Finite Group Databasebeta

← #14664529

Subgroups — #14664529

Order 2816.

368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068699C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066646C214yesmaximal, complemented
4C11×#2628C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C11×#117C2211yescharacteristic
7C11×#400—21no—
8C11×#399—21no—
9C11×#395C2212yes—
10C11×#393C412yes—
11C11×#389—21no—
12C11×#382C411yescharacteristic
13C11×#380—21no—
14#10622820—21no—
15#10622539—21no—
16#10622168—21no—
17#10622168C2212yes—
18#10622166C2212yes—
19#10622163—21no—
20C22×Q8×C11C2×C412yes—
21C23×C4×C11D411yescharacteristic
22C11×C4⋊Q8—41no—
23C11×C4⋊Q8—41no—
24C11×#117—41no—
25C11×#117—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×#4318—22no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95C2×C412yes—
42C22⋊(C11⋊C8)—22no—
43C22⋊(C11⋊C8)—41no—
44C22⋊(C11⋊C8)—41no—
45C4⋊(C11⋊C8)—41no—
46#66867—41no—
47#11819—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C2×Q8×C11—42no—
50C2×Q8×C11—82no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—41no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—82no—
70C11×C22⋊C4—41no—
71C11×C22⋊C4—41no—
72C11×C22⋊C4—82no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77#4318—42no—
78#4318—42no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81#2628D1111yescharacteristic
82#1822—111no—
83#1464—111no—
84#1354—114no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—41no—
89C23×C11—41no—
90C23×C11C2×C22⋊C411yescharacteristic
91Q8×C11—84no—
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—21no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11#9911yescharacteristic
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#13712yes—
115C11⋊C8—82no—
116C11⋊C8—82no—
117C2×C4⋊Q8Dic1111yescharacteristic
118C2×#117C2×D1111yescharacteristic
119#432—221no—
120#407—221no—
121#400—21no—
122#399—21no—
123#395C2×D1112yes—
124#393Dic1112yes—
125#389—21no—
126#382Dic1111yescharacteristic
127#380—21no—
128#343—112no—
129#343—221no—
130#324—112no—
131#323—221no—
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—
149C4×C11—82no—
150C4×C11—82no—
151C22×Q8C2×Dic1112yes—
152C23×C4C22⋊D1111yescharacteristic
153C2×M16—222no—
154C4⋊Q8—41no—
155C4⋊Q8—41no—
156#117—41no—
157#117—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4C22⋊D1111yescharacteristic
163C2×C4⋊C4C22×D1111yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4C2×Dic1111yescharacteristic
166C2×C22⋊C4C22⋊D1111yescharacteristic
167C2×C42C2×Dic1111yescharacteristic
168C2×C42C22⋊D1111yescharacteristic
169C4⋊C8—441no—
170C22⋊C8—222no—
171C22⋊C8—441no—
172C22⋊C8—441no—
173#97—441no—
174#95—21no—
175#95—22no—
176#95—22no—
177#95C2×Dic1112yes—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11—81no—
181C2×C11#151111yescharacteristic
182C2×C11#212211yescharacteristic
183C2×C11#213511yescharacteristic
184C24C22⋊Dic1111yescharacteristic
185C2×Q8—42no—
186C2×Q8—82no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—41no—
193C22×C4C22⋊Dic1111yescharacteristic
194C22×C4C22⋊Dic1111yescharacteristic
195C22×C4C22⋊Dic1111yescharacteristic
196C22×C4C22×Dic1111yescharacteristic
197C22×C4C2×C22⋊D1111yescharacteristic
198C22×C4C2×C22⋊D1111yescharacteristic
199M16—442no—
200M16—442no—
201C2×C8—442no—
202C2×C8—442no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—82no—
210C22⋊C4—41no—
211C22⋊C4—41no—
212C22⋊C4—82no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C11#1181911yescharacteristic, complemented, Sylow
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×C22⋊Dic1111yescharacteristic
224Q8—84no—
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—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4#6689811yescharacteristic
246C2×C4#6689811yescharacteristic
247C2×C4#6699512yes—
248C8—882no—
249C8—882no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#6689811yescharacteristic
258C22#1062283811yescharacteristic
259C22#1062284911yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1306714911yescharacteristic
273C2#1307026611yescharacteristic
274C2#1307031111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2628C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2628D11
hypocenterC11#11819
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
3. #13066646C2semidirect
217. C11#11819semidirect

Maximal subgroups

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

subgroupindex
#130686992
#130669502
#130666462
C11×#26282
#1181911