—22no—
122#14519776C2314yes—
123#14519775—22no—
124#14519775—24no—
125#14519775C2314yes—
126#14519770—24no—
127#14519770—24no—
128#14519769—22no—
129#14519769—22no—
130#14519769D412yes—
131#14519768—22no—
132#14519768C2314yes—
133#14519767—24no—
134#14519767—24no—
135#14519767—24no—
136#14519764C2314yes—
137#14519758—24no—
138#14519757—22no—
139#14519756—22no—
140#14519756—22no—
141#14519756—24no—
142#14519756—22no—
143#14519756—22no—
144#14519756D412yes—
145#14519756D412yes—
146#14519755—24no—
147#14519753—22no—
148#14519753—24no—
149Q8×Dic61—22no—
150C4×Dic122—22no—
151C4×Dic122—22no—
152C4×Dic122—22no—
153C4×Dic122—22no—
154C4×Dic122C2311yescharacteristic
155C4×Dic122C2311yescharacteristic
156C4×Dic122C2312yes—
157C4×Dic122C2312yes—
158#14519742—22no—
159#14519742C2314yes—
160#14519742C2314yes—
161#14519742C2314yes—
162C4×D244C2311yescharacteristic
163C4×D244C2311yescharacteristic
164#14519739C2314yes—
165C4×C22⋊D61—21no—
166C4×C22⋊D61—21no—
167C4×C22⋊D61—24no—
168#14519736—22no—
169#14519736—22no—
170#14519736C2311yescharacteristic
171#14519736C2312yes—
172#14519735—22no—
173#14519734—21no—
174#14519733—24no—
175C2×C4⋊Dic61—21no—
176C2×C4⋊Dic61—21no—
177C4⋊C4×D61—22no—
178C4⋊C4×D61—22no—
179C42×D61—21no—
180#14519710C2311yescharacteristic
181#14519710C2311yescharacteristic
182#14519708C2311yescharacteristic
183#14519708C2311yescharacteristic
184#14519706C2314yes—
185#14519706C2314yes—
186#14519702C2314yes—
187#14519702C2314yes—
188#14519701C2311yescharacteristic
189#14519701C2311yescharacteristic
190#14519700C2314yes—
191#14519700C2314yes—
192#14519700C2314yes—
193#14519700C2314yes—
194#14519700C2311yescharacteristic
195#14519700C2311yescharacteristic
196#14519698C2311yescharacteristic
197#14519698C2311yescharacteristic
198#14519697C2311yescharacteristic
199#14519697C2311yescharacteristic
200#14519687C2314yes—
201C4×#92418C2311yescharacteristic
202C4×#92418C2311yescharacteristic
203C4×#92418C2311yescharacteristic
204C4×#92418C2311yescharacteristic
205C8×Dic61C2314yes—
206C2×#41×C61C2311yescharacteristic
207C22×Q8×C61—21no—
208C2×M16×C61C2312yes—
209C4⋊Q8×C61—21no—
210C4⋊Q8×C61—21no—
211C4⋊Q8×C61C2312yes—
212C4⋊Q8×C61C2312yes—
213C4×Q8×C61C2311yescharacteristic
214C4×Q8×C61C2311yescharacteristic
215C4×D4×C61—21no—
216C4×D4×C61—21no—
217C4×D4×C61C2311yescharacteristic
218C4×D4×C61C2311yescharacteristic
219#117×C61—21no—
220#117×C61C2311yescharacteristic
221C2×C4⋊C4×C61—21no—
222C2×C4⋊C4×C61C2312yes—
223C2×C42×C61—21no—
224C2×C42×C61C2311yescharacteristic
225#107×C61C2314yes—
226#106×C61C2314yes—
227C4⋊C8×C61C2312yes—
228C4⋊C8×C61C2312yes—
229#103×C61C2314yes—
230#102×C61C2314yes—
231#41×C61—22no—
232#41×C61—22no—
233C2×Q8×C61—22no—
234C2×Q8×C61—22no—
235C2×Q8×C61—82no—
236C2×Q8×C61C2411yescharacteristic
237C2×D4×C61—21no—
238C2×D4×C61C2411yescharacteristic
239C22×C4×C61—22no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2411yescharacteristic
246C2×C22⋊D61—21no—
247C22×Dic61—22no—
248Q8×D61—84no—
249#11758222—22no—
250#11758222#4114yes—
251C2×D244C2411yescharacteristic
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—24no—
256C2×Dic122—24no—
257C2×Dic122—24no—
258C2×Dic122—22no—
259C2×Dic122—24no—
260C2×Dic122C2×D412yes—
261C2×Dic122C2×D412yes—
262C2×Dic122C2414yes—
263C2×Dic122C2411yescharacteristic
264M16×C61—24no—
265C2×C8×C61C2414yes—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—22no—
268C4⋊C4×C61—22no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C2414yes—
272C4⋊C4×C61C2411yescharacteristic
273C4⋊C4×C61C2411yescharacteristic
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C42×C61—21no—
278C42×C61—21no—
279C42×C61—21no—
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2411yescharacteristic
283C42×C61C2411yescharacteristic
284C22⋊Dic61—21no—
285C22⋊Dic61—24no—
286C22⋊Dic61—24no—
287C22⋊Dic61C2×D414yes—
288#11758202—22no—
289#11758201—22no—
290#11758200—22no—
291#11758199—22no—
292#11758198—21no—
293#11758198—21no—
294#11758198—24no—
295C4⋊Dic61—22no—
296C4⋊Dic61—22no—
297C4⋊Dic61—22no—
298C4⋊Dic61—22no—
299C4⋊Dic61—24no—
300C4⋊Dic61C2×D412yes—
301C4⋊Dic61C2×D412yes—
302C4⋊Dic61C2×D412yes—
303C4⋊Dic61C2×D412yes—
304C4⋊Dic61C2411yescharacteristic
305C4⋊Dic61C2411yescharacteristic
306#11758196—21no—
307#11758196—21no—
308#11758196—24no—
309#11758196—24no—
310#11758196—24no—
311#11758196—24no—
312#11758196—24no—
313#11758196—24no—
314#11758196—24no—
315#11758196C2×D414yes—
316#11758196C2×D414yes—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—24no—
321C4×Dic61—24no—
322C4×Dic61—24no—
323C4×Dic61C2414yes—
324C2×#92418—22no—
325C2×#92418—22no—
326C2×#92418C2411yescharacteristic
327C2×#92418C2411yescharacteristic
328C2×#92418C2411yescharacteristic
329C2×#92418C2411yescharacteristic
330Dic244—28no—
331#11758190—28no—
332C23×C61—21no—
333C23×C61C22×D411yescharacteristic
334C22×D61—21no—
335Q8×C61—21no—
336Q8×C61—21no—
337Q8×C61—44no—
338Q8×C61—82no—
339D4×C61—21no—
340D4×C61—21no—
341D4×C61—42no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—24no—
347C2×C4×C61—21no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—82no—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C2×#4112yes—
358C2×C4×C612−1+412yes—
359C2×C4×C61C2511yescharacteristic
360C22⋊D61—24no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—24no—
365C2×Dic61—44no—
366C2×Dic61C22×D414yes—
367C2×Dic61C22×D414yes—
368D244—21no—
369D244C2×#4112yes—
370C4×D61—24no—
371C4×D61—42no—
372C4×D61—42no—
373C4×D61—84no—
374Dic122—24no—
375Dic122—24no—
376Dic122—21no—
377Dic122—24no—
378Dic122—24no—
379Dic122—44no—
380Dic122—84no—
381Dic122C2×#4112yes—
382C8×C61—24no—
383#92418—21no—
384#92418—21no—
385#92418—21no—
386#92418—21no—
387#61330—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61#54812yes—
394C22×C61C23×D411yescharacteristic
395C2×D61—22no—
396C2×D61—41no—
397C2×D61—41no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—41no—
401C4×C61—44no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61#54812yes—
405C4×C61#57712yes—
406C4×C61#57812yes—
407C4×C61C22×#4111yescharacteristic
408C4×C61C2×2−1+411yescharacteristic
409Dic61—22no—
410Dic61—24no—
411Dic61—24no—
412Dic61—44no—
413Dic61—41no—
414Dic61—41no—
415#3509—611no—
416#3503—611no—
417#3374—612no—
418#3372—612no—
419#3369—612no—
420#3367—612no—
421#3364—612no—
422#3363—612no—
423#3360—612no—
424#3359—612no—
425#3137—612no—
426C2×#487—611no—
427#3082—612no—
428#3079D6111yescharacteristic, complemented
429#3046—612no—
430#3039—611no—
431#2960—611no—
432#2947—612no—
433C4×#135—611no—
434C2×C61—22no—
435C2×C61—81no—
436C2×C61C2×#54811yescharacteristic
437C2×C61C2×#57711yescharacteristic
438C2×C61C2×#57811yescharacteristic
439D61—42no—
440C2×#137—612no—
441C2×#135—611no—
442Q82—612no—
443#557—612no—
444#557—612no—
445#557—612no—
446#556—612no—
447#556—612no—
448#554—612no—
449#554—1222no—
450#552—1222no—
451#552—1222no—
452D4×Q8—612no—
453D4×Q8—1222no—
454#544—612no—
455#544—1222no—
456#541—1222no—
457#536—612no—
458#533—611no—
459#533—1221no—
460#533—1221no—
461#533—1221no—
462C2×C4⋊Q8—611no—
463C2×C4⋊Q8—1221no—
464C2×C4⋊Q8C2×D6111yescharacteristic
465#520—612no—
466#519—612no—
467C4×#41—611no—
468C4×#41C2×D6111yescharacteristic
469#491—614no—
470#489—614no—
471#488—614no—
472#487—612no—
473#487—612no—
474#487—612no—
475#487—612no—
476#487—614no—
477#479—614no—
478#479—614no—
479#477—614no—
480#477C2×D6112yes—
481#476C2×D6112yes—
482#475—614no—
483#475C2×D6112yes—
484#474C2×D6112yes—
485#464—614no—
486#463—614no—
487#462—612no—
488#462—612no—
489#462—614no—
490#461—612no—
491#461—612no—
492#461—614no—
493#446—612no—
494#446—612no—
495C8×Q8—612no—
496C8×Q8—612no—
497#441—614no—
498#440—614no—
499C4×Q16—611no—
500C4×Q16—611no—
501C4×Q16—614no—
502C4×SD16—611no—
503C4×SD16—611no—
504C4×SD16—611no—
505C4×SD16—611no—
506C4×SD16—614no—
507C4×D8—611no—
508C4×D8—611no—
509#428C2×D6112yes—
510#427—611no—
511#424—612no—
512#423C2×D6111yescharacteristic
513#419—612no—
514#417C2×D6112yes—
515#416—611no—
516#416—611no—
517C2×#103—612no—
518C2×#103—612no—
519#405—612no—
520C2×C4×C8—611no—
521C61#6133011yescharacteristic, complemented, Sylow
522C2×#41—611no—
523C2×#41C22×D6111yescharacteristic
524C22×Q8—21no—
525C22×Q8—612no—
526C22×Q8—1222no—
527#137—1228no—
528#135—1224no—
529C2×Q16—611no—
530C2×Q16—614no—
531C2×SD16—611no—
532C2×SD16—611no—
533C2×SD16—614no—
534C2×D8—611no—
535C2×M16C22×D6112yes—
536C22×C8—611no—
537C22×C8—611no—
538C4⋊Q8—21no—
539C4⋊Q8—21no—
540C4⋊Q8—614no—
541C4⋊Q8—614no—
542C4⋊Q8—611no—
543C4⋊Q8—611no—
544C4⋊Q8—612no—
545C4⋊Q8—612no—
546C4⋊Q8—1222no—
547C4⋊Q8—1222no—
548C4⋊Q8—1224no—
549C4⋊Q8—1222no—
550C4⋊Q8—1221no—
551C4⋊Q8—1221no—
552C4⋊Q8C22×D6112yes—
553C4⋊Q8C22×D6112yes—
554#126—1224no—
555#126—1224no—
556#125—614no—
557#125—612no—
558#125—1222no—
559#125—1222no—
560#125—1222no—
561#125—1224no—
562#125—1224no—
563#125—1224no—
564#124—614no—
565#123—1224no—
566C22⋊Q8—612no—
567C22⋊Q8—612no—
568C22⋊Q8—1224no—
569C22⋊Q8—1224no—
570C22⋊Q8—1222no—
571C22⋊Q8—1222no—
572C22⋊Q8—1222no—
573C22⋊Q8—1222no—
574C22⋊Q8—1224no—
575C22⋊Q8—1222no—
576C22⋊Q8—1222no—
577C4×Q8—612no—
578C4×Q8—612no—
579C4×Q8—614no—
580C4×Q8—614no—
581C4×Q8—614no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—1222no—
585C4×Q8—1222no—
586C4×Q8—1222no—
587C4×Q8—1222no—
588C4×Q8—1222no—
589C4×Q8—1222no—
590C4×Q8C22×D6111yescharacteristic
591C4×Q8C22×D6111yescharacteristic
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—614no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—1224no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4C22×D6111yescharacteristic
601C4×D4C22×D6111yescharacteristic
602#117—21no—
603#117—612no—
604#117—611no—
605#117—1224no—
606#117—1222no—
607#117—1222no—
608#117—1222no—
609#117—1221no—
610#117C22×D6111yescharacteristic
611C2×C4⋊C4—21no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4C22×D6112yes—
617C2×C42—21no—
618C2×C42—1221no—
619C2×C42C22×D6111yescharacteristic
620#107—611no—
621#107—611no—
622#107C22×D6114yes—
623#106—611no—
624#106—611no—
625#106C22×D6114yes—
626C4⋊C8—614no—
627C4⋊C8—614no—
628C4⋊C8C22×D6112yes—
629C4⋊C8C22×D6112yes—
630#103—611no—
631#103—611no—
632#103—614no—
633#103—614no—
634#103—614no—
635#103—614no—
636#103—614no—
637#103—614no—
638#103—611no—
639#103—611no—
640#103C22×D6114yes—
641#102—611no—
642#102—611no—
643#102—611no—
644#102—611no—
645#102C22×D6114yes—
646#97—614no—
647C4×C8—614no—
648C4×C8—611no—
649C4×C8—611no—
650C4×C8—611no—
651C4×C8—611no—
652#41—22no—
653#41—22no—
654#41—614no—
655#41—1222no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—82no—
659C2×Q8—612no—
660C2×Q8—612no—
661C2×Q8—611no—
662C2×Q8—614no—
663C2×Q8—1224no—
664C2×Q8—1222no—
665C2×Q8—1224no—
666C2×Q8—1224no—
667C2×Q8—4884no—
668C2×Q8C23×D6111yescharacteristic
669C2×D4—21no—
670C2×D4—611no—
671C2×D4—1221no—
672C2×D4C23×D6111yescharacteristic
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—1224no—
678C22×C4—1221no—
679C22×C4—1222no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4D4×D6111yescharacteristic
683C22×C4D4×D6111yescharacteristic
684C22×C4C23×D6111yescharacteristic
685Q16—1228no—
686Q16—1222no—
687SD16—1228no—
688SD16—1222no—
689SD16—1222no—
690D8—1222no—
691M16—24no—
692C2×C8—611no—
693C2×C8—611no—
694C2×C8—611no—
695C2×C8—611no—
696C2×C8—1222no—
697C2×C8—1222no—
698C2×C8C23×D6114yes—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—612no—
705C4⋊C4—612no—
706C4⋊C4—614no—
707C4⋊C4—614no—
708C4⋊C4—612no—
709C4⋊C4—612no—
710C4⋊C4—611no—
711C4⋊C4—611no—
712C4⋊C4—1224no—
713C4⋊C4—1224no—
714C4⋊C4—1224no—
715C4⋊C4—1224no—
716C4⋊C4—1224no—
717C4⋊C4—1224no—
718C4⋊C4—1224no—
719C4⋊C4—1224no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4C23×D6111yescharacteristic
727C4⋊C4C23×D6111yescharacteristic
728C4⋊C4C23×D6114yes—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—614no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—614no—
743C42—1224no—
744C42—1224no—
745C42—1224no—
746C42—1221no—
747C42—1221no—
748C42—1221no—
749C42D4×D6111yescharacteristic
750C42D4×D6111yescharacteristic
751C42C23×D6111yescharacteristic
752C42C23×D6111yescharacteristic
753C23—21no—
754C23—1221no—
755C23C2×D4×D6111yescharacteristic
756Q8—21no—
757Q8—21no—
758Q8—44no—
759Q8—82no—
760Q8—612no—
761Q8—1224no—
762Q8—1224no—
763Q8—1221no—
764Q8—1224no—
765Q8—1224no—
766Q8—4884no—
767Q8—2444no—
768D4—21no—
769D4—21no—
770D4—42no—
771D4—612no—
772D4—1224no—
773D4—1221no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—24no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—82no—
784C2×C4—614no—
785C2×C4—614no—
786C2×C4—1221no—
787C2×C4—1224no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1224no—
791C2×C4—4884no—
792C2×C4—2444no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4C2×D4×D6111yescharacteristic
796C2×C4C2×D4×D6111yescharacteristic
797C2×C4C2×D4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C2×C4#41×D6112yes—
801C2×C4#1451982512yes—
802C2×C4C24×D6111yescharacteristic
803C8—24no—
804C8—1221no—
805C8—1221no—
806C8—1221no—
807C8—1221no—
808C22—21no—
809C22—21no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—1222no—
814C22—2441no—
815C22—2441no—
816C22#1684042212yes—
817C22C22×D4×D6111yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—44no—
823C4—41no—
824C4—1222no—
825C4—1224no—
826C4—1224no—
827C4—2444no—
828C4—2441no—
829C4—2441no—
830C4#1684042212yes—
831C4#1684057212yes—
832C4#1684057812yes—
833C4C2×#41×D6111yescharacteristic
834C4C2×#1451982511yescharacteristic
835C2—22no—
836C2—81no—
837C2—2442no—
838C2C2×#1684042211yescharacteristic
839C2C2×#1684057211yescharacteristic
840C2C2×#1684057811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3079C2
socleC22×C61C23×D4
prime radicalC2×#14519797C22
hypercenter#3079D61
hypocenterC61#61330
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #21459705C2semidirect
2. #21459635C2semidirect
3. #21458621C2semidirect
4. #21458599C2semidirect
5. #21458558C2semidirect
6. #21458536C2semidirect
7. #21458503C2semidirect
8. #21458496C2semidirect
9. #21458467C2semidirect
10. #21458460C2semidirect
11. #21456187C2semidirect
12. C2×#16840114C2semidirect
13. #21455659C2semidirect
15. #21455307C2semidirect
16. #21454749C2semidirect
17. #21454660C2semidirect
19. C61×#3079C2semidirect
428. #3079D61semidirect
521. C61#61330semidirect

Maximal subgroups

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

subgroupindex
#214597052
#214596352
#214586212
#214585992
#214585582
#214585362
#214585032
#214584962
#214584672
#214584602
#214561872
C2×#168401142
#214556592
#214553682
#214553072
#214547492
#214546602
C4×#145197972
C61×#30792
#6133061