Finite Group Databasebeta

← #29648268

Subgroups — #29648268

Order 15616.

898 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459741C211yesmaximal, characteristic
2#21454833C211yesmaximal, characteristic, complemented
3#21444451C211yesmaximal, characteristic, complemented
4#21444448C211yesmaximal, characteristic, complemented
5#21444445C211yesmaximal, characteristic, complemented
6#21444440C211yesmaximal, characteristic, complemented
7#21444437C211yesmaximal, characteristic, complemented
8#21444431C211yesmaximal, characteristic, complemented
9#21444429C211yesmaximal, characteristic, complemented
10#21444427C211yesmaximal, characteristic, complemented
11#21444424C211yesmaximal, characteristic, complemented
12#21444408C211yesmaximal, characteristic, complemented
13#21444405C211yesmaximal, characteristic, complemented
14C2×#16839503C211yesmaximal, characteristic, complemented
15C61×#2970C211yesmaximal, characteristic, complemented
16#16840462—21no—
17#16840462—21no—
18#16840461—21no—
19#16840461—21no—
20#16840461—21no—
21#16840461—21no—
22#16840453—21no—
23#16840453—21no—
24#16840374C411yescharacteristic
25#16840374C411yescharacteristic
26#16840367C411yescharacteristic
27#16840367C411yescharacteristic
28#16840340C411yescharacteristic
29#16840340C411yescharacteristic
30#16840312C2211yescharacteristic
31#16840296C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840296C2211yescharacteristic
34#16840296C2211yescharacteristic
35C2×#14519769C2211yescharacteristic
36#16840242C411yescharacteristic
37#16840242C411yescharacteristic
38#16839893—21no—
39#16839834—21no—
40#16839834—21no—
41D4×#92418—21no—
42#16839819C2211yescharacteristic
43#16839819C2211yescharacteristic
44#16839819C2211yescharacteristic
45C4×#11758194C2211yescharacteristic
46C2×#14519688C2211yescharacteristic
47C2×#14519688C2211yescharacteristic
48#16839503C2211yescharacteristic
49#16839503C2211yescharacteristic
50#16839503C2211yescharacteristic
51#16839503C2211yescharacteristic
52#16839503C2211yescharacteristic
53#16839503C2211yescharacteristic
54#16839503C2211yescharacteristic
55#16839503C2211yescharacteristic
56#16839501C2211yescharacteristic
57#16839501C2211yescharacteristic
58#16839501C2211yescharacteristic
59#16839501C2211yescharacteristic
60#16839501C2211yescharacteristic
61#16839501C2211yescharacteristic
62#16839501C2211yescharacteristic
63#16839501C2211yescharacteristic
64C4×#41×C61C2211yescharacteristic
65C61×#446—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#432C2211yescharacteristic
70C61×#432C2211yescharacteristic
71C61×#432C2211yescharacteristic
72C4×M16×C61C2211yescharacteristic
73C2×#97×C61C2211yescharacteristic
74C2×#97×C61C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic
77C2×#11758194—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80#14519777C2×C411yescharacteristic
81#14519774C2×C411yescharacteristic
82#14519771—21no—
83#14519771—21no—
84#14519771—21no—
85#14519771—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519769—21no—
91#14519769—21no—
92#14519769C2×C411yescharacteristic
93#14519769C2×C411yescharacteristic
94#14519769C2311yescharacteristic
95#14519769C2311yescharacteristic
96#14519767—21no—
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519765C2311yescharacteristic
101#14519765C2311yescharacteristic
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519762—21no—
106#14519760—21no—
107#14519760—21no—
108#14519760—21no—
109#14519760—21no—
110#14519756C2×C411yescharacteristic
111#14519756C2×C411yescharacteristic
112#14519756C2×C411yescharacteristic
113#14519756C2×C411yescharacteristic
114#14519753—21no—
115#14519753—21no—
116#14519751—21no—
117#14519751—21no—
118#14519751C2×C411yescharacteristic
119#14519751C2×C411yescharacteristic
120#14519751C2×C411yescharacteristic
121#14519751C2×C411yescharacteristic
122#14519750—21no—
123#14519750—21no—
124#14519750—21no—
125#14519750—21no—
126#14519749—21no—
127#14519749—21no—
128#14519749—21no—
129#14519749—21no—
130#14519748—21no—
131#14519748—21no—
132C4×Dic122C2×C411yescharacteristic
133C4×Dic122C2×C411yescharacteristic
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122C2×C411yescharacteristic
136C4×D244—21no—
137C4×D244—21no—
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141C4×D244C2×C411yescharacteristic
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146#14519737—21no—
147#14519737—21no—
148#14519737—21no—
149#14519737—21no—
150#14519735—21no—
151#14519735—21no—
152#14519734—21no—
153#14519734—21no—
154#14519734—21no—
155#14519734—21no—
156C2×C4⋊Dic61C2×C411yescharacteristic
157C2×C4⋊Dic61C2×C411yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C4⋊#92418—21no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167C22⋊#92418—21no—
168#14519688—21no—
169#14519688—21no—
170#14519688C2311yescharacteristic
171#14519688C2311yescharacteristic
172#14519688C2311yescharacteristic
173#14519688C2311yescharacteristic
174C4×#92418—21no—
175C2×#41×C61C2×C411yescharacteristic
176C2×M16×C61—21no—
177C22×C8×C61—21no—
178C22×C8×C61—21no—
179C4×Q8×C61D411yescharacteristic
180C4×Q8×C61D411yescharacteristic
181C4×D4×C61D411yescharacteristic
182C4×D4×C61D411yescharacteristic
183C4×D4×C61D411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187#117×C61C2×C411yescharacteristic
188#117×C61C2×C411yescharacteristic
189#117×C61C2×C411yescharacteristic
190C2×C42×C61C2311yescharacteristic
191C2×C42×C61C2311yescharacteristic
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61—21no—
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199#97×C61—21no—
200#97×C61—21no—
201#97×C61C2311yescharacteristic
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205C4×C8×C61—21no—
206#41×C61—42no—
207C2×Q8×C61C22⋊C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22⋊C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228#11758222—42no—
229#11758222—42no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244C22×C411yescharacteristic
233C2×D244C22×C411yescharacteristic
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×Dic122C22×C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242M16×C61—42no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—42no—
248C2×C8×C61—42no—
249C4⋊C4×C61C22⋊C411yescharacteristic
250C4⋊C4×C61C22⋊C411yescharacteristic
251C4⋊C4×C61C22⋊C411yescharacteristic
252C4⋊C4×C61C22⋊C411yescharacteristic
253C4⋊C4×C61C22⋊C411yescharacteristic
254C4⋊C4×C61C22⋊C411yescharacteristic
255C22⋊C4×C61C22⋊C411yescharacteristic
256C22⋊C4×C61C22⋊C411yescharacteristic
257C22⋊C4×C61C22⋊C411yescharacteristic
258C22⋊C4×C61C22⋊C411yescharacteristic
259C22⋊C4×C61C22⋊C411yescharacteristic
260C22⋊C4×C61C22⋊C411yescharacteristic
261C42×C61C22×C411yescharacteristic
262C42×C61C22×C411yescharacteristic
263C42×C61C22×C411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2×D411yescharacteristic
269C42×C61C2×D411yescharacteristic
270C42×C61C2411yescharacteristic
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61C22×C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293C4⋊Dic61C22×C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315#11758194—42no—
316C2×#92418—21no—
317C2×#92418—21no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—42no—
321C2×#92418—42no—
322C23×C61C2×C22⋊C411yescharacteristic
323C23×C61C2×C22⋊C411yescharacteristic
324C23×C61C2×C22⋊C411yescharacteristic
325C22×D61—21no—
326C22×D61—21no—
327Q8×C61—41no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—41no—
331C2×C4×C61—22no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C23×C411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C22⋊D61—42no—
353C22⋊D61—42no—
354C22⋊D61—81no—
355C22⋊D61—81no—
356C22⋊D61—81no—
357C22⋊D61—81no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—81no—
365C2×Dic61—81no—
366D244—41no—
367D244—41no—
368D244—81no—
369D244—81no—
370C4×D61—42no—
371C4×D61—42no—
372C4×D61—81no—
373C4×D61—81no—
374C4×D61—81no—
375C4×D61—81no—
376Dic122—41no—
377Dic122—41no—
378C8×C61—22no—
379C8×C61—41no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#92418—41no—
385#92418—41no—
386#17690—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61#41312yes—
396C22×C61C22×C22⋊C411yescharacteristic
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415Dic61—41no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419Dic61—41no—
420Dic61—41no—
421#3512—611no—
422#2970—611no—
423#2970D6111yescharacteristic, complemented
424#1535—611no—
425#1535—611no—
426#1534—611no—
427#1532—611no—
428#1532—611no—
429#1530—611no—
430#1530—611no—
431#1529—611no—
432#1529—611no—
433#1524—611no—
434#1524—611no—
435C2×#330—611no—
436C2×C61—22no—
437C2×C61—41no—
438C2×C61—41no—
439C2×C61C2×#41311yescharacteristic
440C2×C61#290111yescharacteristic
441C2×C61#290111yescharacteristic
442D61—81no—
443D61—81no—
444#553—1221no—
445#553—1221no—
446#553—1221no—
447#553—1221no—
448#553—1221no—
449#553—1221no—
450#552—1221no—
451#552—1221no—
452#541—611no—
453#541—611no—
454#540—611no—
455#540—611no—
456#537—611no—
457#537—611no—
458#532—611no—
459#529—611no—
460#529—611no—
461#529—611no—
462#529—611no—
463C2×#125—611no—
464#520—611no—
465#520—611no—
466C4×#41C2×D6111yescharacteristic
467#446—21no—
468#446—1221no—
469#435—21no—
470#435—21no—
471#435—1221no—
472#435—1221no—
473C8×D4—21no—
474C8×D4—1221no—
475#432—611no—
476#432—611no—
477#432—611no—
478#432C2×D6111yescharacteristic
479#432C2×D6111yescharacteristic
480#432C2×D6111yescharacteristic
481C4×M16—611no—
482C4×M16C2×D6111yescharacteristic
483C2×#97—611no—
484C2×#97—611no—
485C2×#97C2×D6111yescharacteristic
486C2×#97C2×D6111yescharacteristic
487#330—611no—
488#330—611no—
489#330—611no—
490#330—611no—
491#330—611no—
492#330—611no—
493#330—611no—
494#330—611no—
495#329—611no—
496#329—611no—
497#329—611no—
498#329—611no—
499#329—611no—
500#329—611no—
501#329—611no—
502#329—611no—
503C61#1769011yescharacteristic, complemented, Sylow
504C2×#41—611no—
505C2×#41—611no—
506C2×#41C4×D6111yescharacteristic
507C2×M16—21no—
508C2×M16—1221no—
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—1221no—
512C22×C8—1221no—
513C4⋊Q8—611no—
514#127—611no—
515#126—1221no—
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#125—611no—
524#125—611no—
525#125—611no—
526#125—611no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#124—611no—
534#124—611no—
535#123—1221no—
536#123—1221no—
537#123—1221no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543C22⋊Q8—611no—
544C22⋊Q8—611no—
545C22⋊Q8—611no—
546C22⋊Q8—611no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549#121—611no—
550#121—611no—
551#121—611no—
552#121—611no—
553#121—1221no—
554#121—1221no—
555#121—1221no—
556#121—1221no—
557#121—1221no—
558#121—1221no—
559#121—1221no—
560#121—1221no—
561#121—1221no—
562#121—1221no—
563#121—1221no—
564#121—1221no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8D24411yescharacteristic
570C4×Q8C22⋊D6111yescharacteristic
571C4×D4—611no—
572C4×D4—611no—
573C4×D4—611no—
574C4×D4—611no—
575C4×D4—1221no—
576C4×D4—1221no—
577C4×D4—1221no—
578C4×D4—1221no—
579C4×D4—1221no—
580C4×D4—1221no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4—1221no—
585C4×D4D24411yescharacteristic
586C4×D4D24411yescharacteristic
587C4×D4D24411yescharacteristic
588C4×D4C22⋊D6111yescharacteristic
589C4×D4C22⋊D6111yescharacteristic
590C4×D4C22⋊D6111yescharacteristic
591#117—1221no—
592#117—1221no—
593#117—1221no—
594#117—1221no—
595#117—1221no—
596#117—1221no—
597#117C4×D6111yescharacteristic
598#117C4×D6111yescharacteristic
599#117C4×D6111yescharacteristic
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C42C22×D6111yescharacteristic
607C2×C42C22×D6111yescharacteristic
608C2×C42C22×D6111yescharacteristic
609C4⋊C8—21no—
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C22⋊C8—21no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621#97—21no—
622#97—21no—
623#97—611no—
624#97—611no—
625#97—611no—
626#97—611no—
627#97—1221no—
628#97—1221no—
629#97C22×D6111yescharacteristic
630#97C22×D6111yescharacteristic
631#97C22×D6111yescharacteristic
632#97C22×D6111yescharacteristic
633C4×C8—21no—
634C4×C8—1221no—
635#41—42no—
636#41—2442no—
637#41—2442no—
638C2×Q8—611no—
639C2×Q8—611no—
640C2×Q8#1175819811yescharacteristic
641C2×D4—611no—
642C2×D4—611no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4#1175819811yescharacteristic
652C2×D4#1175819811yescharacteristic
653C2×D4#1175819811yescharacteristic
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4C2×C4×D6111yescharacteristic
665C22×C4C2×D24411yescharacteristic
666C22×C4C2×D24411yescharacteristic
667C22×C4C2×D24411yescharacteristic
668C22×C4C2×C22⋊D6111yescharacteristic
669C22×C4C2×C22⋊D6111yescharacteristic
670C22×C4C2×C22⋊D6111yescharacteristic
671M16—42no—
672M16—2442no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—2442no—
684C2×C8—2442no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4#1175819811yescharacteristic
710C4⋊C4#1175819811yescharacteristic
711C4⋊C4#1175819811yescharacteristic
712C4⋊C4#1175819811yescharacteristic
713C4⋊C4#1175819811yescharacteristic
714C4⋊C4#1175819811yescharacteristic
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4#1175819811yescharacteristic
732C22⋊C4#1175819811yescharacteristic
733C22⋊C4#1175819811yescharacteristic
734C22⋊C4#1175819811yescharacteristic
735C22⋊C4#1175819811yescharacteristic
736C22⋊C4#1175819811yescharacteristic
737C42—1221no—
738C42—1221no—
739C42—1221no—
740C42—1221no—
741C42C2×C4×D6111yescharacteristic
742C42C2×C4×D6111yescharacteristic
743C42C2×C4×D6111yescharacteristic
744C42C2×D24411yescharacteristic
745C42C2×D24411yescharacteristic
746C42C2×D24411yescharacteristic
747C42C2×C22⋊D6111yescharacteristic
748C42C2×C22⋊D6111yescharacteristic
749C42C2×C22⋊D6111yescharacteristic
750C42C23×D6111yescharacteristic
751C23—1221no—
752C23—1221no—
753C23C2×#1175819811yescharacteristic
754C23C2×#1175819811yescharacteristic
755C23C2×#1175819811yescharacteristic
756Q8—41no—
757Q8—2441no—
758Q8—2441no—
759D4—22no—
760D4—22no—
761D4—41no—
762D4—4881no—
763D4—4881no—
764D4—4881no—
765D4—4881no—
766D4—4881no—
767D4—4881no—
768D4—2441no—
769D4—2441no—
770D4—2442no—
771D4—2442no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—4881no—
788C2×C4—4881no—
789C2×C4—4881no—
790C2×C4—4881no—
791C2×C4—4881no—
792C2×C4—4881no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4C2×#1175819811yescharacteristic
796C2×C4C2×#1175819811yescharacteristic
797C2×C4C2×#1175819811yescharacteristic
798C2×C4C2×#1175819811yescharacteristic
799C2×C4C2×#1175819811yescharacteristic
800C2×C4C2×#1175819811yescharacteristic
801C2×C4C2×#1175819811yescharacteristic
802C2×C4C2×#1175819811yescharacteristic
803C2×C4C2×#1175819811yescharacteristic
804C2×C4C22×C4×D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4C22×D24411yescharacteristic
807C8—22no—
808C8—41no—
809C8—41no—
810C8—41no—
811C8—1222no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22#1683974412yes—
830C22C22×#1175819811yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—2441no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C2—22no—
850C2—41no—
851C2—41no—
852C2—4881no—
853C2—4881no—
854C2C2×#1683974411yescharacteristic
855C2#2145436411yescharacteristic
856C2#2145436711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2970C2
socleC22×C61C22×C22⋊C4
prime radical#21459741C2
cosocleC42×C61C24
hypercenter#2970D61
hypocenterC61#17690
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #21454833C2semidirect
3. #21444451C2semidirect
4. #21444448C2semidirect
5. #21444445C2semidirect
6. #21444440C2semidirect
7. #21444437C2semidirect
8. #21444431C2semidirect
9. #21444429C2semidirect
10. #21444427C2semidirect
11. #21444424C2semidirect
12. #21444408C2semidirect
13. #21444405C2semidirect
14. C2×#16839503C2semidirect
15. C61×#2970C2semidirect
423. #2970D61semidirect
503. C61#17690semidirect

Maximal subgroups

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

subgroupindex
#214597412
#214548332
#214444512
#214444482
#214444452
#214444402
#214444372
#214444312
#214444292
#214444272
#214444242
#214444082
#214444052
C2×#168395032
C61×#29702
#1769061