Finite Group Databasebeta

← C2×#13080622 #15630475

Subgroups — C2×#13080622 #15630475

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic, complemented
2#13080622C2116yesmaximal, direct product factor
3C2×#10622684C211yesmaximal, characteristic, complemented
4C2×#10622648C211yesmaximal, characteristic, complemented
5C2×#10622646C211yesmaximal, characteristic, complemented
6C2×#10622635C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622651C211yesmaximal, characteristic, complemented
9C2×#10622685C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622846C211yesmaximal, characteristic, complemented
16C2×C11×#550C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic
19C11×#550—24no—
20C11×#550C2218yescomplemented
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×#4325C2211yescharacteristic
31C2×#66992—21no—
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic
40#10623096—24no—
41#10623096C2218yescomplemented
42C2×#66951—21no—
43C2×#66936—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66923C2211yescharacteristic
47#10622851C2218yescomplemented
48#10622851C2218yescomplemented
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#10622685C2218yescomplemented
63#10622684C2218yescomplemented
64#10622652C2218yescomplemented
65#10622651C2218yescomplemented
66#10622648C2218yescomplemented
67#10622646C2218yescomplemented
68#10622639C2218yescomplemented
69#10622635C2218yescomplemented
70#10622624C2218yescomplemented
71C2×#66873C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×#66871C2211yescharacteristic
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
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C23×Dic11—21no—
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C11×#127—28no—
105C11×#127—22no—
106C11×#127C2314yes—
107C11×#121—22no—
108C11×#121—22no—
109C11×#121—28no—
110C11×#121—28no—
111C11×#121C2314yes—
112C11×#121C2314yes—
113C4×Q8×C11—22no—
114C4×Q8×C11C2314yes—
115C4×D4×C11—28no—
116C4×D4×C11D414yes—
117C4×D4×C11C2314yes—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
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×#4325C2314yes—
130#66992—28no—
131C2×#4323—42no—
132C2×#4323—42no—
133C2×#4323C2314yes—
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×#4318C2314yes—
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yes—
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#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182#66871C2314yes—
183C4⋊(C11⋊C8)C2314yes—
184#66867C2314yes—
185C2×#3309—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C11×#41—28no—
192C11×#41—28no—
193C11×#41—44no—
194C11×#41—44no—
195C11×#41—48no—
196C11×#41—48no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11#4114yes—
200C2×Q8×C11C2412yes—
201C2×D4×C11—24no—
202C2×D4×C11—24no—
203C2×D4×C11—24no—
204C2×D4×C11—24no—
205C2×D4×C11—24no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—24no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—22no—
213C2×D4×C11—42no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—82no—
218C2×D4×C11—82no—
219C2×D4×C11—82no—
220C2×D4×C11C2×D414yes—
221C2×D4×C11C2412yes—
222C2×D4×C11C2412yes—
223C22×C4×C11—21no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—21no—
229C22×C4×C11—24no—
230C22×C4×C11—24no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2411yescharacteristic
242C2×C22⋊D11—24no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—82no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—24no—
250C22×Dic11—82no—
251C2×D44—21no—
252C2×D44—22no—
253C2×D44—22no—
254C2×D44C2412yes—
255C2×C4×D11—24no—
256C2×C4×D11—82no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4C2×D414yes—
260C11×C4⋊C4C2412yes—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4C2×D414yes—
264C11×C22⋊C4C2×D414yes—
265C42×C11—24no—
266C42×C11C2×D412yes—
267C42×C11C2412yes—
268C22⋊Dic11—24no—
269#4325—28no—
270#4323—44no—
271#4323—44no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—24no—
279C4⋊Dic11C2412yes—
280C4⋊Dic11C2412yes—
281C4⋊Dic11C2412yes—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284C4×Dic11—24no—
285#4318—44no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—44no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295C2×#553—111no—
296C2×#550D1111yescharacteristic, complemented
297#3309—1116no—
298C2×#490—111no—
299C2×#482—111no—
300C2×#480—111no—
301C2×#479—111no—
302C2×#469—111no—
303C2×#466—111no—
304C2×#459—111no—
305C2×#449—111no—
306C2×#449—111no—
307C2×#440—111no—
308C2×#435—111no—
309C2×#417—111no—
310C2×#416—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11C22×D412yes—
326C23×C11C22×D412yes—
327C23×C11C22×D411yescharacteristic
328C22×D11—22no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332Q8×C11—24no—
333Q8×C11—22no—
334Q8×C11C2×#4114yes—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—44no—
340D4×C11—48no—
341D4×C11—48no—
342D4×C11—48no—
343D4×C11—42no—
344D4×C11—42no—
345D4×C11—84no—
346D4×C11—84no—
347D4×C11—84no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—24no—
355C2×C4×C11—24no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—48no—
362C2×C4×C11—48no—
363C2×C4×C11—42no—
364C2×C4×C11C22×D412yes—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D412yes—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C2×#4112yes—
370C2×C4×C11H(5,𝔽2)12yes—
371C2×C4×C11C2511yescharacteristic
372C22⋊D11—48no—
373C22⋊D11—84no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—84no—
381D44—22no—
382D44—22no—
383D44—42no—
384C4×D11—84no—
385C11⋊C8—22no—
386C11⋊C8—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C22×#41C2×D1111yescharacteristic
390C22×#41C2×D1111yescharacteristic
391C22×SD16—111no—
392C22×D8—111no—
393C22×D8—111no—
394C22×M16—111no—
395C23×C8—111no—
396#553—118no—
397#553—224no—
398#550—24no—
399#550C2×D1118yescomplemented
400C2×#127—21no—
401C2×#127C2×D1111yescharacteristic
402C2×#126—221no—
403C2×#125—111no—
404C2×#123—221no—
405C2×#121—21no—
406C2×#121—21no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#121C2×D1111yescharacteristic
411C2×#121C2×D1111yescharacteristic
412C2×C4×Q8C2×D1111yescharacteristic
413C2×C4×D4—21no—
414C2×C4×D4—111no—
415C2×C4×D4—221no—
416C2×C4×D4C2×D1111yescharacteristic
417C2×#117—111no—
418C22×C4⋊C4—111no—
419#490—118no—
420#482—118no—
421#480—118no—
422#479—118no—
423#469—118no—
424#466—118no—
425#459—118no—
426#449—118no—
427#449—118no—
428#440—118no—
429#435—118no—
430C2×#107—111no—
431C2×#107—111no—
432C2×#106—111no—
433C2×C4⋊C8—111no—
434#417—118no—
435#416—118no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#102—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×C22⋊C8—111no—
447C2×C22⋊C8—111no—
448C2×#97—111no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—44no—
456C22×C11—44no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—84no—
464C22×C11—84no—
465C22×C11#54612yes—
466C22×C11#57512yes—
467C22×C11#57612yes—
468C22×C11C23×D411yescharacteristic
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—84no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—24no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—42no—
479C4×C11#54612yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—42no—
483Dic11—42no—
484Dic11—42no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—42no—
490C2×#41—42no—
491C2×#41C22×D1114yes—
492C2×#41C22×D1114yes—
493C22×Q8C22×D1111yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—111no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4C22⋊D1111yescharacteristic
504C22×D4C22×D1111yescharacteristic
505C22×D4C22×D1111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—224no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—442no—
517C2×D8—442no—
518C2×M16—114no—
519C2×M16—442no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—114no—
525C22×C8—442no—
526#127—28no—
527#127—22no—
528#127C22×D1114yes—
529#126—228no—
530#125—114no—
531#125—222no—
532#123—228no—
533#121—22no—
534#121—22no—
535#121—28no—
536#121—28no—
537#121—114no—
538#121—114no—
539#121—228no—
540#121—222no—
541#121—222no—
542#121C22×D1114yes—
543#121C22×D1114yes—
544C4×Q8—22no—
545C4×Q8C22×D1114yes—
546C4×D4—28no—
547C4×D4—114no—
548C4×D4—228no—
549C4×D4—222no—
550C4×D4C22⋊D1114yes—
551C4×D4C22×D1114yes—
552#117—114no—
553#117—222no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4C22⋊D1111yescharacteristic
564C2×C4⋊C4C22×D1111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4C22⋊D1111yescharacteristic
572C2×C22⋊C4C22⋊D1111yescharacteristic
573C2×C42—21no—
574C2×C42—221no—
575C2×C42C22×D1111yescharacteristic
576#107—114no—
577#107—114no—
578#106—114no—
579C4⋊C8—114no—
580#103—114no—
581#103—114no—
582#103—114no—
583#102—114no—
584#102—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590C22⋊C8—114no—
591C22⋊C8—114no—
592#97—114no—
593C2×C11—42no—
594C2×C11—42no—
595C2×C11—82no—
596C2×C11—82no—
597C2×C11#330914yescomplemented
598C2×C11C2×#54611yescharacteristic
599C2×C11C2×#57511yescharacteristic
600C2×C11C2×#57611yescharacteristic
601D11—82no—
602C24—21no—
603C24—21no—
604C24—221no—
605C24C2×C22⋊D1111yescharacteristic
606C24C2×C22⋊D1111yescharacteristic
607#41—28no—
608#41—28no—
609#41—44no—
610#41—44no—
611#41—48no—
612#41—48no—
613C2×Q8—22no—
614C2×Q8—21no—
615C2×Q8#434114yes—
616C2×Q8C23×D1112yes—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—24no—
629C2×D4—42no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—82no—
634C2×D4—82no—
635C2×D4—82no—
636C2×D4—112no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—222no—
640C2×D4—222no—
641C2×D4—221no—
642C2×D4—444no—
643C2×D4—882no—
644C2×D4C2×C22⋊D1114yes—
645C2×D4C23×D1112yes—
646C2×D4C23×D1112yes—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—882no—
663C22×C4—882no—
664C22×C4C2×C22⋊D1112yes—
665C22×C4C2×C22⋊D1112yes—
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—228no—
674D8—444no—
675D8—444no—
676M16—444no—
677C2×C8—112no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8—222no—
685C2×C8—444no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—112no—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—221no—
692C4⋊C4—221no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C4⋊C4C2×C22⋊D1114yes—
698C4⋊C4C23×D1112yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4C2×C22⋊D1114yes—
706C22⋊C4C2×C22⋊D1114yes—
707C42—24no—
708C42—224no—
709C42C2×C22⋊D1112yes—
710C42C23×D1112yes—
711C11C2×#330911yescharacteristic, complemented, Sylow
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—222no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23C22×C22⋊D1112yes—
731C23C22×C22⋊D1112yes—
732C23C22×C22⋊D1111yescharacteristic
733Q8—24no—
734Q8—22no—
735Q8C2×#434114yes—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—44no—
741D4—48no—
742D4—48no—
743D4—48no—
744D4—42no—
745D4—42no—
746D4—84no—
747D4—84no—
748D4—84no—
749D4—222no—
750D4—222no—
751D4—448no—
752D4—442no—
753D4—884no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—42no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—884no—
777C2×C4—884no—
778C2×C4C2×#434112yes—
779C2×C4#6703712yes—
780C2×C4C22×C22⋊D1112yes—
781C2×C4C22×C22⋊D1112yes—
782C2×C4C22×C22⋊D1112yes—
783C2×C4C22×C22⋊D1112yes—
784C2×C4C22×C22⋊D1111yescharacteristic
785C2×C4C24×D1111yescharacteristic
786C8—222no—
787C8—222no—
788C8—222no—
789C8—222no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—84no—
805C22—84no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—884no—
810C22#1062333712yes—
811C22#1062335312yes—
812C22#1062336612yes—
813C22C23×C22⋊D1111yescharacteristic
814C4—22no—
815C4—22no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—442no—
821C4—442no—
822C4—442no—
823C4#1062333712yes—
824C4C22×#434111yescharacteristic
825C4C2×#6703711yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—82no—
830C2—882no—
831C2#1308062214yesdirect product factor
832C2C2×#1062333711yescharacteristic
833C2C2×#1062335311yescharacteristic
834C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3309
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×#10623096C2semidirect
2. #13080622C2direct (N × H)
3. C2×#10622684C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622646C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622651C2semidirect
9. C2×#10622685C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622639C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622846C2semidirect
16. C2×C11×#550C2semidirect
20. C11×#550C22semidirect
41. #10623096C22semidirect
47. #10622851C22semidirect
48. #10622851C22semidirect
49. #10622846C22semidirect
50. #10622845C22semidirect
62. #10622685C22semidirect
63. #10622684C22semidirect
64. #10622652C22semidirect
65. #10622651C22semidirect
66. #10622648C22semidirect
67. #10622646C22semidirect
68. #10622639C22semidirect
69. #10622635C22semidirect
70. #10622624C22semidirect
296. C2×#550D11semidirect
399. #550C2×D11semidirect
597. C2×C11#3309semidirect
711. C11C2×#3309semidirect
831. C2#13080622direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
#130806222
C2×#106226842
C2×#106226482
C2×#106226462
C2×#106226352
C2×#106226522
C2×#106226512
C2×#106226852
C2×#106228512
C2×#106226392
C2×#106226242
C2×#106228452
C2×#106228462
C2×C11×#5502
C2×#330911