Finite Group Databasebeta

← #46781908

Subgroups — #46781908

Order 33664.

188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682667C211yesmaximal, characteristic
2#30682289C211yesmaximal, characteristic
3#30682234C211yesmaximal, characteristic
4#30682233C211yesmaximal, characteristic
5#30681685C211yesmaximal, characteristic
6#30681670C211yesmaximal, characteristic
7Q8⋊C8×C263C211yesmaximal, characteristic
8#22554470—21no—
9#22554470C2211yescharacteristic
10#22554470C2211yescharacteristic
11#22554461—22no—
12#22554461—21no—
13Q8×Dic263—21no—
14C4×Dic526—21no—
15C4×Dic526C2211yescharacteristic
16#22554404—21no—
17#22554403—21no—
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554395—21no—
20#22554395—22no—
21#22554394—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526D411yescharacteristic
28C2×C263⋊C8—21no—
29C4⋊Dic263—22no—
30C4⋊Dic263—22no—
31C4⋊Dic263—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D412yes—
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37Dic263⋊C4—21no—
38C4×Dic263—22no—
39C4×Dic263—21no—
40C2×Q8×C263D411yescharacteristic
41C2×C8×C263—21no—
42C2×C8×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263D411yescharacteristic
45C42×C263—21no—
46C42×C263C2311yescharacteristic
47Dic526—21no—
48Dic526—21no—
49Dic526—41no—
50Dic526—41no—
51Dic526—42no—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—22no—
55C2×Dic263—41no—
56C263⋊C8—41no—
57Q8×C263—21no—
58Q8×C263Q1612yes—
59C2×C4×C263—21no—
60C2×C4×C263—21no—
61C2×C4×C263C2×D411yescharacteristic
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263C2×D411yescharacteristic
64C8×C263—41no—
65C8×C263—41no—
66C22×C263#12011yescharacteristic
67C4×C263—22no—
68C4×C263—21no—
69C4×C263—41no—
70C4×C263C2×Q1611yescharacteristic
71C4×C263#13511yescharacteristic
72C4×C263#13711yescharacteristic
73C4×C263#13711yescharacteristic
74Dic263—41no—
75Dic263—42no—
76Dic263—41no—
77Dic263—81no—
78C2×C263#45111yescharacteristic
79C2×C263#45211yescharacteristic
80C2×C263#45411yescharacteristic
81C263#163611yescharacteristic, complemented, Sylow
82#1636—2631nomaximal, Sylow
83#557—2631no—
84#487—2631no—
85#477—2631no—
86#477—2631no—
87#332—2631no—
88Q8⋊C8—2631no—
89Q8⋊C8D26311yescharacteristic
90C4⋊Q8—2631no—
91C4⋊Q8—2631no—
92C4⋊Q8—5261no—
93#125—5262no—
94#125—5261no—
95C4×Q8—2631no—
96C4×Q8—5261no—
97C4×Q8—5261no—
98C4×Q8C2×D26311yescharacteristic
99#107—5261no—
100#107—5261no—
101C4⋊C8—2631no—
102C4⋊C8C2×D26311yescharacteristic
103#103—5262no—
104#103—5261no—
105#103—5261no—
106C4×C8C2×D26311yescharacteristic
107C2×Q8—2631no—
108C2×Q8—5261no—
109C2×Q8—5261no—
110C2×Q8D105211yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—5261no—
114C4⋊C4—21no—
115C4⋊C4—2632no—
116C4⋊C4—2631no—
117C4⋊C4—5262no—
118C4⋊C4—5262no—
119C4⋊C4—5262no—
120C4⋊C4—5261no—
121C4⋊C4—5261no—
122C4⋊C4—5261no—
123C4⋊C4—5261no—
124C4⋊C4D105211yescharacteristic
125C42—21no—
126C42—5262no—
127C42—5261no—
128C42C22×D26311yescharacteristic
129Q8—21no—
130Q8—5261no—
131Q8—5261no—
132Q8—10522no—
133Q8—10521no—
134Q8—10521no—
135Q8Dic105212yes—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—5261no—
139C2×C4—5262no—
140C2×C4—5261no—
141C2×C4—10521no—
142C2×C4D4×D26311yescharacteristic
143C2×C4D4×D26311yescharacteristic
144C2×C4C2×D105211yescharacteristic
145C8—41no—
146C8—41no—
147C8—10521no—
148C22#2255444011yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—10521no—
153C4—10521no—
154C4—10522no—
155C4—21041no—
156C4C2×Dic105211yescharacteristic
157C4#2255449111yescharacteristic
158C4#2255450211yescharacteristic
159C4#2255450311yescharacteristic
160C2#3068209611yescharacteristic
161C2#3068210311yescharacteristic
162C2#3068211211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socle, prime radicalC22×C263#120
hypercenterQ8⋊C8D263
hypocenterC263#1636
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
81. C263#1636semidirect

Maximal subgroups

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

subgroupindex
#306826672
#306822892
#306822342
#306822332
#306816852
#306816702
Q8⋊C8×C2632
#1636263