Finite Group Databasebeta

← #14917226

Subgroups — #14917226

Order 2816.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623138C211yesmaximal, characteristic
2#13071791C212yesmaximal, complemented
3#13071753C212yesmaximal, complemented
4#13071677C212yesmaximal, complemented
5#13071653C211yesmaximal, characteristic, complemented
6#13071650C211yesmaximal, characteristic, complemented
7#13071637C211yesmaximal, characteristic, complemented
8#13071634C211yesmaximal, characteristic, complemented
9#13071596C212yesmaximal, complemented
10#13071508C211yesmaximal, characteristic, complemented
11#13071505C211yesmaximal, characteristic, complemented
12#13071437C211yesmaximal, characteristic, complemented
13D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13071430C212yesmaximal, complemented
15#13071427C212yesmaximal, complemented
16#13071309C211yesmaximal, characteristic, complemented
17#13071278C212yesmaximal, complemented
18#13071273C212yesmaximal, complemented
19#13071205C211yesmaximal, characteristic, complemented
20#121×Dic11C211yesmaximal, characteristic, complemented
21#13071122C211yesmaximal, characteristic, complemented
22#13071104C211yesmaximal, characteristic, complemented
23C11×#2324C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C2×#66993C2212yes—
30C2×#66991C2211yescharacteristic
31C2×#66990C2212yes—
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2212yescomplemented
34C2×#66983C2211yescharacteristic
35C22×(C2×D11)⋊C4C2212yes—
36C22×C4×Dic11C2211yescharacteristic, complemented
37#10623138C4116yescomplemented
38C2×#66948C2211yescharacteristic
39C2×#66946C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×#66945C2211yescharacteristic, complemented
42C2×C4⋊C4×D11C2211yescharacteristic, complemented
43C2×#66938C2212yes—
44C2×#66935C2212yes—
45C2×(C22⋊D11)⋊C4C2212yescomplemented
46C2×(C22⋊D11)⋊C4C2212yescomplemented
47C2×C22⋊C4×D11C2212yes—
48C2×C4×D44C2211yescharacteristic
49C2×C4×D44C2212yescomplemented
50C11×#390C2211yescharacteristic
51C11×#390C2212yescomplemented
52C11×#389C2211yescharacteristic, complemented
53C11×#388C2212yescomplemented
54C11×#386C2212yescomplemented
55C11×#385C2212yescomplemented
56C11×#380C2211yescharacteristic, complemented
57C4×C11×C4⋊C4C2211yescharacteristic, complemented
58#10622834C2211yescharacteristic
59#10622833C2212yescomplemented
60#10622826C2212yes—
61#10622826C2212yescomplemented
62#10622825C2211yescharacteristic, complemented
63C4×C22⋊Dic11C2212yescomplemented
64#10622603C2212yes—
65#10622603C2212yescomplemented
66#10622603C2212yescomplemented
67#10622602C2212yescomplemented
68#10622601C2211yescharacteristic
69#10622601C2211yescharacteristic
70#10622601C2211yescharacteristic
71#10622601C2212yescomplemented
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622598C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76C4⋊C4×Dic11C2211yescharacteristic, complemented
77C4⋊C4×Dic11C2212yescomplemented
78#10622587C2211yescharacteristic, complemented
79#10622587C2211yescharacteristic, complemented
80#10622586C2211yescharacteristic, complemented
81#10622571C2211yescharacteristic
82#10622571C2211yescharacteristic
83#10622571C2212yes—
84#10622571C2211yescharacteristic, complemented
85#10622571C2211yescharacteristic, complemented
86#10622571C2212yescomplemented
87#10622570C2212yes—
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622569C2212yes—
91#10622569C2212yes—
92#10622569C2212yescomplemented
93#10622569C2212yescomplemented
94#10622569C2212yescomplemented
95#10622568C2212yes—
96#10622568C2212yes—
97#10622564C2212yescomplemented
98#10622559C2212yescomplemented
99#10622557C2212yescomplemented
100#10622557C2212yescomplemented
101C22⋊C4×Dic11C2212yescomplemented
102#10622553C2212yes—
103#10622553C2212yescomplemented
104#10622552C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2211yescharacteristic
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110C4×Dic11⋊C4C2212yescomplemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yes—
113#10622282C2212yes—
114#10622282C2212yescomplemented
115#10622281C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622264C2212yescomplemented
122#10622264C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C23×Dic11C2311yescharacteristic
137C2×D4×D11—42no—
138C2×D4×D11—42no—
139C2×D4×D11C2×C418yescomplemented
140C2×#4339—42no—
141C2×#4339—42no—
142C2×#4339C2×C418yescomplemented
143C22×D44C2311yescharacteristic
144C22×D44C2312yes—
145C22×D44C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C11×#121C2×C418yescomplemented
153C4×D4×C11—42no—
154C11×#117—42no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176#66993C2×C4116yescomplemented
177#66991C2×C418yescomplemented
178#66990C2×C4116yescomplemented
179D4×Dic11—42no—
180D4×Dic11—44no—
181#66983C2×C418yescomplemented
182C2×(C2×D11)⋊C4—44no—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×C4×Dic11—42no—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220#66948C2×C418yescomplemented
221#66946—42no—
222#66945—42no—
223#66945C2×C418yescomplemented
224C4⋊C4×D11—42no—
225#66938C2×C4116yescomplemented
226#66935C2×C4116yescomplemented
227(C22⋊D11)⋊C4—44no—
228(C22⋊D11)⋊C4—44no—
229C22⋊C4×D11—44no—
230C4×D44—44no—
231C4×D44—42no—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252#34411—111nomaximal, Sylow
253C24×C11C2412yes—
254C24×C11C2411yescharacteristic
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11—42no—
261C23×D11C22×C418yes—
262C23×D11C2411yescharacteristic
263C23×D11C2412yes—
264C23×D11C2411yescharacteristic
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—42no—
268C2×D4×C11—42no—
269C2×D4×C11C22×C414yes—
270C2×D4×C11C22×C418yes—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C2×C22⋊D11—42no—
287C2×C22⋊D11—42no—
288C2×C22⋊D11—41no—
289C2×C22⋊D11—41no—
290C2×C22⋊D11—41no—
291C2×C22⋊D11—41no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11C22×C418yes—
297C2×C22⋊D11C22×C418yes—
298C2×C22⋊D11C22×C418yes—
299C2×C22⋊D11C22×C414yes—
300C2×C22⋊D11C22×C414yes—
301C22×Dic11—22no—
302C22×Dic11—22no—
303C22×Dic11—24no—
304C22×Dic11—41no—
305C22×Dic11—41no—
306C22×Dic11—41no—
307C22×Dic11—41no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319D4×D11—416no—
320#4339—416no—
321C2×D44—22no—
322C2×D44—22no—
323C2×D44—42no—
324C2×D44—42no—
325C2×D44—41no—
326C2×D44—41no—
327C2×D44C22×C414yes—
328C2×D44C22×C414yes—
329C2×D44C22×C418yes—
330C2×C4×D11—24no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×Dic22—41no—
346C2×Dic22—41no—
347C2×Dic22C22×C414yes—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4—41no—
352C11×C4⋊C4—41no—
353C11×C4⋊C4C22×C414yes—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—41no—
358C11×C22⋊C4—41no—
359C11×C22⋊C4—42no—
360C11×C22⋊C4C22×C418yes—
361C42×C11—22no—
362C42×C11—22no—
363C42×C11—42no—
364C22⋊Dic11—24no—
365C22⋊Dic11—42no—
366C22⋊Dic11—42no—
367C22⋊Dic11—42no—
368C22⋊Dic11C22×C418yes—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4—41no—
382(C2×D11)⋊C4—41no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—41no—
385(C2×D11)⋊C4—41no—
386(C2×D11)⋊C4C22×C418yes—
387(C2×D11)⋊C4C22×C418yes—
388(C2×D11)⋊C4C22×C418yes—
389C4⋊Dic11—24no—
390C4⋊Dic11—22no—
391C4⋊Dic11—22no—
392C4⋊Dic11C22×C414yes—
393Dic11⋊C4—24no—
394Dic11⋊C4—42no—
395Dic11⋊C4—42no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—42no—
399C4×Dic11—42no—
400C4×Dic11—42no—
401C4×Dic11—41no—
402C4×Dic11—41no—
403C4×Dic11—42no—
404C4×Dic11C22×C418yes—
405C2×#535—111no—
406#2380—112no—
407#2375—112no—
408#2366—112no—
409#2363—111no—
410#2363—111no—
411#2361—111no—
412#2361—111no—
413#2358—112no—
414#2347—111no—
415#2347—111no—
416D4×C22⋊C4—111no—
417D4×C22⋊C4—111no—
418#2337—112no—
419#2337—112no—
420#2324—111no—
421#2324D1111yescharacteristic, complemented
422#2321—112no—
423#2321—112no—
424#2311—111no—
425C4×#121—111no—
426C4×#121—111no—
427#2297—111no—
428C23×C11—22no—
429C23×C11—21no—
430C23×C11—22no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—21no—
436C23×C11—22no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11C23×C414yes—
441C23×C11C23×C412yes—
442C23×C11C2511yescharacteristic
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—22no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—22no—
461C22×D11—48no—
462C22×D11—48no—
463C22×D11—48no—
464C22×D11—84no—
465C22×D11—84no—
466C22×D11—84no—
467C22×D11—84no—
468C22×D11C23×C412yes—
469C22×D11C23×C414yes—
470C22×D11C23×C412yes—
471D4×C11—28no—
472D4×C11—48no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—22no—
477C2×C4×C11—28no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—84no—
497C2×C4×C11C23×C414yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C23×C412yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C2×C4×C11H(5,𝔽2)12yes—
502C22⋊D11—44no—
503C22⋊D11—44no—
504C22⋊D11—48no—
505C22⋊D11—48no—
506C22⋊D11—48no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—44no—
530C2×Dic11—44no—
531C2×Dic11—84no—
532C2×Dic11C23×C412yes—
533C2×Dic11C23×C414yes—
534C2×Dic11C23×C412yes—
535C2×Dic11H(5,𝔽2)12yes—
536C2×Dic11H(5,𝔽2)12yes—
537D44—28no—
538D44—48no—
539D44—44no—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—84no—
543C4×D11—84no—
544C4×D11—84no—
545Dic22—44no—
546C22×#41—111no—
547C23×D4—111no—
548#535—1116no—
549C2×#127—112no—
550C2×#124—112no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#121—111no—
554C2×#121C2×D1111yescharacteristic
555C2×#120—112no—
556C2×#120—112no—
557C2×C4×D4—111no—
558C2×C4×D4—112no—
559C2×C4×D4—111no—
560C2×C4×D4—112no—
561C2×C4×D4—112no—
562C2×C4×D4—112no—
563C2×C4×D4—111no—
564C2×C4×D4C2×D1111yescharacteristic
565C2×#117—111no—
566C2×#117—111no—
567C2×#117C2×D1111yescharacteristic, complemented
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C22⋊C4—112no—
571C22×C42—111no—
572#391—111no—
573#391—111no—
574#391—112no—
575#390—111no—
576#390—111no—
577#390—111no—
578#390—112no—
579#390—111no—
580#390—112no—
581#390—112no—
582#390—112no—
583#390—111no—
584#390C2×D1111yescharacteristic
585#390C2×D1112yescomplemented
586#389—111no—
587#389—111no—
588#389—111no—
589#389C2×D1111yescharacteristic, complemented
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388—112no—
599#388—112no—
600#388—112no—
601#388C2×D1112yescomplemented
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386—111no—
612#386—111no—
613#386—111no—
614#386—112no—
615#386—111no—
616#386—112no—
617#386—112no—
618#386—112no—
619#386C2×D1112yescomplemented
620#385—112no—
621#385—112no—
622#385—112no—
623#385C2×D1112yescomplemented
624#383—112no—
625#383—112no—
626#380—111no—
627#380—111no—
628#380—111no—
629#380C2×D1111yescharacteristic, complemented
630#379—112no—
631#379—112no—
632C4×C4⋊C4—112no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—111no—
635C4×C4⋊C4—111no—
636C4×C4⋊C4—112no—
637C4×C4⋊C4C2×D1111yescharacteristic, complemented
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—111no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—112no—
646C22×C11—22no—
647C22×C11—24no—
648C22×C11—22no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—22no—
652C22×C11—42no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11—41no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11C24×C411yescharacteristic
661C22×C11C2×H(5,𝔽2)11yescharacteristic
662C22×C11C2×H(5,𝔽2)11yescharacteristic
663C22×C11C2×H(5,𝔽2)11yescharacteristic
664C22×C11C2×H(5,𝔽2)11yescharacteristic
665C22×C11#58511yescharacteristic
666C22×C11#58511yescharacteristic
667C2×D11—22no—
668C2×D11—24no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—24no—
673C2×D11—24no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—41no—
677C2×D11—42no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—42no—
681C2×D11—41no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—42no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—42no—
688C2×D11—816no—
689C4×C11—22no—
690C4×C11—24no—
691C4×C11—42no—
692C4×C11—41no—
693C4×C11—41no—
694C4×C11—42no—
695C4×C11—41no—
696C4×C11—41no—
697C4×C11#51814yes—
698Dic11—22no—
699Dic11—22no—
700Dic11—24no—
701Dic11—22no—
702Dic11—22no—
703Dic11—42no—
704Dic11—41no—
705Dic11—41no—
706Dic11—42no—
707C25—112no—
708C2×#41—118no—
709C2×#41—442no—
710C2×#41—442no—
711C22×Q8—111no—
712C22×D4—112no—
713C22×D4—112no—
714C22×D4—111no—
715C22×D4—112no—
716C22×D4—111no—
717C22×D4—118no—
718C22×D4—111no—
719C22×D4—112no—
720C22×D4—111no—
721C22×D4—442no—
722C22×D4—442no—
723C22×D4C22×D1111yescharacteristic
724C22×D4C22×D1112yes—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—112no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—112no—
733C23×C4C22×D1111yescharacteristic
734C23×C4C22×D1112yes—
735#127—1116no—
736#124—1116no—
737#121—118no—
738#121—118no—
739#121—118no—
740#121C4×D1118yescomplemented
741#120—1116no—
742#120—1116no—
743C4×D4—42no—
744C4×D4—442no—
745C4×D4—444no—
746C4×D4—442no—
747C4×D4—442no—
748C4×D4—444no—
749C4×D4—444no—
750C4×D4—444no—
751#117—42no—
752#117—118no—
753#117—442no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—442no—
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C4⋊C4C22×D1111yescharacteristic
765C2×C4⋊C4C22×D1111yescharacteristic
766C2×C4⋊C4C22×D1112yes—
767C2×C4⋊C4C22×D1111yescharacteristic
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—444no—
794C2×C22⋊C4—444no—
795C2×C22⋊C4C22×D1112yes—
796C2×C22⋊C4C22×D1111yescharacteristic
797C2×C22⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C42—112no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—111no—
810C2×C42—111no—
811C2×C42—442no—
812C2×C42C22×D1111yescharacteristic
813C2×C42C22×D1111yescharacteristic
814C2×C42C22×D1112yes—
815#95—111no—
816#95—111no—
817#95—111no—
818#95—111no—
819#95—112no—
820#95—111no—
821#95—111no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—111no—
826#95—111no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95C22×D1112yes—
833#95C22×D1112yes—
834#95C22×D1112yes—
835C2×C11—44no—
836C2×C11—42no—
837C2×C11C2×#51811yescharacteristic
838C2×C11C4×H(5,𝔽2)11yescharacteristic
839C2×C11C4×H(5,𝔽2)11yescharacteristic
840C2×C11#353711yescharacteristic
841C2×C11#354011yescharacteristic
842C2×C11#354611yescharacteristic
843C2×C11#354611yescharacteristic
844D11—42no—
845D11—44no—
846D11—42no—
847C24—111no—
848C24—112no—
849C24—111no—
850C24—118no—
851C24—442no—
852C24—442no—
853C24—442no—
854C24—442no—
855C24—442no—
856C24—442no—
857C24C23×D1112yes—
858C24C23×D1111yescharacteristic
859#41—4416no—
860C2×Q8—114no—
861C2×Q8—441no—
862C2×Q8—441no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—114no—
868C2×D4—118no—
869C2×D4—118no—
870C2×D4—118no—
871C2×D4—114no—
872C2×D4—114no—
873C2×D4—114no—
874C2×D4—118no—
875C2×D4—222no—
876C2×D4—222no—
877C2×D4—442no—
878C2×D4—441no—
879C2×D4—441no—
880C2×D4—442no—
881C2×D4—4416no—
882C2×D4—442no—
883C2×D4—442no—
884C2×D4—442no—
885C2×D4—442no—
886C2×D4—441no—
887C2×D4—441no—
888C2×D4—441no—
889C2×D4—441no—
890C2×D4—442no—
891C2×D4—442no—
892C2×D4C2×C4×D1114yes—
893C2×D4C2×C4×D1118yes—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—111no—
900C22×C4—112no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—112no—
909C22×C4—112no—
910C22×C4—224no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—224no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—441no—
927C22×C4—441no—
928C22×C4—441no—
929C22×C4—441no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4C2×C4×D1114yes—
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1112yes—
936C22×C4C23×D1112yes—
937C22×C4C23×D1111yescharacteristic
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1112yes—
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—42no—
947C4⋊C4—114no—
948C4⋊C4—224no—
949C4⋊C4—224no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—442no—
953C4⋊C4—442no—
954C4⋊C4C2×C4×D1114yes—
955C22⋊C4—42no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—118no—
962C22⋊C4—118no—
963C22⋊C4—118no—
964C22⋊C4—118no—
965C22⋊C4—222no—
966C22⋊C4—222no—
967C22⋊C4—224no—
968C22⋊C4—222no—
969C22⋊C4—222no—
970C22⋊C4—224no—
971C22⋊C4—442no—
972C22⋊C4—442no—
973C22⋊C4—442no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—441no—
979C22⋊C4—442no—
980C22⋊C4—441no—
981C22⋊C4—441no—
982C22⋊C4—441no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4C2×C4×D1118yes—
987C42—22no—
988C42—22no—
989C42—42no—
990C42—118no—
991C42—222no—
992C42—222no—
993C42—441no—
994C42—441no—
995C42—442no—
996C42—442no—
997C42—442no—
998C42—442no—
999C11#3441111yescharacteristic, complemented, Sylow
1000C23—21no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—21no—
1005C23—22no—
1006C23—22no—
1007C23—21no—
1008C23—22no—
1009C23—21no—
1010C23—22no—
1011C23—21no—
1012C23—112no—
1013C23—114no—
1014C23—112no—
1015C23—221no—
1016C23—222no—
1017C23—221no—
1018C23—222no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—221no—
1023C23—222no—
1024C23—221no—
1025C23—221no—
1026C23—222no—
1027C23—221no—
1028C23—222no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—222no—
1033C23—448no—
1034C23—448no—
1035C23—448no—
1036C23—884no—
1037C23—884no—
1038C23—884no—
1039C23—884no—
1040C23C22×C4×D1114yes—
1041C23C22×C4×D1112yes—
1042C23C24×D1111yescharacteristic
1043Q8—444no—
1044D4—28no—
1045D4—48no—
1046D4—228no—
1047D4—444no—
1048D4—448no—
1049D4—448no—
1050D4—444no—
1051D4—444no—
1052D4—448no—
1053D4—448no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—28no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—84no—
1078C2×C4—112no—
1079C2×C4—114no—
1080C2×C4—112no—
1081C2×C4—112no—
1082C2×C4—112no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—221no—
1089C2×C4—222no—
1090C2×C4—221no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—228no—
1094C2×C4—228no—
1095C2×C4—222no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—222no—
1107C2×C4—444no—
1108C2×C4—444no—
1109C2×C4—884no—
1110C2×C4—884no—
1111C2×C4—884no—
1112C2×C4—884no—
1113C2×C4C22×C4×D1114yes—
1114C2×C4C22×C4×D1112yes—
1115C2×C4C22×C4×D1112yes—
1116C2×C4#6703712yes—
1117C2×C4#6704212yes—
1118C22—22no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—22no—
1123C22—24no—
1124C22—41no—
1125C22—42no—
1126C22—42no—
1127C22—41no—
1128C22—42no—
1129C22—41no—
1130C22—41no—
1131C22—42no—
1132C22—222no—
1133C22—222no—
1134C22—224no—
1135C22—222no—
1136C22—224no—
1137C22—222no—
1138C22—222no—
1139C22—224no—
1140C22—222no—
1141C22—441no—
1142C22—442no—
1143C22—441no—
1144C22—442no—
1145C22—441no—
1146C22—441no—
1147C22—441no—
1148C22—442no—
1149C22—441no—
1150C22—441no—
1151C22—442no—
1152C22—441no—
1153C22—8816no—
1154C22C23×C4×D1111yescharacteristic
1155C22C2×#6703711yescharacteristic
1156C22C2×#6704211yescharacteristic
1157C22D11×H(5,𝔽2)11yescharacteristic
1158C22D11×H(5,𝔽2)11yescharacteristic
1159C22#1062345511yescharacteristic
1160C22#1062345711yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—42no—
1169C4—222no—
1170C4—222no—
1171C4—224no—
1172C4—222no—
1173C4—222no—
1174C4—441no—
1175C4—441no—
1176C4—442no—
1177C4—442no—
1178C4#1062307614yes—
1179C2—44no—
1180C2—42no—
1181C2—442no—
1182C2—444no—
1183C2—442no—
1184C2C2×#1062307611yescharacteristic
1185C2#1308182011yescharacteristic
1186C2#1308182211yescharacteristic
1187C2#1308285411yescharacteristic
1188C2#1308288811yescharacteristic
1189C2#1308297811yescharacteristic
1190C2#1308298611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2324C2
socle, cosocleC23×C11C25
prime radicalC2×#10623138C2
hypercenter#2324D11
hypocenterC11#34411
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13071791C2semidirect
3. #13071753C2semidirect
4. #13071677C2semidirect
5. #13071653C2semidirect
6. #13071650C2semidirect
7. #13071637C2semidirect
8. #13071634C2semidirect
9. #13071596C2semidirect
10. #13071508C2semidirect
11. #13071505C2semidirect
12. #13071437C2semidirect
13. D4×(C2×D11)⋊C4C2semidirect
14. #13071430C2semidirect
15. #13071427C2semidirect
16. #13071309C2semidirect
17. #13071278C2semidirect
18. #13071273C2semidirect
19. #13071205C2semidirect
20. #121×Dic11C2semidirect
21. #13071122C2semidirect
22. #13071104C2semidirect
23. C11×#2324C2semidirect
28. C2×C11×#117C22semidirect
33. C2×D4×Dic11C22semidirect
36. C22×C4×Dic11C22semidirect
37. #10623138C4semidirect
41. C2×#66945C22semidirect
42. C2×C4⋊C4×D11C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
46. C2×(C22⋊D11)⋊C4C22semidirect
49. C2×C4×D44C22semidirect
51. C11×#390C22semidirect
52. C11×#389C22semidirect
53. C11×#388C22semidirect
54. C11×#386C22semidirect
55. C11×#385C22semidirect
56. C11×#380C22semidirect
57. C4×C11×C4⋊C4C22semidirect
59. #10622833C22semidirect
61. #10622826C22semidirect
62. #10622825C22semidirect
63. C4×C22⋊Dic11C22semidirect
65. #10622603C22semidirect
66. #10622603C22semidirect
67. #10622602C22semidirect
71. #10622601C22semidirect
74. #10622598C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. #10622587C22semidirect
79. #10622587C22semidirect
80. #10622586C22semidirect
84. #10622571C22semidirect
85. #10622571C22semidirect
86. #10622571C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
92. #10622569C22semidirect
93. #10622569C22semidirect
94. #10622569C22semidirect
97. #10622564C22semidirect
98. #10622559C22semidirect
99. #10622557C22semidirect
100. #10622557C22semidirect
101. C22⋊C4×Dic11C22semidirect
103. #10622553C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. C4×Dic11⋊C4C22semidirect
111. #10622541C22semidirect
114. #10622282C22semidirect
115. #10622281C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622264C22semidirect
122. #10622264C22semidirect
123. #10622259C22semidirect
139. C2×D4×D11C2×C4semidirect
142. C2×#4339C2×C4semidirect
152. C11×#121C2×C4semidirect
176. #66993C2×C4semidirect
177. #66991C2×C4semidirect
178. #66990C2×C4semidirect
181. #66983C2×C4semidirect
220. #66948C2×C4semidirect
223. #66945C2×C4semidirect
225. #66938C2×C4semidirect
226. #66935C2×C4semidirect
421. #2324D11semidirect
567. C2×#117C2×D11semidirect
585. #390C2×D11semidirect
589. #389C2×D11semidirect
601. #388C2×D11semidirect
619. #386C2×D11semidirect
623. #385C2×D11semidirect
629. #380C2×D11semidirect
637. C4×C4⋊C4C2×D11semidirect
740. #121C4×D11semidirect
999. C11#34411semidirect

Maximal subgroups

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

subgroupindex
C2×#106231382
#130717912
#130717532
#130716772
#130716532
#130716502
#130716372
#130716342
#130715962
#130715082
#130715052
#130714372
D4×(C2×D11)⋊C42
#130714302
#130714272
#130713092
#130712782
#130712732
#130712052
#121×Dic112
#130711222
#130711042
C11×#23242
#3441111