Finite Group Databasebeta

← C2×#13080742 #15630491

Subgroups — C2×#13080742 #15630491

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×#10623072C211yesmaximal, characteristic, complemented
2#13080742C2116yesmaximal, direct product factor
3C2×#10622684C211yesmaximal, characteristic, complemented
4C2×#10622647C211yesmaximal, characteristic, complemented
5C2×#10622648C211yesmaximal, characteristic, complemented
6C2×#10622635C211yesmaximal, characteristic, complemented
7C2×#10622655C211yesmaximal, characteristic, complemented
8C2×#10622654C211yesmaximal, characteristic, complemented
9C2×#10622688C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622852C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622846C211yesmaximal, characteristic, complemented
16C2×C11×#550C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic
19C11×#550—24no—
20C11×#550C2218yes—
21C2×C11×#127—21no—
22C2×C11×#127C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C2×#66988—21no—
32C22×#4324C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C2×#66977C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic
40#10623072—24no—
41#10623072C2218yescomplemented
42C2×#66942—21no—
43C2×#66932—21no—
44C2×#66930—21no—
45C2×#66923C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47#10622852C2218yescomplemented
48#10622852C2218yescomplemented
49#10622846C2218yescomplemented
50#10622845C2218yescomplemented
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62#10622688C2218yescomplemented
63#10622684C2218yescomplemented
64#10622655C2218yescomplemented
65#10622654C2218yescomplemented
66#10622648C2218yescomplemented
67#10622647C2218yescomplemented
68#10622643C2218yescomplemented
69#10622635C2218yescomplemented
70#10622624C2218yescomplemented
71C2×#66874C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×#66872C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C2×C11×#41—22no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—24no—
81C2×C11×#41—42no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C2×C11×#41C2314yes—
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11D411yescharacteristic
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11—21no—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×Dic11—21no—
100C22×Dic22C2311yescharacteristic
101C11×#127—28no—
102C11×#127—22no—
103C11×#127C2314yes—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121—28no—
107C11×#121—28no—
108C11×#121C2314yes—
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⋊C4D411yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×#4326—24no—
128C2×#4326C2314yes—
129#66988—28no—
130C2×#4324—42no—
131C2×#4324—42no—
132C2×#4324C2314yes—
133C2×#4324C2314yes—
134#66979—22no—
135#66979C2314yes—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—22no—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2314yes—
142#66977—22no—
143#66977—22no—
144#66977C2314yes—
145#66977C2314yes—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318C2314yes—
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yes—
161#66942—28no—
162#66932—28no—
163#66930—28no—
164#66923—22no—
165#66923C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66899C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179#66874C2314yes—
180#66872C2314yes—
181#66872C2314yes—
182#66871C2314yes—
183C4⋊(C11⋊C8)C2314yes—
184#66867C2314yes—
185C2×#3317—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C24×C11C2×D411yescharacteristic
190C11×#41—28no—
191C11×#41—28no—
192C11×#41—44no—
193C11×#41—44no—
194C11×#41—48no—
195C11×#41—48no—
196C2×Q8×C11—21no—
197C2×Q8×C11—22no—
198C2×Q8×C11#4114yes—
199C2×Q8×C11C2412yes—
200C2×D4×C11—24no—
201C2×D4×C11—24no—
202C2×D4×C11—24no—
203C2×D4×C11—24no—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—24no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—42no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—82no—
217C2×D4×C11—82no—
218C2×D4×C11—82no—
219C2×D4×C11C2×D414yes—
220C2×D4×C11C2412yes—
221C2×D4×C11C2412yes—
222C22×C4×C11—21no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—21no—
228C22×C4×C11—24no—
229C22×C4×C11—24no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2411yescharacteristic
241C22×Dic11—24no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—44no—
247C2×Dic22—21no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22C2412yes—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4C2×D414yes—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4C2×D414yes—
258C11×C22⋊C4C2×D414yes—
259C42×C11—24no—
260C42×C11C2×D412yes—
261C42×C11C2412yes—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265#4326—28no—
266#4324—44no—
267#4324—44no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—24no—
272C4⋊Dic11C2412yes—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282#4318—44no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—44no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292C2×#552—111no—
293C2×#550D1111yescharacteristic
294#3317—1116no—
295C2×#490—111no—
296C2×#481—111no—
297C2×#482—111no—
298C2×#479—111no—
299C2×#468—111no—
300C2×#465—111no—
301C2×#460—111no—
302C2×#452—111no—
303C2×#452—111no—
304C2×#441—111no—
305C2×#435—111no—
306C2×#417—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11C22×D412yes—
323C23×C11C22×D412yes—
324C23×C11C22×D411yescharacteristic
325Q8×C11—24no—
326Q8×C11—22no—
327Q8×C11C2×#4114yes—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—44no—
333D4×C11—48no—
334D4×C11—48no—
335D4×C11—48no—
336D4×C11—42no—
337D4×C11—42no—
338D4×C11—84no—
339D4×C11—84no—
340D4×C11—84no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—24no—
348C2×C4×C11—24no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—48no—
355C2×C4×C11—48no—
356C2×C4×C11—42no—
357C2×C4×C11C22×D412yes—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C2×#4112yes—
363C2×C4×C11H(5,𝔽2)12yes—
364C2×C4×C11C2511yescharacteristic
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—48no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374Dic22—22no—
375Dic22—22no—
376Dic22—42no—
377C11⋊C8—22no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41C2×D1111yescharacteristic
382C22×#41C2×D1111yescharacteristic
383C22×Q16—111no—
384C22×SD16—111no—
385C22×SD16—111no—
386C22×M16—111no—
387C23×C8—111no—
388#552—118no—
389#552—224no—
390#550—24no—
391#550C2×D1118yes—
392C2×#127—21no—
393C2×#127C2×D1111yescharacteristic
394C2×#126—221no—
395C2×#125—111no—
396C2×#125—221no—
397C2×#123—221no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8—111no—
400C2×#121—21no—
401C2×#121—21no—
402C2×#121C2×D1111yescharacteristic
403C2×#121C2×D1111yescharacteristic
404C2×C4×Q8—111no—
405C2×C4×Q8C2×D1111yescharacteristic
406C2×C4×D4—21no—
407C2×C4×D4C2×D1111yescharacteristic
408C2×#117—111no—
409C2×#117—221no—
410C22×C4⋊C4—111no—
411#490—118no—
412#482—118no—
413#481—118no—
414#479—118no—
415#468—118no—
416#465—118no—
417#460—118no—
418#452—118no—
419#452—118no—
420#441—118no—
421#435—118no—
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#417—118no—
427#416—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×C22⋊C8—111no—
439C2×C22⋊C8—111no—
440C2×#97—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—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—84no—
456C22×C11—84no—
457C22×C11#54612yes—
458C22×C11#57512yes—
459C22×C11#57712yes—
460C22×C11C23×D411yescharacteristic
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—24no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—42no—
467C4×C11#54612yes—
468C4×C11C22×#4111yescharacteristic
469C4×C11C2×H(5,𝔽2)11yescharacteristic
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—24no—
478C2×#41—42no—
479C2×#41—42no—
480C2×#41C22×D1114yes—
481C2×#41C22×D1114yes—
482C22×Q8—111no—
483C22×Q8C22×D1111yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C22×D4C22×D1111yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×Q16—114no—
499C2×Q16—224no—
500C2×SD16—114no—
501C2×SD16—114no—
502C2×SD16—442no—
503C2×SD16—442no—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—114no—
511C22×C8—442no—
512#127—28no—
513#127—22no—
514#127C22×D1114yes—
515#126—228no—
516#125—114no—
517#125—228no—
518#125—222no—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524#121—22no—
525#121—22no—
526#121—28no—
527#121—28no—
528#121C22×D1114yes—
529#121C22×D1114yes—
530C4×Q8—22no—
531C4×Q8—114no—
532C4×Q8—222no—
533C4×Q8C22×D1114yes—
534C4×D4—28no—
535C4×D4C22⋊D1114yes—
536C4×D4C22×D1114yes—
537#117—114no—
538#117—222no—
539#117—228no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—114no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—222no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4C22⋊D1111yescharacteristic
553C2×C4⋊C4C22×D1111yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4C22⋊D1111yescharacteristic
560C2×C22⋊C4C22⋊D1111yescharacteristic
561C2×C42—21no—
562C2×C42—221no—
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#102—114no—
574#102—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579C22⋊C8—114no—
580C22⋊C8—114no—
581#97—114no—
582C2×C11—42no—
583C2×C11—42no—
584C2×C11—82no—
585C2×C11—82no—
586C2×C11#331714yescomplemented
587C2×C11C2×#54611yescharacteristic
588C2×C11C2×#57511yescharacteristic
589C2×C11C2×#57711yescharacteristic
590C24—21no—
591C24—21no—
592C24C2×C22⋊D1111yescharacteristic
593C24C2×C22⋊D1111yescharacteristic
594#41—28no—
595#41—28no—
596#41—44no—
597#41—44no—
598#41—48no—
599#41—48no—
600C2×Q8—22no—
601C2×Q8—21no—
602C2×Q8—112no—
603C2×Q8—221no—
604C2×Q8—222no—
605C2×Q8—222no—
606C2×Q8#434114yes—
607C2×Q8C23×D1112yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—24no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—82no—
625C2×D4—82no—
626C2×D4—82no—
627C2×D4C2×C22⋊D1114yes—
628C2×D4C23×D1112yes—
629C2×D4C23×D1112yes—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—224no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—444no—
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
655Q16—228no—
656SD16—444no—
657SD16—444no—
658M16—444no—
659C2×C8—112no—
660C2×C8—112no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8—222no—
667C2×C8—444no—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—112no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—224no—
676C4⋊C4—221no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4C2×C22⋊D1114yes—
683C4⋊C4C23×D1112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4C2×C22⋊D1114yes—
690C22⋊C4C2×C22⋊D1114yes—
691C42—24no—
692C42—224no—
693C42—224no—
694C42C2×C22⋊D1112yes—
695C42C23×D1112yes—
696C11C2×#331711yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23C22×C22⋊D1112yes—
712C23C22×C22⋊D1112yes—
713C23C22×C22⋊D1111yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—222no—
717Q8—222no—
718Q8—442no—
719Q8C2×#434114yes—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—48no—
728D4—42no—
729D4—42no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
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—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—448no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4—442no—
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—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22#1062333712yes—
787C22#1062335312yes—
788C22#1062336712yes—
789C22C23×C22⋊D1111yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4#1062333712yes—
801C4C22×#434111yescharacteristic
802C4C2×#6703711yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—82no—
807C2#1308074214yesdirect product factor
808C2C2×#1062333711yescharacteristic
809C2C2×#1062335311yescharacteristic
810C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3317
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
2. #13080742C2direct (N × H)
3. C2×#10622684C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622655C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622688C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622852C2semidirect
12. C2×#10622643C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622846C2semidirect
41. #10623072C22semidirect
47. #10622852C22semidirect
48. #10622852C22semidirect
49. #10622846C22semidirect
50. #10622845C22semidirect
62. #10622688C22semidirect
63. #10622684C22semidirect
64. #10622655C22semidirect
65. #10622654C22semidirect
66. #10622648C22semidirect
67. #10622647C22semidirect
68. #10622643C22semidirect
69. #10622635C22semidirect
70. #10622624C22semidirect
586. C2×C11#3317semidirect
696. C11C2×#3317semidirect
807. C2#13080742direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
#130807422
C2×#106226842
C2×#106226472
C2×#106226482
C2×#106226352
C2×#106226552
C2×#106226542
C2×#106226882
C2×#106228522
C2×#106226432
C2×#106226242
C2×#106228452
C2×#106228462
C2×C11×#5502
C2×#331711