Finite Group Databasebeta

← #46825787

Subgroups — #46825787

Order 34432.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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
1#31771577C211yesmaximal, characteristic
2#31771547C211yesmaximal, characteristic
3#31770567C211yesmaximal, characteristic
4C2×#16864411C412yescomplemented
5C2×C4⋊#11761640—21no—
6C2×C22⋊#11761640C412yes—
7#22575510—21no—
8#22575510—21no—
9(C2×#11761640)⋊C4—21no—
10C22×C4×D269C2211yescharacteristic
11C2×#16864385—21no—
12C22⋊#14524130C411yescharacteristic, complemented
13#22575365—21no—
14C22⋊C8×C269C411yescharacteristic, complemented
15C22×#11761640—22no—
16#16864411—42no—
17C2×#14524137—22no—
18C4⋊#11761640—42no—
19C22⋊#11761640—42no—
20C23×D269C2×C411yescharacteristic
21C22×Dic269C2×C411yescharacteristic
22C2×C4×D269—42no—
23C2×C4×D269D411yescharacteristic
24C2×C4×D269D411yescharacteristic
25C2×C4×D269D411yescharacteristic
26C2×C4×D269Q811yescharacteristic
27#16864385—42no—
28C2×#14524130—21no—
29C22×C4×C269C2×C411yescharacteristic
30C2×C8×C269—21no—
31C2×#11761640—42no—
32C2×#11761640—42no—
33C2×#11761640—42no—
34#14524137—42no—
35C22×D269—21no—
36C22×D269—21no—
37C22×D269—41no—
38C22×D269—41no—
39C22×D269C22⋊C411yescharacteristic
40C22×D269C4⋊C411yescharacteristic
41C2×Dic269—22no—
42C2×Dic269C22⋊C411yescharacteristic
43C2×Dic269C4⋊C411yescharacteristic
44C4×D269—22no—
45C4×D269—22no—
46C4×D269—41no—
47C4×D269—41no—
48#14524130—41no—
49C23×C269C4211yescharacteristic
50C2×C4×C269—41no—
51C2×C4×C269C22⋊C411yescharacteristic
52C2×C4×C269C4⋊C411yescharacteristic
53C8×C269—41no—
54C22×C269—21no—
55C22×C269—21no—
56C22×C269—21no—
57C22×C269#9511yescharacteristic
58C2×D269—21no—
59C2×D269—21no—
60C2×D269—21no—
61C2×D269—21no—
62C2×D269—21no—
63C2×D269—42no—
64C2×D269—42no—
65C2×D269#10011yescharacteristic
66C2×D269#10111yescharacteristic
67#11761640—82no—
68C4×C269—21no—
69C4×C269—21no—
70Dic269—21no—
71Dic269#9912yes—
72C2×C269—41no—
73C2×C269#34211yescharacteristic
74C2×C269#34311yescharacteristic
75C2×C269#34411yescharacteristic
76D269—21no—
77D269—21no—
78D269—41no—
79C269#130511yescharacteristic, complemented, Sylow
80#1305—2691nomaximal, Sylow
81#407—2691no—
82#407—2691no—
83#380—2691no—
84C23×C4—2691no—
85C2×M16—2692no—
86C2×M16—5381no—
87C2×C4⋊C4—5381no—
88C2×C22⋊C4—2692no—
89C22⋊C8—2691no—
90C22⋊C8—5381no—
91C22⋊C8—5381no—
92C22⋊C8—5381no—
93C22⋊C8#1176164011yescharacteristic, complemented
94#95—5381no—
95C24—2691no—
96C22×C4—2691no—
97C22×C4—2691no—
98C22×C4—2691no—
99C22×C4—2691no—
100C22×C4—2691no—
101C22×C4—5382no—
102C22×C4—10762no—
103C22×C4C2×#1176164011yescharacteristic
104M16—10762no—
105M16—10762no—
106C2×C8—21no—
107C2×C8—5382no—
108C2×C8—5381no—
109C4⋊C4—10762no—
110C22⋊C4—10762no—
111C23—2691no—
112C23—2691no—
113C23—5381no—
114C23—5381no—
115C23—10761no—
116C23—10761no—
117C23C4×#1176164011yescharacteristic
118C2×C4—41no—
119C2×C4—2691no—
120C2×C4—2691no—
121C2×C4—5382no—
122C2×C4—5382no—
123C2×C4—5382no—
124C2×C4—10761no—
125C2×C4—10761no—
126C2×C4—10762no—
127C2×C4—10762no—
128C2×C4—10762no—
129C2×C4C22⋊#1176164011yescharacteristic
130C2×C4C4⋊#1176164011yescharacteristic
131C8—41no—
132C8—10761no—
133C8—10762no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22—2691no—
138C22—2691no—
139C22—5381no—
140C22—5381no—
141C22—5381no—
142C22—5381no—
143C22—5381no—
144C22—10762no—
145C22—10762no—
146C22(C2×#11761640)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—2692no—
150C4—5381no—
151C4—21522no—
152C2—41no—
153C2—5381no—
154C2—5381no—
155C2—10761no—
156C2#3177148211yescharacteristic
157C2#3177148411yescharacteristic
158C2#3177148711yescharacteristic
subgroupG/H
centerC22(C2×#11761640)⋊C4
commutatorC23×C269C42
FrattiniC22×C4C2×#11761640
FittingC22⋊C8×C269C4
socleC22×C269#95
prime radicalC23×D269C2×C4
cosocleC22×C4×D269C22
hypercenterC22⋊C8#11761640
hypocenterC269#1305
LCSG ▷ C23×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#16864411C4semidirect
12. C22⋊#14524130C4semidirect
14. C22⋊C8×C269C4semidirect
79. C269#1305semidirect
93. C22⋊C8#11761640semidirect

Maximal subgroups

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

subgroupindex
#317715772
#317715472
#317705672
#1305269