Finite Group Databasebeta

← #14722667

Subgroups — #14722667

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077741C211yesmaximal, characteristic, complemented
2#13077741C211yesmaximal, characteristic, complemented
3#13067346C211yesmaximal, characteristic, complemented
4#13067338C211yesmaximal, characteristic, complemented
5#13067333C211yesmaximal, characteristic, complemented
6#13067326C211yesmaximal, characteristic, complemented
7#13067321C211yesmaximal, characteristic, complemented
8#13067311C211yesmaximal, characteristic, complemented
9#13067311C211yesmaximal, characteristic, complemented
10#13067306C211yesmaximal, characteristic, complemented
11#13067293C211yesmaximal, characteristic, complemented
12#13067273C211yesmaximal, characteristic, complemented
13#13067265C211yesmaximal, characteristic, complemented
14C2×#10622185C211yesmaximal, characteristic, complemented
15C11×#3511C211yesmaximal, characteristic
16C11×#556—21no—
17C11×#555—21no—
18C11×#554—21no—
19C11×#553—21no—
20C11×#553—21no—
21C11×#548—21no—
22C11×#548—21no—
23C11×#547—21no—
24C11×#542C412yes—
25C11×#542C412yes—
26C11×#537C412yes—
27C11×#533C2211yescharacteristic
28C11×#533C2211yescharacteristic
29C11×#532C2211yescharacteristic
30C11×#532C2211yescharacteristic
31C11×#532C2211yescharacteristic
32C2×C11×C4⋊Q8C2211yescharacteristic
33C11×#520C412yes—
34C4×C11×#41C2211yescharacteristic
35#10622637—21no—
36#10622637—21no—
37#10622624—21no—
38#10622624—21no—
39#10622624—21no—
40#10622624—21no—
41D4×C11⋊C8—21no—
42D4×C11⋊C8—21no—
43#10622539C2211yescharacteristic
44#10622539C2211yescharacteristic
45#10622539C2211yescharacteristic
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622537C2211yescharacteristic
50#10622537C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622185C2211yescharacteristic
62#10622185C2211yescharacteristic
63#10622184C2211yescharacteristic
64#10622184C2211yescharacteristic
65#10622184C2211yescharacteristic
66#10622184C2211yescharacteristic
67#10622182C2211yescharacteristic
68#10622182C2211yescharacteristic
69#10622182C2211yescharacteristic
70#10622182C2211yescharacteristic
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41C2×C412yes—
74C2×C11×#41C2×C411yescharacteristic
75C22×Q8×C11—21no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8C2×C412yes—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127C2311yescharacteristic
83C11×#126—22no—
84C11×#126—22no—
85C11×#125—21no—
86C11×#125—21no—
87C11×#124—22no—
88C11×#124—22no—
89C11×#124—21no—
90C11×#124—21no—
91C11×#124C2×C412yes—
92C11×#123—22no—
93C11×#123—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8C2×C412yes—
100C11×C22⋊Q8C2×C412yes—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121C2×C412yes—
109C11×#121C2×C412yes—
110C4×Q8×C11—21no—
111C4×Q8×C11—21no—
112C4×Q8×C11C2×C412yes—
113C4×Q8×C11C2×C412yes—
114C4×Q8×C11D411yescharacteristic
115C4×Q8×C11D411yescharacteristic
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11C2×C412yes—
123C4×D4×C11C2×C412yes—
124C4×D4×C11D411yescharacteristic
125C4×D4×C11D411yescharacteristic
126C4×D4×C11D411yescharacteristic
127C4×D4×C11D411yescharacteristic
128C4×D4×C11D411yescharacteristic
129C4×D4×C11D411yescharacteristic
130C11×#117—21no—
131C11×#117—21no—
132C11×#117—22no—
133C11×#117C2×C411yescharacteristic
134C11×#117C2×C411yescharacteristic
135C11×#117C2×C411yescharacteristic
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4—22no—
138C2×C11×C4⋊C4C2×C412yes—
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2311yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×#4318—21no—
143C2×#4318—21no—
144C22×C11⋊C8—21no—
145C22×C11⋊C8—21no—
146C22×C11⋊C8—21no—
147C22×C11⋊C8—21no—
148C22⋊(C11⋊C8)—21no—
149C22⋊(C11⋊C8)—21no—
150C22⋊(C11⋊C8)—21no—
151C22⋊(C11⋊C8)—21no—
152C22⋊(C11⋊C8)—21no—
153C22⋊(C11⋊C8)—21no—
154C4⋊(C11⋊C8)—21no—
155C4⋊(C11⋊C8)—21no—
156C4⋊(C11⋊C8)—21no—
157C4⋊(C11⋊C8)—21no—
158C4⋊(C11⋊C8)—21no—
159C4⋊(C11⋊C8)—21no—
160C4⋊(C11⋊C8)C2311yescharacteristic
161C4⋊(C11⋊C8)C2311yescharacteristic
162C4⋊(C11⋊C8)C2311yescharacteristic
163C4⋊(C11⋊C8)C2311yescharacteristic
164C4⋊(C11⋊C8)C2311yescharacteristic
165C4⋊(C11⋊C8)C2311yescharacteristic
166C4⋊(C11⋊C8)C2311yescharacteristic
167C4⋊(C11⋊C8)C2311yescharacteristic
168#66867—21no—
169#66867—21no—
170#66867—21no—
171#66867—21no—
172C4×C11⋊C8—21no—
173C4×C11⋊C8—21no—
174#17775—111nomaximal, Sylow
175C11×#41—42no—
176C11×#41—44no—
177C11×#41—81no—
178C11×#41—81no—
179C11×#41—81no—
180C11×#41—81no—
181C2×Q8×C11—22no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—81no—
185C2×Q8×C11—81no—
186C2×Q8×C11C22⋊C411yescharacteristic
187C2×Q8×C11C22×C412yes—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11C22⋊C411yescharacteristic
194C2×D4×C11C22⋊C411yescharacteristic
195C2×D4×C11C22⋊C411yescharacteristic
196C2×D4×C11C22×C412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C11×C4⋊C4—22no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4C22⋊C411yescharacteristic
221C11×C4⋊C4C22⋊C411yescharacteristic
222C11×C4⋊C4C22⋊C411yescharacteristic
223C11×C4⋊C4C22⋊C411yescharacteristic
224C11×C4⋊C4C22⋊C411yescharacteristic
225C11×C4⋊C4C22⋊C411yescharacteristic
226C11×C4⋊C4C22×C412yes—
227C11×C4⋊C4C22×C412yes—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4C22⋊C411yescharacteristic
237C11×C22⋊C4C22⋊C411yescharacteristic
238C11×C22⋊C4C22⋊C411yescharacteristic
239C11×C22⋊C4C22⋊C411yescharacteristic
240C11×C22⋊C4C22⋊C411yescharacteristic
241C11×C22⋊C4C22⋊C411yescharacteristic
242C42×C11—22no—
243C42×C11—22no—
244C42×C11C22×C411yescharacteristic
245C42×C11C22×C411yescharacteristic
246C42×C11C22×C411yescharacteristic
247C42×C11C2×D411yescharacteristic
248C42×C11C2×D411yescharacteristic
249C42×C11C2×D411yescharacteristic
250C42×C11C2×D411yescharacteristic
251C42×C11C2×D411yescharacteristic
252C42×C11C2×D411yescharacteristic
253C42×C11C2411yescharacteristic
254#4318—81no—
255#4318—81no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—81no—
265C2×C11⋊C8—81no—
266C2×C11⋊C8—81no—
267C2×C11⋊C8—81no—
268#3511D1111yescharacteristic
269#2990—111no—
270#2990—111no—
271#1559—111no—
272#1557—111no—
273#1556—111no—
274#1554—111no—
275#1553—111no—
276#1551—111no—
277#1551—111no—
278#1550—111no—
279#1547—111no—
280#1542—111no—
281#1540—111no—
282C2×#332—111no—
283C23×C11—22no—
284C23×C11C2×C22⋊C411yescharacteristic
285C23×C11C2×C22⋊C411yescharacteristic
286C23×C11C2×C22⋊C411yescharacteristic
287Q8×C11—41no—
288Q8×C11—42no—
289Q8×C11—41no—
290Q8×C11—41no—
291Q8×C11—41no—
292Q8×C11—41no—
293Q8×C11—82no—
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—41no—
297D4×C11—42no—
298D4×C11—44no—
299D4×C11—41no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—82no—
304D4×C11—82no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—44no—
324C2×C4×C11—82no—
325C2×C4×C11—82no—
326C2×C4×C11—82no—
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C2×C22⋊C411yescharacteristic
332C2×C4×C11C2×C22⋊C411yescharacteristic
333C2×C4×C11C2×C22⋊C411yescharacteristic
334C2×C4×C11C2×C22⋊C411yescharacteristic
335C2×C4×C11C2×C22⋊C411yescharacteristic
336C2×C4×C11C23×C411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C11⋊C8—41no—
340C11⋊C8—41no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347#556—21no—
348#555—21no—
349#554—21no—
350#553—21no—
351#553—21no—
352#548—21no—
353#548—21no—
354#547—21no—
355#542Dic1112yes—
356#542Dic1112yes—
357#537Dic1112yes—
358#533C2×D1111yescharacteristic
359#533C2×D1111yescharacteristic
360#532C2×D1111yescharacteristic
361#532C2×D1111yescharacteristic
362#532C2×D1111yescharacteristic
363C2×C4⋊Q8C2×D1111yescharacteristic
364#520Dic1112yes—
365C4×#41C2×D1111yescharacteristic
366#446—221no—
367#446—221no—
368#435—221no—
369#435—221no—
370#435—221no—
371#435—221no—
372C8×D4—221no—
373C8×D4—221no—
374#432—111no—
375#432—111no—
376#432—111no—
377#432—111no—
378#431—111no—
379#431—111no—
380#423—111no—
381#423—111no—
382C2×C4⋊C8—111no—
383C2×C4⋊C8—111no—
384C2×C4⋊C8—111no—
385C2×C4⋊C8—111no—
386#333—111no—
387#333—111no—
388#333—111no—
389#333—111no—
390#332—111no—
391#332—111no—
392#332—111no—
393#332—111no—
394#332—111no—
395#332—111no—
396#332—111no—
397#332—111no—
398#331—111no—
399#331—111no—
400#331—111no—
401#331—111no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11#41312yes—
414C22×C11C22×C22⋊C411yescharacteristic
415C4×C11—21no—
416C4×C11—21no—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—21no—
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—21no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11#57611yescharacteristic
429C4×C11#57711yescharacteristic
430C4×C11#57711yescharacteristic
431C4×C11#57811yescharacteristic
432C2×#41—21no—
433C2×#41—21no—
434C2×#41C2×Dic1112yes—
435C2×#41C2×Dic1111yescharacteristic
436C22×Q8—21no—
437C2×M16—221no—
438C2×M16—221no—
439C22×C8—221no—
440C22×C8—221no—
441C22×C8—221no—
442C22×C8—221no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8C2×Dic1112yes—
446C4⋊Q8C22×D1111yescharacteristic
447C4⋊Q8C22×D1111yescharacteristic
448C4⋊Q8C22×D1111yescharacteristic
449#127C22×D1111yescharacteristic
450#126—22no—
451#126—22no—
452#125—21no—
453#125—21no—
454#124—22no—
455#124—22no—
456#124—21no—
457#124—21no—
458#124C2×Dic1112yes—
459#123—22no—
460#123—22no—
461C22⋊Q8—22no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8C2×Dic1112yes—
467C22⋊Q8C2×Dic1112yes—
468#121—22no—
469#121—22no—
470#121—22no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121C2×Dic1112yes—
476#121C2×Dic1112yes—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8C2×Dic1112yes—
480C4×Q8C2×Dic1112yes—
481C4×Q8C22⋊D1111yescharacteristic
482C4×Q8C22⋊D1111yescharacteristic
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4C2×Dic1112yes—
490C4×D4C2×Dic1112yes—
491C4×D4C22⋊D1111yescharacteristic
492C4×D4C22⋊D1111yescharacteristic
493C4×D4C22⋊D1111yescharacteristic
494C4×D4C22⋊D1111yescharacteristic
495C4×D4C22⋊D1111yescharacteristic
496C4×D4C22⋊D1111yescharacteristic
497#117—21no—
498#117—21no—
499#117—22no—
500#117C2×Dic1111yescharacteristic
501#117C2×Dic1111yescharacteristic
502#117C2×Dic1111yescharacteristic
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4C2×Dic1112yes—
506C2×C42C22×D1111yescharacteristic
507C2×C42C22×D1111yescharacteristic
508C2×C42C22×D1111yescharacteristic
509C4⋊C8—111no—
510C4⋊C8—111no—
511C4⋊C8—111no—
512C4⋊C8—111no—
513C4⋊C8—111no—
514C4⋊C8—111no—
515C4⋊C8—111no—
516C4⋊C8—111no—
517C4⋊C8—221no—
518C4⋊C8—221no—
519C4⋊C8—221no—
520C4⋊C8—221no—
521C4⋊C8—221no—
522C4⋊C8—221no—
523C22⋊C8—221no—
524C22⋊C8—221no—
525C22⋊C8—221no—
526C22⋊C8—221no—
527C22⋊C8—221no—
528C22⋊C8—221no—
529#97—221no—
530#97—221no—
531#97—221no—
532#97—221no—
533C4×C8—221no—
534C4×C8—221no—
535C2×C11—22no—
536C2×C11—41no—
537C2×C11—41no—
538C2×C11—82no—
539C2×C11C2×#41311yescharacteristic
540C2×C11#289711yescharacteristic
541C2×C11#289811yescharacteristic
542#41—42no—
543#41—44no—
544#41—81no—
545#41—81no—
546#41—81no—
547#41—81no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—81no—
552C2×Q8—81no—
553C2×Q8C22⋊Dic1111yescharacteristic
554C2×Q8C22×Dic1112yes—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4C22⋊Dic1111yescharacteristic
561C2×D4C22⋊Dic1111yescharacteristic
562C2×D4C22⋊Dic1111yescharacteristic
563C2×D4C22×Dic1112yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4C22×Dic1111yescharacteristic
569C22×C4C22×Dic1111yescharacteristic
570C22×C4C22×Dic1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C2×C22⋊D1111yescharacteristic
573C22×C4C2×C22⋊D1111yescharacteristic
574C22×C4C2×C22⋊D1111yescharacteristic
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C2×C22⋊D1111yescharacteristic
577M16—881no—
578M16—881no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—881no—
588C2×C8—881no—
589C2×C8—881no—
590C2×C8—881no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4C22⋊Dic1111yescharacteristic
602C4⋊C4C22⋊Dic1111yescharacteristic
603C4⋊C4C22⋊Dic1111yescharacteristic
604C4⋊C4C22⋊Dic1111yescharacteristic
605C4⋊C4C22⋊Dic1111yescharacteristic
606C4⋊C4C22⋊Dic1111yescharacteristic
607C4⋊C4C22×Dic1112yes—
608C4⋊C4C22×Dic1112yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4C22⋊Dic1111yescharacteristic
618C22⋊C4C22⋊Dic1111yescharacteristic
619C22⋊C4C22⋊Dic1111yescharacteristic
620C22⋊C4C22⋊Dic1111yescharacteristic
621C22⋊C4C22⋊Dic1111yescharacteristic
622C22⋊C4C22⋊Dic1111yescharacteristic
623C42—22no—
624C42—22no—
625C42C22×Dic1111yescharacteristic
626C42C22×Dic1111yescharacteristic
627C42C22×Dic1111yescharacteristic
628C42C2×C22⋊D1111yescharacteristic
629C42C2×C22⋊D1111yescharacteristic
630C42C2×C22⋊D1111yescharacteristic
631C42C2×C22⋊D1111yescharacteristic
632C42C2×C22⋊D1111yescharacteristic
633C42C2×C22⋊D1111yescharacteristic
634C42C23×D1111yescharacteristic
635C11#1777511yescharacteristic, complemented, Sylow
636C23—22no—
637C23C2×C22⋊Dic1111yescharacteristic
638C23C2×C22⋊Dic1111yescharacteristic
639C23C2×C22⋊Dic1111yescharacteristic
640Q8—41no—
641Q8—42no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—82no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—42no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—82no—
657D4—82no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—44no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C2×C22⋊Dic1111yescharacteristic
681C2×C4C2×C22⋊Dic1111yescharacteristic
682C2×C4C2×C22⋊Dic1111yescharacteristic
683C2×C4C2×C22⋊Dic1111yescharacteristic
684C2×C4C2×C22⋊Dic1111yescharacteristic
685C2×C4C2×C22⋊Dic1111yescharacteristic
686C2×C4C2×C22⋊Dic1111yescharacteristic
687C2×C4C2×C22⋊Dic1111yescharacteristic
688C2×C4C2×C22⋊Dic1111yescharacteristic
689C2×C4C23×Dic1111yescharacteristic
690C2×C4C22×C22⋊D1111yescharacteristic
691C2×C4C22×C22⋊D1111yescharacteristic
692C8—441no—
693C8—441no—
694C8—441no—
695C8—441no—
696C8—441no—
697C8—441no—
698C8—441no—
699C8—441no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22#1062285012yes—
712C22C22×C22⋊Dic1111yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4#1062336611yescharacteristic
727C4#1062336711yescharacteristic
728C4#1062336811yescharacteristic
729C4#1062336911yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—82no—
734C2C2×#1062285011yescharacteristic
735C2#1307714211yescharacteristic
736C2#1307714911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3511D11
hypocenterC11#17775
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13077741C2semidirect
2. #13077741C2semidirect
3. #13067346C2semidirect
4. #13067338C2semidirect
5. #13067333C2semidirect
6. #13067326C2semidirect
7. #13067321C2semidirect
8. #13067311C2semidirect
9. #13067311C2semidirect
10. #13067306C2semidirect
11. #13067293C2semidirect
12. #13067273C2semidirect
13. #13067265C2semidirect
14. C2×#10622185C2semidirect
635. C11#17775semidirect

Maximal subgroups

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

subgroupindex
#130777412
#130673462
#130673382
#130673332
#130673262
#130673212
#130673112
#130673062
#130672932
#130672732
#130672652
C2×#106221852
C11×#35112
#1777511