Finite Group Databasebeta

← #14917296

Subgroups — #14917296

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×#10623336C211yesmaximal, characteristic
2#13071786C212yesmaximal, complemented
3#13071755C212yesmaximal, complemented
4#13071725C212yesmaximal, complemented
5#13071659C211yesmaximal, characteristic, complemented
6#13071650C211yesmaximal, characteristic, complemented
7#13071637C211yesmaximal, characteristic, complemented
8#13071628C211yesmaximal, characteristic, complemented
9#13071595C212yesmaximal, complemented
10#13071503C211yesmaximal, characteristic, complemented
11#13071499C211yesmaximal, characteristic, complemented
12D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
13#13071337C212yesmaximal, complemented
14#13071337C212yesmaximal, complemented
15#13071312C211yesmaximal, characteristic, complemented
16#13071303C211yesmaximal, characteristic, complemented
17#13071274C212yesmaximal, complemented
18#13071271C212yesmaximal, complemented
19#13071205C211yesmaximal, characteristic, complemented
20#13071132C211yesmaximal, characteristic, complemented
21C4×#66991C211yesmaximal, characteristic, complemented
22#13071102C211yesmaximal, characteristic, complemented
23D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C2×#67006C2212yes—
30C2×#67006C2212yes—
31C22×C22⋊Dic11C2212yes—
32#10623336C4116yescomplemented
33C2×#66993C2212yes—
34C2×#66991C2211yescharacteristic
35C2×#66991C2211yescharacteristic
36C2×#66991C2211yescharacteristic
37C2×#66991C2211yescharacteristic
38C2×#66989C2212yes—
39C2×D4×Dic11C2211yescharacteristic
40C2×D4×Dic11C2211yescharacteristic
41C2×C4×C22⋊D11C2212yescomplemented
42C2×C4×C22⋊D11C2212yescomplemented
43C2×#66979C2211yescharacteristic
44C2×#66945C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2211yescharacteristic, complemented
46C2×(C22⋊D11)⋊C4C2212yescomplemented
47C2×(C22⋊D11)⋊C4C2212yescomplemented
48C2×#66925C2211yescharacteristic, complemented
49C2×C42×D11C2211yescharacteristic, complemented
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#386C2212yes—
53C11×#386C2212yes—
54C11×#380C2211yescharacteristic
55C11×#379C2212yes—
56C4×C11×C22⋊C4C2211yescharacteristic
57#10622860C2212yes—
58#10622834C2211yescharacteristic
59#10622834C2211yescharacteristic
60#10622833C2212yes—
61#10622833C2212yes—
62#10622826C2212yescomplemented
63#10622826C2212yescomplemented
64#10622825C2211yescharacteristic
65#10622823C2212yescomplemented
66#10622823C2212yescomplemented
67C4×C22⋊Dic11C2211yescharacteristic
68C4×C22⋊Dic11C2212yescomplemented
69C4×C22⋊Dic11C2212yescomplemented
70#10622600C2211yescharacteristic, complemented
71#10622600C2211yescharacteristic, complemented
72C4⋊C4×Dic11C2211yescharacteristic, complemented
73C4⋊C4×Dic11C2211yescharacteristic, complemented
74#10622586C2211yescharacteristic, complemented
75#10622586C2211yescharacteristic, complemented
76#10622571C2212yescomplemented
77#10622571C2212yescomplemented
78#10622570C2212yes—
79#10622570C2211yescharacteristic
80#10622570C2211yescharacteristic
81#10622570C2212yescomplemented
82#10622570C2212yescomplemented
83#10622570C2212yescomplemented
84#10622570C2212yescomplemented
85#10622569C2212yes—
86#10622569C2211yescharacteristic
87#10622569C2211yescharacteristic
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622559C2212yescomplemented
93#10622559C2212yescomplemented
94#10622558C2212yes—
95#10622558C2212yes—
96#10622558C2212yescomplemented
97#10622558C2212yescomplemented
98#10622558C2212yescomplemented
99#10622558C2212yescomplemented
100#10622557C2212yes—
101#10622557C2212yes—
102#10622557C2212yescomplemented
103#10622557C2212yescomplemented
104#10622557C2212yescomplemented
105#10622557C2212yescomplemented
106C22⋊C4×Dic11C2212yescomplemented
107C22⋊C4×Dic11C2212yescomplemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
110C4×C4⋊Dic11C2211yescharacteristic, complemented
111C4×C4⋊Dic11C2211yescharacteristic, complemented
112#10622541C2211yescharacteristic, complemented
113#10622541C2211yescharacteristic, complemented
114#10622278C2212yescomplemented
115#10622278C2211yescharacteristic, complemented
116#10622278C2211yescharacteristic, complemented
117#10622263C2212yescomplemented
118#10622263C2212yescomplemented
119#10622261C2212yescomplemented
120#10622261C2212yescomplemented
121#10622259C2212yescomplemented
122#10622259C2211yescharacteristic, complemented
123#10622259C2211yescharacteristic, complemented
124C25×C11C2312yes—
125C22×D4×C11—42no—
126C22×D4×C11—42no—
127C22×D4×C11C2×C418yescomplemented
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C23×Dic11C2312yes—
141C23×Dic11C2312yes—
142C2×#4339—42no—
143C2×#4339—42no—
144C2×#4339C2×C418yescomplemented
145C22×D44C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C4×D4×C11—42no—
153C4×D4×C11—42no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4—44no—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168#67006C2×C4116yescomplemented
169#67006C2×C4116yescomplemented
170C2×C22⋊Dic11—44no—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185#66993C2×C4116yescomplemented
186#66991C2×C418yescomplemented
187#66991C2×C418yescomplemented
188#66991C2×C418yescomplemented
189#66991C2×C418yescomplemented
190#66989C2×C4116yescomplemented
191D4×Dic11—42no—
192D4×Dic11—42no—
193C4×C22⋊D11—44no—
194C4×C22⋊D11—44no—
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2312yes—
204#66979C2×C418yescomplemented
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226#66945—42no—
227C4⋊C4×D11—42no—
228(C22⋊D11)⋊C4—44no—
229(C22⋊D11)⋊C4—44no—
230#66925—42no—
231C42×D11—42no—
232C11×#95C2311yescharacteristic
233C11×#95C2312yes—
234C11×#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
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#34415—111nomaximal, Sylow
253C24×C11—42no—
254C24×C11—42no—
255C24×C11—42no—
256C24×C11—42no—
257C24×C11—42no—
258C24×C11—42no—
259C24×C11C22×C418yes—
260C24×C11C2411yescharacteristic
261C24×C11C2412yes—
262C24×C11C2412yes—
263C23×D11C2411yescharacteristic
264C23×D11C2411yescharacteristic
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11—416no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C22×C414yes—
273C2×D4×C11C22×C414yes—
274C2×D4×C11C22×C418yes—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—24no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11C22×C414yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11—41no—
297C2×C22⋊D11—41no—
298C2×C22⋊D11—41no—
299C2×C22⋊D11—41no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11C22×C418yes—
305C2×C22⋊D11C22×C418yes—
306C2×C22⋊D11C22×C418yes—
307C2×C22⋊D11C22×C418yes—
308C2×C22⋊D11C22×C414yes—
309C2×C22⋊D11C22×C414yes—
310C22×Dic11—24no—
311C22×Dic11—42no—
312C22×Dic11—42no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11—42no—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326#4339—416no—
327C2×D44—41no—
328C2×D44—41no—
329C2×D44C22×C414yes—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—41no—
339C2×C4×D11—41no—
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×C22⋊C4—24no—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—41no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C11×C22⋊C4—42no—
359C42×C11—22no—
360C42×C11—22no—
361C22⋊Dic11—24no—
362C22⋊Dic11—22no—
363C22⋊Dic11—42no—
364C22⋊Dic11—42no—
365C22⋊Dic11—42no—
366C22⋊Dic11—42no—
367C22⋊Dic11—42no—
368C22⋊Dic11—42no—
369C22⋊Dic11—41no—
370C22⋊Dic11C22×C418yes—
371C22⋊Dic11C22×C418yes—
372C22⋊Dic11C22×C418yes—
373C22⋊Dic11C22×C418yes—
374C22⋊Dic11C22×C418yes—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—41no—
378(C2×D11)⋊C4—41no—
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—
384C4⋊Dic11—22no—
385C4⋊Dic11—22no—
386C4⋊Dic11C22×C414yes—
387C4⋊Dic11C22×C414yes—
388Dic11⋊C4—41no—
389Dic11⋊C4—41no—
390Dic11⋊C4—42no—
391Dic11⋊C4—42no—
392Dic11⋊C4—42no—
393Dic11⋊C4—42no—
394Dic11⋊C4—42no—
395C4×Dic11—24no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—24no—
399C4×Dic11—41no—
400C4×Dic11—41no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11—42no—
404C4×Dic11C22×C418yes—
405C2×#535—111no—
406#2379—112no—
407#2375—112no—
408#2372—112no—
409#2363—111no—
410#2363—111no—
411#2361—111no—
412#2361—111no—
413#2358—112no—
414#2346—111no—
415#2346—111no—
416D4×C22⋊C4—111no—
417D4×C22⋊C4D1111yescharacteristic, complemented
418#2328—112no—
419#2328—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—21no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—21no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—22no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—21no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—48no—
447C23×C11—48no—
448C23×C11—48no—
449C23×C11—84no—
450C23×C11—84no—
451C23×C11—84no—
452C23×C11—84no—
453C23×C11C23×C412yes—
454C23×C11C23×C414yes—
455C23×C11C23×C414yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11C23×C412yes—
470C22×D11C23×C412yes—
471D4×C11—28no—
472D4×C11—28no—
473D4×C11—48no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—28no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
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—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—84no—
495C2×C4×C11—84no—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11H(5,𝔽2)12yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C22⋊D11—44no—
502C22⋊D11—44no—
503C22⋊D11—48no—
504C22⋊D11—48no—
505C22⋊D11—48no—
506C22⋊D11—48no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—84no—
533C2×Dic11—84no—
534C2×Dic11C23×C414yes—
535C2×Dic11C23×C414yes—
536C2×Dic11C23×C412yes—
537C2×Dic11C23×C412yes—
538C2×Dic11H(5,𝔽2)12yes—
539D44—44no—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—44no—
543C4×D11—44no—
544C4×D11—84no—
545Dic22—44no—
546C22×#41—111no—
547C23×D4C2×D1111yescharacteristic
548#535—1116no—
549C2×#127—112no—
550C2×#124—112no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#121—111no—
554C2×#121—111no—
555C2×#120—112no—
556C2×#120—112no—
557C2×C4×D4—111no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—112no—
561C2×C4×D4—112no—
562C2×C4×D4—112no—
563C2×C4×D4C2×D1111yescharacteristic
564C2×C4×D4C2×D1111yescharacteristic
565C2×#117—111no—
566C2×#117—111no—
567C2×#117—111no—
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C22⋊C4C2×D1112yes—
571C22×C42—111no—
572#391—112no—
573#391—111no—
574#391—111no—
575#390—111no—
576#390—111no—
577#390—112no—
578#390—112no—
579#390—112no—
580#390—112no—
581#390—112no—
582#390—111no—
583#390—111no—
584#390C2×D1111yescharacteristic
585#390C2×D1111yescharacteristic
586#389—111no—
587#389—111no—
588#389—111no—
589#389—111no—
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#388—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386—111no—
608#386—111no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—111no—
617#386—111no—
618#386C2×D1112yes—
619#386C2×D1112yes—
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#382—112no—
625#382—112no—
626#380—111no—
627#380—111no—
628#380—111no—
629#380C2×D1111yescharacteristic
630#379—112no—
631#379C2×D1112yes—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—111no—
635C4×C4⋊C4—111no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—111no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4C2×D1111yescharacteristic
644#376—112no—
645#376—112no—
646C22×C11—22no—
647C22×C11—24no—
648C22×C11—24no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—41no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—41no—
667C22×C11—816no—
668C22×C11C24×C411yescharacteristic
669C22×C11C2×H(5,𝔽2)11yescharacteristic
670C22×C11C2×H(5,𝔽2)11yescharacteristic
671C22×C11C2×H(5,𝔽2)11yescharacteristic
672C22×C11C2×H(5,𝔽2)11yescharacteristic
673C22×C11#58511yescharacteristic
674C22×C11#58511yescharacteristic
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—41no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11—41no—
689C4×C11—22no—
690C4×C11—22no—
691C4×C11—42no—
692C4×C11—41no—
693C4×C11—41no—
694C4×C11—42no—
695C4×C11—41no—
696C4×C11#51814yes—
697Dic11—22no—
698Dic11—22no—
699Dic11—24no—
700Dic11—24no—
701Dic11—22no—
702Dic11—41no—
703Dic11—42no—
704Dic11—42no—
705Dic11—41no—
706Dic11—41no—
707C25C22×D1112yes—
708C2×#41—118no—
709C2×#41—442no—
710C2×#41—442no—
711C22×Q8—111no—
712C22×D4—42no—
713C22×D4—42no—
714C22×D4—112no—
715C22×D4—112no—
716C22×D4—112no—
717C22×D4—112no—
718C22×D4—111no—
719C22×D4—111no—
720C22×D4—111no—
721C22×D4C4×D1118yescomplemented
722C22×D4C22×D1111yescharacteristic
723C22×D4C22×D1111yescharacteristic
724C22×D4C22×D1112yes—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—112no—
728C23×C4—112no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
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#121—118no—
741#120—1116no—
742#120—1116no—
743C4×D4—42no—
744C4×D4—42no—
745C4×D4—444no—
746C4×D4—444no—
747C4×D4—444no—
748C4×D4—442no—
749C4×D4—442no—
750C4×D4—444no—
751#117—118no—
752#117—442no—
753#117—442no—
754C2×C4⋊C4—111no—
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⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—442no—
766C2×C4⋊C4C22×D1111yescharacteristic
767C2×C4⋊C4C22×D1111yescharacteristic
768C2×C22⋊C4—44no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
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—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—444no—
793C2×C22⋊C4C22×D1111yescharacteristic
794C2×C22⋊C4C22×D1112yes—
795C2×C22⋊C4C22×D1112yes—
796C2×C22⋊C4C22×D1112yes—
797C2×C22⋊C4C22×D1112yes—
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1111yescharacteristic
802C2×C42—112no—
803C2×C42—111no—
804C2×C42—112no—
805C2×C42—112no—
806C2×C42—111no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42—111no—
811C2×C42—111no—
812C2×C42—442no—
813C2×C42C22×D1111yescharacteristic
814C2×C42C22×D1111yescharacteristic
815#95—111no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—111no—
822#95—111no—
823#95—112no—
824#95—112no—
825#95—111no—
826#95—111no—
827#95—111no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95C22×D1111yescharacteristic
833#95C22×D1112yes—
834#95C22×D1111yescharacteristic
835C2×C11—44no—
836C2×C11—44no—
837C2×C11—42no—
838C2×C11C2×#51811yescharacteristic
839C2×C11C4×H(5,𝔽2)11yescharacteristic
840C2×C11C4×H(5,𝔽2)11yescharacteristic
841C2×C11#354211yescharacteristic
842C2×C11#354211yescharacteristic
843C2×C11#354911yescharacteristic
844C2×C11#355111yescharacteristic
845D11—42no—
846D11—42no—
847C24—42no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24—111no—
854C24—111no—
855C24C2×C4×D1118yes—
856C24C23×D1111yescharacteristic
857C24C23×D1112yes—
858C24C23×D1112yes—
859#41—4416no—
860C2×Q8—114no—
861C2×Q8—441no—
862C2×Q8—441no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—416no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—114no—
871C2×D4—114no—
872C2×D4—118no—
873C2×D4—118no—
874C2×D4—118no—
875C2×D4—118no—
876C2×D4—114no—
877C2×D4—441no—
878C2×D4—441no—
879C2×D4—442no—
880C2×D4—442no—
881C2×D4—442no—
882C2×D4—442no—
883C2×D4—441no—
884C2×D4—441no—
885C2×D4—441no—
886C2×D4—441no—
887C2×D4—442no—
888C2×D4—442no—
889C2×D4—442no—
890C2×D4—442no—
891C2×D4C2×C4×D1114yes—
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—112no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—112no—
913C22×C4—111no—
914C22×C4—222no—
915C22×C4—224no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—441no—
922C22×C4—441no—
923C22×C4—441no—
924C22×C4—441no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4C2×C4×D1114yes—
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1112yes—
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1112yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—114no—
945C4⋊C4—114no—
946C4⋊C4—222no—
947C4⋊C4—222no—
948C4⋊C4—442no—
949C4⋊C4—441no—
950C4⋊C4—441no—
951C4⋊C4—442no—
952C4⋊C4—442no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—41no—
963C22⋊C4—42no—
964C22⋊C4—118no—
965C22⋊C4—118no—
966C22⋊C4—118no—
967C22⋊C4—118no—
968C22⋊C4—118no—
969C22⋊C4—222no—
970C22⋊C4—222no—
971C22⋊C4—224no—
972C22⋊C4—222no—
973C22⋊C4—441no—
974C22⋊C4—441no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—441no—
979C22⋊C4—441no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—441no—
987C42—22no—
988C42—22no—
989C42—118no—
990C42—224no—
991C42—222no—
992C42—222no—
993C42—224no—
994C42—441no—
995C42—441no—
996C42—442no—
997C42—442no—
998C42—442no—
999C11#3441511yescharacteristic, complemented, Sylow
1000C23—21no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—21no—
1017C23—22no—
1018C23—48no—
1019C23—48no—
1020C23—48no—
1021C23—84no—
1022C23—84no—
1023C23—84no—
1024C23—84no—
1025C23—112no—
1026C23—112no—
1027C23—221no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—221no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23C22×C4×D1112yes—
1040C23C22×C4×D1114yes—
1041C23C22×C4×D1114yes—
1042C23C24×D1111yescharacteristic
1043Q8—444no—
1044D4—28no—
1045D4—28no—
1046D4—48no—
1047D4—444no—
1048D4—444no—
1049D4—444no—
1050D4—448no—
1051D4—448no—
1052D4—448no—
1053D4—448no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—28no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—84no—
1075C2×C4—84no—
1076C2×C4—114no—
1077C2×C4—114no—
1078C2×C4—112no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—221no—
1082C2×C4—222no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—228no—
1092C2×C4—228no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—222no—
1096C2×C4—221no—
1097C2×C4—222no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4—884no—
1111C2×C4—884no—
1112C2×C4—884no—
1113C2×C4C22×C4×D1112yes—
1114C2×C4C22×C4×D1112yes—
1115C2×C4#6703712yes—
1116C2×C4#6703712yes—
1117C2×C4#6703712yes—
1118C22—22no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—22no—
1124C22—24no—
1125C22—24no—
1126C22—22no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—42no—
1131C22—41no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—41no—
1136C22—41no—
1137C22—42no—
1138C22—42no—
1139C22—816no—
1140C22—222no—
1141C22—222no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—222no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22—441no—
1150C22—441no—
1151C22—441no—
1152C22—441no—
1153C22—441no—
1154C22C23×C4×D1111yescharacteristic
1155C22C2×#6703711yescharacteristic
1156C22C2×#6703711yescharacteristic
1157C22C2×#6703711yescharacteristic
1158C22#1062345311yescharacteristic
1159C22D11×H(5,𝔽2)11yescharacteristic
1160C22#1062345511yescharacteristic
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—42no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—222no—
1169C4—222no—
1170C4—222no—
1171C4—224no—
1172C4—224no—
1173C4—442no—
1174C4—441no—
1175C4—442no—
1176C4—441no—
1177C4—441no—
1178C4#1062301714yes—
1179C2—42no—
1180C2—44no—
1181C2—44no—
1182C2—442no—
1183C2—442no—
1184C2C2×#1062301711yescharacteristic
1185C2#1308182011yescharacteristic
1186C2C4×#6703711yescharacteristic
1187C2#1308293011yescharacteristic
1188C2#1308293711yescharacteristic
1189C2#1308301811yescharacteristic
1190C2#1308303611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC2×#10623336C2
hypercenterD4×C22⋊C4D11
hypocenterC11#34415
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071786C2semidirect
3. #13071755C2semidirect
4. #13071725C2semidirect
5. #13071659C2semidirect
6. #13071650C2semidirect
7. #13071637C2semidirect
8. #13071628C2semidirect
9. #13071595C2semidirect
10. #13071503C2semidirect
11. #13071499C2semidirect
12. D4×C22⋊Dic11C2semidirect
13. #13071337C2semidirect
14. #13071337C2semidirect
15. #13071312C2semidirect
16. #13071303C2semidirect
17. #13071274C2semidirect
18. #13071271C2semidirect
19. #13071205C2semidirect
20. #13071132C2semidirect
21. C4×#66991C2semidirect
22. #13071102C2semidirect
23. D4×C11×C22⋊C4C2semidirect
32. #10623336C4semidirect
41. C2×C4×C22⋊D11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
44. C2×#66945C22semidirect
45. C2×C4⋊C4×D11C22semidirect
46. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×(C22⋊D11)⋊C4C22semidirect
48. C2×#66925C22semidirect
49. C2×C42×D11C22semidirect
62. #10622826C22semidirect
63. #10622826C22semidirect
65. #10622823C22semidirect
66. #10622823C22semidirect
68. C4×C22⋊Dic11C22semidirect
69. C4×C22⋊Dic11C22semidirect
70. #10622600C22semidirect
71. #10622600C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. C4⋊C4×Dic11C22semidirect
74. #10622586C22semidirect
75. #10622586C22semidirect
76. #10622571C22semidirect
77. #10622571C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
83. #10622570C22semidirect
84. #10622570C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622559C22semidirect
93. #10622559C22semidirect
96. #10622558C22semidirect
97. #10622558C22semidirect
98. #10622558C22semidirect
99. #10622558C22semidirect
102. #10622557C22semidirect
103. #10622557C22semidirect
104. #10622557C22semidirect
105. #10622557C22semidirect
106. C22⋊C4×Dic11C22semidirect
107. C22⋊C4×Dic11C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×C4⋊Dic11C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. #10622541C22semidirect
113. #10622541C22semidirect
114. #10622278C22semidirect
115. #10622278C22semidirect
116. #10622278C22semidirect
117. #10622263C22semidirect
118. #10622263C22semidirect
119. #10622261C22semidirect
120. #10622261C22semidirect
121. #10622259C22semidirect
122. #10622259C22semidirect
123. #10622259C22semidirect
127. C22×D4×C11C2×C4semidirect
144. C2×#4339C2×C4semidirect
168. #67006C2×C4semidirect
169. #67006C2×C4semidirect
185. #66993C2×C4semidirect
186. #66991C2×C4semidirect
187. #66991C2×C4semidirect
188. #66991C2×C4semidirect
189. #66991C2×C4semidirect
190. #66989C2×C4semidirect
204. #66979C2×C4semidirect
417. D4×C22⋊C4D11semidirect
721. C22×D4C4×D11semidirect
999. C11#34415semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
#130717862
#130717552
#130717252
#130716592
#130716502
#130716372
#130716282
#130715952
#130715032
#130714992
D4×C22⋊Dic112
#130713372
#130713122
#130713032
#130712742
#130712712
#130712052
#130711322
C4×#669912
#130711022
D4×C11×C22⋊C42
#3441511