Finite Group Databasebeta

← #29648485

Subgroups — #29648485

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459688C211yesmaximal, characteristic
2#21454927C211yesmaximal, characteristic, complemented
3#21454486C211yesmaximal, characteristic, complemented
4#21444523C211yesmaximal, characteristic, complemented
5#21444515C211yesmaximal, characteristic, complemented
6#21444511C211yesmaximal, characteristic, complemented
7#21444508C211yesmaximal, characteristic, complemented
8#21444485C211yesmaximal, characteristic, complemented
9#21444479C211yesmaximal, characteristic, complemented
10#21444478C211yesmaximal, characteristic, complemented
11#21444475C211yesmaximal, characteristic, complemented
12#21444468C211yesmaximal, characteristic, complemented
13#21444467C211yesmaximal, characteristic, complemented
14#331×D61C211yesmaximal, characteristic, complemented
15C61×#1553C211yesmaximal, characteristic, complemented
16#16840495C412yes—
17#16840494—21no—
18#16840431—21no—
19#16840430C412yes—
20#16840409C412yes—
21#16840407C412yes—
22#16840405—21no—
23#16840400—21no—
24#16840365—21no—
25#16840363—21no—
26#16840328—21no—
27#16840317C2211yescharacteristic
28#16840313C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840310C2211yescharacteristic
31#127×D61C2211yescharacteristic
32#16840234—21no—
33C4×#11758222C2211yescharacteristic
34C8×Dic122—21no—
35C8×D244—21no—
36#16839825—21no—
37#16839825—21no—
38#16839824—21no—
39#16839820—21no—
40#16839818C2211yescharacteristic, complemented
41#16839815C2211yescharacteristic, complemented
42#16839814C2211yescharacteristic
43#16839814C2211yescharacteristic, complemented
44#16839814C2211yescharacteristic, complemented
45#16839784C2211yescharacteristic
46C2×C4⋊#92418C2211yescharacteristic, complemented
47C4⋊C8×D61C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49C4⋊C8×D61C2211yescharacteristic, complemented
50#16839727—21no—
51#16839719—21no—
52#16839510C2211yescharacteristic, complemented
53#16839510C2211yescharacteristic, complemented
54#16839510C2211yescharacteristic, complemented
55#16839510C2211yescharacteristic, complemented
56#16839508C2211yescharacteristic, complemented
57#16839508C2211yescharacteristic, complemented
58#16839506C2211yescharacteristic
59#16839506C2211yescharacteristic
60#16839505C2211yescharacteristic
61#16839505C2211yescharacteristic
62#16839505C2211yescharacteristic
63#16839505C2211yescharacteristic
64C61×#532C2211yescharacteristic
65C61×#432C2211yescharacteristic, complemented
66C61×#431C2211yescharacteristic, complemented
67C61×#332C2211yescharacteristic, complemented
68C61×#332C2211yescharacteristic, complemented
69C61×#331C2211yescharacteristic
70C61×#331C2211yescharacteristic
71C2×#11758226—21no—
72C2×#11758222C2×C412yes—
73C2×#11758222D411yescharacteristic
74C2×#11758224C2×C412yes—
75C2×D4×D61—21no—
76C2×D4×D61—21no—
77C2×D4×D61C2×C412yes—
78C2×#11758189—21no—
79C22×#92418—21no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83#14519777C2311yescharacteristic
84#14519774C2311yescharacteristic
85#14519773—22no—
86#14519773—21no—
87#14519773—21no—
88#14519773C2×C412yes—
89#14519768—21no—
90#14519766—21no—
91#14519765C2×C412yes—
92#14519764C2×C412yes—
93#14519763—22no—
94#14519761—22no—
95#14519760—22no—
96#14519759—22no—
97#14519759—22no—
98#14519757C2×C412yes—
99#14519753—21no—
100#14519752—21no—
101#14519752C2×C412yes—
102#14519751—21no—
103#14519751—21no—
104#14519751—22no—
105#14519750—22no—
106#14519749—22no—
107#14519748—21no—
108#14519748—21no—
109#14519748—22no—
110#14519747—22no—
111#14519745—22no—
112Q8×Dic61—21no—
113C4×Dic122C2×C411yescharacteristic
114C4×Dic122D411yescharacteristic
115#14519742C2×C412yes—
116C4×D244—21no—
117C4×D244—21no—
118C4×D244C2×C411yescharacteristic
119C4×D244D411yescharacteristic
120D4×Dic61—21no—
121D4×Dic61—21no—
122#14519739—21no—
123#14519739C2×C412yes—
124C4×C22⋊D61—22no—
125C4×C22⋊D61C2×C411yescharacteristic
126C4×C22⋊D61C2×C411yescharacteristic
127C4×C22⋊D61D411yescharacteristic
128C4×C22⋊D61D411yescharacteristic
129#14519737—22no—
130#14519736D411yescharacteristic
131#14519735—21no—
132#14519734D411yescharacteristic
133#14519734D411yescharacteristic
134C2×#11758198—22no—
135C22⋊C4×D61—22no—
136C42×D61C2311yescharacteristic
137C42×D61C2311yescharacteristic
138C4⋊#92418—21no—
139C4⋊#92418C2311yescharacteristic
140C4⋊#92418C2311yescharacteristic
141C4⋊#92418C2311yescharacteristic
142C4⋊#92418C2311yescharacteristic
143#14519706—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147C22⋊#92418—21no—
148#14519689—21no—
149#14519689—21no—
150#14519689—21no—
151#14519689—21no—
152#14519687—21no—
153C4×#92418—21no—
154C8×Dic61—21no—
155C8×Dic61—21no—
156C8×Dic61—21no—
157C2×#41×C61—21no—
158C4⋊Q8×C61C2311yescharacteristic
159#127×C61C2311yescharacteristic
160#124×C61—21no—
161#121×C61—21no—
162#121×C61C2×C412yes—
163C4×D4×C61—21no—
164C4×D4×C61C2×C412yes—
165C2×C42×C61C2311yescharacteristic
166C4⋊C8×C61C2311yescharacteristic
167C4⋊C8×C61C2311yescharacteristic
168C4⋊C8×C61C2311yescharacteristic
169C4⋊C8×C61C2311yescharacteristic
170C22⋊C8×C61—21no—
171C22⋊C8×C61—21no—
172#97×C61—21no—
173C4×C8×C61—21no—
174C23×D61—22no—
175#41×C61—81no—
176#41×C61—81no—
177C2×Q8×C61—21no—
178C2×D4×C61—22no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61C22×C412yes—
182C22×C4×C61—22no—
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61C22⋊C411yescharacteristic
192C2×C22⋊D61C22⋊C411yescharacteristic
193C22×Dic61—22no—
194#11758226—81no—
195#11758226—81no—
196#11758224—82no—
197D4×D61—42no—
198D4×D61—42no—
199D4×D61—81no—
200D4×D61—81no—
201D4×D61—82no—
202#11758222—22no—
203#11758222—22no—
204#11758222—82no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—22no—
208C2×D244C22⋊C411yescharacteristic
209C2×D244C22×C412yes—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61C22×C411yescharacteristic
213C2×C4×D61C22×C411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×Dic122C22⋊C411yescharacteristic
219C2×Dic122C22×C412yes—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61C22×C412yes—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C42×C61C22×C411yescharacteristic
229C42×C61C2×D411yescharacteristic
230C42×C61C2×D411yescharacteristic
231C42×C61C2411yescharacteristic
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61C22⋊C411yescharacteristic
235C22⋊Dic61C22⋊C411yescharacteristic
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198C22⋊C411yescharacteristic
242#11758198C22⋊C411yescharacteristic
243#11758198C22⋊C411yescharacteristic
244#11758198C22⋊C411yescharacteristic
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—22no—
248C4⋊Dic61C22⋊C411yescharacteristic
249C4⋊Dic61C22⋊C411yescharacteristic
250#11758196—22no—
251#11758196C22⋊C411yescharacteristic
252#11758196C22⋊C411yescharacteristic
253#11758196C22⋊C411yescharacteristic
254#11758196C22⋊C411yescharacteristic
255C4×Dic61—22no—
256C4×Dic61C22×C411yescharacteristic
257C4×Dic61C22×C411yescharacteristic
258C4×Dic61C2×D411yescharacteristic
259C4×Dic61C2×D411yescharacteristic
260C4×Dic61C2×D411yescharacteristic
261C4×Dic61C2×D411yescharacteristic
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—81no—
267#11758189—42no—
268C8×D61—42no—
269C8×D61—81no—
270C8×D61—81no—
271C23×C61—22no—
272C23×C61C2×C22⋊C411yescharacteristic
273C22×D61—22no—
274C22×D61—44no—
275C22×D61—82no—
276C22×D61—82no—
277C22×D61C2×C22⋊C411yescharacteristic
278C22×D61C2×C22⋊C411yescharacteristic
279Q8×C61—41no—
280Q8×C61—41no—
281D4×C61—42no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—82no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—41no—
293C2×C4×C61—82no—
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C22⋊D61—22no—
301C22⋊D61—22no—
302C22⋊D61—44no—
303C22⋊D61—82no—
304C22⋊D61—82no—
305C22⋊D61—82no—
306C22⋊D61—82no—
307C2×Dic61—22no—
308C2×Dic61—82no—
309C2×Dic61C2×C22⋊C411yescharacteristic
310C2×Dic61C2×C22⋊C411yescharacteristic
311C2×Dic61C2×C22⋊C411yescharacteristic
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C2×C22⋊C411yescharacteristic
314C2×Dic61C2×C22⋊C411yescharacteristic
315D244—22no—
316D244—42no—
317D244—41no—
318D244—41no—
319D244—41no—
320D244—41no—
321D244—82no—
322C4×D61—21no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—21no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—82no—
331C4×D61—82no—
332C4×D61#13512yes—
333C4×D61#13512yes—
334Dic122—22no—
335Dic122—42no—
336C8×C61—41no—
337C8×C61—41no—
338C8×C61—41no—
339C8×C61—41no—
340#92418—41no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#17724—611nomaximal, Sylow
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61C22×C22⋊C411yescharacteristic
352C2×D61—21no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—164no—
361C2×D61#41612yes—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—42no—
367C4×C61C2×#13511yescharacteristic
368C4×C61C2×#13511yescharacteristic
369C4×C61#57611yescharacteristic
370C4×C61#57711yescharacteristic
371Dic61—21no—
372Dic61—21no—
373Dic61—21no—
374Dic61—21no—
375Dic61—21no—
376Dic61—42no—
377Dic61#41612yes—
378#3508—611no—
379#2988—611no—
380#2925—611no—
381#1553—611no—
382#1553D6111yescharacteristic, complemented
383#1551—611no—
384#1551—611no—
385#1550—611no—
386#1545—611no—
387#1543—611no—
388#1543—611no—
389#1542—611no—
390#1540—611no—
391#1540—611no—
392C2×#331—611no—
393C2×C61—41no—
394C2×C61—82no—
395C2×C61#288811yescharacteristic
396C2×C61C2×#41611yescharacteristic
397C2×C61#289711yescharacteristic
398D61—22no—
399D61—41no—
400D61—82no—
401#559—612no—
402#559—1221no—
403#550—612no—
404#550—1221no—
405#546—612no—
406#546—612no—
407#546—1221no—
408#546—1221no—
409#540—1221no—
410#540—1221no—
411#535—1221no—
412#533—611no—
413#532—611no—
414#532—611no—
415#532—611no—
416#532C2×D6111yescharacteristic
417C2×#127—611no—
418#518—1221no—
419C4×#41—611no—
420C8×Q8—1221no—
421C8×D4—1221no—
422C8×D4—1221no—
423C8×D4—1221no—
424#433—1221no—
425#433—1221no—
426#432—611no—
427#432C2×D6111yescharacteristic, complemented
428#431—611no—
429#431—611no—
430#431—611no—
431#431—611no—
432#431C2×D6111yescharacteristic, complemented
433#423—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438#408—1221no—
439#405—1221no—
440#333—611no—
441#333—611no—
442#333—611no—
443#333—611no—
444#332—611no—
445#332—611no—
446#332C2×D6111yescharacteristic, complemented
447#332C2×D6111yescharacteristic, complemented
448#331—611no—
449#331—611no—
450#331—611no—
451#331—611no—
452#331—611no—
453#331—611no—
454#331C2×D6111yescharacteristic
455#331C2×D6111yescharacteristic
456C61#1772411yescharacteristic, complemented, Sylow
457C2×#41—21no—
458C2×#41—611no—
459C2×#41—612no—
460C2×#41—612no—
461C2×#41—1221no—
462C22×D4—612no—
463C22×D4—1221no—
464C22×D4—1221no—
465C2×M16—1221no—
466C22×C8—1221no—
467C22×C8—1221no—
468C22×C8—1221no—
469C22×C8—1221no—
470C4⋊Q8—611no—
471C4⋊Q8C22×D6111yescharacteristic
472#127—612no—
473#127—611no—
474#127—1221no—
475#127—1221no—
476#127—1222no—
477#127C22×D6111yescharacteristic
478#125—1221no—
479#124—21no—
480#124—612no—
481#124—612no—
482#124—1221no—
483#124—1222no—
484#123—1222no—
485#123—1222no—
486#123—1222no—
487#123—1222no—
488C22⋊Q8—612no—
489C22⋊Q8—1221no—
490#121—21no—
491#121—612no—
492#121—1222no—
493#121—1222no—
494#121—1222no—
495#121—1222no—
496#121—1221no—
497#121—1221no—
498#121—1221no—
499#121—1221no—
500#121—1221no—
501#121C4×D6112yes—
502#120—1222no—
503#120—1222no—
504C4×Q8—611no—
505C4×Q8—611no—
506C4×Q8—612no—
507C4×Q8—1221no—
508C4×D4—21no—
509C4×D4—611no—
510C4×D4—611no—
511C4×D4—611no—
512C4×D4—611no—
513C4×D4—612no—
514C4×D4—611no—
515C4×D4—611no—
516C4×D4—1221no—
517C4×D4—1221no—
518C4×D4—1221no—
519C4×D4—1222no—
520C4×D4—1222no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4C4×D6112yes—
524#117—611no—
525#117—611no—
526#117—611no—
527#117—1221no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1222no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42C22×D6111yescharacteristic
533C4⋊C8—611no—
534C4⋊C8—611no—
535C4⋊C8—611no—
536C4⋊C8—611no—
537C4⋊C8—1221no—
538C4⋊C8—1221no—
539C4⋊C8—1221no—
540C4⋊C8—1221no—
541C4⋊C8—1221no—
542C4⋊C8C22×D6111yescharacteristic
543C4⋊C8C22×D6111yescharacteristic
544C4⋊C8C22×D6111yescharacteristic
545C4⋊C8C22×D6111yescharacteristic
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550C22⋊C8—1221no—
551C22⋊C8—1221no—
552C22⋊C8—1221no—
553#97—21no—
554#97—1221no—
555C4×C8—21no—
556C4×C8—1221no—
557C4×C8—1221no—
558C4×C8—1221no—
559C4×C8—1221no—
560C24—1222no—
561#41—81no—
562#41—81no—
563#41—1222no—
564#41—1222no—
565#41—4882no—
566#41—4881no—
567#41—4881no—
568#41—4882no—
569C2×Q8—21no—
570C2×Q8—611no—
571C2×Q8—612no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—611no—
576C2×D4—611no—
577C2×D4—612no—
578C2×D4—611no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—4881no—
588C2×D4—4881no—
589C2×D4—4882no—
590C2×D4—2442no—
591C2×D4—2442no—
592C2×D4C2×C4×D6112yes—
593C22×C4—22no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4C2×C4×D6111yescharacteristic
604C22×C4D4×D6111yescharacteristic
605C22×C4D4×D6111yescharacteristic
606M16—2442no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—4881no—
616C2×C8—4881no—
617C2×C8—4881no—
618C2×C8—2442no—
619C4⋊C4—21no—
620C4⋊C4—611no—
621C4⋊C4—611no—
622C4⋊C4—611no—
623C4⋊C4—611no—
624C4⋊C4—611no—
625C4⋊C4—611no—
626C4⋊C4—1222no—
627C4⋊C4—1222no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4C2×C4×D6112yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—611no—
634C22⋊C4—611no—
635C22⋊C4—611no—
636C22⋊C4—611no—
637C22⋊C4—611no—
638C22⋊C4—611no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C42—611no—
647C42—611no—
648C42—611no—
649C42—611no—
650C42—611no—
651C42—611no—
652C42—1222no—
653C42C2×C4×D6111yescharacteristic
654C42D4×D6111yescharacteristic
655C42D4×D6111yescharacteristic
656C42C23×D6111yescharacteristic
657C23—22no—
658C23—611no—
659C23—611no—
660C23—1222no—
661C23—4882no—
662C23—4882no—
663C23—2444no—
664C23C22⋊C4×D6111yescharacteristic
665Q8—41no—
666Q8—41no—
667Q8—1222no—
668Q8—2442no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—82no—
675D4—1222no—
676D4—1222no—
677D4—1222no—
678D4—4882no—
679D4—4882no—
680D4—4882no—
681D4—4882no—
682D4—4882no—
683D4—2442no—
684D4—2444no—
685D4—2441no—
686D4—2441no—
687D4—2441no—
688D4—2441no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—82no—
696C2×C4—611no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—611no—
700C2×C4—611no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1222no—
711C2×C4—4882no—
712C2×C4—4882no—
713C2×C4—4882no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4C22⋊C4×D6111yescharacteristic
717C2×C4C22⋊C4×D6111yescharacteristic
718C2×C4C22⋊C4×D6111yescharacteristic
719C2×C4C22×C4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×D4×D6111yescharacteristic
722C8—41no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—2441no—
727C8—2441no—
728C8—2441no—
729C8—2441no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—612no—
737C22—1221no—
738C22—1221no—
739C22—1221no—
740C22—1221no—
741C22—1221no—
742C22—9764no—
743C22—2442no—
744C22—2442no—
745C22—2442no—
746C22C2×C22⋊C4×D6111yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—42no—
752C4—612no—
753C4—1221no—
754C4—1221no—
755C4—1221no—
756C4—1221no—
757C4—1221no—
758C4—2442no—
759C4#135×D6111yescharacteristic
760C4#135×D6111yescharacteristic
761C4#1684056611yescharacteristic
762C4#1684057211yescharacteristic
763C2—41no—
764C2—82no—
765C2—1222no—
766C2—4882no—
767C2—2441no—
768C2#2145429611yescharacteristic
769C2#416×D6111yescharacteristic
770C2#2145434411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1553C2
socleC22×C61C22×C22⋊C4
prime radical#21459688C2
cosocleC42×C61C24
hypercenter#1553D61
hypocenterC61#17724
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1553

Complements

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

NH ≅ G/Ntype
2. #21454927C2semidirect
3. #21454486C2semidirect
4. #21444523C2semidirect
5. #21444515C2semidirect
6. #21444511C2semidirect
7. #21444508C2semidirect
8. #21444485C2semidirect
9. #21444479C2semidirect
10. #21444478C2semidirect
11. #21444475C2semidirect
12. #21444468C2semidirect
13. #21444467C2semidirect
14. #331×D61C2semidirect
15. C61×#1553C2semidirect
40. #16839818C22semidirect
41. #16839815C22semidirect
43. #16839814C22semidirect
44. #16839814C22semidirect
46. C2×C4⋊#92418C22semidirect
49. C4⋊C8×D61C22semidirect
52. #16839510C22semidirect
53. #16839510C22semidirect
54. #16839510C22semidirect
55. #16839510C22semidirect
56. #16839508C22semidirect
57. #16839508C22semidirect
65. C61×#432C22semidirect
66. C61×#431C22semidirect
67. C61×#332C22semidirect
68. C61×#332C22semidirect
382. #1553D61semidirect
427. #432C2×D61semidirect
432. #431C2×D61semidirect
446. #332C2×D61semidirect
447. #332C2×D61semidirect
456. C61#17724semidirect

Maximal subgroups

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

subgroupindex
#214596882
#214549272
#214544862
#214445232
#214445152
#214445112
#214445082
#214444852
#214444792
#214444782
#214444752
#214444682
#214444672
#331×D612
C61×#15532
#1772461