Finite Group Databasebeta

← #30552281

Subgroups — #30552281

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic
2C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#21457050C214yesmaximal, complemented
4#21457041C214yesmaximal, complemented
5#21456971C212yesmaximal, complemented
6#21456964C212yesmaximal, complemented
7#21456948C212yesmaximal, complemented
8#21456941C212yesmaximal, complemented
9#21456366C211yesmaximal, characteristic, complemented
10#21456215C211yesmaximal, characteristic, complemented
11#21456213C211yesmaximal, characteristic, complemented
12#21455745C214yesmaximal, complemented
13#21455632C214yesmaximal, complemented
14#21454450C211yesmaximal, characteristic, complemented
15C61×#3165C211yesmaximal, characteristic, complemented
16C22×Q8×D61—21no—
17#16840317C2211yescharacteristic
18#16840317C2211yescharacteristic
19#16840313C2211yescharacteristic
20#16840313C2211yescharacteristic
21#16840312C2211yescharacteristic
22C2×#14519777C2211yescharacteristic
23C2×#14519776—21no—
24C2×#14519776C2212yes—
25C2×#14519775—21no—
26C4⋊Q8×D61—21no—
27C4⋊Q8×D61—21no—
28C4⋊Q8×D61—21no—
29C4⋊Q8×D61—21no—
30C4⋊Q8×D61C2212yes—
31C4⋊Q8×D61C2212yes—
32C4⋊Q8×D61C2212yes—
33C4⋊Q8×D61C2212yes—
34#16840299—21no—
35#16840299—21no—
36#16840298—21no—
37#16840298—21no—
38#16840297C2212yes—
39#16840297C2212yes—
40#16840275—21no—
41#16840275—21no—
42#16840274C2212yes—
43C4×#11758226—21no—
44C4×#11758226—21no—
45#16840230C2212yes—
46C2×C4⋊C4×D61—21no—
47C2×C4⋊C4×D61C2212yes—
48C2×C42×D61C2211yescharacteristic
49#16840172C2214yescomplemented
50#16840165C2212yescomplemented
51#16840158C2212yescomplemented
52#16840124C2214yescomplemented
53#16840122C2214yescomplemented
54#16840114C2212yescomplemented
55#16840113C2212yescomplemented
56#16840110C2212yescomplemented
57#16840109C2212yescomplemented
58#16840099C2218yes—
59#16840094C2218yes—
60#16840082C2218yes—
61#16840077C2218yes—
62#16840056C2218yescomplemented
63#16840051C2218yescomplemented
64#16840046C2218yescomplemented
65#16840041C2218yescomplemented
66#16839817C2212yes—
67#16839817C2212yes—
68#16839813C2212yes—
69#16839813C2212yes—
70#16839805C2214yes—
71#16839785C2212yes—
72#16839764C2214yes—
73#16839761C2214yes—
74#16839725C2212yes—
75C4×#11758194C2211yescharacteristic
76C61×#533C2211yescharacteristic
77C2×C4⋊Q8×C61C2211yescharacteristic
78C61×#501C2214yescomplemented
79C61×#500C2212yescomplemented
80C61×#498C2212yescomplemented
81C61×#428C2214yes—
82C4×M16×C61C2211yescharacteristic
83C2×#11758226—21no—
84C2×#11758226—21no—
85C2×#11758222C2312yes—
86C22×Dic122—21no—
87C22×Dic122—22no—
88C2×Q8×D61—22no—
89C2×Q8×D61—22no—
90C2×Q8×D61—22no—
91C2×Q8×D61—22no—
92C2×Q8×D61—48no—
93C22×C4×D61—22no—
94C22×C4×D61D411yescharacteristic
95C22×C4×D61D411yescharacteristic
96C22×C4×D61C2311yescharacteristic
97C2×#11758194C2312yes—
98#14519777—21no—
99#14519777—21no—
100#14519777C2311yescharacteristic
101#14519777C2312yes—
102#14519777C2312yes—
103#14519776—22no—
104#14519776—22no—
105#14519776—22no—
106#14519776—22no—
107#14519776—22no—
108#14519776—22no—
109#14519776C2314yes—
110#14519776C2314yes—
111#14519775—22no—
112#14519775—22no—
113#14519775—22no—
114#14519775—22no—
115#14519774C2311yescharacteristic
116#14519772—22no—
117#14519772—22no—
118#14519768—21no—
119#14519768—21no—
120#14519766—21no—
121#14519766—21no—
122#14519765C2312yes—
123#14519762—22no—
124#14519762—22no—
125#14519761—22no—
126#14519757C2312yes—
127#14519757C2312yes—
128#14519753—21no—
129#14519753—21no—
130#14519752—21no—
131#14519752—21no—
132#14519752C2312yes—
133#14519752C2312yes—
134#14519751—21no—
135#14519751—21no—
136#14519747—22no—
137Q8×Dic61—21no—
138Q8×Dic61—21no—
139#14519742C2312yes—
140#14519742C2312yes—
141C4×D244—22no—
142C4×D244—22no—
143C4×D244—21no—
144C4×D244—21no—
145#14519739—22no—
146#14519739—22no—
147#14519739—21no—
148#14519739—21no—
149#14519739C2312yes—
150#14519739C2312yes—
151#14519737—22no—
152#14519737—22no—
153#14519735—21no—
154#14519735—21no—
155#14519735—22no—
156#14519735—22no—
157#14519734—22no—
158C2×C4⋊Dic61—21no—
159C2×C4⋊Dic61C2312yes—
160C2×#11758196—22no—
161C2×#11758196—22no—
162C4⋊C4×D61—22no—
163C4⋊C4×D61—22no—
164C4⋊C4×D61—22no—
165C4⋊C4×D61—22no—
166C4⋊C4×D61—22no—
167C4⋊C4×D61—22no—
168C4⋊C4×D61C2314yes—
169C4⋊C4×D61C2314yes—
170C2×C4×Dic61D411yescharacteristic
171C2×C4×Dic61D411yescharacteristic
172C2×C4×Dic61C2311yescharacteristic
173C42×D61—22no—
174C42×D61D411yescharacteristic
175C42×D61D411yescharacteristic
176C42×D61D411yescharacteristic
177C42×D61D411yescharacteristic
178C42×D61C2311yescharacteristic
179C42×D61C2311yescharacteristic
180C42×D61C2311yescharacteristic
181C42×D61C2311yescharacteristic
182#14519710C2318yes—
183#14519708C2318yes—
184#14519706C2314yes—
185#14519706C2314yes—
186#14519702C2318yes—
187#14519700C2318yes—
188#14519699C2318yes—
189#14519697C2318yes—
190#14519689C2314yes—
191#14519689C2314yes—
192#14519688C2312yes—
193C4×#92418C2312yes—
194C22×Q8×C61—21no—
195C2×M16×C61C2312yes—
196C4⋊Q8×C61—21no—
197C4⋊Q8×C61—21no—
198C4⋊Q8×C61C2312yes—
199C4⋊Q8×C61C2312yes—
200C4⋊Q8×C61C2311yescharacteristic
201C4⋊Q8×C61C2311yescharacteristic
202#125×C61C2312yes—
203C22⋊Q8×C61—21no—
204C22⋊Q8×C61—21no—
205C4×Q8×C61—21no—
206C4×Q8×C61—21no—
207#117×C61C2312yes—
208C2×C4⋊C4×C61—21no—
209C2×C4⋊C4×C61C2312yes—
210C2×C42×C61C2311yescharacteristic
211#107×C61C2318yes—
212#106×C61C2318yes—
213#97×C61C2312yes—
214C4×C8×C61C2312yes—
215C23×D61C2×D411yescharacteristic
216C2×Q8×C61—22no—
217C2×Q8×C61—22no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—44no—
221C22×C4×C61—22no—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—22no—
226C22×Dic61—22no—
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230#11758226—44no—
231#11758226—44no—
232Q8×D61—48no—
233Q8×D61—48no—
234Q8×D61—48no—
235Q8×D61—48no—
236#11758222—28no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244C2412yes—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—24no—
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—48no—
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2411yescharacteristic
262C2×C4×D61C2411yescharacteristic
263C2×Dic122—22no—
264C2×Dic122—22no—
265C2×Dic122—24no—
266C2×Dic122—24no—
267C2×Dic122—48no—
268C2×Dic122—44no—
269C2×Dic122C2412yes—
270M16×C61—24no—
271C2×C8×C61C2414yes—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—22no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2412yes—
280C4⋊C4×C61C2414yes—
281C4⋊C4×C61C2412yes—
282C22⋊C4×C61—22no—
283C42×C61—22no—
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D411yescharacteristic
286C42×C61C2411yescharacteristic
287C42×C61C2411yescharacteristic
288#11758198—22no—
289#11758198—22no—
290#11758198—22no—
291#11758198—22no—
292#11758198—22no—
293#11758198—22no—
294#11758198—22no—
295#11758198—22no—
296C4⋊Dic61—22no—
297C4⋊Dic61—22no—
298C4⋊Dic61—22no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—22no—
302C4⋊Dic61—22no—
303C4⋊Dic61C2414yes—
304#11758196—24no—
305#11758196—24no—
306#11758196—24no—
307#11758196—24no—
308#11758196—22no—
309#11758196—22no—
310C4×Dic61—22no—
311C4×Dic61—22no—
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2411yescharacteristic
323C4×Dic61C2411yescharacteristic
324#11758194—24no—
325C2×#92418C2414yes—
326C23×C61C22×D411yescharacteristic
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61C22×D411yescharacteristic
332C22×D61C22×D411yescharacteristic
333Q8×C61—44no—
334Q8×C61—44no—
335Q8×C61—42no—
336Q8×C61—42no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—24no—
342C2×C4×C61—44no—
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C612−1+414yes—
349C2×C4×C61C2511yescharacteristic
350C22⋊D61—44no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—24no—
356C2×Dic61—44no—
357C2×Dic61C22×D411yescharacteristic
358C2×Dic61C22×D411yescharacteristic
359C2×Dic61C22×D411yescharacteristic
360C2×Dic61C22×D411yescharacteristic
361C2×Dic61C22×D411yescharacteristic
362C2×Dic61C22×D411yescharacteristic
363D244—24no—
364D244—44no—
365D244—44no—
366D244—42no—
367D244—42no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—48no—
379C4×D61—48no—
380C4×D61—44no—
381C4×D61—44no—
382C4×D61—44no—
383C4×D61AGL(1,ℤ/8)14yes—
384C4×D61#13714yes—
385Dic122—24no—
386Dic122—48no—
387Dic122—44no—
388Dic122—44no—
389Dic122—48no—
390C8×C61—24no—
391#92418—24no—
392#60860—611nomaximal, Sylow
393C22×C61—21no—
394C22×C61—21no—
395C22×C61#53612yes—
396C22×C61C23×D411yescharacteristic
397C2×D61—28no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61C2×AGL(1,ℤ/8)12yes—
406C2×D61C2×#13712yes—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—44no—
410C4×C61—42no—
411C4×C61—42no—
412C4×C61#53612yes—
413C4×C61C2×AGL(1,ℤ/8)12yes—
414C4×C61C2×#13712yes—
415C4×C61C2×2−1+412yes—
416Dic61—21no—
417Dic61—21no—
418Dic61—21no—
419Dic61—21no—
420Dic61—42no—
421Dic61—44no—
422Dic61C2×AGL(1,ℤ/8)12yes—
423Dic61C2×#13712yes—
424#3444—611no—
425C22×C4⋊Q8—611no—
426#3239—614no—
427#3238—614no—
428#3230—612no—
429#3229—612no—
430#3227—612no—
431#3226—612no—
432#3165—611no—
433#3165D6111yescharacteristic, complemented
434#3141—611no—
435#3141—611no—
436#3092—614no—
437#3079—614no—
438#2920—611no—
439C2×C61—22no—
440C2×C61C2×#53611yescharacteristic
441C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
442C2×C61C22×#13711yescharacteristic
443D61—22no—
444D61—22no—
445D61—82no—
446C23×Q8—1221no—
447#533—611no—
448#533—611no—
449#533C2×D6111yescharacteristic
450#532—611no—
451#532—611no—
452#532—611no—
453C2×C4⋊Q8—612no—
454C2×C4⋊Q8—612no—
455C2×C4⋊Q8—612no—
456C2×C4⋊Q8—612no—
457C2×C4⋊Q8—612no—
458C2×C4⋊Q8—611no—
459C2×C4⋊Q8—1221no—
460C2×C4⋊Q8—1221no—
461C2×C4⋊Q8—1221no—
462C2×C4⋊Q8—1221no—
463C2×C4⋊Q8—1221no—
464C2×C4⋊Q8—1221no—
465C2×C4⋊Q8C2×D6111yescharacteristic
466#529—612no—
467#529—612no—
468#529—1221no—
469#529—1221no—
470#529—1221no—
471#529—1221no—
472#525—612no—
473#525—1221no—
474#525—1221no—
475C4×#41—612no—
476C4×#41—1221no—
477C4×#41—1221no—
478C22×C4⋊C4—612no—
479C22×C4⋊C4—1221no—
480C22×C42—611no—
481#501—614no—
482#501C2×D6114yescomplemented
483#500—612no—
484#500C2×D6112yescomplemented
485#498—612no—
486#498C2×D6112yescomplemented
487#489—614no—
488#489—614no—
489#487—612no—
490#487—612no—
491#486—612no—
492#486—612no—
493#484—618no—
494#483—618no—
495#481—618no—
496#480—618no—
497#477—618no—
498#476—618no—
499#475—618no—
500#474—618no—
501#432—612no—
502#432—612no—
503#431—612no—
504#431—612no—
505#428—614no—
506#428C2×D6114yes—
507#423—612no—
508#417—614no—
509#417—614no—
510#407—612no—
511C4×M16—611no—
512C4×M16C2×D6111yescharacteristic
513C61#6086011yescharacteristic, complemented, Sylow
514C2×#41—612no—
515C2×#41—1221no—
516C2×#41—1221no—
517C22×Q8—21no—
518C22×Q8—1222no—
519C22×Q8—1222no—
520C22×Q8—1222no—
521C22×Q8—1222no—
522C22×Q8—1222no—
523C22×Q8—1221no—
524C22×Q8—2448no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—611no—
528C23×C4—1222no—
529C2×M16—612no—
530C2×M16C22×D6112yes—
531C4⋊Q8—21no—
532C4⋊Q8—21no—
533C4⋊Q8—614no—
534C4⋊Q8—614no—
535C4⋊Q8—612no—
536C4⋊Q8—612no—
537C4⋊Q8—611no—
538C4⋊Q8—1222no—
539C4⋊Q8—1222no—
540C4⋊Q8—1222no—
541C4⋊Q8—1222no—
542C4⋊Q8—1222no—
543C4⋊Q8—1222no—
544C4⋊Q8—1222no—
545C4⋊Q8—1222no—
546C4⋊Q8—1222no—
547C4⋊Q8—1222no—
548C4⋊Q8—1221no—
549C4⋊Q8—1221no—
550C4⋊Q8C22×D6112yes—
551C4⋊Q8C22×D6112yes—
552C4⋊Q8C22×D6111yescharacteristic
553C4⋊Q8C22×D6111yescharacteristic
554#127—611no—
555#126—1222no—
556#126—1222no—
557#125—1221no—
558#125—1221no—
559#125C22×D6112yes—
560#124—612no—
561#124—1221no—
562#124—1221no—
563#123—1222no—
564#123—1222no—
565#123—1222no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—612no—
569C22⋊Q8—612no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572#121—612no—
573#121—612no—
574#121—1221no—
575#121—1221no—
576#121—1221no—
577#121—1221no—
578#120—1222no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—612no—
582C4×Q8—612no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×D4—612no—
586C4×D4—612no—
587C4×D4—1222no—
588C4×D4—1222no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1222no—
592C4×D4—1222no—
593C4×D4—1222no—
594C4×D4—1222no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—1222no—
598#117—1222no—
599#117—1222no—
600#117—1221no—
601#117—1221no—
602#117C22×D6112yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—612no—
605C2×C4⋊C4—614no—
606C2×C4⋊C4—614no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4C22×D6112yes—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—611no—
623C2×C42—611no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—611no—
627C2×C42—611no—
628C2×C42—1222no—
629C2×C42C22×D6111yescharacteristic
630#107—618no—
631#107C22×D6118yes—
632#106—618no—
633#106C22×D6118yes—
634C4⋊C8—614no—
635C4⋊C8—614no—
636#103—618no—
637#103—618no—
638#102—618no—
639#102—618no—
640C22⋊C8—614no—
641C22⋊C8—614no—
642#97—612no—
643#97C22×D6112yes—
644C4×C8—612no—
645C4×C8C22×D6112yes—
646C24—611no—
647#41—1228no—
648#41—2444no—
649#41—2444no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—44no—
655C2×Q8—612no—
656C2×Q8—1224no—
657C2×Q8—1224no—
658C2×Q8—1222no—
659C2×Q8—1222no—
660C2×Q8—2444no—
661C2×Q8—2448no—
662C2×Q8—2448no—
663C2×Q8—2448no—
664C2×Q8—2448no—
665C2×Q8—2448no—
666C2×D4—612no—
667C2×D4—1222no—
668C2×D4—1222no—
669C2×D4—1222no—
670C2×D4—1221no—
671C2×D4—1221no—
672C22×C4—22no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—1224no—
689C22×C4—1224no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1224no—
693C22×C4—1224no—
694C22×C4—1224no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—2448no—
698C22×C4D4×D6111yescharacteristic
699C22×C4D4×D6111yescharacteristic
700C22×C4C23×D6111yescharacteristic
701M16—24no—
702M16—1224no—
703C2×C8—614no—
704C2×C8C23×D6114yes—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—614no—
713C4⋊C4—1224no—
714C4⋊C4—1224no—
715C4⋊C4—1224no—
716C4⋊C4—1224no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4C23×D6114yes—
727C4⋊C4C23×D6112yes—
728C4⋊C4C23×D6112yes—
729C22⋊C4—22no—
730C22⋊C4—1222no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C42—22no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—1222no—
752C42—1222no—
753C42D4×D6111yescharacteristic
754C42D4×D6111yescharacteristic
755C42C23×D6111yescharacteristic
756C42C23×D6111yescharacteristic
757C23—611no—
758C23—611no—
759C23—1222no—
760C23—1222no—
761C23—1222no—
762C23—1222no—
763C23C2×D4×D6111yescharacteristic
764Q8—44no—
765Q8—44no—
766Q8—42no—
767Q8—42no—
768Q8—1224no—
769Q8—2444no—
770Q8—2448no—
771Q8—2448no—
772Q8—2444no—
773D4—1224no—
774D4—2444no—
775D4—2444no—
776D4—2444no—
777D4—2442no—
778D4—2442no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—44no—
785C2×C4—611no—
786C2×C4—611no—
787C2×C4—614no—
788C2×C4—614no—
789C2×C4—611no—
790C2×C4—611no—
791C2×C4—611no—
792C2×C4—611no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1224no—
808C2×C4—2444no—
809C2×C4—2444no—
810C2×C4—2448no—
811C2×C4—2448no—
812C2×C4—2444no—
813C2×C4—2444no—
814C2×C4C2×D4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4C2×D4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4#1451982514yes—
820C2×C4C24×D6111yescharacteristic
821C8—24no—
822C8—1224no—
823C22—21no—
824C22—21no—
825C22—612no—
826C22—612no—
827C22—1228no—
828C22—1221no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22#1684033712yes—
836C22C22×D4×D6111yescharacteristic
837C4—21no—
838C4—21no—
839C4—44no—
840C4—42no—
841C4—42no—
842C4—612no—
843C4—612no—
844C4—1221no—
845C4—1221no—
846C4—1221no—
847C4—1221no—
848C4—2444no—
849C4—2442no—
850C4#1684033712yes—
851C4AGL(1,ℤ/8)×D6112yes—
852C4#137×D6112yes—
853C4C2×#1451982512yes—
854C2—22no—
855C2—1222no—
856C2—1222no—
857C2—4882no—
858C2C2×#1684033711yescharacteristic
859C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
860C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3165C2
socleC22×C61C23×D4
prime radical#21459116C2
hypercenter#3165D61
hypocenterC61#60860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Q8×D61C2semidirect
3. #21457050C2semidirect
4. #21457041C2semidirect
5. #21456971C2semidirect
6. #21456964C2semidirect
7. #21456948C2semidirect
8. #21456941C2semidirect
9. #21456366C2semidirect
10. #21456215C2semidirect
11. #21456213C2semidirect
12. #21455745C2semidirect
13. #21455632C2semidirect
14. #21454450C2semidirect
15. C61×#3165C2semidirect
49. #16840172C22semidirect
50. #16840165C22semidirect
51. #16840158C22semidirect
52. #16840124C22semidirect
53. #16840122C22semidirect
54. #16840114C22semidirect
55. #16840113C22semidirect
56. #16840110C22semidirect
57. #16840109C22semidirect
62. #16840056C22semidirect
63. #16840051C22semidirect
64. #16840046C22semidirect
65. #16840041C22semidirect
78. C61×#501C22semidirect
79. C61×#500C22semidirect
80. C61×#498C22semidirect
433. #3165D61semidirect
482. #501C2×D61semidirect
484. #500C2×D61semidirect
486. #498C2×D61semidirect
513. C61#60860semidirect

Maximal subgroups

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

subgroupindex
#214591162
C2×C4⋊Q8×D612
#214570502
#214570412
#214569712
#214569642
#214569482
#214569412
#214563662
#214562152
#214562132
#214557452
#214556322
#214544502
C61×#31652
#6086061