Finite Group Databasebeta

← C2×#13082407 #15662241

Subgroups — C2×#13082407 #15662241

Order 2816.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67040C211yesmaximal, characteristic, complemented
2C22×#67042C211yesmaximal, characteristic, complemented
3#13082407C2132yesmaximal, direct product factor
4C2×#10623107C211yesmaximal, characteristic, complemented
5C2×#10623348C211yesmaximal, characteristic, complemented
6C2×#10623362C211yesmaximal, characteristic, complemented
7C2×#10623143C213yesmaximal, complemented
8C2×#10623081C213yesmaximal, complemented
9C2×#10623207C213yesmaximal, complemented
10C2×#10623161C213yesmaximal, complemented
11C2×#10623159C213yesmaximal, complemented
12C2×#10623138C213yesmaximal, complemented
13C2×#10623079C213yesmaximal, complemented
14C2×D11×#124C213yesmaximal, complemented
15C2×C4×#4343C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C2×#67042—216no—
20C2×#67042C22116yescomplemented
21C2×#67040—216no—
22C2×#67040C22116yescomplemented
23C22×#4343C2211yescharacteristic
24C22×#4343C2211yescharacteristic
25C22×#4343C2213yescomplemented
26C22×Q8×D11C2213yescomplemented
27C22×Q8×D11C2211yescharacteristic, complemented
28C22×D4×D11C2213yes—
29C22×D4×D11C2213yes—
30C22×#4339C2213yes—
31C22×#4339C2213yescomplemented
32C22×#4339C2213yescomplemented
33C23×D44C2213yes—
34C11×#548C22116yescomplemented
35C2×C11×#124C2213yescomplemented
36C2×C11×C22⋊Q8C2213yescomplemented
37C2×C11×#121C2213yescomplemented
38C2×C4×Q8×C11C2211yescharacteristic, complemented
39C2×C4×D4×C11C2213yescomplemented
40#10623362C22116yescomplemented
41#10623348C22116yescomplemented
42C2×#67000C2213yescomplemented
43C2×#66999C2213yescomplemented
44C2×Q8×Dic11C2211yescharacteristic, complemented
45C2×#66993C2213yescomplemented
46C2×#66991C2213yescomplemented
47C2×#66991C2213yescomplemented
48C2×#66990C2216yescomplemented
49C2×#66989C2213yescomplemented
50C2×#66983C2213yescomplemented
51C2×C4×C22⋊D11C2213yescomplemented
52C2×C4×C22⋊D11C2213yescomplemented
53C2×#66977C2213yescomplemented
54#10623207C22148yescomplemented
55D11×#124C22148yescomplemented
56#10623161C22148yescomplemented
57#10623159C22148yescomplemented
58#10623143C22148yescomplemented
59#10623138C22148yescomplemented
60#10623107C22116yescomplemented
61C4×#4343C22116yescomplemented
62#10623081C22148yescomplemented
63#10623079C22148yescomplemented
64C2×#66950C2213yescomplemented
65C2×#66948C2213yescomplemented
66C2×#66948C2213yescomplemented
67C2×#66947C2216yescomplemented
68C2×#66946C2213yescomplemented
69C2×#66945C2213yescomplemented
70C2×#66941C2213yescomplemented
71C2×#66938C2213yescomplemented
72C2×#66938C2216yescomplemented
73C2×#66938C2211yescharacteristic, complemented
74C2×#66937C2213yescomplemented
75C2×#66937C2213yescomplemented
76C2×#66936C2216yescomplemented
77C2×#66935C2216yescomplemented
78C2×C22⋊C4×D11C2216yescomplemented
79C2×C22⋊C4×D11C2216yescomplemented
80C2×#66928C2213yescomplemented
81C2×C4×D44C2213yescomplemented
82C2×C4×D44C2213yescomplemented
83C2×C42×D11C2213yescomplemented
84C24×D11C2316yes—
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⋊D11C2313yes—
96C22×C22⋊D11C2313yes—
97C22×C22⋊D11C2313yes—
98C22×C22⋊D11C2311yescharacteristic
99C22×C22⋊D11C2313yes—
100C22×C22⋊D11C2313yes—
101#67042—2128no—
102#67040—2128no—
103C2×#4343—28no—
104C2×#4343—224no—
105C2×#4343D4116yescomplemented
106C2×#4343C2318yes—
107C2×#4343C2318yes—
108C2×#4343C23124yescomplemented
109C2×Q8×D11—28no—
110C2×Q8×D11—224no—
111C2×Q8×D11C2318yescomplemented
112C2×Q8×D11C23124yescomplemented
113C2×D4×D11—224no—
114C2×D4×D11—224no—
115C2×D4×D11C23124yes—
116C2×D4×D11C23124yes—
117C2×#4339—224no—
118C2×#4339—224no—
119C2×#4339—224no—
120C2×#4339C23124yes—
121C2×#4339C23124yescomplemented
122C2×#4339C23124yescomplemented
123C22×D44—224no—
124C22×D44C2313yes—
125C22×D44C2313yes—
126C22×D44C2313yes—
127C22×D44C23124yes—
128C22×D44C2313yes—
129C22×D44C2313yes—
130C22×C4×D11C2313yes—
131C22×C4×D11C2313yes—
132C22×C4×D11C2316yes—
133C22×C4×D11C2313yes—
134C22×C4×D11C2313yes—
135C22×C4×D11C2313yes—
136C22×Dic22C2313yes—
137C22×Dic22C2313yes—
138C22×Dic22C2311yescharacteristic
139C11×#124C23124yescomplemented
140C11×C22⋊Q8C23124yescomplemented
141C11×#121C23124yescomplemented
142C4×Q8×C11C2318yescomplemented
143C4×D4×C11C23124yescomplemented
144C2×C11×C4⋊C4C2313yes—
145C2×C11×C4⋊C4C2313yes—
146C2×C11×C22⋊C4C2313yes—
147C2×C11×C22⋊C4C2316yes—
148C2×C11×C22⋊C4C2311yescharacteristic
149C2×C42×C11C2313yes—
150C2×C22⋊Dic11C2313yes—
151C2×C22⋊Dic11C2316yes—
152C2×C22⋊Dic11C2311yescharacteristic
153#67000C23124yescomplemented
154#66999C23124yescomplemented
155Q8×Dic11C2318yescomplemented
156#66993C23124yescomplemented
157#66991C23124yescomplemented
158#66991C23124yescomplemented
159#66990C23148yescomplemented
160#66989C23124yescomplemented
161#66983C23124yescomplemented
162C4×C22⋊D11C23124yescomplemented
163C4×C22⋊D11C23124yescomplemented
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2313yes—
166C2×(C2×D11)⋊C4C2316yes—
167C2×(C2×D11)⋊C4C2316yes—
168C2×(C2×D11)⋊C4C2313yes—
169C2×(C2×D11)⋊C4C2316yes—
170C2×(C2×D11)⋊C4C2311yescharacteristic
171C2×C4⋊Dic11C2313yes—
172C2×C4⋊Dic11C2313yes—
173#66977C23124yescomplemented
174C2×Dic11⋊C4C2313yes—
175C2×Dic11⋊C4C2313yes—
176C2×C4×Dic11C2311yescharacteristic
177C2×C4×Dic11C2313yes—
178C2×C4×Dic11C2313yes—
179#66950C23124yescomplemented
180#66948C23124yescomplemented
181#66948C23124yescomplemented
182#66947C23148yescomplemented
183#66946C23124yescomplemented
184#66945C23124yescomplemented
185#66941C23124yescomplemented
186#66938C2318yescomplemented
187#66938C23124yescomplemented
188#66938C23148yescomplemented
189#66937C23124yescomplemented
190#66937C23124yescomplemented
191#66936C23148yescomplemented
192#66935C23148yescomplemented
193C22⋊C4×D11C23148yescomplemented
194C22⋊C4×D11C23148yescomplemented
195#66928C23124yescomplemented
196C4×D44C23124yescomplemented
197C4×D44C23124yescomplemented
198C42×D11C23124yescomplemented
199C2×#3500—111nomaximal, Sylow
200C24×C11C2413yes—
201C24×C11C2411yescharacteristic
202C23×D11—224no—
203C23×D11—412no—
204C23×D11—412no—
205C23×D11C2413yes—
206C23×D11C2411yescharacteristic
207C23×D11C2413yes—
208C23×D11C24124yes—
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—212no—
231C2×C22⋊D11—212no—
232C2×C22⋊D11—46no—
233C2×C22⋊D11—46no—
234C2×C22⋊D11C24112yes—
235C2×C22⋊D11C24112yes—
236C2×C22⋊D11C24112yes—
237C2×C22⋊D11C2414yes—
238C2×C22⋊D11C24112yes—
239C2×C22⋊D11C24112yes—
240C22×Dic11C2411yescharacteristic
241C22×Dic11C2413yes—
242C22×Dic11C2411yescharacteristic
243C22×Dic11C2413yes—
244C22×Dic11C2411yescharacteristic
245#4343—296no—
246#4343—232no—
247#4343C2×D4164yescomplemented
248Q8×D11—296no—
249Q8×D11—232no—
250D4×D11—296no—
251D4×D11—296no—
252#4339—296no—
253#4339—296no—
254#4339—296no—
255C2×D44—296no—
256C2×D44—212no—
257C2×D44—212no—
258C2×D44—212no—
259C2×D44—46no—
260C2×D44C2×D4124yes—
261C2×D44C24112yes—
262C2×D44C24112yes—
263C2×D44C24112yes—
264C2×D44C24112yes—
265C2×D44C24112yes—
266C2×C4×D11—224no—
267C2×C4×D11—212no—
268C2×C4×D11—212no—
269C2×C4×D11—46no—
270C2×C4×D11—46no—
271C2×C4×D11C2×D4124yes—
272C2×C4×D11C24112yes—
273C2×C4×D11C24112yes—
274C2×C4×D11C24124yes—
275C2×C4×D11C24112yes—
276C2×C4×D11C24112yes—
277C2×C4×D11C24112yes—
278C2×Dic22—24no—
279C2×Dic22—212no—
280C2×Dic22—212no—
281C2×Dic22C24112yes—
282C2×Dic22C24112yes—
283C2×Dic22C2414yes—
284C11×C4⋊C4C24112yes—
285C11×C4⋊C4C24112yes—
286C11×C22⋊C4C24112yes—
287C11×C22⋊C4C24124yes—
288C11×C22⋊C4C2414yes—
289C42×C11C24112yes—
290C22⋊Dic11C24112yes—
291C22⋊Dic11C24124yes—
292C22⋊Dic11C2414yes—
293(C2×D11)⋊C4C2414yes—
294(C2×D11)⋊C4C24112yes—
295(C2×D11)⋊C4C24124yes—
296(C2×D11)⋊C4C24124yes—
297(C2×D11)⋊C4C24112yes—
298(C2×D11)⋊C4C24124yes—
299(C2×D11)⋊C4C2414yes—
300C4⋊Dic11C24112yes—
301C4⋊Dic11C24112yes—
302Dic11⋊C4C24112yes—
303Dic11⋊C4C24112yes—
304C4×Dic11C2414yes—
305C4×Dic11C24112yes—
306C4×Dic11C24112yes—
307C22×2−1+4—111no—
308C22×H(5,𝔽2)—111no—
309#3500—1132no—
310C2×#548—111no—
311C2×#548—111no—
312C2×#548—111no—
313C2×#548D1111yescharacteristic, complemented
314C2×#546—113no—
315C2×#546—113no—
316C2×#546—113no—
317C2×#546—113no—
318C2×#536—113no—
319C2×#535—113no—
320C2×#532—113no—
321C22×#124—113no—
322C2×C4×#41—111no—
323C23×C11—22no—
324C23×C11—26no—
325C23×C11—22no—
326C23×C11—26no—
327C23×C11—22no—
328C23×C11—26no—
329C23×C11C2516yes—
330C23×C11C2512yes—
331C23×C11C2511yescharacteristic
332C22×D11—26no—
333C22×D11—26no—
334C22×D11—22no—
335C22×D11—26no—
336C22×D11—22no—
337C22×D11—26no—
338C22×D11—22no—
339C22×D11—26no—
340C22×D11—248no—
341C22×D11—424no—
342C22×D11—424no—
343C22×D11—848no—
344C22×D11C22×D4112yes—
345C22×D11C2516yes—
346C22×D11C2512yes—
347C22×D11C2516yes—
348Q8×C11—224no—
349Q8×C11C22×D4116yes—
350D4×C11—224no—
351D4×C11—412no—
352C2×C4×C11—26no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—26no—
356C2×C4×C11—224no—
357C2×C4×C11—224no—
358C2×C4×C11C22×D4112yes—
359C2×C4×C11C2516yes—
360C2×C4×C11C2512yes—
361C2×C4×C11C2512yes—
362C2×C4×C11C2516yes—
363C2×C4×C11C2516yes—
364C22⋊D11—224no—
365C22⋊D11—224no—
366C22⋊D11—28no—
367C22⋊D11—224no—
368C22⋊D11—412no—
369C22⋊D11—412no—
370C2×Dic11—26no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—26no—
374C2×Dic11C22×D414yes—
375C2×Dic11C2512yes—
376C2×Dic11C2516yes—
377C2×Dic11C2512yes—
378C2×Dic11C2516yes—
379C2×Dic11C2512yes—
380D44—224no—
381D44—224no—
382D44—224no—
383D44—412no—
384D44C22×D4148yes—
385C4×D11—248no—
386C4×D11—224no—
387C4×D11—224no—
388C4×D11—412no—
389C4×D11—412no—
390C4×D11C22×D4148yes—
391Dic22—224no—
392Dic22—28no—
393Dic22—224no—
394C2×2−1+4—1116no—
395C2×2−1+4—2216no—
396C2×H(5,𝔽2)—1116no—
397C2×H(5,𝔽2)—2216no—
398C22×#41—111no—
399C22×#41—111no—
400C22×#41—113no—
401C22×#41—113no—
402C22×#41—113no—
403C22×#41—113no—
404C22×#41C2×D1111yescharacteristic
405C23×Q8—113no—
406C23×Q8—111no—
407C23×Q8C2×D1111yescharacteristic, complemented
408C23×D4—113no—
409C23×D4—113no—
410C23×D4—113no—
411#548—1116no—
412#548—1116no—
413#548—1116no—
414#548C2×D11116yescomplemented
415#546—1148no—
416#546—1148no—
417#546—1148no—
418#546—1148no—
419#536—1148no—
420#535—1148no—
421#532—1148no—
422C2×C4⋊Q8—113no—
423C2×#127—113no—
424C2×#124—113no—
425C2×#124—113no—
426C2×#124—1148no—
427C2×#124—113no—
428C2×#124—116no—
429C2×#124—111no—
430C2×#124—113no—
431C2×#124C2×D1113yescomplemented
432C2×#123—116no—
433C2×#123—116no—
434C2×C22⋊Q8—113no—
435C2×C22⋊Q8—113no—
436C2×C22⋊Q8—113no—
437C2×C22⋊Q8C2×D1113yescomplemented
438C2×#121—113no—
439C2×#121—113no—
440C2×#121—113no—
441C2×#121—113no—
442C2×#121—113no—
443C2×#121—113no—
444C2×#121—113no—
445C2×#121C2×D1113yescomplemented
446C2×#120—116no—
447C2×#120—116no—
448C4×#41—1116no—
449C2×C4×Q8—111no—
450C2×C4×Q8C2×D1111yescharacteristic, complemented
451C2×C4×D4—113no—
452C2×C4×D4—113no—
453C2×C4×D4—113no—
454C2×C4×D4—113no—
455C2×C4×D4—113no—
456C2×C4×D4C2×D1113yescomplemented
457C2×#117—113no—
458C22×C22⋊C4—116no—
459C22×C22⋊C4—116no—
460C22×C42—113no—
461C22×C11—22no—
462C22×C11—26no—
463C22×C11—22no—
464C22×C11—26no—
465C22×C11—26no—
466C22×C11—22no—
467C22×C11—412no—
468C22×C11—44no—
469C22×C11C23×D412yes—
470C22×C11#58512yes—
471C22×C11#58512yes—
472C22×C11C2611yescharacteristic
473C2×D11—26no—
474C2×D11—26no—
475C2×D11—224no—
476C2×D11—26no—
477C2×D11—22no—
478C2×D11—26no—
479C2×D11—26no—
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—44no—
483C2×D11—412no—
484C2×D11—848no—
485C2×D11C23×D4112yes—
486C4×C11—22no—
487C4×C11—26no—
488C4×C11—26no—
489C4×C11—22no—
490C4×C11C23×D4112yes—
491Dic11—26no—
492Dic11—22no—
493Dic11—22no—
494Dic11—26no—
495Dic11C23×D414yes—
496C25—116no—
4972−1+4—22128no—
498H(5,𝔽2)—22128no—
499C2×#41—28no—
500C2×#41—1116no—
501C2×#41—118no—
502C2×#41—1124no—
503C2×#41—118no—
504C2×#41—1124no—
505C2×#41—1124no—
506C2×#41—1124no—
507C2×#41—2224no—
508C2×#41—2224no—
509C2×#41—2224no—
510C2×#41—2224no—
511C2×#41—228no—
512C2×#41C22×D1118yes—
513C22×Q8—28no—
514C22×Q8—1124no—
515C22×Q8—118no—
516C22×Q8—113no—
517C22×Q8—113no—
518C22×Q8—111no—
519C22×Q8—2224no—
520C22×Q8—228no—
521C22×Q8C22×D1113yes—
522C22×Q8C22×D1111yescharacteristic
523C22×Q8C22×D1118yescomplemented
524C22×D4—113no—
525C22×D4—113no—
526C22×D4—113no—
527C22×D4—111no—
528C22×D4—113no—
529C22×D4—113no—
530C22×D4—1124no—
531C22×D4—1124no—
532C22×D4—113no—
533C22×D4—113no—
534C22×D4—113no—
535C22×D4—113no—
536C22×D4—1124no—
537C22×D4—113no—
538C22×D4—2224no—
539C22×D4—2224no—
540C22×D4—2224no—
541C22×D4C22×D1113yes—
542C22×D4C22×D1113yes—
543C23×C4—113no—
544C23×C4—116no—
545C23×C4—113no—
546C23×C4—113no—
547C23×C4—113no—
548C23×C4—113no—
549C23×C4C22×D1113yes—
550C23×C4C22×D1113yes—
551C4⋊Q8—1124no—
552#127—1124no—
553#124—1124no—
554#124—1124no—
555#124—1124no—
556#124—1148no—
557#124—118no—
558#124—1124no—
559#124C22×D11124yescomplemented
560#123—1148no—
561#123—1148no—
562C22⋊Q8—1124no—
563C22⋊Q8—1124no—
564C22⋊Q8—1124no—
565C22⋊Q8C22×D11124yescomplemented
566#121—1124no—
567#121—1124no—
568#121—1124no—
569#121—1124no—
570#121—1124no—
571#121—1124no—
572#121—1124no—
573#121C22×D11124yescomplemented
574#120—1148no—
575#120—1148no—
576C4×Q8—118no—
577C4×Q8C22×D1118yescomplemented
578C4×D4—1124no—
579C4×D4—1124no—
580C4×D4—1124no—
581C4×D4—1124no—
582C4×D4—1124no—
583C4×D4C22×D11124yescomplemented
584#117—1124no—
585C2×C4⋊C4—113no—
586C2×C4⋊C4—113no—
587C2×C4⋊C4—113no—
588C2×C4⋊C4—113no—
589C2×C4⋊C4C22×D1113yes—
590C2×C4⋊C4C22×D1113yes—
591C2×C22⋊C4—113no—
592C2×C22⋊C4—116no—
593C2×C22⋊C4—111no—
594C2×C22⋊C4—113no—
595C2×C22⋊C4—113no—
596C2×C22⋊C4—116no—
597C2×C22⋊C4—116no—
598C2×C22⋊C4—116no—
599C2×C22⋊C4—111no—
600C2×C22⋊C4—111no—
601C2×C22⋊C4—1148no—
602C2×C22⋊C4—1148no—
603C2×C22⋊C4C22×D1113yes—
604C2×C22⋊C4C22×D1116yes—
605C2×C22⋊C4C22×D1111yescharacteristic
606C2×C42—113no—
607C2×C42—113no—
608C2×C42—111no—
609C2×C42—1124no—
610C2×C42C22×D1113yes—
611C2×C11—46no—
612C2×C11—42no—
613C2×C11#350014yescomplemented
614C2×C11C24×D411yescharacteristic
615C2×C11C2×#58511yescharacteristic
616C2×C11C2×#58511yescharacteristic
617D11—212no—
618D11—42no—
619D11—46no—
620C24—113no—
621C24—113no—
622C24—111no—
623C24—1124no—
624C24—2224no—
625C24—4412no—
626C24—4412no—
627C24C23×D1113yes—
628C24C23×D1111yescharacteristic
629#41—232no—
630#41—1164no—
631#41—2296no—
632#41—2296no—
633#41—2296no—
634#41—2296no—
635#41—2232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—1112no—
639C2×Q8—1112no—
640C2×Q8—114no—
641C2×Q8—2212no—
642C2×Q8—224no—
643C2×Q8—2296no—
644C2×Q8—2232no—
645C2×Q8—2212no—
646C2×Q8D4×D1118yes—
647C2×Q8C23×D11112yes—
648C2×Q8C23×D1114yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—1112no—
652C2×D4—1112no—
653C2×D4—1112no—
654C2×D4—114no—
655C2×D4—1112no—
656C2×D4—1112no—
657C2×D4—1124no—
658C2×D4—1112no—
659C2×D4—1112no—
660C2×D4—1112no—
661C2×D4—1112no—
662C2×D4—1112no—
663C2×D4—2296no—
664C2×D4—2212no—
665C2×D4—2212no—
666C2×D4—2296no—
667C2×D4—2212no—
668C2×D4—224no—
669C2×D4—2296no—
670C2×D4—2212no—
671C2×D4—2212no—
672C2×D4—2212no—
673C2×D4—446no—
674C2×D4—446no—
675C2×D4—446no—
676C2×D4C23×D11112yes—
677C2×D4C23×D11112yes—
678C22×C4—212no—
679C22×C4—212no—
680C22×C4—111no—
681C22×C4—1124no—
682C22×C4—1112no—
683C22×C4—111no—
684C22×C4—113no—
685C22×C4—113no—
686C22×C4—111no—
687C22×C4—1124no—
688C22×C4—1112no—
689C22×C4—1112no—
690C22×C4—1112no—
691C22×C4—1112no—
692C22×C4—2224no—
693C22×C4—2212no—
694C22×C4—2212no—
695C22×C4—446no—
696C22×C4—446no—
697C22×C4C23×D11112yes—
698C22×C4C23×D11112yes—
699C22×C4C23×D1111yescharacteristic
700C22×C4C23×D1113yes—
701C22×C4C23×D1113yes—
702C22×C4C23×D1111yescharacteristic
703C22×C4C23×D1113yes—
704C4⋊C4—1112no—
705C4⋊C4—1112no—
706C4⋊C4—1112no—
707C4⋊C4—1112no—
708C4⋊C4C23×D11112yes—
709C4⋊C4C23×D11112yes—
710C22⋊C4—1112no—
711C22⋊C4—1124no—
712C22⋊C4—114no—
713C22⋊C4—1112no—
714C22⋊C4—1112no—
715C22⋊C4—1124no—
716C22⋊C4—1124no—
717C22⋊C4—1124no—
718C22⋊C4—114no—
719C22⋊C4—114no—
720C22⋊C4C23×D11112yes—
721C22⋊C4C23×D11124yes—
722C22⋊C4C23×D1114yes—
723C42—114no—
724C42—1112no—
725C42—1112no—
726C42C23×D11112yes—
727C11C2×#350011yescharacteristic, complemented, Sylow
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—1112no—
735C23—116no—
736C23—116no—
737C23—112no—
738C23—2248no—
739C23—226no—
740C23—226no—
741C23—222no—
742C23—226no—
743C23—222no—
744C23—226no—
745C23—222no—
746C23—226no—
747C23—4424no—
748C23—4424no—
749C23—8848no—
750C23C24×D1116yes—
751C23C24×D1112yes—
752C23C24×D1111yescharacteristic
753Q8—224no—
754Q8—2224no—
755Q8—228no—
756Q8—2224no—
757Q8C2×D4×D11116yes—
758D4—224no—
759D4—412no—
760D4—1148no—
761D4—2224no—
762D4—2224no—
763D4—2224no—
764D4—228no—
765D4—2224no—
766D4—2224no—
767D4—2224no—
768D4—4412no—
769D4—4412no—
770D4—4412no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—114no—
778C2×C4—112no—
779C2×C4—1148no—
780C2×C4—112no—
781C2×C4—116no—
782C2×C4—116no—
783C2×C4—112no—
784C2×C4—2248no—
785C2×C4—222no—
786C2×C4—226no—
787C2×C4—222no—
788C2×C4—226no—
789C2×C4—2224no—
790C2×C4—2224no—
791C2×C4—4412no—
792C2×C4—4412no—
793C2×C4C2×D4×D11112yes—
794C2×C4C24×D1112yes—
795C2×C4C24×D1116yes—
796C2×C4C24×D1116yes—
797C2×C4C24×D1112yes—
798C2×C4C24×D1116yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—1112no—
808C22—226no—
809C22—226no—
810C22—2224no—
811C22—222no—
812C22—226no—
813C22—222no—
814C22—226no—
815C22—222no—
816C22—226no—
817C22—4412no—
818C22—444no—
819C22—8848no—
820C22C22×D4×D1112yes—
821C22#1062345312yes—
822C22#1062345712yes—
823C22C25×D1111yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—114no—
829C4—222no—
830C4—226no—
831C4—222no—
832C4—226no—
833C4C22×D4×D11112yes—
834C2—46no—
835C2—42no—
836C2—2212no—
837C2—446no—
838C2—442no—
839C2#1308240714yesdirect product factor
840C2C23×D4×D1111yescharacteristic
841C2C2×#1062345311yescharacteristic
842C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#548C2
socleC23×C11C25
hypercenterC2×#548D11
hypocenterC11C2×#3500
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×#67042C2semidirect
3. #13082407C2direct (N × H)
4. C2×#10623107C2semidirect
5. C2×#10623348C2semidirect
6. C2×#10623362C2semidirect
7. C2×#10623143C2semidirect
8. C2×#10623081C2semidirect
9. C2×#10623207C2semidirect
10. C2×#10623161C2semidirect
11. C2×#10623159C2semidirect
12. C2×#10623138C2semidirect
13. C2×#10623079C2semidirect
14. C2×D11×#124C2semidirect
15. C2×C4×#4343C2semidirect
16. C2×C11×#548C2semidirect
18. C23×Q8×C11C22semidirect
20. C2×#67042C22semidirect
22. C2×#67040C22semidirect
25. 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. #10623348C22semidirect
42. C2×#67000C22semidirect
43. C2×#66999C22semidirect
44. C2×Q8×Dic11C22semidirect
45. C2×#66993C22semidirect
46. C2×#66991C22semidirect
47. C2×#66991C22semidirect
48. C2×#66990C22semidirect
49. C2×#66989C22semidirect
50. C2×#66983C22semidirect
51. C2×C4×C22⋊D11C22semidirect
52. C2×C4×C22⋊D11C22semidirect
53. C2×#66977C22semidirect
54. #10623207C22semidirect
55. D11×#124C22semidirect
56. #10623161C22semidirect
57. #10623159C22semidirect
58. #10623143C22semidirect
59. #10623138C22semidirect
60. #10623107C22semidirect
61. C4×#4343C22semidirect
62. #10623081C22semidirect
63. #10623079C22semidirect
64. C2×#66950C22semidirect
65. C2×#66948C22semidirect
66. C2×#66948C22semidirect
67. C2×#66947C22semidirect
68. C2×#66946C22semidirect
69. C2×#66945C22semidirect
70. C2×#66941C22semidirect
71. C2×#66938C22semidirect
72. C2×#66938C22semidirect
73. C2×#66938C22semidirect
74. C2×#66937C22semidirect
75. C2×#66937C22semidirect
76. C2×#66936C22semidirect
77. C2×#66935C22semidirect
78. C2×C22⋊C4×D11C22semidirect
79. C2×C22⋊C4×D11C22semidirect
80. C2×#66928C22semidirect
81. C2×C4×D44C22semidirect
82. C2×C4×D44C22semidirect
83. C2×C42×D11C22semidirect
90. C22×Q8×C11C23semidirect
105. C2×#4343D4semidirect
108. C2×#4343C23semidirect
111. C2×Q8×D11C23semidirect
112. C2×Q8×D11C23semidirect
121. C2×#4339C23semidirect
122. C2×#4339C23semidirect
139. C11×#124C23semidirect
140. C11×C22⋊Q8C23semidirect
141. C11×#121C23semidirect
142. C4×Q8×C11C23semidirect
143. C4×D4×C11C23semidirect
153. #67000C23semidirect
154. #66999C23semidirect
155. Q8×Dic11C23semidirect
156. #66993C23semidirect
157. #66991C23semidirect
158. #66991C23semidirect
159. #66990C23semidirect
160. #66989C23semidirect
161. #66983C23semidirect
162. C4×C22⋊D11C23semidirect
163. C4×C22⋊D11C23semidirect
173. #66977C23semidirect
179. #66950C23semidirect
180. #66948C23semidirect
181. #66948C23semidirect
182. #66947C23semidirect
183. #66946C23semidirect
184. #66945C23semidirect
185. #66941C23semidirect
186. #66938C23semidirect
187. #66938C23semidirect
188. #66938C23semidirect
189. #66937C23semidirect
190. #66937C23semidirect
191. #66936C23semidirect
192. #66935C23semidirect
193. C22⋊C4×D11C23semidirect
194. C22⋊C4×D11C23semidirect
195. #66928C23semidirect
196. C4×D44C23semidirect
197. C4×D44C23semidirect
198. C42×D11C23semidirect
247. #4343C2×D4semidirect
313. C2×#548D11semidirect
407. C23×Q8C2×D11semidirect
414. #548C2×D11semidirect
431. C2×#124C2×D11semidirect
437. C2×C22⋊Q8C2×D11semidirect
445. C2×#121C2×D11semidirect
450. C2×C4×Q8C2×D11semidirect
456. C2×C4×D4C2×D11semidirect
523. C22×Q8C22×D11semidirect
559. #124C22×D11semidirect
565. C22⋊Q8C22×D11semidirect
573. #121C22×D11semidirect
577. C4×Q8C22×D11semidirect
583. C4×D4C22×D11semidirect
613. C2×C11#3500semidirect
727. C11C2×#3500semidirect
839. C2#13082407direct (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×#670422
#130824072
C2×#106231072
C2×#106233482
C2×#106233622
C2×#106231432
C2×#106230812
C2×#106232072
C2×#106231612
C2×#106231592
C2×#106231382
C2×#106230792
C2×D11×#1242
C2×C4×#43432
C2×C11×#5482
C2×#350011