Finite Group Databasebeta

← C2×#13081437 #15633532

Subgroups — C2×#13081437 #15633532

Order 2816.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2#13081437C2116yesmaximal, direct product factor
3C2×#10622695C211yesmaximal, characteristic, complemented
4C2×#10622668C211yesmaximal, characteristic, complemented
5C2×#10622669C211yesmaximal, characteristic, complemented
6C2×#10622635C211yesmaximal, characteristic, complemented
7C2×#10622633C211yesmaximal, characteristic, complemented
8C2×#10622622C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic
10C2×#10622670C211yesmaximal, characteristic
11C2×#10622696C211yesmaximal, characteristic, complemented
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622627C211yesmaximal, characteristic
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×C4×#4325C211yesmaximal, characteristic, complemented
16C2×C11×#556C211yesmaximal, characteristic, complemented
17C11×#556—24no—
18C11×#556C2218yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126—21no—
21C2×C11×#126—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×C22⋊Q8—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117—21no—
30C2×#66999—21no—
31C22×#4325C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34#10623110—24no—
35#10623110C2218yescomplemented
36C2×#66949—21no—
37C2×#66949—21no—
38C2×C4⋊C4×D11—21no—
39C2×C4×D44C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622696C2218yescomplemented
55#10622695C2218yescomplemented
56#10622670C2218yes—
57#10622670C2218yes—
58#10622669C2218yescomplemented
59#10622668C2218yescomplemented
60#10622639C2218yescomplemented
61C4×#4325C2218yescomplemented
62#10622637C2218yescomplemented
63#10622635C2218yescomplemented
64#10622633C2218yescomplemented
65#10622627C2218yes—
66#10622622C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×Dic22—21no—
87C11×C4⋊Q8—22no—
88C11×C4⋊Q8C2314yes—
89C11×#126—28no—
90C11×#126—28no—
91C11×#124—22no—
92C11×#124—22no—
93C11×#124C2314yes—
94C11×#124C2314yes—
95C11×C22⋊Q8—28no—
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×Q8×C11D414yes—
99C4×Q8×C11C2314yes—
100C4×Q8×C11C2314yes—
101C4×Q8×C11C2314yes—
102C4×D4×C11—22no—
103C4×D4×C11C2314yes—
104C11×#117—28no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123#66999—28no—
124C2×#4325—24no—
125C2×#4325—24no—
126C2×#4325C2314yes—
127C2×#4325C2314yes—
128C2×#4323—24no—
129C2×#4323C2314yes—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145#66949—28no—
146#66949—28no—
147C4⋊C4×D11—28no—
148C4×D44—22no—
149C4×D44—22no—
150C4×D44—22no—
151C4×D44C2314yes—
152C4×D44C2314yes—
153C4×D44C2314yes—
154#66923—22no—
155#66923—22no—
156#66923C2314yes—
157#66923C2314yes—
158#66922—22no—
159#66922C2314yes—
160#66899C2314yes—
161#66899C2314yes—
162#66899C2314yes—
163#66899C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169#66873C2314yes—
170#66872C2314yes—
171#66872C2314yes—
172#66871C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175C4⋊(C11⋊C8)C2314yes—
176#66867C2314yes—
177#66867C2314yes—
178C4×C11⋊C8C2314yes—
179C2×#3376—111nomaximal, Sylow
180C24×C11—21no—
181C23×D11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11—42no—
189C2×Q8×C11C2×D414yes—
190C2×Q8×C11C2412yes—
191C2×Q8×C11C2412yes—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11C2412yes—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—24no—
200C22×C4×C11—44no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C2×D44—21no—
212C2×D44—22no—
213C2×D44#4114yes—
214C2×D44C2412yes—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—44no—
219C2×C4×D11—82no—
220C2×C4×D11—82no—
221C2×Dic22—24no—
222C2×Dic22—82no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4C2×D414yes—
229C11×C4⋊C4C2×D414yes—
230C11×C4⋊C4C2×D414yes—
231C11×C4⋊C4C2412yes—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C42×C11—24no—
238C42×C11—24no—
239C42×C11C2×D412yes—
240C42×C11C2×D412yes—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243C42×C11C2412yes—
244C42×C11C2412yes—
245#4325—28no—
246#4325—28no—
247#4323—28no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270C2×#556D1111yescharacteristic, complemented
271C2×#554—111no—
272#3376—1116no—
273C2×#491—111no—
274C2×#489—111no—
275C2×#488—111no—
276C2×#479—111no—
277C2×#475—111no—
278C2×#478—111no—
279C2×#463—111no—
280C2×#463—111no—
281C2×#461—111no—
282C2×#446—111no—
283C2×#442—111no—
284C2×#440—111no—
285C2×C4×SD16—111no—
286C23×C11—22no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11C22×D411yescharacteristic
291C22×D11—24no—
292C22×D11—22no—
293C22×D11—42no—
294C22×D11—42no—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—44no—
300Q8×C11—42no—
301Q8×C11—42no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—42no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—48no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4112yes—
326C2×C4×C112−1+412yes—
327C2×C4×C11C2511yescharacteristic
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334D44—24no—
335D44—22no—
336D44C2×#4114yes—
337C4×D11—48no—
338C4×D11—84no—
339C4×D11—84no—
340Dic22—84no—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C11⋊C8—22no—
344C11⋊C8—22no—
345C22×SD16—111no—
346C22×SD16—111no—
347C22×D8—111no—
348#556—24no—
349#556C2×D1118yescomplemented
350#554—118no—
351#554—224no—
352C2×C4⋊Q8—111no—
353C2×C4⋊Q8C2×D1111yescharacteristic
354C2×#126—21no—
355C2×#126—21no—
356C2×#125—111no—
357C2×#125—111no—
358C2×#124C2×D1111yescharacteristic
359C2×#124C2×D1111yescharacteristic
360C2×C22⋊Q8—21no—
361C2×C22⋊Q8—221no—
362C2×C22⋊Q8—221no—
363C2×C22⋊Q8—221no—
364C2×C4×Q8C2×D1111yescharacteristic
365C2×C4×Q8C2×D1111yescharacteristic
366C2×C4×Q8C2×D1111yescharacteristic
367C2×C4×D4—111no—
368C2×C4×D4—111no—
369C2×C4×D4—111no—
370C2×C4×D4C2×D1111yescharacteristic
371C2×#117—21no—
372C22×C4⋊C4—221no—
373#491—118no—
374#489—118no—
375#488—118no—
376#479—118no—
377#478—118no—
378#475—118no—
379#463—118no—
380#463—118no—
381#461—118no—
382#446—118no—
383#442—118no—
384#440—118no—
385C4×SD16—118no—
386C2×#107—111no—
387C2×#106—111no—
388C2×#106—111no—
389C2×C4⋊C8—111no—
390C2×C4⋊C8—111no—
391C2×C4⋊C8—111no—
392C2×#103—111no—
393C2×#103—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#102—111no—
399C2×#102—111no—
400C2×#102—111no—
401C2×#102—111no—
402C2×#97—111no—
403C2×#97—111no—
404C2×C4×C8—111no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—84no—
409C22×C11#54812yes—
410C22×C11#57512yes—
411C22×C11#57712yes—
412C22×C11C23×D411yescharacteristic
413C2×D11—24no—
414C2×D11—48no—
415C2×D11—42no—
416C2×D11—42no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—22no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11#54812yes—
427C4×C11C22×#4111yescharacteristic
428C4×C11C2×2−1+411yescharacteristic
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432C22×Q8—221no—
433C22×Q8C22⋊D1111yescharacteristic
434C22×Q8C22×D1111yescharacteristic
435C22×Q8C22×D1111yescharacteristic
436C22×D4—111no—
437C22×D4C22×D1111yescharacteristic
438C23×C4—21no—
439C23×C4—221no—
440C23×C4—221no—
441C23×C4—221no—
442C2×SD16—114no—
443C2×SD16—114no—
444C2×SD16—224no—
445C2×SD16—224no—
446C2×D8—114no—
447C2×D8—224no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C4⋊Q8—22no—
453C4⋊Q8—114no—
454C4⋊Q8—222no—
455C4⋊Q8C22×D1114yes—
456#126—28no—
457#126—28no—
458#125—114no—
459#125—114no—
460#125—222no—
461#125—222no—
462#124—22no—
463#124—22no—
464#124C22×D1114yes—
465#124C22×D1114yes—
466C22⋊Q8—28no—
467C22⋊Q8—228no—
468C22⋊Q8—228no—
469C22⋊Q8—228no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8C22⋊D1114yes—
473C4×Q8C22×D1114yes—
474C4×Q8C22×D1114yes—
475C4×Q8C22×D1114yes—
476C4×D4—22no—
477C4×D4—114no—
478C4×D4—114no—
479C4×D4—114no—
480C4×D4—222no—
481C4×D4—222no—
482C4×D4—222no—
483C4×D4C22×D1114yes—
484#117—28no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—228no—
498C2×C4⋊C4C22⋊D1111yescharacteristic
499C2×C4⋊C4C22⋊D1111yescharacteristic
500C2×C4⋊C4C22⋊D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42C22×D1111yescharacteristic
513C2×C42C22×D1111yescharacteristic
514C2×C42C22×D1111yescharacteristic
515#107—114no—
516#106—114no—
517#106—114no—
518C4⋊C8—114no—
519C4⋊C8—114no—
520C4⋊C8—114no—
521#103—114no—
522#103—114no—
523#103—114no—
524#103—114no—
525#103—114no—
526#103—114no—
527#102—114no—
528#102—114no—
529#102—114no—
530#102—114no—
531#97—114no—
532#97—114no—
533C4×C8—114no—
534C2×C11—82no—
535C2×C11#337614yescomplemented
536C2×C11C2×#54811yescharacteristic
537C2×C11C2×#57511yescharacteristic
538C2×C11C2×#57711yescharacteristic
539D11—44no—
540C24—21no—
541C24—221no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—42no—
549C2×Q8—224no—
550C2×Q8—882no—
551C2×Q8C2×C22⋊D1114yes—
552C2×Q8C23×D1112yes—
553C2×Q8C23×D1112yes—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—114no—
558C2×D4—112no—
559C2×D4—222no—
560C2×D4—221no—
561C2×D4C23×D1112yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—44no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—224no—
571C22×C4—224no—
572C22×C4—224no—
573C22×C4—444no—
574C22×C4—882no—
575C22×C4—882no—
576C22×C4C2×C22⋊D1111yescharacteristic
577C22×C4C2×C22⋊D1111yescharacteristic
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C2×C22⋊D1111yescharacteristic
582C22×C4C23×D1111yescharacteristic
583SD16—228no—
584SD16—228no—
585D8—228no—
586C2×C8—112no—
587C2×C8—112no—
588C2×C8—112no—
589C2×C8—112no—
590C2×C8—222no—
591C2×C8—222no—
592C2×C8—222no—
593C2×C8—222no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—112no—
600C4⋊C4—112no—
601C4⋊C4—112no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—224no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4C2×C22⋊D1114yes—
611C4⋊C4C2×C22⋊D1114yes—
612C4⋊C4C2×C22⋊D1114yes—
613C4⋊C4C23×D1112yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—224no—
620C22⋊C4—224no—
621C22⋊C4—224no—
622C42—24no—
623C42—24no—
624C42C2×C22⋊D1112yes—
625C42C2×C22⋊D1112yes—
626C42C2×C22⋊D1112yes—
627C42C23×D1112yes—
628C42C23×D1112yes—
629C42C23×D1112yes—
630C11C2×#337611yescharacteristic, complemented, Sylow
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—224no—
636C23—222no—
637C23—442no—
638C23—442no—
639C23C22×C22⋊D1111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—42no—
646Q8—42no—
647Q8—884no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—114no—
652D4—224no—
653D4—222no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—448no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—884no—
675C2×C4—884no—
676C2×C4#41×D1112yes—
677C2×C4#6704312yes—
678C2×C4C22×C22⋊D1112yes—
679C2×C4C22×C22⋊D1112yes—
680C2×C4C22×C22⋊D1112yes—
681C2×C4C22×C22⋊D1112yes—
682C2×C4C22×C22⋊D1112yes—
683C2×C4C22×C22⋊D1112yes—
684C2×C4C22×C22⋊D1111yescharacteristic
685C2×C4C24×D1111yescharacteristic
686C8—222no—
687C8—222no—
688C8—222no—
689C8—222no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—224no—
695C22—448no—
696C22—442no—
697C22—442no—
698C22#1062335312yes—
699C22#1062336212yes—
700C22#1062336812yes—
701C22C23×C22⋊D1111yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—442no—
712C4—442no—
713C4—442no—
714C4#1062336212yes—
715C4C2×#41×D1111yescharacteristic
716C4C2×#6704311yescharacteristic
717C2—82no—
718C2—444no—
719C2#1308143714yesdirect product factor
720C2C2×#1062336211yescharacteristic
721C2C2×#1062335311yescharacteristic
722C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11C2×#3376
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
2. #13081437C2direct (N × H)
3. C2×#10622695C2semidirect
4. C2×#10622668C2semidirect
5. C2×#10622669C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622633C2semidirect
8. C2×#10622622C2semidirect
11. C2×#10622696C2semidirect
12. C2×#10622637C2semidirect
14. C2×#10622639C2semidirect
15. C2×C4×#4325C2semidirect
16. C2×C11×#556C2semidirect
18. C11×#556C22semidirect
35. #10623110C22semidirect
54. #10622696C22semidirect
55. #10622695C22semidirect
58. #10622669C22semidirect
59. #10622668C22semidirect
60. #10622639C22semidirect
61. C4×#4325C22semidirect
62. #10622637C22semidirect
63. #10622635C22semidirect
64. #10622633C22semidirect
66. #10622622C22semidirect
270. C2×#556D11semidirect
349. #556C2×D11semidirect
535. C2×C11#3376semidirect
630. C11C2×#3376semidirect
719. C2#13081437direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130814372
C2×#106226952
C2×#106226682
C2×#106226692
C2×#106226352
C2×#106226332
C2×#106226222
C2×#106226702
C2×#106226962
C2×#106226372
C2×#106226272
C2×#106226392
C2×C4×#43252
C2×C11×#5562
C2×#337611