Finite Group Databasebeta

← C2×#13082284 #15662085

Subgroups — C2×#13082284 #15662085

Order 2816.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67042C211yesmaximal, characteristic, complemented
2C22×#41×D11C211yesmaximal, characteristic, complemented
3#13082284C2132yesmaximal, direct product factor
4C2×#10623365C211yesmaximal, characteristic, complemented
5C2×#10623107C211yesmaximal, characteristic, complemented
6C2×#10623362C211yesmaximal, characteristic, complemented
7C2×#10623143C213yesmaximal, complemented
8C2×#10623081C213yesmaximal, complemented
9C2×#10623248C213yesmaximal, complemented
10C2×#10623140C213yesmaximal, complemented
11C2×#10623139C213yesmaximal, complemented
12C2×#10623246C213yesmaximal, complemented
13C2×#10623078C213yesmaximal, complemented
14C2×D11×#121C213yesmaximal, complemented
15C2×#10623105C211yesmaximal, characteristic, complemented
16C2×C11×#550C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C22×C11×#41C2211yescharacteristic, complemented
19C2×#67042—216no—
20C2×#67042C22116yescomplemented
21C2×#41×D11—216no—
22C2×#41×D11C22116yescomplemented
23C22×#4343C2211yescharacteristic
24C22×#4343C2211yescharacteristic, complemented
25C22×Q8×D11C2211yescharacteristic, complemented
26C22×#4341C2213yescomplemented
27C22×D4×D11C2213yescomplemented
28C22×D4×D11C2213yescomplemented
29C22×D4×D11C2213yescomplemented
30C22×D4×D11C2216yescomplemented
31C22×#4339C2213yescomplemented
32C22×#4339C2213yescomplemented
33C23×D44C2213yescomplemented
34C23×C4×D11C2213yescomplemented
35C11×#550C22116yescomplemented
36C2×C11×#127C2213yescomplemented
37C2×C11×#121C2213yescomplemented
38C2×C11×#121C2213yescomplemented
39C2×C4×Q8×C11C2211yescharacteristic, complemented
40C2×C4×D4×C11C2213yescomplemented
41#10623365C22116yescomplemented
42#10623362C22116yescomplemented
43C2×Q8×Dic11C2211yescharacteristic, complemented
44C2×#66993C2213yescomplemented
45C2×#66992C2213yescomplemented
46C2×#66992C2216yescomplemented
47C2×#66991C2216yescomplemented
48C2×#66991C2213yescomplemented
49C2×#66991C2213yescomplemented
50C2×#66990C2213yescomplemented
51C2×#66990C2216yescomplemented
52C2×#66990C2216yescomplemented
53C2×#66989C2213yescomplemented
54C2×#66983C2213yescomplemented
55C2×C4×C22⋊D11C2213yescomplemented
56C2×C4×C22⋊D11C2213yescomplemented
57C2×#66977C2213yescomplemented
58#10623248C22148yescomplemented
59#10623246C22148yescomplemented
60#10623143C22148yescomplemented
61#10623140C22148yescomplemented
62#10623139C22148yescomplemented
63D11×#121C22148yescomplemented
64#10623107C22116yescomplemented
65#10623105C22116yescomplemented
66#10623081C22148yescomplemented
67#10623078C22148yescomplemented
68C2×#66950C2213yescomplemented
69C2×#66949C2211yescharacteristic, complemented
70C2×#66948C2213yescomplemented
71C2×#66947C2213yescomplemented
72C2×#66946C2213yescomplemented
73C2×C4⋊C4×D11C2213yescomplemented
74C2×#66937C2213yescomplemented
75C2×#66937C2216yescomplemented
76C2×#66936C2213yescomplemented
77C2×#66935C2213yescomplemented
78C2×C22⋊C4×D11C2216yescomplemented
79C2×#66931C2213yescomplemented
80C2×#66928C2213yescomplemented
81C2×C4×D44C2213yescomplemented
82C2×C4×D44C2213yescomplemented
83C2×#66925C2213yescomplemented
84C24×D11C2313yes—
85C24×D11C2316yes—
86C2×C11×#41—28no—
87C2×C11×#41—28no—
88C2×C11×#41C2318yescomplemented
89C2×C11×#41C2318yescomplemented
90C22×Q8×C11C2311yescharacteristic
91C22×D4×C11C2313yes—
92C22×D4×C11C2313yes—
93C22×D4×C11C2313yes—
94C22×D4×C11C2316yes—
95C23×C4×C11C2313yes—
96C23×C4×C11C2313yes—
97C22×C22⋊D11C2313yes—
98C22×C22⋊D11C2313yes—
99C22×C22⋊D11C2316yes—
100C22×C22⋊D11C2313yes—
101C22×C22⋊D11C2313yes—
102C22×C22⋊D11C2316yes—
103C23×Dic11C2313yes—
104#67042—2128no—
105#41×D11—2128no—
106C2×#4343—28no—
107C2×#4343D4116yescomplemented
108C2×#4343C2318yes—
109C2×#4343C2318yescomplemented
110C2×Q8×D11—28no—
111C2×Q8×D11C2318yescomplemented
112C2×#4341—224no—
113C2×#4341C23124yescomplemented
114C2×D4×D11—224no—
115C2×D4×D11—224no—
116C2×D4×D11—224no—
117C2×D4×D11—424no—
118C2×D4×D11C23124yescomplemented
119C2×D4×D11C23124yescomplemented
120C2×D4×D11C23124yescomplemented
121C2×D4×D11C23148yescomplemented
122C2×#4339—224no—
123C2×#4339—224no—
124C2×#4339C23124yescomplemented
125C2×#4339C23124yescomplemented
126C22×D44—224no—
127C22×D44C2313yes—
128C22×D44C2313yes—
129C22×D44C2313yes—
130C22×D44C2313yes—
131C22×D44C23124yescomplemented
132C22×C4×D11—224no—
133C22×C4×D11C2313yes—
134C22×C4×D11C2313yes—
135C22×C4×D11C2313yes—
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2316yes—
138C22×C4×D11C2313yes—
139C22×C4×D11C23124yescomplemented
140C22×Dic22C2313yes—
141C22×Dic22C2311yescharacteristic
142C11×#127C23124yescomplemented
143C11×#121C23124yescomplemented
144C11×#121C23124yescomplemented
145C4×Q8×C11C2318yescomplemented
146C4×D4×C11C23124yescomplemented
147C2×C11×C4⋊C4C2313yes—
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4C2313yes—
150C2×C11×C22⋊C4C2313yes—
151C2×C42×C11C2313yes—
152C2×C22⋊Dic11C2313yes—
153C2×C22⋊Dic11C2316yes—
154C2×C22⋊Dic11C2313yes—
155Q8×Dic11C2318yescomplemented
156#66993C23124yescomplemented
157#66992C23124yescomplemented
158#66992C23148yescomplemented
159#66991C23124yescomplemented
160#66991C23124yescomplemented
161#66991C23148yescomplemented
162#66990C23148yescomplemented
163#66990C23148yescomplemented
164#66990C23124yescomplemented
165#66989C23124yescomplemented
166#66983C23124yescomplemented
167C4×C22⋊D11C23124yescomplemented
168C4×C22⋊D11C23124yescomplemented
169C2×(C2×D11)⋊C4C2313yes—
170C2×(C2×D11)⋊C4C2313yes—
171C2×(C2×D11)⋊C4C2311yescharacteristic
172C2×(C2×D11)⋊C4C2313yes—
173C2×(C2×D11)⋊C4C2316yes—
174C2×(C2×D11)⋊C4C2313yes—
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×C4⋊Dic11C2313yes—
177C2×C4⋊Dic11C2313yes—
178#66977C23124yescomplemented
179C2×Dic11⋊C4C2311yescharacteristic
180C2×Dic11⋊C4C2313yes—
181C2×Dic11⋊C4C2313yes—
182C2×Dic11⋊C4C2311yescharacteristic
183C2×C4×Dic11C2313yes—
184#66950C23124yescomplemented
185#66949C2318yescomplemented
186#66948C23124yescomplemented
187#66947C23124yescomplemented
188#66946C23124yescomplemented
189C4⋊C4×D11C23124yescomplemented
190#66937C23124yescomplemented
191#66937C23148yescomplemented
192#66936C23124yescomplemented
193#66935C23124yescomplemented
194C22⋊C4×D11C23148yescomplemented
195#66931C23124yescomplemented
196#66928C23124yescomplemented
197C4×D44C23124yescomplemented
198C4×D44C23124yescomplemented
199#66925C23124yescomplemented
200C2×#3488—111nomaximal, Sylow
201C24×C11C2413yes—
202C24×C11C2413yes—
203C23×D11—212no—
204C23×D11—212no—
205C23×D11—224no—
206C23×D11—46no—
207C23×D11—412no—
208C23×D11—412no—
209C23×D11C2413yes—
210C23×D11C24112yes—
211C23×D11C2413yes—
212C23×D11C2411yescharacteristic
213C23×D11C24124yes—
214C11×#41—232no—
215C11×#41—232no—
216C2×Q8×C11C2×D418yescomplemented
217C2×Q8×C11C2414yes—
218C2×D4×C11—212no—
219C2×D4×C11—212no—
220C2×D4×C11—412no—
221C2×D4×C11—46no—
222C2×D4×C11C24112yes—
223C2×D4×C11C24112yes—
224C2×D4×C11C24112yes—
225C2×D4×C11C24124yes—
226C22×C4×C11—212no—
227C22×C4×C11—212no—
228C22×C4×C11C2411yescharacteristic
229C22×C4×C11C2413yes—
230C22×C4×C11C2411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C22×C4×C11C24112yes—
233C22×C4×C11C24112yes—
234C22×C4×C11C2413yes—
235C2×C22⋊D11—212no—
236C2×C22⋊D11—212no—
237C2×C22⋊D11—224no—
238C2×C22⋊D11—212no—
239C2×C22⋊D11—412no—
240C2×C22⋊D11—46no—
241C2×C22⋊D11C24112yes—
242C2×C22⋊D11C24112yes—
243C2×C22⋊D11C24124yes—
244C2×C22⋊D11C24112yes—
245C2×C22⋊D11C24112yes—
246C2×C22⋊D11C24124yes—
247C22×Dic11—212no—
248C22×Dic11C24112yes—
249C22×Dic11C2411yescharacteristic
250C22×Dic11C2413yes—
251C22×Dic11C2411yescharacteristic
252C22×Dic11C2413yes—
253C22×Dic11C2411yescharacteristic
254#4343—232no—
255#4343C2×D4164yescomplemented
256Q8×D11—232no—
257#4341—296no—
258D4×D11—296no—
259D4×D11—296no—
260D4×D11—296no—
261D4×D11—496no—
262#4339—296no—
263#4339—296no—
264C2×D44—296no—
265C2×D44—212no—
266C2×D44—212no—
267C2×D44—212no—
268C2×D44C2×D4124yescomplemented
269C2×D44C24112yes—
270C2×D44C24112yes—
271C2×D44C24112yes—
272C2×D44C24112yes—
273C2×C4×D11—24no—
274C2×C4×D11—296no—
275C2×C4×D11—212no—
276C2×C4×D11—212no—
277C2×C4×D11—212no—
278C2×C4×D11—412no—
279C2×C4×D11C2×D4124yescomplemented
280C2×C4×D11C24112yes—
281C2×C4×D11C24112yes—
282C2×C4×D11C24112yes—
283C2×C4×D11C2414yes—
284C2×C4×D11C24124yes—
285C2×C4×D11C24112yes—
286C2×Dic22—24no—
287C2×Dic22—212no—
288C2×Dic22C24112yes—
289C2×Dic22C2414yes—
290C11×C4⋊C4C24112yes—
291C11×C4⋊C4C2414yes—
292C11×C22⋊C4C24112yes—
293C11×C22⋊C4C24112yes—
294C42×C11C24112yes—
295C22⋊Dic11C24112yes—
296C22⋊Dic11C24124yes—
297C22⋊Dic11C24112yes—
298(C2×D11)⋊C4C24112yes—
299(C2×D11)⋊C4C24112yes—
300(C2×D11)⋊C4C2414yes—
301(C2×D11)⋊C4C24112yes—
302(C2×D11)⋊C4C24124yes—
303(C2×D11)⋊C4C24112yes—
304(C2×D11)⋊C4C2414yes—
305C4⋊Dic11C24112yes—
306C4⋊Dic11C24112yes—
307Dic11⋊C4C2414yes—
308Dic11⋊C4C24112yes—
309Dic11⋊C4C24112yes—
310Dic11⋊C4C2414yes—
311C4×Dic11C24112yes—
312C22×H(5,𝔽2)—111no—
313C23×#41—111no—
314#3488—1132no—
315C2×#550—111no—
316C2×#550D1111yescharacteristic, complemented
317C2×#548—111no—
318C2×#548—111no—
319C2×#546—113no—
320C2×#546—113no—
321C2×D42—113no—
322C2×D42—113no—
323C2×#537—113no—
324C2×#535—113no—
325C2×#525—113no—
326C22×#121—113no—
327C2×#520—111no—
328C23×C11—26no—
329C23×C11—26no—
330C23×C11—26no—
331C23×C11—26no—
332C23×C11—26no—
333C23×C11—26no—
334C23×C11C2516yes—
335C23×C11C2516yes—
336C23×C11C2511yescharacteristic
337C22×D11—22no—
338C22×D11—26no—
339C22×D11—22no—
340C22×D11—26no—
341C22×D11—26no—
342C22×D11—26no—
343C22×D11—26no—
344C22×D11—224no—
345C22×D11—224no—
346C22×D11—248no—
347C22×D11—412no—
348C22×D11—448no—
349C22×D11—424no—
350C22×D11—424no—
351C22×D11—848no—
352C22×D11C22×D4112yes—
353C22×D11H(5,𝔽2)14yescomplemented
354C22×D11C2516yes—
355C22×D11C2516yes—
356C22×D11C2512yes—
357Q8×C11C22×D4116yescomplemented
358D4×C11—224no—
359D4×C11—224no—
360D4×C11—424no—
361D4×C11—412no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—26no—
365C2×C4×C11—22no—
366C2×C4×C11—224no—
367C2×C4×C11—224no—
368C2×C4×C11C22×D4112yes—
369C2×C4×C11C2512yes—
370C2×C4×C11C2516yes—
371C2×C4×C11C2512yes—
372C2×C4×C11C2512yes—
373C2×C4×C11C2516yes—
374C22⋊D11—224no—
375C22⋊D11—248no—
376C22⋊D11—224no—
377C22⋊D11—224no—
378C22⋊D11—424no—
379C22⋊D11—412no—
380C2×Dic11—26no—
381C2×Dic11—22no—
382C2×Dic11—26no—
383C2×Dic11—22no—
384C2×Dic11—224no—
385C2×Dic11C22×D414yes—
386C2×Dic11C2512yes—
387C2×Dic11C2516yes—
388C2×Dic11C2512yes—
389C2×Dic11C2516yes—
390C2×Dic11C2512yes—
391D44—224no—
392D44—224no—
393D44—224no—
394D44C22×D4148yescomplemented
395C4×D11—224no—
396C4×D11—224no—
397C4×D11—224no—
398C4×D11—28no—
399C4×D11—424no—
400C4×D11C22×D4148yescomplemented
401Dic22—224no—
402Dic22—28no—
403C2×H(5,𝔽2)—1116no—
404C2×H(5,𝔽2)—2216no—
405C22×#41—1116no—
406C22×#41—111no—
407C22×#41—111no—
408C22×#41—113no—
409C22×#41—113no—
410C22×#41—113no—
411C22×#41—2216no—
412C22×#41C2×D1111yescharacteristic, complemented
413C22×#41C2×D1111yescharacteristic, complemented
414C23×Q8—111no—
415C23×D4—113no—
416C23×D4—113no—
417C23×D4—113no—
418C23×D4—116no—
419C23×D4—113no—
420C24×C4—113no—
421#550—1116no—
422#550C2×D11116yescomplemented
423#548—1116no—
424#548—1116no—
425#546—1148no—
426#546—1148no—
427D42—1148no—
428D42—1148no—
429#537—1148no—
430#535—1148no—
431C2×#127—113no—
432C2×#127C2×D1113yescomplemented
433C2×#124—113no—
434C2×#124—113no—
435#525—1148no—
436C2×#123—113no—
437C2×#123—113no—
438C2×C22⋊Q8—113no—
439C2×C22⋊Q8—111no—
440C2×C22⋊Q8—113no—
441C2×C22⋊Q8—113no—
442C2×#121—113no—
443C2×#121—116no—
444C2×#121—113no—
445C2×#121—116no—
446C2×#121—113no—
447C2×#121—113no—
448C2×#121—1148no—
449C2×#121—113no—
450C2×#121—113no—
451C2×#121—116no—
452C2×#121C2×D1113yescomplemented
453C2×#121C2×D1113yescomplemented
454C2×#120—113no—
455C2×#120—116no—
456C2×#120—116no—
457C2×#120—113no—
458#520—1116no—
459C2×C4×Q8—111no—
460C2×C4×Q8C2×D1111yescharacteristic, complemented
461C2×C4×D4—113no—
462C2×C4×D4—113no—
463C2×C4×D4—113no—
464C2×C4×D4—113no—
465C2×C4×D4—113no—
466C2×C4×D4C2×D1113yescomplemented
467C2×#117—113no—
468C22×C4⋊C4—113no—
469C22×C22⋊C4—116no—
470C22×C11—26no—
471C22×C11—26no—
472C22×C11—26no—
473C22×C11—26no—
474C22×C11—26no—
475C22×C11—26no—
476C22×C11—412no—
477C22×C11—412no—
478C22×C11C23×D412yes—
479C22×C11C2×H(5,𝔽2)12yes—
480C22×C11#58512yes—
481C22×C11C2611yescharacteristic
482C2×D11—22no—
483C2×D11—26no—
484C2×D11—22no—
485C2×D11—26no—
486C2×D11—28no—
487C2×D11—224no—
488C2×D11—26no—
489C2×D11—26no—
490C2×D11—26no—
491C2×D11—448no—
492C2×D11—412no—
493C2×D11—848no—
494C2×D11C23×D4112yes—
495C2×D11C2×H(5,𝔽2)14yescomplemented
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—26no—
499C4×C11—22no—
500C4×C11C23×D4112yes—
501Dic11—26no—
502Dic11—22no—
503Dic11—26no—
504Dic11—22no—
505Dic11C23×D414yes—
506C25—113no—
507C25—116no—
508H(5,𝔽2)—22128no—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41—1116no—
512C2×#41—118no—
513C2×#41—118no—
514C2×#41—1124no—
515C2×#41—1124no—
516C2×#41—1124no—
517C2×#41—2224no—
518C2×#41—2224no—
519C2×#41—2224no—
520C2×#41—22128no—
521C2×#41—228no—
522C2×#41C22×D1118yescomplemented
523C2×#41C22×D1118yescomplemented
524C22×Q8—118no—
525C22×Q8—111no—
526C22×Q8—113no—
527C22×Q8—228no—
528C22×Q8C22×D1111yescharacteristic
529C22×D4—113no—
530C22×D4—116no—
531C22×D4—113no—
532C22×D4—113no—
533C22×D4—113no—
534C22×D4—116no—
535C22×D4—1124no—
536C22×D4—1124no—
537C22×D4—1124no—
538C22×D4—1148no—
539C22×D4—113no—
540C22×D4—113no—
541C22×D4—113no—
542C22×D4—113no—
543C22×D4—1124no—
544C22×D4—2224no—
545C22×D4—2224no—
546C22×D4—2224no—
547C22×D4—2224no—
548C22×D4—4424no—
549C22×D4C22×D1113yes—
550C22×D4C22×D1113yes—
551C22×D4C22×D1113yes—
552C22×D4C22×D1116yes—
553C23×C4—113no—
554C23×C4—113no—
555C23×C4—113no—
556C23×C4—113no—
557C23×C4—113no—
558C23×C4—111no—
559C23×C4—1124no—
560C23×C4—116no—
561C23×C4—2224no—
562C23×C4C22×D1113yes—
563C23×C4C22×D1113yes—
564#127—1124no—
565#127C22×D11124yescomplemented
566#124—1124no—
567#124—1124no—
568#123—1124no—
569#123—1124no—
570C22⋊Q8—1124no—
571C22⋊Q8—118no—
572C22⋊Q8—1124no—
573C22⋊Q8—1124no—
574#121—1148no—
575#121—1124no—
576#121—1124no—
577#121—1148no—
578#121—1124no—
579#121—1124no—
580#121—1124no—
581#121—1124no—
582#121—1148no—
583#121C22×D11124yescomplemented
584#121C22×D11124yescomplemented
585#120—1124no—
586#120—1148no—
587#120—1148no—
588#120—1124no—
589C4×Q8—118no—
590C4×Q8C22×D1118yescomplemented
591C4×D4—1124no—
592C4×D4—1124no—
593C4×D4—1124no—
594C4×D4—1124no—
595C4×D4—1124no—
596C4×D4C22×D11124yescomplemented
597#117—1124no—
598C2×C4⋊C4—113no—
599C2×C4⋊C4—113no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—113no—
603C2×C4⋊C4—113no—
604C2×C4⋊C4—1124no—
605C2×C4⋊C4C22×D1113yes—
606C2×C4⋊C4C22×D1111yescharacteristic
607C2×C22⋊C4—116no—
608C2×C22⋊C4—113no—
609C2×C22⋊C4—113no—
610C2×C22⋊C4—113no—
611C2×C22⋊C4—116no—
612C2×C22⋊C4—113no—
613C2×C22⋊C4—113no—
614C2×C22⋊C4—111no—
615C2×C22⋊C4—111no—
616C2×C22⋊C4—113no—
617C2×C22⋊C4—1148no—
618C2×C22⋊C4C22×D1113yes—
619C2×C22⋊C4C22×D1113yes—
620C2×C42—113no—
621C2×C42C22×D1113yes—
622C2×C11—46no—
623C2×C11—46no—
624C2×C11#348814yescomplemented
625C2×C11C24×D411yescharacteristic
626C2×C11C22×H(5,𝔽2)11yescharacteristic
627C2×C11C2×#58511yescharacteristic
628D11—24no—
629D11—212no—
630D11—46no—
631C24—113no—
632C24—111no—
633C24—113no—
634C24—1112no—
635C24—1124no—
636C24—2212no—
637C24—2212no—
638C24—2224no—
639C24—446no—
640C24—4412no—
641C24—4412no—
642C24C23×D1113yes—
643C24C23×D1113yes—
644#41—232no—
645#41—232no—
646#41—1164no—
647#41—2296no—
648#41—2296no—
649#41—2296no—
650#41—2232no—
651C2×Q8—114no—
652C2×Q8—1112no—
653C2×Q8—224no—
654C2×Q8—2232no—
655C2×Q8—2212no—
656C2×Q8D4×D1118yescomplemented
657C2×Q8C23×D1114yes—
658C2×D4—212no—
659C2×D4—212no—
660C2×D4—412no—
661C2×D4—46no—
662C2×D4—1112no—
663C2×D4—1124no—
664C2×D4—1112no—
665C2×D4—1112no—
666C2×D4—1112no—
667C2×D4—1124no—
668C2×D4—1124no—
669C2×D4—1112no—
670C2×D4—1112no—
671C2×D4—1112no—
672C2×D4—1112no—
673C2×D4—2296no—
674C2×D4—2212no—
675C2×D4—2212no—
676C2×D4—2296no—
677C2×D4—2212no—
678C2×D4—2296no—
679C2×D4—2296no—
680C2×D4—2212no—
681C2×D4—2224no—
682C2×D4—2212no—
683C2×D4—2212no—
684C2×D4—4412no—
685C2×D4—446no—
686C2×D4—4496no—
687C2×D4C23×D11112yes—
688C2×D4C23×D11112yes—
689C2×D4C23×D11112yes—
690C2×D4C23×D11124yes—
691C22×C4—212no—
692C22×C4—212no—
693C22×C4—111no—
694C22×C4—1124no—
695C22×C4—1112no—
696C22×C4—1112no—
697C22×C4—111no—
698C22×C4—113no—
699C22×C4—113no—
700C22×C4—111no—
701C22×C4—1112no—
702C22×C4—1112no—
703C22×C4—1112no—
704C22×C4—114no—
705C22×C4—1124no—
706C22×C4—224no—
707C22×C4—2296no—
708C22×C4—2212no—
709C22×C4—2212no—
710C22×C4—2212no—
711C22×C4—2212no—
712C22×C4—4412no—
713C22×C4C23×D11112yes—
714C22×C4C23×D11112yes—
715C22×C4C23×D1111yescharacteristic
716C22×C4C23×D1113yes—
717C22×C4C23×D1111yescharacteristic
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1113yes—
720C4⋊C4—1112no—
721C4⋊C4—1112no—
722C4⋊C4—114no—
723C4⋊C4—114no—
724C4⋊C4—1112no—
725C4⋊C4—1112no—
726C4⋊C4C23×D11112yes—
727C4⋊C4C23×D1114yes—
728C22⋊C4—1124no—
729C22⋊C4—1112no—
730C22⋊C4—1112no—
731C22⋊C4—1112no—
732C22⋊C4—1124no—
733C22⋊C4—1112no—
734C22⋊C4—1112no—
735C22⋊C4—114no—
736C22⋊C4—114no—
737C22⋊C4—1112no—
738C22⋊C4C23×D11112yes—
739C22⋊C4C23×D11112yes—
740C42—1112no—
741C42C23×D11112yes—
742C11C2×#348811yescharacteristic, complemented, Sylow
743C23—26no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26no—
749C23—1112no—
750C23—114no—
751C23—116no—
752C23—112no—
753C23—116no—
754C23—2224no—
755C23—2224no—
756C23—2248no—
757C23—222no—
758C23—222no—
759C23—226no—
760C23—226no—
761C23—226no—
762C23—226no—
763C23—226no—
764C23—4412no—
765C23—4424no—
766C23—4424no—
767C23—4448no—
768C23—8848no—
769C23C24×D1116yes—
770C23C24×D1116yes—
771C23C24×D1111yescharacteristic
772Q8—228no—
773Q8—2224no—
774Q8C2×D4×D11116yescomplemented
775D4—224no—
776D4—224no—
777D4—424no—
778D4—412no—
779D4—1148no—
780D4—2224no—
781D4—2224no—
782D4—2224no—
783D4—2224no—
784D4—2248no—
785D4—2224no—
786D4—2224no—
787D4—4424no—
788D4—4412no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—26no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—114no—
796C2×C4—112no—
797C2×C4—1148no—
798C2×C4—112no—
799C2×C4—116no—
800C2×C4—116no—
801C2×C4—112no—
802C2×C4—228no—
803C2×C4—2224no—
804C2×C4—2224no—
805C2×C4—222no—
806C2×C4—226no—
807C2×C4—222no—
808C2×C4—226no—
809C2×C4—2224no—
810C2×C4—2224no—
811C2×C4—4424no—
812C2×C4C2×D4×D11112yes—
813C2×C4C24×D1112yes—
814C2×C4C24×D1116yes—
815C2×C4C24×D1112yes—
816C2×C4C24×D1112yes—
817C2×C4C24×D1116yes—
818C22—26no—
819C22—26no—
820C22—26no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—412no—
826C22—1112no—
827C22—114no—
828C22—222no—
829C22—226no—
830C22—222no—
831C22—226no—
832C22—228no—
833C22—2224no—
834C22—226no—
835C22—226no—
836C22—226no—
837C22—4448no—
838C22—4412no—
839C22—8848no—
840C22C22×D4×D1112yes—
841C22#1062345312yes—
842C22D11×H(5,𝔽2)12yes—
843C22C25×D1111yescharacteristic
844C4—22no—
845C4—22no—
846C4—26no—
847C4—22no—
848C4—114no—
849C4—222no—
850C4—226no—
851C4—226no—
852C4—222no—
853C4C22×D4×D11112yes—
854C2—46no—
855C2—46no—
856C2—224no—
857C2—2212no—
858C2—446no—
859C2#1308228414yesdirect product factor
860C2C23×D4×D1111yescharacteristic
861C2C2×D11×H(5,𝔽2)11yescharacteristic
862C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#550C2
socleC23×C11C25
hypercenterC2×#550D11
hypocenterC11C2×#3488
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#67042C2semidirect
2. C22×#41×D11C2semidirect
3. #13082284C2direct (N × H)
4. C2×#10623365C2semidirect
5. C2×#10623107C2semidirect
6. C2×#10623362C2semidirect
7. C2×#10623143C2semidirect
8. C2×#10623081C2semidirect
9. C2×#10623248C2semidirect
10. C2×#10623140C2semidirect
11. C2×#10623139C2semidirect
12. C2×#10623246C2semidirect
13. C2×#10623078C2semidirect
14. C2×D11×#121C2semidirect
15. C2×#10623105C2semidirect
16. C2×C11×#550C2semidirect
17. C22×C11×#41C22semidirect
18. C22×C11×#41C22semidirect
20. C2×#67042C22semidirect
22. C2×#41×D11C22semidirect
24. C22×#4343C22semidirect
25. C22×Q8×D11C22semidirect
26. C22×#4341C22semidirect
27. C22×D4×D11C22semidirect
28. C22×D4×D11C22semidirect
29. C22×D4×D11C22semidirect
30. C22×D4×D11C22semidirect
31. C22×#4339C22semidirect
32. C22×#4339C22semidirect
33. C23×D44C22semidirect
34. C23×C4×D11C22semidirect
35. C11×#550C22semidirect
36. C2×C11×#127C22semidirect
37. C2×C11×#121C22semidirect
38. C2×C11×#121C22semidirect
39. C2×C4×Q8×C11C22semidirect
40. C2×C4×D4×C11C22semidirect
41. #10623365C22semidirect
42. #10623362C22semidirect
43. C2×Q8×Dic11C22semidirect
44. C2×#66993C22semidirect
45. C2×#66992C22semidirect
46. C2×#66992C22semidirect
47. C2×#66991C22semidirect
48. C2×#66991C22semidirect
49. C2×#66991C22semidirect
50. C2×#66990C22semidirect
51. C2×#66990C22semidirect
52. C2×#66990C22semidirect
53. C2×#66989C22semidirect
54. C2×#66983C22semidirect
55. C2×C4×C22⋊D11C22semidirect
56. C2×C4×C22⋊D11C22semidirect
57. C2×#66977C22semidirect
58. #10623248C22semidirect
59. #10623246C22semidirect
60. #10623143C22semidirect
61. #10623140C22semidirect
62. #10623139C22semidirect
63. D11×#121C22semidirect
64. #10623107C22semidirect
65. #10623105C22semidirect
66. #10623081C22semidirect
67. #10623078C22semidirect
68. C2×#66950C22semidirect
69. C2×#66949C22semidirect
70. C2×#66948C22semidirect
71. C2×#66947C22semidirect
72. C2×#66946C22semidirect
73. C2×C4⋊C4×D11C22semidirect
74. C2×#66937C22semidirect
75. C2×#66937C22semidirect
76. C2×#66936C22semidirect
77. C2×#66935C22semidirect
78. C2×C22⋊C4×D11C22semidirect
79. C2×#66931C22semidirect
80. C2×#66928C22semidirect
81. C2×C4×D44C22semidirect
82. C2×C4×D44C22semidirect
83. C2×#66925C22semidirect
88. C2×C11×#41C23semidirect
89. C2×C11×#41C23semidirect
107. C2×#4343D4semidirect
109. C2×#4343C23semidirect
111. C2×Q8×D11C23semidirect
113. C2×#4341C23semidirect
118. C2×D4×D11C23semidirect
119. C2×D4×D11C23semidirect
120. C2×D4×D11C23semidirect
121. C2×D4×D11C23semidirect
124. C2×#4339C23semidirect
125. C2×#4339C23semidirect
131. C22×D44C23semidirect
139. C22×C4×D11C23semidirect
142. C11×#127C23semidirect
143. C11×#121C23semidirect
144. C11×#121C23semidirect
145. C4×Q8×C11C23semidirect
146. C4×D4×C11C23semidirect
155. Q8×Dic11C23semidirect
156. #66993C23semidirect
157. #66992C23semidirect
158. #66992C23semidirect
159. #66991C23semidirect
160. #66991C23semidirect
161. #66991C23semidirect
162. #66990C23semidirect
163. #66990C23semidirect
164. #66990C23semidirect
165. #66989C23semidirect
166. #66983C23semidirect
167. C4×C22⋊D11C23semidirect
168. C4×C22⋊D11C23semidirect
178. #66977C23semidirect
184. #66950C23semidirect
185. #66949C23semidirect
186. #66948C23semidirect
187. #66947C23semidirect
188. #66946C23semidirect
189. C4⋊C4×D11C23semidirect
190. #66937C23semidirect
191. #66937C23semidirect
192. #66936C23semidirect
193. #66935C23semidirect
194. C22⋊C4×D11C23semidirect
195. #66931C23semidirect
196. #66928C23semidirect
197. C4×D44C23semidirect
198. C4×D44C23semidirect
199. #66925C23semidirect
216. C2×Q8×C11C2×D4semidirect
255. #4343C2×D4semidirect
268. C2×D44C2×D4semidirect
279. C2×C4×D11C2×D4semidirect
316. C2×#550D11semidirect
353. C22×D11H(5,𝔽2)semidirect
357. Q8×C11C22×D4semidirect
394. D44C22×D4semidirect
400. C4×D11C22×D4semidirect
412. C22×#41C2×D11semidirect
413. C22×#41C2×D11semidirect
422. #550C2×D11semidirect
432. C2×#127C2×D11semidirect
452. C2×#121C2×D11semidirect
453. C2×#121C2×D11semidirect
460. C2×C4×Q8C2×D11semidirect
466. C2×C4×D4C2×D11semidirect
495. C2×D11C2×H(5,𝔽2)semidirect
522. C2×#41C22×D11semidirect
523. C2×#41C22×D11semidirect
565. #127C22×D11semidirect
583. #121C22×D11semidirect
584. #121C22×D11semidirect
590. C4×Q8C22×D11semidirect
596. C4×D4C22×D11semidirect
624. C2×C11#3488semidirect
656. C2×Q8D4×D11semidirect
742. C11C2×#3488semidirect
774. Q8C2×D4×D11semidirect
859. C2#13082284direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670422
C22×#41×D112
#130822842
C2×#106233652
C2×#106231072
C2×#106233622
C2×#106231432
C2×#106230812
C2×#106232482
C2×#106231402
C2×#106231392
C2×#106232462
C2×#106230782
C2×D11×#1212
C2×#106231052
C2×C11×#5502
C2×#348811