Finite Group Databasebeta

← #14916544

Subgroups — #14916544

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#13071765C212yesmaximal, complemented
3#13071761C212yesmaximal, complemented
4#13071593C212yesmaximal, complemented
5#13071592C212yesmaximal, complemented
6#13071548C211yesmaximal, characteristic, complemented
7#13071547C211yesmaximal, characteristic, complemented
8#13071545C211yesmaximal, characteristic, complemented
9#13071538C211yesmaximal, characteristic, complemented
10#13071516C211yesmaximal, characteristic, complemented
11C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
12C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
13#13071350C212yesmaximal, complemented
14#13071347C212yesmaximal, complemented
15#13071314C212yesmaximal, complemented
16#13071313C212yesmaximal, complemented
17#13071224C211yesmaximal, characteristic, complemented
18#13071221C211yesmaximal, characteristic, complemented
19#13071209C211yesmaximal, characteristic, complemented
20#13071205C211yesmaximal, characteristic, complemented
21C2×#10622600C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic, complemented
30C2×#66992C2211yescharacteristic
31C2×#66990C2211yescharacteristic
32C2×C4×C22⋊D11C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×C4×C22⋊D11C2211yescharacteristic
36C22×(C2×D11)⋊C4C2212yes—
37C2×#66979C2211yescharacteristic, complemented
38C22×C4⋊Dic11C2211yescharacteristic
39#10623078C4116yescomplemented
40C2×#66949C2211yescharacteristic
41C2×#66947C2211yescharacteristic
42C2×#66946C2212yes—
43C2×#66945C2211yescharacteristic, complemented
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic, complemented
47C2×#66937C2211yescharacteristic
48C2×#66936C2211yescharacteristic
49C2×#66935C2211yescharacteristic
50C2×C22⋊C4×D11C2212yes—
51C2×#66931C2211yescharacteristic
52C2×C4×D44C2211yescharacteristic
53C2×#66925C2211yescharacteristic
54C11×#389C2212yescomplemented
55C11×#385C2212yes—
56C11×#385C2212yescomplemented
57C11×#384C2211yescharacteristic, complemented
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic, complemented
60C4×C11×C4⋊C4C2211yescharacteristic, complemented
61#10622833C2212yes—
62#10622826C2212yes—
63#10622826C2212yescomplemented
64#10622825C2211yescharacteristic
65#10622825C2211yescharacteristic, complemented
66#10622823C2212yes—
67#10622823C2212yescomplemented
68C2×C11⋊#95C2212yes—
69#10622603C2212yes—
70#10622603C2212yes—
71#10622602C2212yes—
72#10622602C2212yes—
73#10622602C2212yescomplemented
74#10622602C2212yescomplemented
75#10622601C2212yes—
76#10622600C2211yescharacteristic
77#10622600C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic
80#10622600C2212yes—
81#10622600C2211yescharacteristic
82#10622600C2211yescharacteristic
83#10622600C2212yes—
84#10622600C2211yescharacteristic, complemented
85#10622600C2211yescharacteristic, complemented
86#10622594C2212yescomplemented
87#10622591C2212yescomplemented
88#10622591C2212yescomplemented
89#10622590C2211yescharacteristic, complemented
90#10622589C2211yescharacteristic, complemented
91C4⋊C4×Dic11C2211yescharacteristic, complemented
92C4⋊C4×Dic11C2211yescharacteristic, complemented
93#10622587C2212yescomplemented
94#10622586C2212yescomplemented
95#10622585C2212yescomplemented
96#10622585C2212yescomplemented
97#10622571C2212yes—
98#10622570C2212yes—
99#10622569C2212yes—
100#10622569C2212yescomplemented
101#10622564C2212yescomplemented
102#10622557C2212yescomplemented
103#10622555C2212yes—
104C22⋊C4×Dic11C2212yes—
105C22⋊C4×Dic11C2212yes—
106#10622553C2212yes—
107#10622553C2212yescomplemented
108C4×(C2×D11)⋊C4C2212yes—
109#10622549C2211yescharacteristic, complemented
110C4×C4⋊Dic11C2211yescharacteristic, complemented
111#10622546C2212yescomplemented
112#10622283C2212yescomplemented
113#10622282C2212yes—
114#10622280C2212yes—
115#10622279C2212yes—
116#10622278C2212yes—
117#10622278C2212yes—
118D11×#95C2212yes—
119#10622268C2212yescomplemented
120#10622266C2212yescomplemented
121#10622265C2212yescomplemented
122#10622265C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
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×C11—44no—
154C4×D4×C11C2×C418yescomplemented
155C2×C11×C4⋊C4—42no—
156C2×C11×C4⋊C4—42no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177#66992C2×C418yescomplemented
178#66990C2×C418yescomplemented
179C4×C22⋊D11—44no—
180C4×C22⋊D11—44no—
181C4×C22⋊D11C2×C418yescomplemented
182C4×C22⋊D11C2×C418yescomplemented
183C2×(C2×D11)⋊C4—44no—
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)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199#66979—42no—
200C2×C4⋊Dic11—42no—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222#66949C2×C418yescomplemented
223#66947C2×C418yescomplemented
224#66946—44no—
225#66945—42no—
226C4⋊C4×D11—42no—
227C4⋊C4×D11—42no—
228C4⋊C4×D11—42no—
229#66937C2×C418yescomplemented
230#66936C2×C418yescomplemented
231#66935C2×C418yescomplemented
232C22⋊C4×D11—44no—
233#66931C2×C418yescomplemented
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×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11C22×C414yes—
283C22×C4×C11C22×C414yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C2×C22⋊D11—22no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—41no—
298C2×C22⋊D11—41no—
299C2×C22⋊D11—41no—
300C2×C22⋊D11—41no—
301C2×C22⋊D11C22×C414yes—
302C2×C22⋊D11C22×C414yes—
303C2×C22⋊D11C22×C414yes—
304C2×C22⋊D11C22×C414yes—
305C22×Dic11—24no—
306C22×Dic11—41no—
307C22×Dic11—41no—
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⋊C4—42no—
361C11×C4⋊C4—42no—
362C11×C4⋊C4—42no—
363C11×C4⋊C4C22×C414yes—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4C22×C414yes—
367C11×C22⋊C4C22×C414yes—
368C42×C11—42no—
369C42×C11C22×C414yes—
370C22⋊Dic11—24no—
371C22⋊Dic11—42no—
372C22⋊Dic11—42no—
373C22⋊Dic11C22×C414yes—
374C22⋊Dic11C22×C414yes—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
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)⋊C4—42no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4C22×C414yes—
385(C2×D11)⋊C4C22×C414yes—
386(C2×D11)⋊C4C22×C414yes—
387(C2×D11)⋊C4C22×C414yes—
388(C2×D11)⋊C4C22×C414yes—
389(C2×D11)⋊C4C22×C414yes—
390C4⋊Dic11—22no—
391C4⋊Dic11—22no—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—42no—
395C4⋊Dic11C22×C414yes—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4—42no—
399Dic11⋊C4—42no—
400Dic11⋊C4—42no—
401Dic11⋊C4C22×C414yes—
402Dic11⋊C4C22×C414yes—
403Dic11⋊C4C22×C414yes—
404Dic11⋊C4C22×C414yes—
405C4×Dic11—42no—
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#2352—111no—
420D4×C4⋊C4—111no—
421D4×C4⋊C4—111no—
422D4×C4⋊C4—111no—
423D4×C4⋊C4D1111yescharacteristic, complemented
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×C11—84no—
502C2×C4×C11C23×C412yes—
503C2×C4×C11C23×C412yes—
504C2×C4×C11C23×C412yes—
505C2×C4×C11C23×C412yes—
506C2×C4×C11C23×C412yes—
507C2×C4×C11H(5,𝔽2)12yes—
508C2×C4×C11H(5,𝔽2)12yes—
509C22⋊D11—28no—
510C22⋊D11—28no—
511C22⋊D11—44no—
512C22⋊D11—44no—
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—21no—
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—22no—
535C2×Dic11—44no—
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×D4C2×D1112yes—
571C2×C4×D4C2×D1111yescharacteristic
572C2×#117—111no—
573C2×#117—111no—
574C2×#117—111no—
575C22×C4⋊C4—111no—
576C22×C4⋊C4—111no—
577C22×C4⋊C4—111no—
578C22×C4⋊C4—111no—
579C22×C4⋊C4C2×D1111yescharacteristic
580C22×C4⋊C4C2×D1111yescharacteristic, complemented
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#389C2×D1112yescomplemented
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#387—112no—
600#387—112no—
601#387—112no—
602#387—112no—
603#387—112no—
604#387—112no—
605#387—112no—
606#387—112no—
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#385—112no—
616#385—112no—
617#385—112no—
618#385—112no—
619#385—112no—
620#385—112no—
621#385C2×D1112yes—
622#385C2×D1112yescomplemented
623#384—111no—
624#384C2×D1111yescharacteristic, complemented
625#382—111no—
626#382—111no—
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⋊C4—112no—
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—442no—
738C23×C4—442no—
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1112yes—
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—44no—
752C4×D4—118no—
753C4×D4—118no—
754C4×D4—118no—
755C4×D4—444no—
756C4×D4—444no—
757C4×D4—444no—
758C4×D4C4×D1118yescomplemented
759#117—118no—
760#117—442no—
761#117—442no—
762C2×C4⋊C4—42no—
763C2×C4⋊C4—42no—
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—111no—
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—442no—
780C2×C4⋊C4—442no—
781C2×C4⋊C4—442no—
782C2×C4⋊C4—442no—
783C2×C4⋊C4C22×D1111yescharacteristic
784C2×C4⋊C4C22×D1111yescharacteristic
785C2×C4⋊C4C22×D1111yescharacteristic
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1112yes—
788C2×C4⋊C4C22×D1112yes—
789C2×C4⋊C4C22×D1112yes—
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—112no—
812C2×C22⋊C4—444no—
813C2×C22⋊C4—444no—
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×C42—112no—
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#95—112no—
842#95—112no—
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—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—114no—
915C22×C4—114no—
916C22×C4—112no—
917C22×C4—112no—
918C22×C4—112no—
919C22×C4—112no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—4416no—
930C22×C4—441no—
931C22×C4—441no—
932C22×C4—441no—
933C22×C4—441no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4—441no—
942C22×C4—441no—
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—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—114no—
965C4⋊C4—114no—
966C4⋊C4—114no—
967C4⋊C4—114no—
968C4⋊C4—114no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—222no—
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—114no—
983C22⋊C4—114no—
984C22⋊C4—114no—
985C22⋊C4—114no—
986C22⋊C4—114no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—442no—
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—114no—
1006C42—442no—
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#6703712yes—
1054C23#6704012yes—
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—84no—
1088C2×C4—112no—
1089C2×C4—112no—
1090C2×C4—112no—
1091C2×C4—112no—
1092C2×C4—112no—
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—221no—
1103C2×C4—228no—
1104C2×C4—228no—
1105C2×C4—228no—
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—222no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—444no—
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#1062303514yes—
1168C22C23×C4×D1111yescharacteristic
1169C22C2×#6703711yescharacteristic
1170C22C2×#6703711yescharacteristic
1171C22C2×#6704011yescharacteristic
1172C22C2×#6704211yescharacteristic
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×#1062303511yescharacteristic
1201C2#1308283911yescharacteristic
1202C2#1308284411yescharacteristic
1203C2#1308284711yescharacteristic
1204C2#1308285711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenterD4×C4⋊C4D11
hypocenterC11#34360
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071765C2semidirect
3. #13071761C2semidirect
4. #13071593C2semidirect
5. #13071592C2semidirect
6. #13071548C2semidirect
7. #13071547C2semidirect
8. #13071545C2semidirect
9. #13071538C2semidirect
10. #13071516C2semidirect
11. C4⋊C4×C22⋊D11C2semidirect
12. C4⋊C4×C22⋊D11C2semidirect
13. #13071350C2semidirect
14. #13071347C2semidirect
15. #13071314C2semidirect
16. #13071313C2semidirect
17. #13071224C2semidirect
18. #13071221C2semidirect
19. #13071209C2semidirect
20. #13071205C2semidirect
21. C2×#10622600C2semidirect
22. D11×#380C2semidirect
23. D4×C11×C4⋊C4C2semidirect
29. C22×C11×C4⋊C4C22semidirect
37. C2×#66979C22semidirect
39. #10623078C4semidirect
43. C2×#66945C22semidirect
46. C2×C4⋊C4×D11C22semidirect
54. C11×#389C22semidirect
56. C11×#385C22semidirect
57. C11×#384C22semidirect
59. C11×#380C22semidirect
60. C4×C11×C4⋊C4C22semidirect
63. #10622826C22semidirect
65. #10622825C22semidirect
67. #10622823C22semidirect
73. #10622602C22semidirect
74. #10622602C22semidirect
84. #10622600C22semidirect
85. #10622600C22semidirect
86. #10622594C22semidirect
87. #10622591C22semidirect
88. #10622591C22semidirect
89. #10622590C22semidirect
90. #10622589C22semidirect
91. C4⋊C4×Dic11C22semidirect
92. C4⋊C4×Dic11C22semidirect
93. #10622587C22semidirect
94. #10622586C22semidirect
95. #10622585C22semidirect
96. #10622585C22semidirect
100. #10622569C22semidirect
101. #10622564C22semidirect
102. #10622557C22semidirect
107. #10622553C22semidirect
109. #10622549C22semidirect
110. C4×C4⋊Dic11C22semidirect
111. #10622546C22semidirect
112. #10622283C22semidirect
119. #10622268C22semidirect
120. #10622266C22semidirect
121. #10622265C22semidirect
122. #10622265C22semidirect
123. #10622259C22semidirect
138. C2×#4339C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
154. C4×D4×C11C2×C4semidirect
177. #66992C2×C4semidirect
178. #66990C2×C4semidirect
181. C4×C22⋊D11C2×C4semidirect
182. C4×C22⋊D11C2×C4semidirect
222. #66949C2×C4semidirect
223. #66947C2×C4semidirect
229. #66937C2×C4semidirect
230. #66936C2×C4semidirect
231. #66935C2×C4semidirect
233. #66931C2×C4semidirect
234. C4×D44C2×C4semidirect
235. #66925C2×C4semidirect
423. D4×C4⋊C4D11semidirect
580. C22×C4⋊C4C2×D11semidirect
590. #389C2×D11semidirect
622. #385C2×D11semidirect
624. #384C2×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
#130717652
#130717612
#130715932
#130715922
#130715482
#130715472
#130715452
#130715382
#130715162
C4⋊C4×C22⋊D112
#130713502
#130713472
#130713142
#130713132
#130712242
#130712212
#130712092
#130712052
C2×#106226002
D11×#3802
D4×C11×C4⋊C42
#3436011