Finite Group Databasebeta

← #29657211

Subgroups — #29657211

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457156C211yesmaximal, characteristic, complemented
2#21456141C211yesmaximal, characteristic, complemented
3#21455918C211yesmaximal, characteristic, complemented
4#21445047C211yesmaximal, characteristic, complemented
5#21445047C211yesmaximal, characteristic, complemented
6#21445033C211yesmaximal, characteristic, complemented
7#21445026C211yesmaximal, characteristic, complemented
8#21445019C211yesmaximal, characteristic, complemented
9#21445012C211yesmaximal, characteristic, complemented
10#21444998C211yesmaximal, characteristic, complemented
11#21444998C211yesmaximal, characteristic, complemented
12#21444514C211yesmaximal, characteristic, complemented
13#21444279C211yesmaximal, characteristic, complemented
14C2×D4⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3519C211yesmaximal, characteristic
16#16840319C2211yescharacteristic, complemented
17#16840116—22no—
18#16840112C2211yescharacteristic, complemented
19#16840112C2211yescharacteristic, complemented
20#16840108C2211yescharacteristic, complemented
21#16840108C2211yescharacteristic, complemented
22#16840097—21no—
23#16840066—21no—
24#16840047C2211yescharacteristic, complemented
25#16840042C2211yescharacteristic
26#16840042C2211yescharacteristic, complemented
27#16840042C2211yescharacteristic, complemented
28#16840001—21no—
29#16839989—21no—
30#16839981—21no—
31#16839972C2211yescharacteristic, complemented
32#16839967C2211yescharacteristic
33#16839967C2211yescharacteristic, complemented
34#16839967C2211yescharacteristic, complemented
35#16839913—21no—
36#16839862—21no—
37#16839862—21no—
38#16839819C2211yescharacteristic, complemented
39C2×C4⋊#92418C2211yescharacteristic, complemented
40#16839758—22no—
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839511C2211yescharacteristic, complemented
43#16839511C2211yescharacteristic, complemented
44#16839506C2211yescharacteristic, complemented
45#16839506C2211yescharacteristic, complemented
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C61×#555C2211yescharacteristic
55C61×#554C2211yescharacteristic
56C61×#553—21no—
57C61×#553—21no—
58C61×#550C2211yescharacteristic
59C61×#546—22no—
60C61×#546—21no—
61D42×C61—21no—
62D42×C61C2211yescharacteristic
63C61×#540—21no—
64C61×#538—22no—
65C61×#532C2211yescharacteristic
66C61×#529C2211yescharacteristic
67C61×#525—21no—
68C2×#121×C61—21no—
69C61×#518—21no—
70C2×C4×D4×C61C2211yescharacteristic
71C2×#11758202—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C22×#92418—21no—
76C22×#92418—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519769—21no—
80#14519756—21no—
81#14519756—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84#14519736—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519701—21no—
95#14519701—22no—
96#14519701—22no—
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519698—21no—
102#14519698—22no—
103#14519698—22no—
104#14519698—21no—
105#14519698—21no—
106C22⋊#92418—21no—
107#14519688—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61—21no—
112C2×#41×C61D412yes—
113C22×D4×C61—22no—
114C22×D4×C61—21no—
115C22×D4×C61—21no—
116C22×D4×C61D411yescharacteristic
117C23×C4×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119#127×C61—21no—
120#127×C61C2311yescharacteristic
121#126×C61—22no—
122#126×C61—21no—
123#125×C61—21no—
124#125×C61D411yescharacteristic
125#124×C61—22no—
126#124×C61D412yes—
127#124×C61D411yescharacteristic
128#123×C61—22no—
129#123×C61—22no—
130#123×C61—22no—
131#123×C61—21no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61D411yescharacteristic
135#121×C61—22no—
136#121×C61—22no—
137#121×C61—22no—
138#121×C61—22no—
139#121×C61—22no—
140#121×C61—21no—
141#121×C61—21no—
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61D411yescharacteristic
148#120×C61—22no—
149#120×C61—22no—
150#120×C61—22no—
151C4×Q8×C61C2311yescharacteristic
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61D411yescharacteristic
163C4×D4×C61D411yescharacteristic
164C4×D4×C61C2311yescharacteristic
165C4×D4×C61C2311yescharacteristic
166C4×D4×C61C2311yescharacteristic
167#117×C61—21no—
168#117×C61—21no—
169#117×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C24×C61—22no—
177C24×C61—21no—
178#41×C61—44no—
179#41×C61—81no—
180#41×C61—81no—
181C2×Q8×C61C2×D411yescharacteristic
182C2×Q8×C61C2×D412yes—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—21no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—41no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61—81no—
198C2×D4×C61—81no—
199C2×D4×C61—84no—
200C2×D4×C61C2×D411yescharacteristic
201C2×D4×C61C2×D411yescharacteristic
202C2×D4×C61C2×D411yescharacteristic
203C2×D4×C61C2×D412yes—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61—81no—
214C22×C4×C61—81no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C2×Dic122—21no—
219C2×Dic122—21no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C2×D411yescharacteristic
230C4⋊C4×C61C2×D411yescharacteristic
231C4⋊C4×C61C2×D411yescharacteristic
232C4⋊C4×C61C2×D411yescharacteristic
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C42×C61—22no—
250C42×C61—21no—
251C42×C61C2×D411yescharacteristic
252C42×C61C2×D411yescharacteristic
253C42×C61C2×D411yescharacteristic
254C42×C61C2411yescharacteristic
255C22⋊Dic61—41no—
256#11758202—81no—
257#11758200—42no—
258#11758200—42no—
259#11758200—81no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264#11758196—41no—
265#11758196—41no—
266C4×Dic61—41no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—42no—
274C2×#92418—81no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—22no—
279C23×C61—42no—
280C23×C61—44no—
281C23×C61—42no—
282C23×C61—81no—
283C23×C61—82no—
284C23×C61—82no—
285C23×C61#12011yescharacteristic
286Q8×C61—21no—
287Q8×C61—21no—
288Q8×C61—42no—
289D4×C61—21no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—44no—
297D4×C61—42no—
298D4×C61—44no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—82no—
304D4×C61—82no—
305D4×C61—82no—
306D4×C61—82no—
307D4×C61#13512yes—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—81no—
326C2×C4×C61—81no—
327C2×C4×C61—82no—
328C2×C4×C61—81no—
329C2×C4×C61—82no—
330C2×C4×C61—82no—
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61#12011yescharacteristic
333C2×C4×C61#12011yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×Dic61—41no—
338C2×Dic61—41no—
339Dic122—41no—
340Dic122—41no—
341Dic122—41no—
342Dic122—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#92418—41no—
348#92418—41no—
349#18628—611nomaximal, Sylow
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—22no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—42no—
358C22×C61—41no—
359C22×C61—42no—
360C22×C61—41no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—84no—
365C22×C61—164no—
366C22×C61#45512yes—
367C22×C61C2×#12011yescharacteristic
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—42no—
378C4×C61C2×#13511yescharacteristic
379C4×C61#57511yescharacteristic
380C4×C61#57611yescharacteristic
381C4×C61#57711yescharacteristic
382Dic61—81no—
383Dic61—81no—
384#3519D6111yescharacteristic
385#3248—611no—
386#3131—611no—
387#3110—611no—
388#1646—611no—
389#1646—611no—
390#1644—611no—
391#1643—611no—
392#1642—611no—
393#1641—611no—
394#1639—611no—
395#1639—611no—
396#1551—611no—
397#1494—611no—
398C2×D4⋊C8—611no—
399C2×C61—22no—
400C2×C61—42no—
401C2×C61—81no—
402C2×C61—82no—
403C2×C61—81no—
404C2×C61#300211yescharacteristic
405C2×C61#301211yescharacteristic
406C2×C61C2×#45511yescharacteristic
407#555C2×D6111yescharacteristic
408#554C2×D6111yescharacteristic
409#553—21no—
410#553—21no—
411#550C2×D6111yescharacteristic
412#546—22no—
413#546—21no—
414D42—21no—
415D42C2×D6111yescharacteristic
416#540—21no—
417#538—22no—
418#533—611no—
419#532C2×D6111yescharacteristic
420#529C2×D6111yescharacteristic
421#525—21no—
422C2×#121—21no—
423#518—21no—
424C2×C4×D4C2×D6111yescharacteristic
425#488—1222no—
426#487—611no—
427#487—611no—
428#486—611no—
429#486—611no—
430#484—1221no—
431#479—1221no—
432#475—611no—
433#474—611no—
434#474—611no—
435#474—611no—
436#467—1221no—
437#465—1221no—
438#464—1221no—
439#462—611no—
440#461—611no—
441#461—611no—
442#461—611no—
443#450—1221no—
444#440—1221no—
445#440—1221no—
446#432—611no—
447C2×C4⋊C8—611no—
448#416—1222no—
449C2×C4×C8—611no—
450#333—611no—
451#333—611no—
452#331—611no—
453#331—611no—
454Q8⋊C8—611no—
455Q8⋊C8—611no—
456D4⋊C8—611no—
457D4⋊C8—611no—
458D4⋊C8—611no—
459D4⋊C8—611no—
460D4⋊C8—611no—
461D4⋊C8—611no—
462C61#1862811yescharacteristic, complemented, Sylow
463C2×#41—21no—
464C2×#41C22⋊D6112yes—
465C22×D4—22no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C22⋊D6111yescharacteristic
469C23×C4—21no—
470C2×Q16—1221no—
471C2×SD16—1221no—
472C2×SD16—1221no—
473C2×SD16—1221no—
474C22×C8—1221no—
475C22×C8—1221no—
476C4⋊Q8—611no—
477C4⋊Q8—611no—
478C4⋊Q8C22×D6111yescharacteristic
479#127—21no—
480#127C22×D6111yescharacteristic
481#126—22no—
482#126—21no—
483#125—21no—
484#125—1221no—
485#125C22⋊D6111yescharacteristic
486#124—22no—
487#124C22⋊D6111yescharacteristic
488#124C22⋊D6112yes—
489#123—22no—
490#123—22no—
491#123—22no—
492#123—21no—
493C22⋊Q8—21no—
494C22⋊Q8—22no—
495C22⋊Q8—1221no—
496C22⋊Q8—1221no—
497C22⋊Q8C22⋊D6111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—21no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121C22⋊D6111yescharacteristic
511#120—22no—
512#120—22no—
513#120—22no—
514C4×Q8—1221no—
515C4×Q8—1221no—
516C4×Q8C22×D6111yescharacteristic
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4C22⋊D6111yescharacteristic
528C4×D4C22⋊D6111yescharacteristic
529C4×D4C22×D6111yescharacteristic
530C4×D4C22×D6111yescharacteristic
531C4×D4C22×D6111yescharacteristic
532#117—21no—
533#117—21no—
534#117—21no—
535#117—1221no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4C22⋊D6111yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—21no—
541C2×C42C22×D6111yescharacteristic
542#107—1221no—
543#107—1221no—
544#107—1221no—
545#106—1221no—
546C4⋊C8—611no—
547C4⋊C8—611no—
548C4⋊C8—611no—
549C4⋊C8—611no—
550C4⋊C8—1221no—
551#103—1222no—
552#103—1222no—
553#103—1221no—
554#103—1221no—
555#103—1221no—
556#103—1221no—
557#103—1221no—
558#102—1222no—
559#102—1222no—
560#102—1221no—
561#102—1221no—
562#102—1221no—
563C22⋊C8—1221no—
564#97—1221no—
565C4×C8—611no—
566C4×C8—611no—
567C4×C8—1221no—
568C24—22no—
569C24—21no—
570#41—44no—
571#41—81no—
572#41—81no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8C2×C22⋊D6111yescharacteristic
576C2×Q8C2×C22⋊D6112yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—84no—
594C2×D4C2×C22⋊D6111yescharacteristic
595C2×D4C2×C22⋊D6111yescharacteristic
596C2×D4C2×C22⋊D6111yescharacteristic
597C2×D4C2×C22⋊D6112yes—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C2×C22⋊D6111yescharacteristic
612Q16—4881no—
613SD16—4881no—
614SD16—2442no—
615SD16—2442no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—4881no—
623C2×C8—2442no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—2441no—
638C4⋊C4—2441no—
639C4⋊C4C2×C22⋊D6111yescharacteristic
640C4⋊C4C2×C22⋊D6111yescharacteristic
641C4⋊C4C2×C22⋊D6111yescharacteristic
642C4⋊C4C2×C22⋊D6111yescharacteristic
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—22no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—22no—
659C22⋊C4—2441no—
660C42—22no—
661C42—21no—
662C42—2441no—
663C42C2×C22⋊D6111yescharacteristic
664C42C2×C22⋊D6111yescharacteristic
665C42C2×C22⋊D6111yescharacteristic
666C42C23×D6111yescharacteristic
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—42no—
672C23—44no—
673C23—42no—
674C23—81no—
675C23—82no—
676C23—82no—
677C23#1451974611yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—42no—
681Q8—2441no—
682Q8—2441no—
683Q8—2441no—
684Q8—2441no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—42no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4#1451979712yes—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4#1451974611yescharacteristic
730C2×C4#1451974611yescharacteristic
731C2×C4#1451974611yescharacteristic
732C2×C4C22×C22⋊D6111yescharacteristic
733C2×C4C22×C22⋊D6111yescharacteristic
734C2×C4C22×C22⋊D6111yescharacteristic
735C8—2441no—
736C8—2441no—
737C8—2441no—
738C8—2441no—
739C8—2441no—
740C8—2441no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—42no—
755C22—84no—
756C22—164no—
757C22#1683994012yes—
758C22C2×#1451974611yescharacteristic
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—4881no—
770C4—4881no—
771C4C2×#1451979711yescharacteristic
772C4#1684056011yescharacteristic
773C4#1684056511yescharacteristic
774C4#1684057311yescharacteristic
775C2—22no—
776C2—42no—
777C2—81no—
778C2—81no—
779C2—82no—
780C2#2145503711yescharacteristic
781C2#2145512311yescharacteristic
782C2C2×#1683994011yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3519C2
socleC22×C61C2×#120
hypercenter#3519D61
hypocenterC61#18628
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #21457156C2semidirect
2. #21456141C2semidirect
3. #21455918C2semidirect
4. #21445047C2semidirect
5. #21445047C2semidirect
6. #21445033C2semidirect
7. #21445026C2semidirect
8. #21445019C2semidirect
9. #21445012C2semidirect
10. #21444998C2semidirect
11. #21444998C2semidirect
12. #21444514C2semidirect
13. #21444279C2semidirect
14. C2×D4⋊#92418C2semidirect
16. #16840319C22semidirect
18. #16840112C22semidirect
19. #16840112C22semidirect
20. #16840108C22semidirect
21. #16840108C22semidirect
24. #16840047C22semidirect
26. #16840042C22semidirect
27. #16840042C22semidirect
31. #16839972C22semidirect
33. #16839967C22semidirect
34. #16839967C22semidirect
38. #16839819C22semidirect
39. C2×C4⋊#92418C22semidirect
41. C2×C4×#92418C22semidirect
42. #16839511C22semidirect
43. #16839511C22semidirect
44. #16839506C22semidirect
45. #16839506C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
50. D4⋊#92418C22semidirect
51. D4⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
462. C61#18628semidirect

Maximal subgroups

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

subgroupindex
#214571562
#214561412
#214559182
#214450472
#214450332
#214450262
#214450192
#214450122
#214449982
#214445142
#214442792
C2×D4⋊#924182
C61×#35192
#1862861