Finite Group Databasebeta

← #13069882

Subgroups — #13069882

Order 1408.

256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C22×#4326C211yesmaximal, characteristic
2C2×C11×#101C211yesmaximal, characteristic
3#10622838C211yesmaximal, characteristic
4C2×#66888C211yesmaximal, characteristic
5#10622733C211yesmaximal, characteristic
6#10622732C211yesmaximal, characteristic
7#10622196C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C2×#4326—22no—
13C2×#4326—22no—
14C2×#4326—22no—
15#66979C2211yescharacteristic
16C2×#4318C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18C11×#101—22no—
19#66899—22no—
20#66888—22no—
21#66880—22no—
22Dic11⋊C8—22no—
23C2×Q8×C11—21no—
24C2×Q8×C11—21no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11D412yes—
29C22×C4×C11—21no—
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—21no—
32C2×Dic22—21no—
33C2×Dic22—21no—
34C2×Dic22—21no—
35C2×Dic22—21no—
36C2×Dic22—21no—
37C2×Dic22D412yes—
38C11×M16—21no—
39C11×M16—21no—
40C11×M16—21no—
41C11×M16—21no—
42C2×C8×C11—21no—
43C2×C8×C11—21no—
44C22⋊Dic11—21no—
45#4326—28no—
46C4⋊Dic11D412yes—
47C4×Dic11—21no—
48#4318—21no—
49#4318—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8—21no—
53C2×C11⋊C8D412yes—
54#2047—111nomaximal, Sylow
55C23×C11#4111yescharacteristic
56Q8×C11—22no—
57Q8×C11—22no—
58Q8×C11—41no—
59Q8×C11—41no—
60C2×C4×C11—22no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—41no—
72C2×Dic11—41no—
73Dic22—22no—
74Dic22—22no—
75Dic22—41no—
76Dic22—41no—
77C8×C11—41no—
78C8×C11—41no—
79C11⋊C8—22no—
80C11⋊C8—41no—
81C22×Q16—111no—
82#424—111no—
83#419—111no—
84#419—111no—
85C2×#101—111no—
86C2×#101D1111yescharacteristic
87#341—111no—
88C22×C11—22no—
89C22×C11#12111yescharacteristic
90C22×C11#12311yescharacteristic
91C22×C11#12311yescharacteristic
92C4×C11—42no—
93C4×C11#12011yescharacteristic
94C4×C11#12111yescharacteristic
95C4×C11#12111yescharacteristic
96C4×C11#12411yescharacteristic
97Dic11—42no—
98Dic11—42no—
99C22×Q8—111no—
100C22×Q8C2×D1111yescharacteristic
101C2×Q16—222no—
102C2×Q16—222no—
103C2×Q16—222no—
104C2×M16—111no—
105C2×M16C2×D1111yescharacteristic
106C2×M16C2×D1111yescharacteristic
107C22×C8—111no—
108#117—111no—
109C4⋊C8—222no—
110#103—222no—
111#103—222no—
112#101—22no—
113#101—222no—
114C2×C11—21no—
115C2×C11—21no—
116C2×C11#39411yescharacteristic
117C2×C11#47312yes—
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8—112no—
124C2×Q8—221no—
125C2×Q8—221no—
126C2×Q8—221no—
127C2×Q8—221no—
128C2×Q8—221no—
129C2×Q8C22⋊D1112yes—
130C22×C4—21no—
131C22×C4—221no—
132C22×C4C22×D1111yescharacteristic
133Q16—228no—
134M16—21no—
135M16—21no—
136M16—21no—
137M16—21no—
138M16—221no—
139M16—221no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—112no—
143C2×C8—221no—
144C2×C8—221no—
145C2×C8—221no—
146C4⋊C4—112no—
147C22⋊C4—221no—
148C42—221no—
149C11#204711yescharacteristic, complemented, Sylow
150C23#433911yescharacteristic
151Q8—22no—
152Q8—22no—
153Q8—41no—
154Q8—41no—
155Q8—222no—
156Q8—222no—
157Q8—441no—
158Q8—441no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4—441no—
165C2×C4—441no—
166C2×C4#433911yescharacteristic
167C2×C4D4×D1111yescharacteristic
168C2×C4D4×D1111yescharacteristic
169C2×C4D4×D1111yescharacteristic
170C2×C4#434111yescharacteristic
171C2×C4C2×C22⋊D1111yescharacteristic
172C8—41no—
173C8—41no—
174C8—222no—
175C8—441no—
176C22—22no—
177C22#6693611yescharacteristic
178C22#6693711yescharacteristic
179C22#6698211yescharacteristic
180C4—42no—
181C4—442no—
182C4—442no—
183C4#6693711yescharacteristic
184C4#6693811yescharacteristic
185C4#6699011yescharacteristic
186C4#6699211yescharacteristic
187C2—21no—
188C2—21no—
189C2#1062236812yes—
190C2#1062257211yescharacteristic
subgroupG/H
centerC22#66937
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#101C2
socleC22×C11#121
prime radicalC23×C11#41
hypercenterC2×#101D11
hypocenterC11#2047
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
149. C11#2047semidirect

Maximal subgroups

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

subgroupindex
C22×#43262
C2×C11×#1012
#106228382
C2×#668882
#106227332
#106227322
#106221962
#204711