Finite Group Databasebeta

← #46781931

Subgroups — #46781931

Order 33664.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682673C211yesmaximal, characteristic
2#30682286C211yesmaximal, characteristic
3#30682220C211yesmaximal, characteristic, complemented
4#30681681C211yesmaximal, characteristic
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681668C211yesmaximal, characteristic, complemented
7#462×C263C211yesmaximal, characteristic, complemented
8#22554467C2211yescharacteristic
9#22554459—21no—
10#22554458—21no—
11#22554455—22no—
12C4×Dic526C2211yescharacteristic
13C4×D1052—21no—
14#22554432—21no—
15#22554401—21no—
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554393—21no—
18#22554390—22no—
19C4×C263⋊C8C2211yescharacteristic
20C2×Q16×C263—21no—
21C4⋊Q8×C263C2211yescharacteristic
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24#103×C263—21no—
25C2×Dic526D411yescharacteristic
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052D412yes—
29C2×C4×D263—22no—
30C2×C263⋊C8—21no—
31C2×C263⋊C8—21no—
32C4⋊Dic263D411yescharacteristic
33Dic263⋊C4—21no—
34(C2×D263)⋊C4—22no—
35(C2×D263)⋊C4—22no—
36(C2×D263)⋊C4—22no—
37C4×Dic263—21no—
38C2×Q8×C263—21no—
39C2×Q8×C263D411yescharacteristic
40Q16×C263—42no—
41C2×C8×C263—21no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D411yescharacteristic
46C42×C263—21no—
47C42×C263C2311yescharacteristic
48C22×D263—22no—
49Dic526—21no—
50Dic526—21no—
51D1052—42no—
52D1052—41no—
53D1052—41no—
54D1052—41no—
55D1052—41no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C4×D263—82no—
59C263⋊C8—41no—
60C263⋊C8—41no—
61Q8×C263—21no—
62Q8×C263—21no—
63Q8×C263—41no—
64Q8×C263—41no—
65C2×C4×C263—21no—
66C2×C4×C263—21no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—41no—
72C22×C263#12011yescharacteristic
73C2×D263—42no—
74C2×D263—42no—
75C2×D263—42no—
76C4×C263—21no—
77C4×C263—41no—
78C4×C263—41no—
79C4×C263—81no—
80C4×C263#13511yescharacteristic
81C4×C263#13511yescharacteristic
82C4×C263AGL(1,ℤ/8)11yescharacteristic
83C4×C263#13711yescharacteristic
84Dic263—41no—
85Dic263—41no—
86C2×C263#44911yescharacteristic
87C2×C263#45211yescharacteristic
88C2×C263#45511yescharacteristic
89D263—82no—
90C263#164011yescharacteristic, complemented, Sylow
91#1640—2631nomaximal, Sylow
92#559—2631no—
93#486—2631no—
94#475—2631no—
95#462D26311yescharacteristic, complemented
96#331—2631no—
97Q8⋊C8—2631no—
98Q8⋊C8—2631no—
99C2×Q16—21no—
100C4⋊Q8C2×D26311yescharacteristic
101#127—2631no—
102#124—5261no—
103#124—5261no—
104#123—5262no—
105C4×Q8—2631no—
106C4×Q8C2×D26311yescharacteristic
107C4×D4—5261no—
108C4×D4—5261no—
109#106—5261no—
110C4⋊C8—2631no—
111C4⋊C8C2×D26311yescharacteristic
112#103—21no—
113#103—5261no—
114#102—5262no—
115C4×C8—2631no—
116C2×Q8—21no—
117C2×Q8—2631no—
118C2×Q8C22⋊D26311yescharacteristic
119C2×D4—2632no—
120C2×D4—5261no—
121C2×D4—5261no—
122C22×C4—5262no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—5261no—
126C2×C8—5261no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2631no—
131C4⋊C4—5261no—
132C4⋊C4C22⋊D26311yescharacteristic
133C22⋊C4—5262no—
134C22⋊C4—5262no—
135C22⋊C4—5262no—
136C42—21no—
137C42—5261no—
138C42C22×D26311yescharacteristic
139C23—5262no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—5261no—
145Q8—5261no—
146D4—10522no—
147D4—10521no—
148D4—10521no—
149D4—10521no—
150D4—10521no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—5261no—
155C2×C4—5261no—
156C2×C4—21042no—
157C2×C4D4×D26311yescharacteristic
158C2×C4D4×D26311yescharacteristic
159C2×C4C2×C22⋊D26311yescharacteristic
160C8—41no—
161C8—10521no—
162C8—10521no—
163C22—10522no—
164C22—10522no—
165C22—10522no—
166C22#2255443811yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—10521no—
172C4—10521no—
173C4#2255449011yescharacteristic
174C4#2255449311yescharacteristic
175C4#2255449611yescharacteristic
176C4#2255450211yescharacteristic
177C2—21042no—
178C2#3068208111yescharacteristic
179C2#3068209911yescharacteristic
180C2#3068211411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#462×C263C2
socleC22×C263#120
prime radical#22554467C22
hypercenter#462D263
hypocenterC263#1640
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #30682220C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
6. #30681668C2semidirect
7. #462×C263C2semidirect
90. C263#1640semidirect
95. #462D263semidirect

Maximal subgroups

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

subgroupindex
#306826732
#306822862
#306822202
#306816812
Q8⋊(C263⋊C8)2
#306816682
#462×C2632
#1640263