Finite Group Databasebeta

← #14664832

Subgroups — #14664832

Order 2816.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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#13073601C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13066623C214yesmaximal
4C11×#1461C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66997—21no—
7C2×#66922C411yescharacteristic
8C11×#431—21no—
9C2×#66900—21no—
10#10622596C412yes—
11#10622596C2212yes—
12#10622587—21no—
13C4×C4⋊Dic11C411yescharacteristic
14#10622541—21no—
15#10622541—21no—
16#10622537—21no—
17C11×#324—21no—
18C11×#324C2212yes—
19#10622168C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×Dic22—21no—
22C4×Q8×C11—41no—
23C4×Q8×C11—41no—
24C2×C11×C4⋊C4C2×C411yescharacteristic
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30#66997—42no—
31#66997—42no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C412yes—
35C2×Dic11⋊C4—22no—
36C2×Dic11⋊C4—22no—
37C2×C4×Dic11—21no—
38C2×#4318—22no—
39#66922—41no—
40#66922—41no—
41C11×C4⋊C8—41no—
42C11×C22⋊C8—22no—
43C4×C8×C11—41no—
44#66900—42no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95C2×C412yes—
48C4⋊(C11⋊C8)—41no—
49C4⋊(C11⋊C8)—41no—
50#11883—111nomaximal, Sylow
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11D812yes—
54C2×Q8×C11SD1612yes—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×Dic22—42no—
65C2×Dic22—42no—
66C2×Dic22—42no—
67C2×C8×C11—42no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C4⋊Dic11—24no—
78C4⋊Dic11—42no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81Dic11⋊C4—44no—
82Dic11⋊C4—42no—
83Dic11⋊C4—42no—
84C4×Dic11—42no—
85#4318—42no—
86#4318—42no—
87C2×C11⋊C8—42no—
88#2546—111no—
89#1801—111no—
90#1461D1111yescharacteristic
91#1346—114no—
92C23×C11C2×C22⋊C411yescharacteristic
93Q8×C11—42no—
94Q8×C11—42no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#9911yescharacteristic
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11#10212yes—
111C2×C4×C11#10212yes—
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11C2×SD1611yescharacteristic
114C2×Dic11—24no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120Dic22—84no—
121C8×C11—82no—
122C11⋊C8—82no—
123C2×C4⋊Q8—111no—
124C2×C4⋊Q8—221no—
125C2×C4×Q8C2×D1111yescharacteristic
126#431—21no—
127#423—221no—
128C2×#101—221no—
129#398—112no—
130#398—112no—
131#391—221no—
132#389—221no—
133#389—221no—
134C4×C4⋊C4—111no—
135#343—112no—
136#324—21no—
137#324C2×D1112yes—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11C2×#9911yescharacteristic
141C22×C11C2×#10211yescharacteristic
142C22×C11#42111yescharacteristic
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—22no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11#35612yes—
152Dic11—44no—
153Dic11—82no—
154C22×Q8—221no—
155C22×Q8D4411yescharacteristic
156C2×M16—222no—
157C4⋊Q8—441no—
158C4⋊Q8—441no—
159C4⋊Q8—442no—
160C4⋊Q8—442no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—112no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4—222no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4—222no—
168C2×C4⋊C4C4×D1111yescharacteristic
169C2×C4⋊C4C22⋊D1111yescharacteristic
170C2×C4⋊C4C22×D1111yescharacteristic
171C2×C42—221no—
172C2×C42C4×D1111yescharacteristic
173C2×C42D4411yescharacteristic
174C2×C42C22⋊D1111yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—441no—
177C4⋊C8—441no—
178#101—442no—
179C22⋊C8—22no—
180C4×C8—41no—
181#95—112no—
182#95—222no—
183#95—222no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11#151911yescharacteristic
187C2×C11#212311yescharacteristic
188C2×C11C2×#35611yescharacteristic
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—442no—
192C2×Q8—442no—
193C2×Q8—442no—
194C2×Q8#431412yes—
195C2×Q8D8812yes—
196C22×C4—222no—
197C22×C4—222no—
198C22×C4(C2×D11)⋊C411yescharacteristic
199C22×C4(C2×D11)⋊C411yescharacteristic
200C22×C4(C2×D11)⋊C411yescharacteristic
201C22×C4(C2×D11)⋊C411yescharacteristic
202C22×C4C2×C4×D1111yescharacteristic
203C22×C4C2×D4411yescharacteristic
204C22×C4C2×C22⋊D1111yescharacteristic
205M16—442no—
206M16—442no—
207C2×C8—42no—
208C2×C8—442no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—224no—
213C4⋊C4—442no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—444no—
217C4⋊C4—442no—
218C4⋊C4—442no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—442no—
226C11#1188311yescharacteristic, complemented, Sylow
227C23C2×(C2×D11)⋊C411yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—884no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—224no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4#6687011yescharacteristic
251C2×C4#6687011yescharacteristic
252C2×C4#6688512yes—
253C2×C4#6688512yes—
254C2×C4C2×#431411yescharacteristic
255C2×C4C2×D8811yescharacteristic
256C8—82no—
257C8—882no—
258C22—21no—
259C22—21no—
260C22C2×#6687011yescharacteristic
261C22C2×#6688511yescharacteristic
262C22#1062275211yescharacteristic
263C4—21no—
264C4—22no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—444no—
272C4—882no—
273C4#1062211612yes—
274C2—21no—
275C2—21no—
276C2#1306718511yescharacteristic
277C2#1307026911yescharacteristic
278C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1461C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1461D11
hypocenterC11#11883
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
226. C11#11883semidirect

Maximal subgroups

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

subgroupindex
#130736012
#130686122
#130666232
C11×#14612
#1188311