Finite Group Databasebeta

← C2×#13080869 #15630626

Subgroups — C2×#13080869 #15630626

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic, complemented
2#13080869C2116yesmaximal, direct product factor
3C2×#10622669C211yesmaximal, characteristic, complemented
4C2×#10622648C211yesmaximal, characteristic, complemented
5C2×#10622656C211yesmaximal, characteristic, complemented
6C2×#10622635C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic, complemented
11C2×#10622840C211yesmaximal, characteristic, complemented
12C2×C4×#4325C211yesmaximal, characteristic, complemented
13C2×#10622625C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622838C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C11×#548—24no—
20C11×#548C2218yescomplemented
21C2×C11×#124—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C2×#66992—21no—
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C22×#4318C2211yescharacteristic
40#10623096—24no—
41#10623096C2218yescomplemented
42C2×#66951—21no—
43C2×#66936—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66923C2211yescharacteristic
47#10622851C2218yescomplemented
48#10622845C2218yescomplemented
49#10622840C2218yescomplemented
50#10622838C2218yescomplemented
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66899C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62#10622670C2218yescomplemented
63#10622669C2218yescomplemented
64#10622662C2218yescomplemented
65#10622656C2218yescomplemented
66#10622652C2218yescomplemented
67#10622648C2218yescomplemented
68C4×#4325C2218yescomplemented
69#10622635C2218yescomplemented
70#10622625C2218yescomplemented
71C2×#66873C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×#66872C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11—21no—
82C22×Q8×C11—22no—
83C22×Q8×C11—24no—
84C22×Q8×C11—42no—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2314yes—
87C22×Q8×C11C2311yescharacteristic
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11D411yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C23×C4×C11—21no—
93C23×C4×C11—21no—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C23×Dic11—21no—
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C11×#124—28no—
102C11×#124—22no—
103C11×#124C2314yes—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—28no—
106C11×C22⋊Q8C2314yes—
107C11×#121—28no—
108C11×#121—22no—
109C11×#121C2314yes—
110C4×Q8×C11—22no—
111C4×Q8×C11C2314yes—
112C4×D4×C11—28no—
113C4×D4×C11D414yes—
114C4×D4×C11C2314yes—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C42×C11—21no—
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128C2×#4325—24no—
129C2×#4325—42no—
130C2×#4325C2314yes—
131C2×#4325C2314yes—
132#66992—28no—
133C2×#4323—42no—
134C2×#4323C2314yes—
135#66983—22no—
136#66983—22no—
137#66983C2314yes—
138#66983C2314yes—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142#66979—22no—
143#66979C2314yes—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11—22no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2314yes—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318—42no—
155C2×#4318C2314yes—
156C2×#4318C2314yes—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161#66951—28no—
162#66936—28no—
163(C22⋊D11)⋊C4—28no—
164C4×D44—22no—
165C4×D44C2314yes—
166#66923—22no—
167#66923C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66899C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66872C2314yes—
182#66871C2314yes—
183C4⋊(C11⋊C8)C2314yes—
184C4×C11⋊C8C2314yes—
185C2×#3326—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C11×#41—28no—
191C11×#41—44no—
192C11×#41—48no—
193C2×Q8×C11—21no—
194C2×Q8×C11—24no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—28no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—44no—
201C2×Q8×C11—44no—
202C2×Q8×C11—48no—
203C2×Q8×C11#4114yes—
204C2×Q8×C11C2412yes—
205C2×Q8×C11C2412yes—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—21no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—42no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11C2×D414yes—
215C2×D4×C11C2412yes—
216C22×C4×C11—21no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—24no—
224C22×C4×C11—24no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2411yescharacteristic
236C2×C22⋊D11—24no—
237C2×C22⋊D11—24no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—82no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—24no—
244C22×Dic11—82no—
245C2×D44—21no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—82no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2×D414yes—
255C11×C4⋊C4C2412yes—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4C2×D414yes—
261C11×C22⋊C4C2×D414yes—
262C42×C11—24no—
263C42×C11C2×D412yes—
264C42×C11C2412yes—
265C22⋊Dic11—24no—
266#4325—28no—
267#4325—44no—
268#4323—44no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—24no—
276C4⋊Dic11C2412yes—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281C4×Dic11—24no—
282#4318—44no—
283#4318—44no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292C2×#553—111no—
293C2×#548D1111yescharacteristic, complemented
294#3326—1116no—
295C2×#488—111no—
296C2×#482—111no—
297C2×#483—111no—
298C2×#479—111no—
299C2×#469—111no—
300C2×#468—111no—
301C2×#463—111no—
302C2×#449—111no—
303C2×#448—111no—
304C2×C4×SD16—111no—
305C2×#436—111no—
306C2×#417—111no—
307C2×#419—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11C22×D412yes—
319C23×C11C22×D412yes—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325Q8×C11—24no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—48no—
330Q8×C11—42no—
331Q8×C11C2×#4114yes—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—44no—
335D4×C11—48no—
336D4×C11—48no—
337D4×C11—42no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—48no—
353C2×C4×C11—48no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D412yes—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C2×#4112yes—
362C2×C4×C11H(5,𝔽2)12yes—
363C2×C4×C11C2511yescharacteristic
364C22⋊D11—48no—
365C22⋊D11—84no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—84no—
373D44—22no—
374D44—22no—
375D44—42no—
376C4×D11—84no—
377C11⋊C8—22no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41C2×D1111yescharacteristic
382C23×Q8C2×D1111yescharacteristic
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×M16—111no—
387C22×M16—111no—
388#553—118no—
389#553—224no—
390#548—24no—
391#548C2×D1118yescomplemented
392C2×#126—221no—
393C2×#125—111no—
394C2×#124—21no—
395C2×#124C2×D1111yescharacteristic
396C2×#123—221no—
397C2×C22⋊Q8—21no—
398C2×C22⋊Q8C2×D1111yescharacteristic
399C2×#121—21no—
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121C2×D1111yescharacteristic
404C2×C4×Q8C2×D1111yescharacteristic
405C2×C4×D4—21no—
406C2×C4×D4—111no—
407C2×C4×D4—221no—
408C2×C4×D4C2×D1111yescharacteristic
409C2×#117—111no—
410C22×C4⋊C4—111no—
411#488—118no—
412#483—118no—
413#482—118no—
414#479—118no—
415#469—118no—
416#468—118no—
417#463—118no—
418#449—118no—
419#448—118no—
420C4×SD16—118no—
421#436—118no—
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#419—118no—
427#417—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×C22⋊C8—111no—
439C2×C22⋊C8—111no—
440C2×C4×C8—111no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—44no—
448C22×C11—44no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—84no—
453C22×C11#54612yes—
454C22×C11#57512yes—
455C22×C11#57712yes—
456C22×C11C23×D411yescharacteristic
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—84no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—24no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#54612yes—
469C4×C11C22×#4111yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—22no—
475C2×#41—24no—
476C2×#41—42no—
477C2×#41C22×D1114yes—
478C22×Q8—21no—
479C22×Q8—22no—
480C22×Q8—24no—
481C22×Q8—42no—
482C22×Q8C22×D1111yescharacteristic
483C22×Q8C22×D1114yes—
484C22×Q8C22×D1111yescharacteristic
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—111no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4C22⋊D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—224no—
501C2×SD16—442no—
502C2×D8—114no—
503C2×D8—442no—
504C2×M16—114no—
505C2×M16—114no—
506C2×M16—442no—
507C2×M16—442no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—111no—
512#126—228no—
513#125—114no—
514#125—222no—
515#124—28no—
516#124—22no—
517#124C22×D1114yes—
518#123—228no—
519C22⋊Q8—22no—
520C22⋊Q8—28no—
521C22⋊Q8C22×D1114yes—
522#121—28no—
523#121—22no—
524#121—114no—
525#121—114no—
526#121—228no—
527#121—222no—
528#121—222no—
529#121C22×D1114yes—
530C4×Q8—22no—
531C4×Q8C22×D1114yes—
532C4×D4—28no—
533C4×D4—114no—
534C4×D4—228no—
535C4×D4—222no—
536C4×D4C22⋊D1114yes—
537C4×D4C22×D1114yes—
538#117—114no—
539#117—222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4C22⋊D1111yescharacteristic
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4C22⋊D1111yescharacteristic
561C2×C22⋊C4C22⋊D1111yescharacteristic
562C2×C42—21no—
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
565#107—114no—
566#106—114no—
567#106—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579C22⋊C8—114no—
580C22⋊C8—114no—
581C4×C8—114no—
582C2×C11—42no—
583C2×C11—42no—
584C2×C11—82no—
585C2×C11#332614yescomplemented
586C2×C11C2×#54611yescharacteristic
587C2×C11C2×#57511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589D11—82no—
590C24—21no—
591C24—221no—
592C24C2×C22⋊D1111yescharacteristic
593C24C2×C22⋊D1111yescharacteristic
594#41—28no—
595#41—44no—
596#41—48no—
597C2×Q8—22no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—28no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—44no—
605C2×Q8—44no—
606C2×Q8—48no—
607C2×Q8#434114yes—
608C2×Q8C23×D1112yes—
609C2×Q8C23×D1112yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—21no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—112no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—221no—
624C2×D4—444no—
625C2×D4—882no—
626C2×D4C2×C22⋊D1114yes—
627C2×D4C23×D1112yes—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—882no—
645C22×C4—882no—
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1112yes—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655SD16—228no—
656SD16—444no—
657D8—444no—
658M16—444no—
659M16—444no—
660C2×C8—112no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—112no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8—222no—
667C2×C8—222no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—112no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—224no—
677C4⋊C4—221no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4C2×C22⋊D1114yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4C2×C22⋊D1114yes—
691C22⋊C4C2×C22⋊D1114yes—
692C42—24no—
693C42—224no—
694C42C2×C22⋊D1112yes—
695C42C23×D1112yes—
696C11C2×#332611yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—222no—
708C23—442no—
709C23—442no—
710C23—442no—
711C23C22×C22⋊D1112yes—
712C23C22×C22⋊D1112yes—
713C23C22×C22⋊D1111yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8C2×#434114yes—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—48no—
726D4—42no—
727D4—222no—
728D4—222no—
729D4—448no—
730D4—442no—
731D4—884no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—884no—
757C2×C4—884no—
758C2×C4C2×#434112yes—
759C2×C4#6703712yes—
760C2×C4C22×C22⋊D1112yes—
761C2×C4C22×C22⋊D1112yes—
762C2×C4C22×C22⋊D1112yes—
763C2×C4C22×C22⋊D1112yes—
764C2×C4C22×C22⋊D1111yescharacteristic
765C2×C4C24×D1111yescharacteristic
766C8—222no—
767C8—222no—
768C8—222no—
769C8—222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—884no—
786C22#1062333712yes—
787C22#1062335312yes—
788C22#1062336812yes—
789C22C23×C22⋊D1111yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4#1062333712yes—
801C4C22×#434111yescharacteristic
802C4C2×#6703711yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—882no—
807C2#1308086914yesdirect product factor
808C2C2×#1062333711yescharacteristic
809C2C2×#1062335311yescharacteristic
810C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11C2×#3326
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#10623096C2semidirect
2. #13080869C2direct (N × H)
3. C2×#10622669C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622656C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622840C2semidirect
12. C2×C4×#4325C2semidirect
13. C2×#10622625C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622838C2semidirect
16. C2×C11×#548C2semidirect
20. C11×#548C22semidirect
41. #10623096C22semidirect
47. #10622851C22semidirect
48. #10622845C22semidirect
49. #10622840C22semidirect
50. #10622838C22semidirect
62. #10622670C22semidirect
63. #10622669C22semidirect
64. #10622662C22semidirect
65. #10622656C22semidirect
66. #10622652C22semidirect
67. #10622648C22semidirect
68. C4×#4325C22semidirect
69. #10622635C22semidirect
70. #10622625C22semidirect
293. C2×#548D11semidirect
391. #548C2×D11semidirect
585. C2×C11#3326semidirect
696. C11C2×#3326semidirect
807. C2#13080869direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
#130808692
C2×#106226692
C2×#106226482
C2×#106226562
C2×#106226352
C2×#106226522
C2×#106226622
C2×#106226702
C2×#106228512
C2×#106228402
C2×C4×#43252
C2×#106226252
C2×#106228452
C2×#106228382
C2×C11×#5482
C2×#332611