Finite Group Databasebeta

← #14722714

Subgroups — #14722714

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082502C211yesmaximal, characteristic
2#13077741C211yesmaximal, characteristic
3#13067347C211yesmaximal, characteristic, complemented
4#13067344C211yesmaximal, characteristic, complemented
5#13067341C211yesmaximal, characteristic, complemented
6#13067327C211yesmaximal, characteristic, complemented
7#13067324C211yesmaximal, characteristic, complemented
8#13067317C211yesmaximal, characteristic, complemented
9#13067314C211yesmaximal, characteristic, complemented
10#13067307C211yesmaximal, characteristic, complemented
11#13067304C211yesmaximal, characteristic, complemented
12#13067274C211yesmaximal, characteristic, complemented
13#13067271C211yesmaximal, characteristic, complemented
14C2×#10622119C211yesmaximal, characteristic, complemented
15C11×#2990C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17#10623356C412yes—
18#10623098—21no—
19#10623098—21no—
20#10623073—21no—
21#10623073—21no—
22#10623072—21no—
23#10623072—21no—
24#10623072—21no—
25#10623072—21no—
26#10623049C412yes—
27#10623049C412yes—
28#10623047C412yes—
29#10623001C2211yescharacteristic
30#10623001C2211yescharacteristic
31#10623001C2211yescharacteristic
32#10623001C2211yescharacteristic
33#10623001C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C11×#446—21no—
36C11×#435—21no—
37C11×#435—21no—
38C8×D4×C11—21no—
39C11×#432C2211yescharacteristic
40C11×#432C2211yescharacteristic
41C11×#431C2211yescharacteristic
42C11×#423C2211yescharacteristic
43C2×C11×C4⋊C8C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45#10622637—21no—
46#10622624—21no—
47#10622624—21no—
48D4×C11⋊C8—21no—
49#10622539C2211yescharacteristic
50#10622539C2211yescharacteristic
51#10622538C2211yescharacteristic
52#10622537C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622124C2211yescharacteristic
58#10622124C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622119C2211yescharacteristic
64#10622119C2211yescharacteristic
65#10622119C2211yescharacteristic
66#10622119C2211yescharacteristic
67#10622119C2211yescharacteristic
68#10622119C2211yescharacteristic
69#10622119C2211yescharacteristic
70#10622119C2211yescharacteristic
71C2×C11×#41C2×C411yescharacteristic
72C22×Dic22C2×C412yes—
73C2×C11×M16—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11D411yescharacteristic
78C4×D4×C11D411yescharacteristic
79C4×D4×C11D411yescharacteristic
80C4×D4×C11D411yescharacteristic
81C4×D4×C11D411yescharacteristic
82C4×D4×C11D411yescharacteristic
83C4×D4×C11D411yescharacteristic
84C11×#117C2×C411yescharacteristic
85C11×#117C2×C411yescharacteristic
86C11×#117C2×C411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90#66997—22no—
91#66989—22no—
92#66988—22no—
93#66988—22no—
94#66979—21no—
95#66979—21no—
96#66979—21no—
97#66979—21no—
98#66979C2×C412yes—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101#66977—21no—
102#66977—21no—
103#66977—21no—
104#66977—21no—
105#66977—21no—
106#66977—21no—
107#66977C2×C412yes—
108#66977C2×C412yes—
109#66977C2×C412yes—
110#66977C2×C412yes—
111C2×#4318—21no—
112C22×C11⋊C8—21no—
113C22×C11⋊C8—21no—
114#66942—22no—
115#66942—22no—
116#66942—22no—
117#66942—22no—
118#66940—22no—
119#66940—22no—
120#66932—22no—
121#66932—22no—
122#66932—22no—
123#66932—22no—
124#66930—22no—
125#66930—22no—
126#66923—21no—
127#66923—21no—
128#66923—21no—
129#66923—21no—
130#66923C2×C412yes—
131#66922—21no—
132#66922—21no—
133#66922C2×C412yes—
134#66922C2311yescharacteristic
135#66922C2311yescharacteristic
136#66922C2311yescharacteristic
137#66922C2311yescharacteristic
138C4×Dic22—21no—
139C4×Dic22—21no—
140C4×Dic22—21no—
141C4×Dic22—21no—
142C4×Dic22—21no—
143C4×Dic22—21no—
144C4×Dic22C2×C412yes—
145C4×Dic22C2×C412yes—
146C4×Dic22C2×C412yes—
147C4×Dic22C2×C412yes—
148C11×C4⋊C8—21no—
149C11×C4⋊C8—21no—
150C11×C4⋊C8—21no—
151C11×C4⋊C8C2311yescharacteristic
152C11×C4⋊C8C2311yescharacteristic
153C11×C4⋊C8C2311yescharacteristic
154C11×C4⋊C8C2311yescharacteristic
155C11×C22⋊C8—21no—
156C11×C22⋊C8—21no—
157C11×C22⋊C8—21no—
158C11×#97—21no—
159C11×#97—21no—
160C4×C8×C11—21no—
161C22⋊(C11⋊C8)—21no—
162C22⋊(C11⋊C8)—21no—
163C22⋊(C11⋊C8)—21no—
164C4⋊(C11⋊C8)—21no—
165C4⋊(C11⋊C8)—21no—
166C4⋊(C11⋊C8)—21no—
167C4⋊(C11⋊C8)C2311yescharacteristic
168C4⋊(C11⋊C8)C2311yescharacteristic
169C4⋊(C11⋊C8)C2311yescharacteristic
170C4⋊(C11⋊C8)C2311yescharacteristic
171#66867—21no—
172#66867—21no—
173C4×C11⋊C8—21no—
174#17780—111nomaximal, Sylow
175C11×#41—42no—
176C2×Q8×C11C22⋊C411yescharacteristic
177C2×D4×C11C22⋊C411yescharacteristic
178C2×D4×C11C22⋊C411yescharacteristic
179C2×D4×C11C22⋊C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×Dic11—22no—
190C2×Dic22—22no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—44no—
194C2×Dic22C22×C412yes—
195C2×Dic22C22×C412yes—
196C11×M16—81no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—81no—
202C2×C8×C11—81no—
203C11×C4⋊C4C22⋊C411yescharacteristic
204C11×C4⋊C4C22⋊C411yescharacteristic
205C11×C4⋊C4C22⋊C411yescharacteristic
206C11×C4⋊C4C22⋊C411yescharacteristic
207C11×C4⋊C4C22⋊C411yescharacteristic
208C11×C4⋊C4C22⋊C411yescharacteristic
209C11×C22⋊C4C22⋊C411yescharacteristic
210C11×C22⋊C4C22⋊C411yescharacteristic
211C11×C22⋊C4C22⋊C411yescharacteristic
212C11×C22⋊C4C22⋊C411yescharacteristic
213C11×C22⋊C4C22⋊C411yescharacteristic
214C11×C22⋊C4C22⋊C411yescharacteristic
215C42×C11C22×C411yescharacteristic
216C42×C11C22×C411yescharacteristic
217C42×C11C22×C411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222C42×C11C2×D411yescharacteristic
223C42×C11C2×D411yescharacteristic
224C42×C11C2411yescharacteristic
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—22no—
229C22⋊Dic11—22no—
230C4⋊Dic11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11C22×C412yes—
239C4⋊Dic11C22×C412yes—
240Dic11⋊C4—22no—
241Dic11⋊C4—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245Dic11⋊C4—22no—
246Dic11⋊C4—22no—
247Dic11⋊C4—22no—
248Dic11⋊C4—22no—
249Dic11⋊C4—22no—
250C4×Dic11—22no—
251C4×Dic11—22no—
252C4×Dic11—22no—
253C4×Dic11—22no—
254C4×Dic11—22no—
255#4318—81no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—81no—
261C2×C11⋊C8—81no—
262#3509—111no—
263#2990—111no—
264#2990D1111yescharacteristic
265#1559—111no—
266#1559—111no—
267#1558—111no—
268#1554—111no—
269#1554—111no—
270#1552—111no—
271#1552—111no—
272#1550—111no—
273#1550—111no—
274#1542—111no—
275#1542—111no—
276C2×#333—111no—
277C23×C11C2×C22⋊C411yescharacteristic
278C23×C11C2×C22⋊C411yescharacteristic
279C23×C11C2×C22⋊C411yescharacteristic
280Q8×C11—41no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—41no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11C2×C22⋊C411yescharacteristic
300C2×C4×C11C2×C22⋊C411yescharacteristic
301C2×C4×C11C2×C22⋊C411yescharacteristic
302C2×C4×C11C2×C22⋊C411yescharacteristic
303C2×C4×C11C2×C22⋊C411yescharacteristic
304C2×C4×C11C2×C22⋊C411yescharacteristic
305C2×C4×C11C2×C22⋊C411yescharacteristic
306C2×C4×C11C2×C22⋊C411yescharacteristic
307C2×C4×C11C2×C22⋊C411yescharacteristic
308C2×C4×C11C23×C411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D411yescharacteristic
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—44no—
316Dic22—44no—
317Dic22—41no—
318Dic22—41no—
319Dic22—41no—
320Dic22—41no—
321Dic22—42no—
322Dic22—42no—
323C8×C11—41no—
324C8×C11—41no—
325C8×C11—41no—
326C8×C11—41no—
327C11⋊C8—41no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C11⋊C8—41no—
331#557—221no—
332#557—221no—
333#556—221no—
334#556—221no—
335#552—221no—
336#552—221no—
337#552—221no—
338#552—221no—
339#541—112no—
340#541—112no—
341#536—112no—
342#533—111no—
343#533—111no—
344#533—111no—
345#533—111no—
346#533—111no—
347C2×C4⋊Q8—111no—
348#519—112no—
349C4×#41C2×D1111yescharacteristic
350#446—21no—
351#446—221no—
352#435—21no—
353#435—21no—
354#435—221no—
355#435—221no—
356C8×D4—21no—
357C8×D4—221no—
358#432—111no—
359#432—111no—
360#432C2×D1111yescharacteristic
361#432C2×D1111yescharacteristic
362#431—111no—
363#431C2×D1111yescharacteristic
364#423—111no—
365#423C2×D1111yescharacteristic
366C2×C4⋊C8—111no—
367C2×C4⋊C8—111no—
368C2×C4⋊C8C2×D1111yescharacteristic
369C2×C4⋊C8C2×D1111yescharacteristic
370#333—111no—
371#333—111no—
372#333—111no—
373#333—111no—
374#333—111no—
375#333—111no—
376#333—111no—
377#333—111no—
378#332—111no—
379#332—111no—
380#332—111no—
381#332—111no—
382#332—111no—
383#332—111no—
384#332—111no—
385#332—111no—
386C22×C11—21no—
387C22×C11—21no—
388C22×C11—21no—
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11#41312yes—
395C22×C11C22×C22⋊C411yescharacteristic
396C4×C11—21no—
397C4×C11—21no—
398C4×C11—21no—
399C4×C11—21no—
400C4×C11—21no—
401C4×C11—21no—
402C4×C11—21no—
403C4×C11—21no—
404C4×C11—21no—
405C4×C11—21no—
406C4×C11#57711yescharacteristic
407C4×C11#57711yescharacteristic
408C4×C11#57811yescharacteristic
409C4×C11#57811yescharacteristic
410Dic11—42no—
411Dic11—42no—
412Dic11—42no—
413Dic11—42no—
414C2×#41C4×D1111yescharacteristic
415C22×Q8—112no—
416C2×M16—21no—
417C2×M16—221no—
418C22×C8—21no—
419C22×C8—21no—
420C22×C8—221no—
421C22×C8—221no—
422C4⋊Q8—112no—
423C4⋊Q8—111no—
424C4⋊Q8—111no—
425C4⋊Q8—111no—
426C4⋊Q8—111no—
427C4⋊Q8—222no—
428C4⋊Q8—221no—
429C4⋊Q8—221no—
430#126—222no—
431#126—222no—
432#126—222no—
433#126—222no—
434#125—112no—
435#125—222no—
436#125—222no—
437#125—222no—
438#125—222no—
439#125—221no—
440#125—221no—
441#125—221no—
442#125—221no—
443#124—222no—
444#123—222no—
445#123—222no—
446C22⋊Q8—112no—
447C22⋊Q8—112no—
448C22⋊Q8—112no—
449C22⋊Q8—112no—
450C22⋊Q8—221no—
451C22⋊Q8—221no—
452C22⋊Q8—221no—
453C22⋊Q8—221no—
454C22⋊Q8—221no—
455C22⋊Q8—221no—
456C4×Q8—112no—
457C4×Q8—112no—
458C4×Q8—112no—
459C4×Q8—112no—
460C4×Q8—222no—
461C4×Q8—222no—
462C4×Q8—221no—
463C4×Q8—221no—
464C4×Q8—221no—
465C4×Q8—221no—
466C4×Q8—221no—
467C4×Q8—221no—
468C4×Q8D4411yescharacteristic
469C4×Q8C22⋊D1111yescharacteristic
470C4×D4D4411yescharacteristic
471C4×D4D4411yescharacteristic
472C4×D4D4411yescharacteristic
473C4×D4C22⋊D1111yescharacteristic
474C4×D4C22⋊D1111yescharacteristic
475C4×D4C22⋊D1111yescharacteristic
476#117—112no—
477#117—221no—
478#117—221no—
479#117—221no—
480#117—221no—
481#117—222no—
482#117—222no—
483#117C4×D1111yescharacteristic
484#117C4×D1111yescharacteristic
485#117C4×D1111yescharacteristic
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C42C22×D1111yescharacteristic
489C2×C42C22×D1111yescharacteristic
490C2×C42C22×D1111yescharacteristic
491C4⋊C8—21no—
492C4⋊C8—21no—
493C4⋊C8—21no—
494C4⋊C8—111no—
495C4⋊C8—111no—
496C4⋊C8—111no—
497C4⋊C8—111no—
498C4⋊C8—221no—
499C4⋊C8—221no—
500C4⋊C8—221no—
501C4⋊C8C22×D1111yescharacteristic
502C4⋊C8C22×D1111yescharacteristic
503C4⋊C8C22×D1111yescharacteristic
504C4⋊C8C22×D1111yescharacteristic
505C22⋊C8—21no—
506C22⋊C8—21no—
507C22⋊C8—21no—
508C22⋊C8—221no—
509C22⋊C8—221no—
510C22⋊C8—221no—
511#97—21no—
512#97—21no—
513#97—221no—
514#97—221no—
515C4×C8—21no—
516C4×C8—221no—
517C2×C11—22no—
518C2×C11—41no—
519C2×C11—41no—
520C2×C11C2×#41311yescharacteristic
521C2×C11#289811yescharacteristic
522C2×C11#289811yescharacteristic
523#41—42no—
524C2×Q8—112no—
525C2×Q8—112no—
526C2×Q8—222no—
527C2×Q8—221no—
528C2×Q8—221no—
529C2×Q8—444no—
530C2×Q8(C2×D11)⋊C411yescharacteristic
531C2×D4(C2×D11)⋊C411yescharacteristic
532C2×D4(C2×D11)⋊C411yescharacteristic
533C2×D4(C2×D11)⋊C411yescharacteristic
534C22×C4—222no—
535C22×C4C2×C4×D1111yescharacteristic
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C2×C4×D1111yescharacteristic
538C22×C4C2×D4411yescharacteristic
539C22×C4C2×D4411yescharacteristic
540C22×C4C2×D4411yescharacteristic
541C22×C4C2×C22⋊D1111yescharacteristic
542C22×C4C2×C22⋊D1111yescharacteristic
543C22×C4C2×C22⋊D1111yescharacteristic
544M16—81no—
545M16—881no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—81no—
551C2×C8—81no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—881no—
557C2×C8—881no—
558C4⋊C4—112no—
559C4⋊C4—112no—
560C4⋊C4—222no—
561C4⋊C4—222no—
562C4⋊C4—222no—
563C4⋊C4—222no—
564C4⋊C4—222no—
565C4⋊C4—222no—
566C4⋊C4—222no—
567C4⋊C4—222no—
568C4⋊C4—222no—
569C4⋊C4—222no—
570C4⋊C4—222no—
571C4⋊C4—222no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4(C2×D11)⋊C411yescharacteristic
579C4⋊C4(C2×D11)⋊C411yescharacteristic
580C4⋊C4(C2×D11)⋊C411yescharacteristic
581C4⋊C4(C2×D11)⋊C411yescharacteristic
582C4⋊C4(C2×D11)⋊C411yescharacteristic
583C4⋊C4(C2×D11)⋊C411yescharacteristic
584C22⋊C4—222no—
585C22⋊C4—222no—
586C22⋊C4—222no—
587C22⋊C4—222no—
588C22⋊C4—222no—
589C22⋊C4(C2×D11)⋊C411yescharacteristic
590C22⋊C4(C2×D11)⋊C411yescharacteristic
591C22⋊C4(C2×D11)⋊C411yescharacteristic
592C22⋊C4(C2×D11)⋊C411yescharacteristic
593C22⋊C4(C2×D11)⋊C411yescharacteristic
594C22⋊C4(C2×D11)⋊C411yescharacteristic
595C42—222no—
596C42—222no—
597C42—222no—
598C42—222no—
599C42—222no—
600C42C2×C4×D1111yescharacteristic
601C42C2×C4×D1111yescharacteristic
602C42C2×C4×D1111yescharacteristic
603C42C2×D4411yescharacteristic
604C42C2×D4411yescharacteristic
605C42C2×D4411yescharacteristic
606C42C2×C22⋊D1111yescharacteristic
607C42C2×C22⋊D1111yescharacteristic
608C42C2×C22⋊D1111yescharacteristic
609C42C23×D1111yescharacteristic
610C11#1778011yescharacteristic, complemented, Sylow
611C23C2×(C2×D11)⋊C411yescharacteristic
612C23C2×(C2×D11)⋊C411yescharacteristic
613C23C2×(C2×D11)⋊C411yescharacteristic
614Q8—41no—
615Q8—442no—
616Q8—442no—
617Q8—444no—
618Q8—441no—
619Q8—441no—
620Q8—441no—
621Q8—441no—
622D4—22no—
623D4—22no—
624D4—41no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—444no—
645C2×C4C2×(C2×D11)⋊C411yescharacteristic
646C2×C4C2×(C2×D11)⋊C411yescharacteristic
647C2×C4C2×(C2×D11)⋊C411yescharacteristic
648C2×C4C2×(C2×D11)⋊C411yescharacteristic
649C2×C4C2×(C2×D11)⋊C411yescharacteristic
650C2×C4C2×(C2×D11)⋊C411yescharacteristic
651C2×C4C2×(C2×D11)⋊C411yescharacteristic
652C2×C4C2×(C2×D11)⋊C411yescharacteristic
653C2×C4C2×(C2×D11)⋊C411yescharacteristic
654C2×C4C22×C4×D1111yescharacteristic
655C2×C4C22×D4411yescharacteristic
656C2×C4C22×C22⋊D1111yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C8—441no—
662C8—441no—
663C8—441no—
664C8—441no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22#1062274512yes—
674C22C22×(C2×D11)⋊C411yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—442no—
686C4—442no—
687C4—442no—
688C4—442no—
689C4#1062328211yescharacteristic
690C4#1062328411yescharacteristic
691C4#1062336711yescharacteristic
692C4#1062336911yescharacteristic
693C2—22no—
694C2—41no—
695C2—41no—
696C2C2×#1062274511yescharacteristic
697C2#1307714611yescharacteristic
698C2#1307715011yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2990C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#2990D11
hypocenterC11#17780
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #13067347C2semidirect
4. #13067344C2semidirect
5. #13067341C2semidirect
6. #13067327C2semidirect
7. #13067324C2semidirect
8. #13067317C2semidirect
9. #13067314C2semidirect
10. #13067307C2semidirect
11. #13067304C2semidirect
12. #13067274C2semidirect
13. #13067271C2semidirect
14. C2×#10622119C2semidirect
610. C11#17780semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130777412
#130673472
#130673442
#130673412
#130673272
#130673242
#130673172
#130673142
#130673072
#130673042
#130672742
#130672712
C2×#106221192
C11×#29902
#1778011