Finite Group Databasebeta

← #13079507

Subgroups — #13079507

Order 1408.

378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C11×#536C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic
3#10622847C211yesmaximal, characteristic
4#10622841C212yesmaximal, complemented
5#10622665C212yesmaximal, complemented
6#10622664C212yesmaximal, complemented
7#10622663C212yesmaximal, complemented
8#10622658C212yesmaximal, complemented
9#10622609C212yesmaximal, complemented
10C2×C11×#41C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C11×C4⋊Q8—21no—
14C11×#124—21no—
15C11×#123—21no—
16C11×#123—21no—
17C11×C22⋊Q8C2212yes—
18C11×C22⋊Q8C2212yes—
19C11×#117C2211yescharacteristic
20#66997—21no—
21C2×#4326C2212yes—
22C2×#4326C2212yes—
23#66989—21no—
24#66988—21no—
25#66988—21no—
26#66979C2211yescharacteristic
27#66977C2212yes—
28#66977C2212yes—
29C2×#4318C2211yescharacteristic
30C22×C11⋊C8C2211yescharacteristic
31#66899C2212yes—
32#66899C2212yes—
33C22⋊(C11⋊C8)C2212yes—
34C22⋊(C11⋊C8)C2212yes—
35#66874C2212yes—
36#66874C2212yes—
37#66872C2212yes—
38#66871C2212yes—
39C11×#41—41no—
40C11×#41—41no—
41C2×Q8×C11—21no—
42C2×Q8×C11—41no—
43C2×Q8×C11—41no—
44C2×Q8×C11D411yescharacteristic
45C2×Q8×C11C2312yes—
46C2×D4×C11D411yescharacteristic
47C2×D4×C11D411yescharacteristic
48C2×D4×C11D411yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11C2311yescharacteristic
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×Dic11—21no—
54C2×Dic22—21no—
55C2×Dic22—41no—
56C2×Dic22—41no—
57C2×Dic22C2312yes—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4C2312yes—
61C11×C22⋊C4—21no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—22no—
64C42×C11—21no—
65C22⋊Dic11—22no—
66C22⋊Dic11—22no—
67C22⋊Dic11—21no—
68#4326—42no—
69#4326—42no—
70C4⋊Dic11C2312yes—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73C4×Dic11—21no—
74#4318—41no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8C2312yes—
77C2×C11⋊C8C2312yes—
78#3202—111nomaximal, Sylow
79C23×C11C2×D411yescharacteristic
80C23×C11C2×D411yescharacteristic
81C23×C11C2×D411yescharacteristic
82Q8×C11—22no—
83Q8×C11—22no—
84Q8×C11—41no—
85Q8×C11—42no—
86D4×C11—41no—
87D4×C11—41no—
88D4×C11—41no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—42no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2411yescharacteristic
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—42no—
105Dic22—22no—
106Dic22—22no—
107Dic22—42no—
108C11⋊C8—22no—
109C11⋊C8—22no—
110#536—111no—
111#536D1111yescharacteristic
112#485—112no—
113#485—112no—
114#470—112no—
115#467—112no—
116#451—112no—
117#451—112no—
118#408—111no—
119C22×C11—21no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11C22×D411yescharacteristic
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—42no—
130C4×C11—42no—
131C4×C11H(5,𝔽2)11yescharacteristic
132C4×C11H(5,𝔽2)11yescharacteristic
133Dic11—42no—
134Dic11—42no—
135C2×#41C2×D1111yescharacteristic
136C22×Q8—111no—
137C22×Q8C2×D1111yescharacteristic
138C2×Q16—112no—
139C2×Q16—112no—
140C2×M16—111no—
141C22×C8—111no—
142C4⋊Q8—21no—
143C4⋊Q8—221no—
144#124—21no—
145#124—221no—
146#123—21no—
147#123—21no—
148#123—221no—
149#123—221no—
150C22⋊Q8—112no—
151C22⋊Q8—112no—
152C22⋊Q8C2×D1112yes—
153C22⋊Q8C2×D1112yes—
154#117—111no—
155#117C2×D1111yescharacteristic
156#107—112no—
157#106—112no—
158#103—112no—
159#103—112no—
160#103—112no—
161#103—112no—
162C22⋊C8—112no—
163C22⋊C8—112no—
164C2×C11—41no—
165C2×C11—41no—
166C2×C11—41no—
167C2×C11#53411yescharacteristic
168C2×C11#57812yes—
169#41—41no—
170#41—41no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—112no—
175C2×Q8—221no—
176C2×Q8—441no—
177C2×Q8—441no—
178C2×Q8C22⋊D1111yescharacteristic
179C2×Q8C22×D1112yes—
180C2×D4C22⋊D1111yescharacteristic
181C2×D4C22⋊D1111yescharacteristic
182C2×D4C22⋊D1111yescharacteristic
183C22×C4—21no—
184C22×C4—221no—
185C22×C4C22×D1111yescharacteristic
186C22×C4C22×D1111yescharacteristic
187C22×C4C22×D1111yescharacteristic
188Q16—442no—
189Q16—442no—
190M16—441no—
191C2×C8—112no—
192C2×C8—112no—
193C2×C8—441no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—112no—
197C4⋊C4—222no—
198C4⋊C4—222no—
199C4⋊C4C22×D1112yes—
200C22⋊C4—21no—
201C22⋊C4—22no—
202C22⋊C4—22no—
203C22⋊C4—221no—
204C22⋊C4—222no—
205C22⋊C4—222no—
206C42—21no—
207C42—221no—
208C11#320211yescharacteristic, complemented, Sylow
209C23C2×C22⋊D1111yescharacteristic
210C23C2×C22⋊D1111yescharacteristic
211C23C2×C22⋊D1111yescharacteristic
212Q8—22no—
213Q8—22no—
214Q8—41no—
215Q8—42no—
216Q8—222no—
217Q8—222no—
218Q8—442no—
219D4—41no—
220D4—41no—
221D4—41no—
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—42no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—442no—
234C2×C4C2×C22⋊D1111yescharacteristic
235C2×C4C2×C22⋊D1111yescharacteristic
236C2×C4C2×C22⋊D1111yescharacteristic
237C2×C4C23×D1111yescharacteristic
238C8—222no—
239C8—222no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22C22×C22⋊D1111yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—442no—
253C4—442no—
254C4#6703711yescharacteristic
255C4#6703711yescharacteristic
256C2—41no—
257C2—41no—
258C2—41no—
259C2#1062333511yescharacteristic
260C2#1062336912yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#536C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#536D11
hypocenterC11#3202
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
4. #10622841C2semidirect
5. #10622665C2semidirect
6. #10622664C2semidirect
7. #10622663C2semidirect
8. #10622658C2semidirect
9. #10622609C2semidirect
208. C11#3202semidirect

Maximal subgroups

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

subgroupindex
C11×#5362
#106233562
#106228472
#106228412
#106226652
#106226642
#106226632
#106226582
#106226092
#320211