Finite Group Databasebeta

← #13069756

Subgroups — #13069756

Order 1408.

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

normal subgroups only

This group has 290 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
1C2×#66941C211yesmaximal, characteristic
2C2×#66880C211yesmaximal, characteristic
3#10622587C211yesmaximal, characteristic
4C2×#66874C211yesmaximal, characteristic
5C11×#340C211yesmaximal, characteristic
6#10622188C211yesmaximal, characteristic
7#10622167C211yesmaximal, characteristic
8C22×Dic22—21no—
9C22×Dic22C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×Dic11⋊C4—21no—
15C2×C4×Dic11C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17#66941—22no—
18#66941—22no—
19C11⋊#95—21no—
20C11⋊#95—21no—
21#66880—22no—
22#66874—22no—
23C22×C4×C11—21no—
24C22×C4×C11—21no—
25C22×C4×C11C2311yescharacteristic
26C22×Dic11—21no—
27C22×Dic11—21no—
28C22×Dic11D411yescharacteristic
29C22×Dic11D411yescharacteristic
30C2×Dic22—24no—
31C2×Dic22—21no—
32C2×Dic22—21no—
33C2×Dic22—21no—
34C2×Dic22—21no—
35C2×Dic22—21no—
36C2×Dic22—42no—
37C2×Dic22—42no—
38C2×Dic22Q812yescomplemented
39C2×C8×C11—21no—
40C2×C8×C11—21no—
41C2×C8×C11—21no—
42C11×C4⋊C4—21no—
43C11×C4⋊C4—21no—
44C11×C4⋊C4—21no—
45C11×C4⋊C4D412yes—
46C4⋊Dic11—21no—
47C4⋊Dic11D412yes—
48Dic11⋊C4—24no—
49C4×Dic11—21no—
50C4×Dic11—21no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8—21no—
53C2×C11⋊C8—21no—
54#2024—111nomaximal, Sylow
55C23×C11C2×D411yescharacteristic
56C2×C4×C11—22no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11C2×D411yescharacteristic
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×Q811yescharacteristic
65C2×C4×C11#4111yescharacteristic
66C2×C4×C11#4111yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×Dic11—21no—
69C2×Dic11—21no—
70C2×Dic11—21no—
71C2×Dic11—21no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—41no—
75C2×Dic11—41no—
76C2×Dic11—41no—
77C2×Dic11—41no—
78C2×Dic11SD1612yes—
79C2×Dic11Q1612yes—
80Dic22—22no—
81Dic22—22no—
82Dic22—48no—
83Dic22—41no—
84Dic22—41no—
85C8×C11—41no—
86C11⋊C8—41no—
87C2×C4⋊Q8—111no—
88C2×#103—111no—
89C2×#103—111no—
90#391—111no—
91#340—111no—
92#340D1111yescharacteristic
93#336—111no—
94C22×C11#12011yescharacteristic
95C22×C11C22⋊Q811yescharacteristic
96C22×C11#12411yescharacteristic
97C22×C11C2×SD1611yescharacteristic
98C22×C11C2×Q1611yescharacteristic
99C22×C11AGL(1,ℤ/8)11yescharacteristic
100C22×C11#13711yescharacteristic
101C4×C11—42no—
102C4×C11—81no—
103C4×C11C22⋊Q811yescharacteristic
104C4×C11C22⋊Q811yescharacteristic
105C4×C11#12411yescharacteristic
106C4×C11#12411yescharacteristic
107Dic11—22no—
108Dic11—22no—
109Dic11—42no—
110Dic11—42no—
111C22×Q8—111no—
112C22×Q8—221no—
113C22×C8—111no—
114C22×C8C2×D1111yescharacteristic
115C4⋊Q8—222no—
116C4⋊Q8—222no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—221no—
119C2×C4⋊C4C2×D1111yescharacteristic
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C42—111no—
122#103—222no—
123#103—222no—
124#95—221no—
125#95—221no—
126C2×C11#39311yescharacteristic
127C2×C11#45011yescharacteristic
128C2×C11#45111yescharacteristic
129C2×C11#47511yescharacteristic
130C2×C11#47711yescharacteristic
131C2×C11#48711yescharacteristic
132C2×C11#48911yescharacteristic
133C2×Q8—112no—
134C2×Q8—224no—
135C2×Q8—221no—
136C2×Q8—221no—
137C2×Q8—221no—
138C2×Q8—221no—
139C2×Q8—221no—
140C2×Q8—442no—
141C2×Q8—442no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—111no—
145C22×C4—111no—
146C22×C4—221no—
147C22×C4—221no—
148C22×C4C22×D1111yescharacteristic
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—221no—
153C2×C8—221no—
154C2×C8—221no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—112no—
159C4⋊C4—224no—
160C4⋊C4—221no—
161C4⋊C4D4412yes—
162C42—221no—
163C42—221no—
164C11#202411yescharacteristic, complemented, Sylow
165C23D4×D1111yescharacteristic
166Q8—222no—
167Q8—222no—
168Q8—448no—
169Q8—441no—
170Q8—441no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—112no—
178C2×C4—112no—
179C2×C4—221no—
180C2×C4—221no—
181C2×C4—221no—
182C2×C4—221no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—441no—
186C2×C4—441no—
187C2×C4—441no—
188C2×C4—441no—
189C2×C4C2×D4411yescharacteristic
190C2×C4#433911yescharacteristic
191C2×C4#433911yescharacteristic
192C2×C4D4×D1111yescharacteristic
193C2×C4#434111yescharacteristic
194C2×C4Q8×D1111yescharacteristic
195C8—41no—
196C8—441no—
197C22#6693511yescharacteristic
198C22#6693811yescharacteristic
199C22#6694911yescharacteristic
200C22#6696411yescharacteristic
201C22SD16×D1111yescharacteristic
202C22#6696811yescharacteristic
203C22Q16×D1111yescharacteristic
204C4—42no—
205C4—81no—
206C4—222no—
207C4—222no—
208C4—442no—
209C4—442no—
210C4#6692811yescharacteristic
211C4#6693811yescharacteristic
212C4#6694911yescharacteristic
213C4#6695011yescharacteristic
214C2#1062228611yescharacteristic
215C2#1062237811yescharacteristic
216C2#1062238911yescharacteristic
217C2#1062240511yescharacteristic
218C2#1062242111yescharacteristic
219C2#1062246711yescharacteristic
220C2#1062248811yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socle, prime radicalC23×C11C2×D4
hypercenter#340D11
hypocenterC11#2024
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
38. C2×Dic22Q8semidirect
164. C11#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C2×#668802
#106225872
C2×#668742
C11×#3402
#106221882
#106221672
#202411