Finite Group Databasebeta

← #13069765

Subgroups — #13069765

Order 1408.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#66943C211yesmaximal, characteristic
2C2×C11×#103C211yesmaximal, characteristic
3#10622843C211yesmaximal, characteristic
4C2×#66899C211yesmaximal, characteristic
5#10622189C211yesmaximal, characteristic
6#10622188C211yesmaximal, characteristic
7#10622167C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11—21no—
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×Dic11⋊C4—21no—
15C2×C4×Dic11C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17#66943—22no—
18#66943—22no—
19C11×#103—22no—
20#66899—22no—
21C11⋊#95—21no—
22C11⋊#95—21no—
23C2×Q8×C11—21no—
24C2×Q8×C11—21no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11Q812yes—
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—21no—
33C22×Dic11—21no—
34C22×Dic11D411yescharacteristic
35C22×Dic11D411yescharacteristic
36C2×C8×C11—21no—
37C2×C8×C11—21no—
38C2×C8×C11—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4D412yes—
41C4⋊Dic11—24no—
42C4⋊Dic11—21no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11D412yes—
46Dic11⋊C4—24no—
47C4×Dic11—21no—
48C4×Dic11—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8—21no—
52#2026—111nomaximal, Sylow
53C23×C11C2×D411yescharacteristic
54Q8×C11—22no—
55Q8×C11—22no—
56Q8×C11—41no—
57Q8×C11—41no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×Q811yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×Dic11—21no—
71C2×Dic11—21no—
72C2×Dic11—22no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80C2×Dic11—41no—
81C2×Dic11—41no—
82C8×C11—41no—
83C11⋊C8—41no—
84C2×#125—111no—
85C2×#103—111no—
86C2×#103D1111yescharacteristic
87#391—111no—
88#340—111no—
89#340—111no—
90#336—111no—
91C22×C11#12011yescharacteristic
92C22×C11C22⋊Q811yescharacteristic
93C22×C11#12411yescharacteristic
94C22×C11#13511yescharacteristic
95C22×C11#13511yescharacteristic
96C22×C11#13711yescharacteristic
97C22×C11#13711yescharacteristic
98C4×C11—42no—
99C4×C11—42no—
100C4×C11C22⋊Q811yescharacteristic
101C4×C11C22⋊Q811yescharacteristic
102C4×C11#12411yescharacteristic
103C4×C11#12411yescharacteristic
104Dic11—41no—
105Dic11—41no—
106Dic11—42no—
107Dic11—81no—
108C22×Q8C2×D1111yescharacteristic
109C22×C8—111no—
110C22×C8C2×D1111yescharacteristic
111#125—222no—
112#125—222no—
113C2×C4⋊C4—111no—
114C2×C4⋊C4—111no—
115C2×C4⋊C4—221no—
116C2×C4⋊C4—221no—
117C2×C4⋊C4C2×D1111yescharacteristic
118C2×C42—111no—
119#103—22no—
120#103—222no—
121#95—221no—
122#95—221no—
123C2×C11#39311yescharacteristic
124C2×C11#45211yescharacteristic
125C2×C11#45211yescharacteristic
126C2×C11#47911yescharacteristic
127C2×C11#47911yescharacteristic
128C2×C11#48811yescharacteristic
129C2×C11#49111yescharacteristic
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8Dic2212yes—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—111no—
139C22×C4—111no—
140C22×C4—221no—
141C22×C4—221no—
142C22×C4C22×D1111yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—221no—
147C2×C8—221no—
148C2×C8—221no—
149C4⋊C4—21no—
150C4⋊C4—112no—
151C4⋊C4—224no—
152C4⋊C4—224no—
153C4⋊C4—221no—
154C4⋊C4—221no—
155C4⋊C4—221no—
156C4⋊C4C22⋊D1112yes—
157C42—221no—
158C42—221no—
159C11#202611yescharacteristic, complemented, Sylow
160C23D4×D1111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—221no—
172C2×C4—221no—
173C2×C4—221no—
174C2×C4—221no—
175C2×C4—221no—
176C2×C4—221no—
177C2×C4—222no—
178C2×C4—441no—
179C2×C4—441no—
180C2×C4—441no—
181C2×C4—441no—
182C2×C4—441no—
183C2×C4C2×Dic2211yescharacteristic
184C2×C4#433911yescharacteristic
185C2×C4D4×D1111yescharacteristic
186C2×C4#434111yescharacteristic
187C2×C4#434111yescharacteristic
188C2×C4C2×C22⋊D1111yescharacteristic
189C8—41no—
190C8—441no—
191C22#6693111yescharacteristic
192C22#6693811yescharacteristic
193C22#6696811yescharacteristic
194C22#6696911yescharacteristic
195C22#6697111yescharacteristic
196C22#6697211yescharacteristic
197C22#6699011yescharacteristic
198C4—42no—
199C4—42no—
200C4—441no—
201C4—441no—
202C4—442no—
203C4—881no—
204C4#6693111yescharacteristic
205C4#6693811yescharacteristic
206C4#6697711yescharacteristic
207C4#6698911yescharacteristic
208C2#1062240911yescharacteristic
209C2#1062241011yescharacteristic
210C2#1062241211yescharacteristic
211C2#1062241311yescharacteristic
212C2#1062256011yescharacteristic
213C2#1062278611yescharacteristic
214C2#1062280011yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#103C2
socle, prime radicalC23×C11C2×D4
hypercenterC2×#103D11
hypocenterC11#2026
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
159. C11#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×C11×#1032
#106228432
C2×#668992
#106221892
#106221882
#106221672
#202611