Finite Group Databasebeta

← #14913933

Subgroups — #14913933

Order 2816.

2914 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2#13071586C212yesmaximal, complemented
3#13071551C212yesmaximal, complemented
4#13071550C212yesmaximal, complemented
5#13071522C212yesmaximal, complemented
6#13071486C211yesmaximal, characteristic, complemented
7#13071480C211yesmaximal, characteristic, complemented
8#13071468C211yesmaximal, characteristic, complemented
9#13071465C211yesmaximal, characteristic, complemented
10#13071462C211yesmaximal, characteristic, complemented
11C22⋊C4×C22⋊D11C211yesmaximal, characteristic
12#13071432C211yesmaximal, characteristic
13#13071257C212yesmaximal, complemented
14#13071246C212yesmaximal, complemented
15#13071244C212yesmaximal, complemented
16#13071011C211yesmaximal, characteristic, complemented
17#13071010C211yesmaximal, characteristic, complemented
18#13070995C211yesmaximal, characteristic, complemented
19#13070994C211yesmaximal, characteristic, complemented
20C2×#10622556C211yesmaximal, characteristic, complemented
21D11×#381C211yesmaximal, characteristic, complemented
22#13070975C212yesmaximal, complemented
23C11×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C2×(C22⋊D11)⋊C4C4116yescomplemented
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×(C22⋊D11)⋊C4C2211yescharacteristic
39C2×(C22⋊D11)⋊C4C2211yescharacteristic
40C2×(C22⋊D11)⋊C4C2211yescharacteristic
41C2×(C22⋊D11)⋊C4C2211yescharacteristic
42C2×(C22⋊D11)⋊C4C2211yescharacteristic
43C2×(C22⋊D11)⋊C4C2211yescharacteristic
44C2×(C22⋊D11)⋊C4C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×#66930C2211yescharacteristic
49C2×#66930C2211yescharacteristic
50C11×#388C2212yescomplemented
51C11×#388C2212yescomplemented
52C11×#385C2212yescomplemented
53C11×#381C2211yescharacteristic
54C11×#380C2211yescharacteristic
55C11×#379C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C4×C11×C22⋊C4C2212yescomplemented
58#10622860C2211yescharacteristic
59#10622826C2212yes—
60#10622825C2211yescharacteristic
61#10622824C2211yescharacteristic
62C4×C22⋊Dic11C2211yescharacteristic
63C2×C11⋊#95C2212yescomplemented
64C2×C11⋊#95C2212yescomplemented
65#10622603C2212yescomplemented
66#10622602C2212yescomplemented
67#10622600C2212yescomplemented
68#10622600C2212yescomplemented
69#10622591C2212yescomplemented
70#10622590C2212yescomplemented
71C4⋊C4×Dic11C2212yescomplemented
72#10622585C2212yescomplemented
73#10622571C2212yes—
74#10622570C2212yes—
75#10622570C2212yes—
76#10622569C2212yes—
77#10622569C2212yes—
78#10622568C2211yescharacteristic
79#10622568C2211yescharacteristic
80#10622564C2212yescomplemented
81#10622564C2212yescomplemented
82#10622563C2212yescomplemented
83#10622556C2211yescharacteristic
84#10622556C2211yescharacteristic
85#10622556C2211yescharacteristic
86#10622556C2211yescharacteristic
87#10622556C2211yescharacteristic
88#10622556C2211yescharacteristic
89#10622556C2212yescomplemented
90#10622556C2212yescomplemented
91#10622555C2211yescharacteristic
92#10622555C2211yescharacteristic
93#10622555C2212yescomplemented
94#10622555C2212yescomplemented
95C22⋊C4×Dic11C2211yescharacteristic
96C22⋊C4×Dic11C2211yescharacteristic
97C22⋊C4×Dic11C2212yescomplemented
98C22⋊C4×Dic11C2212yescomplemented
99C22⋊C4×Dic11C2212yescomplemented
100#10622553C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yescomplemented
102C4×(C2×D11)⋊C4C2212yescomplemented
103C4×(C2×D11)⋊C4C2212yescomplemented
104#10622546C2212yescomplemented
105#10622545C2212yescomplemented
106C4×Dic11⋊C4C2212yescomplemented
107C4×Dic11⋊C4C2212yescomplemented
108#10622283C2212yescomplemented
109#10622282C2212yescomplemented
110#10622281C2212yescomplemented
111#10622279C2212yescomplemented
112#10622277C2212yescomplemented
113#10622277C2212yescomplemented
114D11×#95C2212yescomplemented
115D11×#95C2212yescomplemented
116#10622268C2212yescomplemented
117#10622265C2212yescomplemented
118#10622264C2212yescomplemented
119#10622264C2212yescomplemented
120#10622263C2212yescomplemented
121#10622262C2212yescomplemented
122#10622261C2212yescomplemented
123#10622260C2212yescomplemented
124C25×C11C2311yescharacteristic
125C24×D11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11—28no—
130C22×C22⋊D11C2×C418yes—
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11—42no—
136C23×Dic11—42no—
137C23×Dic11C2×C418yescomplemented
138C23×Dic11C2311yescharacteristic
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2312yes—
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C22×C4×D11—42no—
147C22×C4×D11—42no—
148C22×C4×D11C2×C418yescomplemented
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C11×#117—42no—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4—42no—
159C2×C11×C22⋊C4C2×C418yescomplemented
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C42×C11C2312yes—
172C2×C42×C11C2312yes—
173C2×C22⋊Dic11—42no—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C4×C22⋊D11—28no—
182C2×(C2×D11)⋊C4C2×C418yescomplemented
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)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193#66979—42no—
194C2×C4⋊Dic11C2312yes—
195C2×C4⋊Dic11C2312yes—
196C2×Dic11⋊C4C2×C418yescomplemented
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×C4×Dic11C2×C418yescomplemented
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216(C22⋊D11)⋊C4—28no—
217(C22⋊D11)⋊C4C2×C418yes—
218(C22⋊D11)⋊C4C2×C418yes—
219(C22⋊D11)⋊C4C2×C418yescomplemented
220(C22⋊D11)⋊C4C2×C418yescomplemented
221(C22⋊D11)⋊C4C2×C418yescomplemented
222(C22⋊D11)⋊C4C2×C418yescomplemented
223(C22⋊D11)⋊C4C2×C418yescomplemented
224(C22⋊D11)⋊C4C2×C418yescomplemented
225C22⋊C4×D11—42no—
226C22⋊C4×D11—42no—
227#66930—42no—
228#66930—42no—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34190—111nomaximal, Sylow
254C24×C11—24no—
255C24×C11—22no—
256C24×C11—22no—
257C24×C11—42no—
258C24×C11C22×C414yes—
259C24×C11C2411yescharacteristic
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C23×D11—22no—
263C23×D11—22no—
264C23×D11—24no—
265C23×D11—42no—
266C23×D11C22×C414yes—
267C23×D11C2411yescharacteristic
268C23×D11C2411yescharacteristic
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—24no—
272C22×C4×C11—42no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11C22×C414yes—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C2×C22⋊D11—232no—
286C2×C22⋊D11—24no—
287C2×C22⋊D11—24no—
288C2×C22⋊D11—24no—
289C2×C22⋊D11C22×C414yes—
290C2×C22⋊D11C22×C414yes—
291C2×C22⋊D11C22×C414yes—
292C2×C22⋊D11C22×C414yes—
293C2×C22⋊D11#4118yes—
294C22×Dic11—24no—
295C22×Dic11—24no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—416no—
301C22×Dic11—41no—
302C22×Dic11—41no—
303C22×Dic11—41no—
304C22×Dic11—41no—
305C22×Dic11—41no—
306C22×Dic11—41no—
307C22×Dic11—41no—
308C22×Dic11—41no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11C22×C414yes—
312C22×Dic11C22×C414yes—
313C22×Dic11C22×C414yes—
314C22×Dic11C22×C414yes—
315C22×Dic11C22×C414yes—
316C22×Dic11C22×C414yes—
317C22×Dic11C22×C414yes—
318C22×Dic11C2412yes—
319C22×Dic11C2412yes—
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—416no—
331C2×C4×D11—41no—
332C2×C4×D11—41no—
333C2×C4×D11—41no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—41no—
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×C4×D11C22×C414yes—
346C2×C4×D11C22×C414yes—
347C11×C4⋊C4—42no—
348C11×C4⋊C4—42no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—22no—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4C22×C414yes—
357C11×C22⋊C4C22×C414yes—
358C11×C22⋊C4C22×C414yes—
359C11×C22⋊C4C22×C414yes—
360C42×C11—42no—
361C42×C11—42no—
362C22⋊Dic11—24no—
363C22⋊Dic11—22no—
364C22⋊Dic11—22no—
365C22⋊Dic11—22no—
366C22⋊Dic11—22no—
367C22⋊Dic11—42no—
368C22⋊Dic11—42no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4C22×C414yes—
376(C2×D11)⋊C4C22×C414yes—
377(C2×D11)⋊C4C22×C414yes—
378(C2×D11)⋊C4C22×C414yes—
379C4⋊Dic11—42no—
380C4⋊Dic11—42no—
381Dic11⋊C4—24no—
382Dic11⋊C4—24no—
383Dic11⋊C4—42no—
384Dic11⋊C4—42no—
385Dic11⋊C4C22×C414yes—
386Dic11⋊C4C22×C414yes—
387Dic11⋊C4C22×C414yes—
388Dic11⋊C4C22×C414yes—
389C4×Dic11—24no—
390C4×Dic11—24no—
391C4×Dic11—42no—
392C4×Dic11—42no—
393C4×Dic11—42no—
394C4×Dic11—42no—
395C4×Dic11C22×C414yes—
396C4×Dic11C22×C414yes—
397C4×Dic11C22×C414yes—
398C4×Dic11C22×C414yes—
399C22×C4×D4—111no—
400#2357—112no—
401#2353—112no—
402#2353—112no—
403#2349—112no—
404#2344—111no—
405#2344—111no—
406#2342—111no—
407#2342—111no—
408#2342—111no—
409#2342D1111yescharacteristic, complemented
410D4×C22⋊C4—111no—
411D4×C22⋊C4—111no—
412#2319—112no—
413#2318—112no—
414#2318—112no—
415#2283—111no—
416#2283—111no—
417#2280—111no—
418#2280—111no—
419C2×#381—111no—
420C2×#381—111no—
421#2275—112no—
422C23×C11—22no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—28no—
428C23×C11—28no—
429C23×C11—22no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—22no—
433C23×C11—44no—
434C23×C11—48no—
435C23×C11—48no—
436C23×C11C23×C412yes—
437C23×C11C23×C412yes—
438C23×C11C23×C412yes—
439C23×C11C2×#4114yes—
440C23×C11H(5,𝔽2)12yes—
441C23×C11H(5,𝔽2)12yes—
442C23×C11C2511yescharacteristic
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—22no—
446C22×D11—28no—
447C22×D11—22no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—22no—
451C22×D11—28no—
452C22×D11—44no—
453C22×D11—48no—
454C22×D11—48no—
455C22×D11C23×C412yes—
456C22×D11C23×C412yes—
457C22×D11C2×#4114yes—
458C2×C4×C11—28no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—44no—
478C2×C4×C11—84no—
479C2×C4×C11C23×C412yes—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C412yes—
483C22⋊D11—28no—
484C22⋊D11—28no—
485C22⋊D11—28no—
486C22⋊D11#117116yescomplemented
487C2×Dic11—28no—
488C2×Dic11—28no—
489C2×Dic11—22no—
490C2×Dic11—21no—
491C2×Dic11—21no—
492C2×Dic11—21no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—28no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—44no—
512C2×Dic11—44no—
513C2×Dic11—44no—
514C2×Dic11—44no—
515C2×Dic11—84no—
516C2×Dic11C23×C412yes—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C412yes—
519C2×Dic11C23×C412yes—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C2×#4114yes—
523C4×D11—44no—
524C4×D11—44no—
525C4×D11—44no—
526C4×D11—44no—
527C4×D11—84no—
528C4×D11—84no—
529C23×D4—111no—
530C24×C4—111no—
531C24×C4—111no—
532C2×C4×D4—112no—
533C2×C4×D4—111no—
534C2×C4×D4—111no—
535C2×C4×D4—111no—
536C2×C4×D4—111no—
537C2×C4×D4—111no—
538C2×C4×D4—111no—
539C2×C4×D4—111no—
540C2×C4×D4—111no—
541C2×C4×D4—112no—
542C2×C4×D4—1116no—
543C2×#117—111no—
544C2×#117—111no—
545C2×#117—111no—
546C2×#117C2×D1111yescharacteristic
547C22×C4⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C22⋊C4—111no—
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4C2×D1111yescharacteristic
553C22×C22⋊C4C2×D1111yescharacteristic
554C22×C42—111no—
555#390—112no—
556#390—112no—
557#389—112no—
558#389—112no—
559#388—112no—
560#388—112no—
561#388—112no—
562#388—112no—
563#388—112no—
564#388—112no—
565#388C2×D1112yescomplemented
566#388C2×D1112yescomplemented
567#387—112no—
568#387—112no—
569#387—112no—
570#387—112no—
571#386—112no—
572#386—112no—
573#386—112no—
574#386—112no—
575#385—112no—
576#385—112no—
577#385—112no—
578#385C2×D1112yescomplemented
579#383—112no—
580#383—112no—
581#382—112no—
582#382—112no—
583#381—111no—
584#381—112no—
585#381—111no—
586#381—111no—
587#381—112no—
588#381—111no—
589#381—111no—
590#381—111no—
591#381—111no—
592#381—112no—
593#381—112no—
594#381C2×D1111yescharacteristic
595#380—111no—
596#380—112no—
597#380—112no—
598#380—112no—
599#380—111no—
600#380—111no—
601#380—112no—
602#380C2×D1111yescharacteristic
603#379—111no—
604#379—111no—
605#379—111no—
606#379C2×D1111yescharacteristic
607C4×C4⋊C4—112no—
608C4×C4⋊C4—112no—
609C4×C4⋊C4—112no—
610C4×C4⋊C4—112no—
611C4×C22⋊C4—111no—
612C4×C22⋊C4—112no—
613C4×C22⋊C4—111no—
614C4×C22⋊C4—111no—
615C4×C22⋊C4—112no—
616C4×C22⋊C4—112no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4—112no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4C2×D1111yescharacteristic
622C4×C22⋊C4C2×D1112yescomplemented
623#376—112no—
624#376—112no—
625C2×#95—112no—
626C2×#95—112no—
627C2×#95—112no—
628C2×#95—112no—
629C22×C11—22no—
630C22×C11—22no—
631C22×C11—22no—
632C22×C11—22no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—24no—
636C22×C11—24no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—416no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11C2×#11714yes—
644C22×C11#51814yes—
645C22×C11C24×C411yescharacteristic
646C22×C11C22×#4112yes—
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C22×C11C2×H(5,𝔽2)11yescharacteristic
649C22×C11#58512yes—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—22no—
657C2×D11—416no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11C2×#11714yes—
661C4×C11—22no—
662C4×C11—22no—
663C4×C11—22no—
664C4×C11—22no—
665C4×C11—42no—
666C4×C11—42no—
667C4×C11—42no—
668C4×C11—42no—
669Dic11—22no—
670Dic11—22no—
671Dic11—22no—
672Dic11—22no—
673Dic11—22no—
674Dic11—42no—
675Dic11—42no—
676Dic11—42no—
677Dic11—42no—
678Dic11C2×#11714yes—
679C25—111no—
680C25C22×D1111yescharacteristic
681C22×D4—111no—
682C22×D4—118no—
683C22×D4—111no—
684C22×D4—111no—
685C22×D4—111no—
686C22×D4—228no—
687C23×C4—111no—
688C23×C4—111no—
689C23×C4—111no—
690C23×C4—118no—
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—111no—
694C23×C4—111no—
695C23×C4—118no—
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—112no—
701C23×C4—112no—
702C23×C4—112no—
703C23×C4—442no—
704C23×C4—442no—
705C23×C4—442no—
706C23×C4—442no—
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1112yes—
709C23×C4C22×D1111yescharacteristic
710C4×D4—118no—
711C4×D4—118no—
712C4×D4—118no—
713C4×D4—118no—
714C4×D4—118no—
715C4×D4—118no—
716C4×D4—118no—
717C4×D4—118no—
718C4×D4—228no—
719C4×D4—228no—
720#117—42no—
721#117—442no—
722#117—442no—
723#117—442no—
724C2×C4⋊C4—118no—
725C2×C4⋊C4—111no—
726C2×C4⋊C4—111no—
727C2×C4⋊C4—111no—
728C2×C4⋊C4—111no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—112no—
734C2×C4⋊C4—112no—
735C2×C4⋊C4C22×D1112yes—
736C2×C4⋊C4C22×D1112yes—
737C2×C22⋊C4—42no—
738C2×C22⋊C4—118no—
739C2×C22⋊C4—111no—
740C2×C22⋊C4—111no—
741C2×C22⋊C4—111no—
742C2×C22⋊C4—111no—
743C2×C22⋊C4—111no—
744C2×C22⋊C4—111no—
745C2×C22⋊C4—111no—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—442no—
757C2×C22⋊C4—442no—
758C2×C22⋊C4—442no—
759C2×C22⋊C4C4×D1118yescomplemented
760C2×C22⋊C4C22×D1111yescharacteristic
761C2×C22⋊C4C22×D1111yescharacteristic
762C2×C22⋊C4C22×D1111yescharacteristic
763C2×C22⋊C4C22×D1111yescharacteristic
764C2×C22⋊C4C22×D1112yes—
765C2×C22⋊C4C22×D1112yes—
766C2×C22⋊C4C22×D1112yes—
767C2×C22⋊C4C22×D1111yescharacteristic
768C2×C22⋊C4C22×D1111yescharacteristic
769C2×C22⋊C4C22×D1111yescharacteristic
770C2×C22⋊C4C22×D1111yescharacteristic
771C2×C42—118no—
772C2×C42—111no—
773C2×C42—111no—
774C2×C42—111no—
775C2×C42—111no—
776C2×C42—112no—
777C2×C42—112no—
778C2×C42—112no—
779C2×C42—112no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42C22×D1112yes—
783C2×C42C22×D1112yes—
784#95—112no—
785#95—112no—
786#95—112no—
787#95—112no—
788#95—112no—
789#95—112no—
790#95—112no—
791#95—112no—
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#95—112no—
804#95C22×D1112yes—
805#95C22×D1112yes—
806#95C22×D1112yes—
807#95C22×D1112yes—
808C2×C11—24no—
809C2×C11—24no—
810C2×C11—42no—
811C2×C11C22×#11711yescharacteristic
812C2×C11C2×#51811yescharacteristic
813C2×C11#342811yescharacteristic
814C2×C11#351312yes—
815C2×C11#351312yes—
816D11—24no—
817D11—42no—
818C24—22no—
819C24—24no—
820C24—22no—
821C24—42no—
822C24—111no—
823C24—111no—
824C24—114no—
825C24—224no—
826C24—222no—
827C24—222no—
828C24—442no—
829C24C2×C4×D1114yes—
830C24C23×D1111yescharacteristic
831C24C23×D1111yescharacteristic
832C24C23×D1111yescharacteristic
833C2×D4—114no—
834C2×D4—118no—
835C2×D4—114no—
836C2×D4—114no—
837C2×D4—114no—
838C2×D4—224no—
839C2×D4—2232no—
840C2×D4—224no—
841C2×D4—224no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—24no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—111no—
849C22×C4—114no—
850C22×C4—114no—
851C22×C4—114no—
852C22×C4—111no—
853C22×C4—111no—
854C22×C4—111no—
855C22×C4—111no—
856C22×C4—111no—
857C22×C4—114no—
858C22×C4—114no—
859C22×C4—114no—
860C22×C4—114no—
861C22×C4—114no—
862C22×C4—114no—
863C22×C4—114no—
864C22×C4—114no—
865C22×C4—112no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—224no—
870C22×C4—224no—
871C22×C4—224no—
872C22×C4—222no—
873C22×C4—222no—
874C22×C4—222no—
875C22×C4—222no—
876C22×C4—224no—
877C22×C4—4416no—
878C22×C4—441no—
879C22×C4—441no—
880C22×C4—441no—
881C22×C4—441no—
882C22×C4—441no—
883C22×C4—441no—
884C22×C4—441no—
885C22×C4—441no—
886C22×C4—442no—
887C22×C4—442no—
888C22×C4—442no—
889C22×C4—442no—
890C22×C4—4416no—
891C22×C4—441no—
892C22×C4—441no—
893C22×C4—441no—
894C22×C4—441no—
895C22×C4—441no—
896C22×C4—441no—
897C22×C4—441no—
898C22×C4—441no—
899C22×C4—442no—
900C22×C4—442no—
901C22×C4C2×C4×D1114yes—
902C22×C4C2×C4×D1114yes—
903C22×C4C23×D1112yes—
904C22×C4C23×D1112yes—
905C22×C4C23×D1112yes—
906C22×C4C23×D1112yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—114no—
914C4⋊C4—114no—
915C4⋊C4—114no—
916C4⋊C4—114no—
917C4⋊C4—224no—
918C4⋊C4—224no—
919C4⋊C4—442no—
920C4⋊C4—442no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C22⋊C4—22no—
924C22⋊C4—22no—
925C22⋊C4—22no—
926C22⋊C4—24no—
927C22⋊C4—22no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—114no—
931C22⋊C4—114no—
932C22⋊C4—114no—
933C22⋊C4—114no—
934C22⋊C4—224no—
935C22⋊C4—224no—
936C22⋊C4—222no—
937C22⋊C4—224no—
938C22⋊C4—222no—
939C22⋊C4—222no—
940C22⋊C4—222no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4C2×C4×D1114yes—
948C22⋊C4C2×C4×D1114yes—
949C22⋊C4C2×C4×D1114yes—
950C22⋊C4C2×C4×D1114yes—
951C42—42no—
952C42—42no—
953C42—114no—
954C42—114no—
955C42—114no—
956C42—114no—
957C42—224no—
958C42—224no—
959C42—442no—
960C42—442no—
961C42—442no—
962C42—442no—
963C11#3419011yescharacteristic, complemented, Sylow
964C23—21no—
965C23—22no—
966C23—21no—
967C23—22no—
968C23—22no—
969C23—28no—
970C23—28no—
971C23—21no—
972C23—22no—
973C23—21no—
974C23—22no—
975C23—44no—
976C23—48no—
977C23—48no—
978C23—112no—
979C23—114no—
980C23—112no—
981C23—228no—
982C23—221no—
983C23—221no—
984C23—222no—
985C23—228no—
986C23—221no—
987C23—222no—
988C23—221no—
989C23—222no—
990C23—444no—
991C23—448no—
992C23—448no—
993C23C22×C4×D1112yes—
994C23C22×C4×D1112yes—
995C23C22×C4×D1112yes—
996C23#6703712yes—
997C23#41×D1114yes—
998C23#6704212yes—
999C23C24×D1111yescharacteristic
1000D4—1116no—
1001D4—228no—
1002D4—228no—
1003D4—228no—
1004C2×C4—28no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—44no—
1024C2×C4—84no—
1025C2×C4—112no—
1026C2×C4—114no—
1027C2×C4—112no—
1028C2×C4—112no—
1029C2×C4—112no—
1030C2×C4—112no—
1031C2×C4—112no—
1032C2×C4—228no—
1033C2×C4—228no—
1034C2×C4—228no—
1035C2×C4—221no—
1036C2×C4—221no—
1037C2×C4—221no—
1038C2×C4—221no—
1039C2×C4—222no—
1040C2×C4—221no—
1041C2×C4—221no—
1042C2×C4—221no—
1043C2×C4—221no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—444no—
1057C2×C4—444no—
1058C2×C4—444no—
1059C2×C4—444no—
1060C2×C4—444no—
1061C2×C4—444no—
1062C2×C4—444no—
1063C2×C4—444no—
1064C2×C4—884no—
1065C2×C4—884no—
1066C2×C4—884no—
1067C2×C4C22×C4×D1112yes—
1068C2×C4C22×C4×D1112yes—
1069C2×C4C22×C4×D1112yes—
1070C2×C4C22×C4×D1112yes—
1071C22—24no—
1072C22—24no—
1073C22—22no—
1074C22—24no—
1075C22—24no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—416no—
1083C22—42no—
1084C22—42no—
1085C22—114no—
1086C22—224no—
1087C22—224no—
1088C22—222no—
1089C22—222no—
1090C22—222no—
1091C22—222no—
1092C22—222no—
1093C22—4416no—
1094C22—442no—
1095C22—442no—
1096C22D11×#11714yes—
1097C22#1062307614yes—
1098C22C23×C4×D1111yescharacteristic
1099C22C2×#6703711yescharacteristic
1100C22C2×#41×D1112yes—
1101C22C2×#6704211yescharacteristic
1102C22#1062345512yes—
1103C4—22no—
1104C4—22no—
1105C4—22no—
1106C4—22no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—114no—
1112C4—222no—
1113C4—222no—
1114C4—222no—
1115C4—222no—
1116C4—222no—
1117C4—442no—
1118C4—442no—
1119C4—442no—
1120C4—442no—
1121C2—24no—
1122C2—24no—
1123C2—42no—
1124C2—224no—
1125C2—442no—
1126C2C2×D11×#11711yescharacteristic
1127C2C2×#1062307611yescharacteristic
1128C2#1308181411yescharacteristic
1129C2#1308254312yes—
1130C2#1308254912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2342C2
socle, cosocleC23×C11C25
prime radicalC23×C22⋊D11C22
hypercenter#2342D11
hypocenterC11#34190
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #13071586C2semidirect
3. #13071551C2semidirect
4. #13071550C2semidirect
5. #13071522C2semidirect
6. #13071486C2semidirect
7. #13071480C2semidirect
8. #13071468C2semidirect
9. #13071465C2semidirect
10. #13071462C2semidirect
13. #13071257C2semidirect
14. #13071246C2semidirect
15. #13071244C2semidirect
16. #13071011C2semidirect
17. #13071010C2semidirect
18. #13070995C2semidirect
19. #13070994C2semidirect
20. C2×#10622556C2semidirect
21. D11×#381C2semidirect
22. #13070975C2semidirect
23. C11×#2342C2semidirect
36. C2×(C22⋊D11)⋊C4C4semidirect
50. C11×#388C22semidirect
51. C11×#388C22semidirect
52. C11×#385C22semidirect
57. C4×C11×C22⋊C4C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622603C22semidirect
66. #10622602C22semidirect
67. #10622600C22semidirect
68. #10622600C22semidirect
69. #10622591C22semidirect
70. #10622590C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. #10622585C22semidirect
80. #10622564C22semidirect
81. #10622564C22semidirect
82. #10622563C22semidirect
89. #10622556C22semidirect
90. #10622556C22semidirect
93. #10622555C22semidirect
94. #10622555C22semidirect
97. C22⋊C4×Dic11C22semidirect
98. C22⋊C4×Dic11C22semidirect
99. C22⋊C4×Dic11C22semidirect
100. #10622553C22semidirect
101. C4×(C2×D11)⋊C4C22semidirect
102. C4×(C2×D11)⋊C4C22semidirect
103. C4×(C2×D11)⋊C4C22semidirect
104. #10622546C22semidirect
105. #10622545C22semidirect
106. C4×Dic11⋊C4C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. #10622283C22semidirect
109. #10622282C22semidirect
110. #10622281C22semidirect
111. #10622279C22semidirect
112. #10622277C22semidirect
113. #10622277C22semidirect
114. D11×#95C22semidirect
115. D11×#95C22semidirect
116. #10622268C22semidirect
117. #10622265C22semidirect
118. #10622264C22semidirect
119. #10622264C22semidirect
120. #10622263C22semidirect
121. #10622262C22semidirect
122. #10622261C22semidirect
123. #10622260C22semidirect
137. C23×Dic11C2×C4semidirect
148. C22×C4×D11C2×C4semidirect
159. C2×C11×C22⋊C4C2×C4semidirect
182. C2×(C2×D11)⋊C4C2×C4semidirect
196. C2×Dic11⋊C4C2×C4semidirect
205. C2×C4×Dic11C2×C4semidirect
219. (C22⋊D11)⋊C4C2×C4semidirect
220. (C22⋊D11)⋊C4C2×C4semidirect
221. (C22⋊D11)⋊C4C2×C4semidirect
222. (C22⋊D11)⋊C4C2×C4semidirect
223. (C22⋊D11)⋊C4C2×C4semidirect
224. (C22⋊D11)⋊C4C2×C4semidirect
409. #2342D11semidirect
486. C22⋊D11#117semidirect
565. #388C2×D11semidirect
566. #388C2×D11semidirect
578. #385C2×D11semidirect
622. C4×C22⋊C4C2×D11semidirect
759. C2×C22⋊C4C4×D11semidirect
963. C11#34190semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
#130715862
#130715512
#130715502
#130715222
#130714862
#130714802
#130714682
#130714652
#130714622
C22⋊C4×C22⋊D112
#130714322
#130712572
#130712462
#130712442
#130710112
#130710102
#130709952
#130709942
C2×#106225562
D11×#3812
#130709752
C11×#23422
#3419011