Finite Group Databasebeta

← #14662972

Subgroups — #14662972

Order 2816.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622331C211yesmaximal, characteristic
2#13070416C212yesmaximal, complemented
3#13066555C212yesmaximal, complemented
4#13066540C211yesmaximal, characteristic
5C11×#1314C211yesmaximal, characteristic
6C22×C4×Dic11C411yescharacteristic
7C2×C11×C22⋊C8C2211yescharacteristic
8C2×C22⋊(C11⋊C8)C411yescharacteristic
9C2×Dic11⋊C8C411yescharacteristic
10C2×Dic11⋊C8C2211yescharacteristic
11C2×C8×Dic11C411yescharacteristic
12C2×C8×Dic11C2211yescharacteristic
13#10622331—22no—
14#10622331—22no—
15C11×C22⋊C16C2212yes—
16C22⋊(C11⋊C16)C2212yes—
17#10622140—22no—
18Dic11⋊C16—22no—
19C23×C4×C11C2×C411yescharacteristic
20C23×Dic11C811yescharacteristic
21C23×Dic11C811yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11C2311yescharacteristic
24C2×C4×Dic11—21no—
25C2×C4×Dic11—21no—
26C2×C4×Dic11—21no—
27C2×C4×Dic11—21no—
28C2×C4×Dic11C811yescharacteristic
29C2×C4×Dic11C811yescharacteristic
30C2×C4×Dic11C2×C411yescharacteristic
31C2×C4×Dic11C2×C411yescharacteristic
32C22×C11⋊C8C2×C411yescharacteristic
33C22×C11⋊C8C2×C411yescharacteristic
34C2×C11×C16—22no—
35C11×C22⋊C8—22no—
36C22⋊(C11⋊C8)—22no—
37Dic11⋊C8—22no—
38Dic11⋊C8—22no—
39C8×Dic11—21no—
40C8×Dic11—21no—
41C8×Dic11D412yes—
42C8×Dic11D412yes—
43C2×C11⋊C16—22no—
44#11460—111nomaximal, Sylow
45C24×C11C2×C811yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11—41no—
49C22×C4×C11—41no—
50C22×C4×C11C2×C811yescharacteristic
51C22×C4×C11C22×C411yescharacteristic
52C22×Dic11—21no—
53C22×Dic11—21no—
54C22×Dic11—22no—
55C22×Dic11—21no—
56C22×Dic11—21no—
57C22×Dic11—22no—
58C22×Dic11—42no—
59C22×Dic11C2×C811yescharacteristic
60C22×Dic11C2×C811yescharacteristic
61C22×Dic11C2×C811yescharacteristic
62C22×Dic11C2×C811yescharacteristic
63C2×C8×C11—21no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C2×C8×C11C2×D412yes—
67C4×Dic11—21no—
68C4×Dic11—21no—
69C4×Dic11—21no—
70C4×Dic11—21no—
71C4×Dic11—21no—
72C4×Dic11—21no—
73C4×Dic11C22⋊C411yescharacteristic
74C4×Dic11C22⋊C411yescharacteristic
75C4×Dic11M1611yescharacteristic
76C4×Dic11M1611yescharacteristic
77C2×C11⋊C8—21no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—41no—
80C2×C11⋊C8C22⋊C412yes—
81C11×C16—42no—
82C11⋊C16—42no—
83C2×#431—111no—
84#2163—112no—
85#1322—112no—
86#1314—111no—
87#1314D1111yescharacteristic
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—41no—
91C23×C11—41no—
92C23×C11M3212yes—
93C23×C11C22×C811yescharacteristic
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—42no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11C2×C22⋊C411yescharacteristic
102C2×C4×C11C2×M1611yescharacteristic
103C2×Dic11—24no—
104C2×Dic11—24no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—21no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—41no—
114C2×Dic11C22⋊C811yescharacteristic
115C2×Dic11C22⋊C811yescharacteristic
116C2×Dic11C22⋊C811yescharacteristic
117C2×Dic11C22⋊C811yescharacteristic
118C2×Dic11M3212yes—
119C8×C11—22no—
120C8×C11—41no—
121C11⋊C8—22no—
122C11⋊C8—41no—
123C22×C42—111no—
124#431—222no—
125#431—222no—
126C2×C4⋊C8—111no—
127C2×C4⋊C8—111no—
128C2×C22⋊C8—111no—
129C2×C22⋊C8C2×D1111yescharacteristic
130C2×C4×C8—111no—
131C2×C4×C8—111no—
132C4⋊C16—222no—
133C22⋊C16—112no—
134C22⋊C16C2×D1112yes—
135#346—222no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—22no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11C2×C22⋊C811yescharacteristic
144C22×C11C2×M3211yescharacteristic
145C22×C11C2×M3211yescharacteristic
146C4×C11—21no—
147C4×C11—41no—
148C4×C11#41011yescharacteristic
149C4×C11#41311yescharacteristic
150Dic11—21no—
151Dic11—21no—
152Dic11—22no—
153Dic11—21no—
154Dic11—41no—
155Dic11#34912yes—
156C23×C4—111no—
157C23×C4—111no—
158C23×C4C4×D1111yescharacteristic
159C22×C8—111no—
160C22×C8—111no—
161C22×C8C4×D1111yescharacteristic
162C22×C8C22×D1111yescharacteristic
163C2×C42—111no—
164C2×C42—111no—
165C2×C42—111no—
166C2×C42—111no—
167C2×C42—221no—
168C2×C42—221no—
169C2×C42—221no—
170C2×C42—221no—
171C2×C16—22no—
172C2×C16—222no—
173C4⋊C8—222no—
174C4⋊C8—222no—
175C22⋊C8—22no—
176C22⋊C8—222no—
177C4×C8—112no—
178C4×C8—112no—
179C4×C8—221no—
180C4×C8—221no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11—42no—
184C2×C11#145811yescharacteristic
185C2×C11#211211yescharacteristic
186C2×C11C2×#34911yescharacteristic
187C24C8×D1111yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4—111no—
195C22×C4—111no—
196C22×C4—221no—
197C22×C4—221no—
198C22×C4—222no—
199C22×C4—221no—
200C22×C4—221no—
201C22×C4—222no—
202C22×C4—442no—
203C22×C4C8×D1111yescharacteristic
204C22×C4C2×C4×D1111yescharacteristic
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—112no—
209C2×C8—221no—
210C2×C8—441no—
211C2×C8—441no—
212C2×C8D4×D1112yes—
213C42—111no—
214C42—111no—
215C42—111no—
216C42—111no—
217C42—221no—
218C42—221no—
219C42—221no—
220C42—221no—
221C42—221no—
222C42—221no—
223C16—42no—
224C16—442no—
225C11#1146011yescharacteristic, complemented, Sylow
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23#6686212yes—
231C23C2×C8×D1111yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—111no—
240C2×C4—112no—
241C2×C4—111no—
242C2×C4—111no—
243C2×C4—111no—
244C2×C4—222no—
245C2×C4—224no—
246C2×C4—224no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4—221no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4—441no—
255C2×C4C22⋊C4×D1111yescharacteristic
256C2×C4M16×D1111yescharacteristic
257C8—22no—
258C8—41no—
259C8—222no—
260C8—441no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—42no—
265C22—42no—
266C22—41no—
267C22—41no—
268C22D11×C22⋊C811yescharacteristic
269C22C2×#6686211yescharacteristic
270C22D11×M3211yescharacteristic
271C4—21no—
272C4—41no—
273C4—112no—
274C4—222no—
275C4—221no—
276C4—221no—
277C4—221no—
278C4—441no—
279C4#1062235311yescharacteristic
280C4#1062235811yescharacteristic
281C2—21no—
282C2—21no—
283C2—42no—
284C2#1306692711yescharacteristic
285C2#1307022511yescharacteristic
286C2D11×#34911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC23×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#1314C2
socleC22×C11C2×C22⋊C8
prime radicalC24×C11C2×C8
cosocleC22×C8×C11C23
hypercenter#1314D11
hypocenterC11#11460
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #13070416C2semidirect
3. #13066555C2semidirect
225. C11#11460semidirect

Maximal subgroups

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

subgroupindex
C2×#106223312
#130704162
#130665552
#130665402
C11×#13142
#1146011