Finite Group Databasebeta

← #14662905

Subgroups — #14662905

Order 2816.

450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 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×D11×C4⋊C8C211yesmaximal, characteristic
2#13070225C212yesmaximal
3#13066556C211yesmaximal, characteristic, complemented
4#13066555C212yesmaximal, complemented
5C11×#1322C211yesmaximal, characteristic, complemented
6C22×C8×D11C411yescharacteristic
7C22×C8×D11C2211yescharacteristic
8C2×C42×D11C411yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×Dic11⋊C8C411yescharacteristic
11C2×Dic11⋊C8C2211yescharacteristic
12C2×C4⋊(C11⋊C8)C411yescharacteristic
13C2×#66862—22no—
14D11×C4⋊C8—22no—
15D11×C4⋊C8—22no—
16C11×C22⋊C16C2212yes—
17C22⋊(C11⋊C16)C2212yes—
18(C2×D11)⋊C16—22no—
19C22×C4×D11C811yescharacteristic
20C22×C4×D11C811yescharacteristic
21C22×C4×D11C2×C411yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11C2311yescharacteristic
24C2×C42×C11C2×C411yescharacteristic
25C2×C4×Dic11C811yescharacteristic
26C2×C4×Dic11C811yescharacteristic
27C2×C4×Dic11C2×C411yescharacteristic
28C22×C11⋊C8C2×C411yescharacteristic
29C22×C11⋊C8C2×C411yescharacteristic
30C2×C8×D11—21no—
31C2×C8×D11—21no—
32C2×C8×D11—42no—
33C2×C8×D11—42no—
34C2×C8×D11D412yes—
35C2×C8×D11D412yes—
36C42×D11—21no—
37C42×D11—21no—
38C42×D11—21no—
39C42×D11—21no—
40C2×C11×C16—22no—
41C11×C4⋊C8—22no—
42Dic11⋊C8—22no—
43Dic11⋊C8—22no—
44C2×C11⋊C16—22no—
45C4⋊(C11⋊C8)—22no—
46#66862—44no—
47#11440—111nomaximal, Sylow
48C23×D11C2×C811yescharacteristic
49C22×C4×C11C2×C811yescharacteristic
50C22×C4×C11C2×C811yescharacteristic
51C22×C4×C11C22×C411yescharacteristic
52C22×Dic11C2×C811yescharacteristic
53C22×Dic11C2×C811yescharacteristic
54C22×Dic11C2×C811yescharacteristic
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×C4×D11—21no—
59C2×C4×D11—21no—
60C2×C4×D11—21no—
61C2×C4×D11—21no—
62C2×C4×D11—22no—
63C2×C4×D11—42no—
64C2×C4×D11C22⋊C411yescharacteristic
65C2×C4×D11C22⋊C411yescharacteristic
66C2×C4×D11M1611yescharacteristic
67C2×C4×D11M1611yescharacteristic
68C2×C8×C11—21no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11C2×D412yes—
72C42×C11—21no—
73C42×C11—21no—
74C4×Dic11—21no—
75C4×Dic11—21no—
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11—21no—
79C4×Dic11—21no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—41no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8C22⋊C412yes—
84C8×D11—24no—
85C8×D11—42no—
86C8×D11—42no—
87C8×D11—42no—
88C11×C16—42no—
89C11⋊C16—42no—
90C22×C4⋊C8—111no—
91#2112—112no—
92#1322—111no—
93#1322—112no—
94#1322D1111yescharacteristic, complemented
95C23×C11C22×C811yescharacteristic
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—22no—
99C22×D11—22no—
100C22×D11C22⋊C811yescharacteristic
101C22×D11C22⋊C811yescharacteristic
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—41no—
108C2×C4×C11M3212yescomplemented
109C2×C4×C11C2×C22⋊C411yescharacteristic
110C2×C4×C11C2×M1611yescharacteristic
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115C2×Dic11—41no—
116C2×Dic11C22⋊C811yescharacteristic
117C2×Dic11C22⋊C811yescharacteristic
118C2×Dic11M3212yescomplemented
119C4×D11—24no—
120C4×D11—24no—
121C4×D11—22no—
122C4×D11—21no—
123C4×D11—21no—
124C4×D11—22no—
125C4×D11—42no—
126C4×D11—42no—
127C4×D11#9912yes—
128C4×D11#10112yes—
129C8×C11—22no—
130C8×C11—41no—
131C11⋊C8—22no—
132C11⋊C8—41no—
133C23×C8—111no—
134C23×C8—111no—
135C22×C42—111no—
136C2×M32—222no—
137C2×C4⋊C8—111no—
138C2×C4⋊C8—111no—
139C2×C4⋊C8—111no—
140C2×C4⋊C8—222no—
141C2×C4⋊C8—222no—
142C2×C4⋊C8C2×D1111yescharacteristic
143C22⋊C16—112no—
144C22⋊C16—222no—
145C22⋊C16C2×D1112yes—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11C2×C22⋊C811yescharacteristic
149C22×C11C2×M3211yescharacteristic
150C22×C11C2×M3211yescharacteristic
151C2×D11—24no—
152C2×D11—24no—
153C2×D11—21no—
154C2×D11—21no—
155C2×D11—21no—
156C2×D11—21no—
157C2×D11#32412yes—
158C2×D11#34912yes—
159C4×C11—22no—
160C4×C11—21no—
161C4×C11—41no—
162C4×C11C2×#9911yescharacteristic
163C4×C11C2×#10111yescharacteristic
164Dic11—22no—
165Dic11—21no—
166Dic11—41no—
167Dic11#32412yes—
168C23×C4—111no—
169C23×C4—111no—
170C23×C4—111no—
171C22×C8—111no—
172C22×C8—112no—
173C22×C8—112no—
174C22×C8—111no—
175C22×C8—221no—
176C22×C8—221no—
177C22×C8—442no—
178C22×C8—442no—
179C22×C8C4×D1111yescharacteristic
180C22×C8C22×D1111yescharacteristic
181C2×C42—111no—
182C2×C42—111no—
183C2×C42—111no—
184C2×C42—221no—
185C2×C42—221no—
186C2×C42—221no—
187C2×C42—221no—
188C2×C42C4×D1111yescharacteristic
189M32—444no—
190C2×C16—22no—
191C2×C16—222no—
192C4⋊C8—22no—
193C4⋊C8—222no—
194C4⋊C8—222no—
195C4⋊C8—222no—
196C2×C11—21no—
197C2×C11—21no—
198C2×C11C2×#32411yescharacteristic
199C2×C11#211211yescharacteristic
200C2×C11C2×#34911yescharacteristic
201D11—22no—
202D11—22no—
203C24—111no—
204C22×C4—111no—
205C22×C4—111no—
206C22×C4—111no—
207C22×C4—111no—
208C22×C4—111no—
209C22×C4—111no—
210C22×C4—111no—
211C22×C4—222no—
212C22×C4—222no—
213C22×C4—222no—
214C22×C4—221no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4—222no—
219C22×C4—442no—
220C22×C4C8×D1111yescharacteristic
221C22×C4C8×D1111yescharacteristic
222C22×C4C2×C4×D1111yescharacteristic
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—112no—
227C2×C8—224no—
228C2×C8—221no—
229C2×C8—442no—
230C2×C8—442no—
231C2×C8—442no—
232C2×C8—441no—
233C2×C8—441no—
234C2×C8D4×D1112yes—
235C42—21no—
236C42—21no—
237C42—221no—
238C42—221no—
239C42—221no—
240C42—221no—
241C42—221no—
242C42—221no—
243C16—42no—
244C16—442no—
245C11#1144011yescharacteristic, complemented, Sylow
246C23—111no—
247C23—111no—
248C23—222no—
249C23—222no—
250C23—221no—
251C23—221no—
252C23C2×C8×D1111yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—111no—
260C2×C4—112no—
261C2×C4—112no—
262C2×C4—112no—
263C2×C4—111no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—224no—
267C2×C4—224no—
268C2×C4—222no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—441no—
277C2×C4#6686212yescomplemented
278C2×C4C22⋊C4×D1111yescharacteristic
279C2×C4M16×D1111yescharacteristic
280C8—22no—
281C8—41no—
282C8—222no—
283C8—441no—
284C22—21no—
285C22—21no—
286C22—112no—
287C22—112no—
288C22—224no—
289C22—224no—
290C22—221no—
291C22—221no—
292C22—221no—
293C22—221no—
294C22D11×C22⋊C811yescharacteristic
295C22C2×#6686211yescharacteristic
296C22D11×M3211yescharacteristic
297C4—22no—
298C4—21no—
299C4—41no—
300C4—112no—
301C4—222no—
302C4—221no—
303C4—441no—
304C4D11×#9911yescharacteristic
305C4D11×#10111yescharacteristic
306C2—21no—
307C2—21no—
308C2—222no—
309C2—222no—
310C2D11×#32411yescharacteristic
311C2#1307022511yescharacteristic
312C2D11×#34911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC23×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#1322C2
socleC22×C11C2×C22⋊C8
prime radicalC23×D11C2×C8
cosocleC22×C8×C11C23
hypercenter#1322D11
hypocenterC11#11440
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
3. #13066556C2semidirect
4. #13066555C2semidirect
5. C11×#1322C2semidirect
94. #1322D11semidirect
108. C2×C4×C11M32semidirect
118. C2×Dic11M32semidirect
245. C11#11440semidirect
277. C2×C4#66862semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊C82
#130702252
#130665562
#130665552
C11×#13222
#1144011