Finite Group Databasebeta

← #14917768

Subgroups — #14917768

Order 2816.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623205C211yesmaximal, characteristic
2#13071769C212yesmaximal, complemented
3#13071756C212yesmaximal, complemented
4#13071691C211yesmaximal, characteristic, complemented
5#13071680C211yesmaximal, characteristic, complemented
6#13071680C211yesmaximal, characteristic, complemented
7#13071667C212yesmaximal, complemented
8#13071592C212yesmaximal, complemented
9#13071454C211yesmaximal, characteristic, complemented
10#13071445C211yesmaximal, characteristic, complemented
11#13071437C211yesmaximal, characteristic, complemented
12D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
13#13071379C212yesmaximal, complemented
14#13071340C211yesmaximal, characteristic, complemented
15#13071323C211yesmaximal, characteristic, complemented
16#13071313C212yesmaximal, complemented
17#13071278C212yesmaximal, complemented
18#13071276C212yesmaximal, complemented
19#13071221C211yesmaximal, characteristic, complemented
20C4×#66993C211yesmaximal, characteristic, complemented
21#13071159C211yesmaximal, characteristic, complemented
22#13071109C211yesmaximal, characteristic, complemented
23C11×#2367C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29C2×#67000C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66993C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yescomplemented
34C2×C4×C22⋊D11C2212yescomplemented
35C22×(C2×D11)⋊C4C2212yes—
36#10623205C4116yescomplemented
37C2×#66946C2211yescharacteristic
38C2×#66946C2211yescharacteristic, complemented
39C2×#66946C2212yescomplemented
40C2×#66937C2212yes—
41C2×#66937C2212yes—
42C2×#66935C2212yes—
43C2×#66935C2212yes—
44C2×C22⋊C4×D11C2212yes—
45C2×#66927C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×C4×D44C2212yescomplemented
48C2×C4×D44C2211yescharacteristic, complemented
49C2×#66925C2211yescharacteristic
50C11×#391C2211yescharacteristic, complemented
51C11×#390C2211yescharacteristic
52C11×#388C2212yescomplemented
53C11×#388C2212yescomplemented
54C11×#385C2212yescomplemented
55C4×C11×C4⋊C4C2211yescharacteristic, complemented
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2212yescomplemented
58#10622843C2211yescharacteristic, complemented
59#10622834C2211yescharacteristic
60#10622826C2212yes—
61#10622603C2211yescharacteristic
62#10622603C2211yescharacteristic
63#10622602C2212yescomplemented
64#10622602C2212yescomplemented
65#10622601C2211yescharacteristic
66#10622601C2212yes—
67#10622601C2212yescomplemented
68#10622601C2211yescharacteristic, complemented
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2212yescomplemented
72#10622591C2211yescharacteristic, complemented
73#10622591C2211yescharacteristic, complemented
74#10622590C2211yescharacteristic, complemented
75#10622589C2211yescharacteristic, complemented
76#10622571C2212yes—
77#10622571C2212yescomplemented
78#10622571C2212yescomplemented
79#10622570C2212yescomplemented
80#10622570C2212yescomplemented
81#10622569C2212yes—
82#10622569C2212yes—
83#10622569C2212yescomplemented
84#10622569C2212yescomplemented
85#10622568C2212yes—
86#10622568C2212yes—
87#10622564C2212yescomplemented
88#10622564C2212yescomplemented
89#10622563C2212yescomplemented
90C22⋊C4×Dic11C2212yescomplemented
91#10622553C2212yes—
92#10622553C2212yescomplemented
93#10622553C2212yescomplemented
94#10622552C2211yescharacteristic
95#10622552C2212yes—
96#10622552C2211yescharacteristic, complemented
97#10622552C2212yescomplemented
98C4×(C2×D11)⋊C4C2211yescharacteristic
99C4×(C2×D11)⋊C4C2211yescharacteristic
100C4×(C2×D11)⋊C4C2212yescomplemented
101C4×C4⋊Dic11C2211yescharacteristic, complemented
102C4×C4⋊Dic11C2211yescharacteristic, complemented
103#10622546C2212yescomplemented
104#10622545C2211yescharacteristic, complemented
105C42×Dic11C2211yescharacteristic, complemented
106#10622283C2211yescharacteristic
107#10622283C2211yescharacteristic
108#10622283C2212yescomplemented
109#10622283C2212yescomplemented
110#10622282C2212yes—
111#10622279C2212yescomplemented
112#10622279C2212yescomplemented
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yescomplemented
116#10622278C2212yescomplemented
117#10622278C2212yescomplemented
118#10622278C2212yescomplemented
119#10622277C2212yescomplemented
120D11×#95C2212yescomplemented
121#10622268C2211yescharacteristic, complemented
122#10622268C2211yescharacteristic, complemented
123#10622265C2212yescomplemented
124C24×D11C2312yes—
125C22×Q8×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C23×Dic11C2312yes—
132C2×#4343—42no—
133C2×#4343—42no—
134C2×#4343C2×C418yescomplemented
135C2×D4×D11—42no—
136C2×D4×D11—42no—
137C2×D4×D11C2×C418yescomplemented
138C22×D44C2311yescharacteristic
139C22×D44C2311yescharacteristic
140C22×D44C2312yes—
141C22×D44C2312yes—
142C22×D44C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C11×#124C2×C418yescomplemented
150C4×Q8×C11—42no—
151C4×D4×C11—42no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C42×C11C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170#67000C2×C418yescomplemented
171Q8×Dic11—42no—
172#66993C2×C418yescomplemented
173D4×Dic11—42no—
174C4×C22⋊D11—44no—
175C4×C22⋊D11—44no—
176C2×(C2×D11)⋊C4—44no—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217#66946—42no—
218#66946—42no—
219#66946—44no—
220#66937C2×C4116yescomplemented
221#66937C2×C4116yescomplemented
222#66935C2×C4116yescomplemented
223#66935C2×C4116yescomplemented
224C22⋊C4×D11—44no—
225#66927C2×C418yescomplemented
226C4×D44—44no—
227C4×D44—42no—
228C4×D44—42no—
229#66925C2×C418yescomplemented
230C11×#95C2312yes—
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252#34438—111nomaximal, Sylow
253C24×C11C2412yes—
254C23×D11—42no—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11C22×C418yes—
261C23×D11C2411yescharacteristic
262C23×D11C2412yes—
263C23×D11C2412yes—
264C2×Q8×C11—22no—
265C2×Q8×C11—22no—
266C2×Q8×C11C22×C414yes—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11C22×C414yes—
270C22×C4×C11—24no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11C2412yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C2×C22⋊D11—42no—
284C2×C22⋊D11—42no—
285C2×C22⋊D11—42no—
286C2×C22⋊D11—42no—
287C2×C22⋊D11—42no—
288C2×C22⋊D11—42no—
289C2×C22⋊D11C22×C418yes—
290C2×C22⋊D11C22×C418yes—
291C2×C22⋊D11C22×C418yes—
292C22×Dic11—42no—
293C22×Dic11—42no—
294C22×Dic11—42no—
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304#4343—416no—
305D4×D11—416no—
306C2×D44—22no—
307C2×D44—22no—
308C2×D44—22no—
309C2×D44—22no—
310C2×D44—42no—
311C2×D44—42no—
312C2×D44—42no—
313C2×D44—42no—
314C2×D44—42no—
315C2×D44—42no—
316C2×D44C22×C414yes—
317C2×D44C22×C414yes—
318C2×D44C22×C418yes—
319C2×D44C22×C418yes—
320C2×D44C22×C418yes—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—24no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11C22×C414yes—
338C2×C4×D11C22×C418yes—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—22no—
342C11×C4⋊C4—41no—
343C11×C4⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4C22×C418yes—
348C11×C22⋊C4C22×C418yes—
349C42×C11—22no—
350C42×C11—22no—
351C42×C11—42no—
352C42×C11—42no—
353C42×C11C22×C414yes—
354C22⋊Dic11—24no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357(C2×D11)⋊C4—24no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—42no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—41no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—41no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4C22×C414yes—
376(C2×D11)⋊C4C22×C414yes—
377(C2×D11)⋊C4C22×C418yes—
378(C2×D11)⋊C4C22×C418yes—
379C4⋊Dic11—22no—
380C4⋊Dic11—22no—
381C4⋊Dic11—22no—
382C4⋊Dic11—41no—
383C4⋊Dic11—42no—
384Dic11⋊C4—42no—
385Dic11⋊C4—42no—
386Dic11⋊C4C22×C414yes—
387Dic11⋊C4C22×C414yes—
388C4×Dic11—22no—
389C4×Dic11—22no—
390C4×Dic11—22no—
391C4×Dic11—22no—
392C4×Dic11—42no—
393C4×Dic11—41no—
394C4×Dic11—41no—
395C4×Dic11—42no—
396C4×Dic11C22×C414yes—
397C2×#535—111no—
398#2377—112no—
399#2375—112no—
400#2367—111no—
401#2367D1111yescharacteristic, complemented
402#2366—111no—
403#2366—111no—
404#2364—112no—
405#2358—112no—
406#2341—111no—
407#2339—111no—
408D4×C22⋊C4—111no—
409D4×C22⋊C4—111no—
410#2333—112no—
411#2328—111no—
412#2326—111no—
413#2325—112no—
414#2321—112no—
415#2321—112no—
416#2314—111no—
417C4×#127—111no—
418C4×#124—111no—
419#2298—111no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11C23×C414yes—
427C23×C11C2511yescharacteristic
428C22×D11—21no—
429C22×D11—21no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—21no—
443C22×D11—21no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—48no—
447C22×D11—48no—
448C22×D11—48no—
449C22×D11—84no—
450C22×D11—84no—
451C22×D11—84no—
452C22×D11—84no—
453C22×D11C23×C412yes—
454C22×D11C23×C414yes—
455C22×D11C23×C414yes—
456Q8×C11—28no—
457D4×C11—28no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—84no—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C414yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11H(5,𝔽2)12yes—
487C2×C4×C11H(5,𝔽2)12yes—
488C2×C4×C11H(5,𝔽2)12yes—
489C22⋊D11—48no—
490C22⋊D11—48no—
491C22⋊D11—48no—
492C2×Dic11—21no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—84no—
516C2×Dic11C23×C412yes—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C412yes—
519C2×Dic11H(5,𝔽2)12yes—
520D44—28no—
521D44—28no—
522D44—48no—
523D44—48no—
524D44—48no—
525C4×D11—28no—
526C4×D11—48no—
527C4×D11—84no—
528C4×D11—84no—
529C4×D11—84no—
530C4×D11—84no—
531C22×#41—111no—
532C23×D4—111no—
533#535—1116no—
534C2×#127—111no—
535C2×#127—111no—
536C2×#124—111no—
537C2×#124C2×D1111yescharacteristic
538C2×#121—112no—
539C2×#121—112no—
540C2×#120—112no—
541C2×#120—112no—
542C2×C4×Q8—111no—
543C2×C4×Q8C2×D1111yescharacteristic, complemented
544C2×C4×D4—111no—
545C2×C4×D4—112no—
546C2×C4×D4—112no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×C4×D4—111no—
551C2×C4×D4—112no—
552C2×C4×D4—111no—
553C2×C4×D4C2×D1111yescharacteristic
554C2×#117—111no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391—111no—
558#391C2×D1111yescharacteristic, complemented
559#390—111no—
560#390—111no—
561#390—112no—
562#390—111no—
563#390—112no—
564#390—112no—
565#390—112no—
566#390—112no—
567#390—112no—
568#390—111no—
569#390—111no—
570#390C2×D1111yescharacteristic
571#388—111no—
572#388—111no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—111no—
580#388—111no—
581#388—112no—
582#388—112no—
583#388C2×D1112yescomplemented
584#388C2×D1112yescomplemented
585#387—111no—
586#387—111no—
587#387—112no—
588#387—112no—
589#387—111no—
590#387—111no—
591#386—112no—
592#386—112no—
593#386—112no—
594#386—112no—
595#386—112no—
596#386—112no—
597#386—112no—
598#386—112no—
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#385—112no—
606#385—112no—
607#385—112no—
608#385C2×D1112yescomplemented
609#384—111no—
610#382—111no—
611#381—112no—
612#380—111no—
613#380—111no—
614#380—112no—
615#379—112no—
616#379—112no—
617C4×C4⋊C4—111no—
618C4×C4⋊C4—111no—
619C4×C4⋊C4C2×D1111yescharacteristic, complemented
620C4×C4⋊C4C2×D1111yescharacteristic, complemented
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—111no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4C2×D1112yescomplemented
628#376—111no—
629C2×#95—112no—
630C43—111no—
631C22×C11—24no—
632C22×C11—24no—
633C22×C11—24no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11C24×C411yescharacteristic
639C22×C11C2×H(5,𝔽2)11yescharacteristic
640C22×C11C2×H(5,𝔽2)11yescharacteristic
641C22×C11C2×H(5,𝔽2)11yescharacteristic
642C22×C11C2×H(5,𝔽2)11yescharacteristic
643C22×C11#58511yescharacteristic
644C22×C11#58511yescharacteristic
645C2×D11—22no—
646C2×D11—24no—
647C2×D11—24no—
648C2×D11—22no—
649C2×D11—22no—
650C2×D11—24no—
651C2×D11—24no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—41no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—41no—
666C2×D11—816no—
667C4×C11—24no—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—42no—
672C4×C11—41no—
673C4×C11—42no—
674C4×C11—41no—
675C4×C11—41no—
676C4×C11#51814yes—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—42no—
682Dic11—41no—
683Dic11—42no—
684Dic11—41no—
685Dic11—41no—
686C25—112no—
687C2×#41—118no—
688C2×#41—442no—
689C2×#41—442no—
690C22×Q8C22×D1111yescharacteristic
691C22×D4—112no—
692C22×D4—112no—
693C22×D4—112no—
694C22×D4—118no—
695C22×D4—111no—
696C22×D4—111no—
697C22×D4—112no—
698C22×D4—112no—
699C22×D4—112no—
700C22×D4—442no—
701C22×D4—442no—
702C22×D4C22×D1111yescharacteristic
703C23×C4—111no—
704C23×C4—112no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—112no—
708C23×C4—112no—
709C23×C4—112no—
710C23×C4C22×D1112yes—
711#127—118no—
712#127—118no—
713#124—118no—
714#124C4×D1118yescomplemented
715#121—1116no—
716#121—1116no—
717#120—1116no—
718#120—1116no—
719C4×Q8—42no—
720C4×Q8—442no—
721C4×D4—42no—
722C4×D4—442no—
723C4×D4—442no—
724C4×D4—444no—
725C4×D4—444no—
726C4×D4—442no—
727C4×D4—442no—
728C4×D4—442no—
729C4×D4—444no—
730C4×D4—444no—
731#117—118no—
732C2×C4⋊C4—111no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4C22×D1111yescharacteristic
742C2×C4⋊C4C22×D1111yescharacteristic
743C2×C4⋊C4C22×D1111yescharacteristic
744C2×C4⋊C4C22×D1112yes—
745C2×C4⋊C4C22×D1111yescharacteristic
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—111no—
752C2×C22⋊C4—111no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—444no—
772C2×C22⋊C4—444no—
773C2×C22⋊C4C22×D1112yes—
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C22⋊C4C22×D1112yes—
778C2×C42—111no—
779C2×C42—111no—
780C2×C42—111no—
781C2×C42—111no—
782C2×C42—111no—
783C2×C42—112no—
784C2×C42—112no—
785C2×C42—111no—
786C2×C42—111no—
787C2×C42C22×D1111yescharacteristic
788C2×C42C22×D1111yescharacteristic
789C2×C42C22×D1112yes—
790C2×C42C22×D1112yes—
791C2×C42C22×D1111yescharacteristic
792#95—111no—
793#95—112no—
794#95—112no—
795#95—111no—
796#95—111no—
797#95—111no—
798#95—111no—
799#95—111no—
800#95—111no—
801#95—112no—
802#95—111no—
803#95—111no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—111no—
809#95C22×D1112yes—
810#95C22×D1112yes—
811#95C22×D1111yescharacteristic
812#95C22×D1112yes—
813#95C22×D1111yescharacteristic
814C2×C11—44no—
815C2×C11C2×#51811yescharacteristic
816C2×C11C4×H(5,𝔽2)11yescharacteristic
817C2×C11C4×H(5,𝔽2)11yescharacteristic
818C2×C11#354311yescharacteristic
819C2×C11#354611yescharacteristic
820C2×C11#355811yescharacteristic
821C2×C11#356211yescharacteristic
822D11—44no—
823D11—44no—
824D11—42no—
825C24—111no—
826C24—112no—
827C24—112no—
828C24—118no—
829C24—442no—
830C24—442no—
831C24—442no—
832C24—442no—
833C24—442no—
834C24—442no—
835C24C23×D1112yes—
836#41—4416no—
837C2×Q8—22no—
838C2×Q8—22no—
839C2×Q8C2×C4×D1114yes—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—118no—
843C2×D4—118no—
844C2×D4—118no—
845C2×D4—114no—
846C2×D4—114no—
847C2×D4—118no—
848C2×D4—118no—
849C2×D4—118no—
850C2×D4—222no—
851C2×D4—222no—
852C2×D4—222no—
853C2×D4—222no—
854C2×D4—442no—
855C2×D4—442no—
856C2×D4—442no—
857C2×D4—442no—
858C2×D4—442no—
859C2×D4—442no—
860C2×D4—4416no—
861C2×D4—442no—
862C2×D4—442no—
863C2×D4—442no—
864C2×D4—442no—
865C2×D4—442no—
866C2×D4—442no—
867C2×D4C2×C4×D1114yes—
868C22×C4—24no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—111no—
872C22×C4—111no—
873C22×C4—111no—
874C22×C4—111no—
875C22×C4—114no—
876C22×C4—118no—
877C22×C4—111no—
878C22×C4—111no—
879C22×C4—112no—
880C22×C4—112no—
881C22×C4—111no—
882C22×C4—224no—
883C22×C4—222no—
884C22×C4—222no—
885C22×C4—224no—
886C22×C4—442no—
887C22×C4—442no—
888C22×C4—442no—
889C22×C4—442no—
890C22×C4—442no—
891C22×C4—442no—
892C22×C4—442no—
893C22×C4—442no—
894C22×C4—442no—
895C22×C4—442no—
896C22×C4—442no—
897C22×C4—442no—
898C22×C4—442no—
899C22×C4—442no—
900C22×C4—442no—
901C22×C4C23×D1112yes—
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1112yes—
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1112yes—
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—42no—
915C4⋊C4—41no—
916C4⋊C4—114no—
917C4⋊C4—114no—
918C4⋊C4—222no—
919C4⋊C4—222no—
920C4⋊C4—222no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4—442no—
924C4⋊C4—441no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—114no—
929C22⋊C4—114no—
930C22⋊C4—118no—
931C22⋊C4—118no—
932C22⋊C4—222no—
933C22⋊C4—224no—
934C22⋊C4—224no—
935C22⋊C4—222no—
936C22⋊C4—224no—
937C22⋊C4—442no—
938C22⋊C4—442no—
939C22⋊C4—442no—
940C22⋊C4—442no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—441no—
948C22⋊C4—442no—
949C22⋊C4—441no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4C2×C4×D1118yes—
954C22⋊C4C2×C4×D1118yes—
955C42—22no—
956C42—22no—
957C42—42no—
958C42—42no—
959C42—114no—
960C42—222no—
961C42—222no—
962C42—222no—
963C42—222no—
964C42—442no—
965C42—442no—
966C42—441no—
967C42—441no—
968C42C2×C4×D1114yes—
969C11#3443811yescharacteristic, complemented, Sylow
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—112no—
977C23—114no—
978C23—114no—
979C23—222no—
980C23—222no—
981C23—221no—
982C23—221no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—221no—
988C23—221no—
989C23—222no—
990C23—222no—
991C23—221no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—221no—
997C23—448no—
998C23—448no—
999C23—448no—
1000C23—884no—
1001C23—884no—
1002C23—884no—
1003C23—884no—
1004C23C22×C4×D1114yes—
1005C23C24×D1111yescharacteristic
1006Q8—28no—
1007D4—28no—
1008D4—228no—
1009D4—228no—
1010D4—448no—
1011D4—448no—
1012D4—448no—
1013D4—448no—
1014D4—448no—
1015D4—448no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—84no—
1040C2×C4—112no—
1041C2×C4—112no—
1042C2×C4—112no—
1043C2×C4—112no—
1044C2×C4—221no—
1045C2×C4—221no—
1046C2×C4—221no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—228no—
1053C2×C4—222no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—222no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—448no—
1069C2×C4—884no—
1070C2×C4—884no—
1071C2×C4—884no—
1072C2×C4—884no—
1073C2×C4—884no—
1074C2×C4C22×C4×D1112yes—
1075C2×C4C22×C4×D1112yes—
1076C2×C4C22×C4×D1114yes—
1077C2×C4C22×C4×D1112yes—
1078C2×C4#6703712yes—
1079C2×C4#6704212yes—
1080C2×C4#6704212yes—
1081C22—24no—
1082C22—24no—
1083C22—24no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—222no—
1089C22—224no—
1090C22—224no—
1091C22—224no—
1092C22—224no—
1093C22—222no—
1094C22—224no—
1095C22—224no—
1096C22—222no—
1097C22—442no—
1098C22—442no—
1099C22—441no—
1100C22—442no—
1101C22—442no—
1102C22—441no—
1103C22—441no—
1104C22—442no—
1105C22—442no—
1106C22—441no—
1107C22—442no—
1108C22—442no—
1109C22—8816no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22C2×#6704211yescharacteristic
1113C22C2×#6704211yescharacteristic
1114C22#1062345311yescharacteristic
1115C22D11×H(5,𝔽2)11yescharacteristic
1116C22#1062345711yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—22no—
1120C4—22no—
1121C4—42no—
1122C4—42no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—222no—
1127C4—222no—
1128C4—222no—
1129C4—222no—
1130C4—441no—
1131C4—442no—
1132C4—441no—
1133C4—442no—
1134C4—441no—
1135C4#1062307614yes—
1136C2—44no—
1137C2—442no—
1138C2—444no—
1139C2—444no—
1140C2C2×#1062307611yescharacteristic
1141C2#1308182211yescharacteristic
1142C2C4×#6704211yescharacteristic
1143C2#1308294811yescharacteristic
1144C2#1308299111yescharacteristic
1145C2#1308313611yescharacteristic
1146C2#1308320511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2367C2
socle, cosocleC23×C11C25
prime radicalC2×#10623205C2
hypercenter#2367D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. #13071769C2semidirect
3. #13071756C2semidirect
4. #13071691C2semidirect
5. #13071680C2semidirect
6. #13071680C2semidirect
7. #13071667C2semidirect
8. #13071592C2semidirect
9. #13071454C2semidirect
10. #13071445C2semidirect
11. #13071437C2semidirect
12. D4×(C2×D11)⋊C4C2semidirect
13. #13071379C2semidirect
14. #13071340C2semidirect
15. #13071323C2semidirect
16. #13071313C2semidirect
17. #13071278C2semidirect
18. #13071276C2semidirect
19. #13071221C2semidirect
20. C4×#66993C2semidirect
21. #13071159C2semidirect
22. #13071109C2semidirect
23. C11×#2367C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
36. #10623205C4semidirect
38. C2×#66946C22semidirect
39. C2×#66946C22semidirect
47. C2×C4×D44C22semidirect
48. C2×C4×D44C22semidirect
50. C11×#391C22semidirect
52. C11×#388C22semidirect
53. C11×#388C22semidirect
54. C11×#385C22semidirect
55. C4×C11×C4⋊C4C22semidirect
56. C4×C11×C4⋊C4C22semidirect
57. C4×C11×C22⋊C4C22semidirect
58. #10622843C22semidirect
63. #10622602C22semidirect
64. #10622602C22semidirect
67. #10622601C22semidirect
68. #10622601C22semidirect
71. #10622600C22semidirect
72. #10622591C22semidirect
73. #10622591C22semidirect
74. #10622590C22semidirect
75. #10622589C22semidirect
77. #10622571C22semidirect
78. #10622571C22semidirect
79. #10622570C22semidirect
80. #10622570C22semidirect
83. #10622569C22semidirect
84. #10622569C22semidirect
87. #10622564C22semidirect
88. #10622564C22semidirect
89. #10622563C22semidirect
90. C22⋊C4×Dic11C22semidirect
92. #10622553C22semidirect
93. #10622553C22semidirect
96. #10622552C22semidirect
97. #10622552C22semidirect
100. C4×(C2×D11)⋊C4C22semidirect
101. C4×C4⋊Dic11C22semidirect
102. C4×C4⋊Dic11C22semidirect
103. #10622546C22semidirect
104. #10622545C22semidirect
105. C42×Dic11C22semidirect
108. #10622283C22semidirect
109. #10622283C22semidirect
111. #10622279C22semidirect
112. #10622279C22semidirect
115. #10622278C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
118. #10622278C22semidirect
119. #10622277C22semidirect
120. D11×#95C22semidirect
121. #10622268C22semidirect
122. #10622268C22semidirect
123. #10622265C22semidirect
134. C2×#4343C2×C4semidirect
137. C2×D4×D11C2×C4semidirect
149. C11×#124C2×C4semidirect
170. #67000C2×C4semidirect
172. #66993C2×C4semidirect
220. #66937C2×C4semidirect
221. #66937C2×C4semidirect
222. #66935C2×C4semidirect
223. #66935C2×C4semidirect
225. #66927C2×C4semidirect
229. #66925C2×C4semidirect
401. #2367D11semidirect
543. C2×C4×Q8C2×D11semidirect
558. #391C2×D11semidirect
583. #388C2×D11semidirect
584. #388C2×D11semidirect
608. #385C2×D11semidirect
619. C4×C4⋊C4C2×D11semidirect
620. C4×C4⋊C4C2×D11semidirect
627. C4×C22⋊C4C2×D11semidirect
714. #124C4×D11semidirect
969. C11#34438semidirect

Maximal subgroups

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

subgroupindex
C2×#106232052
#130717692
#130717562
#130716912
#130716802
#130716672
#130715922
#130714542
#130714452
#130714372
D4×(C2×D11)⋊C42
#130713792
#130713402
#130713232
#130713132
#130712782
#130712762
#130712212
C4×#669932
#130711592
#130711092
C11×#23672
#3443811