Finite Group Databasebeta

← #14761641

Subgroups — #14761641

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622443C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic
3C4×#66989C211yesmaximal, characteristic
4#13069552C211yesmaximal, characteristic, complemented
5#13069219C214yesmaximal, complemented
6#13068732C211yesmaximal, characteristic, complemented
7#13068390C214yesmaximal, complemented
8C4×C8×Dic11C211yesmaximal, characteristic, complemented
9C11×#1954C211yesmaximal, characteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66989C411yescharacteristic
12C23×C11⋊C8C2212yes—
13C2×C4×Dic22C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8C2214yes—
16C2×C4×C8×C11C2211yescharacteristic
17#10622834C411yescharacteristic
18C4×C22⋊Dic11C2214yes—
19C2×C22⋊(C11⋊C8)C2212yes—
20C2×Dic11⋊C8C2212yes—
21C2×C8×Dic11C2212yes—
22C2×C8×Dic11C2212yes—
23C2×C8×Dic11C2212yes—
24D4×C11⋊C8—24no—
25#10622590C411yescharacteristic
26#10622587C411yescharacteristic
27#10622558C414yes—
28C42×Dic11C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622443—24no—
32#10622188C2214yes—
33#10622188C2214yes—
34C22×D4×C11C2×C411yescharacteristic
35C23×C4×C11C2312yes—
36C22×Dic22C2×C411yescharacteristic
37C22×C8×C11C2312yes—
38C22×C8×C11C2312yes—
39C4×D4×C11—22no—
40C4×D4×C11—22no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4C2×C412yes—
43C2×C42×C11C2311yescharacteristic
44C2×C22⋊Dic11C2×C414yes—
45C2×C22⋊Dic11C2×C414yes—
46#66989C818yescomplemented
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4C2×C412yes—
49C2×C4×Dic11C2×C412yes—
50C2×C4×Dic11C2×C411yescharacteristic
51C2×C4×Dic11C2×C411yescharacteristic
52C2×C4×Dic11C2312yes—
53C2×C4×Dic11C2312yes—
54C22×C11⋊C8—24no—
55C22×C11⋊C8—28no—
56C22×C11⋊C8C2312yes—
57C22×C11⋊C8C2311yescharacteristic
58C22×C11⋊C8C2311yescharacteristic
59C4×Dic22—22no—
60C4×Dic22—22no—
61C11×C4⋊C8—22no—
62C11×C22⋊C8—28no—
63C4×C8×C11—22no—
64C11⋊#95C2×C414yes—
65C11⋊#95C2×C414yes—
66C22⋊(C11⋊C8)—24no—
67Dic11⋊C8—24no—
68C8×Dic11—24no—
69C8×Dic11—24no—
70C8×Dic11—24no—
71C4⋊(C11⋊C8)—22no—
72C4×C11⋊C8D414yes—
73C8×#124—111nomaximal, Sylow
74C24×C11C22×C412yes—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11C2×C814yes—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—22no—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2411yescharacteristic
86C22×Dic11C22×C412yes—
87C22×Dic11C22×C412yes—
88C22×Dic11C22×C412yes—
89C22×Dic11C22×C412yes—
90C2×Dic22—22no—
91C2×Dic22—22no—
92C2×Dic22C2×C814yescomplemented
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—24no—
97C2×C8×C11#4114yes—
98C11×C4⋊C4—22no—
99C11×C22⋊C4—24no—
100C42×C11C2×D412yes—
101C42×C11#4112yes—
102C22⋊Dic11—28no—
103C22⋊Dic11C2×C8116yescomplemented
104C4⋊Dic11—22no—
105Dic11⋊C4—24no—
106C4×Dic11—24no—
107C4×Dic11—22no—
108C4×Dic11—22no—
109C4×Dic11—22no—
110C4×Dic11—22no—
111C4×Dic11—22no—
112C4×Dic11C2×C814yescomplemented
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—48no—
117C2×C11⋊C8C2×D412yes—
118C2×C11⋊C8C2×D412yes—
119C2×C11⋊C8#4114yes—
120C2×C8×Q8—111no—
121C2×C8×D4—111no—
122C4×#124—111no—
123#1984—111no—
124#1954D1111yescharacteristic
125#1923—114no—
126#1831—111no—
127C8×C22⋊C4—114no—
128C42×C8—111no—
129C23×C11—22no—
130C23×C11—24no—
131C23×C11—24no—
132C23×C11—22no—
133C23×C11C22×C814yes—
134C23×C11C23×C411yescharacteristic
135D4×C11—28no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—42no—
140C2×C4×C11—44no—
141C2×C4×C11—42no—
142C2×C4×C11C4×D412yes—
143C2×C4×C11C4×D412yes—
144C2×C4×C11C22×C812yes—
145C2×C4×C11#13112yes—
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C2×C4×C11C2×#4112yes—
149C2×C4×C11C2×#4112yes—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—24no—
158C2×Dic11C22×C814yes—
159C2×Dic11C22×C814yes—
160C2×Dic11#13114yes—
161Dic22—28no—
162C8×C11—24no—
163C8×C11—42no—
164C11⋊C8—22no—
165C11⋊C8—42no—
166C11⋊C8#12414yescomplemented
167C23×C8—112no—
168C2×#124—111no—
169C2×C4×Q8—111no—
170C2×C4×D4C2×D1111yescharacteristic
171C8×Q8—224no—
172C8×D4—224no—
173C2×C4⋊C8—112no—
174C2×C4⋊C8—111no—
175C2×C4⋊C8C2×D1111yescharacteristic
176C2×C22⋊C8—112no—
177C2×C22⋊C8C2×D1114yes—
178C2×C4×C8—111no—
179C2×C4×C8—112no—
180C2×C4×C8—112no—
181C2×C4×C8—112no—
182C2×C4×C8C2×D1111yescharacteristic
183#391—111no—
184#390—111no—
185#388—114no—
186#382—111no—
187C4×C22⋊C4—114no—
188C43—111no—
189#336—114no—
190#336—114no—
191C22×C11—24no—
192C22×C11—28no—
193C22×C11—42no—
194C22×C11—44no—
195C22×C11—42no—
196C22×C11C2×C4×D411yescharacteristic
197C22×C11C4×#4112yes—
198C22×C11C23×C811yescharacteristic
199C22×C11C2×#13111yescharacteristic
200C22×C11C2×#13112yes—
201C4×C11—22no—
202C4×C11—42no—
203C4×C11C8×D414yes—
204C4×C11C2×#12411yescharacteristic
205C4×C11#52912yes—
206C4×C11#53211yescharacteristic
207Dic11—24no—
208Dic11—24no—
209Dic11—24no—
210Dic11—42no—
211C22×Q8—111no—
212C22×D4C4×D1111yescharacteristic
213C23×C4C22×D1112yes—
214C22×C8—111no—
215C22×C8—111no—
216C22×C8—112no—
217C22×C8—228no—
218C22×C8—224no—
219C22×C8C22×D1112yes—
220C22×C8C22×D1112yes—
221#124—118no—
222C4×Q8—222no—
223C4×Q8—222no—
224C4×D4—22no—
225C4×D4—22no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—112no—
228C2×C4⋊C4C4×D1111yescharacteristic
229C2×C22⋊C4—114no—
230C2×C22⋊C4—114no—
231C2×C22⋊C4C4×D1112yes—
232C2×C42—111no—
233C2×C42—112no—
234C2×C42—111no—
235C2×C42—112no—
236C2×C42—112no—
237C2×C42C22×D1111yescharacteristic
238C4⋊C8—22no—
239C4⋊C8—224no—
240C4⋊C8—222no—
241C22⋊C8—28no—
242C22⋊C8—224no—
243C4×C8—22no—
244C4×C8—114no—
245C4×C8—224no—
246C4×C8—224no—
247C4×C8—224no—
248#95—114no—
249#95—114no—
250C2×C11—44no—
251C2×C11C4×#12411yescharacteristic
252C2×C11C2×C8×D411yescharacteristic
253C2×C11#293111yescharacteristic
254C2×C11C8×#4112yes—
255C2×C11#296612yes—
256C24C2×C4×D1112yes—
257C2×Q8—114no—
258C2×Q8—222no—
259C2×Q8—222no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4C8×D1114yes—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—112no—
268C22×C4—112no—
269C22×C4—112no—
270C22×C4—112no—
271C22×C4C2×C4×D1112yes—
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4C23×D1111yescharacteristic
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—24no—
279C2×C8—112no—
280C2×C8—114no—
281C2×C8—112no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—224no—
285C2×C8—448no—
286C2×C8#434114yes—
287C4⋊C4—22no—
288C4⋊C4—224no—
289C4⋊C4—222no—
290C22⋊C4—24no—
291C22⋊C4—1116no—
292C22⋊C4—228no—
293C42—114no—
294C42—224no—
295C42—222no—
296C42—222no—
297C42—222no—
298C42—222no—
299C42—222no—
300C42D4×D1112yes—
301C42#434112yes—
302C11C8×#12411yescharacteristic, complemented, Sylow
303C23—22no—
304C23—22no—
305C23—24no—
306C23—24no—
307C23C2×C8×D1114yes—
308C23C22×C4×D1111yescharacteristic
309Q8—228no—
310D4—28no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—114no—
318C2×C4—114no—
319C2×C4—114no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—224no—
328C2×C4(C22⋊D11)⋊C412yes—
329C2×C4(C22⋊D11)⋊C412yes—
330C2×C4C2×C8×D1112yes—
331C2×C4#6696012yes—
332C2×C4C2×D4×D1111yescharacteristic
333C2×C4C2×#434112yes—
334C2×C4C2×#434111yescharacteristic
335C2×C4#41×D1112yes—
336C8—24no—
337C8—42no—
338C8—114no—
339C8—222no—
340C8—442no—
341C22—24no—
342C22—28no—
343C22—42no—
344C22—42no—
345C22—44no—
346C22C2×(C22⋊D11)⋊C411yescharacteristic
347C22C4×#434112yes—
348C22C22×C8×D1111yescharacteristic
349C22C2×#6696011yescharacteristic
350C22D11×#13112yes—
351C4—22no—
352C4—42no—
353C4—224no—
354C4—224no—
355C4—224no—
356C4—442no—
357C4(C22⋊D11)⋊C814yes—
358C4#1062313112yes—
359C4D11×#12411yescharacteristic
360C4#1062324711yescharacteristic
361C2—44no—
362C2#1307116311yescharacteristic
363C2C2×(C22⋊D11)⋊C811yescharacteristic
364C2#1307732411yescharacteristic
365C2C8×#434112yes—
366C2#1307759412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1954C2
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1954D11
hypocenterC11C8×#124
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
4. #13069552C2semidirect
5. #13069219C2semidirect
6. #13068732C2semidirect
7. #13068390C2semidirect
8. C4×C8×Dic11C2semidirect
46. #66989C8semidirect
92. C2×Dic22C2×C8semidirect
103. C22⋊Dic11C2×C8semidirect
112. C4×Dic11C2×C8semidirect
166. C11⋊C8#124semidirect
302. C11C8×#124semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
C2×D4×C11⋊C82
C4×#669892
#130695522
#130692192
#130687322
#130683902
C4×C8×Dic112
C11×#19542
C8×#12411