Finite Group Databasebeta

← #14916539

Subgroups — #14916539

Order 2816.

2714 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2#13071763C212yesmaximal, complemented
3#13071758C212yesmaximal, complemented
4#13071598C212yesmaximal, complemented
5#13071596C212yesmaximal, complemented
6#13071546C211yesmaximal, characteristic, complemented
7#13071542C211yesmaximal, characteristic, complemented
8#13071541C211yesmaximal, characteristic, complemented
9C4⋊C4×D44C211yesmaximal, characteristic, complemented
10D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
11#13071512C211yesmaximal, characteristic, complemented
12#13071512C211yesmaximal, characteristic, complemented
13#13071344C212yesmaximal, complemented
14#13071343C212yesmaximal, complemented
15#13071320C212yesmaximal, complemented
16#13071317C212yesmaximal, complemented
17#13071226C211yesmaximal, characteristic, complemented
18#13071221C211yesmaximal, characteristic, complemented
19#13071205C211yesmaximal, characteristic, complemented
20#13071204C211yesmaximal, characteristic, complemented
21C2×#10622600C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2352C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic, complemented
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×D4×Dic11C2212yes—
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2212yes—
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic, complemented
37#10623078C4116yescomplemented
38C2×#66949C2211yescharacteristic
39C2×#66947C2211yescharacteristic
40C2×#66945C2211yescharacteristic, complemented
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×#66937C2211yescharacteristic
45C2×#66936C2211yescharacteristic
46C2×#66935C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2212yes—
48C2×(C22⋊D11)⋊C4C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×#66931C2211yescharacteristic
51C2×C4×D44C2212yes—
52C2×C4×D44C2211yescharacteristic
53C2×#66925C2211yescharacteristic
54C11×#388C2212yescomplemented
55C11×#387C2212yescomplemented
56C11×#386C2212yes—
57C11×#382C2211yescharacteristic, complemented
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic, complemented
60C4×C11×C4⋊C4C2211yescharacteristic, complemented
61C4×C11×C22⋊C4C2212yes—
62#10622826C2212yes—
63#10622825C2211yescharacteristic
64#10622825C2211yescharacteristic, complemented
65C4×C22⋊Dic11C2212yes—
66C2×C11⋊#95C2212yes—
67#10622603C2212yescomplemented
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2212yes—
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic
75#10622600C2212yes—
76#10622600C2211yescharacteristic, complemented
77#10622600C2211yescharacteristic, complemented
78#10622598C2212yescomplemented
79#10622591C2212yescomplemented
80#10622590C2211yescharacteristic, complemented
81#10622589C2211yescharacteristic, complemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622571C2212yes—
85#10622571C2212yescomplemented
86#10622570C2212yes—
87#10622569C2212yes—
88#10622569C2212yescomplemented
89#10622563C2212yes—
90#10622563C2212yescomplemented
91#10622559C2212yes—
92#10622559C2212yescomplemented
93#10622558C2212yescomplemented
94#10622555C2212yes—
95#10622553C2212yes—
96#10622552C2212yes—
97C4×(C2×D11)⋊C4C2212yes—
98#10622548C2211yescharacteristic, complemented
99C4×C4⋊Dic11C2211yescharacteristic, complemented
100#10622546C2212yescomplemented
101#10622546C2212yescomplemented
102#10622542C2212yescomplemented
103#10622541C2212yescomplemented
104#10622283C2212yes—
105#10622283C2212yes—
106#10622282C2212yes—
107#10622282C2212yescomplemented
108#10622281C2212yes—
109#10622281C2212yes—
110#10622281C2212yescomplemented
111#10622281C2212yescomplemented
112#10622280C2212yes—
113#10622279C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116D11×#95C2212yes—
117#10622268C2212yescomplemented
118#10622268C2212yescomplemented
119#10622267C2212yescomplemented
120#10622265C2212yescomplemented
121#10622260C2212yescomplemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C23×Dic11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C2×#4339—42no—
137C2×#4339—42no—
138C2×#4339C2×C418yescomplemented
139C22×D44C2311yescharacteristic
140C22×D44C2311yescharacteristic
141C22×C4×D11—42no—
142C22×C4×D11—42no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×Dic22C2311yescharacteristic
153C4×D4×C11C2×C418yescomplemented
154C11×#117—42no—
155C2×C11×C4⋊C4—42no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174#66992C2×C418yescomplemented
175#66990C2×C418yescomplemented
176D4×Dic11—44no—
177C4×C22⋊D11C2×C418yescomplemented
178C4×C22⋊D11C2×C418yescomplemented
179C2×(C2×D11)⋊C4—44no—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×C4⋊Dic11—42no—
196C2×C4⋊Dic11—42no—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220#66949C2×C418yescomplemented
221#66947C2×C418yescomplemented
222#66945—42no—
223C4⋊C4×D11—42no—
224C4⋊C4×D11—42no—
225C4⋊C4×D11—42no—
226#66937C2×C418yescomplemented
227#66936C2×C418yescomplemented
228#66935C2×C418yescomplemented
229(C22⋊D11)⋊C4—44no—
230(C22⋊D11)⋊C4—44no—
231C22⋊C4×D11—44no—
232#66931C2×C418yescomplemented
233C4×D44—44no—
234C4×D44C2×C418yescomplemented
235#66925C2×C418yescomplemented
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—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256#34360—111nomaximal, Sylow
257C24×C11C2411yescharacteristic
258C24×C11C2411yescharacteristic
259C23×D11—22no—
260C23×D11—22no—
261C23×D11—22no—
262C23×D11—22no—
263C23×D11—41no—
264C23×D11—41no—
265C23×D11C22×C414yes—
266C23×D11C2411yescharacteristic
267C23×D11C2411yescharacteristic
268C23×D11C2411yescharacteristic
269C2×D4×C11—22no—
270C2×D4×C11—22no—
271C2×D4×C11C22×C414yes—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—24no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11C22×C414yes—
280C22×C4×C11C22×C414yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C2×C22⋊D11—22no—
291C2×C22⋊D11—22no—
292C2×C22⋊D11—22no—
293C2×C22⋊D11—22no—
294C2×C22⋊D11—41no—
295C2×C22⋊D11—41no—
296C2×C22⋊D11—41no—
297C2×C22⋊D11—41no—
298C2×C22⋊D11C22×C414yes—
299C2×C22⋊D11C22×C414yes—
300C2×C22⋊D11C22×C414yes—
301C2×C22⋊D11C22×C414yes—
302C22×Dic11—24no—
303C22×Dic11—41no—
304C22×Dic11—41no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C22×C414yes—
311C22×Dic11C2412yes—
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320#4339—416no—
321C2×D44—22no—
322C2×D44—22no—
323C2×D44—41no—
324C2×D44—41no—
325C2×D44C22×C414yes—
326C2×D44C22×C414yes—
327C2×C4×D11—24no—
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—22no—
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×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—416no—
347C2×C4×D11C22×C414yes—
348C2×C4×D11C22×C414yes—
349C2×C4×D11C22×C414yes—
350C2×C4×D11C22×C414yes—
351C2×C4×D11C22×C414yes—
352C2×Dic22—41no—
353C2×Dic22—41no—
354C2×Dic22C22×C414yes—
355C11×C4⋊C4—22no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—42no—
360C11×C4⋊C4C22×C414yes—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—42no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4C22×C414yes—
365C11×C22⋊C4C22×C414yes—
366C42×C11—42no—
367C42×C11—42no—
368C42×C11C22×C414yes—
369C22⋊Dic11—24no—
370C22⋊Dic11—42no—
371C22⋊Dic11C22×C414yes—
372C22⋊Dic11C22×C414yes—
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4C22×C414yes—
383(C2×D11)⋊C4C22×C414yes—
384(C2×D11)⋊C4C22×C414yes—
385(C2×D11)⋊C4C22×C414yes—
386(C2×D11)⋊C4C22×C414yes—
387(C2×D11)⋊C4C22×C414yes—
388C4⋊Dic11—22no—
389C4⋊Dic11—22no—
390C4⋊Dic11—22no—
391C4⋊Dic11—22no—
392C4⋊Dic11—42no—
393C4⋊Dic11—42no—
394C4⋊Dic11—42no—
395C4⋊Dic11—42no—
396C4⋊Dic11C22×C414yes—
397Dic11⋊C4—42no—
398Dic11⋊C4—42no—
399Dic11⋊C4—42no—
400Dic11⋊C4—42no—
401Dic11⋊C4—42no—
402Dic11⋊C4C22×C414yes—
403Dic11⋊C4C22×C414yes—
404Dic11⋊C4C22×C414yes—
405Dic11⋊C4C22×C414yes—
406C4×Dic11—42no—
407C4×Dic11—42no—
408C4×Dic11—42no—
409C4×Dic11—42no—
410C4×Dic11C22×C414yes—
411C2×#525—111no—
412#2376—112no—
413#2376—112no—
414#2358—112no—
415#2358—112no—
416#2352—111no—
417#2352—111no—
418#2352—111no—
419#2352D1111yescharacteristic, complemented
420D4×C4⋊C4—111no—
421D4×C4⋊C4—111no—
422D4×C4⋊C4—111no—
423D4×C4⋊C4—111no—
424#2329—112no—
425#2329—112no—
426#2325—112no—
427#2325—112no—
428#2314—111no—
429#2314—111no—
430#2311—111no—
431#2311—111no—
432C2×#380—111no—
433C2×#380—111no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11C23×C412yes—
445C23×C11C23×C412yes—
446C23×C11H(5,𝔽2)12yes—
447C23×C112−1+412yes—
448C23×C11C2511yescharacteristic
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—28no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
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—28no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11C23×C412yes—
473C22×D11C23×C412yes—
474C22×D11C23×C412yes—
475C22×D11H(5,𝔽2)12yes—
476C22×D112−1+412yes—
477D4×C11—28no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—28no—
487C2×C4×C11—28no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—84no—
501C2×C4×C11C23×C412yes—
502C2×C4×C11C23×C412yes—
503C2×C4×C11C23×C412yes—
504C2×C4×C11C23×C412yes—
505C2×C4×C11C23×C412yes—
506C2×C4×C11H(5,𝔽2)12yes—
507C2×C4×C11H(5,𝔽2)12yes—
508C22⋊D11—28no—
509C22⋊D11—28no—
510C22⋊D11—44no—
511C22⋊D11—44no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—44no—
535C2×Dic11—84no—
536C2×Dic11—84no—
537C2×Dic11C23×C412yes—
538C2×Dic11C23×C412yes—
539C2×Dic11C23×C412yes—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542D44—28no—
543D44—44no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—28no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—84no—
550C4×D11—84no—
551C4×D11—84no—
552Dic22—44no—
553C22×#41—111no—
554C24×C4—111no—
555#525—1116no—
556C2×#123—111no—
557C2×#123—111no—
558C2×C22⋊Q8—111no—
559C2×C22⋊Q8—111no—
560C2×#121—111no—
561C2×#121—111no—
562C2×#120—111no—
563C2×#120—111no—
564C2×C4×D4—111no—
565C2×C4×D4—111no—
566C2×C4×D4—112no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—111no—
570C2×C4×D4—112no—
571C2×C4×D4C2×D1111yescharacteristic
572C2×#117—111no—
573C2×#117—111no—
574C2×#117C2×D1111yescharacteristic, complemented
575C22×C4⋊C4—111no—
576C22×C4⋊C4—111no—
577C22×C4⋊C4—111no—
578C22×C4⋊C4—111no—
579C22×C4⋊C4—111no—
580C22×C4⋊C4C2×D1111yescharacteristic
581C22×C22⋊C4—112no—
582C22×C22⋊C4—112no—
583#391—112no—
584#391—112no—
585#390—112no—
586#390—112no—
587#389—112no—
588#389—112no—
589#389—112no—
590#389—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388C2×D1112yescomplemented
599#387—112no—
600#387—112no—
601#387—112no—
602#387—112no—
603#387—112no—
604#387—112no—
605#387—112no—
606#387C2×D1112yescomplemented
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386C2×D1112yes—
615#385—112no—
616#385—112no—
617#385—112no—
618#385—112no—
619#385—112no—
620#385—112no—
621#385—112no—
622#385—112no—
623#384—111no—
624#384—111no—
625#382—111no—
626#382C2×D1111yescharacteristic, complemented
627#380—111no—
628#380—111no—
629#380—111no—
630#380—111no—
631#380—111no—
632#380—111no—
633#380—111no—
634#380—111no—
635#380—112no—
636#380—111no—
637#380—111no—
638#380—112no—
639#380—112no—
640#380—112no—
641#380C2×D1111yescharacteristic
642#380C2×D1111yescharacteristic, complemented
643C4×C4⋊C4—111no—
644C4×C4⋊C4—111no—
645C4×C4⋊C4—111no—
646C4×C4⋊C4C2×D1111yescharacteristic, complemented
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4C2×D1112yes—
651C2×#95—112no—
652C2×#95—112no—
653C22×C11—22no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11#52014yes—
667C22×C11C24×C411yescharacteristic
668C22×C11C2×H(5,𝔽2)11yescharacteristic
669C22×C11C2×H(5,𝔽2)11yescharacteristic
670C22×C11C2×H(5,𝔽2)11yescharacteristic
671C22×C11C2×H(5,𝔽2)11yescharacteristic
672C22×C11C2×2−1+411yescharacteristic
673C22×C11C2×2−1+411yescharacteristic
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—416no—
687C2×D11—41no—
688C2×D11—41no—
689C2×D11—41no—
690C2×D11—41no—
691C2×D11—41no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—41no—
695C2×D11#52014yes—
696C4×C11—22no—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—42no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11—42no—
704C4×C11#51814yes—
705Dic11—22no—
706Dic11—22no—
707Dic11—22no—
708Dic11—22no—
709Dic11—22no—
710Dic11—42no—
711Dic11—42no—
712Dic11—42no—
713Dic11—42no—
714C25—111no—
715C2×#41—118no—
716C2×#41—442no—
717C2×#41—442no—
718C22×Q8—111no—
719C22×D4—111no—
720C22×D4—111no—
721C22×D4—111no—
722C22×D4—111no—
723C22×D4—111no—
724C22×D4—111no—
725C22×D4C22×D1111yescharacteristic
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—118no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—112no—
734C23×C4—112no—
735C23×C4—112no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—442no—
739C23×C4—442no—
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1111yescharacteristic
742C23×C4C22×D1112yes—
743#123—118no—
744#123—118no—
745C22⋊Q8—118no—
746C22⋊Q8—118no—
747#121—118no—
748#121—118no—
749#120—118no—
750#120—118no—
751C4×D4—118no—
752C4×D4—118no—
753C4×D4—118no—
754C4×D4—444no—
755C4×D4—444no—
756C4×D4—444no—
757C4×D4—444no—
758C4×D4C4×D1118yescomplemented
759#117—42no—
760#117—118no—
761#117—442no—
762C2×C4⋊C4—42no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—442no—
782C2×C4⋊C4—442no—
783C2×C4⋊C4—442no—
784C2×C4⋊C4—442no—
785C2×C4⋊C4—442no—
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1111yescharacteristic
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1112yes—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—444no—
812C2×C22⋊C4—444no—
813C2×C22⋊C4C22×D1112yes—
814C2×C22⋊C4C22×D1112yes—
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1111yescharacteristic
817C2×C22⋊C4C22×D1111yescharacteristic
818C2×C42—111no—
819C2×C42—112no—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—112no—
823C2×C42C22×D1112yes—
824C2×C42C22×D1112yes—
825C2×C42C22×D1111yescharacteristic
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95C22×D1112yes—
842#95C22×D1112yes—
843#95C22×D1112yes—
844#95C22×D1112yes—
845#95C22×D1112yes—
846C2×C11—24no—
847C2×C11—42no—
848C2×C11C2×#51811yescharacteristic
849C2×C11C2×#52011yescharacteristic
850C2×C11C2×#52011yescharacteristic
851C2×C11#353611yescharacteristic
852C2×C11#353611yescharacteristic
853C2×C11#353711yescharacteristic
854C2×C11#353811yescharacteristic
855D11—24no—
856D11—42no—
857D11—42no—
858C24—111no—
859C24—111no—
860C24—111no—
861C24—114no—
862C24—222no—
863C24—222no—
864C24—222no—
865C24—222no—
866C24—441no—
867C24—441no—
868C24C23×D1111yescharacteristic
869C24C23×D1111yescharacteristic
870#41—4416no—
871C2×Q8—114no—
872C2×Q8—441no—
873C2×Q8—441no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—114no—
877C2×D4—114no—
878C2×D4—114no—
879C2×D4—114no—
880C2×D4—114no—
881C2×D4—114no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—222no—
887C2×D4—222no—
888C2×D4—441no—
889C2×D4—441no—
890C2×D4—441no—
891C2×D4—441no—
892C2×D4—441no—
893C2×D4—441no—
894C2×D4C2×C4×D1114yes—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—24no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—114no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—112no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—112no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—224no—
926C22×C4—4416no—
927C22×C4—441no—
928C22×C4—441no—
929C22×C4—441no—
930C22×C4—441no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—441no—
939C22×C4—441no—
940C22×C4—442no—
941C22×C4—442no—
942C22×C4—442no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4C2×C4×D1114yes—
946C22×C4C2×C4×D1114yes—
947C22×C4C23×D1112yes—
948C22×C4C23×D1112yes—
949C22×C4C23×D1112yes—
950C22×C4C23×D1112yes—
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1111yescharacteristic
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—42no—
961C4⋊C4—114no—
962C4⋊C4—114no—
963C4⋊C4—114no—
964C4⋊C4—114no—
965C4⋊C4—114no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—222no—
969C4⋊C4—222no—
970C4⋊C4—442no—
971C4⋊C4—442no—
972C4⋊C4—442no—
973C4⋊C4—442no—
974C4⋊C4—442no—
975C4⋊C4—442no—
976C4⋊C4—442no—
977C4⋊C4—442no—
978C4⋊C4—442no—
979C4⋊C4C2×C4×D1114yes—
980C22⋊C4—24no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—114no—
984C22⋊C4—114no—
985C22⋊C4—114no—
986C22⋊C4—114no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—114no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4C2×C4×D1114yes—
1003C22⋊C4C2×C4×D1114yes—
1004C42—42no—
1005C42—42no—
1006C42—114no—
1007C42—442no—
1008C42—442no—
1009C42—442no—
1010C42—442no—
1011C42C2×C4×D1114yes—
1012C11#3436011yescharacteristic, complemented, Sylow
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—112no—
1024C23—112no—
1025C23—112no—
1026C23—112no—
1027C23—112no—
1028C23—228no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—221no—
1033C23—228no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—444no—
1047C23—444no—
1048C23—444no—
1049C23—444no—
1050C23—444no—
1051C23C22×C4×D1112yes—
1052C23C22×C4×D1112yes—
1053C23#6704212yes—
1054C23#6704312yes—
1055C23C24×D1111yescharacteristic
1056Q8—444no—
1057D4—28no—
1058D4—228no—
1059D4—228no—
1060D4—228no—
1061D4—444no—
1062D4—444no—
1063D4—444no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—28no—
1073C2×C4—28no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—84no—
1087C2×C4—112no—
1088C2×C4—112no—
1089C2×C4—112no—
1090C2×C4—112no—
1091C2×C4—112no—
1092C2×C4—221no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—228no—
1103C2×C4—228no—
1104C2×C4—228no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—444no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—884no—
1121C2×C4—884no—
1122C2×C4—884no—
1123C2×C4—884no—
1124C2×C4—884no—
1125C2×C4C22×C4×D1112yes—
1126C2×C4C22×C4×D1112yes—
1127C2×C4C22×C4×D1112yes—
1128C2×C4C22×C4×D1112yes—
1129C2×C4C22×C4×D1112yes—
1130C2×C4#6703712yes—
1131C2×C4#6704212yes—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—114no—
1146C22—222no—
1147C22—222no—
1148C22—222no—
1149C22—222no—
1150C22—222no—
1151C22—222no—
1152C22—222no—
1153C22—222no—
1154C22—222no—
1155C22—222no—
1156C22—222no—
1157C22—222no—
1158C22—4416no—
1159C22—441no—
1160C22—441no—
1161C22—441no—
1162C22—441no—
1163C22—441no—
1164C22—441no—
1165C22—441no—
1166C22—441no—
1167C22#1062305414yes—
1168C22C23×C4×D1111yescharacteristic
1169C22C2×#6703711yescharacteristic
1170C22C2×#6704211yescharacteristic
1171C22C2×#6704211yescharacteristic
1172C22C2×#6704311yescharacteristic
1173C22D11×H(5,𝔽2)11yescharacteristic
1174C22D11×2−1+411yescharacteristic
1175C4—22no—
1176C4—22no—
1177C4—22no—
1178C4—22no—
1179C4—42no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—222no—
1184C4—222no—
1185C4—222no—
1186C4—222no—
1187C4—222no—
1188C4—442no—
1189C4—442no—
1190C4—442no—
1191C4—442no—
1192C4#1062307614yes—
1193C2—24no—
1194C2—42no—
1195C2—224no—
1196C2—442no—
1197C2—442no—
1198C2C2×#1062307611yescharacteristic
1199C2D11×#52011yescharacteristic
1200C2C2×#1062305411yescharacteristic
1201C2#1308283211yescharacteristic
1202C2#1308283611yescharacteristic
1203C2#1308285211yescharacteristic
1204C2#1308286211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2352C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2352D11
hypocenterC11#34360
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13071763C2semidirect
3. #13071758C2semidirect
4. #13071598C2semidirect
5. #13071596C2semidirect
6. #13071546C2semidirect
7. #13071542C2semidirect
8. #13071541C2semidirect
9. C4⋊C4×D44C2semidirect
10. D4×C4⋊Dic11C2semidirect
11. #13071512C2semidirect
12. #13071512C2semidirect
13. #13071344C2semidirect
14. #13071343C2semidirect
15. #13071320C2semidirect
16. #13071317C2semidirect
17. #13071226C2semidirect
18. #13071221C2semidirect
19. #13071205C2semidirect
20. #13071204C2semidirect
21. C2×#10622600C2semidirect
22. D11×#380C2semidirect
23. C11×#2352C2semidirect
27. C2×C11×#117C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. #10623078C4semidirect
40. C2×#66945C22semidirect
43. C2×C4⋊C4×D11C22semidirect
54. C11×#388C22semidirect
55. C11×#387C22semidirect
57. C11×#382C22semidirect
59. C11×#380C22semidirect
60. C4×C11×C4⋊C4C22semidirect
64. #10622825C22semidirect
67. #10622603C22semidirect
76. #10622600C22semidirect
77. #10622600C22semidirect
78. #10622598C22semidirect
79. #10622591C22semidirect
80. #10622590C22semidirect
81. #10622589C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
85. #10622571C22semidirect
88. #10622569C22semidirect
90. #10622563C22semidirect
92. #10622559C22semidirect
93. #10622558C22semidirect
98. #10622548C22semidirect
99. C4×C4⋊Dic11C22semidirect
100. #10622546C22semidirect
101. #10622546C22semidirect
102. #10622542C22semidirect
103. #10622541C22semidirect
107. #10622282C22semidirect
110. #10622281C22semidirect
111. #10622281C22semidirect
117. #10622268C22semidirect
118. #10622268C22semidirect
119. #10622267C22semidirect
120. #10622265C22semidirect
121. #10622260C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
138. C2×#4339C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
153. C4×D4×C11C2×C4semidirect
174. #66992C2×C4semidirect
175. #66990C2×C4semidirect
177. C4×C22⋊D11C2×C4semidirect
178. C4×C22⋊D11C2×C4semidirect
220. #66949C2×C4semidirect
221. #66947C2×C4semidirect
226. #66937C2×C4semidirect
227. #66936C2×C4semidirect
228. #66935C2×C4semidirect
232. #66931C2×C4semidirect
234. C4×D44C2×C4semidirect
235. #66925C2×C4semidirect
419. #2352D11semidirect
574. C2×#117C2×D11semidirect
598. #388C2×D11semidirect
606. #387C2×D11semidirect
626. #382C2×D11semidirect
642. #380C2×D11semidirect
646. C4×C4⋊C4C2×D11semidirect
758. C4×D4C4×D11semidirect
1012. C11#34360semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
#130717632
#130717582
#130715982
#130715962
#130715462
#130715422
#130715412
C4⋊C4×D442
D4×C4⋊Dic112
#130715122
#130713442
#130713432
#130713202
#130713172
#130712262
#130712212
#130712052
#130712042
C2×#106226002
D11×#3802
C11×#23522
#3436011