Finite Group Databasebeta

← #46825785

Subgroups — #46825785

Order 34432.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#31771576C211yesmaximal, characteristic
2#31771547C211yesmaximal, characteristic
3#31770568C211yesmaximal, characteristic
4C2×#16864412—21no—
5C2×C4⋊#11761640—21no—
6C2×C22⋊#11761640C412yes—
7#22575510—21no—
8C22⋊#14524137C412yescomplemented
9(C2×#11761640)⋊C4—21no—
10C22×C4×D269C2211yescharacteristic
11C2×#16864386C411yescharacteristic, complemented
12#22575365—21no—
13#22575365—21no—
14C2×M16×C269C411yescharacteristic, complemented
15C22×#11761640—22no—
16#16864412—41no—
17#16864412—41no—
18C2×#14524137—22no—
19C4⋊#11761640—41no—
20C4⋊#11761640—41no—
21C22⋊#11761640—42no—
22C23×D269C2×C411yescharacteristic
23C22×Dic269C2×C411yescharacteristic
24C2×C4×D269—41no—
25C2×C4×D269—41no—
26C2×C4×D269D411yescharacteristic
27C2×C4×D269D411yescharacteristic
28C2×C4×D269D411yescharacteristic
29C2×C4×D269Q811yescharacteristic
30#16864386—41no—
31C2×#14524130—21no—
32C22×C4×C269C2×C411yescharacteristic
33M16×C269—41no—
34C2×C8×C269—21no—
35C2×#11761640—42no—
36C2×#11761640—42no—
37C2×#11761640—42no—
38#14524137—42no—
39C22×D269—21no—
40C22×D269—21no—
41C22×D269—41no—
42C22×D269—41no—
43C22×D269C22⋊C411yescharacteristic
44C22×D269C4⋊C411yescharacteristic
45C2×Dic269—41no—
46C2×Dic269C22⋊C411yescharacteristic
47C2×Dic269C4⋊C411yescharacteristic
48C4×D269—21no—
49C4×D269—21no—
50C4×D269—21no—
51C4×D269—21no—
52C4×D269—41no—
53C4×D269—41no—
54#14524130—41no—
55C23×C269C4211yescharacteristic
56C2×C4×C269—21no—
57C2×C4×C269—21no—
58C2×C4×C269C22⋊C411yescharacteristic
59C2×C4×C269C4⋊C411yescharacteristic
60C8×C269—41no—
61C22×C269—21no—
62C22×C269—21no—
63C22×C269—21no—
64C22×C269#9511yescharacteristic
65C2×D269—21no—
66C2×D269—21no—
67C2×D269—21no—
68C2×D269—21no—
69C2×D269—21no—
70C2×D269—42no—
71C2×D269—42no—
72C2×D269#10011yescharacteristic
73C2×D269#10111yescharacteristic
74#11761640—82no—
75C4×C269—21no—
76C4×C269#9911yescharacteristic
77C4×C269#9911yescharacteristic
78Dic269—21no—
79Dic269—21no—
80C2×C269—41no—
81C2×C269#34211yescharacteristic
82C2×C269#34311yescharacteristic
83C2×C269#34411yescharacteristic
84D269—21no—
85D269—21no—
86D269—41no—
87C269#130511yescharacteristic, complemented, Sylow
88#1305—2691nomaximal, Sylow
89#407—2691no—
90#407—2691no—
91#380—2691no—
92C23×C4—2691no—
93C2×M16—2691no—
94C2×M16—5381no—
95C2×M16#1176164011yescharacteristic, complemented
96C2×C4⋊C4—5381no—
97C2×C22⋊C4—2692no—
98C22⋊C8—2692no—
99C22⋊C8—5381no—
100C22⋊C8—5381no—
101C22⋊C8—5381no—
102#95—5381no—
103C24—2691no—
104C22×C4—2691no—
105C22×C4—2691no—
106C22×C4—2691no—
107C22×C4—2691no—
108C22×C4—2691no—
109C22×C4—5382no—
110C22×C4—10761no—
111C22×C4—10761no—
112C22×C4C2×#1176164011yescharacteristic
113M16—41no—
114M16—10761no—
115M16—10761no—
116M16—10761no—
117C2×C8—21no—
118C2×C8—5382no—
119C2×C8—5381no—
120C4⋊C4—10761no—
121C4⋊C4—10761no—
122C22⋊C4—10762no—
123C23—2691no—
124C23—2691no—
125C23—5381no—
126C23—5381no—
127C23—10761no—
128C23—10761no—
129C23C4×#1176164011yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—2691no—
133C2×C4—2691no—
134C2×C4—5381no—
135C2×C4—5381no—
136C2×C4—5381no—
137C2×C4—5381no—
138C2×C4—10761no—
139C2×C4—10761no—
140C2×C4—10761no—
141C2×C4—10762no—
142C2×C4—10762no—
143C2×C4—10762no—
144C2×C4C22⋊#1176164011yescharacteristic
145C2×C4C4⋊#1176164011yescharacteristic
146C8—41no—
147C8—10762no—
148C8—10761no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—2691no—
153C22—2691no—
154C22—5381no—
155C22—5381no—
156C22—5381no—
157C22—5381no—
158C22—5381no—
159C22—10762no—
160C22—10762no—
161C22(C2×#11761640)⋊C411yescharacteristic
162C4—21no—
163C4—5381no—
164C4—5381no—
165C4—21522no—
166C4#2257551111yescharacteristic
167C4#2257551211yescharacteristic
168C2—41no—
169C2—5381no—
170C2—5381no—
171C2—10761no—
172C2#3177148311yescharacteristic
173C2#3177148411yescharacteristic
174C2#3177148811yescharacteristic
subgroupG/H
centerC22(C2×#11761640)⋊C4
commutatorC23×C269C42
FrattiniC22×C4C2×#11761640
FittingC2×M16×C269C4
socleC22×C269#95
prime radicalC23×D269C2×C4
cosocleC22×C4×D269C22
hypercenterC2×M16#11761640
hypocenterC269#1305
LCSG ▷ C23×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C22⋊#14524137C4semidirect
11. C2×#16864386C4semidirect
14. C2×M16×C269C4semidirect
87. C269#1305semidirect
95. C2×M16#11761640semidirect

Maximal subgroups

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

subgroupindex
#317715762
#317715472
#317705682
#1305269