Finite Group Databasebeta

← #14913512

Subgroups — #14913512

Order 2816.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2#13071748C212yesmaximal, complemented
3#13071744C212yesmaximal, complemented
4#13071697C212yesmaximal, complemented
5#13071693C212yesmaximal, complemented
6#13071664C212yesmaximal, complemented
7#13071660C212yesmaximal, complemented
8#13071596C212yesmaximal, complemented
9#13071592C212yesmaximal, complemented
10#13071111C211yesmaximal, characteristic, complemented
11#13071109C211yesmaximal, characteristic, complemented
12#13071104C211yesmaximal, characteristic, complemented
13#13071102C211yesmaximal, characteristic, complemented
14#13071060C211yesmaximal, characteristic, complemented
15#13071055C211yesmaximal, characteristic, complemented
16#13071053C211yesmaximal, characteristic, complemented
17C4×D4×Dic11C211yesmaximal, characteristic, complemented
18C42×C22⋊D11C211yesmaximal, characteristic, complemented
19C4×#66946C211yesmaximal, characteristic, complemented
20C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
21C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×D4×Dic11C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C22×(C2×D11)⋊C4C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic, complemented
38#10623078C4116yescomplemented
39C2×#66949C2211yescharacteristic
40C2×#66947C2211yescharacteristic
41C2×#66946C2212yes—
42C2×#66937C2211yescharacteristic
43C2×#66936C2211yescharacteristic
44C2×#66935C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×C22⋊C4×D11C2212yes—
47C2×#66931C2211yescharacteristic
48C2×C4×D44C2211yescharacteristic
49C2×#66925C2211yescharacteristic
50C2×#66925C2211yescharacteristic, complemented
51C2×C42×D11C2211yescharacteristic
52C2×C42×D11C2211yescharacteristic
53C2×C42×D11C2211yescharacteristic, complemented
54C11×#388C2212yescomplemented
55C11×#387C2212yescomplemented
56C11×#386C2212yes—
57C11×#385C2212yes—
58C4×C11×C4⋊C4C2211yescharacteristic, complemented
59C4×C11×C22⋊C4C2211yescharacteristic
60C4×C11×C22⋊C4C2211yescharacteristic, complemented
61C11×#376C2211yescharacteristic, complemented
62C4×C22⋊Dic11C2212yes—
63C4×C22⋊Dic11C2211yescharacteristic
64C4×C22⋊Dic11C2211yescharacteristic, complemented
65C2×C11⋊#95C2212yes—
66#10622603C2212yes—
67#10622602C2212yes—
68#10622601C2212yes—
69#10622591C2212yescomplemented
70#10622591C2212yescomplemented
71C4⋊C4×Dic11C2212yescomplemented
72C4⋊C4×Dic11C2212yescomplemented
73#10622587C2212yescomplemented
74#10622571C2212yes—
75#10622571C2212yes—
76#10622571C2212yescomplemented
77#10622570C2212yes—
78#10622569C2212yes—
79#10622569C2212yescomplemented
80#10622559C2212yes—
81#10622557C2212yescomplemented
82C22⋊C4×Dic11C2212yes—
83C22⋊C4×Dic11C2212yes—
84C22⋊C4×Dic11C2212yescomplemented
85C22⋊C4×Dic11C2212yescomplemented
86C4×(C2×D11)⋊C4C2211yescharacteristic
87C4×(C2×D11)⋊C4C2211yescharacteristic
88C4×(C2×D11)⋊C4C2211yescharacteristic
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×(C2×D11)⋊C4C2212yes—
91C4×(C2×D11)⋊C4C2211yescharacteristic
92C4×(C2×D11)⋊C4C2212yes—
93C4×(C2×D11)⋊C4C2211yescharacteristic
94C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
95C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
96C4×(C2×D11)⋊C4C2212yescomplemented
97C4×C4⋊Dic11C2211yescharacteristic, complemented
98#10622545C2211yescharacteristic, complemented
99C4×Dic11⋊C4C2211yescharacteristic, complemented
100C4×Dic11⋊C4C2211yescharacteristic, complemented
101C4×Dic11⋊C4C2212yescomplemented
102C42×Dic11C2211yescharacteristic, complemented
103C42×Dic11C2211yescharacteristic, complemented
104#10622283C2212yes—
105#10622283C2212yescomplemented
106#10622282C2212yes—
107#10622282C2212yes—
108#10622282C2212yescomplemented
109#10622281C2212yes—
110#10622279C2212yes—
111#10622279C2212yes—
112#10622279C2212yes—
113#10622279C2212yescomplemented
114#10622278C2212yes—
115#10622278C2212yes—
116D11×#95C2212yes—
117#10622268C2212yescomplemented
118#10622266C2212yescomplemented
119#10622265C2212yescomplemented
120#10622265C2212yescomplemented
121#10622265C2212yescomplemented
122#10622262C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
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×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×Dic22C2311yescharacteristic
153C4×D4×C11C2×C418yescomplemented
154C11×#117—42no—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C42×C11—42no—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2312yes—
174#66992C2×C418yescomplemented
175#66990C2×C418yescomplemented
176D4×Dic11—28no—
177C4×C22⋊D11—28no—
178C4×C22⋊D11C2×C418yescomplemented
179C4×C22⋊D11C2×C418yescomplemented
180C2×(C2×D11)⋊C4—28no—
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×(C2×D11)⋊C4C2312yes—
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×C4×Dic11—42no—
206C2×C4×Dic11—42no—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221#66949C2×C418yescomplemented
222#66947C2×C418yescomplemented
223#66946—28no—
224#66937C2×C418yescomplemented
225#66936C2×C418yescomplemented
226#66935C2×C418yescomplemented
227(C22⋊D11)⋊C4—28no—
228C22⋊C4×D11—28no—
229#66931C2×C418yescomplemented
230C4×D44C2×C418yescomplemented
231#66925—42no—
232#66925C2×C418yescomplemented
233C42×D11—42no—
234C42×D11—42no—
235C42×D11—42no—
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#34152—111nomaximal, Sylow
257C24×C11C2411yescharacteristic
258C24×C11C2411yescharacteristic
259C23×D11—24no—
260C23×D11—24no—
261C23×D11—41no—
262C23×D11—41no—
263C23×D11C22×C414yes—
264C23×D11C2411yescharacteristic
265C23×D11C2411yescharacteristic
266C23×D11C2411yescharacteristic
267C2×D4×C11—24no—
268C2×D4×C11C22×C414yes—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—24no—
274C22×C4×C11—24no—
275C22×C4×C11—42no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C22×C414yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C2×C22⋊D11—24no—
288C2×C22⋊D11—24no—
289C2×C22⋊D11—41no—
290C2×C22⋊D11—41no—
291C2×C22⋊D11—41no—
292C2×C22⋊D11—41no—
293C2×C22⋊D11C22×C414yes—
294C2×C22⋊D11C22×C414yes—
295C2×C22⋊D11C22×C414yes—
296C2×C22⋊D11C22×C414yes—
297C22×Dic11—24no—
298C22×Dic11—24no—
299C22×Dic11—24no—
300C22×Dic11—24no—
301C22×Dic11—42no—
302C22×Dic11—42no—
303C22×Dic11—41no—
304C22×Dic11—41no—
305C22×Dic11C22×C414yes—
306C22×Dic11C2412yes—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315#4339—416no—
316C2×D44—24no—
317C2×D44—41no—
318C2×D44—41no—
319C2×D44C22×C414yes—
320C2×D44C22×C414yes—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—24no—
325C2×C4×D11—24no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—41no—
339C2×C4×D11—41no—
340C2×C4×D11—416no—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×C4×D11C22×C414yes—
346C2×Dic22—41no—
347C2×Dic22—41no—
348C2×Dic22C22×C414yes—
349C11×C4⋊C4—24no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4C22×C414yes—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4C22×C414yes—
356C11×C22⋊C4C22×C414yes—
357C42×C11—22no—
358C42×C11—22no—
359C42×C11—22no—
360C42×C11—22no—
361C42×C11—42no—
362C42×C11C22×C414yes—
363C22⋊Dic11—24no—
364C22⋊Dic11C22×C414yes—
365C22⋊Dic11C22×C414yes—
366C22⋊Dic11#4118yescomplemented
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—24no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—24no—
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—
379(C2×D11)⋊C4C22×C414yes—
380(C2×D11)⋊C4C22×C414yes—
381(C2×D11)⋊C4#4118yescomplemented
382C4⋊Dic11—24no—
383C4⋊Dic11C22×C414yes—
384Dic11⋊C4—24no—
385Dic11⋊C4—24no—
386Dic11⋊C4—42no—
387Dic11⋊C4C22×C414yes—
388Dic11⋊C4C22×C414yes—
389Dic11⋊C4C22×C414yes—
390Dic11⋊C4C22×C414yes—
391C4×Dic11—24no—
392C4×Dic11—24no—
393C4×Dic11—24no—
394C4×Dic11—24no—
395C4×Dic11—22no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—42no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11—42no—
404C4×Dic11C22×C414yes—
405C2×#525—111no—
406#2374—112no—
407#2374—112no—
408#2368—112no—
409#2368—112no—
410#2364—112no—
411#2364—112no—
412#2358—112no—
413#2358—112no—
414#2298—111no—
415#2298—111no—
416#2297—111no—
417#2297—111no—
418#2290—111no—
419#2290—111no—
420#2290—111no—
421#2290D1111yescharacteristic, complemented
422C42×D4—111no—
423C42×D4—111no—
424C42×D4—111no—
425C42×D4—111no—
426C2×C4×C22⋊C4—111no—
427C2×C4×C22⋊C4—111no—
428C23×C11—22no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11C23×C412yes—
436C23×C11C23×C412yes—
437C23×C11C2×#4114yes—
438C23×C11C2511yescharacteristic
439C22×D11—22no—
440C22×D11—21no—
441C22×D11—21no—
442C22×D11—28no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—28no—
452C22×D11—44no—
453C22×D11—48no—
454C22×D11—48no—
455C22×D11C23×C412yes—
456C22×D11C23×C412yes—
457C22×D11C23×C412yes—
458C22×D11C2×#4114yes—
459D4×C11—28no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—28no—
469C2×C4×C11—28no—
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—22no—
478C2×C4×C11—22no—
479C2×C4×C11—48no—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C2×#4114yes—
486C2×C4×C11H(5,𝔽2)12yes—
487C2×C4×C11H(5,𝔽2)12yes—
488C22⋊D11—28no—
489C22⋊D11—28no—
490C22⋊D11—44no—
491C22⋊D11—44no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—44no—
510C2×Dic11—48no—
511C2×Dic11—48no—
512C2×Dic11C23×C412yes—
513C2×Dic11C23×C412yes—
514C2×Dic11C23×C412yes—
515C2×Dic11C23×C412yes—
516C2×Dic11C23×C412yes—
517C2×Dic11C2×#4114yes—
518C2×Dic11C2×#4114yes—
519C2×Dic11C2×#4114yes—
520D44—28no—
521D44—44no—
522C4×D11—28no—
523C4×D11—28no—
524C4×D11—28no—
525C4×D11—44no—
526C4×D11—44no—
527C4×D11—48no—
528C4×D11—48no—
529C4×D11—48no—
530Dic22—44no—
531C22×#41—111no—
532C24×C4—111no—
533#525—1116no—
534C2×#123—111no—
535C2×#123—111no—
536C2×C22⋊Q8—111no—
537C2×C22⋊Q8—111no—
538C2×#121—111no—
539C2×#121—111no—
540C2×#120—111no—
541C2×#120—111no—
542C2×C4×D4—111no—
543C2×C4×D4—111no—
544C2×C4×D4—112no—
545C2×C4×D4—112no—
546C2×C4×D4—112no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4C2×D1111yescharacteristic
550C2×#117—111no—
551C2×#117—111no—
552C2×#117C2×D1111yescharacteristic, complemented
553C22×C22⋊C4—112no—
554C22×C22⋊C4—112no—
555C22×C42—111no—
556C22×C42—111no—
557C22×C42—111no—
558C22×C42—111no—
559C22×C42—111no—
560C22×C42C2×D1111yescharacteristic
561#391—112no—
562#391—112no—
563#390—112no—
564#390—112no—
565#388—112no—
566#388—112no—
567#388—112no—
568#388—112no—
569#388—112no—
570#388—112no—
571#388—112no—
572#388C2×D1112yescomplemented
573#387—112no—
574#387—112no—
575#387—112no—
576#387—112no—
577#387—112no—
578#387—112no—
579#387—112no—
580#387C2×D1112yescomplemented
581#386—112no—
582#386—112no—
583#386—112no—
584#386—112no—
585#386—112no—
586#386—112no—
587#386—112no—
588#386C2×D1112yes—
589#385—112no—
590#385—112no—
591#385—112no—
592#385C2×D1112yes—
593C4×C4⋊C4—112no—
594C4×C4⋊C4—112no—
595C4×C4⋊C4—112no—
596C4×C4⋊C4—111no—
597C4×C4⋊C4—111no—
598C4×C4⋊C4—111no—
599C4×C4⋊C4—112no—
600C4×C4⋊C4C2×D1111yescharacteristic, complemented
601C4×C22⋊C4—112no—
602C4×C22⋊C4—111no—
603C4×C22⋊C4—111no—
604C4×C22⋊C4—112no—
605C4×C22⋊C4—112no—
606C4×C22⋊C4—112no—
607C4×C22⋊C4—112no—
608C4×C22⋊C4—112no—
609C4×C22⋊C4—112no—
610C4×C22⋊C4—112no—
611C4×C22⋊C4—111no—
612C4×C22⋊C4—111no—
613C4×C22⋊C4—111no—
614C4×C22⋊C4—111no—
615C4×C22⋊C4—111no—
616C4×C22⋊C4—111no—
617C4×C22⋊C4—111no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4C2×D1111yescharacteristic
624C4×C22⋊C4C2×D1111yescharacteristic, complemented
625#376—111no—
626#376C2×D1111yescharacteristic, complemented
627C2×#95—112no—
628C2×#95—112no—
629C43—111no—
630C43—111no—
631C22×C11—22no—
632C22×C11—22no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—22no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11C4×#4114yes—
641C22×C11C24×C411yescharacteristic
642C22×C11C22×#4112yes—
643C22×C11C22×#4112yes—
644C22×C11C2×H(5,𝔽2)11yescharacteristic
645C22×C11C2×H(5,𝔽2)11yescharacteristic
646C2×D11—22no—
647C2×D11—22no—
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—416no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11C4×#4114yes—
662C4×C11—22no—
663C4×C11—22no—
664C4×C11—22no—
665C4×C11—22no—
666C4×C11—24no—
667C4×C11—42no—
668C4×C11—42no—
669C4×C11—42no—
670C4×C11#51814yes—
671Dic11—22no—
672Dic11—22no—
673Dic11—22no—
674Dic11—22no—
675Dic11—22no—
676Dic11—24no—
677Dic11—24no—
678Dic11—24no—
679Dic11—42no—
680C25—111no—
681C2×#41—118no—
682C2×#41—442no—
683C2×#41—442no—
684C22×Q8—111no—
685C22×D4—111no—
686C22×D4—111no—
687C22×D4—111no—
688C22×D4—111no—
689C22×D4—111no—
690C22×D4—111no—
691C22×D4C22×D1111yescharacteristic
692C23×C4—111no—
693C23×C4—111no—
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—118no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—112no—
700C23×C4—112no—
701C23×C4—112no—
702C23×C4—112no—
703C23×C4—112no—
704C23×C4—442no—
705C23×C4—442no—
706C23×C4C22×D1112yes—
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1111yescharacteristic
709#123—118no—
710#123—118no—
711C22⋊Q8—118no—
712C22⋊Q8—118no—
713#121—118no—
714#121—118no—
715#120—118no—
716#120—118no—
717C4×D4—118no—
718C4×D4—118no—
719C4×D4—118no—
720C4×D4—228no—
721C4×D4—228no—
722C4×D4—228no—
723C4×D4—228no—
724C4×D4C4×D1118yescomplemented
725#117—42no—
726#117—118no—
727#117—442no—
728C2×C4⋊C4—111no—
729C2×C4⋊C4—111no—
730C2×C4⋊C4—111no—
731C2×C4⋊C4—111no—
732C2×C4⋊C4—111no—
733C2×C4⋊C4—112no—
734C2×C4⋊C4—112no—
735C2×C4⋊C4—112no—
736C2×C4⋊C4—112no—
737C2×C4⋊C4C22×D1112yes—
738C2×C4⋊C4C22×D1112yes—
739C2×C4⋊C4C22×D1111yescharacteristic
740C2×C22⋊C4—112no—
741C2×C22⋊C4—111no—
742C2×C22⋊C4—111no—
743C2×C22⋊C4—112no—
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—112no—
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—228no—
760C2×C22⋊C4—228no—
761C2×C22⋊C4C22×D1112yes—
762C2×C22⋊C4C22×D1112yes—
763C2×C22⋊C4C22×D1112yes—
764C2×C22⋊C4C22×D1111yescharacteristic
765C2×C22⋊C4C22×D1111yescharacteristic
766C2×C42—42no—
767C2×C42—111no—
768C2×C42—112no—
769C2×C42—112no—
770C2×C42—112no—
771C2×C42—112no—
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—442no—
782C2×C42—442no—
783C2×C42—442no—
784C2×C42—442no—
785C2×C42—442no—
786C2×C42C22×D1111yescharacteristic
787C2×C42C22×D1111yescharacteristic
788C2×C42C22×D1111yescharacteristic
789C2×C42C22×D1111yescharacteristic
790C2×C42C22×D1112yes—
791C2×C42C22×D1111yescharacteristic
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#95—112no—
805#95—112no—
806#95—112no—
807#95C22×D1112yes—
808#95C22×D1112yes—
809#95C22×D1112yes—
810#95C22×D1112yes—
811#95C22×D1112yes—
812C2×C11—24no—
813C2×C11—42no—
814C2×C11C2×C4×#4111yescharacteristic
815C2×C11C2×C4×#4111yescharacteristic
816C2×C11C2×#51811yescharacteristic
817C2×C11#348112yes—
818C2×C11#348112yes—
819D11—24no—
820D11—42no—
821D11—42no—
822C24—111no—
823C24—111no—
824C24—111no—
825C24—114no—
826C24—224no—
827C24—224no—
828C24—441no—
829C24—441no—
830C24C23×D1111yescharacteristic
831C24C23×D1111yescharacteristic
832#41—4416no—
833C2×Q8—114no—
834C2×Q8—441no—
835C2×Q8—441no—
836C2×D4—24no—
837C2×D4—114no—
838C2×D4—114no—
839C2×D4—114no—
840C2×D4—114no—
841C2×D4—114no—
842C2×D4—114no—
843C2×D4—224no—
844C2×D4—224no—
845C2×D4—224no—
846C2×D4—441no—
847C2×D4—441no—
848C2×D4—441no—
849C2×D4—441no—
850C2×D4—441no—
851C2×D4—441no—
852C2×D4C2×C4×D1114yes—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—42no—
860C22×C4—111no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—111no—
865C22×C4—111no—
866C22×C4—111no—
867C22×C4—111no—
868C22×C4—114no—
869C22×C4—114no—
870C22×C4—114no—
871C22×C4—114no—
872C22×C4—114no—
873C22×C4—114no—
874C22×C4—112no—
875C22×C4—224no—
876C22×C4—224no—
877C22×C4—224no—
878C22×C4—224no—
879C22×C4—224no—
880C22×C4—224no—
881C22×C4—224no—
882C22×C4—224no—
883C22×C4—222no—
884C22×C4—222no—
885C22×C4—222no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—222no—
889C22×C4—224no—
890C22×C4—224no—
891C22×C4—4416no—
892C22×C4—442no—
893C22×C4—442no—
894C22×C4—442no—
895C22×C4—441no—
896C22×C4—441no—
897C22×C4—441no—
898C22×C4—441no—
899C22×C4—442no—
900C22×C4—442no—
901C22×C4—441no—
902C22×C4—441no—
903C22×C4C2×C4×D1114yes—
904C22×C4C2×C4×D1114yes—
905C22×C4C23×D1112yes—
906C22×C4C23×D1112yes—
907C22×C4C23×D1112yes—
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C22×C4C23×D1111yescharacteristic
912C22×C4C23×D1112yes—
913C22×C4C23×D1111yescharacteristic
914C4⋊C4—24no—
915C4⋊C4—42no—
916C4⋊C4—114no—
917C4⋊C4—114no—
918C4⋊C4—114no—
919C4⋊C4—114no—
920C4⋊C4—114no—
921C4⋊C4—224no—
922C4⋊C4—224no—
923C4⋊C4—224no—
924C4⋊C4—442no—
925C4⋊C4C2×C4×D1114yes—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—42no—
929C22⋊C4—114no—
930C22⋊C4—114no—
931C22⋊C4—118no—
932C22⋊C4—114no—
933C22⋊C4—114no—
934C22⋊C4—114no—
935C22⋊C4—114no—
936C22⋊C4—114no—
937C22⋊C4—114no—
938C22⋊C4—118no—
939C22⋊C4—224no—
940C22⋊C4—224no—
941C22⋊C4—224no—
942C22⋊C4—224no—
943C22⋊C4—224no—
944C22⋊C4—224no—
945C22⋊C4—224no—
946C22⋊C4—224no—
947C22⋊C4—442no—
948C22⋊C4C2×C4×D1114yes—
949C22⋊C4C2×C4×D1114yes—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—42no—
955C42—114no—
956C42—224no—
957C42—224no—
958C42—224no—
959C42—222no—
960C42—224no—
961C42—222no—
962C42—222no—
963C42—222no—
964C42—442no—
965C42—442no—
966C42—442no—
967C42—442no—
968C42—442no—
969C42C2×C4×D1114yes—
970C11#3415211yescharacteristic, complemented, Sylow
971C23—21no—
972C23—22no—
973C23—21no—
974C23—21no—
975C23—22no—
976C23—22no—
977C23—21no—
978C23—112no—
979C23—114no—
980C23—112no—
981C23—112no—
982C23—228no—
983C23—221no—
984C23—222no—
985C23—221no—
986C23—228no—
987C23—221no—
988C23—221no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—221no—
994C23—221no—
995C23—444no—
996C23—448no—
997C23—448no—
998C23C22×C4×D1112yes—
999C23C22×C4×D1112yes—
1000C23#41×D1114yes—
1001C23C24×D1111yescharacteristic
1002Q8—444no—
1003D4—28no—
1004D4—228no—
1005D4—228no—
1006D4—228no—
1007D4—444no—
1008D4—444no—
1009D4—444no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—28no—
1019C2×C4—28no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—48no—
1030C2×C4—112no—
1031C2×C4—112no—
1032C2×C4—112no—
1033C2×C4—112no—
1034C2×C4—112no—
1035C2×C4—114no—
1036C2×C4—114no—
1037C2×C4—114no—
1038C2×C4—222no—
1039C2×C4—221no—
1040C2×C4—221no—
1041C2×C4—221no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—221no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—228no—
1053C2×C4—228no—
1054C2×C4—228no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—444no—
1059C2×C4—444no—
1060C2×C4—448no—
1061C2×C4—448no—
1062C2×C4—448no—
1063C2×C4—444no—
1064C2×C4—448no—
1065C2×C4—448no—
1066C2×C4C22×C4×D1112yes—
1067C2×C4C22×C4×D1112yes—
1068C2×C4C22×C4×D1112yes—
1069C2×C4C22×C4×D1112yes—
1070C2×C4C22×C4×D1112yes—
1071C2×C4#6703712yes—
1072C2×C4#41×D1114yes—
1073C2×C4#6704212yes—
1074C22—24no—
1075C22—24no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—42no—
1082C22—42no—
1083C22—114no—
1084C22—224no—
1085C22—224no—
1086C22—222no—
1087C22—222no—
1088C22—222no—
1089C22—222no—
1090C22—222no—
1091C22—222no—
1092C22—222no—
1093C22—222no—
1094C22—4416no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22#1062305314yes—
1100C22C23×C4×D1111yescharacteristic
1101C22C2×#6703711yescharacteristic
1102C22C2×#41×D1112yes—
1103C22C2×#41×D1112yes—
1104C22C2×#6704211yescharacteristic
1105C4—24no—
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—22no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—224no—
1114C4—224no—
1115C4—224no—
1116C4—222no—
1117C4—222no—
1118C4—222no—
1119C4—222no—
1120C4—222no—
1121C4—442no—
1122C4#1062307614yes—
1123C2—24no—
1124C2—42no—
1125C2—224no—
1126C2—442no—
1127C2—442no—
1128C2C4×#41×D1111yescharacteristic
1129C2C2×#1062305311yescharacteristic
1130C2C2×#1062307611yescharacteristic
1131C2#1308221812yes—
1132C2#1308222212yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2290C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2290D11
hypocenterC11#34152
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #13071748C2semidirect
3. #13071744C2semidirect
4. #13071697C2semidirect
5. #13071693C2semidirect
6. #13071664C2semidirect
7. #13071660C2semidirect
8. #13071596C2semidirect
9. #13071592C2semidirect
10. #13071111C2semidirect
11. #13071109C2semidirect
12. #13071104C2semidirect
13. #13071102C2semidirect
14. #13071060C2semidirect
15. #13071055C2semidirect
16. #13071053C2semidirect
17. C4×D4×Dic11C2semidirect
18. C42×C22⋊D11C2semidirect
19. C4×#66946C2semidirect
20. C4×(C22⋊D11)⋊C4C2semidirect
21. C2×C4×(C2×D11)⋊C4C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2290C2semidirect
27. C2×C11×#117C22semidirect
37. C22×C4×Dic11C22semidirect
38. #10623078C4semidirect
50. C2×#66925C22semidirect
53. C2×C42×D11C22semidirect
54. C11×#388C22semidirect
55. C11×#387C22semidirect
58. C4×C11×C4⋊C4C22semidirect
60. C4×C11×C22⋊C4C22semidirect
61. C11×#376C22semidirect
64. C4×C22⋊Dic11C22semidirect
69. #10622591C22semidirect
70. #10622591C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. #10622587C22semidirect
76. #10622571C22semidirect
79. #10622569C22semidirect
81. #10622557C22semidirect
84. C22⋊C4×Dic11C22semidirect
85. C22⋊C4×Dic11C22semidirect
94. C4×(C2×D11)⋊C4C22semidirect
95. C4×(C2×D11)⋊C4C22semidirect
96. C4×(C2×D11)⋊C4C22semidirect
97. C4×C4⋊Dic11C22semidirect
98. #10622545C22semidirect
99. C4×Dic11⋊C4C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C42×Dic11C22semidirect
103. C42×Dic11C22semidirect
105. #10622283C22semidirect
108. #10622282C22semidirect
113. #10622279C22semidirect
117. #10622268C22semidirect
118. #10622266C22semidirect
119. #10622265C22semidirect
120. #10622265C22semidirect
121. #10622265C22semidirect
122. #10622262C22semidirect
123. #10622259C22semidirect
138. C2×#4339C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
153. C4×D4×C11C2×C4semidirect
174. #66992C2×C4semidirect
175. #66990C2×C4semidirect
178. C4×C22⋊D11C2×C4semidirect
179. C4×C22⋊D11C2×C4semidirect
221. #66949C2×C4semidirect
222. #66947C2×C4semidirect
224. #66937C2×C4semidirect
225. #66936C2×C4semidirect
226. #66935C2×C4semidirect
229. #66931C2×C4semidirect
230. C4×D44C2×C4semidirect
232. #66925C2×C4semidirect
366. C22⋊Dic11#41semidirect
381. (C2×D11)⋊C4#41semidirect
421. #2290D11semidirect
552. C2×#117C2×D11semidirect
572. #388C2×D11semidirect
580. #387C2×D11semidirect
600. C4×C4⋊C4C2×D11semidirect
624. C4×C22⋊C4C2×D11semidirect
626. #376C2×D11semidirect
724. C4×D4C4×D11semidirect
970. C11#34152semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
#130717482
#130717442
#130716972
#130716932
#130716642
#130716602
#130715962
#130715922
#130711112
#130711092
#130711042
#130711022
#130710602
#130710552
#130710532
C4×D4×Dic112
C42×C22⋊D112
C4×#669462
C4×(C22⋊D11)⋊C42
C2×C4×(C2×D11)⋊C42
C4×C22⋊C4×D112
C11×#22902
#3415211