Finite Group Databasebeta

← #14646781

Subgroups — #14646781

Order 2816.

388 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 119 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#13067379C211yesmaximal, characteristic, complemented
2#13067379C211yesmaximal, characteristic, complemented
3#13067251C212yesmaximal
4#13066527C212yesmaximal, complemented
5C11×#2931C211yesmaximal, characteristic
6C2×C11×#131C412yes—
7C11×#532C2211yescharacteristic
8C11×#436—21no—
9C11×#436—21no—
10C8×D4×C11—21no—
11C8×D4×C11—21no—
12C11×#423C2211yescharacteristic
13C11×#408C412yes—
14C2×C4×C8×C11C2211yescharacteristic
15#10622539C2212yes—
16#10622539C2212yes—
17#10622178—24no—
18#10622096—21no—
19#10622096—21no—
20#10622095—21no—
21#10622095—21no—
22C2×C11×#41C2×C412yes—
23C11×#131—44no—
24C2×C11×M16—22no—
25C2×C11×M16C2×C412yes—
26C22×C8×C11—22no—
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11C2×C411yescharacteristic
29C11×C4⋊Q8Q811yescharacteristic
30C11×#127Q811yescharacteristic
31C11×#124D412yes—
32C11×#121—21no—
33C11×#121—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C11×C4⋊C8—21no—
38C11×C4⋊C8—21no—
39C11×C22⋊C8—22no—
40C11×C22⋊C8—22no—
41C4×C8×C11D411yescharacteristic
42C4×C8×C11D411yescharacteristic
43C4×C8×C11D411yescharacteristic
44C4×C8×C11D411yescharacteristic
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—22no—
49#66867—22no—
50#66867—22no—
51#8634—111nomaximal, Sylow
52C11×#41—42no—
53C11×#41—42no—
54C2×Q8×C11C4⋊C412yes—
55C2×D4×C11—22no—
56C2×D4×C11—21no—
57C2×D4×C11—21no—
58C2×D4×C11C4⋊C412yes—
59C22×C4×C11—22no—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C11×M16—42no—
64C11×M16—44no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—41no—
68C2×C8×C11—44no—
69C2×C8×C11C22⋊C411yescharacteristic
70C2×C8×C11C22⋊C411yescharacteristic
71C2×C8×C11C22⋊C411yescharacteristic
72C2×C8×C11C22⋊C411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4—22no—
77C42×C11C2×D411yescharacteristic
78C42×C11C2×D411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11C2×Q811yescharacteristic
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83#2931D1111yescharacteristic
84#1568—111no—
85#1568—111no—
86#1536—112no—
87#1307—112no—
88C23×C11—22no—
89C23×C11#11711yescharacteristic
90Q8×C11—42no—
91D4×C11—42no—
92D4×C11—42no—
93D4×C11—42no—
94D4×C11—44no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11C2×C22⋊C411yescharacteristic
103C2×C4×C11C2×C4⋊C411yescharacteristic
104C2×C4×C11#12111yescharacteristic
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11C22⋊Q811yescharacteristic
107C2×C4×C11C22⋊Q811yescharacteristic
108C8×C11—21no—
109C8×C11—21no—
110C8×C11—21no—
111C8×C11—42no—
112C8×C11#10012yes—
113C11⋊C8—82no—
114C11⋊C8—82no—
115C2×#131Dic1112yes—
116#532C2×D1111yescharacteristic
117#436—21no—
118#436—21no—
119C8×D4—21no—
120C8×D4—21no—
121#432—112no—
122#432—112no—
123#423C2×D1111yescharacteristic
124#408Dic1112yes—
125C2×C4×C8C2×D1111yescharacteristic
126#335—221no—
127#335—221no—
128#334—221no—
129#334—221no—
130#329—224no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11#38011yescharacteristic
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—42no—
144C4×C11C2×#10011yescharacteristic
145C4×C11#41311yescharacteristic
146C2×#41C2×Dic1112yes—
147#131—44no—
148C2×M16—22no—
149C2×M16C2×Dic1112yes—
150C22×C8—22no—
151C22×C8C2×Dic1111yescharacteristic
152C22×C8C2×Dic1111yescharacteristic
153C4⋊Q8Dic2211yescharacteristic
154#127Dic2211yescharacteristic
155#124D4412yes—
156#121—21no—
157#121—21no—
158C4×D4—21no—
159C4×D4—21no—
160C2×C42C22×D1111yescharacteristic
161C4⋊C8—21no—
162C4⋊C8—21no—
163C4⋊C8—222no—
164C4⋊C8—222no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167C22⋊C8—222no—
168C22⋊C8—222no—
169#97—222no—
170#97—222no—
171C4×C8C22⋊D1111yescharacteristic
172C4×C8C22⋊D1111yescharacteristic
173C4×C8C22⋊D1111yescharacteristic
174C4×C8C22⋊D1111yescharacteristic
175C2×C11—41no—
176C2×C11—82no—
177C2×C11#180011yescharacteristic
178C2×C11#181411yescharacteristic
179C2×C11#181411yescharacteristic
180#41—42no—
181#41—42no—
182C2×Q8C4⋊Dic1112yes—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4C4⋊Dic1112yes—
187C22×C4—22no—
188C22×C4#433911yescharacteristic
189C22×C4#433911yescharacteristic
190C22×C4C22×Dic1111yescharacteristic
191M16—44no—
192M16—42no—
193C2×C8—22no—
194C2×C8—22no—
195C2×C8—41no—
196C2×C8—44no—
197C2×C8—442no—
198C2×C8—442no—
199C2×C8C22⋊Dic1111yescharacteristic
200C2×C8C22⋊Dic1111yescharacteristic
201C2×C8C22⋊Dic1111yescharacteristic
202C2×C8C22⋊Dic1111yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—21no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C42C2×Dic2211yescharacteristic
208C42C2×D4411yescharacteristic
209C42C2×C22⋊D1111yescharacteristic
210C42C2×C22⋊D1111yescharacteristic
211C11#863411yescharacteristic, complemented, Sylow
212C23—22no—
213C23#6697911yescharacteristic
214Q8—42no—
215D4—42no—
216D4—42no—
217D4—42no—
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4#6697711yescharacteristic
227C2×C4#6697711yescharacteristic
228C2×C4C2×C4⋊Dic1111yescharacteristic
229C2×C4#6698311yescharacteristic
230C2×C4#6698311yescharacteristic
231C2×C4C2×C22⋊Dic1111yescharacteristic
232C8—21no—
233C8—21no—
234C8—21no—
235C8—42no—
236C8—882no—
237C8—882no—
238C8#6689712yes—
239C22—21no—
240C22—21no—
241C22—21no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22#1062282511yescharacteristic
246C4—21no—
247C4—21no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4C2×#6689711yescharacteristic
253C4#1062285011yescharacteristic
254C2—41no—
255C2—82no—
256C2#1306860811yescharacteristic
257C2#1306867011yescharacteristic
258C2#1306867011yescharacteristic
subgroupG/H
centerC22#10622825
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2931C2
socleC22×C11#380
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#2931D11
hypocenterC11#8634
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. #13067379C2semidirect
2. #13067379C2semidirect
4. #13066527C2semidirect
211. C11#8634semidirect

Maximal subgroups

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

subgroupindex
#130673792
#130672512
#130665272
C11×#29312
#863411