Finite Group Databasebeta

← C2×#13082295 #15662178

Subgroups — C2×#13082295 #15662178

Order 2816.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67040C211yesmaximal, characteristic, complemented
2C22×#41×D11C211yesmaximal, characteristic, complemented
3#13082295C2132yesmaximal, direct product factor
4C2×Q8×D44C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
6C2×#10623362C211yesmaximal, characteristic, complemented
7C2×#10623082C213yesmaximal, complemented
8C2×#10623162C213yesmaximal, complemented
9C2×#10623143C213yesmaximal, complemented
10C2×#10623207C213yesmaximal, complemented
11C2×#10623139C213yesmaximal, complemented
12C2×#10623206C213yesmaximal, complemented
13C2×#10623078C213yesmaximal, complemented
14C2×D11×C22⋊Q8C213yesmaximal, complemented
15C2×#10623105C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C2×#41×D11—216no—
20C2×#41×D11C22116yescomplemented
21C2×#67040—216no—
22C2×#67040C22116yescomplemented
23C22×#4343C2211yescharacteristic
24C22×#4343C2213yescomplemented
25C22×Q8×D11C2211yescharacteristic
26C22×Q8×D11C2213yescomplemented
27C22×Q8×D11C2211yescharacteristic, complemented
28C22×#4341C2213yes—
29C22×D4×D11C2213yes—
30C22×#4339C2213yes—
31C22×#4339C2213yescomplemented
32C22×#4339C2213yescomplemented
33C23×C4×D11C2213yes—
34C11×#548C22116yescomplemented
35C2×C11×#124C2213yescomplemented
36C2×C11×C22⋊Q8C2213yescomplemented
37C2×C11×#121C2213yescomplemented
38C2×C4×Q8×C11C2211yescharacteristic, complemented
39C2×C4×D4×C11C2213yescomplemented
40#10623362C22116yescomplemented
41Q8×C22⋊D11C22116yescomplemented
42C2×#66999C2213yes—
43C2×Q8×Dic11C2211yescharacteristic, complemented
44C2×#66997C2213yescomplemented
45C2×#66992C2213yescomplemented
46C2×#66991C2213yescomplemented
47C2×#66991C2216yescomplemented
48C2×#66990C2213yes—
49C2×#66989C2213yescomplemented
50C2×C4×C22⋊D11C2213yes—
51C2×C4×C22⋊D11C2213yescomplemented
52C2×#66977C2213yescomplemented
53C2×#66977C2213yescomplemented
54#10623207C22148yescomplemented
55#10623206C22148yescomplemented
56#10623162C22148yescomplemented
57D11×C22⋊Q8C22148yescomplemented
58#10623143C22148yescomplemented
59#10623139C22148yescomplemented
60Q8×D44C22116yescomplemented
61#10623105C22116yescomplemented
62#10623082C22148yescomplemented
63#10623078C22148yescomplemented
64C2×#66950C2213yes—
65C2×#66950C2213yescomplemented
66C2×#66949C2213yes—
67C2×#66947C2213yescomplemented
68C2×#66946C2213yescomplemented
69C2×C4⋊C4×D11C2213yescomplemented
70C2×C4⋊C4×D11C2216yescomplemented
71C2×#66937C2211yescharacteristic
72C2×#66937C2216yescomplemented
73C2×#66936C2213yescomplemented
74C2×#66936C2216yescomplemented
75C2×#66936C2216yescomplemented
76C2×#66935C2213yes—
77C2×C22⋊C4×D11C2216yes—
78C2×#66931C2213yescomplemented
79C2×#66931C2216yescomplemented
80C2×C4×D44C2213yes—
81C2×C4×D44C2213yescomplemented
82C2×#66925C2213yescomplemented
83C2×#66922C2213yescomplemented
84C24×D11C2313yes—
85C2×C11×#41—28no—
86C2×C11×#41C2318yes—
87C22×Q8×C11—28no—
88C22×Q8×C11C2313yes—
89C22×Q8×C11C2311yescharacteristic
90C22×Q8×C11C2318yescomplemented
91C22×D4×C11C2313yes—
92C22×D4×C11C2313yes—
93C23×C4×C11C2313yes—
94C23×C4×C11C2313yes—
95C22×C22⋊D11C2316yes—
96C22×C22⋊D11C2313yes—
97C22×C22⋊D11C2311yescharacteristic
98C22×C22⋊D11C2311yescharacteristic
99C22×C22⋊D11C2313yes—
100C23×Dic11C2313yes—
101#41×D11—2128no—
102#67040—2128no—
103C2×#4343—224no—
104C2×#4343D4116yescomplemented
105C2×#4343C2318yes—
106C2×#4343C23124yescomplemented
107C2×Q8×D11—28no—
108C2×Q8×D11—28no—
109C2×Q8×D11—224no—
110C2×Q8×D11C2318yes—
111C2×Q8×D11C2318yescomplemented
112C2×Q8×D11C23124yescomplemented
113C2×#4341—224no—
114C2×#4341C23124yes—
115C2×D4×D11—224no—
116C2×D4×D11C23124yes—
117C2×#4339—224no—
118C2×#4339—224no—
119C2×#4339—224no—
120C2×#4339C23124yes—
121C2×#4339C23124yescomplemented
122C2×#4339C23124yescomplemented
123C22×D44C2311yescharacteristic
124C22×D44C2313yes—
125C22×D44C2313yes—
126C22×C4×D11—224no—
127C22×C4×D11C2313yes—
128C22×C4×D11C2313yes—
129C22×C4×D11C2316yes—
130C22×C4×D11C2313yes—
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C23124yes—
133C22×C4×D11C2316yes—
134C22×C4×D11C2313yes—
135C22×Dic22C2313yes—
136C22×Dic22C2313yes—
137C22×Dic22C2313yes—
138C11×#124C23124yescomplemented
139C11×C22⋊Q8C23124yescomplemented
140C11×#121C23124yescomplemented
141C4×Q8×C11C2318yescomplemented
142C4×D4×C11C23124yescomplemented
143C2×C11×C4⋊C4C2313yes—
144C2×C11×C4⋊C4C2313yes—
145C2×C11×C22⋊C4C2316yes—
146C2×C11×C22⋊C4C2313yes—
147C2×C11×C22⋊C4C2311yescharacteristic
148C2×C42×C11C2313yes—
149C2×C22⋊Dic11C2316yes—
150C2×C22⋊Dic11C2313yes—
151C2×C22⋊Dic11C2313yes—
152#66999C23124yes—
153Q8×Dic11C2318yescomplemented
154#66997C23124yescomplemented
155#66992C23124yescomplemented
156#66991C23148yescomplemented
157#66991C23124yescomplemented
158#66990C23124yes—
159#66989C23124yescomplemented
160C4×C22⋊D11C23124yes—
161C4×C22⋊D11C23124yescomplemented
162C2×(C2×D11)⋊C4C2313yes—
163C2×(C2×D11)⋊C4C2313yes—
164C2×(C2×D11)⋊C4C2313yes—
165C2×(C2×D11)⋊C4C2313yes—
166C2×(C2×D11)⋊C4C2313yes—
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×C4⋊Dic11C2313yes—
169C2×C4⋊Dic11C2316yes—
170C2×C4⋊Dic11C2313yes—
171#66977C23124yescomplemented
172#66977C23124yescomplemented
173C2×Dic11⋊C4C2311yescharacteristic
174C2×Dic11⋊C4C2313yes—
175C2×Dic11⋊C4C2313yes—
176C2×Dic11⋊C4C2316yes—
177C2×Dic11⋊C4C2313yes—
178C2×C4×Dic11C2313yes—
179#66950C23124yes—
180#66950C23124yescomplemented
181#66949C23124yes—
182#66947C23124yescomplemented
183#66946C23124yescomplemented
184C4⋊C4×D11C23148yescomplemented
185C4⋊C4×D11C23124yescomplemented
186#66937C2318yes—
187#66937C23148yescomplemented
188#66936C23124yescomplemented
189#66936C23148yescomplemented
190#66936C23148yescomplemented
191#66935C23124yes—
192C22⋊C4×D11C23148yes—
193#66931C23124yescomplemented
194#66931C23148yescomplemented
195C4×D44C23124yes—
196C4×D44C23124yescomplemented
197#66925C23124yescomplemented
198#66922C23124yescomplemented
199C2×#3489—111nomaximal, Sylow
200C24×C11C2413yes—
201C24×C11C2411yescharacteristic
202C23×D11—212no—
203C23×D11—212no—
204C23×D11—46no—
205C23×D11C2411yescharacteristic
206C23×D11C24112yes—
207C23×D11C2413yes—
208C23×D11C2411yescharacteristic
209C11×#41—232no—
210C2×Q8×C11—232no—
211C2×Q8×C11—212no—
212C2×Q8×C11C2×D418yes—
213C2×Q8×C11C24112yes—
214C2×Q8×C11C2414yes—
215C2×D4×C11—212no—
216C2×D4×C11—46no—
217C2×D4×C11C24112yes—
218C2×D4×C11C24112yes—
219C22×C4×C11—212no—
220C22×C4×C11—212no—
221C22×C4×C11C2413yes—
222C22×C4×C11C2411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2413yes—
225C22×C4×C11C24112yes—
226C22×C4×C11C24112yes—
227C22×C4×C11C2413yes—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—212no—
230C2×C22⋊D11—224no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—46no—
233C2×C22⋊D11C24124yes—
234C2×C22⋊D11C24112yes—
235C2×C22⋊D11C2414yes—
236C2×C22⋊D11C2414yes—
237C2×C22⋊D11C24112yes—
238C22×Dic11—212no—
239C22×Dic11C24112yes—
240C22×Dic11C2411yescharacteristic
241C22×Dic11C2413yes—
242C22×Dic11C2413yes—
243C22×Dic11C2413yes—
244C22×Dic11C2411yescharacteristic
245#4343—296no—
246#4343C2×D4164yescomplemented
247Q8×D11—296no—
248Q8×D11—232no—
249Q8×D11—232no—
250#4341—296no—
251D4×D11—296no—
252#4339—296no—
253#4339—296no—
254#4339—296no—
255C2×D44—212no—
256C2×D44—24no—
257C2×D44C2×D4124yes—
258C2×D44C2414yes—
259C2×D44C24112yes—
260C2×D44C24112yes—
261C2×C4×D11—24no—
262C2×C4×D11—296no—
263C2×C4×D11—212no—
264C2×C4×D11—224no—
265C2×C4×D11—212no—
266C2×C4×D11—212no—
267C2×C4×D11—412no—
268C2×C4×D11C2×D4124yes—
269C2×C4×D11C24112yes—
270C2×C4×D11C24112yes—
271C2×C4×D11C24124yes—
272C2×C4×D11C24112yes—
273C2×C4×D11C2414yes—
274C2×C4×D11C24124yes—
275C2×C4×D11C24112yes—
276C2×Dic22—212no—
277C2×Dic22—212no—
278C2×Dic22—212no—
279C2×Dic22C24112yes—
280C2×Dic22C24112yes—
281C2×Dic22C24112yes—
282C11×C4⋊C4C24112yes—
283C11×C4⋊C4C24112yes—
284C11×C22⋊C4C24124yes—
285C11×C22⋊C4C24112yes—
286C11×C22⋊C4C2414yes—
287C42×C11C24112yes—
288C22⋊Dic11C24124yes—
289C22⋊Dic11C24112yes—
290C22⋊Dic11C24112yes—
291(C2×D11)⋊C4C24112yes—
292(C2×D11)⋊C4C24112yes—
293(C2×D11)⋊C4C24112yes—
294(C2×D11)⋊C4C24112yes—
295(C2×D11)⋊C4C24112yes—
296(C2×D11)⋊C4C2414yes—
297C4⋊Dic11C24112yes—
298C4⋊Dic11C24124yes—
299C4⋊Dic11C24112yes—
300Dic11⋊C4C2414yes—
301Dic11⋊C4C24112yes—
302Dic11⋊C4C24112yes—
303Dic11⋊C4C24124yes—
304Dic11⋊C4C24112yes—
305C4×Dic11C24112yes—
306C22×2−1+4—111no—
307C23×#41—111no—
308#3489—1132no—
309C2×D4×Q8—111no—
310C2×D4×Q8—111no—
311C2×#548—111no—
312C2×#548D1111yescharacteristic, complemented
313C2×#547—113no—
314C2×#547—113no—
315C2×#546—113no—
316C2×#546—113no—
317C2×#537—113no—
318C2×#536—113no—
319C2×#525—113no—
320C22×C22⋊Q8—113no—
321C2×#520—111no—
322C23×C11—26no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—26no—
326C23×C11—26no—
327C23×C11—22no—
328C23×C11C2516yes—
329C23×C11C2512yes—
330C23×C11C2511yescharacteristic
331C22×D11—22no—
332C22×D11—26no—
333C22×D11—26no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—224no—
339C22×D11—224no—
340C22×D11—412no—
341C22×D11—448no—
342C22×D11C22×D4112yes—
343C22×D112−1+414yescomplemented
344C22×D11C2512yes—
345C22×D11C2516yes—
346C22×D11C2512yes—
347Q8×C11—224no—
348Q8×C11C22×D4116yes—
349D4×C11—224no—
350D4×C11—412no—
351C2×C4×C11—26no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—26no—
355C2×C4×C11—224no—
356C2×C4×C11—224no—
357C2×C4×C11C22×D4112yes—
358C2×C4×C11C2516yes—
359C2×C4×C11C2512yes—
360C2×C4×C11C2512yes—
361C2×C4×C11C2516yes—
362C2×C4×C11C2516yes—
363C22⋊D11—224no—
364C22⋊D11—248no—
365C22⋊D11—28no—
366C22⋊D11—28no—
367C22⋊D11—412no—
368C2×Dic11—26no—
369C2×Dic11—26no—
370C2×Dic11—22no—
371C2×Dic11—26no—
372C2×Dic11—224no—
373C2×Dic11C22×D414yes—
374C2×Dic11C2512yes—
375C2×Dic11C2516yes—
376C2×Dic11C2516yes—
377C2×Dic11C2516yes—
378C2×Dic11C2512yes—
379D44—224no—
380D44—28no—
381D44C22×D4148yes—
382C4×D11—224no—
383C4×D11—248no—
384C4×D11—224no—
385C4×D11—224no—
386C4×D11—28no—
387C4×D11—424no—
388C4×D11C22×D4148yes—
389Dic22—224no—
390Dic22—224no—
391Dic22—224no—
392C2×2−1+4—1116no—
393C2×2−1+4—2216no—
394C22×#41—1116no—
395C22×#41—111no—
396C22×#41—113no—
397C22×#41—113no—
398C22×#41—113no—
399C22×#41—113no—
400C22×#41—113no—
401C22×#41—2216no—
402C22×#41C2×D1111yescharacteristic
403C23×Q8—111no—
404C23×Q8—113no—
405C23×Q8—111no—
406C23×Q8C2×D1111yescharacteristic, complemented
407C23×D4—113no—
408C24×C4—113no—
409D4×Q8—1116no—
410D4×Q8—1116no—
411#548—1116no—
412#548C2×D11116yescomplemented
413#547—1148no—
414#547—1148no—
415#546—1148no—
416#546—1148no—
417#537—1148no—
418#536—1148no—
419C2×C4⋊Q8—113no—
420C2×C4⋊Q8—113no—
421C2×#124—113no—
422C2×#124C2×D1113yescomplemented
423#525—1148no—
424C2×#123—113no—
425C2×#123—113no—
426C2×#123—116no—
427C2×#123—116no—
428C2×C22⋊Q8—113no—
429C2×C22⋊Q8—113no—
430C2×C22⋊Q8—113no—
431C2×C22⋊Q8—1148no—
432C2×C22⋊Q8—113no—
433C2×C22⋊Q8—113no—
434C2×C22⋊Q8—113no—
435C2×C22⋊Q8—116no—
436C2×C22⋊Q8—113no—
437C2×C22⋊Q8C2×D1113yescomplemented
438C2×#121—116no—
439C2×#121—113no—
440C2×#121—113no—
441C2×#121—111no—
442C2×#121—116no—
443C2×#121C2×D1113yescomplemented
444C2×#120—113no—
445C2×#120—113no—
446#520—1116no—
447C2×C4×Q8—111no—
448C2×C4×Q8C2×D1111yescharacteristic, complemented
449C2×C4×D4—113no—
450C2×C4×D4—113no—
451C2×C4×D4—113no—
452C2×C4×D4—113no—
453C2×C4×D4—113no—
454C2×C4×D4C2×D1113yescomplemented
455C2×#117—113no—
456C22×C4⋊C4—113no—
457C22×C4⋊C4—116no—
458C22×C22⋊C4—116no—
459C22×C11—22no—
460C22×C11—26no—
461C22×C11—26no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—26no—
465C22×C11—412no—
466C22×C11—44no—
467C22×C11C23×D412yes—
468C22×C11C2×2−1+412yes—
469C22×C11#58512yes—
470C22×C11C2611yescharacteristic
471C2×D11—22no—
472C2×D11—26no—
473C2×D11—22no—
474C2×D11—26no—
475C2×D11—28no—
476C2×D11—224no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—448no—
481C2×D11—44no—
482C2×D11C23×D4112yes—
483C2×D11C2×2−1+414yescomplemented
484C4×C11—22no—
485C4×C11—26no—
486C4×C11—22no—
487C4×C11—26no—
488C4×C11C23×D4112yes—
489Dic11—26no—
490Dic11—26no—
491Dic11—22no—
492Dic11—26no—
493Dic11C23×D414yes—
494C25—113no—
4952−1+4—22128no—
496C2×#41—28no—
497C2×#41—1116no—
498C2×#41—118no—
499C2×#41—1124no—
500C2×#41—1124no—
501C2×#41—1124no—
502C2×#41—1124no—
503C2×#41—1124no—
504C2×#41—2224no—
505C2×#41—2224no—
506C2×#41—2224no—
507C2×#41—2224no—
508C2×#41—2224no—
509C2×#41—22128no—
510C2×#41C22×D1118yes—
511C22×Q8—28no—
512C22×Q8—1124no—
513C22×Q8—118no—
514C22×Q8—118no—
515C22×Q8—113no—
516C22×Q8—113no—
517C22×Q8—113no—
518C22×Q8—2224no—
519C22×Q8—228no—
520C22×Q8—228no—
521C22×Q8C22×D1113yes—
522C22×Q8C22×D1111yescharacteristic
523C22×Q8C22×D1118yescomplemented
524C22×D4—111no—
525C22×D4—113no—
526C22×D4—111no—
527C22×D4—116no—
528C22×D4—113no—
529C22×D4—1124no—
530C22×D4—113no—
531C22×D4—111no—
532C22×D4—113no—
533C22×D4—2224no—
534C22×D4C22×D1113yes—
535C22×D4C22×D1113yes—
536C23×C4—113no—
537C23×C4—113no—
538C23×C4—116no—
539C23×C4—113no—
540C23×C4—113no—
541C23×C4—113no—
542C23×C4—111no—
543C23×C4—1124no—
544C23×C4—116no—
545C23×C4—2224no—
546C23×C4C22×D1113yes—
547C23×C4C22×D1113yes—
548C4⋊Q8—1124no—
549C4⋊Q8—1124no—
550#124—1124no—
551#124C22×D11124yescomplemented
552#123—1124no—
553#123—1124no—
554#123—1148no—
555#123—1148no—
556C22⋊Q8—1124no—
557C22⋊Q8—1124no—
558C22⋊Q8—1124no—
559C22⋊Q8—1124no—
560C22⋊Q8—1124no—
561C22⋊Q8—1124no—
562C22⋊Q8—1148no—
563C22⋊Q8—1124no—
564C22⋊Q8C22×D11124yescomplemented
565#121—1124no—
566#121—1148no—
567#121—1124no—
568#121—118no—
569#121—1148no—
570#121C22×D11124yescomplemented
571#120—1124no—
572#120—1124no—
573C4×Q8—118no—
574C4×Q8C22×D1118yescomplemented
575C4×D4—1124no—
576C4×D4—1124no—
577C4×D4—1124no—
578C4×D4—1124no—
579C4×D4—1124no—
580C4×D4C22×D11124yescomplemented
581#117—1124no—
582C2×C4⋊C4—113no—
583C2×C4⋊C4—113no—
584C2×C4⋊C4—113no—
585C2×C4⋊C4—116no—
586C2×C4⋊C4—116no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—113no—
589C2×C4⋊C4—113no—
590C2×C4⋊C4—1124no—
591C2×C4⋊C4—1148no—
592C2×C4⋊C4C22×D1113yes—
593C2×C4⋊C4C22×D1113yes—
594C2×C22⋊C4—116no—
595C2×C22⋊C4—113no—
596C2×C22⋊C4—113no—
597C2×C22⋊C4—113no—
598C2×C22⋊C4—113no—
599C2×C22⋊C4—113no—
600C2×C22⋊C4—113no—
601C2×C22⋊C4—111no—
602C2×C22⋊C4—113no—
603C2×C22⋊C4—1148no—
604C2×C22⋊C4C22×D1116yes—
605C2×C22⋊C4C22×D1111yescharacteristic
606C2×C22⋊C4C22×D1113yes—
607C2×C42—113no—
608C2×C42C22×D1113yes—
609C2×C11—46no—
610C2×C11—42no—
611C2×C11#348914yescomplemented
612C2×C11C24×D411yescharacteristic
613C2×C11C22×2−1+411yescharacteristic
614C2×C11C2×#58511yescharacteristic
615D11—24no—
616D11—212no—
617D11—42no—
618C24—111no—
619C24—113no—
620C24—111no—
621C24—1112no—
622C24—2212no—
623C24—2212no—
624C24—446no—
625C24C23×D1113yes—
626C24C23×D1111yescharacteristic
627#41—232no—
628#41—1164no—
629#41—2296no—
630#41—2296no—
631#41—2296no—
632#41—2296no—
633#41—2296no—
634C2×Q8—232no—
635C2×Q8—212no—
636C2×Q8—1112no—
637C2×Q8—1112no—
638C2×Q8—1112no—
639C2×Q8—2212no—
640C2×Q8—2296no—
641C2×Q8—2232no—
642C2×Q8—2232no—
643C2×Q8—2212no—
644C2×Q8—2212no—
645C2×Q8D4×D1118yes—
646C2×Q8C23×D11112yes—
647C2×Q8C23×D1114yes—
648C2×D4—212no—
649C2×D4—46no—
650C2×D4—114no—
651C2×D4—1112no—
652C2×D4—114no—
653C2×D4—1124no—
654C2×D4—1112no—
655C2×D4—1124no—
656C2×D4—1112no—
657C2×D4—114no—
658C2×D4—1112no—
659C2×D4—2212no—
660C2×D4—224no—
661C2×D4—224no—
662C2×D4—2296no—
663C2×D4—2224no—
664C2×D4—2212no—
665C2×D4—224no—
666C2×D4—446no—
667C2×D4C23×D11112yes—
668C2×D4C23×D11112yes—
669C22×C4—212no—
670C22×C4—212no—
671C22×C4—111no—
672C22×C4—1124no—
673C22×C4—1112no—
674C22×C4—1112no—
675C22×C4—111no—
676C22×C4—113no—
677C22×C4—113no—
678C22×C4—113no—
679C22×C4—1124no—
680C22×C4—1112no—
681C22×C4—1112no—
682C22×C4—1112no—
683C22×C4—114no—
684C22×C4—1124no—
685C22×C4—224no—
686C22×C4—2296no—
687C22×C4—2212no—
688C22×C4—2224no—
689C22×C4—2212no—
690C22×C4—2212no—
691C22×C4—2212no—
692C22×C4—4412no—
693C22×C4C23×D11112yes—
694C22×C4C23×D11112yes—
695C22×C4C23×D1111yescharacteristic
696C22×C4C23×D1113yes—
697C22×C4C23×D1113yes—
698C22×C4C23×D1111yescharacteristic
699C22×C4C23×D1113yes—
700C4⋊C4—1112no—
701C4⋊C4—1112no—
702C4⋊C4—1112no—
703C4⋊C4—1124no—
704C4⋊C4—1124no—
705C4⋊C4—114no—
706C4⋊C4—1112no—
707C4⋊C4—1112no—
708C4⋊C4C23×D11112yes—
709C4⋊C4C23×D11112yes—
710C22⋊C4—1124no—
711C22⋊C4—1112no—
712C22⋊C4—1112no—
713C22⋊C4—1112no—
714C22⋊C4—1112no—
715C22⋊C4—1112no—
716C22⋊C4—1112no—
717C22⋊C4—114no—
718C22⋊C4—1112no—
719C22⋊C4C23×D11124yes—
720C22⋊C4C23×D1114yes—
721C22⋊C4C23×D11112yes—
722C42—1112no—
723C42C23×D11112yes—
724C11C2×#348911yescharacteristic, complemented, Sylow
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—22no—
730C23—26no—
731C23—1112no—
732C23—114no—
733C23—112no—
734C23—116no—
735C23—112no—
736C23—2224no—
737C23—2224no—
738C23—222no—
739C23—226no—
740C23—222no—
741C23—226no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—4412no—
746C23—4448no—
747C23C24×D1116yes—
748C23C24×D1112yes—
749C23C24×D1111yescharacteristic
750Q8—224no—
751Q8—2224no—
752Q8—2224no—
753Q8—2224no—
754Q8C2×D4×D11116yes—
755D4—224no—
756D4—412no—
757D4—1148no—
758D4—2224no—
759D4—228no—
760D4—228no—
761D4—2248no—
762D4—2224no—
763D4—228no—
764D4—4412no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—22no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—114no—
772C2×C4—112no—
773C2×C4—1148no—
774C2×C4—112no—
775C2×C4—116no—
776C2×C4—116no—
777C2×C4—116no—
778C2×C4—228no—
779C2×C4—2224no—
780C2×C4—2248no—
781C2×C4—2224no—
782C2×C4—226no—
783C2×C4—226no—
784C2×C4—226no—
785C2×C4—222no—
786C2×C4—2224no—
787C2×C4—2224no—
788C2×C4—4424no—
789C2×C4C2×D4×D11112yes—
790C2×C4C24×D1112yes—
791C2×C4C24×D1116yes—
792C2×C4C24×D1116yes—
793C2×C4C24×D1112yes—
794C2×C4C24×D1116yes—
795C22—22no—
796C22—26no—
797C22—22no—
798C22—26no—
799C22—22no—
800C22—26no—
801C22—412no—
802C22—44no—
803C22—1112no—
804C22—114no—
805C22—222no—
806C22—226no—
807C22—226no—
808C22—222no—
809C22—228no—
810C22—2224no—
811C22—222no—
812C22—222no—
813C22—222no—
814C22—4448no—
815C22—444no—
816C22C22×D4×D1112yes—
817C22#1062345312yes—
818C22D11×2−1+412yes—
819C22C25×D1111yescharacteristic
820C4—22no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—114no—
825C4—226no—
826C4—226no—
827C4—222no—
828C4—226no—
829C4C22×D4×D11112yes—
830C2—46no—
831C2—42no—
832C2—224no—
833C2—2212no—
834C2—442no—
835C2#1308229514yesdirect product factor
836C2C23×D4×D1111yescharacteristic
837C2C2×D11×2−1+411yescharacteristic
838C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#548C2
socleC23×C11C25
hypercenterC2×#548D11
hypocenterC11C2×#3489
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#67040C2semidirect
2. C22×#41×D11C2semidirect
3. #13082295C2direct (N × H)
4. C2×Q8×D44C2semidirect
5. C2×Q8×C22⋊D11C2semidirect
6. C2×#10623362C2semidirect
7. C2×#10623082C2semidirect
8. C2×#10623162C2semidirect
9. C2×#10623143C2semidirect
10. C2×#10623207C2semidirect
11. C2×#10623139C2semidirect
12. C2×#10623206C2semidirect
13. C2×#10623078C2semidirect
14. C2×D11×C22⋊Q8C2semidirect
15. C2×#10623105C2semidirect
16. C2×C11×#548C2semidirect
18. C23×Q8×C11C22semidirect
20. C2×#41×D11C22semidirect
22. C2×#67040C22semidirect
24. C22×#4343C22semidirect
26. C22×Q8×D11C22semidirect
27. C22×Q8×D11C22semidirect
31. C22×#4339C22semidirect
32. C22×#4339C22semidirect
34. C11×#548C22semidirect
35. C2×C11×#124C22semidirect
36. C2×C11×C22⋊Q8C22semidirect
37. C2×C11×#121C22semidirect
38. C2×C4×Q8×C11C22semidirect
39. C2×C4×D4×C11C22semidirect
40. #10623362C22semidirect
41. Q8×C22⋊D11C22semidirect
43. C2×Q8×Dic11C22semidirect
44. C2×#66997C22semidirect
45. C2×#66992C22semidirect
46. C2×#66991C22semidirect
47. C2×#66991C22semidirect
49. C2×#66989C22semidirect
51. C2×C4×C22⋊D11C22semidirect
52. C2×#66977C22semidirect
53. C2×#66977C22semidirect
54. #10623207C22semidirect
55. #10623206C22semidirect
56. #10623162C22semidirect
57. D11×C22⋊Q8C22semidirect
58. #10623143C22semidirect
59. #10623139C22semidirect
60. Q8×D44C22semidirect
61. #10623105C22semidirect
62. #10623082C22semidirect
63. #10623078C22semidirect
65. C2×#66950C22semidirect
67. C2×#66947C22semidirect
68. C2×#66946C22semidirect
69. C2×C4⋊C4×D11C22semidirect
70. C2×C4⋊C4×D11C22semidirect
72. C2×#66937C22semidirect
73. C2×#66936C22semidirect
74. C2×#66936C22semidirect
75. C2×#66936C22semidirect
78. C2×#66931C22semidirect
79. C2×#66931C22semidirect
81. C2×C4×D44C22semidirect
82. C2×#66925C22semidirect
83. C2×#66922C22semidirect
90. C22×Q8×C11C23semidirect
104. C2×#4343D4semidirect
106. C2×#4343C23semidirect
111. C2×Q8×D11C23semidirect
112. C2×Q8×D11C23semidirect
121. C2×#4339C23semidirect
122. C2×#4339C23semidirect
138. C11×#124C23semidirect
139. C11×C22⋊Q8C23semidirect
140. C11×#121C23semidirect
141. C4×Q8×C11C23semidirect
142. C4×D4×C11C23semidirect
153. Q8×Dic11C23semidirect
154. #66997C23semidirect
155. #66992C23semidirect
156. #66991C23semidirect
157. #66991C23semidirect
159. #66989C23semidirect
161. C4×C22⋊D11C23semidirect
171. #66977C23semidirect
172. #66977C23semidirect
180. #66950C23semidirect
182. #66947C23semidirect
183. #66946C23semidirect
184. C4⋊C4×D11C23semidirect
185. C4⋊C4×D11C23semidirect
187. #66937C23semidirect
188. #66936C23semidirect
189. #66936C23semidirect
190. #66936C23semidirect
193. #66931C23semidirect
194. #66931C23semidirect
196. C4×D44C23semidirect
197. #66925C23semidirect
198. #66922C23semidirect
246. #4343C2×D4semidirect
312. C2×#548D11semidirect
343. C22×D112−1+4semidirect
406. C23×Q8C2×D11semidirect
412. #548C2×D11semidirect
422. C2×#124C2×D11semidirect
437. C2×C22⋊Q8C2×D11semidirect
443. C2×#121C2×D11semidirect
448. C2×C4×Q8C2×D11semidirect
454. C2×C4×D4C2×D11semidirect
483. C2×D11C2×2−1+4semidirect
523. C22×Q8C22×D11semidirect
551. #124C22×D11semidirect
564. C22⋊Q8C22×D11semidirect
570. #121C22×D11semidirect
574. C4×Q8C22×D11semidirect
580. C4×D4C22×D11semidirect
611. C2×C11#3489semidirect
724. C11C2×#3489semidirect
835. C2#13082295direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670402
C22×#41×D112
#130822952
C2×Q8×D442
C2×Q8×C22⋊D112
C2×#106233622
C2×#106230822
C2×#106231622
C2×#106231432
C2×#106232072
C2×#106231392
C2×#106232062
C2×#106230782
C2×D11×C22⋊Q82
C2×#106231052
C2×C11×#5482
C2×#348911