Finite Group Databasebeta

← #46825985

Subgroups — #46825985

Order 34432.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#31771591C211yesmaximal, characteristic
2#31771584C211yesmaximal, characteristic
3#31770571C211yesmaximal, characteristic
4D269⋊M16—21no—
5#22575532—21no—
6#22575514C412yescomplemented
7#22575513—21no—
8#22575512C412yes—
9#22575511—21no—
10C2×#16864402C2211yescharacteristic
11C2×#16864386C411yescharacteristic, complemented
12#22575365—21no—
13#22575365—21no—
14C22×C8×C269C411yescharacteristic, complemented
15#16864412—41no—
16#16864411—22no—
17D269⋊C8—41no—
18C4⋊#11761640—41no—
19C22⋊#11761640—22no—
20C4×#11761640—41no—
21#16864402—41no—
22#16864402—41no—
23C2×Dic538C2×C411yescharacteristic
24C2×D1076C2×C411yescharacteristic
25C2×C22⋊D269D411yescharacteristic
26C2×C22⋊D269Q811yescharacteristic
27C2×C4×D269D411yescharacteristic
28C2×C4×D269D411yescharacteristic
29#16864386—41no—
30C2×#14524130—21no—
31C22×C4×C269C2×C411yescharacteristic
32C2×C8×C269—21no—
33C2×C8×C269—41no—
34C2×#11761640—42no—
35#14524137—42no—
36C22×D269C22⋊C411yescharacteristic
37C22×D269C4⋊C411yescharacteristic
38Dic538—41no—
39D1076—41no—
40C22⋊D269—41no—
41C22⋊D269—41no—
42C2×Dic269C22⋊C411yescharacteristic
43C2×Dic269C4⋊C411yescharacteristic
44C4×D269—21no—
45C4×D269—21no—
46C4×D269—21no—
47C4×D269—21no—
48#14524130—41no—
49C23×C269C4⋊C411yescharacteristic
50C2×C4×C269—21no—
51C2×C4×C269—21no—
52C2×C4×C269C4211yescharacteristic
53C2×C4×C269C22⋊C411yescharacteristic
54C8×C269—41no—
55C22×C269—21no—
56C22×C269—41no—
57C22×C269#9511yescharacteristic
58C2×D269—21no—
59C2×D269—21no—
60C2×D269—41no—
61C2×D269—41no—
62#11761640—82no—
63C4×C269—21no—
64C4×C269#9911yescharacteristic
65C4×C269#9911yescharacteristic
66Dic269—21no—
67Dic269—21no—
68C2×C269—21no—
69C2×C269—41no—
70C2×C269#34211yescharacteristic
71D269—41no—
72D269—41no—
73C269#139511yescharacteristic, complemented, Sylow
74#1395—2691nomaximal, Sylow
75#413—2691no—
76#410—2691no—
77#408—2691no—
78C2×#41—2691no—
79C2×M16—2691no—
80C2×M16—5381no—
81C22×C8#1176164011yescharacteristic, complemented
82#117—5381no—
83#101—2692no—
84#100—5381no—
85#99—2692no—
86#99—5381no—
87C22⋊C8—5381no—
88C22⋊C8—5381no—
89#41—10761no—
90#41—10761no—
91C2×Q8—2691no—
92C2×D4—2691no—
93C2×D4—2691no—
94C2×D4—2691no—
95C22×C4—2691no—
96C22×C4—2691no—
97C22×C4C2×#1176164011yescharacteristic
98M16—5382no—
99M16—10761no—
100M16—10761no—
101C2×C8—21no—
102C2×C8—41no—
103C2×C8—5381no—
104C2×C8—10761no—
105C4⋊C4—10761no—
106C22⋊C4—5382no—
107C42—10761no—
108C23—2691no—
109C23—2691no—
110C23C4⋊#1176164011yescharacteristic
111Q8—10761no—
112D4—10761no—
113D4—10761no—
114D4—10761no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—2691no—
118C2×C4—2691no—
119C2×C4—5381no—
120C2×C4—5381no—
121C2×C4—5381no—
122C2×C4—5381no—
123C2×C4—10762no—
124C2×C4C4×#1176164011yescharacteristic
125C2×C4C22⋊#1176164011yescharacteristic
126C8—41no—
127C8—10762no—
128C8—10761no—
129C22—21no—
130C22—41no—
131C22—5381no—
132C22—5381no—
133C22—10761no—
134C22—10761no—
135C22(C2×#11761640)⋊C411yescharacteristic
136C4—21no—
137C4—5381no—
138C4—5381no—
139C4—21522no—
140C4#2257551111yescharacteristic
141C4#2257551211yescharacteristic
142C2—21no—
143C2—41no—
144C2—10761no—
145C2—10761no—
146C2#3177148311yescharacteristic
subgroupG/H
centerC4#22575512
commutatorC2×C4×C269C42
FrattiniC22×C4C2×#11761640
FittingC22×C8×C269C4
socleC2×C269#342
prime radical, cosocleC2×#16864402C22
hypercenterC22×C8#11761640
hypocenterC269#1395
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
6. #22575514C4semidirect
11. C2×#16864386C4semidirect
14. C22×C8×C269C4semidirect
73. C269#1395semidirect
81. C22×C8#11761640semidirect

Maximal subgroups

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

subgroupindex
#317715912
#317715842
#317705712
#1395269