Finite Group Databasebeta

← #13080899

Subgroups — #13080899

Order 1408.

374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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
1D4×Q8×C11C211yesmaximal, characteristic
2#10623073C211yesmaximal, characteristic
3#10622841C212yesmaximal, complemented
4#10622838C212yesmaximal, complemented
5#10622703C211yesmaximal, characteristic, complemented
6#10622694C211yesmaximal, characteristic, complemented
7#10622665C212yesmaximal, complemented
8#10622658C212yesmaximal, complemented
9C4×#4326C211yesmaximal, characteristic, complemented
10#10622633C211yesmaximal, characteristic, complemented
11#10622625C211yesmaximal, characteristic
12C22×Q8×C11C2212yes—
13C11×C4⋊Q8—21no—
14C11×C4⋊Q8C2211yescharacteristic
15C11×C22⋊Q8—22no—
16C11×C22⋊Q8C2212yes—
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11—21no—
19C4×D4×C11C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C2×#4326C2212yes—
22#66989—21no—
23#66979C2212yes—
24#66977C2212yes—
25C2×#4318C2212yes—
26#66940—21no—
27#66932—22no—
28#66922C2211yescharacteristic
29C4×Dic22C2211yescharacteristic
30#66899C2211yescharacteristic
31#66899C2212yes—
32#66899C2212yes—
33#66899C2212yes—
34#66899C2212yes—
35C22⋊(C11⋊C8)C2212yes—
36#66874C2211yescharacteristic
37#66872C2212yes—
38#66871C2211yescharacteristic
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—24no—
43C2×Q8×C11—42no—
44C2×Q8×C11C2312yes—
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11D411yescharacteristic
47C22×C4×C11—22no—
48C22×C4×C11C2312yes—
49C2×Dic22—21no—
50C2×Dic22C2311yescharacteristic
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4D411yescharacteristic
56C11×C4⋊C4C2311yescharacteristic
57C11×C22⋊C4—22no—
58C11×C22⋊C4D412yes—
59C42×C11—21no—
60C42×C11C2311yescharacteristic
61C22⋊Dic11—22no—
62C22⋊Dic11—22no—
63#4326—22no—
64#4326—42no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2312yes—
68Dic11⋊C4—21no—
69Dic11⋊C4—22no—
70C4×Dic11—21no—
71C4×Dic11—22no—
72#4318—42no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76#3328—111nomaximal, Sylow
77C23×C11C2×D412yes—
78Q8×C11—21no—
79Q8×C11—22no—
80Q8×C11—22no—
81Q8×C11—44no—
82Q8×C11#4112yes—
83D4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—44no—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2411yescharacteristic
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97Dic22—21no—
98Dic22—21no—
99Dic22—42no—
100C11⋊C8—21no—
101C11⋊C8—21no—
102C11⋊C8—22no—
103#556—111no—
104D4×Q8D1111yescharacteristic
105#487—111no—
106#485—112no—
107#475—111no—
108#470—112no—
109#462—111no—
110#451—112no—
111C4×Q16—111no—
112#436—111no—
113#419—112no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—22no—
117C22×C11C22×D411yescharacteristic
118C4×C11—22no—
119C4×C11—22no—
120C4×C11—21no—
121C4×C11—42no—
122C4×C11—41no—
123C4×C11#13712yes—
124C4×C11C2×#4111yescharacteristic
125C4×C11H(5,𝔽2)11yescharacteristic
126Dic11—41no—
127Dic11—42no—
128Dic11—41no—
129C22×Q8C2×D1112yes—
130C2×Q16—111no—
131C2×Q16—112no—
132C2×M16—112no—
133C4⋊Q8—21no—
134C4⋊Q8—111no—
135C4⋊Q8C2×D1111yescharacteristic
136#126—222no—
137#124—221no—
138C22⋊Q8—22no—
139C22⋊Q8—112no—
140C22⋊Q8C2×D1112yes—
141C4×Q8—111no—
142C4×Q8—221no—
143C4×Q8C2×D1111yescharacteristic
144C4×D4—21no—
145C4×D4C2×D1111yescharacteristic
146#117—112no—
147#107—111no—
148#106—112no—
149C4⋊C8—111no—
150#103—111no—
151#103—112no—
152#103—112no—
153#103—112no—
154#103—112no—
155#103—111no—
156C22⋊C8—112no—
157C4×C8—111no—
158C2×C11—42no—
159C2×C11#54611yescharacteristic
160C2×C11C2×#13711yescharacteristic
161C2×C11#57811yescharacteristic
162C2×Q8—22no—
163C2×Q8—24no—
164C2×Q8—42no—
165C2×Q8—111no—
166C2×Q8—221no—
167C2×Q8C22×D1112yes—
168C2×Q8C22×D1111yescharacteristic
169C2×D4C22⋊D1111yescharacteristic
170C22×C4—22no—
171C22×C4C22×D1112yes—
172Q16—222no—
173Q16—442no—
174M16—442no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8—112no—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—22no—
182C4⋊C4—112no—
183C4⋊C4—111no—
184C4⋊C4—221no—
185C4⋊C4—222no—
186C4⋊C4—221no—
187C4⋊C4C22⋊D1111yescharacteristic
188C4⋊C4C22×D1111yescharacteristic
189C22⋊C4—22no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C22⋊C4C22⋊D1112yes—
193C42—21no—
194C42—222no—
195C42—221no—
196C42C22×D1111yescharacteristic
197C11#332811yescharacteristic, complemented, Sylow
198C23C2×C22⋊D1112yes—
199Q8—21no—
200Q8—22no—
201Q8—22no—
202Q8—44no—
203Q8—221no—
204Q8—221no—
205Q8—442no—
206Q8#434112yes—
207D4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—44no—
214C2×C4—221no—
215C2×C4—222no—
216C2×C4—221no—
217C2×C4C2×C22⋊D1112yes—
218C2×C4C2×C22⋊D1111yescharacteristic
219C2×C4C2×C22⋊D1111yescharacteristic
220C2×C4C23×D1111yescharacteristic
221C8—221no—
222C8—221no—
223C8—222no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22C22×C22⋊D1111yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—42no—
232C4—41no—
233C4—441no—
234C4—442no—
235C4—441no—
236C4#6699512yes—
237C4C2×#434111yescharacteristic
238C4#6703711yescharacteristic
239C2—42no—
240C2#1062333711yescharacteristic
241C2C2×#6699511yescharacteristic
242C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingD4×Q8×C11C2
socleC22×C11C22×D4
prime radicalC2×D4×C11D4
hypercenterD4×Q8D11
hypocenterC11#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
3. #10622841C2semidirect
4. #10622838C2semidirect
5. #10622703C2semidirect
6. #10622694C2semidirect
7. #10622665C2semidirect
8. #10622658C2semidirect
9. C4×#4326C2semidirect
10. #10622633C2semidirect
197. C11#3328semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C112
#106230732
#106228412
#106228382
#106227032
#106226942
#106226652
#106226582
C4×#43262
#106226332
#106226252
#332811