Finite Group Databasebeta

← #30552370

Subgroups — #30552370

Order 15616.

1754 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459224C211yesmaximal, characteristic, complemented
2C2×#16840365C211yesmaximal, characteristic
3#21457078C214yesmaximal, complemented
4#21457076C214yesmaximal, complemented
5#21457070C214yesmaximal, complemented
6#21457068C214yesmaximal, complemented
7#21456369C212yesmaximal, complemented
8#21456191C212yesmaximal, complemented
9#21455760C211yesmaximal, characteristic, complemented
10#21455759C211yesmaximal, characteristic, complemented
11#21455755C211yesmaximal, characteristic, complemented
12#21455615C212yesmaximal, complemented
13#21455613C212yesmaximal, complemented
14#21454454C211yesmaximal, characteristic, complemented
15C61×#3094C211yesmaximal, characteristic, complemented
16#16840393C2212yescomplemented
17#16840393C2212yescomplemented
18#16840390—21no—
19#16840390—21no—
20#16840390C2212yescomplemented
21#16840390C2212yescomplemented
22#16840388—21no—
23#16840388—21no—
24#16840365—22no—
25#16840365—22no—
26#16840365C2214yes—
27#16840365C2214yes—
28#16840319—22no—
29#16840315—22no—
30#16840315C2212yes—
31#16840315C2212yes—
32C2×#14519773C2211yescharacteristic
33C2×#14519768C2211yescharacteristic
34C2×#14519761—21no—
35C2×#14519759—21no—
36C2×#14519751C2211yescharacteristic
37C2×#14519749—21no—
38C2×#14519748—21no—
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×#14519736C2211yescharacteristic
42C2×#14519736C2211yescharacteristic
43#16840170C2214yescomplemented
44#16840169C2214yescomplemented
45#16840163C2214yescomplemented
46#16840162C2214yescomplemented
47#16840125C2214yescomplemented
48#16840125C2214yescomplemented
49#16840107C2214yescomplemented
50#16840107C2214yescomplemented
51#16840087C2214yescomplemented
52#16840086C2214yescomplemented
53#16840083C2214yescomplemented
54#16840081C2212yescomplemented
55#16840080C2212yescomplemented
56#16840078C2212yescomplemented
57#16840076C2212yescomplemented
58#16840075C2212yescomplemented
59#16840073C2212yescomplemented
60#16840065C2214yescomplemented
61#16840064C2214yescomplemented
62#16840061C2214yescomplemented
63#16840060C2214yescomplemented
64#16840051C2214yescomplemented
65#16840050C2214yescomplemented
66#16840041C2214yescomplemented
67#16840040C2214yescomplemented
68#16839820C2214yescomplemented
69#16839820C2214yescomplemented
70#16839805C2212yes—
71#16839804C2212yes—
72#16839802C2212yes—
73#16839785C2212yes—
74#16839768C2212yes—
75#16839767C2212yes—
76#16839766C2212yes—
77#16839726C2211yescharacteristic
78M16×Dic61C2212yes—
79C2×#121×C61C2211yescharacteristic
80C2×#117×C61C2211yescharacteristic
81C61×#482C2214yescomplemented
82C61×#481C2212yescomplemented
83C61×#480C2212yescomplemented
84C61×#428C2212yes—
85C61×#418C2212yes—
86C61×#407C2211yescharacteristic
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C2×#11758194C2312yes—
94#14519777—22no—
95#14519777—22no—
96#14519776—22no—
97#14519776—22no—
98#14519776C2312yes—
99#14519776C2312yes—
100#14519776C2312yes—
101#14519776C2312yes—
102#14519773—22no—
103#14519773C2314yes—
104#14519769—22no—
105#14519769—22no—
106#14519768—22no—
107#14519768—22no—
108#14519768—22no—
109#14519768C2314yes—
110#14519768C2312yes—
111#14519768C2312yes—
112#14519768C2312yes—
113#14519768C2312yes—
114#14519761—24no—
115#14519761—24no—
116#14519759—24no—
117#14519759—24no—
118#14519756—22no—
119#14519756—22no—
120#14519756—22no—
121#14519756—22no—
122#14519754—22no—
123#14519754—22no—
124#14519754—22no—
125#14519754—22no—
126#14519754—22no—
127#14519754—22no—
128#14519754—22no—
129#14519754—22no—
130#14519751—21no—
131#14519751—21no—
132#14519751C2312yes—
133#14519751C2312yes—
134#14519749—24no—
135#14519749—24no—
136#14519748—24no—
137#14519748—24no—
138C4×Dic122—22no—
139C4×Dic122—22no—
140C4×Dic122—22no—
141C4×Dic122—22no—
142D4×Dic61—22no—
143D4×Dic61C2314yes—
144#14519739—22no—
145#14519739C2314yes—
146#14519736—21no—
147#14519736—21no—
148#14519736D412yes—
149#14519736D412yes—
150#14519736C2312yes—
151#14519736C2312yes—
152#14519736C2312yes—
153#14519736C2312yes—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61D411yescharacteristic
156C2×C4⋊Dic61D411yescharacteristic
157C2×C4⋊Dic61C2311yescharacteristic
158C2×C4⋊Dic61C2311yescharacteristic
159C2×C4⋊Dic61C2311yescharacteristic
160C2×#11758196—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61D411yescharacteristic
164C2×C22⋊Dic61D411yescharacteristic
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×C4×Dic61—21no—
168C2×C4×Dic61C2311yescharacteristic
169C2×C4×Dic61C2311yescharacteristic
170#14519711C2314yes—
171#14519710C2314yes—
172#14519710C2314yes—
173#14519709C2314yes—
174#14519708C2314yes—
175#14519708C2314yes—
176#14519706C2314yes—
177#14519706C2314yes—
178#14519699C2314yes—
179#14519699C2314yes—
180#14519698C2314yes—
181#14519698C2314yes—
182#14519697C2314yes—
183#14519697C2314yes—
184C22⋊#92418C2312yes—
185C22⋊#92418C2312yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×D4×C61—21no—
189C22×D4×C61C2311yescharacteristic
190C23×C4×C61C2311yescharacteristic
191C2×M16×C61C2312yes—
192#121×C61—21no—
193#121×C61—21no—
194#121×C61C2312yes—
195#121×C61C2312yes—
196#117×C61—21no—
197#117×C61—21no—
198#117×C61C2312yes—
199#117×C61C2312yes—
200C2×C4⋊C4×C61C2311yescharacteristic
201C2×C4⋊C4×C61C2311yescharacteristic
202C2×C4⋊C4×C61C2311yescharacteristic
203C2×C22⋊C4×C61—21no—
204C2×C22⋊C4×C61—21no—
205C2×C42×C61—21no—
206#107×C61C2314yes—
207#106×C61C2314yes—
208#102×C61C2314yes—
209#102×C61C2314yes—
210C22⋊C8×C61C2312yes—
211C22⋊C8×C61C2312yes—
212C24×C61—21no—
213C24×C61C2×D411yescharacteristic
214C23×D61—21no—
215C2×D4×C61—22no—
216C2×D4×C61—22no—
217C2×D4×C61—21no—
218C2×D4×C61—24no—
219C2×D4×C61—82no—
220C2×D4×C61C2412yes—
221C22×C4×C61—24no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C2×C22⋊D61—22no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—24no—
234C2×C22⋊D61—24no—
235C2×C22⋊D61—82no—
236C2×C22⋊D61—82no—
237C2×C22⋊D61—82no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—24no—
242C22×Dic61—82no—
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C2×D244—24no—
248C2×D244—21no—
249C2×D244C2412yes—
250C2×C4×D61—24no—
251C2×C4×D61—82no—
252C2×Dic122—22no—
253C2×Dic122—22no—
254C2×Dic122—22no—
255C2×Dic122—22no—
256M16×C61—24no—
257C2×C8×C61C2414yes—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C2412yes—
262C4⋊C4×C61C2412yes—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—22no—
267C22⋊C4×C61—22no—
268C42×C61—22no—
269C42×C61—22no—
270C22⋊Dic61—22no—
271C22⋊Dic61—22no—
272C22⋊Dic61—24no—
273C22⋊Dic61C2×D412yes—
274C22⋊Dic61C2×D412yes—
275C22⋊Dic61C2×D412yes—
276C22⋊Dic61C2×D412yes—
277#11758198—22no—
278#11758198—22no—
279#11758198—24no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—24no—
284C4⋊Dic61—22no—
285C4⋊Dic61—22no—
286C4⋊Dic61—22no—
287C4⋊Dic61—22no—
288C4⋊Dic61C2×D412yes—
289C4⋊Dic61C2×D412yes—
290C4⋊Dic61C2×D412yes—
291C4⋊Dic61C2×D412yes—
292C4⋊Dic61C2412yes—
293C4⋊Dic61C2412yes—
294C4⋊Dic61C2412yes—
295#11758196—24no—
296#11758196—22no—
297#11758196—22no—
298#11758196—22no—
299#11758196—22no—
300#11758196—22no—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304C4×Dic61—22no—
305C4×Dic61—22no—
306C4×Dic61C2×D412yes—
307C4×Dic61C2×D412yes—
308C4×Dic61C2412yes—
309C4×Dic61C2412yes—
310#11758194—24no—
311C2×#92418C2414yes—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61C22×D411yescharacteristic
320C23×C61C22×D411yescharacteristic
321C23×C61C22×D411yescharacteristic
322C22×D61—22no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326D4×C61—24no—
327D4×C61—42no—
328D4×C61—82no—
329D4×C61—82no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—42no—
339C2×C4×C61—81no—
340C2×C4×C61—81no—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C612−1+414yes—
345C2×C4×C61C2511yescharacteristic
346C22⋊D61—84no—
347C22⋊D61—84no—
348C22⋊D61—82no—
349C22⋊D61—82no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—42no—
358C2×Dic61—84no—
359C2×Dic61—81no—
360C2×Dic61—81no—
361C2×Dic61C22×D412yes—
362C2×Dic61C22×D412yes—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365D244—24no—
366D244—42no—
367C4×D61—84no—
368Dic122—82no—
369Dic122—82no—
370Dic122—82no—
371Dic122—82no—
372C8×C61—24no—
373#92418—24no—
374#60868—611nomaximal, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—82no—
387C22×C61—84no—
388C22×C61#53612yes—
389C22×C61C23×D411yescharacteristic
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—84no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—42no—
397C4×C61—42no—
398C4×C61—42no—
399C4×C61#53612yes—
400C4×C61C2×2−1+412yes—
401Dic61—22no—
402Dic61—22no—
403Dic61—22no—
404Dic61—22no—
405Dic61—42no—
406Dic61—42no—
407Dic61—42no—
408#3458—611no—
409C2×#540—611no—
410#3241—614no—
411#3241—614no—
412#3241—614no—
413#3241—614no—
414#3166—612no—
415#3138—612no—
416#3094—611no—
417#3094—611no—
418#3094—611no—
419#3094D6111yescharacteristic, complemented
420#3077—612no—
421#3077—612no—
422#2921—611no—
423C2×C61—22no—
424C2×C61—41no—
425C2×C61—41no—
426C2×C61—82no—
427C2×C61C2×#53611yescharacteristic
428C2×C61#358511yescharacteristic
429C2×C61#358511yescharacteristic
430D61—82no—
431#544—612no—
432#544—612no—
433#544—612no—
434#544—612no—
435#544—1221no—
436#544—1221no—
437#543—1221no—
438#543—1221no—
439#540—614no—
440#540—614no—
441#540—1222no—
442#540—1222no—
443#533—612no—
444#533—612no—
445#533—1222no—
446#533—1222no—
447C2×#127—611no—
448C2×#125—611no—
449C2×#123—1221no—
450C2×#123—1221no—
451C2×#121—611no—
452C2×#121—1221no—
453C2×#121—1221no—
454C2×#121C2×D6111yescharacteristic
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×#117—611no—
458C2×#117—611no—
459C2×#117C2×D6111yescharacteristic
460#501—614no—
461#501—614no—
462#499—614no—
463#499—614no—
464#490—614no—
465#490—614no—
466#486—614no—
467#486—614no—
468#482—614no—
469#482—614no—
470#482—614no—
471#482C2×D6114yescomplemented
472#481—612no—
473#481—612no—
474#481—612no—
475#481C2×D6112yescomplemented
476#480—612no—
477#480—612no—
478#480—612no—
479#480C2×D6112yescomplemented
480#478—614no—
481#478—614no—
482#478—614no—
483#478—614no—
484#476—614no—
485#476—614no—
486#474—614no—
487#474—614no—
488#433—614no—
489#433—614no—
490#428—612no—
491#428—612no—
492#428—612no—
493#428C2×D6112yes—
494#423—612no—
495#418—612no—
496#418—612no—
497#418—612no—
498#418C2×D6112yes—
499#407—611no—
500#407C2×D6111yescharacteristic
501C4×M16—612no—
502C61#6086811yescharacteristic, complemented, Sylow
503C22×D4—21no—
504C22×D4—611no—
505C22×D4—1221no—
506C22×D4—1221no—
507C22×D4—1221no—
508C22×D4C22×D6111yescharacteristic
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4C22×D6111yescharacteristic
512C2×M16—612no—
513C2×M16C22×D6112yes—
514C4⋊Q8—612no—
515C4⋊Q8—612no—
516C4⋊Q8—612no—
517C4⋊Q8—612no—
518C4⋊Q8—1222no—
519C4⋊Q8—1222no—
520C4⋊Q8—1222no—
521C4⋊Q8—1222no—
522#127—614no—
523#127—1222no—
524#125—614no—
525#125—612no—
526#125—612no—
527#125—612no—
528#125—612no—
529#125—1222no—
530#125—1222no—
531#125—1222no—
532#125—1222no—
533#125—1222no—
534#123—1224no—
535#123—1224no—
536#123—1224no—
537#123—1224no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C22⋊Q8—1222no—
542C22⋊Q8—1222no—
543C22⋊Q8—1222no—
544C22⋊Q8—1222no—
545C22⋊Q8—1222no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550#121—21no—
551#121—21no—
552#121—612no—
553#121—612no—
554#121—1224no—
555#121—1224no—
556#121—1224no—
557#121—1224no—
558#121—1221no—
559#121—1221no—
560#121C22×D6112yes—
561#121C22×D6112yes—
562C4×Q8—1222no—
563C4×Q8—1222no—
564C4×Q8—1222no—
565C4×Q8—1222no—
566C4×D4—614no—
567C4×D4—614no—
568C4×D4—1222no—
569C4×D4—1222no—
570#117—21no—
571#117—21no—
572#117—612no—
573#117—612no—
574#117—612no—
575#117—612no—
576#117—612no—
577#117—612no—
578#117—1221no—
579#117—1221no—
580#117C22×D6112yes—
581#117C22×D6112yes—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4C22×D6111yescharacteristic
590C2×C4⋊C4C22×D6111yescharacteristic
591C2×C4⋊C4C22×D6111yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—611no—
595C2×C22⋊C4—611no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C42—21no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—1221no—
604#107—614no—
605#107—614no—
606#107—614no—
607#107C22×D6114yes—
608#106—614no—
609#106—614no—
610#106—614no—
611#106C22×D6114yes—
612C4⋊C8—614no—
613C4⋊C8—614no—
614#102—614no—
615#102—614no—
616#102—614no—
617#102—614no—
618#102—614no—
619#102—614no—
620#102C22×D6114yes—
621#102C22×D6114yes—
622C22⋊C8—612no—
623C22⋊C8—612no—
624C22⋊C8C22×D6112yes—
625C22⋊C8C22×D6112yes—
626#97—614no—
627C4×C8—614no—
628C24—21no—
629C24—1221no—
630C24D4×D6111yescharacteristic
631C2×Q8—1222no—
632C2×Q8—1222no—
633C2×Q8—1222no—
634C2×Q8—1222no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—24no—
639C2×D4—82no—
640C2×D4—612no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1222no—
644C2×D4—1222no—
645C2×D4—1221no—
646C2×D4—1224no—
647C2×D4—4882no—
648C2×D4—4882no—
649C2×D4—4882no—
650C2×D4C23×D6112yes—
651C22×C4—24no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—4882no—
665C22×C4—4882no—
666C22×C4D4×D6111yescharacteristic
667C22×C4D4×D6111yescharacteristic
668C22×C4D4×D6111yescharacteristic
669C22×C4C23×D6111yescharacteristic
670C22×C4C23×D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672M16—24no—
673M16—1224no—
674C2×C8—614no—
675C2×C8C23×D6114yes—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—612no—
680C4⋊C4—612no—
681C4⋊C4—612no—
682C4⋊C4—612no—
683C4⋊C4—612no—
684C4⋊C4—612no—
685C4⋊C4—612no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1222no—
689C4⋊C4—1222no—
690C4⋊C4—1222no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C4⋊C4—1222no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1222no—
698C4⋊C4—1222no—
699C4⋊C4—1222no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4C23×D6112yes—
704C4⋊C4C23×D6112yes—
705C4⋊C4C23×D6112yes—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—612no—
711C22⋊C4—612no—
712C22⋊C4—612no—
713C22⋊C4—612no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1222no—
717C22⋊C4—1222no—
718C22⋊C4—1222no—
719C22⋊C4—1222no—
720C42—22no—
721C42—22no—
722C42—612no—
723C42—612no—
724C42—612no—
725C42—612no—
726C42—1222no—
727C42—1222no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—1222no—
736C23—2442no—
737C23—2442no—
738C23—2442no—
739C23C2×D4×D6111yescharacteristic
740C23C2×D4×D6111yescharacteristic
741C23C2×D4×D6111yescharacteristic
742Q8—4882no—
743Q8—4882no—
744Q8—4882no—
745Q8—4882no—
746D4—24no—
747D4—42no—
748D4—82no—
749D4—82no—
750D4—1224no—
751D4—4884no—
752D4—4884no—
753D4—4882no—
754D4—4882no—
755D4—2442no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—612no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—4884no—
775C2×C4—4884no—
776C2×C4—4881no—
777C2×C4—4881no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2442no—
783C2×C4C2×D4×D6111yescharacteristic
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4#1451982414yes—
787C2×C4C24×D6111yescharacteristic
788C8—24no—
789C8—1224no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—82no—
802C22—84no—
803C22—4884no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22#1684033412yes—
808C22C22×D4×D6111yescharacteristic
809C4—21no—
810C4—21no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—1222no—
815C4—1222no—
816C4—1222no—
817C4—1222no—
818C4—2442no—
819C4—2442no—
820C4—2442no—
821C4#1684033412yes—
822C4C2×#1451982412yes—
823C2—22no—
824C2—41no—
825C2—41no—
826C2—82no—
827C2—4882no—
828C2C2×#1684033411yescharacteristic
829C2#2146059511yescharacteristic
830C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3094C2
socleC22×C61C23×D4
prime radicalC2×#16840365C2
hypercenter#3094D61
hypocenterC61#60868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #21459224C2semidirect
3. #21457078C2semidirect
4. #21457076C2semidirect
5. #21457070C2semidirect
6. #21457068C2semidirect
7. #21456369C2semidirect
8. #21456191C2semidirect
9. #21455760C2semidirect
10. #21455759C2semidirect
11. #21455755C2semidirect
12. #21455615C2semidirect
13. #21455613C2semidirect
14. #21454454C2semidirect
15. C61×#3094C2semidirect
16. #16840393C22semidirect
17. #16840393C22semidirect
20. #16840390C22semidirect
21. #16840390C22semidirect
43. #16840170C22semidirect
44. #16840169C22semidirect
45. #16840163C22semidirect
46. #16840162C22semidirect
47. #16840125C22semidirect
48. #16840125C22semidirect
49. #16840107C22semidirect
50. #16840107C22semidirect
51. #16840087C22semidirect
52. #16840086C22semidirect
53. #16840083C22semidirect
54. #16840081C22semidirect
55. #16840080C22semidirect
56. #16840078C22semidirect
57. #16840076C22semidirect
58. #16840075C22semidirect
59. #16840073C22semidirect
60. #16840065C22semidirect
61. #16840064C22semidirect
62. #16840061C22semidirect
63. #16840060C22semidirect
64. #16840051C22semidirect
65. #16840050C22semidirect
66. #16840041C22semidirect
67. #16840040C22semidirect
68. #16839820C22semidirect
69. #16839820C22semidirect
81. C61×#482C22semidirect
82. C61×#481C22semidirect
83. C61×#480C22semidirect
419. #3094D61semidirect
471. #482C2×D61semidirect
475. #481C2×D61semidirect
479. #480C2×D61semidirect
502. C61#60868semidirect

Maximal subgroups

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

subgroupindex
#214592242
C2×#168403652
#214570782
#214570762
#214570702
#214570682
#214563692
#214561912
#214557602
#214557592
#214557552
#214556152
#214556132
#214544542
C61×#30942
#6086861