Finite Group Databasebeta

← #14662982

Subgroups — #14662982

Order 2816.

314 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 107 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#13077258C211yesmaximal, characteristic
2#13070415C211yesmaximal, characteristic, complemented
3#13066557C212yesmaximal, complemented
4#13066541C212yesmaximal
5C11×#2162C211yesmaximal, characteristic, complemented
6C4×#4339C411yescharacteristic
7C2×C4×C8×C11C2211yescharacteristic
8#10622723C411yescharacteristic
9#10622723C2211yescharacteristic
10#10622715C411yescharacteristic
11#10622715C2211yescharacteristic
12C4×#4318C411yescharacteristic
13#10622303—21no—
14#10622303—21no—
15#10622298—21no—
16#10622298—21no—
17C11×C4⋊C16—21no—
18C11×C22⋊C16C2212yes—
19C4×C11×C16—21no—
20C22⋊(C11⋊C16)C2212yes—
21C4⋊(C11⋊C16)—21no—
22C4×C11⋊C16—21no—
23C2×#4339C2×C411yescharacteristic
24C22×C8×C11C2×C411yescharacteristic
25C22×C8×C11C2311yescharacteristic
26C2×C42×C11C2×C411yescharacteristic
27C4×C22⋊D11—21no—
28C4×C22⋊D11—21no—
29#66979C2×C411yescharacteristic
30C2×#4318C2×C411yescharacteristic
31C2×#4318C2×C411yescharacteristic
32C4×D44C811yescharacteristic
33C4×D44C811yescharacteristic
34#66925—21no—
35C42×D11—21no—
36C4×Dic22C811yescharacteristic
37C4×Dic22C811yescharacteristic
38C2×C11×C16—22no—
39C4×C8×C11D411yescharacteristic
40C4×C8×C11D411yescharacteristic
41C4×C8×C11D411yescharacteristic
42C4×C8×C11D411yescharacteristic
43(C2×D11)⋊C8—21no—
44(C2×D11)⋊C8—21no—
45(C2×D11)⋊C8—21no—
46(C2×D11)⋊C8—21no—
47Dic11⋊C8—21no—
48Dic11⋊C8—21no—
49Dic11⋊C8—21no—
50Dic11⋊C8—21no—
51C2×C11⋊C16—22no—
52#66867—21no—
53C4×C11⋊C8—21no—
54#11462—111nomaximal, Sylow
55C22×C4×C11M1611yescharacteristic
56C22×C4×C11M1611yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C2×C22⋊D11—21no—
59#4339—41no—
60#4339—41no—
61C2×D44C2×C811yescharacteristic
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11—21no—
65C2×Dic22C2×C811yescharacteristic
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C2×C8×C11C22⋊C411yescharacteristic
69C2×C8×C11C22⋊C411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C2×C8×C11C2×D411yescharacteristic
72C42×C11C22⋊C411yescharacteristic
73C42×C11C22⋊C411yescharacteristic
74C42×C11C2×C811yescharacteristic
75C42×C11C2×C811yescharacteristic
76C22⋊Dic11—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79C4⋊Dic11C2×C811yescharacteristic
80C4⋊Dic11C2×C811yescharacteristic
81Dic11⋊C4—21no—
82Dic11⋊C4—21no—
83C4×Dic11—21no—
84C4×Dic11—21no—
85C4×Dic11—21no—
86#4318—41no—
87#4318—41no—
88C2×C11⋊C8—21no—
89C2×C11⋊C8—21no—
90C11×C16—42no—
91C11⋊C16—42no—
92#2922—111no—
93#2162—111no—
94#2162D1111yescharacteristic, complemented
95#1323—112no—
96#1315—112no—
97C23×C11C2×M1611yescharacteristic
98C22×D11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11C22⋊C811yescharacteristic
104C2×C4×C11C22⋊C811yescharacteristic
105C2×C4×C11C22⋊C811yescharacteristic
106C2×C4×C11C22⋊C811yescharacteristic
107C2×C4×C11C2×C22⋊C411yescharacteristic
108C2×C4×C11C22×C811yescharacteristic
109C22⋊D11—42no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113D44—41no—
114C4×D11—42no—
115C4×D11—42no—
116C4×D11—41no—
117C4×D11—41no—
118Dic22—41no—
119C8×C11—21no—
120C8×C11—21no—
121C8×C11—21no—
122C8×C11—21no—
123C11⋊C8—41no—
124C11⋊C8—41no—
125C4×#41—111no—
126#433—221no—
127#433—221no—
128#431—221no—
129#431—221no—
130#424—111no—
131#424—111no—
132#408—111no—
133#408—111no—
134C4×M16—111no—
135C2×C4×C8C2×D1111yescharacteristic
136C4⋊C16—21no—
137C4⋊C16—221no—
138C22⋊C16—112no—
139C22⋊C16C2×D1112yes—
140C4×C16—21no—
141C4×C16—221no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11C2×C22⋊C811yescharacteristic
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—41no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—21no—
152C4×C11#35012yes—
153C4×C11#35012yes—
154C4×C11#41011yescharacteristic
155C4×C11#41311yescharacteristic
156Dic11—41no—
157Dic11—41no—
158Dic11—41no—
159C2×#41—111no—
160C2×M16—111no—
161C2×M16—111no—
162C22×C8C4×D1111yescharacteristic
163C22×C8C22×D1111yescharacteristic
164C4×Q8—111no—
165C4×Q8—111no—
166C4×D4—111no—
167C4×D4—111no—
168C4×D4—221no—
169C4×D4—221no—
170#117—111no—
171#117—221no—
172C2×C42—221no—
173C2×C42C4×D1111yescharacteristic
174C2×C16—22no—
175C2×C16—222no—
176C4⋊C8—221no—
177C4⋊C8—221no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C22⋊C8—221no—
181C22⋊C8—221no—
182C22⋊C8—221no—
183C22⋊C8—221no—
184#97—221no—
185C4×C8—221no—
186C4×C8D4411yescharacteristic
187C4×C8D4411yescharacteristic
188C4×C8C22⋊D1111yescharacteristic
189C4×C8C22⋊D1111yescharacteristic
190C2×C11—41no—
191C2×C11#145811yescharacteristic
192C2×C11C2×#35011yescharacteristic
193C2×C11C2×#35011yescharacteristic
194D11—81no—
195#41—441no—
196#41—441no—
197C2×Q8—111no—
198C2×D4—111no—
199C2×D4—221no—
200C22×C4—221no—
201C22×C4—221no—
202C22×C4—221no—
203C22×C4#431311yescharacteristic
204C22×C4#431311yescharacteristic
205C22×C4C2×C4×D1111yescharacteristic
206M16—441no—
207M16—441no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—221no—
211C2×C8—221no—
212C2×C8(C2×D11)⋊C411yescharacteristic
213C2×C8(C2×D11)⋊C411yescharacteristic
214C2×C8C2×D4411yescharacteristic
215C2×C8C2×C22⋊D1111yescharacteristic
216C4⋊C4—111no—
217C4⋊C4—111no—
218C4⋊C4—221no—
219C4⋊C4—221no—
220C22⋊C4—221no—
221C22⋊C4—221no—
222C22⋊C4—221no—
223C42—221no—
224C42—221no—
225C42—221no—
226C42C8×D1111yescharacteristic
227C42C8×D1111yescharacteristic
228C42(C2×D11)⋊C411yescharacteristic
229C42(C2×D11)⋊C411yescharacteristic
230C16—42no—
231C16—442no—
232C11#1146211yescharacteristic, complemented, Sylow
233C23—221no—
234C23C2×#431311yescharacteristic
235Q8—441no—
236D4—441no—
237D4—442no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—221no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4—441no—
246C2×C4—441no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4(C2×D11)⋊C811yescharacteristic
250C2×C4(C2×D11)⋊C811yescharacteristic
251C2×C4(C2×D11)⋊C811yescharacteristic
252C2×C4(C2×D11)⋊C811yescharacteristic
253C2×C4C2×C8×D1111yescharacteristic
254C2×C4C2×(C2×D11)⋊C411yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—21no—
259C8—441no—
260C8—441no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—441no—
265C22—441no—
266C22—441no—
267C22C2×(C2×D11)⋊C811yescharacteristic
268C4—21no—
269C4—21no—
270C4—21no—
271C4—441no—
272C4—441no—
273C4—441no—
274C4#1062214612yes—
275C4#1062215312yes—
276C4#1062261911yescharacteristic
277C4#1062274511yescharacteristic
278C2—41no—
279C2—881no—
280C2#1306692811yescharacteristic
281C2C2×#1062214611yescharacteristic
282C2C2×#1062215311yescharacteristic
subgroupG/H
centerC42(C2×D11)⋊C4
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2162C2
socleC22×C11C2×C22⋊C8
prime radicalC2×#4339C2×C4
cosocleC22×C8×C11C23
hypercenter#2162D11
hypocenterC11#11462
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
2. #13070415C2semidirect
3. #13066557C2semidirect
5. C11×#2162C2semidirect
94. #2162D11semidirect
232. C11#11462semidirect

Maximal subgroups

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

subgroupindex
#130772582
#130704152
#130665572
#130665412
C11×#21622
#1146211