Finite Group Databasebeta

← #46825987

Subgroups — #46825987

Order 34432.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#31771586C211yesmaximal, characteristic
2#31771580C211yesmaximal, characteristic
3#31770588C211yesmaximal, characteristic
4C2×#16864412C411yescharacteristic, complemented
5C2×D269⋊C8C411yescharacteristic, complemented
6#22575532—21no—
7#22575512—21no—
8#22575512C412yes—
9#22575510—21no—
10#22575510—21no—
11C2×#16864403C2211yescharacteristic
12M16×D269—21no—
13#22575372C411yescharacteristic, complemented
14#22575369—21no—
15#101×C269C411yescharacteristic, complemented
16#16864412—41no—
17D269⋊C8—41no—
18C2×#14524137—21no—
19C2×#14524137—21no—
20C4⋊#11761640—41no—
21C22⋊#11761640—22no—
22C4×#11761640—41no—
23#16864403—41no—
24#16864403—41no—
25C2×D1076C2×C411yescharacteristic
26C2×D1076D411yescharacteristic
27C2×D1076Q811yescharacteristic
28C2×C4×D269C2×C411yescharacteristic
29C2×C4×D269D411yescharacteristic
30C2×C4×D269D411yescharacteristic
31#16864386—21no—
32#16864385—41no—
33C8×D269—41no—
34C2×Q8×C269C2×C411yescharacteristic
35M16×C269—21no—
36C2×#11761640—42no—
37#14524137—41no—
38#14524137—41no—
39C22×D269C22⋊C411yescharacteristic
40C22×D269C4⋊C411yescharacteristic
41C22×D269C4⋊C411yescharacteristic
42D1076—41no—
43D1076—41no—
44D1076—41no—
45C2×Dic269C22⋊C411yescharacteristic
46C4×D269—21no—
47C4×D269—21no—
48C4×D269—21no—
49C4×D269—21no—
50C4×D269—21no—
51C4×D269—21no—
52#14524130—41no—
53Q8×C269—41no—
54C2×C4×C269C4211yescharacteristic
55C2×C4×C269C22⋊C411yescharacteristic
56C2×C4×C269C4⋊C411yescharacteristic
57C8×C269—41no—
58C22×C269#9511yescharacteristic
59C2×D269—21no—
60C2×D269—21no—
61C2×D269—21no—
62C2×D269—41no—
63C2×D269—41no—
64C2×D269—41no—
65#11761640—82no—
66C4×C269—21no—
67C4×C269—21no—
68C4×C269—21no—
69Dic269#9911yescharacteristic
70Dic269#9911yescharacteristic
71C2×C269—21no—
72C2×C269#34211yescharacteristic
73D269—41no—
74D269—41no—
75D269—41no—
76C269#139511yescharacteristic, complemented, Sylow
77#1395—2691nomaximal, Sylow
78#413—2691no—
79#410—2691no—
80#408—2691no—
81C2×#41—2691no—
82C2×M16—2691no—
83C2×M16—5381no—
84C22×C8—2691no—
85#117—5381no—
86#101—2691no—
87#101#1176164011yescharacteristic, complemented
88#100—5381no—
89#99—2692no—
90#99—5381no—
91C22⋊C8—5381no—
92C22⋊C8—5381no—
93#41—10761no—
94#41—10761no—
95C2×Q8C2×#1176164011yescharacteristic
96C2×D4—2691no—
97C2×D4—2691no—
98C2×D4—2691no—
99C22×C4—2691no—
100C22×C4—2691no—
101C22×C4—2691no—
102M16—21no—
103M16—5381no—
104M16—10761no—
105M16—10761no—
106C2×C8—5381no—
107C2×C8—5381no—
108C2×C8—10761no—
109C2×C8—10761no—
110C4⋊C4—10761no—
111C22⋊C4—5382no—
112C42—10761no—
113C23—2691no—
114C23—2691no—
115C23—2691no—
116Q8—41no—
117D4—10761no—
118D4—10761no—
119D4—10761no—
120C2×C4—2691no—
121C2×C4—5381no—
122C2×C4—5381no—
123C2×C4—5381no—
124C2×C4—5381no—
125C2×C4—5381no—
126C2×C4—5381no—
127C2×C4—10762no—
128C2×C4C4×#1176164011yescharacteristic
129C2×C4C22⋊#1176164011yescharacteristic
130C2×C4C4⋊#1176164011yescharacteristic
131C8—41no—
132C8—10761no—
133C8—10761no—
134C8—10761no—
135C22—5381no—
136C22—5381no—
137C22—5381no—
138C22—10761no—
139C22—10761no—
140C22—10761no—
141C22(C2×#11761640)⋊C411yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—2691no—
146C4—2691no—
147C4—21522no—
148C2—21no—
149C2—10761no—
150C2—10761no—
151C2—10761no—
152C2#3177148211yescharacteristic
subgroupG/H
centerC2#31771482
commutatorC2×C4×C269C42
FrattiniC2×Q8C2×#11761640
Fitting#101×C269C4
socleC2×C269#342
prime radical, cosocleC2×#16864403C22
hypercenter#101#11761640
hypocenterC269#1395
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
4. C2×#16864412C4semidirect
5. C2×D269⋊C8C4semidirect
13. #22575372C4semidirect
15. #101×C269C4semidirect
76. C269#1395semidirect
87. #101#11761640semidirect

Maximal subgroups

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

subgroupindex
#317715862
#317715802
#317705882
#1395269