Finite Group Databasebeta

← #14917770

Subgroups — #14917770

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×#10623361C211yesmaximal, characteristic
2#13071770C212yesmaximal, complemented
3#13071753C212yesmaximal, complemented
4#13071683C211yesmaximal, characteristic, complemented
5#13071683C211yesmaximal, characteristic, complemented
6#13071677C211yesmaximal, characteristic, complemented
7#13071677C211yesmaximal, characteristic, complemented
8#13071666C212yesmaximal, complemented
9#13071597C212yesmaximal, complemented
10#13071446C211yesmaximal, characteristic, complemented
11C22⋊C4×D44C211yesmaximal, characteristic, complemented
12#13071436C211yesmaximal, characteristic, complemented
13#13071381C212yesmaximal, complemented
14#13071340C211yesmaximal, characteristic, complemented
15#13071323C211yesmaximal, characteristic, complemented
16#13071316C212yesmaximal, complemented
17#13071275C212yesmaximal, complemented
18#13071275C212yesmaximal, complemented
19#13071223C211yesmaximal, characteristic, complemented
20#13071180C211yesmaximal, characteristic, complemented
21C4×#67000C211yesmaximal, characteristic, complemented
22#13071112C211yesmaximal, characteristic, complemented
23C11×#2341C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic, complemented
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28#10623361C4116yescomplemented
29C2×#67000C2211yescharacteristic
30C2×#67000C2211yescharacteristic
31C2×#66993C2211yescharacteristic
32C2×#66993C2211yescharacteristic
33C2×#66990C2212yes—
34C2×#66990C2212yes—
35C2×D4×Dic11C2211yescharacteristic, complemented
36C2×D4×Dic11C2211yescharacteristic, complemented
37C2×#66983C2212yes—
38C2×#66983C2212yes—
39C2×#66979C2211yescharacteristic
40C2×#66946C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×(C22⋊D11)⋊C4C2212yescomplemented
43C2×(C22⋊D11)⋊C4C2212yescomplemented
44C2×(C22⋊D11)⋊C4C2212yescomplemented
45C2×(C22⋊D11)⋊C4C2212yescomplemented
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C4×D44C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C11×#390C2212yes—
51C11×#390C2212yes—
52C11×#390C2211yescharacteristic, complemented
53C11×#390C2211yescharacteristic, complemented
54C11×#380C2211yescharacteristic
55C11×#380C2212yescomplemented
56C4×C11×C22⋊C4C2211yescharacteristic
57C4×C11×C22⋊C4C2212yescomplemented
58#10622843C2211yescharacteristic, complemented
59#10622843C2211yescharacteristic, complemented
60#10622833C2212yes—
61#10622833C2212yes—
62#10622825C2211yescharacteristic
63#10622824C2212yescomplemented
64C4×C22⋊Dic11C2211yescharacteristic
65C2×C11⋊#95C2212yescomplemented
66#10622603C2212yescomplemented
67#10622603C2212yescomplemented
68#10622603C2212yescomplemented
69#10622603C2212yescomplemented
70#10622602C2212yescomplemented
71#10622602C2212yescomplemented
72#10622602C2212yescomplemented
73#10622602C2212yescomplemented
74#10622601C2211yescharacteristic
75#10622601C2211yescharacteristic
76#10622590C2211yescharacteristic, complemented
77#10622589C2211yescharacteristic, complemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80#10622571C2212yescomplemented
81#10622571C2212yescomplemented
82#10622571C2212yescomplemented
83#10622571C2212yescomplemented
84#10622570C2212yescomplemented
85#10622570C2212yescomplemented
86#10622570C2212yescomplemented
87#10622570C2212yescomplemented
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622568C2212yes—
93#10622568C2212yes—
94#10622558C2211yescharacteristic
95#10622558C2211yescharacteristic
96#10622558C2212yes—
97#10622557C2211yescharacteristic
98#10622557C2211yescharacteristic
99#10622557C2212yes—
100#10622553C2212yescomplemented
101#10622553C2212yescomplemented
102#10622553C2212yescomplemented
103#10622553C2212yescomplemented
104#10622552C2211yescharacteristic
105#10622552C2211yescharacteristic
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×(C2×D11)⋊C4C2212yescomplemented
108C4×(C2×D11)⋊C4C2212yescomplemented
109C4×(C2×D11)⋊C4C2212yescomplemented
110#10622545C2211yescharacteristic, complemented
111C4×Dic11⋊C4C2211yescharacteristic, complemented
112C4×Dic11⋊C4C2211yescharacteristic, complemented
113C42×Dic11C2211yescharacteristic, complemented
114#10622278C2212yes—
115#10622278C2212yes—
116#10622278C2212yes—
117#10622278C2212yes—
118#10622267C2211yescharacteristic, complemented
119#10622267C2211yescharacteristic, complemented
120#10622267C2212yescomplemented
121#10622266C2211yescharacteristic, complemented
122#10622266C2211yescharacteristic, complemented
123#10622266C2212yescomplemented
124C24×D11C2312yes—
125C2×C11×#41—42no—
126C2×C11×#41—42no—
127C2×C11×#41C2×C418yescomplemented
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C23×Dic11C2312yes—
138C23×Dic11C2312yes—
139C22×D44—42no—
140C22×D44—42no—
141C22×D44C2×C418yescomplemented
142C22×D44C2311yescharacteristic
143C22×D44C2311yescharacteristic
144C22×D44C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C4×Q8×C11—42no—
150C4×Q8×C11—42no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C22⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C42×C11C2312yes—
166C2×C22⋊Dic11C2311yescharacteristic
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173#67000C2×C418yescomplemented
174#67000C2×C418yescomplemented
175#66993C2×C418yescomplemented
176#66993C2×C418yescomplemented
177#66990C2×C4116yescomplemented
178#66990C2×C4116yescomplemented
179D4×Dic11—42no—
180D4×Dic11—42no—
181#66983C2×C4116yescomplemented
182#66983C2×C4116yescomplemented
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199#66979C2×C418yescomplemented
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220#66946—42no—
221#66946—42no—
222(C22⋊D11)⋊C4—44no—
223(C22⋊D11)⋊C4—44no—
224(C22⋊D11)⋊C4—44no—
225(C22⋊D11)⋊C4—44no—
226C22⋊C4×D11—44no—
227C22⋊C4×D11—44no—
228C4×D44—42no—
229C4×D44—42no—
230C11×#95C2311yescharacteristic
231C11×#95C2311yescharacteristic
232C11×#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252#34438—111nomaximal, Sylow
253C24×C11C2411yescharacteristic
254C24×C11C2412yes—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11—42no—
261C23×D11C22×C418yes—
262C23×D11C2412yes—
263C23×D11C2412yes—
264C11×#41—416no—
265C2×Q8×C11—22no—
266C2×Q8×C11—22no—
267C2×Q8×C11C22×C414yes—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C22×C414yes—
273C2×D4×C11C22×C418yes—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11C22×C414yes—
279C22×C4×C11C22×C418yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C2×C22⋊D11—42no—
290C2×C22⋊D11—42no—
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11C22×C418yes—
298C2×C22⋊D11C22×C418yes—
299C2×C22⋊D11C22×C418yes—
300C2×C22⋊D11C22×C418yes—
301C22×Dic11—24no—
302C22×Dic11—42no—
303C22×Dic11—42no—
304C22×Dic11—42no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C2×D44—22no—
318C2×D44—22no—
319C2×D44—22no—
320C2×D44—22no—
321C2×D44—42no—
322C2×D44—42no—
323C2×D44—416no—
324C2×D44C22×C414yes—
325C2×D44C22×C414yes—
326C2×D44C22×C418yes—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
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×D11—42no—
338C2×C4×D11—42no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—42no—
342C11×C4⋊C4—42no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—24no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—41no—
349C11×C22⋊C4—42no—
350C42×C11—22no—
351C42×C11—22no—
352C42×C11—42no—
353C42×C11—42no—
354C22⋊Dic11—22no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11—41no—
359C22⋊Dic11C22×C414yes—
360C22⋊Dic11C22×C414yes—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—24no—
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—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4C22×C418yes—
374(C2×D11)⋊C4C22×C418yes—
375(C2×D11)⋊C4C22×C418yes—
376(C2×D11)⋊C4C22×C418yes—
377C4⋊Dic11—22no—
378C4⋊Dic11—22no—
379C4⋊Dic11C22×C414yes—
380C4⋊Dic11C22×C414yes—
381Dic11⋊C4—22no—
382Dic11⋊C4—22no—
383Dic11⋊C4—42no—
384Dic11⋊C4—42no—
385Dic11⋊C4—41no—
386Dic11⋊C4—41no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390C4×Dic11—22no—
391C4×Dic11—42no—
392C4×Dic11—42no—
393C4×Dic11—41no—
394C4×Dic11—41no—
395C4×Dic11C22×C414yes—
396C4×Dic11C22×C414yes—
397C2×#535—111no—
398#2377—112no—
399#2375—112no—
400#2367—111no—
401#2367—111no—
402#2366—111no—
403#2366—111no—
404#2364—112no—
405#2358—112no—
406#2341D1111yescharacteristic, complemented
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—21no—
421C23×C11—21no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—21no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11—22no—
430C23×C11—21no—
431C23×C11—22no—
432C23×C11C23×C412yes—
433C23×C11C23×C414yes—
434C23×C11C2511yescharacteristic
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—48no—
448C22×D11—48no—
449C22×D11—48no—
450C22×D11—84no—
451C22×D11—84no—
452C22×D11—84no—
453C22×D11—84no—
454C22×D11C23×C414yes—
455C22×D11C23×C414yes—
456Q8×C11—28no—
457D4×C11—28no—
458D4×C11—48no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—28no—
466C2×C4×C11—21no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—48no—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C23×C414yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11H(5,𝔽2)12yes—
486C2×C4×C11H(5,𝔽2)12yes—
487C2×C4×C11H(5,𝔽2)12yes—
488C22⋊D11—48no—
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—21no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—84no—
518C2×Dic11—84no—
519C2×Dic11C23×C412yes—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C23×C412yes—
523C2×Dic11H(5,𝔽2)12yes—
524D44—28no—
525D44—28no—
526D44—48no—
527C4×D11—84no—
528C4×D11—84no—
529C4×D11—84no—
530C4×D11—84no—
531C22×#41C2×D1111yescharacteristic
532C23×D4—111no—
533#535—1116no—
534C2×#127—111no—
535C2×#127—111no—
536C2×#124—111no—
537C2×#124—111no—
538C2×#121—112no—
539C2×#121—112no—
540C2×#120—112no—
541C2×#120—112no—
542C2×C4×Q8C2×D1111yescharacteristic, complemented
543C2×C4×Q8C2×D1111yescharacteristic, complemented
544C2×C4×D4—111no—
545C2×C4×D4—111no—
546C2×C4×D4—111no—
547C2×C4×D4—111no—
548C2×C4×D4—112no—
549C2×C4×D4—112no—
550C2×C4×D4—112no—
551C2×C4×D4—112no—
552C2×C4×D4—111no—
553C2×C4×D4—111no—
554C2×#117—111no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391—111no—
558#391—111no—
559#390—111no—
560#390—111no—
561#390—112no—
562#390—112no—
563#390—112no—
564#390—112no—
565#390—111no—
566#390—111no—
567#390C2×D1112yes—
568#390C2×D1112yes—
569#390C2×D1111yescharacteristic, complemented
570#390C2×D1111yescharacteristic, complemented
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—111no—
578#388—111no—
579#388—111no—
580#388—111no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#387—112no—
586#387—112no—
587#387—111no—
588#387—111no—
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#385—112no—
609#384—111no—
610#382—111no—
611#381—112no—
612#380—111no—
613#380C2×D1111yescharacteristic
614#380C2×D1112yescomplemented
615#379—112no—
616#379—112no—
617C4×C4⋊C4—111no—
618C4×C4⋊C4—111no—
619C4×C4⋊C4—111no—
620C4×C4⋊C4—111no—
621C4×C22⋊C4—111no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4C2×D1111yescharacteristic
627C4×C22⋊C4C2×D1112yescomplemented
628#376—111no—
629C2×#95—112no—
630C43—111no—
631C22×C11—22no—
632C22×C11—24no—
633C22×C11—22no—
634C22×C11—22no—
635C22×C11—24no—
636C22×C11—24no—
637C22×C11—41no—
638C22×C11—42no—
639C22×C11—41no—
640C22×C11—42no—
641C22×C11—41no—
642C22×C11—42no—
643C22×C11—41no—
644C22×C11—42no—
645C22×C11C24×C411yescharacteristic
646C22×C11C2×H(5,𝔽2)11yescharacteristic
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C22×C11C2×H(5,𝔽2)11yescharacteristic
649C22×C11C2×H(5,𝔽2)11yescharacteristic
650C22×C11#58511yescharacteristic
651C22×C11#58511yescharacteristic
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—816no—
667C4×C11—22no—
668C4×C11—24no—
669C4×C11—22no—
670C4×C11—42no—
671C4×C11—41no—
672C4×C11—41no—
673C4×C11—42no—
674C4×C11—41no—
675C4×C11#51814yes—
676Dic11—22no—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—42no—
682Dic11—41no—
683Dic11—42no—
684Dic11—41no—
685Dic11—41no—
686C25—112no—
687C2×#41—42no—
688C2×#41—42no—
689C2×#41C4×D1118yescomplemented
690C22×Q8C22×D1111yescharacteristic
691C22×D4—112no—
692C22×D4—112no—
693C22×D4—112no—
694C22×D4—112no—
695C22×D4—118no—
696C22×D4—111no—
697C22×D4—111no—
698C22×D4—112no—
699C22×D4—442no—
700C22×D4—442no—
701C22×D4C22×D1111yescharacteristic
702C22×D4C22×D1112yes—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—112no—
708C23×C4—112no—
709C23×C4C22×D1111yescharacteristic
710C23×C4C22×D1112yes—
711#127—118no—
712#127—118no—
713#124—118no—
714#124—118no—
715#121—1116no—
716#121—1116no—
717#120—1116no—
718#120—1116no—
719C4×Q8—42no—
720C4×Q8—42no—
721C4×D4—442no—
722C4×D4—442no—
723C4×D4—444no—
724C4×D4—444no—
725C4×D4—442no—
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—111no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4C22×D1111yescharacteristic
743C2×C4⋊C4C22×D1111yescharacteristic
744C2×C4⋊C4C22×D1112yes—
745C2×C4⋊C4C22×D1112yes—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
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—111no—
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—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—444no—
770C2×C22⋊C4—444no—
771C2×C22⋊C4C22×D1111yescharacteristic
772C2×C22⋊C4C22×D1112yes—
773C2×C22⋊C4C22×D1112yes—
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4C22×D1112yes—
778C2×C42—111no—
779C2×C42—111no—
780C2×C42—111no—
781C2×C42—111no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—111no—
787C2×C42—111no—
788C2×C42C22×D1111yescharacteristic
789C2×C42C22×D1111yescharacteristic
790C2×C42C22×D1112yes—
791C2×C42C22×D1112yes—
792#95—111no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—111no—
797#95—111no—
798#95—111no—
799#95—111no—
800#95—111no—
801#95—111no—
802#95—111no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—111no—
810#95—111no—
811#95C22×D1111yescharacteristic
812#95C22×D1111yescharacteristic
813#95C22×D1112yes—
814C2×C11—42no—
815C2×C11—44no—
816C2×C11C2×#51811yescharacteristic
817C2×C11C4×H(5,𝔽2)11yescharacteristic
818C2×C11C4×H(5,𝔽2)11yescharacteristic
819C2×C11#354311yescharacteristic
820C2×C11#354611yescharacteristic
821C2×C11#355811yescharacteristic
822C2×C11#356211yescharacteristic
823D11—44no—
824D11—44no—
825C24—112no—
826C24—112no—
827C24—118no—
828C24—442no—
829C24—442no—
830C24—442no—
831C24—442no—
832C24—442no—
833C24—442no—
834C24C23×D1111yescharacteristic
835C24C23×D1112yes—
836#41—416no—
837C2×Q8—22no—
838C2×Q8—22no—
839C2×Q8C2×C4×D1114yes—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—118no—
845C2×D4—118no—
846C2×D4—118no—
847C2×D4—118no—
848C2×D4—114no—
849C2×D4—114no—
850C2×D4—118no—
851C2×D4—222no—
852C2×D4—222no—
853C2×D4—222no—
854C2×D4—222no—
855C2×D4—4416no—
856C2×D4—442no—
857C2×D4—442no—
858C2×D4—442no—
859C2×D4—442no—
860C2×D4—442no—
861C2×D4—442no—
862C2×D4—442no—
863C2×D4—442no—
864C2×D4—442no—
865C2×D4—442no—
866C2×D4C2×C4×D1114yes—
867C2×D4C2×C4×D1118yes—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—111no—
873C22×C4—111no—
874C22×C4—111no—
875C22×C4—111no—
876C22×C4—111no—
877C22×C4—111no—
878C22×C4—111no—
879C22×C4—112no—
880C22×C4—111no—
881C22×C4—112no—
882C22×C4—224no—
883C22×C4—224no—
884C22×C4—224no—
885C22×C4—442no—
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×C4C2×C4×D1114yes—
901C22×C4C2×C4×D1118yes—
902C22×C4C23×D1112yes—
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1112yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1112yes—
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—114no—
916C4⋊C4—114no—
917C4⋊C4—222no—
918C4⋊C4—222no—
919C4⋊C4—222no—
920C4⋊C4—222no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4—441no—
924C4⋊C4—441no—
925C22⋊C4—22no—
926C22⋊C4—24no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—41no—
931C22⋊C4—42no—
932C22⋊C4—114no—
933C22⋊C4—114no—
934C22⋊C4—118no—
935C22⋊C4—118no—
936C22⋊C4—118no—
937C22⋊C4—118no—
938C22⋊C4—224no—
939C22⋊C4—222no—
940C22⋊C4—224no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—442no—
948C22⋊C4—442no—
949C22⋊C4—442no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—441no—
955C42—22no—
956C42—22no—
957C42—42no—
958C42—42no—
959C42—114no—
960C42—114no—
961C42—222no—
962C42—222no—
963C42—222no—
964C42—222no—
965C42—442no—
966C42—442no—
967C42—441no—
968C42—441no—
969C11#3443811yescharacteristic, complemented, Sylow
970C23—22no—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—22no—
976C23—22no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—21no—
981C23—22no—
982C23—114no—
983C23—114no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—448no—
997C23—448no—
998C23—448no—
999C23—884no—
1000C23—884no—
1001C23—884no—
1002C23—884no—
1003C23C22×C4×D1112yes—
1004C23C22×C4×D1114yes—
1005C23C24×D1111yescharacteristic
1006Q8—28no—
1007D4—28no—
1008D4—48no—
1009D4—228no—
1010D4—228no—
1011D4—448no—
1012D4—448no—
1013D4—448no—
1014D4—448no—
1015D4—448no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—28no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—48no—
1039C2×C4—112no—
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—221no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—222no—
1068C2×C4—221no—
1069C2×C4—884no—
1070C2×C4—884no—
1071C2×C4—884no—
1072C2×C4—884no—
1073C2×C4—884no—
1074C2×C4—884no—
1075C2×C4C22×C4×D1114yes—
1076C2×C4C22×C4×D1112yes—
1077C2×C4C22×C4×D1112yes—
1078C2×C4#6703712yes—
1079C2×C4#6703712yes—
1080C2×C4#6704212yes—
1081C22—22no—
1082C22—24no—
1083C22—24no—
1084C22—22no—
1085C22—24no—
1086C22—22no—
1087C22—42no—
1088C22—41no—
1089C22—41no—
1090C22—42no—
1091C22—41no—
1092C22—42no—
1093C22—42no—
1094C22—41no—
1095C22—224no—
1096C22—224no—
1097C22—224no—
1098C22—224no—
1099C22—224no—
1100C22—224no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—8816no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22C2×#6703711yescharacteristic
1113C22C2×#6704211yescharacteristic
1114C22#1062345311yescharacteristic
1115C22D11×H(5,𝔽2)11yescharacteristic
1116C22#1062345711yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—22no—
1120C4—41no—
1121C4—42no—
1122C4—41no—
1123C4—42no—
1124C4—41no—
1125C4—222no—
1126C4—222no—
1127C4—222no—
1128C4—222no—
1129C4—222no—
1130C4—442no—
1131C4—441no—
1132C4—441no—
1133C4—441no—
1134C4—442no—
1135C4#1062301714yes—
1136C2—42no—
1137C2—44no—
1138C2—444no—
1139C2—444no—
1140C2C2×#1062301711yescharacteristic
1141C2#1308182211yescharacteristic
1142C2C4×#6704211yescharacteristic
1143C2#1308294011yescharacteristic
1144C2#1308297511yescharacteristic
1145C2#1308313311yescharacteristic
1146C2#1308320711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2341C2
socle, cosocleC23×C11C25
prime radicalC2×#10623361C2
hypercenter#2341D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. #13071770C2semidirect
3. #13071753C2semidirect
4. #13071683C2semidirect
5. #13071683C2semidirect
6. #13071677C2semidirect
7. #13071677C2semidirect
8. #13071666C2semidirect
9. #13071597C2semidirect
10. #13071446C2semidirect
11. C22⋊C4×D44C2semidirect
12. #13071436C2semidirect
13. #13071381C2semidirect
14. #13071340C2semidirect
15. #13071323C2semidirect
16. #13071316C2semidirect
17. #13071275C2semidirect
18. #13071275C2semidirect
19. #13071223C2semidirect
20. #13071180C2semidirect
21. C4×#67000C2semidirect
22. #13071112C2semidirect
23. C11×#2341C2semidirect
26. C2×C4×Q8×C11C22semidirect
27. C2×C4×Q8×C11C22semidirect
28. #10623361C4semidirect
35. C2×D4×Dic11C22semidirect
36. C2×D4×Dic11C22semidirect
42. C2×(C22⋊D11)⋊C4C22semidirect
43. C2×(C22⋊D11)⋊C4C22semidirect
44. C2×(C22⋊D11)⋊C4C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
52. C11×#390C22semidirect
53. C11×#390C22semidirect
55. C11×#380C22semidirect
57. C4×C11×C22⋊C4C22semidirect
58. #10622843C22semidirect
59. #10622843C22semidirect
63. #10622824C22semidirect
65. C2×C11⋊#95C22semidirect
66. #10622603C22semidirect
67. #10622603C22semidirect
68. #10622603C22semidirect
69. #10622603C22semidirect
70. #10622602C22semidirect
71. #10622602C22semidirect
72. #10622602C22semidirect
73. #10622602C22semidirect
76. #10622590C22semidirect
77. #10622589C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. #10622571C22semidirect
81. #10622571C22semidirect
82. #10622571C22semidirect
83. #10622571C22semidirect
84. #10622570C22semidirect
85. #10622570C22semidirect
86. #10622570C22semidirect
87. #10622570C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
100. #10622553C22semidirect
101. #10622553C22semidirect
102. #10622553C22semidirect
103. #10622553C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. #10622545C22semidirect
111. C4×Dic11⋊C4C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. C42×Dic11C22semidirect
118. #10622267C22semidirect
119. #10622267C22semidirect
120. #10622267C22semidirect
121. #10622266C22semidirect
122. #10622266C22semidirect
123. #10622266C22semidirect
127. C2×C11×#41C2×C4semidirect
141. C22×D44C2×C4semidirect
173. #67000C2×C4semidirect
174. #67000C2×C4semidirect
175. #66993C2×C4semidirect
176. #66993C2×C4semidirect
177. #66990C2×C4semidirect
178. #66990C2×C4semidirect
181. #66983C2×C4semidirect
182. #66983C2×C4semidirect
199. #66979C2×C4semidirect
406. #2341D11semidirect
542. C2×C4×Q8C2×D11semidirect
543. C2×C4×Q8C2×D11semidirect
569. #390C2×D11semidirect
570. #390C2×D11semidirect
614. #380C2×D11semidirect
627. C4×C22⋊C4C2×D11semidirect
689. C2×#41C4×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×#106233612
#130717702
#130717532
#130716832
#130716772
#130716662
#130715972
#130714462
C22⋊C4×D442
#130714362
#130713812
#130713402
#130713232
#130713162
#130712752
#130712232
#130711802
C4×#670002
#130711122
C11×#23412
#3443811