Finite Group Databasebeta

← #29648837

Subgroups — #29648837

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459730C211yesmaximal, characteristic
2#21454936C211yesmaximal, characteristic, complemented
3#21444552C211yesmaximal, characteristic, complemented
4#21444547C211yesmaximal, characteristic, complemented
5#21444544C211yesmaximal, characteristic, complemented
6#21444542C211yesmaximal, characteristic, complemented
7#21444530C211yesmaximal, characteristic, complemented
8#21444522C211yesmaximal, characteristic, complemented
9#21444515C211yesmaximal, characteristic, complemented
10#21444512C211yesmaximal, characteristic, complemented
11#21444507C211yesmaximal, characteristic, complemented
12#21444499C211yesmaximal, characteristic, complemented
13#21444479C211yesmaximal, characteristic, complemented
14#21444474C211yesmaximal, characteristic, complemented
15C61×#2925C211yesmaximal, characteristic, complemented
16#16840485C412yes—
17#16840477—21no—
18#16840472—21no—
19#16840458—21no—
20#16840458—21no—
21#16840421C412yes—
22#16840421C412yes—
23#16840417C412yes—
24#16840383—21no—
25#16840383—21no—
26#16840340—21no—
27#16840319C2211yescharacteristic
28#16840319C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840312C2211yescharacteristic
31#16840312C2211yescharacteristic
32C2×#14519777C2211yescharacteristic
33#16840242—21no—
34#16839893—21no—
35#16839840—21no—
36#16839834—21no—
37#16839834—21no—
38#16839819C2211yescharacteristic
39#16839819C2211yescharacteristic
40#16839815C2211yescharacteristic
41#16839786C2211yescharacteristic
42#16839786C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839510C2211yescharacteristic
45#16839510C2211yescharacteristic
46#16839510C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839510C2211yescharacteristic
51#16839510C2211yescharacteristic
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839505C2211yescharacteristic
57#16839505C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C4×#41×C61C2211yescharacteristic
61C61×#433—21no—
62C61×#433—21no—
63C61×#432C2211yescharacteristic
64C61×#432C2211yescharacteristic
65C61×#431C2211yescharacteristic
66C61×#431C2211yescharacteristic
67C61×#423C2211yescharacteristic
68C2×C4⋊C8×C61C2211yescharacteristic
69C61×#408—21no—
70C61×#405—21no—
71C2×#11758222—21no—
72C2×#11758222C2×C412yes—
73C2×#11758222C2×C412yes—
74C22×Dic122C2×C412yes—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C22×#92418—21no—
78#14519777—21no—
79#14519777—21no—
80#14519777C2×C412yes—
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519777C2311yescharacteristic
84#14519774C2311yescharacteristic
85#14519772—22no—
86#14519772—22no—
87#14519769—21no—
88#14519769—21no—
89#14519765—21no—
90#14519765C2×C412yes—
91#14519765C2×C412yes—
92#14519763—22no—
93#14519763—22no—
94#14519759—22no—
95#14519759—22no—
96#14519756—21no—
97#14519756—21no—
98#14519756C2×C412yes—
99#14519756C2×C412yes—
100#14519755—22no—
101#14519755—22no—
102#14519753—22no—
103#14519751—21no—
104#14519751—21no—
105#14519751—21no—
106#14519751—21no—
107#14519751—21no—
108#14519751C2×C412yes—
109#14519749—22no—
110#14519749—22no—
111#14519748—22no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122C2×C412yes—
115C4×Dic122C2×C412yes—
116C4×D244—21no—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244—21no—
120C4×D244—21no—
121C4×D244C2×C412yes—
122#14519737—22no—
123#14519737—22no—
124#14519736—21no—
125#14519736—21no—
126#14519735—22no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C4⋊C4×D61—22no—
130C4⋊#92418—21no—
131C4⋊#92418—21no—
132C4⋊#92418—21no—
133C4⋊#92418C2311yescharacteristic
134C4⋊#92418C2311yescharacteristic
135C4⋊#92418C2311yescharacteristic
136C4⋊#92418C2311yescharacteristic
137C22⋊#92418—21no—
138C22⋊#92418—21no—
139C22⋊#92418—21no—
140#14519688—21no—
141#14519688—21no—
142C4×#92418—21no—
143C2×#41×C61D411yescharacteristic
144C2×M16×C61—21no—
145C22×C8×C61—21no—
146C4×Q8×C61C2×C411yescharacteristic
147C4×Q8×C61D411yescharacteristic
148C4×D4×C61C2×C411yescharacteristic
149C4×D4×C61C2×C411yescharacteristic
150C4×D4×C61C2×C411yescharacteristic
151C4×D4×C61D411yescharacteristic
152C4×D4×C61D411yescharacteristic
153C4×D4×C61D411yescharacteristic
154#117×C61D411yescharacteristic
155#117×C61D411yescharacteristic
156#117×C61D411yescharacteristic
157C2×C42×C61C2311yescharacteristic
158C2×C42×C61C2311yescharacteristic
159C2×C42×C61C2311yescharacteristic
160C4⋊C8×C61—21no—
161C4⋊C8×C61—21no—
162C4⋊C8×C61C2311yescharacteristic
163C4⋊C8×C61C2311yescharacteristic
164C4⋊C8×C61C2311yescharacteristic
165C4⋊C8×C61C2311yescharacteristic
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168C22⋊C8×C61—21no—
169C22⋊C8×C61—21no—
170#97×C61—21no—
171#97×C61—21no—
172C4×C8×C61—21no—
173C4×C8×C61—21no—
174#41×C61—41no—
175#41×C61—41no—
176C2×Q8×C61C22⋊C411yescharacteristic
177C2×D4×C61C22⋊C411yescharacteristic
178C2×D4×C61C22⋊C411yescharacteristic
179C2×D4×C61C22⋊C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C22×Dic61—22no—
193#11758222—42no—
194#11758222—42no—
195#11758222—82no—
196#11758222—82no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244C22×C412yes—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×Dic122—21no—
204C2×Dic122—22no—
205C2×Dic122—82no—
206C2×Dic122C22×C412yes—
207C2×Dic122C22×C412yes—
208M16×C61—42no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—42no—
214C4⋊C4×C61C22⋊C411yescharacteristic
215C4⋊C4×C61C22⋊C411yescharacteristic
216C4⋊C4×C61C22⋊C411yescharacteristic
217C4⋊C4×C61C22⋊C411yescharacteristic
218C4⋊C4×C61C22⋊C411yescharacteristic
219C4⋊C4×C61C22⋊C411yescharacteristic
220C22⋊C4×C61C22⋊C411yescharacteristic
221C22⋊C4×C61C22⋊C411yescharacteristic
222C22⋊C4×C61C22⋊C411yescharacteristic
223C22⋊C4×C61C22⋊C411yescharacteristic
224C22⋊C4×C61C22⋊C411yescharacteristic
225C22⋊C4×C61C22⋊C411yescharacteristic
226C42×C61C22×C411yescharacteristic
227C42×C61C22×C411yescharacteristic
228C42×C61C22×C411yescharacteristic
229C42×C61C2×D411yescharacteristic
230C42×C61C2×D411yescharacteristic
231C42×C61C2×D411yescharacteristic
232C42×C61C2×D411yescharacteristic
233C42×C61C2×D411yescharacteristic
234C42×C61C2×D411yescharacteristic
235C42×C61C2411yescharacteristic
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244C4⋊Dic61—22no—
245C4⋊Dic61—22no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61C22×C412yes—
252#11758196—22no—
253#11758196—22no—
254#11758196—22no—
255#11758196—22no—
256C4×Dic61—22no—
257C4×Dic61—22no—
258#11758194—81no—
259#11758194—81no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—81no—
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61C2×C22⋊C411yescharacteristic
267C23×C61C2×C22⋊C411yescharacteristic
268C22×D61—22no—
269Q8×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—41no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
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—44no—
301C22⋊D61—82no—
302C22⋊D61—82no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—82no—
307D244—42no—
308D244—41no—
309D244—41no—
310D244—41no—
311D244—41no—
312C4×D61—44no—
313C4×D61—82no—
314C4×D61—82no—
315Dic122—41no—
316Dic122—41no—
317Dic122—42no—
318Dic122—42no—
319Dic122—82no—
320C8×C61—41no—
321C8×C61—41no—
322C8×C61—41no—
323C8×C61—41no—
324#92418—41no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#17768—611nomaximal, Sylow
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—21no—
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61C22×C22⋊C411yescharacteristic
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C4×C61—21no—
343C4×C61—21no—
344C4×C61—21no—
345C4×C61—21no—
346C4×C61—21no—
347C4×C61—21no—
348C4×C61—21no—
349C4×C61—21no—
350C4×C61—21no—
351C4×C61—21no—
352C4×C61#57511yescharacteristic
353C4×C61#57511yescharacteristic
354C4×C61#57711yescharacteristic
355C4×C61#57811yescharacteristic
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359#3511—611no—
360#2989—611no—
361#2925D6111yescharacteristic, complemented
362#1560—611no—
363#1559—611no—
364#1558—611no—
365#1557—611no—
366#1554—611no—
367#1553—611no—
368#1551—611no—
369#1551—611no—
370#1550—611no—
371#1548—611no—
372#1543—611no—
373#1542—611no—
374C2×C61—41no—
375C2×C61—41no—
376C2×C61—41no—
377C2×C61#288811yescharacteristic
378C2×C61#289611yescharacteristic
379C2×C61#289811yescharacteristic
380D61—82no—
381#556—612no—
382#555—1221no—
383#554—1221no—
384#553—1221no—
385#553—1221no—
386#548—612no—
387#548—612no—
388#547—612no—
389#542—1221no—
390#542—1221no—
391#537—1221no—
392#533—611no—
393#533—611no—
394#532—611no—
395#532—611no—
396#532—611no—
397C2×C4⋊Q8—611no—
398#520—1221no—
399C4×#41C2×D6111yescharacteristic
400#446—1221no—
401#436—1221no—
402#435—1221no—
403#435—1221no—
404#433—21no—
405#433—21no—
406#432—611no—
407#432—611no—
408#432C2×D6111yescharacteristic
409#432C2×D6111yescharacteristic
410#431—611no—
411#431C2×D6111yescharacteristic
412#431C2×D6111yescharacteristic
413#423—611no—
414#423—611no—
415#423C2×D6111yescharacteristic
416C2×C4⋊C8—611no—
417C2×C4⋊C8C2×D6111yescharacteristic
418#408—21no—
419#405—21no—
420#333—611no—
421#333—611no—
422#333—611no—
423#333—611no—
424#333—611no—
425#333—611no—
426#333—611no—
427#333—611no—
428#332—611no—
429#332—611no—
430#332—611no—
431#332—611no—
432#331—611no—
433#331—611no—
434#331—611no—
435#331—611no—
436C61#1776811yescharacteristic, complemented, Sylow
437C2×#41—612no—
438C2×#41—612no—
439C2×#41—1221no—
440C2×#41C22⋊D6111yescharacteristic
441C22×Q8—612no—
442C2×M16—21no—
443C2×M16—1221no—
444C2×M16—1221no—
445C22×C8—21no—
446C22×C8—1221no—
447C4⋊Q8—612no—
448C4⋊Q8—611no—
449C4⋊Q8—611no—
450C4⋊Q8—611no—
451C4⋊Q8—1221no—
452C4⋊Q8—1221no—
453#127—611no—
454#126—1222no—
455#126—1222no—
456#125—1221no—
457#125—1221no—
458#124—612no—
459#124—612no—
460#124—1222no—
461#124—1222no—
462#124—1221no—
463#123—1222no—
464#123—1222no—
465C22⋊Q8—612no—
466C22⋊Q8—612no—
467C22⋊Q8—1222no—
468C22⋊Q8—1221no—
469C22⋊Q8—1221no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472#121—612no—
473#121—1222no—
474#121—1222no—
475#121—1222no—
476#121—1221no—
477#121—1221no—
478#121—1221no—
479#121—1221no—
480#121—1221no—
481C4×Q8—612no—
482C4×Q8—612no—
483C4×Q8—1221no—
484C4×Q8—1221no—
485C4×Q8C4×D6111yescharacteristic
486C4×Q8D24411yescharacteristic
487C4×D4—612no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1221no—
491C4×D4—1221no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1221no—
495C4×D4C4×D6111yescharacteristic
496C4×D4C4×D6111yescharacteristic
497C4×D4C4×D6111yescharacteristic
498C4×D4D24411yescharacteristic
499C4×D4D24411yescharacteristic
500C4×D4D24411yescharacteristic
501#117—1221no—
502#117—1221no—
503#117—1222no—
504#117C22⋊D6111yescharacteristic
505#117C22⋊D6111yescharacteristic
506#117C22⋊D6111yescharacteristic
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1222no—
510C2×C42C22×D6111yescharacteristic
511C2×C42C22×D6111yescharacteristic
512C2×C42C22×D6111yescharacteristic
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—611no—
516C4⋊C8—611no—
517C4⋊C8—611no—
518C4⋊C8—611no—
519C4⋊C8—1221no—
520C4⋊C8—1221no—
521C4⋊C8—1221no—
522C4⋊C8C22×D6111yescharacteristic
523C4⋊C8C22×D6111yescharacteristic
524C4⋊C8C22×D6111yescharacteristic
525C4⋊C8C22×D6111yescharacteristic
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530C22⋊C8—1221no—
531C22⋊C8—1221no—
532C22⋊C8—1221no—
533#97—21no—
534#97—21no—
535#97—1221no—
536#97—1221no—
537C4×C8—21no—
538C4×C8—21no—
539C4×C8—1221no—
540#41—41no—
541#41—41no—
542#41—4882no—
543#41—4882no—
544#41—2442no—
545#41—2442no—
546C2×Q8—612no—
547C2×Q8—612no—
548C2×Q8—1221no—
549C2×Q8—1222no—
550C2×Q8—4882no—
551C2×Q8#1175819811yescharacteristic
552C2×D4—612no—
553C2×D4—1222no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4#1175819811yescharacteristic
559C2×D4#1175819811yescharacteristic
560C2×D4#1175819811yescharacteristic
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4C2×C4×D6111yescharacteristic
566C22×C4C2×C4×D6111yescharacteristic
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4C2×D24411yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4C2×D24411yescharacteristic
571C22×C4C2×C22⋊D6111yescharacteristic
572C22×C4C2×C22⋊D6111yescharacteristic
573C22×C4C2×C22⋊D6111yescharacteristic
574M16—42no—
575M16—4881no—
576M16—4881no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—42no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—4881no—
587C4⋊C4—612no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1222no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4#1175819811yescharacteristic
600C4⋊C4#1175819811yescharacteristic
601C4⋊C4#1175819811yescharacteristic
602C4⋊C4#1175819811yescharacteristic
603C4⋊C4#1175819811yescharacteristic
604C4⋊C4#1175819811yescharacteristic
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4#1175819811yescharacteristic
614C22⋊C4#1175819811yescharacteristic
615C22⋊C4#1175819811yescharacteristic
616C22⋊C4#1175819811yescharacteristic
617C22⋊C4#1175819811yescharacteristic
618C22⋊C4#1175819811yescharacteristic
619C42—1222no—
620C42—1222no—
621C42C2×C4×D6111yescharacteristic
622C42C2×C4×D6111yescharacteristic
623C42C2×C4×D6111yescharacteristic
624C42C2×D24411yescharacteristic
625C42C2×D24411yescharacteristic
626C42C2×D24411yescharacteristic
627C42C2×C22⋊D6111yescharacteristic
628C42C2×C22⋊D6111yescharacteristic
629C42C2×C22⋊D6111yescharacteristic
630C42C23×D6111yescharacteristic
631C23—1222no—
632C23C2×#1175819811yescharacteristic
633C23C2×#1175819811yescharacteristic
634C23C2×#1175819811yescharacteristic
635Q8—41no—
636Q8—4882no—
637Q8—2442no—
638Q8—2442no—
639Q8—2441no—
640Q8—2441no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—4882no—
645D4—4882no—
646D4—2442no—
647D4—2444no—
648D4—2441no—
649D4—2441no—
650D4—2441no—
651D4—2441no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—4882no—
671C2×C4—4882no—
672C2×C4—4882no—
673C2×C4—2444no—
674C2×C4C2×#1175819811yescharacteristic
675C2×C4C2×#1175819811yescharacteristic
676C2×C4C2×#1175819811yescharacteristic
677C2×C4C2×#1175819811yescharacteristic
678C2×C4C2×#1175819811yescharacteristic
679C2×C4C2×#1175819811yescharacteristic
680C2×C4C2×#1175819811yescharacteristic
681C2×C4C2×#1175819811yescharacteristic
682C2×C4C2×#1175819811yescharacteristic
683C2×C4C22×C4×D6111yescharacteristic
684C2×C4C22×C22⋊D6111yescharacteristic
685C2×C4C22×D24411yescharacteristic
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—2441no—
691C8—2441no—
692C8—2441no—
693C8—2441no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—2442no—
704C22—2442no—
705C22—2442no—
706C22C22×#1175819811yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—21no—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—2442no—
718C4—2442no—
719C4—2442no—
720C4#1684056011yescharacteristic
721C4#1684056011yescharacteristic
722C4#1684057411yescharacteristic
723C4#1684057911yescharacteristic
724C2—41no—
725C2—41no—
726C2—41no—
727C2—4882no—
728C2#2145429711yescharacteristic
729C2#2145433611yescharacteristic
730C2#2145435311yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2925C2
socleC22×C61C22×C22⋊C4
prime radical#21459730C2
cosocleC42×C61C24
hypercenter#2925D61
hypocenterC61#17768
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #21454936C2semidirect
3. #21444552C2semidirect
4. #21444547C2semidirect
5. #21444544C2semidirect
6. #21444542C2semidirect
7. #21444530C2semidirect
8. #21444522C2semidirect
9. #21444515C2semidirect
10. #21444512C2semidirect
11. #21444507C2semidirect
12. #21444499C2semidirect
13. #21444479C2semidirect
14. #21444474C2semidirect
15. C61×#2925C2semidirect
361. #2925D61semidirect
436. C61#17768semidirect

Maximal subgroups

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

subgroupindex
#214597302
#214549362
#214445522
#214445472
#214445442
#214445422
#214445302
#214445222
#214445152
#214445122
#214445072
#214444992
#214444792
#214444742
C61×#29252
#1776861