Finite Group Databasebeta

← #14664526

Subgroups — #14664526

Order 2816.

368 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#13074437C211yesmaximal, characteristic
2#13068699C211yesmaximal, characteristic
3#13066644C214yesmaximal, complemented
4C11×#1464C211yesmaximal, characteristic
5C2×C11×#117C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C11×#432—21no—
8#10622825—21no—
9#10622820—21no—
10#10622599C2212yes—
11#10622592—21no—
12#10622562C412yes—
13#10622560—21no—
14#10622549C411yescharacteristic
15#10622541—21no—
16C11×#324C2212yes—
17C11×#323—21no—
18#10622168—21no—
19#10622168C2212yes—
20C23×C4×C11D411yescharacteristic
21C22×Dic22—21no—
22C11×#117—41no—
23C11×#117—41no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C11×C22⋊C4C2×C411yescharacteristic
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×Dic11⋊C4—22no—
35C2×#4318—22no—
36#66922—41no—
37#66922—41no—
38C11×C4⋊C8—41no—
39C11×C22⋊C8—22no—
40C11×#97—41no—
41C11⋊#95—21no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95C2×C412yes—
45C22⋊(C11⋊C8)—41no—
46C22⋊(C11⋊C8)—41no—
47#11818—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—22no—
52C22×C4×C11—41no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×Dic22—42no—
62C2×Dic22—82no—
63C2×C8×C11—42no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C42×C11—21no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C22⋊Dic11—82no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77Dic11⋊C4—82no—
78#4318—42no—
79#4318—42no—
80C2×C11⋊C8—42no—
81#2628—111no—
82#1822—111no—
83#1464D1111yescharacteristic
84#1353—114no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—41no—
89C23×C11—41no—
90C23×C11C2×C22⋊C411yescharacteristic
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11#9911yescharacteristic
106C2×C4×C11#9911yescharacteristic
107C2×C4×C11#13712yes—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114Dic22—84no—
115C8×C11—82no—
116C11⋊C8—82no—
117C2×C4⋊Q8—111no—
118C2×#117C2×D1111yescharacteristic
119#432—21no—
120#407—221no—
121#400—112no—
122#399—112no—
123#395—221no—
124#393—221no—
125#389—221no—
126#382—111no—
127#380—221no—
128#343—112no—
129#343—221no—
130#324C2×D1112yes—
131#323—21no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—42no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—81no—
139C22×C11C2×#9911yescharacteristic
140C22×C11#41911yescharacteristic
141C22×C11#42111yescharacteristic
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11—41no—
148C4×C11—41no—
149Dic11—82no—
150Dic11—82no—
151C22×Q8—221no—
152C23×C4D4411yescharacteristic
153C2×M16—222no—
154C4⋊Q8—441no—
155C4⋊Q8—441no—
156#117—41no—
157#117—41no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4—221no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—222no—
162C2×C4⋊C4D4411yescharacteristic
163C2×C4⋊C4C22×D1111yescharacteristic
164C2×C22⋊C4—222no—
165C2×C22⋊C4C4×D1111yescharacteristic
166C2×C22⋊C4C22⋊D1111yescharacteristic
167C2×C42C4×D1111yescharacteristic
168C2×C42C22⋊D1111yescharacteristic
169C4⋊C8—41no—
170C22⋊C8—22no—
171C22⋊C8—441no—
172C22⋊C8—441no—
173#97—41no—
174#95—112no—
175#95—221no—
176#95—222no—
177#95—222no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11—81no—
181C2×C11#151111yescharacteristic
182C2×C11#212311yescharacteristic
183C2×C11#213411yescharacteristic
184C24(C2×D11)⋊C411yescharacteristic
185C2×Q8—442no—
186C2×Q8—882no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—41no—
191C22×C4—222no—
192C22×C4—222no—
193C22×C4(C2×D11)⋊C411yescharacteristic
194C22×C4(C2×D11)⋊C411yescharacteristic
195C22×C4(C2×D11)⋊C411yescharacteristic
196C22×C4C2×C4×D1111yescharacteristic
197C22×C4C2×D4411yescharacteristic
198C22×C4C2×C22⋊D1111yescharacteristic
199M16—442no—
200M16—442no—
201C2×C8—42no—
202C2×C8—442no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—442no—
206C4⋊C4—442no—
207C4⋊C4—441no—
208C4⋊C4—441no—
209C4⋊C4—882no—
210C22⋊C4—41no—
211C22⋊C4—41no—
212C22⋊C4—882no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C11#1181811yescharacteristic, complemented, Sylow
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×(C2×D11)⋊C411yescharacteristic
224Q8—884no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4#6687011yescharacteristic
246C2×C4#6687011yescharacteristic
247C2×C4#6696212yes—
248C8—82no—
249C8—882no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#6687011yescharacteristic
258C22#1062273311yescharacteristic
259C22#1062275211yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—882no—
268C4—882no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1306715011yescharacteristic
273C2#1307026911yescharacteristic
274C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1464D11
hypocenterC11#11818
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13066644C2semidirect
217. C11#11818semidirect

Maximal subgroups

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

subgroupindex
#130744372
#130686992
#130666442
C11×#14642
#1181811