Finite Group Databasebeta

← #30549710

Subgroups — #30549710

Order 15616.

1790 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459643C211yesmaximal, characteristic
2#21459635C211yesmaximal, characteristic
3#21456370C212yesmaximal, complemented
4#21456368C211yesmaximal, characteristic, complemented
5#21456364C212yesmaximal, complemented
6#21456361C211yesmaximal, characteristic, complemented
7#21456355C212yesmaximal, complemented
8#21456354C214yesmaximal, complemented
9#21456347C212yesmaximal, complemented
10#21456346C214yesmaximal, complemented
11#21456343C211yesmaximal, characteristic, complemented
12#21456340C212yesmaximal, complemented
13#501×D61C212yesmaximal, complemented
14#21454415C212yesmaximal
15#21454410C212yesmaximal
16#21454244C211yesmaximal, characteristic
17C2×C61×#501C211yesmaximal, characteristic, complemented
18C2×#14519783C2212yes—
19#16840492—21no—
20#16840489—21no—
21#16840489—21no—
22#16840487—21no—
23#16840473—21no—
24#16840468—21no—
25#16840468—21no—
26#16840467—22no—
27#16840467—22no—
28#16840467—22no—
29#16840427—21no—
30Q8×C22⋊D61—22no—
31#16840393C2212yes—
32#16840393C2211yescharacteristic
33#16840393C2211yescharacteristic
34#16840392C2212yes—
35#16840392C2212yes—
36#16840389C2214yes—
37#16840319C2211yescharacteristic
38#16840319C2211yescharacteristic
39#16840318C2212yes—
40#16840317C2212yes—
41C4⋊Q8×D61C2212yes—
42#125×D61C2212yes—
43#16840243C2211yescharacteristic
44#16840243C2212yes—
45#16840243C2211yescharacteristic
46C4×#11758222C2211yescharacteristic
47#16840172C2212yes—
48#16840172C2212yes—
49#16840171C2211yescharacteristic
50#16840171C2211yescharacteristic
51#16840171C2212yes—
52#16840171C2212yes—
53#16840171C2211yescharacteristic
54#16840171C2211yescharacteristic
55#16840170C2214yes—
56#16840170C2214yes—
57#16840169C2214yes—
58#16840169C2214yes—
59#16840168C2212yes—
60#16840168C2212yes—
61#16840166C2214yes—
62#16840165C2212yes—
63#16840163C2214yes—
64#16840162C2214yes—
65#16840161C2214yes—
66#16840159C2214yes—
67#16840158C2212yes—
68#16839803C2214yes—
69#16839803C2214yes—
70#16839802C2212yes—
71#16839802C2212yes—
72#16839802C2212yes—
73#16839802C2212yes—
74#16839801C2214yes—
75#16839801C2214yes—
76#16839800C2212yes—
77#16839800C2212yes—
78#16839799C2214yes—
79#16839797C2214yes—
80#107×D61C2214yes—
81#106×D61C2214yes—
82#16839719C2214yes—
83#16839717C2212yes—
84C4×#11758194C2211yescharacteristic
85#16839714C2212yes—
86#97×D61C2212yes—
87C2×C4⋊Q8×C61C2211yescharacteristic
88C2×#125×C61C2211yescharacteristic
89C61×#501C2212yes—
90C61×#501C2214yes—
91C61×#501C2212yes—
92C2×#107×C61C2212yes—
93C2×#106×C61C2212yes—
94C2×#97×C61C2211yescharacteristic
95C2×#11758222C2311yescharacteristic
96C2×Q8×D61—22no—
97#14519783Q8116yescomplemented
98C2×#11758194C2312yes—
99C2×#11758189C2314yes—
100C2×C8×D61C2314yes—
101#14519777C2311yescharacteristic
102#14519777C2311yescharacteristic
103#14519777C2311yescharacteristic
104#14519777C2311yescharacteristic
105#14519776—21no—
106#14519776—21no—
107#14519776—22no—
108#14519776—22no—
109#14519776—22no—
110#14519776—22no—
111#14519776C2314yes—
112#14519776C2312yes—
113#14519776C2312yes—
114#14519775—24no—
115#14519775—22no—
116#14519769C2311yescharacteristic
117#14519769C2311yescharacteristic
118#14519769C2312yes—
119#14519768—21no—
120#14519768—21no—
121#14519768—22no—
122#14519768C2312yes—
123#14519768C2312yes—
124#14519768C2314yes—
125#14519767—24no—
126#14519767—22no—
127#14519767—22no—
128#14519767—22no—
129#14519767—22no—
130#14519757—22no—
131#14519757—22no—
132#14519757—22no—
133#14519756—21no—
134#14519756—21no—
135#14519756—21no—
136#14519756—21no—
137#14519756—22no—
138#14519756—22no—
139#14519756—24no—
140#14519755—22no—
141#14519755—22no—
142#14519755—22no—
143#14519755—22no—
144#14519755—24no—
145#14519753—22no—
146#14519753—24no—
147Q8×Dic61—22no—
148C4×Dic122—21no—
149C4×Dic122—21no—
150C4×Dic122—21no—
151C4×Dic122—21no—
152C4×Dic122D411yescharacteristic
153C4×Dic122D411yescharacteristic
154#14519742—22no—
155#14519742—21no—
156#14519742—21no—
157#14519742—22no—
158#14519742—22no—
159#14519742—22no—
160C4×D244D411yescharacteristic
161C4×D244D411yescharacteristic
162#14519739—21no—
163#14519739—21no—
164#14519739—22no—
165C4×C22⋊D61—22no—
166C4×C22⋊D61—22no—
167C4×C22⋊D61—24no—
168C4×C22⋊D61D412yes—
169C4×C22⋊D61D412yes—
170#14519736C2311yescharacteristic
171#14519736C2311yescharacteristic
172#14519736C2312yes—
173#14519736C2311yescharacteristic
174#14519735C2312yes—
175#14519735C2314yes—
176#14519735C2312yes—
177#14519734C2312yes—
178C4⋊C4×D61—22no—
179C4⋊C4×D61—22no—
180C4⋊C4×D61—22no—
181C4⋊C4×D61C2312yes—
182C4⋊C4×D61C2312yes—
183C4⋊C4×D61C2314yes—
184C42×D61C2312yes—
185#14519711C2312yes—
186#14519711C2312yes—
187#14519711C2312yes—
188#14519711C2312yes—
189#14519710C2314yes—
190#14519710C2314yes—
191#14519710C2314yes—
192#14519710C2314yes—
193#14519709C2312yes—
194#14519709C2312yes—
195#14519709C2312yes—
196#14519709C2312yes—
197#14519708C2314yes—
198#14519708C2314yes—
199#14519708C2314yes—
200#14519708C2314yes—
201#14519688C2312yes—
202#14519687C2314yes—
203C4×#92418C2312yes—
204C8×Dic61C2314yes—
205C22×Q8×C61—21no—
206C22×C8×C61C2312yes—
207C4⋊Q8×C61—21no—
208C4⋊Q8×C61—21no—
209C4⋊Q8×C61C2312yes—
210C4⋊Q8×C61C2312yes—
211#125×C61—21no—
212#125×C61—21no—
213#125×C61C2312yes—
214#125×C61C2312yes—
215C2×C4⋊C4×C61—21no—
216C2×C4⋊C4×C61—21no—
217C2×C4⋊C4×C61—21no—
218C2×C4⋊C4×C61C2312yes—
219C2×C4⋊C4×C61C2311yescharacteristic
220C2×C4⋊C4×C61C2311yescharacteristic
221C2×C42×C61C2311yescharacteristic
222#107×C61C2314yes—
223#107×C61C2314yes—
224#106×C61C2314yes—
225#106×C61C2314yes—
226#97×C61C2311yescharacteristic
227#97×C61C2311yescharacteristic
228#97×C61C2312yes—
229C2×Q8×C61—22no—
230C2×Q8×C61—22no—
231C2×Q8×C61—82no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—22no—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61C2×D412yes—
239Q8×D61—84no—
240#11758222C2×Q818yes—
241C2×D244C2×D411yescharacteristic
242C2×C4×D61—24no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61C2×D412yes—
246C2×C4×D61C2×D412yes—
247C2×C4×D61C2412yes—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—21no—
252C2×Dic122—24no—
253C2×Dic122—22no—
254C2×Dic122—22no—
255C2×Dic122C2×D411yescharacteristic
256C2×C8×C61C2×Q818yescomplemented
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—22no—
264C4⋊C4×C61—22no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—22no—
268C4⋊C4×C61C2412yes—
269C4⋊C4×C61C2414yes—
270C4⋊C4×C61C2412yes—
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2411yescharacteristic
274C42×C61C2411yescharacteristic
275C22⋊Dic61—22no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61C2×D412yes—
279#11758198—24no—
280#11758198—22no—
281#11758198—22no—
282#11758198C2×D412yes—
283#11758198C2×D412yes—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—22no—
289C4⋊Dic61—22no—
290C4⋊Dic61—24no—
291C4⋊Dic61C2×D411yescharacteristic
292C4⋊Dic61C2×D411yescharacteristic
293C4⋊Dic61C2411yescharacteristic
294C4⋊Dic61C2411yescharacteristic
295C4⋊Dic61C2412yes—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2411yescharacteristic
298C4⋊Dic61C2411yescharacteristic
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—22no—
304#11758196—22no—
305#11758196—24no—
306#11758196—22no—
307#11758196—22no—
308#11758196—22no—
309#11758196—22no—
310#11758196—24no—
311#11758196—24no—
312#11758196—22no—
313#11758196—22no—
314#11758196C2×D412yes—
315#11758196C2×D412yes—
316C4×Dic61—22no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C4×Dic61—24no—
322C4×Dic61C2×D412yes—
323C4×Dic61C2×D412yes—
324C4×Dic61C2412yes—
325#11758194C2×Q818yescomplemented
326C2×#92418C2414yes—
327#11758189C2×Q8116yescomplemented
328C8×D61C2×Q8116yescomplemented
329C23×C61C22×D411yescharacteristic
330C22×D61C22×D412yes—
331Q8×C61—44no—
332Q8×C61—82no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—81no—
339C2×C4×C61—81no—
340C2×C4×C61—82no—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×Q814yes—
347C2×C4×C61C2511yescharacteristic
348C22⋊D61C4⋊Q818yes—
349C2×Dic61—22no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358D244C4⋊Q814yes—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—82no—
362C4×D61—82no—
363C4×D61—84no—
364C4×D61C22×Q818yes—
365Dic122—42no—
366Dic122—42no—
367Dic122—82no—
368Dic122—82no—
369Dic122—84no—
370Dic122—81no—
371Dic122—81no—
372Dic122C4⋊Q814yes—
373C8×C61C22×Q814yes—
374C8×C61C22×Q814yes—
375#92418C22×Q818yes—
376#60668—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61C2×C4⋊Q812yes—
380C22×C61C23×D411yescharacteristic
381C2×D61—22no—
382C2×D61—22no—
383C2×D61C2×C4⋊Q814yes—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—42no—
389C4×C61—44no—
390C4×C61—42no—
391C4×C61C2×C4⋊Q812yes—
392C4×C61C23×Q812yes—
393Dic61—22no—
394Dic61—22no—
395Dic61—42no—
396Dic61—41no—
397Dic61—41no—
398Dic61—42no—
399Dic61—41no—
400Dic61—41no—
401Dic61C2×C4⋊Q814yes—
402#3504—611no—
403#3503—611no—
404#3166—612no—
405#3166—611no—
406#3165—612no—
407#3165—611no—
408#3164—614no—
409#3164—612no—
410#3163—614no—
411#3163—612no—
412#3162—612no—
413#3162—611no—
414C2×#501—612no—
415C2×#501D6111yescharacteristic, complemented
416#2913—612no—
417#2912—612no—
418#2875—611no—
419C2×C61—22no—
420C2×C61C22×C4⋊Q811yescharacteristic
421C2×C61#358511yescharacteristic
422C2×C61#358611yescharacteristic
423D61—24no—
424C2×#131—612no—
425Q82—1221no—
426#557—1221no—
427#557—1221no—
428#557—1221no—
429#554—1222no—
430#554—1222no—
431#554—1222no—
432#554—1221no—
433#554—1221no—
434#554—1221no—
435D4×Q8—1221no—
436D4×Q8—1222no—
437#544—614no—
438#544—612no—
439#544—612no—
440#544—611no—
441#544—612no—
442#544—611no—
443#533—612no—
444#533—612no—
445#533—611no—
446#533—611no—
447C2×C4⋊Q8—612no—
448C2×C4⋊Q8C2×D6111yescharacteristic
449C2×#125—612no—
450C2×#125C2×D6111yescharacteristic
451#520—611no—
452#520—612no—
453#520—611no—
454C4×#41—611no—
455#501—612no—
456#501—612no—
457#501—612no—
458#501—612no—
459#501—614no—
460#501—614no—
461#501—614no—
462#501—614no—
463#501—611no—
464#501—611no—
465#501—612no—
466#501—612no—
467#501—611no—
468#501—611no—
469#501C2×D6112yes—
470#501C2×D6114yes—
471#501C2×D6112yes—
472#500—612no—
473#500—614no—
474#499—614no—
475#499—614no—
476#499—614no—
477#498—612no—
478#498—614no—
479#428—612no—
480#428—612no—
481#428—612no—
482#428—612no—
483#428—614no—
484#428—614no—
485#428—614no—
486#428—614no—
487#427—612no—
488#427—612no—
489#427—614no—
490#427—614no—
491C2×#107—614no—
492C2×#107C2×D6112yes—
493C2×#106—614no—
494C2×#106C2×D6112yes—
495#405—612no—
496#405—614no—
497C4×M16—611no—
498C4×M16—612no—
499C2×#97—612no—
500C2×#97C2×D6111yescharacteristic
501C61#6066811yescharacteristic, complemented, Sylow
502C2×#41—611no—
503C22×Q8—21no—
504C22×Q8—1222no—
505#131—6116no—
506C2×M16—612no—
507C2×M16—614no—
508C22×C8—614no—
509C22×C8C22×D6112yes—
510C4⋊Q8—21no—
511C4⋊Q8—21no—
512C4⋊Q8—614no—
513C4⋊Q8—612no—
514C4⋊Q8—612no—
515C4⋊Q8—611no—
516C4⋊Q8—611no—
517C4⋊Q8—611no—
518C4⋊Q8—611no—
519C4⋊Q8—1222no—
520C4⋊Q8—1222no—
521C4⋊Q8—1222no—
522C4⋊Q8—1222no—
523C4⋊Q8—1222no—
524C4⋊Q8—1221no—
525C4⋊Q8—1221no—
526C4⋊Q8—1224no—
527C4⋊Q8C22×D6112yes—
528C4⋊Q8C22×D6112yes—
529#125—21no—
530#125—21no—
531#125—612no—
532#125—612no—
533#125—614no—
534#125—611no—
535#125—611no—
536#125—612no—
537#125—1222no—
538#125—1222no—
539#125—1222no—
540#125—1222no—
541#125—1224no—
542#125—1221no—
543#125—1221no—
544#125—1222no—
545#125C22×D6112yes—
546#125C22×D6112yes—
547C22⋊Q8—1224no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550C22⋊Q8—1222no—
551C22⋊Q8—1222no—
552C22⋊Q8—1224no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555C22⋊Q8—1224no—
556C22⋊Q8—1222no—
557C22⋊Q8—1222no—
558C22⋊Q8—1222no—
559C22⋊Q8—1222no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563C22⋊Q8—1221no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—1222no—
567C4×Q8—1222no—
568C4×Q8—1222no—
569C4×Q8—1222no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1222no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×D4—612no—
578C4×D4—612no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—1222no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4—1224no—
585C4×D4—1222no—
586C4×D4—1222no—
587#117—611no—
588#117—612no—
589#117—611no—
590#117—611no—
591#117—612no—
592#117—612no—
593#117—614no—
594#117—612no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—612no—
599C2×C4⋊C4—612no—
600C2×C4⋊C4—614no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4C22×D6111yescharacteristic
605C2×C4⋊C4C22×D6111yescharacteristic
606C2×C4⋊C4C22×D6112yes—
607C2×C42—612no—
608C2×C42C22×D6111yescharacteristic
609#107—612no—
610#107—612no—
611#107—612no—
612#107—612no—
613#107—614no—
614#107—614no—
615#107—614no—
616#107—614no—
617#107C22×D6114yes—
618#107C22×D6114yes—
619#106—612no—
620#106—612no—
621#106—612no—
622#106—612no—
623#106—614no—
624#106—614no—
625#106—614no—
626#106—614no—
627#106C22×D6114yes—
628#106C22×D6114yes—
629#97—614no—
630#97—612no—
631#97C22×D6111yescharacteristic
632#97C22×D6111yescharacteristic
633#97C22×D6112yes—
634C4×C8—614no—
635C4×C8—612no—
636#41—618no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—82no—
640C2×Q8—611no—
641C2×Q8—1222no—
642C2×Q8—1222no—
643C2×Q8—1224no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—1221no—
647C2×Q8—1221no—
648C2×Q8—4884no—
649C2×D4—612no—
650C2×D4—611no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—612no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1224no—
660C22×C4D4×D6111yescharacteristic
661C22×C4D4×D6111yescharacteristic
662C22×C4C23×D6111yescharacteristic
663M16—618no—
664M16—6116no—
665C2×C8—614no—
666C2×C8—6116no—
667C2×C8Q8×D6118yescomplemented
668C2×C8C23×D6112yes—
669C2×C8C23×D6112yes—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—612no—
680C4⋊C4—612no—
681C4⋊C4—611no—
682C4⋊C4—611no—
683C4⋊C4—611no—
684C4⋊C4—611no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—1222no—
690C4⋊C4—1222no—
691C4⋊C4—1224no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C4⋊C4—1224no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1224no—
698C4⋊C4—1222no—
699C4⋊C4—1222no—
700C4⋊C4—1224no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4C23×D6112yes—
712C4⋊C4C23×D6114yes—
713C4⋊C4C23×D6112yes—
714C22⋊C4—612no—
715C22⋊C4—612no—
716C22⋊C4—612no—
717C22⋊C4—1222no—
718C22⋊C4—1222no—
719C22⋊C4—1224no—
720C22⋊C4—1222no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C42—612no—
724C42—612no—
725C42—612no—
726C42—1222no—
727C42—1222no—
728C42—1224no—
729C42—1222no—
730C42—1221no—
731C42—1221no—
732C42D4×D6111yescharacteristic
733C42D4×D6111yescharacteristic
734C42C23×D6111yescharacteristic
735C42C23×D6111yescharacteristic
736C23—612no—
737C23C2×D4×D6111yescharacteristic
738Q8—44no—
739Q8—82no—
740Q8—614no—
741Q8—4881no—
742Q8—4881no—
743Q8—4882no—
744Q8—4882no—
745Q8—4884no—
746Q8—2442no—
747Q8—2442no—
748D4—618no—
749D4—614no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—82no—
758C2×C4—612no—
759C2×C4—618no—
760C2×C4—612no—
761C2×C4—612no—
762C2×C4—1222no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1222no—
768C2×C4—4882no—
769C2×C4—4882no—
770C2×C4—4884no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C2×D4×D6111yescharacteristic
776C2×C4C2×D4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×Q8×D6114yes—
779C2×C4C24×D6111yescharacteristic
780C8—618no—
781C8C2×Q8×D6114yes—
782C8C2×Q8×D6114yes—
783C22—21no—
784C22—21no—
785C22—614no—
786C22—1222no—
787C22—1222no—
788C22C4⋊Q8×D6112yes—
789C22C22×D4×D6111yescharacteristic
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—44no—
795C4—42no—
796C4—42no—
797C4—614no—
798C4—1222no—
799C4—1222no—
800C4—2441no—
801C4—2442no—
802C4—2441no—
803C4—2441no—
804C4—2441no—
805C4—2442no—
806C4C4⋊Q8×D6112yes—
807C4C22×Q8×D6112yes—
808C2—22no—
809C2—1224no—
810C2C2×C4⋊Q8×D6111yescharacteristic
811C2#2146059511yescharacteristic
812C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#501C2
socleC22×C61C23×D4
prime radicalC2×#11758222C23
hypercenterC2×#501D61
hypocenterC61#60668
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #21456370C2semidirect
4. #21456368C2semidirect
5. #21456364C2semidirect
6. #21456361C2semidirect
7. #21456355C2semidirect
8. #21456354C2semidirect
9. #21456347C2semidirect
10. #21456346C2semidirect
11. #21456343C2semidirect
12. #21456340C2semidirect
13. #501×D61C2semidirect
17. C2×C61×#501C2semidirect
97. #14519783Q8semidirect
256. C2×C8×C61C2×Q8semidirect
325. #11758194C2×Q8semidirect
327. #11758189C2×Q8semidirect
328. C8×D61C2×Q8semidirect
415. C2×#501D61semidirect
501. C61#60668semidirect
667. C2×C8Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#214596432
#214596352
#214563702
#214563682
#214563642
#214563612
#214563552
#214563542
#214563472
#214563462
#214563432
#214563402
#501×D612
#214544152
#214544102
#214542442
C2×C61×#5012
#6066861