Finite Group Databasebeta

← #14914335

Subgroups — #14914335

Order 2816.

2698 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2#13071748C212yesmaximal, complemented
3#13071745C212yesmaximal, complemented
4#13071656C211yesmaximal, characteristic, complemented
5#13071653C211yesmaximal, characteristic, complemented
6#13071648C211yesmaximal, characteristic, complemented
7#13071639C211yesmaximal, characteristic, complemented
8#13071585C212yesmaximal, complemented
9#13071555C212yesmaximal, complemented
10#13071505C211yesmaximal, characteristic, complemented
11#13071500C211yesmaximal, characteristic, complemented
12#13071454C211yesmaximal, characteristic, complemented
13#13071445C211yesmaximal, characteristic, complemented
14#13071276C212yesmaximal, complemented
15#13071273C212yesmaximal, complemented
16#13071244C212yesmaximal, complemented
17C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
18C4×#66983C211yesmaximal, characteristic, complemented
19#13071122C211yesmaximal, characteristic, complemented
20#13070998C211yesmaximal, characteristic, complemented
21#13070975C212yesmaximal, complemented
22C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11C2212yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36#10623158C4116yescomplemented
37C2×#66948C2211yescharacteristic
38C2×#66947C2212yes—
39C2×#66946C2212yes—
40C2×#66946C2211yescharacteristic, complemented
41C2×#66945C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×#66935C2212yes—
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×C4×D44C2211yescharacteristic, complemented
48C11×#391C2211yescharacteristic, complemented
49C11×#389C2211yescharacteristic, complemented
50C11×#387C2212yescomplemented
51C11×#385C2212yes—
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic, complemented
54C4×C11×C4⋊C4C2212yescomplemented
55C4×C11×C22⋊C4C2212yes—
56#10622843C2211yescharacteristic, complemented
57#10622826C2212yes—
58#10622825C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622603C2212yes—
62#10622603C2212yes—
63#10622603C2212yescomplemented
64#10622601C2212yes—
65#10622601C2212yes—
66#10622601C2211yescharacteristic, complemented
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622600C2212yescomplemented
70#10622598C2211yescharacteristic, complemented
71#10622594C2212yescomplemented
72#10622591C2212yescomplemented
73#10622590C2212yescomplemented
74C4⋊C4×Dic11C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76C4⋊C4×Dic11C2212yescomplemented
77#10622586C2211yescharacteristic, complemented
78#10622571C2212yes—
79#10622568C2212yes—
80#10622563C2212yes—
81C22⋊C4×Dic11C2212yes—
82C22⋊C4×Dic11C2212yes—
83#10622553C2212yes—
84#10622553C2212yes—
85#10622553C2212yescomplemented
86#10622552C2212yes—
87#10622552C2212yes—
88#10622552C2211yescharacteristic, complemented
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×(C2×D11)⋊C4C2211yescharacteristic
91C4×(C2×D11)⋊C4C2211yescharacteristic
92C4×(C2×D11)⋊C4C2211yescharacteristic
93C4×(C2×D11)⋊C4C2211yescharacteristic
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2212yescomplemented
98C4×(C2×D11)⋊C4C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×C4⋊Dic11C2211yescharacteristic, complemented
101C4×Dic11⋊C4C2212yescomplemented
102C4×Dic11⋊C4C2212yescomplemented
103#10622541C2211yescharacteristic, complemented
104#10622283C2212yes—
105#10622283C2212yes—
106#10622283C2212yescomplemented
107#10622282C2212yes—
108#10622282C2212yes—
109#10622282C2212yescomplemented
110#10622279C2212yes—
111#10622279C2212yescomplemented
112#10622279C2212yescomplemented
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116#10622278C2212yes—
117#10622277C2212yes—
118#10622277C2212yescomplemented
119D11×#95C2212yescomplemented
120#10622268C2212yescomplemented
121#10622264C2212yescomplemented
122#10622262C2212yescomplemented
123#10622261C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×Q8×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2312yes—
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C2×#4343—42no—
134C2×#4343—42no—
135C2×#4343C2×C418yescomplemented
136C22×D44C2311yescharacteristic
137C22×D44C2312yes—
138C22×D44C2312yes—
139C22×C4×D11—42no—
140C22×C4×D11—42no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C11×C22⋊Q8C2×C418yescomplemented
150C4×Q8×C11—42no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C42×C11—42no—
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163C2×C42×C11C2312yes—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C22⋊Dic11C2312yes—
167#66999C2×C418yescomplemented
168Q8×Dic11—42no—
169#66983C2×C418yes—
170C4×C22⋊D11—28no—
171C2×(C2×D11)⋊C4—24no—
172C2×(C2×D11)⋊C4—24no—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊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×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×C4×Dic11—42no—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215#66948C2×C418yescomplemented
216#66947C2×C4116yescomplemented
217#66946—42no—
218#66946C2×C4116yescomplemented
219#66945—42no—
220#66945—42no—
221#66945C2×C418yescomplemented
222#66935C2×C4116yescomplemented
223(C22⋊D11)⋊C4—28no—
224(C22⋊D11)⋊C4C2×C4116yescomplemented
225C4×D44—42no—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250#34223—111nomaximal, Sylow
251C24×C11C2411yescharacteristic
252C23×D11—22no—
253C23×D11—22no—
254C23×D11—41no—
255C23×D11—41no—
256C23×D11—41no—
257C23×D11—41no—
258C23×D11C22×C414yes—
259C23×D11C2411yescharacteristic
260C23×D11C2411yescharacteristic
261C23×D11C2412yes—
262C2×Q8×C11—22no—
263C2×Q8×C11—22no—
264C2×Q8×C11C22×C414yes—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—41no—
269C22×C4×C11—41no—
270C22×C4×C11—41no—
271C22×C4×C11—41no—
272C22×C4×C11C22×C414yes—
273C22×C4×C11#4114yescomplemented
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C2×C22⋊D11—24no—
285C2×C22⋊D11—24no—
286C2×C22⋊D11C22×C418yes—
287C22×Dic11—22no—
288C22×Dic11—41no—
289C22×Dic11—41no—
290C22×Dic11—41no—
291C22×Dic11—41no—
292C22×Dic11—41no—
293C22×Dic11—41no—
294C22×Dic11C22×C414yes—
295C22×Dic11#4114yescomplemented
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2412yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2412yes—
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2411yescharacteristic
305#4343—416no—
306C2×D44—22no—
307C2×D44—22no—
308C2×D44—42no—
309C2×D44—42no—
310C2×D44—42no—
311C2×D44—42no—
312C2×D44C22×C414yes—
313C2×D44C22×C418yes—
314C2×D44C22×C418yes—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—41no—
322C2×C4×D11—41no—
323C2×C4×D11—41no—
324C2×C4×D11—41no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—416no—
332C2×C4×D11C22×C414yes—
333C2×C4×D11C22×C414yes—
334C2×C4×D11C22×C418yes—
335C2×C4×D11C22×C414yes—
336C2×C4×D11C22×C414yes—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—42no—
340C11×C4⋊C4—42no—
341C11×C4⋊C4C22×C414yes—
342C11×C4⋊C4C22×C418yes—
343C11×C22⋊C4—24no—
344C11×C22⋊C4C22×C418yes—
345C42×C11—22no—
346C42×C11—22no—
347C42×C11—41no—
348C42×C11—41no—
349C42×C11—42no—
350C42×C11—42no—
351C22⋊Dic11—24no—
352(C2×D11)⋊C4—24no—
353(C2×D11)⋊C4—22no—
354(C2×D11)⋊C4—22no—
355(C2×D11)⋊C4—22no—
356(C2×D11)⋊C4—22no—
357(C2×D11)⋊C4—22no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—22no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4C22×C418yes—
371(C2×D11)⋊C4C22×C418yes—
372(C2×D11)⋊C4C22×C418yes—
373(C2×D11)⋊C4C22×C418yes—
374C4⋊Dic11—22no—
375C4⋊Dic11—22no—
376C4⋊Dic11—42no—
377C4⋊Dic11—42no—
378C4⋊Dic11C22×C414yes—
379Dic11⋊C4—24no—
380Dic11⋊C4—24no—
381Dic11⋊C4C22×C418yes—
382C4×Dic11—24no—
383C4×Dic11—24no—
384C4×Dic11—22no—
385C4×Dic11—22no—
386C4×Dic11—42no—
387C4×Dic11—42no—
388C4×Dic11—41no—
389C4×Dic11—41no—
390C4×Dic11—42no—
391C4×Dic11—42no—
392C4×Dic11C22×C418yes—
393C2×#525—111no—
394#2374—112no—
395#2374—112no—
396#2363—111no—
397#2363—111no—
398#2362—111no—
399#2362—111no—
400#2357—112no—
401#2353—112no—
402#2347—111no—
403#2346—111no—
404#2341—111no—
405#2339—111no—
406#2321—112no—
407#2321—112no—
408#2318—112no—
409C4×C22⋊Q8—111no—
410C4×C22⋊Q8D1111yescharacteristic, complemented
411C4×#121—111no—
412C4×#121—111no—
413#2280—111no—
414#2275—112no—
415C2×C4×C22⋊C4—111no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—21no—
419C23×C11—21no—
420C23×C11C23×C412yes—
421C23×C11C2×#4112yes—
422C23×C11C2×#4112yes—
423C23×C11C2511yescharacteristic
424C22×D11—28no—
425C22×D11—21no—
426C22×D11—21no—
427C22×D11—21no—
428C22×D11—21no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—22no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—22no—
441C22×D11—21no—
442C22×D11—21no—
443C22×D11—44no—
444C22×D11—44no—
445C22×D11—44no—
446C22×D11—44no—
447C22×D11—44no—
448C22×D11—44no—
449C22×D11C23×C412yes—
450C22×D11C23×C412yes—
451C22×D11C23×C414yes—
452Q8×C11—28no—
453C2×C4×C11—21no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—28no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—44no—
477C2×C4×C11—44no—
478C2×C4×C11C23×C414yes—
479C2×C4×C11C23×C414yes—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C2×#4112yes—
483C2×C4×C11C2×#4112yes—
484C2×C4×C11H(5,𝔽2)12yes—
485C2×C4×C11H(5,𝔽2)12yes—
486C22⋊D11—216no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—21no—
492C2×Dic11—21no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—21no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—44no—
510C2×Dic11—44no—
511C2×Dic11—44no—
512C2×Dic11C23×C412yes—
513C2×Dic11C23×C414yes—
514C2×Dic11C23×C412yes—
515C2×Dic11C2×#4112yes—
516C2×Dic11C2×#4112yes—
517D44—28no—
518D44—48no—
519D44—48no—
520C4×D11—28no—
521C4×D11—28no—
522C4×D11—44no—
523C4×D11—44no—
524C4×D11—48no—
525C4×D11—84no—
526C4×D11—84no—
527C22×#41—111no—
528C24×C4—111no—
529#525—1116no—
530C2×#123—112no—
531C2×C22⋊Q8—111no—
532C2×C22⋊Q8C2×D1111yescharacteristic
533C2×#121—111no—
534C2×#121—111no—
535C2×#120—112no—
536C2×C4×Q8—111no—
537C2×C4×Q8C2×D1111yescharacteristic, complemented
538C2×C4×D4—112no—
539C2×C4×D4—112no—
540C2×C4×D4—111no—
541C2×C4×D4—112no—
542C2×C4×D4—112no—
543C2×C4×D4—111no—
544C2×#117—111no—
545C2×#117—111no—
546C2×#117—111no—
547C22×C22⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C42—111no—
550C22×C42C2×D1111yescharacteristic
551#391—111no—
552#391C2×D1111yescharacteristic, complemented
553#390—112no—
554#390—112no—
555#390—111no—
556#390—112no—
557#390—112no—
558#390—111no—
559#389—111no—
560#389—111no—
561#389—111no—
562#389C2×D1111yescharacteristic, complemented
563#388—112no—
564#388—112no—
565#388—112no—
566#388—112no—
567#388—112no—
568#388—112no—
569#388—112no—
570#388—112no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#387—112no—
576#387—112no—
577#387—112no—
578#387C2×D1112yescomplemented
579#386—112no—
580#386—112no—
581#386—112no—
582#386—112no—
583#386—112no—
584#386—112no—
585#385—112no—
586#385C2×D1112yes—
587#383—112no—
588#382—112no—
589#381—112no—
590#381—112no—
591#380—111no—
592#380—112no—
593#380—111no—
594#380—111no—
595#380C2×D1111yescharacteristic
596#379—112no—
597C4×C4⋊C4—111no—
598C4×C4⋊C4—111no—
599C4×C4⋊C4—112no—
600C4×C4⋊C4—111no—
601C4×C4⋊C4—112no—
602C4×C4⋊C4—112no—
603C4×C4⋊C4—112no—
604C4×C4⋊C4C2×D1111yescharacteristic, complemented
605C4×C4⋊C4C2×D1112yescomplemented
606C4×C22⋊C4—112no—
607C4×C22⋊C4—112no—
608C4×C22⋊C4—111no—
609C4×C22⋊C4—111no—
610C4×C22⋊C4—112no—
611C4×C22⋊C4—111no—
612C4×C22⋊C4—112no—
613C4×C22⋊C4—111no—
614C4×C22⋊C4—111no—
615C4×C22⋊C4—111no—
616C4×C22⋊C4—112no—
617C4×C22⋊C4—111no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4C2×D1112yes—
623#376—112no—
624C2×#95—111no—
625C2×#95—111no—
626C2×#95—112no—
627C22×C11—22no—
628C22×C11—22no—
629C22×C11—22no—
630C22×C11—22no—
631C22×C11—22no—
632C22×C11—22no—
633C22×C11C4×#4114yes—
634C22×C11C24×C411yescharacteristic
635C22×C11C22×#4111yescharacteristic
636C22×C11C22×#4111yescharacteristic
637C22×C11C2×H(5,𝔽2)11yescharacteristic
638C22×C11C2×H(5,𝔽2)11yescharacteristic
639C22×C11#58511yescharacteristic
640C22×C11#58511yescharacteristic
641C2×D11—22no—
642C2×D11—22no—
643C2×D11—24no—
644C2×D11—22no—
645C2×D11—22no—
646C2×D11—24no—
647C2×D11—22no—
648C2×D11—22no—
649C2×D11—24no—
650C2×D11—416no—
651C2×D11—41no—
652C2×D11—41no—
653C2×D11—41no—
654C2×D11—41no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—41no—
662C2×D11—41no—
663C4×C11—22no—
664C4×C11—24no—
665C4×C11—24no—
666C4×C11—22no—
667C4×C11—22no—
668C4×C11—42no—
669C4×C11—42no—
670C4×C11—41no—
671C4×C11—41no—
672C4×C11#51814yes—
673Dic11—24no—
674Dic11—22no—
675Dic11—22no—
676Dic11—22no—
677Dic11—22no—
678Dic11—42no—
679Dic11—42no—
680Dic11—41no—
681Dic11—41no—
682C25—111no—
683C2×#41—118no—
684C2×#41—442no—
685C2×#41—442no—
686C22×Q8C22×D1111yescharacteristic
687C22×D4—112no—
688C22×D4—111no—
689C22×D4—112no—
690C22×D4—112no—
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—111no—
694C23×C4—111no—
695C23×C4—118no—
696C23×C4—111no—
697C23×C4—112no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—112no—
701C23×C4—112no—
702C23×C4—442no—
703C23×C4—442no—
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1111yescharacteristic
707#123—1116no—
708C22⋊Q8—118no—
709C22⋊Q8C4×D1118yescomplemented
710#121—118no—
711#121—118no—
712#120—1116no—
713C4×Q8—42no—
714C4×Q8—442no—
715C4×D4—1116no—
716C4×D4—1116no—
717C4×D4—228no—
718C4×D4—228no—
719C4×D4—442no—
720C4×D4—442no—
721#117—118no—
722#117—442no—
723#117—442no—
724C2×C4⋊C4—111no—
725C2×C4⋊C4—112no—
726C2×C4⋊C4—111no—
727C2×C4⋊C4—111no—
728C2×C4⋊C4—112no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4C22×D1111yescharacteristic
733C2×C4⋊C4C22×D1111yescharacteristic
734C2×C4⋊C4C22×D1112yes—
735C2×C4⋊C4C22×D1112yes—
736C2×C4⋊C4C22×D1111yescharacteristic
737C2×C4⋊C4C22×D1112yes—
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—111no—
744C2×C22⋊C4—111no—
745C2×C22⋊C4—111no—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—111no—
749C2×C22⋊C4—111no—
750C2×C22⋊C4—111no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—224no—
762C2×C22⋊C4—224no—
763C2×C22⋊C4C22×D1112yes—
764C2×C22⋊C4C22×D1112yes—
765C2×C42—42no—
766C2×C42—112no—
767C2×C42—112no—
768C2×C42—112no—
769C2×C42—111no—
770C2×C42—111no—
771C2×C42—112no—
772C2×C42—112no—
773C2×C42—112no—
774C2×C42—111no—
775C2×C42—112no—
776C2×C42—111no—
777C2×C42—442no—
778C2×C42C22×D1111yescharacteristic
779C2×C42C22×D1111yescharacteristic
780C2×C42C22×D1112yes—
781C2×C42C22×D1111yescharacteristic
782C2×C42C22×D1111yescharacteristic
783C2×C42C22×D1112yes—
784#95—111no—
785#95—111no—
786#95—111no—
787#95—111no—
788#95—111no—
789#95—111no—
790#95—111no—
791#95—111no—
792#95—112no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—112no—
797#95—112no—
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95C22×D1112yes—
804#95C22×D1112yes—
805#95C22×D1112yes—
806#95C22×D1112yes—
807#95C22×D1112yes—
808C2×C11—24no—
809C2×C11C2×C4×#4111yescharacteristic
810C2×C11C2×#51811yescharacteristic
811C2×C11#342811yescharacteristic
812C2×C11#350511yescharacteristic
813C2×C11#350511yescharacteristic
814C2×C11#350611yescharacteristic
815C2×C11#350611yescharacteristic
816D11—44no—
817D11—42no—
818D11—42no—
819C24—111no—
820C24—111no—
821C24—112no—
822C24—114no—
823C24—222no—
824C24—222no—
825C24—441no—
826C24—441no—
827C24—441no—
828C24—441no—
829C24C23×D1111yescharacteristic
830#41—4416no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8C2×C4×D1114yes—
834C2×D4—118no—
835C2×D4—114no—
836C2×D4—118no—
837C2×D4—118no—
838C2×D4—224no—
839C2×D4—224no—
840C2×D4—222no—
841C2×D4—222no—
842C2×D4—442no—
843C2×D4—442no—
844C2×D4—442no—
845C2×D4—442no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—111no—
854C22×C4—111no—
855C22×C4—111no—
856C22×C4—112no—
857C22×C4—111no—
858C22×C4—114no—
859C22×C4—114no—
860C22×C4—114no—
861C22×C4—114no—
862C22×C4—114no—
863C22×C4—118no—
864C22×C4—114no—
865C22×C4—112no—
866C22×C4—111no—
867C22×C4—111no—
868C22×C4—112no—
869C22×C4—224no—
870C22×C4—222no—
871C22×C4—222no—
872C22×C4—222no—
873C22×C4—222no—
874C22×C4—222no—
875C22×C4—224no—
876C22×C4—4416no—
877C22×C4—441no—
878C22×C4—441no—
879C22×C4—441no—
880C22×C4—441no—
881C22×C4—442no—
882C22×C4—442no—
883C22×C4—442no—
884C22×C4—442no—
885C22×C4—442no—
886C22×C4—442no—
887C22×C4—441no—
888C22×C4—441no—
889C22×C4—441no—
890C22×C4—441no—
891C22×C4—441no—
892C22×C4—441no—
893C22×C4C2×C4×D1114yes—
894C22×C4#434314yescomplemented
895C22×C4C23×D1111yescharacteristic
896C22×C4C23×D1111yescharacteristic
897C22×C4C23×D1112yes—
898C22×C4C23×D1112yes—
899C22×C4C23×D1111yescharacteristic
900C22×C4C23×D1112yes—
901C22×C4C23×D1112yes—
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—114no—
910C4⋊C4—118no—
911C4⋊C4—224no—
912C4⋊C4—222no—
913C4⋊C4—224no—
914C4⋊C4—222no—
915C4⋊C4—442no—
916C4⋊C4—442no—
917C4⋊C4C2×C4×D1114yes—
918C4⋊C4C2×C4×D1118yes—
919C22⋊C4—24no—
920C22⋊C4—118no—
921C22⋊C4—118no—
922C22⋊C4—118no—
923C22⋊C4—118no—
924C22⋊C4—222no—
925C22⋊C4—222no—
926C22⋊C4—222no—
927C22⋊C4—222no—
928C22⋊C4—224no—
929C22⋊C4—224no—
930C22⋊C4—222no—
931C22⋊C4—222no—
932C22⋊C4—222no—
933C22⋊C4—222no—
934C22⋊C4—224no—
935C22⋊C4—442no—
936C22⋊C4—442no—
937C22⋊C4—442no—
938C22⋊C4—442no—
939C22⋊C4—442no—
940C22⋊C4—442no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4C2×C4×D1118yes—
944C42—22no—
945C42—22no—
946C42—41no—
947C42—41no—
948C42—42no—
949C42—42no—
950C42—118no—
951C42—224no—
952C42—224no—
953C42—222no—
954C42—222no—
955C42—441no—
956C42—441no—
957C42—442no—
958C42—442no—
959C42—442no—
960C42—442no—
961C11#3422311yescharacteristic, complemented, Sylow
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—112no—
967C23—112no—
968C23—114no—
969C23—228no—
970C23—221no—
971C23—222no—
972C23—221no—
973C23—221no—
974C23—221no—
975C23—222no—
976C23—221no—
977C23—221no—
978C23—222no—
979C23—221no—
980C23—222no—
981C23—221no—
982C23—222no—
983C23—221no—
984C23—221no—
985C23—222no—
986C23—221no—
987C23—221no—
988C23—444no—
989C23—444no—
990C23—444no—
991C23—444no—
992C23—444no—
993C23—444no—
994C23C22×C4×D1112yes—
995C23C2×#434312yes—
996C23#41×D1112yes—
997C23C24×D1111yescharacteristic
998Q8—28no—
999D4—2216no—
1000D4—228no—
1001D4—448no—
1002D4—448no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—28no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—112no—
1029C2×C4—114no—
1030C2×C4—112no—
1031C2×C4—112no—
1032C2×C4—112no—
1033C2×C4—221no—
1034C2×C4—221no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—221no—
1038C2×C4—221no—
1039C2×C4—221no—
1040C2×C4—221no—
1041C2×C4—221no—
1042C2×C4—221no—
1043C2×C4—228no—
1044C2×C4—228no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—222no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—444no—
1058C2×C4—444no—
1059C2×C4—448no—
1060C2×C4—444no—
1061C2×C4—444no—
1062C2×C4—444no—
1063C2×C4—884no—
1064C2×C4—884no—
1065C2×C4C22×C4×D1114yes—
1066C2×C4C22×C4×D1112yes—
1067C2×C4C22×C4×D1114yes—
1068C2×C4C22×C4×D1112yes—
1069C2×C4#6703712yes—
1070C2×C4C2×#434312yes—
1071C2×C4C2×#434312yes—
1072C2×C4#6704212yes—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—224no—
1080C22—222no—
1081C22—222no—
1082C22—222no—
1083C22—222no—
1084C22—224no—
1085C22—222no—
1086C22—224no—
1087C22—222no—
1088C22—4416no—
1089C22—442no—
1090C22—441no—
1091C22—441no—
1092C22—442no—
1093C22—441no—
1094C22—441no—
1095C22—441no—
1096C22—441no—
1097C22—442no—
1098C22—441no—
1099C22—441no—
1100C22—442no—
1101C22C4×#434314yes—
1102C22C23×C4×D1111yescharacteristic
1103C22C2×#6703711yescharacteristic
1104C22C22×#434311yescharacteristic
1105C22C2×#41×D1111yescharacteristic
1106C22C2×#6704211yescharacteristic
1107C22#1062345311yescharacteristic
1108C22#1062345311yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—24no—
1113C4—24no—
1114C4—42no—
1115C4—41no—
1116C4—41no—
1117C4—42no—
1118C4—222no—
1119C4—222no—
1120C4—224no—
1121C4—222no—
1122C4—222no—
1123C4—442no—
1124C4—441no—
1125C4—441no—
1126C4—442no—
1127C4#1062307614yes—
1128C2—24no—
1129C2—442no—
1130C2—442no—
1131C2—444no—
1132C2C2×C4×#434311yescharacteristic
1133C2C2×#1062307611yescharacteristic
1134C2#1308181511yescharacteristic
1135C2#1308245111yescharacteristic
1136C2#1308245711yescharacteristic
1137C2#1308245911yescharacteristic
1138C2#1308247011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×C22⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC2×#10623158C2
hypercenterC4×C22⋊Q8D11
hypocenterC11#34223
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13071748C2semidirect
3. #13071745C2semidirect
4. #13071656C2semidirect
5. #13071653C2semidirect
6. #13071648C2semidirect
7. #13071639C2semidirect
8. #13071585C2semidirect
9. #13071555C2semidirect
10. #13071505C2semidirect
11. #13071500C2semidirect
12. #13071454C2semidirect
13. #13071445C2semidirect
14. #13071276C2semidirect
15. #13071273C2semidirect
16. #13071244C2semidirect
17. C22⋊Q8×Dic11C2semidirect
18. C4×#66983C2semidirect
19. #13071122C2semidirect
20. #13070998C2semidirect
21. #13070975C2semidirect
22. C2×C4×(C2×D11)⋊C4C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
36. #10623158C4semidirect
40. C2×#66946C22semidirect
47. C2×C4×D44C22semidirect
48. C11×#391C22semidirect
49. C11×#389C22semidirect
50. C11×#387C22semidirect
53. C4×C11×C4⋊C4C22semidirect
54. C4×C11×C4⋊C4C22semidirect
56. #10622843C22semidirect
63. #10622603C22semidirect
66. #10622601C22semidirect
69. #10622600C22semidirect
70. #10622598C22semidirect
71. #10622594C22semidirect
72. #10622591C22semidirect
73. #10622590C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. #10622586C22semidirect
85. #10622553C22semidirect
88. #10622552C22semidirect
97. C4×(C2×D11)⋊C4C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×C4⋊Dic11C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. #10622541C22semidirect
106. #10622283C22semidirect
109. #10622282C22semidirect
111. #10622279C22semidirect
112. #10622279C22semidirect
118. #10622277C22semidirect
119. D11×#95C22semidirect
120. #10622268C22semidirect
121. #10622264C22semidirect
122. #10622262C22semidirect
123. #10622261C22semidirect
135. C2×#4343C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
149. C11×C22⋊Q8C2×C4semidirect
167. #66999C2×C4semidirect
215. #66948C2×C4semidirect
216. #66947C2×C4semidirect
218. #66946C2×C4semidirect
221. #66945C2×C4semidirect
222. #66935C2×C4semidirect
224. (C22⋊D11)⋊C4C2×C4semidirect
273. C22×C4×C11#41semidirect
295. C22×Dic11#41semidirect
410. C4×C22⋊Q8D11semidirect
537. C2×C4×Q8C2×D11semidirect
552. #391C2×D11semidirect
562. #389C2×D11semidirect
578. #387C2×D11semidirect
604. C4×C4⋊C4C2×D11semidirect
605. C4×C4⋊C4C2×D11semidirect
709. C22⋊Q8C4×D11semidirect
894. C22×C4#4343semidirect
961. C11#34223semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
#130717482
#130717452
#130716562
#130716532
#130716482
#130716392
#130715852
#130715552
#130715052
#130715002
#130714542
#130714452
#130712762
#130712732
#130712442
C22⋊Q8×Dic112
C4×#669832
#130711222
#130709982
#130709752
C2×C4×(C2×D11)⋊C42
C4×C11×C22⋊Q82
#3422311