Finite Group Databasebeta

← #46825865

Subgroups — #46825865

Order 34432.

146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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#31771483C211yesmaximal, characteristic
2#31771449C211yesmaximal, characteristic
3#31770531C211yesmaximal, characteristic
4C2×C22⋊#11761640—21no—
5C22⋊#14524137—21no—
6C2×#16864379—21no—
7C2×#16864379C2211yescharacteristic
8#22575360—21no—
9#22575360C411yescharacteristic, complemented
10C2×C4⋊C4×C269C411yescharacteristic, complemented
11C22×#11761640—41no—
12C2×#14524137—41no—
13C22⋊#11761640—22no—
14C22⋊#11761640—41no—
15C23×D269D411yescharacteristic
16C22×Dic269—21no—
17C22×Dic269D411yescharacteristic
18#16864379—41no—
19#16864379—41no—
20#16864379—41no—
21C22×C4×C269—21no—
22C22×C4×C269C2×C411yescharacteristic
23C4⋊C4×C269—41no—
24C2×#11761640—42no—
25C2×#11761640—81no—
26C2×#11761640—81no—
27#14524137—81no—
28C22×D269—21no—
29C22×D269—21no—
30C22×D269—41no—
31C22×D269—41no—
32C22×D269D811yescharacteristic
33C22×D269SD1611yescharacteristic
34C2×Dic269—21no—
35C2×Dic269—41no—
36C2×Dic269—41no—
37C2×Dic269—41no—
38C2×Dic269—41no—
39C23×C269C22⋊C411yescharacteristic
40C2×C4×C269—21no—
41C2×C4×C269—41no—
42C2×C4×C269—41no—
43C2×C4×C269—41no—
44C2×C4×C269—41no—
45C22×C269—21no—
46C22×C269—21no—
47C22×C269#9911yescharacteristic
48C22×C269#10211yescharacteristic
49C22×C269#10411yescharacteristic
50C2×D269—21no—
51C2×D269—21no—
52C2×D269—41no—
53C2×D269—41no—
54C2×D269—41no—
55C2×D269—41no—
56C2×D269—81no—
57#11761640—82no—
58C4×C269—41no—
59C4×C269—81no—
60Dic269—41no—
61Dic269—81no—
62C2×C269—21no—
63C2×C269—21no—
64C2×C269#32711yescharacteristic
65C2×C269#35211yescharacteristic
66C2×C269#35411yescharacteristic
67D269—41no—
68D269—41no—
69C269#134411yescharacteristic, complemented, Sylow
70#1344—2691nomaximal, Sylow
71#397—2691no—
72#342—2691no—
73#323—2691no—
74C2×C4⋊C4#1176164011yescharacteristic, complemented
75C2×C22⋊C4—2691no—
76C2×C22⋊C4—5381no—
77C2×C22⋊C4—5381no—
78C22⋊C8—5381no—
79#95—2691no—
80#95—5381no—
81C24—2691no—
82C22×C4—21no—
83C22×C4—2691no—
84C22×C4—5381no—
85C22×C4—10761no—
86C22×C4C2×#1176164011yescharacteristic
87C2×C8—10761no—
88C4⋊C4—41no—
89C22⋊C4—5382no—
90C22⋊C4—10761no—
91C22⋊C4—10761no—
92C22⋊C4—10761no—
93C22⋊C4—10761no—
94C23—2691no—
95C23—2691no—
96C23—5381no—
97C23—5381no—
98C23—10761no—
99C23—10761no—
100C23C22⋊#1176164011yescharacteristic
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—5381no—
107C2×C4—10761no—
108C2×C4—10761no—
109C2×C4—10761no—
110C2×C4—10762no—
111C2×C4—10761no—
112C2×C4—21521no—
113C2×C4—21521no—
114C8—21521no—
115C22—21no—
116C22—21no—
117C22—5381no—
118C22—5381no—
119C22—10761no—
120C22—10761no—
121C22—10761no—
122C22—10761no—
123C22—21521no—
124C22#2257551111yescharacteristic
125C22#2257551511yescharacteristic
126C22#2257551711yescharacteristic
127C4—41no—
128C4—81no—
129C4—10761no—
130C4—21521no—
131C4—21522no—
132C2—21no—
133C2—21no—
134C2—10761no—
135C2—10761no—
136C2#3177145611yescharacteristic
137C2#3177150711yescharacteristic
138C2#3177151111yescharacteristic
subgroupG/H
centerC22#22575511
commutatorC22×C4×C269C2×C4
FrattiniC22×C4C2×#11761640
FittingC2×C4⋊C4×C269C4
socleC22×C269#99
prime radicalC23×D269D4
cosocleC2×#16864379C22
hypercenterC2×C4⋊C4#11761640
hypocenterC269#1344
LCSG ▷ C22×C4×C269 ▷ C23×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #22575360C4semidirect
10. C2×C4⋊C4×C269C4semidirect
69. C269#1344semidirect
74. C2×C4⋊C4#11761640semidirect

Maximal subgroups

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

subgroupindex
#317714832
#317714492
#317705312
#1344269