Finite Group Databasebeta

← C2×#41×C22⋊D11 #15660730

Subgroups — C2×#41×C22⋊D11 #15660730

Order 2816.

12314 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×#41×D11C211yesmaximal, characteristic, complemented
2#41×C22⋊D11C2132yesmaximal, direct product factor
3C2×#10623365C211yesmaximal, characteristic, complemented
4C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
5C2×#10623348C211yesmaximal, characteristic, complemented
6C2×#10623362C211yesmaximal, characteristic, complemented
7C2×#10623355C213yesmaximal, complemented
8C2×#10623337C213yesmaximal, complemented
9C2×#10623360C213yesmaximal, complemented
10C2×D4×C22⋊D11C213yesmaximal, complemented
11C2×#10623363C213yesmaximal, complemented
12C2×#10623322C213yesmaximal, complemented
13C2×#10623359C213yesmaximal, complemented
14C2×#41×Dic11C211yesmaximal, characteristic, complemented
15C22×C4×C22⋊D11C213yesmaximal, complemented
16C23×C11×#41C211yesmaximal, characteristic, complemented
17C22×C11×#41—216no—
18C22×C11×#41C2211yescharacteristic
19C22×C11×#41C2213yescomplemented
20C22×C11×#41C2213yescomplemented
21C22×C11×#41C2211yescharacteristic, complemented
22C22×C11×#41C22116yescomplemented
23C23×Q8×C11C2211yescharacteristic, complemented
24C23×D4×C11C2213yescomplemented
25C24×C4×C11C2213yescomplemented
26C23×C22⋊D11C2213yes—
27C2×#41×D11—216no—
28C2×#41×D11C22116yescomplemented
29C22×#4343C2211yescharacteristic, complemented
30C22×Q8×D11C2211yescharacteristic, complemented
31C22×#4341C2213yescomplemented
32C22×D4×D11C2213yescomplemented
33C22×#4339C2213yescomplemented
34C23×C4×D11C2213yescomplemented
35C2×#67006C2216yescomplemented
36C22×C22⋊Dic11C2213yescomplemented
37#10623365C22116yescomplemented
38#10623363C22148yescomplemented
39#10623362C22116yescomplemented
40#10623360C22148yescomplemented
41#10623359C22148yescomplemented
42#41×Dic11C22116yescomplemented
43#10623355C22148yescomplemented
44#10623348C22116yescomplemented
45Q8×C22⋊D11C22116yescomplemented
46C2×#67000C2213yescomplemented
47C2×#66999C2213yescomplemented
48C2×#66999C2213yescomplemented
49C2×Q8×Dic11C2211yescharacteristic, complemented
50C2×Q8×Dic11C2211yescharacteristic, complemented
51C2×#66997C2213yescomplemented
52#10623337C22148yescomplemented
53C2×#66993C2213yescomplemented
54C2×#66992C2216yescomplemented
55C2×#66992C2216yescomplemented
56D4×C22⋊D11C22148yescomplemented
57C2×#66991C2213yescomplemented
58C2×#66991C2213yescomplemented
59C2×#66990C2216yescomplemented
60C2×#66989C2213yescomplemented
61C2×#66988C2216yescomplemented
62C2×D4×Dic11C2213yescomplemented
63C2×D4×Dic11C2213yescomplemented
64#10623322C22148yescomplemented
65C2×#66983C2213yescomplemented
66C2×#66983C2213yescomplemented
67C2×#66982C2216yescomplemented
68C2×C4×C22⋊D11C2211yescharacteristic
69C2×C4×C22⋊D11C2213yes—
70C2×C4×C22⋊D11C2213yescomplemented
71C2×C4×C22⋊D11C2216yescomplemented
72C2×C4×C22⋊D11C2213yescomplemented
73C2×C4×C22⋊D11C2213yescomplemented
74C2×C4×C22⋊D11C2213yescomplemented
75C2×C4×C22⋊D11C2213yescomplemented
76C2×C4×C22⋊D11C2213yescomplemented
77C2×C4×C22⋊D11C22148yescomplemented
78C22×(C2×D11)⋊C4C2213yescomplemented
79C2×#66979C2213yescomplemented
80C2×#66977C2213yescomplemented
81C2×#66977C2213yescomplemented
82C22×Dic11⋊C4C2213yescomplemented
83C22×C4×Dic11C2213yescomplemented
84C25×C11C2313yes—
85C24×D11C2313yes—
86C2×C11×#41—2128no—
87C2×C11×#41—28no—
88C2×C11×#41—224no—
89C2×C11×#41—224no—
90C2×C11×#41D4116yescomplemented
91C2×C11×#41C2318yes—
92C2×C11×#41C23124yescomplemented
93C2×C11×#41C23124yescomplemented
94C2×C11×#41C2318yescomplemented
95C22×Q8×C11—28no—
96C22×Q8×C11C2313yes—
97C22×Q8×C11C2311yescharacteristic
98C22×Q8×C11C2318yescomplemented
99C22×D4×C11—224no—
100C22×D4×C11C2316yes—
101C22×D4×C11C2313yes—
102C22×D4×C11C2313yes—
103C22×D4×C11C23124yescomplemented
104C23×C4×C11—224no—
105C23×C4×C11C2313yes—
106C23×C4×C11C2313yes—
107C23×C4×C11C2313yes—
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2313yes—
110C23×C4×C11C2313yes—
111C23×C4×C11C23124yescomplemented
112C22×C22⋊D11—224no—
113C22×C22⋊D11C2313yes—
114C22×C22⋊D11C2313yes—
115C22×C22⋊D11C23124yes—
116C22×C22⋊D11C2313yes—
117C22×C22⋊D11C2316yes—
118C22×C22⋊D11C2316yes—
119C22×C22⋊D11C2311yescharacteristic
120C23×Dic11C2313yes—
121C23×Dic11C2313yes—
122C23×Dic11C2313yes—
123#41×D11—2128no—
124C2×#4343—28no—
125C2×#4343C2318yescomplemented
126C2×Q8×D11—28no—
127C2×Q8×D11C2318yescomplemented
128C2×#4341—224no—
129C2×#4341C23124yescomplemented
130C2×D4×D11—224no—
131C2×D4×D11C23124yescomplemented
132C2×#4339—224no—
133C2×#4339C23124yescomplemented
134C22×D44C2313yes—
135C22×C4×D11—224no—
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2313yes—
138C22×C4×D11C2313yes—
139C22×C4×D11C2313yes—
140C22×C4×D11C23124yescomplemented
141C22×Dic22C2313yes—
142#67006C23148yescomplemented
143C2×C22⋊Dic11C2313yes—
144C2×C22⋊Dic11C2316yes—
145C2×C22⋊Dic11C2316yes—
146C2×C22⋊Dic11C2311yescharacteristic
147C2×C22⋊Dic11C2313yes—
148C2×C22⋊Dic11C2313yes—
149C2×C22⋊Dic11C23124yescomplemented
150#67000C23124yescomplemented
151#66999C23124yescomplemented
152#66999C23124yescomplemented
153Q8×Dic11C2318yescomplemented
154Q8×Dic11C2318yescomplemented
155#66997C23124yescomplemented
156#66993C23124yescomplemented
157#66992C23148yescomplemented
158#66992C23148yescomplemented
159#66991C23124yescomplemented
160#66991C23124yescomplemented
161#66990C23148yescomplemented
162#66989C23124yescomplemented
163#66988C23148yescomplemented
164D4×Dic11C23124yescomplemented
165D4×Dic11C23124yescomplemented
166#66983C23124yescomplemented
167#66983C23124yescomplemented
168#66982C23148yescomplemented
169C4×C22⋊D11C2318yes—
170C4×C22⋊D11C23124yes—
171C4×C22⋊D11C23124yescomplemented
172C4×C22⋊D11C23124yescomplemented
173C4×C22⋊D11C23124yescomplemented
174C4×C22⋊D11C23124yescomplemented
175C4×C22⋊D11C23124yescomplemented
176C4×C22⋊D11C23124yescomplemented
177C4×C22⋊D11C23148yescomplemented
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2313yes—
180C2×(C2×D11)⋊C4C2313yes—
181C2×(C2×D11)⋊C4C2313yes—
182C2×(C2×D11)⋊C4C2316yes—
183C2×(C2×D11)⋊C4C23124yescomplemented
184#66979C23124yescomplemented
185C2×C4⋊Dic11C2313yes—
186C2×C4⋊Dic11C2313yes—
187#66977C23124yescomplemented
188#66977C23124yescomplemented
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2313yes—
191C2×Dic11⋊C4C2313yes—
192C2×Dic11⋊C4C2313yes—
193C2×Dic11⋊C4C2316yes—
194C2×Dic11⋊C4C23124yescomplemented
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2313yes—
197C2×C4×Dic11C2313yes—
198C2×C4×Dic11C2313yes—
199C2×C4×Dic11C23124yescomplemented
200C2×D4×#41—111nomaximal, Sylow
201C24×C11—212no—
202C24×C11—212no—
203C24×C11—46no—
204C24×C11C2413yes—
205C24×C11C24112yes—
206C24×C11C2413yes—
207C24×C11C2411yescharacteristic
208C23×D11—212no—
209C23×D11—212no—
210C23×D11—46no—
211C23×D11C2413yes—
212C23×D11C24112yes—
213C23×D11C2411yescharacteristic
214C11×#41—232no—
215C11×#41—296no—
216C11×#41—296no—
217C11×#41C2×D4164yescomplemented
218C2×Q8×C11—232no—
219C2×Q8×C11—212no—
220C2×Q8×C11C2×D418yescomplemented
221C2×Q8×C11C24112yes—
222C2×Q8×C11C2414yes—
223C2×D4×C11—224no—
224C2×D4×C11—296no—
225C2×D4×C11—212no—
226C2×D4×C11C2×D4124yescomplemented
227C2×D4×C11C24124yes—
228C2×D4×C11C24112yes—
229C2×D4×C11C24112yes—
230C22×C4×C11—212no—
231C22×C4×C11—24no—
232C22×C4×C11—212no—
233C22×C4×C11—212no—
234C22×C4×C11—212no—
235C22×C4×C11—296no—
236C22×C4×C11C2×D4124yescomplemented
237C22×C4×C11C2411yescharacteristic
238C22×C4×C11C2413yes—
239C22×C4×C11C24112yes—
240C22×C4×C11C24112yes—
241C22×C4×C11C24112yes—
242C22×C4×C11C2414yes—
243C22×C4×C11C24112yes—
244C22×C4×C11C2413yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C24112yes—
247C2×C22⋊D11—296no—
248C2×C22⋊D11—212no—
249C2×C22⋊D11—224no—
250C2×C22⋊D11—212no—
251C2×C22⋊D11—212no—
252C2×C22⋊D11—412no—
253C2×C22⋊D11#4118yesdirect product factor
254C2×C22⋊D11C24112yes—
255C2×C22⋊D11C24112yes—
256C2×C22⋊D11C24112yes—
257C2×C22⋊D11C24124yes—
258C2×C22⋊D11C24124yes—
259C2×C22⋊D11C2414yes—
260C22×Dic11—212no—
261C22×Dic11—212no—
262C22×Dic11—46no—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2413yes—
265C22×Dic11C2413yes—
266C22×Dic11C24112yes—
267C22×Dic11C2413yes—
268C22×Dic11C2411yescharacteristic
269C22×Dic11C24112yes—
270C22×Dic11C24112yes—
271C22×Dic11C2411yescharacteristic
272#4343—232no—
273Q8×D11—232no—
274#4341—296no—
275D4×D11—296no—
276#4339—296no—
277C2×D44—212no—
278C2×D44C24112yes—
279C2×C4×D11—24no—
280C2×C4×D11—212no—
281C2×C4×D11—212no—
282C2×C4×D11—212no—
283C2×C4×D11—296no—
284C2×C4×D11C2414yes—
285C2×C4×D11C24112yes—
286C2×C4×D11C24112yes—
287C2×C4×D11C24112yes—
288C2×Dic22—212no—
289C2×Dic22C24112yes—
290C22⋊Dic11C24112yes—
291C22⋊Dic11C24124yes—
292C22⋊Dic11C24124yes—
293C22⋊Dic11C2414yes—
294C22⋊Dic11C24112yes—
295C22⋊Dic11C24112yes—
296(C2×D11)⋊C4C2414yes—
297(C2×D11)⋊C4C24112yes—
298(C2×D11)⋊C4C24112yes—
299(C2×D11)⋊C4C24112yes—
300(C2×D11)⋊C4C24124yes—
301C4⋊Dic11C24112yes—
302C4⋊Dic11C24112yes—
303Dic11⋊C4C2414yes—
304Dic11⋊C4C24112yes—
305Dic11⋊C4C24112yes—
306Dic11⋊C4C24112yes—
307Dic11⋊C4C24124yes—
308C4×Dic11C2414yes—
309C4×Dic11C24112yes—
310C4×Dic11C24112yes—
311C4×Dic11C24112yes—
312C23×#41—111no—
313C23×#41D1111yescharacteristic, complemented
314D4×#41—1132no—
315C2×#550—111no—
316C2×D4×Q8—111no—
317C2×#548—111no—
318C2×#548—111no—
319C2×#547—113no—
320C2×#546—113no—
321C2×#546—113no—
322C2×D42—113no—
323C2×#532—113no—
324C2×#525—113no—
325C2×#525—113no—
326C2×C4×#41—111no—
327C22×C4×D4—113no—
328C23×C11—22no—
329C23×C11—26no—
330C23×C11—26no—
331C23×C11—22no—
332C23×C11—224no—
333C23×C11—26no—
334C23×C11—26no—
335C23×C11—224no—
336C23×C11—26no—
337C23×C11—412no—
338C23×C11—448no—
339C23×C11C22×D4112yes—
340C23×C11C2×#4114yescomplemented
341C23×C11C2516yes—
342C23×C11C2516yes—
343C23×C11C2512yes—
344C23×C11C2511yescharacteristic
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—26no—
348C22×D11—224no—
349C22×D11—26no—
350C22×D11—26no—
351C22×D11—224no—
352C22×D11—412no—
353C22×D11—448no—
354C22×D11C2×#4114yescomplemented
355C22×D11C2516yes—
356C22×D11C2512yes—
357Q8×C11—224no—
358Q8×C11C22×D4116yescomplemented
359D4×C11—248no—
360D4×C11—224no—
361D4×C11C22×D4148yescomplemented
362C2×C4×C11—22no—
363C2×C4×C11—26no—
364C2×C4×C11—224no—
365C2×C4×C11—28no—
366C2×C4×C11—224no—
367C2×C4×C11—224no—
368C2×C4×C11—224no—
369C2×C4×C11C22×D4112yes—
370C2×C4×C11C22×D414yes—
371C2×C4×C11C22×D4148yescomplemented
372C2×C4×C11C2512yes—
373C2×C4×C11C2516yes—
374C2×C4×C11C2512yes—
375C2×C4×C11C2516yes—
376C22⋊D11—248no—
377C22⋊D11—224no—
378C22⋊D11—224no—
379C22⋊D11—224no—
380C22⋊D11—424no—
381C22⋊D11C2×#41116yesdirect product factor
382C2×Dic11—26no—
383C2×Dic11—22no—
384C2×Dic11—224no—
385C2×Dic11—26no—
386C2×Dic11—22no—
387C2×Dic11—26no—
388C2×Dic11—224no—
389C2×Dic11—412no—
390C2×Dic11C2×#4114yescomplemented
391C2×Dic11C2512yes—
392C2×Dic11C2516yes—
393C2×Dic11C2516yes—
394C2×Dic11C2516yes—
395C2×Dic11C2512yes—
396C2×Dic11C2512yes—
397D44—224no—
398C4×D11—28no—
399C4×D11—224no—
400C4×D11—224no—
401C4×D11—224no—
402Dic22—224no—
403C22×#41—216no—
404C22×#41—1116no—
405C22×#41—111no—
406C22×#41—113no—
407C22×#41—113no—
408C22×#41—2216no—
409C22×#41C2×D1111yescharacteristic
410C22×#41C2×D1113yescomplemented
411C22×#41C2×D1113yescomplemented
412C22×#41C2×D1111yescharacteristic, complemented
413C22×#41C2×D11116yescomplemented
414C23×Q8—111no—
415C23×Q8C2×D1111yescharacteristic, complemented
416C23×D4—113no—
417C23×D4—113no—
418C23×D4C2×D1113yescomplemented
419C24×C4—113no—
420C24×C4C2×D1113yescomplemented
421#550—1116no—
422D4×Q8—1116no—
423#548—1116no—
424#548—1116no—
425#547—1148no—
426#546—1148no—
427#546—1148no—
428D42—1148no—
429#532—1148no—
430C2×C4⋊Q8—113no—
431C2×#127—113no—
432C2×#124—113no—
433C2×#124—113no—
434#525—1148no—
435#525—1148no—
436C2×#123—116no—
437C2×#123—116no—
438C2×C22⋊Q8—113no—
439C2×C22⋊Q8—113no—
440C2×C22⋊Q8—113no—
441C2×C22⋊Q8—113no—
442C2×#121—113no—
443C2×#121—113no—
444C2×#121—116no—
445C2×#121—116no—
446C2×#121—113no—
447C2×#121—113no—
448C2×#120—116no—
449C2×#120—116no—
450C4×#41—1116no—
451C2×C4×Q8—111no—
452C2×C4×Q8—111no—
453C2×C4×D4—113no—
454C2×C4×D4—113no—
455C2×C4×D4—111no—
456C2×C4×D4—113no—
457C2×C4×D4—113no—
458C2×C4×D4—113no—
459C2×C4×D4—113no—
460C2×C4×D4—113no—
461C2×C4×D4—113no—
462C2×C4×D4—113no—
463C2×C4×D4—116no—
464C2×C4×D4—1148no—
465C2×#117—113no—
466C22×C4⋊C4—113no—
467C22×C22⋊C4—113no—
468C22×C22⋊C4—113no—
469C22×C42—113no—
470C22×C11—22no—
471C22×C11—26no—
472C22×C11—26no—
473C22×C11—22no—
474C22×C11—224no—
475C22×C11—28no—
476C22×C11—26no—
477C22×C11—26no—
478C22×C11—26no—
479C22×C11—448no—
480C22×C11—412no—
481C22×C11C23×D4112yes—
482C22×C11C23×D412yes—
483C22×C11C22×#4112yes—
484C22×C11C22×#4114yescomplemented
485C22×C11#58512yes—
486C22×C11C2611yescharacteristic
487C2×D11—22no—
488C2×D11—22no—
489C2×D11—28no—
490C2×D11—26no—
491C2×D11—26no—
492C2×D11—26no—
493C2×D11—448no—
494C2×D11—412no—
495C2×D11C22×#4114yescomplemented
496C4×C11—22no—
497C4×C11—26no—
498C4×C11C23×D414yes—
499C4×C11C23×D4112yes—
500Dic11—26no—
501Dic11—22no—
502Dic11—26no—
503Dic11—22no—
504Dic11—26no—
505Dic11C22×#4114yescomplemented
506C25—113no—
507C25C22×D1113yes—
508C2×#41—2128no—
509C2×#41—28no—
510C2×#41—224no—
511C2×#41—224no—
512C2×#41—118no—
513C2×#41—1124no—
514C2×#41—1124no—
515C2×#41—22128no—
516C2×#41—228no—
517C2×#41—2224no—
518C2×#41—2224no—
519C2×#41C22⋊D11116yesdirect product factor
520C2×#41C22×D1118yes—
521C2×#41C22×D11124yescomplemented
522C2×#41C22×D11124yescomplemented
523C2×#41C22×D1118yescomplemented
524C22×Q8—28no—
525C22×Q8—118no—
526C22×Q8—113no—
527C22×Q8—228no—
528C22×Q8C22×D1113yes—
529C22×Q8C22×D1111yescharacteristic
530C22×Q8C22×D1118yescomplemented
531C22×D4—224no—
532C22×D4—111no—
533C22×D4—113no—
534C22×D4—113no—
535C22×D4—113no—
536C22×D4—1124no—
537C22×D4—116no—
538C22×D4—116no—
539C22×D4—1124no—
540C22×D4—113no—
541C22×D4—2224no—
542C22×D4—2224no—
543C22×D4C22×D1116yes—
544C22×D4C22×D1113yes—
545C22×D4C22×D1113yes—
546C22×D4C22×D11124yescomplemented
547C23×C4—224no—
548C23×C4—113no—
549C23×C4—113no—
550C23×C4—113no—
551C23×C4—113no—
552C23×C4—113no—
553C23×C4—1124no—
554C23×C4—111no—
555C23×C4—113no—
556C23×C4—2224no—
557C23×C4C22×D1113yes—
558C23×C4C22×D1113yes—
559C23×C4C22×D1113yes—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1113yes—
562C23×C4C22×D1113yes—
563C23×C4C22×D11124yescomplemented
564C4⋊Q8—1124no—
565#127—1124no—
566#124—1124no—
567#124—1124no—
568#123—1148no—
569#123—1148no—
570C22⋊Q8—1124no—
571C22⋊Q8—1124no—
572C22⋊Q8—1124no—
573C22⋊Q8—1124no—
574#121—1124no—
575#121—1124no—
576#121—1148no—
577#121—1148no—
578#121—1124no—
579#121—1124no—
580#120—1148no—
581#120—1148no—
582C4×Q8—118no—
583C4×Q8—118no—
584C4×D4—1124no—
585C4×D4—1124no—
586C4×D4—118no—
587C4×D4—1124no—
588C4×D4—1124no—
589C4×D4—1124no—
590C4×D4—1124no—
591C4×D4—1124no—
592C4×D4—1124no—
593C4×D4—1124no—
594C4×D4—1148no—
595#117—1124no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—113no—
598C2×C4⋊C4—113no—
599C2×C4⋊C4—113no—
600C2×C4⋊C4—1124no—
601C2×C4⋊C4—113no—
602C2×C4⋊C4—113no—
603C2×C4⋊C4—116no—
604C2×C22⋊C4—111no—
605C2×C22⋊C4—113no—
606C2×C22⋊C4—113no—
607C2×C22⋊C4—113no—
608C2×C22⋊C4—1124no—
609C2×C22⋊C4—116no—
610C2×C22⋊C4—116no—
611C2×C22⋊C4—111no—
612C2×C22⋊C4—113no—
613C2×C22⋊C4—113no—
614C2×C22⋊C4—113no—
615C2×C22⋊C4—1124no—
616C2×C22⋊C4—116no—
617C2×C42—113no—
618C2×C42—113no—
619C2×C42—1124no—
620C2×C42—113no—
621C2×C42—111no—
622C2×C11—212no—
623C2×C11—24no—
624C2×C11—46no—
625C2×C11D4×#4114yescomplemented
626C2×C11C24×D411yescharacteristic
627C2×C11C23×#4111yescharacteristic
628C2×C11C2×#58511yescharacteristic
629D11—24no—
630D11—46no—
631C24—212no—
632C24—212no—
633C24—46no—
634C24—111no—
635C24—113no—
636C24—1112no—
637C24—2212no—
638C24—2212no—
639C24—446no—
640C24C23×D1113yes—
641C24C23×D11112yes—
642C24C23×D1111yescharacteristic
643C24C23×D1113yes—
644#41—232no—
645#41—296no—
646#41—296no—
647#41—2232no—
648#41—2296no—
649#41—2296no—
650#41C2×C22⋊D11164yesdirect product factor
651C2×Q8—232no—
652C2×Q8—212no—
653C2×Q8—1112no—
654C2×Q8—2232no—
655C2×Q8—2212no—
656C2×Q8C2×C22⋊D1118yescomplemented
657C2×Q8C23×D11112yes—
658C2×Q8C23×D1114yes—
659C2×D4—224no—
660C2×D4—296no—
661C2×D4—212no—
662C2×D4—118no—
663C2×D4—114no—
664C2×D4—1112no—
665C2×D4—1112no—
666C2×D4—1112no—
667C2×D4—1124no—
668C2×D4—1124no—
669C2×D4—1112no—
670C2×D4—2212no—
671C2×D4—2296no—
672C2×D4—2212no—
673C2×D4—2212no—
674C2×D4—2224no—
675C2×D4—2296no—
676C2×D4—2212no—
677C2×D4—4412no—
678C2×D4C2×C22⋊D11124yescomplemented
679C2×D4C23×D11124yes—
680C2×D4C23×D11112yes—
681C2×D4C23×D11112yes—
682C22×C4—212no—
683C22×C4—24no—
684C22×C4—212no—
685C22×C4—212no—
686C22×C4—212no—
687C22×C4—296no—
688C22×C4—111no—
689C22×C4—111no—
690C22×C4—113no—
691C22×C4—113no—
692C22×C4—1112no—
693C22×C4—111no—
694C22×C4—113no—
695C22×C4—1112no—
696C22×C4—1112no—
697C22×C4—114no—
698C22×C4—1112no—
699C22×C4—1112no—
700C22×C4—1112no—
701C22×C4—2212no—
702C22×C4—2212no—
703C22×C4—224no—
704C22×C4—2212no—
705C22×C4—2212no—
706C22×C4—2212no—
707C22×C4—2296no—
708C22×C4—446no—
709C22×C4C2×C22⋊D11124yescomplemented
710C22×C4C23×D1111yescharacteristic
711C22×C4C23×D1113yes—
712C22×C4C23×D11112yes—
713C22×C4C23×D1114yes—
714C22×C4C23×D11112yes—
715C22×C4C23×D11112yes—
716C22×C4C23×D11112yes—
717C22×C4C23×D1113yes—
718C22×C4C23×D11112yes—
719C22×C4C23×D1111yescharacteristic
720C4⋊C4—114no—
721C4⋊C4—1112no—
722C4⋊C4—1112no—
723C4⋊C4—1112no—
724C4⋊C4—1112no—
725C4⋊C4—1112no—
726C4⋊C4—1124no—
727C22⋊C4—114no—
728C22⋊C4—1112no—
729C22⋊C4—1112no—
730C22⋊C4—1112no—
731C22⋊C4—1124no—
732C22⋊C4—1124no—
733C22⋊C4—114no—
734C22⋊C4—1112no—
735C22⋊C4—1112no—
736C22⋊C4—1112no—
737C22⋊C4—1124no—
738C42—114no—
739C42—1112no—
740C42—1112no—
741C42—1112no—
742C11C2×D4×#4111yescharacteristic, complemented, Sylow
743C23—26no—
744C23—26no—
745C23—22no—
746C23—22no—
747C23—26no—
748C23—224no—
749C23—26no—
750C23—224no—
751C23—26no—
752C23—412no—
753C23—448no—
754C23—114no—
755C23—112no—
756C23—116no—
757C23—2224no—
758C23—222no—
759C23—222no—
760C23—226no—
761C23—226no—
762C23—2224no—
763C23—226no—
764C23—4412no—
765C23—4448no—
766C23#41×D1114yescomplemented
767C23C22×C22⋊D11112yes—
768C23C24×D1116yes—
769C23C24×D1112yes—
770C23C24×D1116yes—
771C23C24×D1111yescharacteristic
772Q8—224no—
773Q8—2224no—
774Q8C22×C22⋊D11116yescomplemented
775D4—248no—
776D4—224no—
777D4—1116no—
778D4—2224no—
779D4—2224no—
780D4—2224no—
781D4—2248no—
782D4—2224no—
783D4—4424no—
784D4C22×C22⋊D11148yescomplemented
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—224no—
788C2×C4—28no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—114no—
793C2×C4—112no—
794C2×C4—112no—
795C2×C4—116no—
796C2×C4—116no—
797C2×C4—112no—
798C2×C4—116no—
799C2×C4—2224no—
800C2×C4—226no—
801C2×C4—222no—
802C2×C4—226no—
803C2×C4—222no—
804C2×C4—226no—
805C2×C4—2224no—
806C2×C4—228no—
807C2×C4—2224no—
808C2×C4—2224no—
809C2×C4—2224no—
810C2×C4—4412no—
811C2×C4C22×C22⋊D1114yes—
812C2×C4C22×C22⋊D11112yes—
813C2×C4C22×C22⋊D11148yescomplemented
814C2×C4C24×D1112yes—
815C2×C4C24×D1116yes—
816C2×C4C24×D1112yes—
817C2×C4C24×D1116yes—
818C22—22no—
819C22—26no—
820C22—26no—
821C22—22no—
822C22—28no—
823C22—224no—
824C22—26no—
825C22—26no—
826C22—26no—
827C22—448no—
828C22—412no—
829C22—114no—
830C22—222no—
831C22—222no—
832C22—228no—
833C22—226no—
834C22—226no—
835C22—226no—
836C22—4448no—
837C22—4412no—
838C22C2×#41×D1112yes—
839C22C2×#41×D1114yescomplemented
840C22#1062345312yes—
841C22C23×C22⋊D11112yes—
842C22C23×C22⋊D1112yes—
843C22C25×D1111yescharacteristic
844C4—22no—
845C4—26no—
846C4—114no—
847C4—222no—
848C4—226no—
849C4—226no—
850C4—222no—
851C4—226no—
852C4C23×C22⋊D1114yes—
853C4C23×C22⋊D11112yes—
854C2—24no—
855C2—212no—
856C2—46no—
857C2—224no—
858C2—446no—
859C2#41×C22⋊D1114yesdirect product factor
860C2C24×C22⋊D1111yescharacteristic
861C2C22×#41×D1111yescharacteristic
862C2C2×#1062345311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC23×C11×#41C2
socleC23×C11C25
hypercenterC23×#41D11
hypocenterC11C2×D4×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#41×D11C2semidirect
2. #41×C22⋊D11C2direct (N × H)
3. C2×#10623365C2semidirect
4. C2×Q8×C22⋊D11C2semidirect
5. C2×#10623348C2semidirect
6. C2×#10623362C2semidirect
7. C2×#10623355C2semidirect
8. C2×#10623337C2semidirect
9. C2×#10623360C2semidirect
10. C2×D4×C22⋊D11C2semidirect
11. C2×#10623363C2semidirect
12. C2×#10623322C2semidirect
13. C2×#10623359C2semidirect
14. C2×#41×Dic11C2semidirect
15. C22×C4×C22⋊D11C2semidirect
16. C23×C11×#41C2semidirect
19. C22×C11×#41C22semidirect
20. C22×C11×#41C22semidirect
21. C22×C11×#41C22semidirect
22. C22×C11×#41C22semidirect
23. C23×Q8×C11C22semidirect
24. C23×D4×C11C22semidirect
25. C24×C4×C11C22semidirect
28. C2×#41×D11C22semidirect
29. C22×#4343C22semidirect
30. C22×Q8×D11C22semidirect
31. C22×#4341C22semidirect
32. C22×D4×D11C22semidirect
33. C22×#4339C22semidirect
34. C23×C4×D11C22semidirect
35. C2×#67006C22semidirect
36. C22×C22⋊Dic11C22semidirect
37. #10623365C22semidirect
38. #10623363C22semidirect
39. #10623362C22semidirect
40. #10623360C22semidirect
41. #10623359C22semidirect
42. #41×Dic11C22semidirect
43. #10623355C22semidirect
44. #10623348C22semidirect
45. Q8×C22⋊D11C22semidirect
46. C2×#67000C22semidirect
47. C2×#66999C22semidirect
48. C2×#66999C22semidirect
49. C2×Q8×Dic11C22semidirect
50. C2×Q8×Dic11C22semidirect
51. C2×#66997C22semidirect
52. #10623337C22semidirect
53. C2×#66993C22semidirect
54. C2×#66992C22semidirect
55. C2×#66992C22semidirect
56. D4×C22⋊D11C22semidirect
57. C2×#66991C22semidirect
58. C2×#66991C22semidirect
59. C2×#66990C22semidirect
60. C2×#66989C22semidirect
61. C2×#66988C22semidirect
62. C2×D4×Dic11C22semidirect
63. C2×D4×Dic11C22semidirect
64. #10623322C22semidirect
65. C2×#66983C22semidirect
66. C2×#66983C22semidirect
67. C2×#66982C22semidirect
70. C2×C4×C22⋊D11C22semidirect
71. C2×C4×C22⋊D11C22semidirect
72. C2×C4×C22⋊D11C22semidirect
73. C2×C4×C22⋊D11C22semidirect
74. C2×C4×C22⋊D11C22semidirect
75. C2×C4×C22⋊D11C22semidirect
76. C2×C4×C22⋊D11C22semidirect
77. C2×C4×C22⋊D11C22semidirect
78. C22×(C2×D11)⋊C4C22semidirect
79. C2×#66979C22semidirect
80. C2×#66977C22semidirect
81. C2×#66977C22semidirect
82. C22×Dic11⋊C4C22semidirect
83. C22×C4×Dic11C22semidirect
90. C2×C11×#41D4semidirect
92. C2×C11×#41C23semidirect
93. C2×C11×#41C23semidirect
94. C2×C11×#41C23semidirect
98. C22×Q8×C11C23semidirect
103. C22×D4×C11C23semidirect
111. C23×C4×C11C23semidirect
125. C2×#4343C23semidirect
127. C2×Q8×D11C23semidirect
129. C2×#4341C23semidirect
131. C2×D4×D11C23semidirect
133. C2×#4339C23semidirect
140. C22×C4×D11C23semidirect
142. #67006C23semidirect
149. C2×C22⋊Dic11C23semidirect
150. #67000C23semidirect
151. #66999C23semidirect
152. #66999C23semidirect
153. Q8×Dic11C23semidirect
154. Q8×Dic11C23semidirect
155. #66997C23semidirect
156. #66993C23semidirect
157. #66992C23semidirect
158. #66992C23semidirect
159. #66991C23semidirect
160. #66991C23semidirect
161. #66990C23semidirect
162. #66989C23semidirect
163. #66988C23semidirect
164. D4×Dic11C23semidirect
165. D4×Dic11C23semidirect
166. #66983C23semidirect
167. #66983C23semidirect
168. #66982C23semidirect
171. C4×C22⋊D11C23semidirect
172. C4×C22⋊D11C23semidirect
173. C4×C22⋊D11C23semidirect
174. C4×C22⋊D11C23semidirect
175. C4×C22⋊D11C23semidirect
176. C4×C22⋊D11C23semidirect
177. C4×C22⋊D11C23semidirect
183. C2×(C2×D11)⋊C4C23semidirect
184. #66979C23semidirect
187. #66977C23semidirect
188. #66977C23semidirect
194. C2×Dic11⋊C4C23semidirect
199. C2×C4×Dic11C23semidirect
217. C11×#41C2×D4semidirect
220. C2×Q8×C11C2×D4semidirect
226. C2×D4×C11C2×D4semidirect
236. C22×C4×C11C2×D4semidirect
253. C2×C22⋊D11#41direct (N × H)
313. C23×#41D11semidirect
340. C23×C11C2×#41semidirect
354. C22×D11C2×#41semidirect
358. Q8×C11C22×D4semidirect
361. D4×C11C22×D4semidirect
371. C2×C4×C11C22×D4semidirect
381. C22⋊D11C2×#41direct (N × H)
390. C2×Dic11C2×#41semidirect
410. C22×#41C2×D11semidirect
411. C22×#41C2×D11semidirect
412. C22×#41C2×D11semidirect
413. C22×#41C2×D11semidirect
415. C23×Q8C2×D11semidirect
418. C23×D4C2×D11semidirect
420. C24×C4C2×D11semidirect
484. C22×C11C22×#41semidirect
495. C2×D11C22×#41semidirect
505. Dic11C22×#41semidirect
519. C2×#41C22⋊D11direct (N × H)
521. C2×#41C22×D11semidirect
522. C2×#41C22×D11semidirect
523. C2×#41C22×D11semidirect
530. C22×Q8C22×D11semidirect
546. C22×D4C22×D11semidirect
563. C23×C4C22×D11semidirect
625. C2×C11D4×#41semidirect
650. #41C2×C22⋊D11direct (N × H)
656. C2×Q8C2×C22⋊D11semidirect
678. C2×D4C2×C22⋊D11semidirect
709. C22×C4C2×C22⋊D11semidirect
742. C11C2×D4×#41semidirect
766. C23#41×D11semidirect
774. Q8C22×C22⋊D11semidirect
784. D4C22×C22⋊D11semidirect
813. C2×C4C22×C22⋊D11semidirect
839. C22C2×#41×D11semidirect
859. C2#41×C22⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D112
#41×C22⋊D112
C2×#106233652
C2×Q8×C22⋊D112
C2×#106233482
C2×#106233622
C2×#106233552
C2×#106233372
C2×#106233602
C2×D4×C22⋊D112
C2×#106233632
C2×#106233222
C2×#106233592
C2×#41×Dic112
C22×C4×C22⋊D112
C23×C11×#412
C2×D4×#4111