Finite Group Databasebeta

← #14640348

Subgroups — #14640348

Order 2816.

406 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2#13068310C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic
4C22×C42×C11C2211yescharacteristic
5C22×#4318C412yes—
6C2×C11×C4⋊C8—21no—
7C2×C11×C22⋊C8C412yes—
8C2×C22⋊(C11⋊C8)C412yes—
9C2×C4⋊(C11⋊C8)—21no—
10C11×#336—21no—
11#10622162—21no—
12#10622162—21no—
13#10622162—21no—
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11C2×C411yescharacteristic
16C23×C4×C11C2×C411yescharacteristic
17C22×C8×C11—22no—
18C2×C42×C11—42no—
19C2×C42×C11D411yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×C42×C11D411yescharacteristic
22C2×C42×C11Q811yescharacteristic
23C2×#4318—22no—
24C2×#4318—42no—
25C2×#4318—42no—
26C2×#4318C814yescomplemented
27C22×C11⋊C8—22no—
28C22×C11⋊C8—22no—
29C11×C4⋊C8—42no—
30C11×C22⋊C8—42no—
31C22⋊(C11⋊C8)—42no—
32C4⋊(C11⋊C8)—42no—
33#7034—111nomaximal, Sylow
34C24×C11C4211yescharacteristic
35C22×C4×C11—22no—
36C22×C4×C11—21no—
37C22×C4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11—21no—
41C22×C4×C11—21no—
42C22×C4×C11—41no—
43C22×C4×C11—41no—
44C22×C4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11C22⋊C411yescharacteristic
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11C22⋊C411yescharacteristic
49C22×C4×C11C4⋊C411yescharacteristic
50C22×C4×C11C4⋊C411yescharacteristic
51C22×C4×C11C4⋊C411yescharacteristic
52C22×C4×C11C2×C812yes—
53C22×C4×C11M1612yes—
54C2×C8×C11—42no—
55C2×C8×C11—42no—
56C2×C8×C11—42no—
57C42×C11—22no—
58C42×C11—22no—
59C42×C11—41no—
60C42×C11—41no—
61#4318—44no—
62#4318—44no—
63C2×C11⋊C8—24no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8—42no—
66C2×C11⋊C8—42no—
67C2×C11⋊C8—42no—
68C2×C11⋊C8—42no—
69#1797—111no—
70#1797D1111yescharacteristic
71#1728—111no—
72C23×C11—21no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11#9511yescharacteristic
79C23×C11C4×C811yescharacteristic
80C23×C11#9711yescharacteristic
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
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—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11C22⋊C812yes—
102C2×C4×C11#9912yes—
103C2×C4×C11#10011yescharacteristic
104C2×C4×C11#10011yescharacteristic
105C2×C4×C11#10011yescharacteristic
106C2×C4×C11#10111yescharacteristic
107C2×C4×C11#10111yescharacteristic
108C2×C4×C11#10111yescharacteristic
109C2×C4×C11C4⋊C812yes—
110C8×C11—82no—
111C11⋊C8—44no—
112C11⋊C8—82no—
113C22×M16—112no—
114C22×C42C2×D1111yescharacteristic
115C2×C4⋊C8—21no—
116C2×C4⋊C8—221no—
117C2×C22⋊C8—112no—
118C2×C22⋊C8Dic1112yes—
119#336—21no—
120#336—221no—
121#336—221no—
122#336—221no—
123C22×C11—21no—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—41no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11#33611yescharacteristic
134C22×C11#34211yescharacteristic
135C22×C11#34311yescharacteristic
136C22×C11#34311yescharacteristic
137C22×C11#34311yescharacteristic
138C22×C11#34411yescharacteristic
139C22×C11#34411yescharacteristic
140C4×C11—22no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11#32312yes—
148C4×C11#32412yes—
149C23×C4C4×D1111yescharacteristic
150C23×C4C4×D1111yescharacteristic
151C23×C4C2×Dic1111yescharacteristic
152C2×M16—114no—
153C2×M16—222no—
154C2×M16—442no—
155C2×M16—442no—
156C22×C8—22no—
157C22×C8—222no—
158C22×C8—222no—
159C2×C42—42no—
160C2×C42Dic2211yescharacteristic
161C2×C42D4411yescharacteristic
162C2×C42C22⋊D1111yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C4⋊C8—42no—
165C4⋊C8—442no—
166C22⋊C8—42no—
167C22⋊C8—442no—
168C2×C11—41no—
169C2×C11—41no—
170C2×C11#128011yescharacteristic
171C2×C11#128311yescharacteristic
172C2×C11#128311yescharacteristic
173C2×C11#130511yescharacteristic
174C2×C11#130511yescharacteristic
175C2×C11#130711yescharacteristic
176C2×C11#130911yescharacteristic
177C24C4×Dic1111yescharacteristic
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4C8×D1112yes—
190C22×C4#431312yes—
191C22×C4Dic11⋊C411yescharacteristic
192C22×C4Dic11⋊C411yescharacteristic
193C22×C4C4⋊Dic1111yescharacteristic
194C22×C4(C2×D11)⋊C411yescharacteristic
195C22×C4(C2×D11)⋊C411yescharacteristic
196C22×C4C22⋊Dic1111yescharacteristic
197M16—444no—
198M16—444no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—42no—
202C2×C8—224no—
203C2×C8—442no—
204C2×C8—442no—
205C2×C8—442no—
206C2×C8—442no—
207C2×C8—442no—
208C42—22no—
209C42—22no—
210C42—41no—
211C42—41no—
212C11#703411yescharacteristic, complemented, Sylow
213C23—21no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23C8×Dic1111yescharacteristic
220C23#6687911yescharacteristic
221C23C11⋊#9511yescharacteristic
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4#6687012yes—
243C2×C4Dic11⋊C812yes—
244C2×C4(C2×D11)⋊C812yes—
245C2×C4#6688711yescharacteristic
246C2×C4#6688711yescharacteristic
247C2×C4#6688811yescharacteristic
248C2×C4#6688811yescharacteristic
249C2×C4#6689711yescharacteristic
250C2×C4#6690011yescharacteristic
251C8—82no—
252C8—444no—
253C8—882no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22#1062216511yescharacteristic
265C22#1062216811yescharacteristic
266C22#1062217111yescharacteristic
267C22#1062218811yescharacteristic
268C22#1062219211yescharacteristic
269C22#1062219211yescharacteristic
270C22#1062219411yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4#1062210612yes—
279C4#1062210712yes—
280C2—41no—
281C2—41no—
282C2#1306645811yescharacteristic
283C2#1306646511yescharacteristic
284C2#1306646611yescharacteristic
285C2#1306652211yescharacteristic
286C2#1306652311yescharacteristic
287C2#1306652611yescharacteristic
288C2C11⋊#130911yescharacteristic
subgroupG/H
centerC23C11⋊#95
commutatorC23×C11C4×C8
FrattiniC22×C42C2×D11
FittingC11×#1797C2
socleC23×C11#95
prime radicalC24×C11C42
cosocleC22×C42×C11C22
hypercenter#1797D11
hypocenterC11#7034
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
26. C2×#4318C8semidirect
212. C11#7034semidirect

Maximal subgroups

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

subgroupindex
#130685962
#130683102
C11×#17972
#703411