Finite Group Databasebeta

← #14917218

Subgroups — #14917218

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#13071756C212yesmaximal, complemented
4#13071678C212yesmaximal, complemented
5#13071658C211yesmaximal, characteristic, complemented
6#13071652C211yesmaximal, characteristic, complemented
7#13071632C211yesmaximal, characteristic, complemented
8#13071592C212yesmaximal, complemented
9#13071508C211yesmaximal, characteristic, complemented
10#13071505C211yesmaximal, characteristic, complemented
11#13071437C211yesmaximal, characteristic, complemented
12D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
13#13071430C212yesmaximal, complemented
14#13071427C212yesmaximal, complemented
15#13071312C211yesmaximal, characteristic, complemented
16#13071310C211yesmaximal, characteristic, complemented
17#13071272C212yesmaximal, complemented
18#13071270C212yesmaximal, complemented
19#13071209C211yesmaximal, characteristic, complemented
20#13071124C211yesmaximal, characteristic, complemented
21C4×#66991C211yesmaximal, characteristic, complemented
22#13071102C211yesmaximal, characteristic, complemented
23C11×#2361C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yescomplemented
29C22×C11×C4⋊C4C2211yescharacteristic, complemented
30C2×#66993C2212yes—
31C2×#66991C2211yescharacteristic
32C2×#66990C2212yes—
33C2×D4×Dic11C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×C4×C22⋊D11C2212yescomplemented
36C2×C4×C22⋊D11C2212yescomplemented
37C22×(C2×D11)⋊C4C2212yes—
38C2×#66979C2211yescharacteristic, complemented
39#10623138C4116yescomplemented
40C2×#66948C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66946C2212yescomplemented
43C2×#66945C2211yescharacteristic
44C2×#66938C2212yes—
45C2×#66935C2212yes—
46C2×C22⋊C4×D11C2212yes—
47C2×C4×D44C2211yescharacteristic
48C2×#66925C2211yescharacteristic, complemented
49C2×C42×D11C2211yescharacteristic, complemented
50C11×#390C2211yescharacteristic
51C11×#389C2211yescharacteristic, complemented
52C11×#388C2212yescomplemented
53C11×#386C2212yescomplemented
54C11×#385C2212yescomplemented
55C4×C11×C4⋊C4C2211yescharacteristic, complemented
56C4×C11×C22⋊C4C2211yescharacteristic, complemented
57#10622834C2211yescharacteristic
58#10622834C2212yescomplemented
59#10622833C2212yescomplemented
60#10622826C2212yes—
61#10622826C2212yes—
62#10622826C2212yescomplemented
63#10622826C2212yescomplemented
64C4×C22⋊Dic11C2211yescharacteristic, complemented
65C4×C22⋊Dic11C2212yescomplemented
66#10622603C2212yes—
67#10622603C2212yescomplemented
68#10622603C2212yescomplemented
69#10622602C2212yescomplemented
70#10622601C2211yescharacteristic
71#10622601C2212yes—
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic, complemented
75#10622600C2211yescharacteristic, complemented
76#10622598C2211yescharacteristic, complemented
77C4⋊C4×Dic11C2211yescharacteristic, complemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2212yescomplemented
80#10622587C2212yescomplemented
81#10622586C2211yescharacteristic, complemented
82#10622571C2212yes—
83#10622571C2212yescomplemented
84#10622570C2211yescharacteristic
85#10622570C2211yescharacteristic
86#10622570C2212yescomplemented
87#10622570C2212yescomplemented
88#10622569C2212yes—
89#10622569C2212yes—
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622569C2211yescharacteristic, complemented
93#10622569C2211yescharacteristic, complemented
94#10622568C2212yes—
95#10622568C2212yes—
96#10622564C2212yescomplemented
97#10622559C2212yescomplemented
98#10622557C2212yescomplemented
99#10622557C2212yescomplemented
100C22⋊C4×Dic11C2212yescomplemented
101#10622553C2212yes—
102#10622553C2212yescomplemented
103#10622552C2211yescharacteristic
104#10622552C2212yescomplemented
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2211yescharacteristic
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108C4×Dic11⋊C4C2212yescomplemented
109#10622541C2211yescharacteristic, complemented
110#10622283C2212yes—
111#10622282C2212yes—
112#10622282C2212yescomplemented
113#10622281C2212yescomplemented
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116#10622278C2211yescharacteristic
117#10622278C2211yescharacteristic
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622264C2212yescomplemented
121#10622264C2212yescomplemented
122#10622259C2211yescharacteristic, complemented
123#10622259C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2312yes—
136C2×D4×D11—42no—
137C2×D4×D11—42no—
138C2×D4×D11C2×C418yescomplemented
139C2×#4339—42no—
140C2×#4339—42no—
141C2×#4339C2×C418yescomplemented
142C22×D44C2311yescharacteristic
143C22×D44C2311yescharacteristic
144C22×D44C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C11×#121C2×C418yescomplemented
153C4×D4×C11—42no—
154C4×D4×C11—44no—
155C2×C11×C4⋊C4—42no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177#66993C2×C4116yescomplemented
178#66991C2×C418yescomplemented
179#66990C2×C4116yescomplemented
180D4×Dic11—42no—
181#66983C2×C418yescomplemented
182C4×C22⋊D11—44no—
183C4×C22⋊D11—44no—
184C2×(C2×D11)⋊C4—44no—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204#66979—42no—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222#66948C2×C418yescomplemented
223#66946—42no—
224#66946—44no—
225#66945C2×C418yescomplemented
226#66938C2×C4116yescomplemented
227#66935C2×C4116yescomplemented
228C22⋊C4×D11—44no—
229C4×D44—42no—
230#66925—42no—
231C42×D11—42no—
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
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—24no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11C22×C414yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C2×C22⋊D11—42no—
290C2×C22⋊D11—42no—
291C2×C22⋊D11—41no—
292C2×C22⋊D11—41no—
293C2×C22⋊D11—41no—
294C2×C22⋊D11—41no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11—42no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11C22×C418yes—
300C2×C22⋊D11C22×C418yes—
301C2×C22⋊D11C22×C418yes—
302C2×C22⋊D11C22×C414yes—
303C2×C22⋊D11C22×C414yes—
304C22×Dic11—42no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316D4×D11—416no—
317#4339—416no—
318C2×D44—22no—
319C2×D44—22no—
320C2×D44—42no—
321C2×D44—42no—
322C2×D44—41no—
323C2×D44—41no—
324C2×D44C22×C414yes—
325C2×D44C22×C414yes—
326C2×D44C22×C418yes—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
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—24no—
350C11×C4⋊C4—22no—
351C11×C4⋊C4—42no—
352C11×C4⋊C4C22×C414yes—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—41no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C11×C22⋊C4C22×C418yes—
359C42×C11—22no—
360C42×C11—22no—
361C42×C11—42no—
362C22⋊Dic11—24no—
363C22⋊Dic11—22no—
364C22⋊Dic11—42no—
365C22⋊Dic11—42no—
366C22⋊Dic11—41no—
367C22⋊Dic11—42no—
368C22⋊Dic11C22×C418yes—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—41no—
373(C2×D11)⋊C4—41no—
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—41no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—41no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4C22×C418yes—
386(C2×D11)⋊C4C22×C418yes—
387(C2×D11)⋊C4C22×C418yes—
388C4⋊Dic11—22no—
389C4⋊Dic11—22no—
390C4⋊Dic11—42no—
391C4⋊Dic11C22×C414yes—
392Dic11⋊C4—24no—
393Dic11⋊C4—41no—
394Dic11⋊C4—41no—
395Dic11⋊C4—42no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—41no—
399C4×Dic11—41no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11—42no—
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#2361D1111yescharacteristic, complemented
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#2324—111no—
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—21no—
431C23×C11—22no—
432C23×C11—21no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—22no—
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—22no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—21no—
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—21no—
475C2×C4×C11—21no—
476C2×C4×C11—22no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—28no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—84no—
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—
502C2×C4×C11H(5,𝔽2)12yes—
503C22⋊D11—44no—
504C22⋊D11—44no—
505C22⋊D11—48no—
506C22⋊D11—48no—
507C22⋊D11—48no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—84no—
532C2×Dic11C23×C412yes—
533C2×Dic11C23×C414yes—
534C2×Dic11C23×C412yes—
535C2×Dic11H(5,𝔽2)12yes—
536D44—28no—
537D44—48no—
538D44—44no—
539C4×D11—28no—
540C4×D11—28no—
541C4×D11—44no—
542C4×D11—44no—
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—112no—
560C2×C4×D4—111no—
561C2×C4×D4—112no—
562C2×C4×D4—111no—
563C2×C4×D4C2×D1111yescharacteristic
564C2×C4×D4C2×D1112yescomplemented
565C2×#117—111no—
566C2×#117—111no—
567C2×#117—111no—
568C22×C4⋊C4C2×D1111yescharacteristic, complemented
569C22×C22⋊C4—112no—
570C22×C22⋊C4—112no—
571C22×C42—111no—
572#391—112no—
573#391—111no—
574#391—111no—
575#390—112no—
576#390—111no—
577#390—112no—
578#390—111no—
579#390—111no—
580#390—111no—
581#390—112no—
582#390—112no—
583#390—112no—
584#390—111no—
585#390C2×D1111yescharacteristic
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—112no—
612#386—111no—
613#386—112no—
614#386—111no—
615#386—112no—
616#386—111no—
617#386—111no—
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#380—111no—
630#379—112no—
631#379—112no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—112no—
634C4×C4⋊C4—111no—
635C4×C4⋊C4—112no—
636C4×C4⋊C4—111no—
637C4×C4⋊C4C2×D1111yescharacteristic, complemented
638C4×C22⋊C4—112no—
639C4×C22⋊C4—111no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4C2×D1111yescharacteristic, complemented
646C22×C11—22no—
647C22×C11—24no—
648C22×C11—22no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—22no—
652C22×C11—41no—
653C22×C11—42no—
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—42no—
680C2×D11—41no—
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—22no—
692C4×C11—42no—
693C4×C11—42no—
694C4×C11—41no—
695C4×C11—41no—
696C4×C11—41no—
697C4×C11#51814yes—
698Dic11—22no—
699Dic11—22no—
700Dic11—24no—
701Dic11—22no—
702Dic11—41no—
703Dic11—42no—
704Dic11—41no—
705Dic11—42no—
706Dic11—41no—
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—112no—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—112no—
731C23×C4—111no—
732C23×C4C22×D1111yescharacteristic
733C23×C4C22×D1112yes—
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—44no—
745C4×D4—442no—
746C4×D4—442no—
747C4×D4—442no—
748C4×D4—444no—
749C4×D4—444no—
750C4×D4—444no—
751#117—118no—
752#117—442no—
753#117—442no—
754C2×C4⋊C4—42no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C4⋊C4C22×D1111yescharacteristic
765C2×C4⋊C4C22×D1112yes—
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—111no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—444no—
795C2×C22⋊C4—444no—
796C2×C22⋊C4C22×D1111yescharacteristic
797C2×C22⋊C4C22×D1112yes—
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1111yescharacteristic
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—112no—
819#95—112no—
820#95—111no—
821#95—111no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—111no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95C22×D1111yescharacteristic
832#95C22×D1112yes—
833#95C22×D1111yescharacteristic
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—24no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—111no—
903C22×C4—112no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—112no—
911C22×C4—112no—
912C22×C4—111no—
913C22×C4—222no—
914C22×C4—224no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—441no—
921C22×C4—441no—
922C22×C4—441no—
923C22×C4—441no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
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×D1112yes—
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—42no—
946C4⋊C4—114no—
947C4⋊C4—224no—
948C4⋊C4—222no—
949C4⋊C4—222no—
950C4⋊C4—441no—
951C4⋊C4—441no—
952C4⋊C4—442no—
953C4⋊C4—442no—
954C4⋊C4C2×C4×D1114yes—
955C22⋊C4—22no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—41no—
960C22⋊C4—118no—
961C22⋊C4—118no—
962C22⋊C4—118no—
963C22⋊C4—118no—
964C22⋊C4—222no—
965C22⋊C4—224no—
966C22⋊C4—222no—
967C22⋊C4—222no—
968C22⋊C4—224no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4—442no—
972C22⋊C4—441no—
973C22⋊C4—441no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—441no—
980C22⋊C4—442no—
981C22⋊C4—441no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—441no—
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—21no—
1007C23—22no—
1008C23—22no—
1009C23—21no—
1010C23—21no—
1011C23—22no—
1012C23—112no—
1013C23—114no—
1014C23—112no—
1015C23—221no—
1016C23—222no—
1017C23—221no—
1018C23—222no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—222no—
1023C23—221no—
1024C23—221no—
1025C23—221no—
1026C23—222no—
1027C23—221no—
1028C23—221no—
1029C23—222no—
1030C23—222no—
1031C23—221no—
1032C23—221no—
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—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—28no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—84no—
1077C2×C4—84no—
1078C2×C4—112no—
1079C2×C4—114no—
1080C2×C4—112no—
1081C2×C4—112no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—228no—
1091C2×C4—228no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—222no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—222no—
1106C2×C4—221no—
1107C2×C4—444no—
1108C2×C4—444no—
1109C2×C4—884no—
1110C2×C4—884no—
1111C2×C4—884no—
1112C2×C4C22×C4×D1114yes—
1113C2×C4C22×C4×D1112yes—
1114C2×C4C22×C4×D1112yes—
1115C2×C4#6703712yes—
1116C2×C4#6703712yes—
1117C2×C4#6704212yes—
1118C22—22no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—22no—
1123C22—24no—
1124C22—42no—
1125C22—41no—
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—441no—
1143C22—442no—
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×#6703711yescharacteristic
1157C22C2×#6704211yescharacteristic
1158C22#1062345311yescharacteristic
1159C22D11×H(5,𝔽2)11yescharacteristic
1160C22#1062345711yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—42no—
1169C4—222no—
1170C4—222no—
1171C4—224no—
1172C4—222no—
1173C4—441no—
1174C4—442no—
1175C4—441no—
1176C4—441no—
1177C4—442no—
1178C4#1062307614yes—
1179C2—44no—
1180C2—42no—
1181C2—442no—
1182C2—444no—
1183C2—442no—
1184C2C2×#1062307611yescharacteristic
1185C2C4×#6703711yescharacteristic
1186C2#1308182211yescharacteristic
1187C2#1308284711yescharacteristic
1188C2#1308289011yescharacteristic
1189C2#1308298711yescharacteristic
1190C2#1308298911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2361C2
socle, cosocleC23×C11C25
prime radicalC2×#10623138C2
hypercenter#2361D11
hypocenterC11#34411
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. #13071791C2semidirect
3. #13071756C2semidirect
4. #13071678C2semidirect
5. #13071658C2semidirect
6. #13071652C2semidirect
7. #13071632C2semidirect
8. #13071592C2semidirect
9. #13071508C2semidirect
10. #13071505C2semidirect
11. #13071437C2semidirect
12. D4×(C2×D11)⋊C4C2semidirect
13. #13071430C2semidirect
14. #13071427C2semidirect
15. #13071312C2semidirect
16. #13071310C2semidirect
17. #13071272C2semidirect
18. #13071270C2semidirect
19. #13071209C2semidirect
20. #13071124C2semidirect
21. C4×#66991C2semidirect
22. #13071102C2semidirect
23. C11×#2361C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C22×C11×C4⋊C4C22semidirect
35. C2×C4×C22⋊D11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
38. C2×#66979C22semidirect
39. #10623138C4semidirect
42. C2×#66946C22semidirect
48. C2×#66925C22semidirect
49. C2×C42×D11C22semidirect
51. C11×#389C22semidirect
52. C11×#388C22semidirect
53. C11×#386C22semidirect
54. C11×#385C22semidirect
55. C4×C11×C4⋊C4C22semidirect
56. C4×C11×C22⋊C4C22semidirect
58. #10622834C22semidirect
59. #10622833C22semidirect
62. #10622826C22semidirect
63. #10622826C22semidirect
64. C4×C22⋊Dic11C22semidirect
65. C4×C22⋊Dic11C22semidirect
67. #10622603C22semidirect
68. #10622603C22semidirect
69. #10622602C22semidirect
74. #10622600C22semidirect
75. #10622600C22semidirect
76. #10622598C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. #10622587C22semidirect
81. #10622586C22semidirect
83. #10622571C22semidirect
86. #10622570C22semidirect
87. #10622570C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622569C22semidirect
93. #10622569C22semidirect
96. #10622564C22semidirect
97. #10622559C22semidirect
98. #10622557C22semidirect
99. #10622557C22semidirect
100. C22⋊C4×Dic11C22semidirect
102. #10622553C22semidirect
104. #10622552C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. #10622541C22semidirect
112. #10622282C22semidirect
113. #10622281C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622264C22semidirect
121. #10622264C22semidirect
122. #10622259C22semidirect
123. #10622259C22semidirect
138. C2×D4×D11C2×C4semidirect
141. C2×#4339C2×C4semidirect
152. C11×#121C2×C4semidirect
177. #66993C2×C4semidirect
178. #66991C2×C4semidirect
179. #66990C2×C4semidirect
181. #66983C2×C4semidirect
222. #66948C2×C4semidirect
225. #66945C2×C4semidirect
226. #66938C2×C4semidirect
227. #66935C2×C4semidirect
412. #2361D11semidirect
564. C2×C4×D4C2×D11semidirect
568. C22×C4⋊C4C2×D11semidirect
589. #389C2×D11semidirect
601. #388C2×D11semidirect
619. #386C2×D11semidirect
623. #385C2×D11semidirect
637. C4×C4⋊C4C2×D11semidirect
645. C4×C22⋊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
#130717562
#130716782
#130716582
#130716522
#130716322
#130715922
#130715082
#130715052
#130714372
D4×(C2×D11)⋊C42
#130714302
#130714272
#130713122
#130713102
#130712722
#130712702
#130712092
#130711242
C4×#669912
#130711022
C11×#23612
#3441111