Finite Group Databasebeta

← #46826117

Subgroups — #46826117

Order 34432.

264 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 76 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#31771622C212yesmaximal, complemented
2#31771451C212yesmaximal, complemented
3#31771448C212yesmaximal
4C2×#22575409C211yesmaximal, characteristic
5#22575520—22no—
6C22⋊#14524137C2214yes—
7C4×#14524137—22no—
8C23×Dic269C411yescharacteristic
9#22575409—22no—
10#22575409—22no—
11C2×#16864381C411yescharacteristic
12C2×#16864381C2211yescharacteristic
13C2×C22⋊Dic269C2211yescharacteristic
14C2×C4×Dic269C411yescharacteristic
15C2×C4×Dic269C2211yescharacteristic
16C2×C22⋊C4×C269C411yescharacteristic
17C2×#14524137—24no—
18C22×Dic269—21no—
19C22×Dic269—21no—
20C22×Dic269—22no—
21C22×Dic269C814yescomplemented
22C22×Dic269C2×C411yescharacteristic
23C22×Dic269C2×C411yescharacteristic
24C22×Dic269C2×C411yescharacteristic
25C22×Dic269C2311yescharacteristic
26#16864381—22no—
27#16864381—22no—
28C22⋊Dic269—22no—
29C4×Dic269—21no—
30C4×Dic269—21no—
31C4×Dic269D412yes—
32C4×Dic269D412yes—
33C24×C269C2×C411yescharacteristic
34C22×C4×C269C2×C411yescharacteristic
35C22×C4×C269C2×C411yescharacteristic
36C22⋊C4×C269—22no—
37#14524137—44no—
38C2×Dic269—21no—
39C2×Dic269—21no—
40C2×Dic269—24no—
41C2×Dic269—24no—
42C2×Dic269—21no—
43C2×Dic269—41no—
44C2×Dic269—41no—
45C2×Dic269C22⋊C411yescharacteristic
46C2×Dic269C22⋊C411yescharacteristic
47C2×Dic269C2×C812yes—
48C2×Dic269C2×C812yes—
49C2×Dic269M1612yes—
50C2×Dic269C2×D412yes—
51C23×C269—21no—
52C23×C269—21no—
53C23×C269—41no—
54C23×C269—41no—
55C23×C269C2×C812yes—
56C23×C269C22×C411yescharacteristic
57C2×C4×C269—21no—
58C2×C4×C269—41no—
59C2×C4×C269—41no—
60C2×C4×C269C22⋊C412yes—
61C22×C269—21no—
62C22×C269—21no—
63C22×C269—22no—
64C22×C269—42no—
65C22×C269—42no—
66C22×C269—41no—
67C22×C269—41no—
68C22×C269C2×C22⋊C411yescharacteristic
69C22×C269C22×C811yescharacteristic
70C22×C269C2×M1611yescharacteristic
71C4×C269—22no—
72C4×C269—41no—
73Dic269—22no—
74Dic269—22no—
75Dic269—41no—
76Dic269C22⋊C812yes—
77Dic269C22⋊C812yes—
78C2×C269—21no—
79C2×C269—21no—
80C2×C269—42no—
81C2×C269C2×C22⋊C811yescharacteristic
82C2×C269#41011yescharacteristic
83C2×C269#41311yescharacteristic
84C269#145811yescharacteristic, complemented, Sylow
85#1458—2691nomaximal, Sylow
86C2×#117—2691no—
87#431—2692no—
88#324—2692no—
89#323—2692no—
90C23×C4—2691no—
91#117—5382no—
92#117—5382no—
93C2×C4⋊C4—2691no—
94C2×C4⋊C4—2691no—
95C2×C22⋊C4—2691no—
96C2×C22⋊C4#1176164011yescharacteristic
97C2×C42—2691no—
98C2×C42—2691no—
99C4⋊C8—5382no—
100C22⋊C8—2694no—
101C4×C8—5382no—
102C24C2×#1176164011yescharacteristic
103C22×C4—2691no—
104C22×C4—2694no—
105C22×C4—2691no—
106C22×C4—2691no—
107C22×C4—2691no—
108C22×C4—5381no—
109C22×C4—5381no—
110C22×C4—5382no—
111C22×C4C2×#1176164011yescharacteristic
112C22×C4C2×#1176164011yescharacteristic
113C2×C8—5384no—
114C4⋊C4—5382no—
115C4⋊C4—5382no—
116C22⋊C4—22no—
117C22⋊C4—5382no—
118C42—2692no—
119C42—2692no—
120C42—5381no—
121C42—5381no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23D269⋊C812yes—
127C23C22×#1176164011yescharacteristic
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—2691no—
132C2×C4—2691no—
133C2×C4—2692no—
134C2×C4—2692no—
135C2×C4—2692no—
136C2×C4—2692no—
137C2×C4—5384no—
138C2×C4—5384no—
139C2×C4—5381no—
140C2×C4—5381no—
141C2×C4—5381no—
142C2×C4—10761no—
143C2×C4—10761no—
144C2×C4C22⋊#1176164012yes—
145C8—10764no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊#1176164011yescharacteristic
154C22C2×D269⋊C811yescharacteristic
155C22D269⋊M1611yescharacteristic
156C4—22no—
157C4—41no—
158C4—2692no—
159C4—2692no—
160C4—5382no—
161C4—5382no—
162C4—10761no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2D269⋊(C22⋊C8)11yescharacteristic
167C2#3177158511yescharacteristic
168C2#3177159211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11761640
commutatorC22×C269C22×C8
FrattiniC23C22×#11761640
FittingC2×C22⋊C4×C269C4
socleC22×C269C2×C22⋊C4
prime radicalC24×C269C2×C4
cosocleC22×Dic269C23
hypercenterC2×C22⋊C4#11761640
hypocenterC269#1458
LCSG ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #31771622C2semidirect
2. #31771451C2semidirect
21. C22×Dic269C8semidirect
84. C269#1458semidirect

Maximal subgroups

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

subgroupindex
#317716222
#317714512
#317714482
C2×#225754092
#1458269