Finite Group Databasebeta

← #30552393

Subgroups — #30552393

Order 15616.

1690 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic, complemented
2C2×#16840384C211yesmaximal, characteristic
3#21457124C214yesmaximal, complemented
4#21457122C214yesmaximal, complemented
5#21457109C214yesmaximal, complemented
6#21457107C214yesmaximal, complemented
7#21456363C212yesmaximal, complemented
8#21456207C212yesmaximal, complemented
9#21455765C212yesmaximal, complemented
10#21455761C212yesmaximal
11#21455624C211yesmaximal, characteristic, complemented
12#21455618C211yesmaximal, characteristic, complemented
13#21455612C211yesmaximal, characteristic, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3078C211yesmaximal, characteristic, complemented
16#16840392C2212yescomplemented
17#16840392C2212yescomplemented
18#16840391—21no—
19#16840391—21no—
20#16840389C2212yescomplemented
21#16840389C2212yescomplemented
22#16840387—21no—
23#16840387—21no—
24#16840384—22no—
25#16840384—22no—
26#16840384C2214yes—
27#16840384C2214yes—
28#16840319C2211yescharacteristic
29#16840316—22no—
30#16840316—22no—
31#16840315C2212yes—
32C2×#14519776C2211yescharacteristic
33C2×#14519771—21no—
34C2×#14519766C2211yescharacteristic
35C2×#14519765—21no—
36C2×#14519762—21no—
37C2×#14519755—21no—
38C2×#14519753C2211yescharacteristic
39C2×#14519752C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#117×D61C2212yes—
43#16840170C2214yescomplemented
44#16840169C2214yescomplemented
45#16840166C2214yescomplemented
46#16840159C2214yescomplemented
47#16840123C2214yescomplemented
48#16840123C2214yescomplemented
49#16840118C2214yescomplemented
50#16840118C2214yescomplemented
51#16840102C2214yescomplemented
52#16840101C2214yescomplemented
53#16840096C2214yescomplemented
54#16840091C2214yescomplemented
55#16840089C2214yes—
56#16840088C2214yes—
57#16840082C2214yes—
58#16840077C2214yes—
59#16840069C2214yescomplemented
60#16840063C2214yescomplemented
61#16840059C2214yescomplemented
62#16840057C2212yescomplemented
63#16840053C2212yescomplemented
64#16840049C2212yescomplemented
65#16840047C2212yescomplemented
66#16840043C2212yescomplemented
67#16840039C2212yescomplemented
68#16839822C2214yescomplemented
69#16839822C2214yescomplemented
70#16839805C2212yes—
71#16839804C2212yes—
72#16839802C2212yes—
73#16839786C2211yescharacteristic
74#16839771C2212yes—
75#16839768C2212yes—
76#16839766C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×Q8×C61C2211yescharacteristic
81C61×#479C2214yescomplemented
82C61×#477C2212yescomplemented
83C61×#475C2212yescomplemented
84C61×#428C2212yes—
85C61×#423C2211yescharacteristic
86C61×#419C2212yes—
87C22×Dic122—21no—
88C22×D244—21no—
89C22×D244C2311yescharacteristic
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×#11758194C2312yes—
93#14519777C2311yescharacteristic
94#14519777C2311yescharacteristic
95#14519776—22no—
96#14519776—22no—
97#14519776—22no—
98#14519776C2314yes—
99#14519776C2312yes—
100#14519776C2312yes—
101#14519775—22no—
102#14519775—22no—
103#14519771—24no—
104#14519771—24no—
105#14519769C2312yes—
106#14519768C2312yes—
107#14519768C2312yes—
108#14519767—22no—
109#14519767—22no—
110#14519767—22no—
111#14519767—22no—
112#14519766—22no—
113#14519766C2314yes—
114#14519765—24no—
115#14519765—24no—
116#14519762—24no—
117#14519762—24no—
118#14519757—22no—
119#14519757—22no—
120#14519756—21no—
121#14519756—21no—
122#14519755—22no—
123#14519755—22no—
124#14519755—22no—
125#14519755—22no—
126#14519755—24no—
127#14519755—24no—
128#14519754—22no—
129#14519754—22no—
130#14519753—22no—
131#14519753—22no—
132#14519753—22no—
133#14519753C2314yes—
134#14519752—22no—
135#14519752C2314yes—
136C4×Dic122—21no—
137C4×Dic122—21no—
138C4×Dic122—22no—
139C4×Dic122—22no—
140C4×D244—21no—
141C4×D244—21no—
142C4×D244C2312yes—
143C4×D244C2312yes—
144#14519736C2312yes—
145#14519735C2312yes—
146#14519735C2312yes—
147#14519734—22no—
148#14519734D412yes—
149#14519734D412yes—
150#14519734C2312yes—
151#14519734C2312yes—
152#14519733—22no—
153C2×C4⋊Dic61C2311yescharacteristic
154C2×#11758196—21no—
155C2×#11758196—21no—
156C2×#11758196D411yescharacteristic
157C2×#11758196D411yescharacteristic
158C4⋊C4×D61C2312yes—
159C4⋊C4×D61C2312yes—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198D411yescharacteristic
166C2×#11758198D411yescharacteristic
167C22⋊C4×D61—22no—
168C2×C4×Dic61C2311yescharacteristic
169C42×D61—22no—
170#14519711C2314yes—
171#14519710C2314yes—
172#14519710C2314yes—
173#14519709C2314yes—
174#14519708C2314yes—
175#14519708C2314yes—
176C4⋊#92418C2312yes—
177C4⋊#92418C2312yes—
178#14519701C2314yes—
179#14519701C2314yes—
180#14519699C2314yes—
181#14519699C2314yes—
182#14519697C2314yes—
183#14519697C2314yes—
184#14519689C2314yes—
185#14519689C2314yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×Q8×C61C2311yescharacteristic
189C2×M16×C61C2312yes—
190C4⋊Q8×C61C2311yescharacteristic
191C4⋊Q8×C61C2311yescharacteristic
192#125×C61C2312yes—
193C22⋊Q8×C61—21no—
194C22⋊Q8×C61—21no—
195C4×Q8×C61—21no—
196C4×Q8×C61—21no—
197C4×Q8×C61—21no—
198C4×Q8×C61—21no—
199C4×Q8×C61C2312yes—
200C4×Q8×C61C2312yes—
201#117×C61C2312yes—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C42×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#107×C61C2314yes—
207#106×C61C2314yes—
208C4⋊C8×C61C2312yes—
209C4⋊C8×C61C2312yes—
210#103×C61C2314yes—
211#103×C61C2314yes—
212C23×D61—21no—
213C23×D61C2×D411yescharacteristic
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—22no—
218C2×Q8×C61—22no—
219C2×Q8×C61C2412yes—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—21no—
232C2×D244—24no—
233C2×D244—82no—
234C2×D244C2412yes—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—82no—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2412yes—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—24no—
247C2×Dic122—22no—
248C2×Dic122—22no—
249C2×Dic122—82no—
250M16×C61—24no—
251C2×C8×C61C2414yes—
252C4⋊C4×C61—22no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—22no—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2412yes—
260C4⋊C4×C61C2412yes—
261C4⋊C4×C61C2412yes—
262C22⋊C4×C61—22no—
263C42×C61—22no—
264C42×C61—22no—
265C42×C61—22no—
266C42×C61C2×D411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2411yescharacteristic
269C42×C61C2411yescharacteristic
270C22⋊Dic61—22no—
271#11758198—22no—
272#11758198—22no—
273#11758198—24no—
274#11758198—22no—
275#11758198—22no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198C2×D412yes—
280#11758198C2×D412yes—
281#11758198C2×D412yes—
282#11758198C2×D412yes—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—22no—
287C4⋊Dic61—22no—
288C4⋊Dic61C2412yes—
289C4⋊Dic61C2412yes—
290C4⋊Dic61C2412yes—
291#11758196—22no—
292#11758196—22no—
293#11758196—22no—
294#11758196—22no—
295#11758196—24no—
296#11758196—24no—
297#11758196—22no—
298#11758196—22no—
299#11758196—22no—
300#11758196—22no—
301#11758196C2×D412yes—
302#11758196C2×D412yes—
303#11758196C2×D412yes—
304#11758196C2×D412yes—
305C4×Dic61—22no—
306C4×Dic61—22no—
307C4×Dic61—22no—
308C4×Dic61C2×D412yes—
309C4×Dic61C2412yes—
310#11758194—24no—
311C2×#92418C2414yes—
312C23×C61C22×D411yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61C22×D412yes—
321Q8×C61—22no—
322Q8×C61—22no—
323Q8×C61—42no—
324Q8×C61—81no—
325Q8×C61—81no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C612−1+412yes—
340C2×C4×C612−1+412yes—
341C2×C4×C61C2511yescharacteristic
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—42no—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351C2×Dic61C22×D412yes—
352D244—22no—
353D244—22no—
354D244—42no—
355D244—84no—
356C4×D61—24no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—82no—
360C4×D61—82no—
361C4×D61—82no—
362C4×D61—82no—
363Dic122—82no—
364Dic122—82no—
365Dic122—84no—
366Dic122—81no—
367Dic122—81no—
368C8×C61—24no—
369#92418—24no—
370#60870—611nomaximal, Sylow
371C22×C61—21no—
372C22×C61—21no—
373C22×C61#53612yes—
374C22×C61C23×D411yescharacteristic
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—82no—
382C2×D61—84no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61#53612yes—
392C4×C61C2×2−1+411yescharacteristic
393C4×C61C2×2−1+411yescharacteristic
394Dic61—22no—
395Dic61—22no—
396Dic61—22no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400#3458—611no—
401C2×#542—611no—
402#3244—614no—
403#3244—614no—
404#3243—614no—
405#3243—614no—
406#3165—612no—
407#3140—612no—
408#3095—612no—
409#3094—612no—
410#3078—611no—
411#3078D6111yescharacteristic, complemented
412#3077—611no—
413#3077—611no—
414#2921—611no—
415C2×C61—22no—
416C2×C61C2×#53611yescharacteristic
417C2×C61#358511yescharacteristic
418C2×C61#358611yescharacteristic
419D61—42no—
420D61—82no—
421#544—612no—
422#544—612no—
423#544—612no—
424#544—612no—
425#544—1221no—
426#544—1221no—
427#543—1221no—
428#543—1221no—
429#542—614no—
430#542—614no—
431#542—1222no—
432#542—1222no—
433#533—612no—
434#533—611no—
435#533—1222no—
436#533—1222no—
437#533C2×D6111yescharacteristic
438C2×C4⋊Q8—611no—
439C2×#126—1221no—
440C2×#124—611no—
441C2×#124—1221no—
442C2×#123—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—1221no—
445C2×#121—611no—
446C2×C4×Q8C2×D6111yescharacteristic
447C2×C4×D4—611no—
448C2×#117—611no—
449C2×#117—612no—
450#501—614no—
451#501—614no—
452#500—614no—
453#498—614no—
454#489—614no—
455#489—614no—
456#488—614no—
457#488—614no—
458#485—614no—
459#485—614no—
460#484—614no—
461#483—614no—
462#482—614no—
463#482—614no—
464#481—614no—
465#480—614no—
466#479—614no—
467#479C2×D6114yescomplemented
468#478—614no—
469#478—614no—
470#477—612no—
471#477C2×D6112yescomplemented
472#476—612no—
473#476—612no—
474#475—612no—
475#475C2×D6112yescomplemented
476#474—612no—
477#474—612no—
478#433—614no—
479#433—614no—
480#428—612no—
481#428—612no—
482#428—612no—
483#428C2×D6112yes—
484#423—611no—
485#423C2×D6111yescharacteristic
486#419—612no—
487#419C2×D6112yes—
488#418—612no—
489#418—612no—
490#407—612no—
491C4×M16—612no—
492C61#6087011yescharacteristic, complemented, Sylow
493C22×Q8—1221no—
494C22×Q8C22×D6111yescharacteristic
495C22×D4—611no—
496C22×D4—1221no—
497C23×C4—611no—
498C23×C4—1221no—
499C2×M16—612no—
500C2×M16C22×D6112yes—
501C4⋊Q8—614no—
502C4⋊Q8—612no—
503C4⋊Q8—612no—
504C4⋊Q8—611no—
505C4⋊Q8—611no—
506C4⋊Q8—1222no—
507C4⋊Q8—1222no—
508C4⋊Q8—1222no—
509C4⋊Q8—1222no—
510C4⋊Q8—1222no—
511C4⋊Q8C22×D6111yescharacteristic
512C4⋊Q8C22×D6111yescharacteristic
513#126—1224no—
514#126—1224no—
515#125—612no—
516#125—612no—
517#125—612no—
518#125—1222no—
519#125—1222no—
520#125—1222no—
521#125—1222no—
522#125C22×D6112yes—
523#124—614no—
524#124—1224no—
525#124—1224no—
526#124—1222no—
527#123—1224no—
528#123—1224no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—614no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536C22⋊Q8—1222no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C22⋊Q8—1222no—
542C22⋊Q8—1224no—
543C22⋊Q8—1224no—
544C22⋊Q8—1222no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547#121—614no—
548#121—1222no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—1222no—
554C4×Q8—1222no—
555C4×Q8—1221no—
556C4×Q8—1221no—
557C4×Q8C22×D6112yes—
558C4×Q8C22×D6112yes—
559C4×D4—612no—
560C4×D4—612no—
561C4×D4—1221no—
562C4×D4—1221no—
563#117—612no—
564#117—612no—
565#117—612no—
566#117—612no—
567#117—612no—
568#117—612no—
569#117—612no—
570#117—1222no—
571#117—1222no—
572#117C22×D6112yes—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—612no—
578C2×C4⋊C4—612no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4C22×D6111yescharacteristic
582C2×C22⋊C4—611no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—1222no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C42—21no—
591C2×C42—611no—
592C2×C42—1222no—
593C2×C42C22×D6111yescharacteristic
594#107—614no—
595#107—614no—
596#107—614no—
597#107C22×D6114yes—
598#106—614no—
599#106—614no—
600#106—614no—
601#106C22×D6114yes—
602C4⋊C8—612no—
603C4⋊C8—612no—
604C4⋊C8C22×D6112yes—
605C4⋊C8C22×D6112yes—
606#103—614no—
607#103—614no—
608#103C22×D6114yes—
609#103C22×D6114yes—
610#102—614no—
611#102—614no—
612#102—614no—
613#102—614no—
614C22⋊C8—614no—
615C22⋊C8—614no—
616#97—614no—
617C4×C8—614no—
618C24—611no—
619C24—1221no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—1222no—
626C2×Q8—1222no—
627C2×Q8—1224no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—4882no—
631C2×Q8C23×D6112yes—
632C2×D4—612no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1222no—
636C2×D4—1222no—
637C2×D4—4882no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1221no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—4882no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656M16—24no—
657M16—1224no—
658C2×C8—614no—
659C2×C8C23×D6114yes—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—612no—
668C4⋊C4—612no—
669C4⋊C4—612no—
670C4⋊C4—612no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—1222no—
675C4⋊C4—1222no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—1221no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4C23×D6112yes—
690C4⋊C4C23×D6112yes—
691C4⋊C4C23×D6112yes—
692C22⋊C4—22no—
693C22⋊C4—612no—
694C22⋊C4—612no—
695C22⋊C4—612no—
696C22⋊C4—612no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1222no—
701C22⋊C4—1222no—
702C22⋊C4—1224no—
703C22⋊C4—1222no—
704C22⋊C4—1222no—
705C22⋊C4—1222no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—612no—
710C42—612no—
711C42—1222no—
712C42—1222no—
713C42—1222no—
714C42D4×D6111yescharacteristic
715C42D4×D6111yescharacteristic
716C42C23×D6111yescharacteristic
717C42C23×D6111yescharacteristic
718C23—612no—
719C23—1222no—
720C23—1222no—
721C23—2441no—
722C23—2441no—
723C23—2442no—
724C23—2442no—
725C23—2442no—
726C23C2×D4×D6111yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—42no—
730Q8—81no—
731Q8—81no—
732Q8—4881no—
733Q8—4881no—
734Q8—4882no—
735Q8—4882no—
736Q8—4884no—
737D4—1222no—
738D4—1222no—
739D4—4884no—
740D4—2442no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—612no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—1222no—
753C2×C4—1224no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—4882no—
760C2×C4—4882no—
761C2×C4—4882no—
762C2×C4—4882no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2442no—
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4#1451982412yes—
772C2×C4#1451982512yes—
773C2×C4C24×D6111yescharacteristic
774C8—24no—
775C8—1224no—
776C22—21no—
777C22—21no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—4884no—
782C22—4882no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22#1684033512yes—
787C22C22×D4×D6111yescharacteristic
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—1222no—
797C4—1222no—
798C4—1222no—
799C4—2442no—
800C4—2442no—
801C4—2442no—
802C4#1684033512yes—
803C4C2×#1451982411yescharacteristic
804C4C2×#1451982511yescharacteristic
805C2—22no—
806C2—4882no—
807C2—2442no—
808C2C2×#1684033511yescharacteristic
809C2#2146059611yescharacteristic
810C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3078C2
socleC22×C61C23×D4
prime radicalC2×#14519752C22
hypercenter#3078D61
hypocenterC61#60870
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
1. #21459222C2semidirect
3. #21457124C2semidirect
4. #21457122C2semidirect
5. #21457109C2semidirect
6. #21457107C2semidirect
7. #21456363C2semidirect
8. #21456207C2semidirect
9. #21455765C2semidirect
11. #21455624C2semidirect
12. #21455618C2semidirect
13. #21455612C2semidirect
14. #21454456C2semidirect
15. C61×#3078C2semidirect
16. #16840392C22semidirect
17. #16840392C22semidirect
20. #16840389C22semidirect
21. #16840389C22semidirect
43. #16840170C22semidirect
44. #16840169C22semidirect
45. #16840166C22semidirect
46. #16840159C22semidirect
47. #16840123C22semidirect
48. #16840123C22semidirect
49. #16840118C22semidirect
50. #16840118C22semidirect
51. #16840102C22semidirect
52. #16840101C22semidirect
53. #16840096C22semidirect
54. #16840091C22semidirect
59. #16840069C22semidirect
60. #16840063C22semidirect
61. #16840059C22semidirect
62. #16840057C22semidirect
63. #16840053C22semidirect
64. #16840049C22semidirect
65. #16840047C22semidirect
66. #16840043C22semidirect
67. #16840039C22semidirect
68. #16839822C22semidirect
69. #16839822C22semidirect
81. C61×#479C22semidirect
82. C61×#477C22semidirect
83. C61×#475C22semidirect
411. #3078D61semidirect
467. #479C2×D61semidirect
471. #477C2×D61semidirect
475. #475C2×D61semidirect
492. C61#60870semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168403842
#214571242
#214571222
#214571092
#214571072
#214563632
#214562072
#214557652
#214557612
#214556242
#214556182
#214556122
#214544562
C61×#30782
#6087061