Finite Group Databasebeta

← #14907277

Subgroups — #14907277

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077548C211yesmaximal, characteristic
2#13070524C212yesmaximal, complemented
3#13070522C212yesmaximal, complemented
4#13070522C212yesmaximal, complemented
5C16×Dic22C212yesmaximal, complemented
6#13070375C211yesmaximal, characteristic
7#13070374C211yesmaximal, characteristic
8C2×Dic11⋊C16C211yesmaximal, characteristic
9#13070215C211yesmaximal, characteristic
10M32×Dic11C211yesmaximal, characteristic
11C11×#2108C211yesmaximal, characteristic
12#10623048C411yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15C11×#405C2211yescharacteristic
16#10622732C411yescharacteristic
17#10622731C411yescharacteristic
18#10622714C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21C22×C11⋊C16C2211yescharacteristic
22#10622612C411yescharacteristic
23#10622314C412yes—
24#10622314C412yes—
25C8×Dic22C2212yes—
26C8×Dic22C2212yes—
27C11×#346C2212yes—
28C4×C11×C16C2212yes—
29#10622140C2212yes—
30#10622140C2212yes—
31Dic11⋊C16C2211yescharacteristic
32Dic11⋊C16C2211yescharacteristic
33Dic11⋊C16C2211yescharacteristic
34Dic11⋊C16C2211yescharacteristic
35Dic11⋊C16C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38C16×Dic11C2212yes—
39C4⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41C2×C11×M16C2×C411yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C11×#117C2×C411yescharacteristic
44#66979C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×#4318C2×C411yescharacteristic
47C22×C11⋊C8C2×C411yescharacteristic
48#66943C811yescharacteristic
49#66943C811yescharacteristic
50#66941C811yescharacteristic
51#66941C811yescharacteristic
52#66931C812yes—
53#66931C812yes—
54C4×Dic22C2×C412yes—
55C4×Dic22C2×C412yes—
56C11×M32Q814yescomplemented
57C2×C11×C16—22no—
58C2×C11×C16C2311yescharacteristic
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2312yes—
61C11×#97C2×C412yes—
62C4×C8×C11C2312yes—
63#66879C2×C412yes—
64Dic11⋊C8C2×C412yes—
65Dic11⋊C8C2×C412yes—
66Dic11⋊C8C2×C412yes—
67Dic11⋊C8C2×C412yes—
68C8×Dic11C2×C411yescharacteristic
69C8×Dic11C2×C411yescharacteristic
70C8×Dic11C2311yescharacteristic
71C8×Dic11C2312yes—
72C8×Dic11C2311yescharacteristic
73#66876—22no—
74C2×C11⋊C16—22no—
75C2×C11⋊C16C2311yescharacteristic
76C2×C11⋊C16C2312yes—
77C2×C11⋊C16C2311yescharacteristic
78C4⋊(C11⋊C8)C2×C412yes—
79C4⋊(C11⋊C8)C2×C412yes—
80#33476—111nomaximal, Sylow
81C22×C4×C11C22×C411yescharacteristic
82C22×Dic11C2×C811yescharacteristic
83C22×Dic11C2×C811yescharacteristic
84C2×Dic22C2×C812yes—
85C2×Dic22C2×C812yes—
86C11×M16—22no—
87C2×C8×C11C22×C412yes—
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C2×Q812yes—
90C2×C8×C11#4112yes—
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4C2×C811yescharacteristic
93C11×C4⋊C4C2×C811yescharacteristic
94C11×C22⋊C4C2×C812yes—
95C42×C11C22×C412yes—
96C22⋊Dic11C2×C812yes—
97C4⋊Dic11C2×C812yes—
98C4⋊Dic11C2×C812yes—
99C4⋊Dic11C2×C811yescharacteristic
100C4⋊Dic11C2×C811yescharacteristic
101Dic11⋊C4C2×C812yes—
102Dic11⋊C4C2×C812yes—
103Dic11⋊C4C2×C812yes—
104Dic11⋊C4C2×C812yes—
105C4×Dic11C2×C811yescharacteristic
106C4×Dic11C2×C811yescharacteristic
107C4×Dic11C22×C411yescharacteristic
108C4×Dic11C22×C411yescharacteristic
109C4×Dic11C22×C412yes—
110#4318—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8C22×C411yescharacteristic
113C2×C11⋊C8C22×C411yescharacteristic
114C2×C11⋊C8C22×C412yes—
115C11×C16—21no—
116C11×C16—21no—
117C11×C16C2×Q814yes—
118C11⋊C16—21no—
119C11⋊C16—21no—
120C11⋊C16—22no—
121#2960—111no—
122#2183—112no—
123#2183—112no—
124#2183—112no—
125Q8×C16—112no—
126#2151—111no—
127#2151—111no—
128C2×C4⋊C16—111no—
129#2108—111no—
130#2108D1111yescharacteristic
131C4×M32—111no—
132C23×C11C22×C811yescharacteristic
133C2×C4×C11C4×Q812yes—
134C2×C4×C11C22×C812yes—
135C2×C4×C11C22×C812yes—
136C2×C4×C11C22×C811yescharacteristic
137C2×C4×C11#13112yes—
138C2×C4×C11C23×C411yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11C22×C811yescharacteristic
142C2×Dic11C22×C811yescharacteristic
143C2×Dic11C22×C811yescharacteristic
144C2×Dic11C22×C812yes—
145C2×Dic11C22×C812yes—
146C2×Dic11C22×C811yescharacteristic
147Dic22—24no—
148Dic22—42no—
149C8×C11—22no—
150C8×C11C4×Q812yes—
151C8×C11C22×Q811yescharacteristic
152C8×C11C2×#4111yescharacteristic
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—22no—
156#533—111no—
157C2×M32—111no—
158C2×M32C2×D1111yescharacteristic
159C22×C16—111no—
160C22×C16C2×D1111yescharacteristic
161#446—112no—
162#446—112no—
163C8×Q8—112no—
164C8×Q8—112no—
165#424—111no—
166#424—111no—
167#423—111no—
168#405—111no—
169#405C2×D1111yescharacteristic
170C2×C4×C8—111no—
171C4⋊C16—111no—
172C4⋊C16—111no—
173C4⋊C16—111no—
174C4⋊C16—111no—
175C4⋊C16—112no—
176C4⋊C16—112no—
177C4⋊C16—112no—
178C4⋊C16—112no—
179#346—112no—
180#346—112no—
181#346C2×D1112yes—
182C4×C16—112no—
183C4×C16—112no—
184C4×C16C2×D1112yes—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11C8×Q812yes—
188C22×C11C23×C811yescharacteristic
189C4×C11—22no—
190C4×C11—22no—
191C4×C11C8×Q812yes—
192C4×C11C2×C4×Q811yescharacteristic
193C4×C11C2×#13111yescharacteristic
194Dic11—22no—
195Dic11—21no—
196Dic11—21no—
197Dic11—22no—
198Dic11—21no—
199Dic11#50412yes—
200C2×M16—111no—
201C2×M16C4×D1111yescharacteristic
202C22×C8—111no—
203C22×C8C22×D1111yescharacteristic
204C4⋊Q8—111no—
205C4⋊Q8—111no—
206#125—111no—
207#125—111no—
208C22⋊Q8—112no—
209C22⋊Q8—112no—
210C4×Q8—112no—
211C4×Q8—112no—
212#117—111no—
213#117C4×D1111yescharacteristic
214C2×C42—111no—
215M32—222no—
216M32Dic2214yescomplemented
217C2×C16—22no—
218C2×C16—111no—
219C2×C16—112no—
220C2×C16—111no—
221C2×C16—222no—
222C2×C16C22×D1111yescharacteristic
223C2×C16C22×D1111yescharacteristic
224C2×C16C22×D1112yes—
225C4⋊C8—112no—
226C4⋊C8—112no—
227C4⋊C8—112no—
228C4⋊C8—112no—
229C4⋊C8—112no—
230C4⋊C8—112no—
231#97—112no—
232#97C4×D1112yes—
233C4×C8—111no—
234C4×C8—111no—
235C4×C8—111no—
236C4×C8—112no—
237C4×C8—111no—
238C4×C8C22×D1112yes—
239C2×C11—22no—
240C2×C11C2×C8×Q811yescharacteristic
241C2×C11C2×#50411yescharacteristic
242C2×C11#340711yescharacteristic
243C2×Q8—112no—
244C2×Q8—112no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4C2×C4×D1111yescharacteristic
248M16—22no—
249M16—222no—
250C2×C8—111no—
251C2×C8—111no—
252C2×C8—112no—
253C2×C8—222no—
254C2×C8C2×Dic2212yes—
255C2×C8C2×C4×D1112yes—
256C2×C8C2×C4×D1111yescharacteristic
257C2×C8#433912yes—
258C2×C8C23×D1111yescharacteristic
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—112no—
262C4⋊C4—112no—
263C4⋊C4—112no—
264C4⋊C4—112no—
265C4⋊C4—112no—
266C4⋊C4—112no—
267C4⋊C4C8×D1111yescharacteristic
268C4⋊C4C8×D1111yescharacteristic
269C22⋊C4—112no—
270C22⋊C4C8×D1112yes—
271C42—111no—
272C42—111no—
273C42—111no—
274C42—111no—
275C42—112no—
276C42C2×C4×D1112yes—
277C16—21no—
278C16—21no—
279C16—221no—
280C16—221no—
281C16—222no—
282C16C2×Dic2214yes—
283C11#3347611yescharacteristic, complemented, Sylow
284C23C2×C8×D1111yescharacteristic
285Q8—224no—
286Q8—442no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—111no—
291C2×C4—112no—
292C2×C4—112no—
293C2×C4—222no—
294C2×C4—441no—
295C2×C4C4×Dic2212yes—
296C2×C4C2×C8×D1112yes—
297C2×C4C2×C8×D1112yes—
298C2×C4C2×C8×D1111yescharacteristic
299C2×C4#6695412yes—
300C2×C4C22×C4×D1111yescharacteristic
301C8—22no—
302C8—221no—
303C8—221no—
304C8—222no—
305C8C4×Dic2212yes—
306C8C22×Dic2211yescharacteristic
307C8C2×#433911yescharacteristic
308C22—21no—
309C22—21no—
310C22C8×Dic2212yes—
311C22C22×C8×D1111yescharacteristic
312C4—22no—
313C4—22no—
314C4—112no—
315C4—221no—
316C4—222no—
317C4—221no—
318C4—221no—
319C4—222no—
320C4C8×Dic2212yes—
321C4C2×C4×Dic2211yescharacteristic
322C4C2×#6695411yescharacteristic
323C2—22no—
324C2C2×C8×Dic2211yescharacteristic
325C2D11×#50411yescharacteristic
326C2#1308171711yescharacteristic
subgroupG/H
center, FrattiniC2×C8C23×D11
commutator, socleC22×C11C23×C8
FittingC11×#2108C2
prime radicalC23×C11C22×C8
cosocleC2×C8×C11C24
hypercenter#2108D11
hypocenterC11#33476
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ #2108

Complements

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

NH ≅ G/Ntype
2. #13070524C2semidirect
3. #13070522C2semidirect
4. #13070522C2semidirect
5. C16×Dic22C2semidirect
56. C11×M32Q8semidirect
216. M32Dic22semidirect
283. C11#33476semidirect

Maximal subgroups

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

subgroupindex
#130775482
#130705242
#130705222
C16×Dic222
#130703752
#130703742
C2×Dic11⋊C162
#130702152
M32×Dic112
C11×#21082
#3347611