Finite Group Databasebeta

← #30552371

Subgroups — #30552371

Order 15616.

1754 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#21459222C211yesmaximal, characteristic, complemented
2C2×#16840363C211yesmaximal, characteristic
3#21457079C214yesmaximal, complemented
4#21457077C214yesmaximal, complemented
5#21457071C214yesmaximal, complemented
6#21457069C214yesmaximal, complemented
7#21456369C212yesmaximal, complemented
8#21456191C212yesmaximal, complemented
9#21455761C212yesmaximal, complemented
10#21455757C212yesmaximal, complemented
11#21455618C211yesmaximal, characteristic, complemented
12#21455616C211yesmaximal, characteristic, complemented
13#21455612C211yesmaximal, characteristic, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3077C211yesmaximal, characteristic, complemented
16#16840392C2212yescomplemented
17#16840392C2212yescomplemented
18#16840391—21no—
19#16840391—21no—
20#16840389C2212yescomplemented
21#16840389C2212yescomplemented
22#16840387—21no—
23#16840387—21no—
24#16840363—22no—
25#16840363—22no—
26#16840363C2214yes—
27#16840363C2214yes—
28#16840319C2211yescharacteristic
29#16840316—22no—
30#16840316—22no—
31#16840315C2212yes—
32C2×#14519773C2211yescharacteristic
33C2×#14519768C2211yescharacteristic
34C2×#14519760—21no—
35C2×#14519759—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519751—21no—
38C2×#14519750—21no—
39C2×#14519748C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#117×D61C2212yes—
43#16840170C2214yescomplemented
44#16840169C2214yescomplemented
45#16840163C2214yescomplemented
46#16840162C2214yescomplemented
47#16840125C2214yescomplemented
48#16840125C2214yescomplemented
49#16840107C2214yescomplemented
50#16840107C2214yescomplemented
51#16840089C2214yescomplemented
52#16840088C2214yescomplemented
53#16840085C2214yescomplemented
54#16840084C2214yescomplemented
55#16840082C2214yescomplemented
56#16840079C2214yescomplemented
57#16840077C2214yescomplemented
58#16840074C2214yescomplemented
59#16840063C2214yescomplemented
60#16840062C2214yescomplemented
61#16840059C2214yescomplemented
62#16840053C2212yescomplemented
63#16840052C2212yescomplemented
64#16840049C2212yescomplemented
65#16840043C2212yescomplemented
66#16840042C2212yescomplemented
67#16840039C2212yescomplemented
68#16839822C2214yescomplemented
69#16839822C2214yescomplemented
70#16839805C2212yes—
71#16839804C2212yes—
72#16839802C2212yes—
73#16839786C2211yescharacteristic
74#16839768C2212yes—
75#16839767C2212yes—
76#16839766C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×D4×C61C2211yescharacteristic
81C61×#478C2214yescomplemented
82C61×#476C2212yescomplemented
83C61×#474C2212yescomplemented
84C61×#428C2212yes—
85C61×#423C2211yescharacteristic
86C61×#418C2212yes—
87C22×D244—21no—
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61C2311yescharacteristic
94C2×#11758194C2312yes—
95#14519777C2311yescharacteristic
96#14519777C2311yescharacteristic
97#14519776—22no—
98#14519776—22no—
99#14519776C2312yes—
100#14519776C2312yes—
101#14519775—22no—
102#14519775—22no—
103#14519773—22no—
104#14519773C2314yes—
105#14519769C2312yes—
106#14519768—22no—
107#14519768C2314yes—
108#14519768C2312yes—
109#14519768C2312yes—
110#14519767—22no—
111#14519767—22no—
112#14519767—22no—
113#14519767—22no—
114#14519760—24no—
115#14519760—24no—
116#14519759—24no—
117#14519759—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#14519754—22no—
127#14519754—22no—
128#14519753—22no—
129#14519753—22no—
130#14519752—22no—
131#14519752C2314yes—
132#14519751—24no—
133#14519751—24no—
134#14519750—24no—
135#14519750—24no—
136#14519748—22no—
137#14519748C2314yes—
138C4×Dic122—21no—
139C4×Dic122—21no—
140C4×Dic122—22no—
141C4×Dic122—22no—
142C4×D244—21no—
143C4×D244—21no—
144C4×D244C2312yes—
145C4×D244C2312yes—
146#14519736C2312yes—
147#14519735C2312yes—
148#14519735C2312yes—
149#14519734—22no—
150#14519734D412yes—
151#14519734D412yes—
152#14519734C2312yes—
153#14519734C2312yes—
154#14519733—22no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61C2311yescharacteristic
157C2×#11758196—21no—
158C2×#11758196D411yescharacteristic
159C2×#11758196D411yescharacteristic
160C4⋊C4×D61C2312yes—
161C4⋊C4×D61C2312yes—
162C2×C22⋊Dic61—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#14519699C2314yes—
179#14519699C2314yes—
180#14519698C2314yes—
181#14519698C2314yes—
182#14519697C2314yes—
183#14519697C2314yes—
184#14519689C2314yes—
185#14519689C2314yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×D4×C61C2311yescharacteristic
189C23×C4×C61—21no—
190C2×M16×C61C2312yes—
191C4⋊Q8×C61C2311yescharacteristic
192C4⋊Q8×C61C2311yescharacteristic
193#125×C61C2312yes—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C4×Q8×C61—21no—
197C4×Q8×C61—21no—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2312yes—
201C4×D4×C61C2312yes—
202#117×C61C2312yes—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#107×C61C2314yes—
207#106×C61C2314yes—
208C4⋊C8×C61C2312yes—
209C4⋊C8×C61C2312yes—
210#102×C61C2314yes—
211#102×C61C2314yes—
212C24×C61—21no—
213C23×D61—21no—
214C23×D61C2×D411yescharacteristic
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—22no—
219C2×D4×C61—22no—
220C2×D4×C61C2412yes—
221C22×C4×C61—21no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—82no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—24no—
231C2×C22⋊D61—82no—
232C2×C22⋊D61—82no—
233C2×C22⋊D61—82no—
234C22×Dic61—21no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—21no—
241C2×D244—24no—
242C2×D244—82no—
243C2×D244C2412yes—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—82no—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2412yes—
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122—22no—
256C2×Dic122—22no—
257M16×C61—24no—
258C2×C8×C61C2414yes—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C2412yes—
265C4⋊C4×C61C2412yes—
266C4⋊C4×C61C2412yes—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—22no—
269C22⋊C4×C61—22no—
270C42×C61—22no—
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2411yescharacteristic
274C42×C61C2411yescharacteristic
275C22⋊Dic61—22no—
276C22⋊Dic61—24no—
277#11758198—22no—
278#11758198—22no—
279#11758198—22no—
280#11758198—22no—
281#11758198—24no—
282#11758198C2×D412yes—
283#11758198C2×D412yes—
284#11758198C2×D412yes—
285#11758198C2×D412yes—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—24no—
290C4⋊Dic61—22no—
291C4⋊Dic61—22no—
292C4⋊Dic61C2412yes—
293C4⋊Dic61C2412yes—
294C4⋊Dic61C2412yes—
295#11758196—22no—
296#11758196—22no—
297#11758196—22no—
298#11758196—22no—
299#11758196—24no—
300#11758196—22no—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304#11758196C2×D412yes—
305#11758196C2×D412yes—
306#11758196C2×D412yes—
307#11758196C2×D412yes—
308C4×Dic61—22no—
309C4×Dic61—22no—
310C4×Dic61—22no—
311C4×Dic61C2×D412yes—
312C4×Dic61C2412yes—
313#11758194—24no—
314C2×#92418C2414yes—
315C23×C61—22no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61C22×D412yes—
328Q8×C61—81no—
329Q8×C61—81no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—42no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—42no—
339C2×C4×C61—82no—
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×C612−1+412yes—
347C2×C4×C612−1+412yes—
348C2×C4×C61C2511yescharacteristic
349C22⋊D61—84no—
350C22⋊D61—84no—
351C22⋊D61—84no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—42no—
359C2×Dic61C22×D412yes—
360C2×Dic61C22×D412yes—
361C2×Dic61C22×D412yes—
362D244—22no—
363D244—22no—
364D244—42no—
365D244—84no—
366C4×D61—24no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—82no—
370C4×D61—82no—
371C4×D61—82no—
372C4×D61—82no—
373Dic122—82no—
374Dic122—82no—
375Dic122—81no—
376Dic122—81no—
377C8×C61—24no—
378#92418—24no—
379#60868—611nomaximal, Sylow
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—84no—
386C22×C61#53612yes—
387C22×C61C23×D411yescharacteristic
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—82no—
395C2×D61—84no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61#53612yes—
404C4×C61C2×2−1+411yescharacteristic
405C4×C61C2×2−1+411yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—22no—
409Dic61—42no—
410Dic61—42no—
411Dic61—42no—
412#3458—611no—
413C2×#540—611no—
414#3241—614no—
415#3241—614no—
416#3241—614no—
417#3241—614no—
418#3166—612no—
419#3138—612no—
420#3094—612no—
421#3094—612no—
422#3077—611no—
423#3077—611no—
424#3077—611no—
425#3077D6111yescharacteristic, complemented
426#2921—611no—
427C2×C61—22no—
428C2×C61—82no—
429C2×C61C2×#53611yescharacteristic
430C2×C61#358511yescharacteristic
431C2×C61#358511yescharacteristic
432D61—42no—
433D61—82no—
434#544—612no—
435#544—612no—
436#544—612no—
437#544—612no—
438#544—1221no—
439#544—1221no—
440#543—1221no—
441#543—1221no—
442#540—614no—
443#540—614no—
444#540—1222no—
445#540—1222no—
446#533—612no—
447#533—611no—
448#533—1222no—
449#533—1222no—
450#533C2×D6111yescharacteristic
451C2×#127—611no—
452C2×#125—611no—
453C2×#123—1221no—
454C2×#123—1221no—
455C2×#121—611no—
456C2×#121—611no—
457C2×#121—1221no—
458C2×#121—1221no—
459C2×C4×D4—611no—
460C2×C4×D4C2×D6111yescharacteristic
461C2×#117—611no—
462C2×#117—612no—
463#501—614no—
464#501—614no—
465#499—614no—
466#499—614no—
467#490—614no—
468#490—614no—
469#486—614no—
470#486—614no—
471#482—614no—
472#482—614no—
473#482—614no—
474#482—614no—
475#481—614no—
476#481—614no—
477#480—614no—
478#480—614no—
479#478—614no—
480#478—614no—
481#478—614no—
482#478C2×D6114yescomplemented
483#476—612no—
484#476—612no—
485#476—612no—
486#476C2×D6112yescomplemented
487#474—612no—
488#474—612no—
489#474—612no—
490#474C2×D6112yescomplemented
491#433—614no—
492#433—614no—
493#428—612no—
494#428—612no—
495#428—612no—
496#428C2×D6112yes—
497#423—611no—
498#423C2×D6111yescharacteristic
499#418—612no—
500#418—612no—
501#418—612no—
502#418C2×D6112yes—
503#407—612no—
504C4×M16—612no—
505C61#6086811yescharacteristic, complemented, Sylow
506C22×D4—611no—
507C22×D4—1221no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4C22×D6111yescharacteristic
512C23×C4—21no—
513C23×C4—611no—
514C23×C4—1221no—
515C2×M16—612no—
516C2×M16C22×D6112yes—
517C4⋊Q8—612no—
518C4⋊Q8—612no—
519C4⋊Q8—611no—
520C4⋊Q8—611no—
521C4⋊Q8—1222no—
522C4⋊Q8—1222no—
523C4⋊Q8—1222no—
524C4⋊Q8—1222no—
525C4⋊Q8C22×D6111yescharacteristic
526C4⋊Q8C22×D6111yescharacteristic
527#127—614no—
528#127—1222no—
529#125—614no—
530#125—612no—
531#125—612no—
532#125—612no—
533#125—1222no—
534#125—1222no—
535#125—1222no—
536#125—1222no—
537#125—1222no—
538#125C22×D6112yes—
539#123—1224no—
540#123—1224no—
541#123—1224no—
542#123—1224no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—1222no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550C22⋊Q8—1222no—
551C22⋊Q8—1222no—
552C22⋊Q8—1222no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557#121—614no—
558#121—614no—
559#121—1224no—
560#121—1224no—
561#121—1224no—
562#121—1224no—
563#121—1222no—
564#121—1222no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—1222no—
568C4×Q8—1222no—
569C4×Q8—1221no—
570C4×Q8—1221no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—612no—
574C4×D4—612no—
575C4×D4—1221no—
576C4×D4—1221no—
577C4×D4C22×D6112yes—
578C4×D4C22×D6112yes—
579#117—612no—
580#117—612no—
581#117—612no—
582#117—612no—
583#117—612no—
584#117—612no—
585#117—612no—
586#117—1222no—
587#117—1222no—
588#117C22×D6112yes—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—612no—
593C2×C4⋊C4—612no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—1222no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C42—611no—
605C2×C42—1222no—
606C2×C42C22×D6111yescharacteristic
607#107—614no—
608#107—614no—
609#107—614no—
610#107C22×D6114yes—
611#106—614no—
612#106—614no—
613#106—614no—
614#106C22×D6114yes—
615C4⋊C8—612no—
616C4⋊C8—612no—
617C4⋊C8C22×D6112yes—
618C4⋊C8C22×D6112yes—
619#102—614no—
620#102—614no—
621#102—614no—
622#102—614no—
623#102—614no—
624#102—614no—
625#102C22×D6114yes—
626#102C22×D6114yes—
627C22⋊C8—614no—
628C22⋊C8—614no—
629#97—614no—
630C4×C8—614no—
631C24—21no—
632C24—611no—
633C24—1221no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—1222no—
637C2×Q8—1222no—
638C2×Q8—1221no—
639C2×Q8—1221no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—612no—
644C2×D4—1224no—
645C2×D4—1224no—
646C2×D4—1224no—
647C2×D4—1224no—
648C2×D4—1221no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4—4882no—
652C2×D4—4882no—
653C2×D4—4882no—
654C2×D4—4882no—
655C2×D4C23×D6112yes—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—82no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1221no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—4882no—
673C22×C4D4×D6111yescharacteristic
674C22×C4D4×D6111yescharacteristic
675C22×C4C23×D6111yescharacteristic
676M16—24no—
677M16—1224no—
678C2×C8—614no—
679C2×C8C23×D6114yes—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—612no—
688C4⋊C4—612no—
689C4⋊C4—612no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1222no—
697C4⋊C4—1222no—
698C4⋊C4—1222no—
699C4⋊C4—1222no—
700C4⋊C4—1222no—
701C4⋊C4—1222no—
702C4⋊C4—1221no—
703C4⋊C4—1222no—
704C4⋊C4—1222no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4C23×D6112yes—
708C4⋊C4C23×D6112yes—
709C4⋊C4C23×D6112yes—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—612no—
714C22⋊C4—612no—
715C22⋊C4—612no—
716C22⋊C4—612no—
717C22⋊C4—1224no—
718C22⋊C4—1222no—
719C22⋊C4—1222no—
720C22⋊C4—1224no—
721C22⋊C4—1222no—
722C22⋊C4—1222no—
723C22⋊C4—1222no—
724C42—22no—
725C42—612no—
726C42—612no—
727C42—1222no—
728C42—1222no—
729C42—1222no—
730C42D4×D6111yescharacteristic
731C42D4×D6111yescharacteristic
732C42C23×D6111yescharacteristic
733C42C23×D6111yescharacteristic
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—612no—
739C23—1222no—
740C23—1222no—
741C23—2441no—
742C23—2441no—
743C23—2442no—
744C23—2442no—
745C23—2442no—
746C23C2×D4×D6111yescharacteristic
747Q8—81no—
748Q8—81no—
749Q8—4881no—
750Q8—4881no—
751Q8—4882no—
752Q8—4882no—
753D4—22no—
754D4—22no—
755D4—42no—
756D4—1222no—
757D4—1222no—
758D4—4884no—
759D4—4884no—
760D4—4884no—
761D4—4884no—
762D4—2442no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—82no—
770C2×C4—82no—
771C2×C4—612no—
772C2×C4—612no—
773C2×C4—612no—
774C2×C4—1222no—
775C2×C4—1224no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—4882no—
782C2×C4—4882no—
783C2×C4—4882no—
784C2×C4—4882no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2442no—
788C2×C4C2×D4×D6111yescharacteristic
789C2×C4C2×D4×D6111yescharacteristic
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4#1451982412yes—
794C2×C4#1451982512yes—
795C2×C4C24×D6111yescharacteristic
796C8—24no—
797C8—1224no—
798C22—21no—
799C22—21no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—84no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—4884no—
808C22—4882no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22#1684033512yes—
813C22C22×D4×D6111yescharacteristic
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—1222no—
822C4—1222no—
823C4—1222no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4#1684033512yes—
828C4C2×#1451982411yescharacteristic
829C4C2×#1451982511yescharacteristic
830C2—22no—
831C2—82no—
832C2—4882no—
833C2—2442no—
834C2C2×#1684033511yescharacteristic
835C2#2146059511yescharacteristic
836C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3077C2
socleC22×C61C23×D4
prime radicalC2×#16840363C2
hypercenter#3077D61
hypocenterC61#60868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #21459222C2semidirect
3. #21457079C2semidirect
4. #21457077C2semidirect
5. #21457071C2semidirect
6. #21457069C2semidirect
7. #21456369C2semidirect
8. #21456191C2semidirect
9. #21455761C2semidirect
10. #21455757C2semidirect
11. #21455618C2semidirect
12. #21455616C2semidirect
13. #21455612C2semidirect
14. #21454456C2semidirect
15. C61×#3077C2semidirect
16. #16840392C22semidirect
17. #16840392C22semidirect
20. #16840389C22semidirect
21. #16840389C22semidirect
43. #16840170C22semidirect
44. #16840169C22semidirect
45. #16840163C22semidirect
46. #16840162C22semidirect
47. #16840125C22semidirect
48. #16840125C22semidirect
49. #16840107C22semidirect
50. #16840107C22semidirect
51. #16840089C22semidirect
52. #16840088C22semidirect
53. #16840085C22semidirect
54. #16840084C22semidirect
55. #16840082C22semidirect
56. #16840079C22semidirect
57. #16840077C22semidirect
58. #16840074C22semidirect
59. #16840063C22semidirect
60. #16840062C22semidirect
61. #16840059C22semidirect
62. #16840053C22semidirect
63. #16840052C22semidirect
64. #16840049C22semidirect
65. #16840043C22semidirect
66. #16840042C22semidirect
67. #16840039C22semidirect
68. #16839822C22semidirect
69. #16839822C22semidirect
81. C61×#478C22semidirect
82. C61×#476C22semidirect
83. C61×#474C22semidirect
425. #3077D61semidirect
482. #478C2×D61semidirect
486. #476C2×D61semidirect
490. #474C2×D61semidirect
505. C61#60868semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168403632
#214570792
#214570772
#214570712
#214570692
#214563692
#214561912
#214557612
#214557572
#214556182
#214556162
#214556122
#214544562
C61×#30772
#6086861