Finite Group Databasebeta

← #46781820

Subgroups — #46781820

Order 33664.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682649C211yesmaximal, characteristic, complemented
2#30682312C211yesmaximal, characteristic, complemented
3#30682139C211yesmaximal, characteristic, complemented
4#30682134C211yesmaximal, characteristic
5#30681668C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#333×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—21no—
9C2×#16862363—22no—
10C2×D2104—21no—
11#22554467C2211yescharacteristic
12#22554461—21no—
13#22554450—21no—
14#22554446—22no—
15C4×Dic526C2211yescharacteristic
16C4×D1052C2211yescharacteristic
17#22554432—21no—
18C4⋊C4×D263—21no—
19#22554392—21no—
20#22554392—21no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526D411yescharacteristic
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052D411yescharacteristic
30C2×C4×D263—22no—
31C2×C4×D263—21no—
32#16862365—42no—
33#16862363—44no—
34D2104—42no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—22no—
37C4⋊Dic263D411yescharacteristic
38C4⋊Dic263D411yescharacteristic
39Dic263⋊C4—22no—
40Dic263⋊C4—21no—
41(C2×D263)⋊C4—22no—
42(C2×D263)⋊C4—21no—
43C4×Dic263—21no—
44C2×Q8×C263D412yes—
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51C22×D263—41no—
52Dic526—21no—
53Dic526—21no—
54D1052—21no—
55D1052—42no—
56D1052—41no—
57D1052—41no—
58D1052—41no—
59D1052—41no—
60D1052SD1612yescomplemented
61C2×Dic263—21no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C4×D263—41no—
65C4×D263—41no—
66C4×D263—82no—
67C263⋊C8—22no—
68Q8×C263—42no—
69C2×C4×C263—22no—
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C8×C263—41no—
74C8×C263—41no—
75C22×C263#12011yescharacteristic
76C2×D263—22no—
77C2×D263—41no—
78C2×D263—41no—
79C2×D263—81no—
80C2×D263—81no—
81C2×D263—81no—
82C4×C263—21no—
83C4×C263—42no—
84C4×C263C2×SD1611yescharacteristic
85C4×C263#13511yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87C4×C263#13711yescharacteristic
88Dic263—41no—
89Dic263—41no—
90Dic263—41no—
91C2×C263#44811yescharacteristic
92C2×C263#44911yescharacteristic
93C2×C263#45311yescharacteristic
94D263—42no—
95D263—161no—
96C263#162211yescharacteristic, complemented, Sylow
97#1622—2631nomaximal, Sylow
98#554—2631no—
99#492—2631no—
100#460—2631no—
101#459—2631no—
102#333D26311yescharacteristic, complemented
103Q8⋊C8—2631no—
104D4⋊C8—2631no—
105C2×SD16—5261no—
106C2×SD16—5262no—
107C2×D8—5261no—
108C4⋊Q8C2×D26311yescharacteristic
109#127—2631no—
110#125—5261no—
111C22⋊Q8—5261no—
112C22⋊Q8—5262no—
113C4×Q8—2631no—
114C4×D4—2631no—
115C4×D4—5261no—
116C2×C4⋊C4—5261no—
117C4⋊C8C2×D26311yescharacteristic
118C4⋊C8C2×D26311yescharacteristic
119#102—5261no—
120#102—5261no—
121C4×C8—2631no—
122C2×Q8—2631no—
123C2×Q8D105212yes—
124C2×D4—2631no—
125C2×D4—5261no—
126C2×D4—5261no—
127C2×D4—5261no—
128C22×C4—5262no—
129C22×C4—5261no—
130SD16—10522no—
131SD16—10524no—
132D8—10522no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5261no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2631no—
139C4⋊C4—2631no—
140C4⋊C4—5262no—
141C4⋊C4—5262no—
142C4⋊C4—5261no—
143C22⋊C4—5262no—
144C22⋊C4—5261no—
145C42—5261no—
146C42C22×D26311yescharacteristic
147C23—5261no—
148C23—10521no—
149Q8—42no—
150Q8—5261no—
151Q8—5261no—
152D4—2632no—
153D4—5261no—
154D4—10522no—
155D4—10521no—
156D4—10521no—
157D4—10521no—
158D4—10521no—
159C2×C4—22no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—5261no—
163C2×C4—10521no—
164C2×C4—10521no—
165C2×C4—21042no—
166C2×C4D4×D26311yescharacteristic
167C2×C4D4×D26311yescharacteristic
168C2×C4C2×D105211yescharacteristic
169C8—41no—
170C8—41no—
171C8—5262no—
172C22—5262no—
173C22—10521no—
174C22—10521no—
175C22—21041no—
176C22—21041no—
177C22—21041no—
178C22#2255444011yescharacteristic
179C4—21no—
180C4—42no—
181C4—10521no—
182C4—10521no—
183C4—10521no—
184C4SD16×D26311yescharacteristic
185C4#2255449311yescharacteristic
186C4#2255449711yescharacteristic
187C4#2255450211yescharacteristic
188C2—10522no—
189C2—42081no—
190C2#3068207811yescharacteristic
191C2#3068208611yescharacteristic
192C2#3068210811yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#333×C263C2
socleC22×C263#120
prime radical#30682134C2
hypercenter#333D263
hypocenterC263#1622
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #30682649C2semidirect
2. #30682312C2semidirect
3. #30682139C2semidirect
5. #30681668C2semidirect
6. #30681665C2semidirect
7. #333×C263C2semidirect
60. D1052SD16semidirect
96. C263#1622semidirect
102. #333D263semidirect

Maximal subgroups

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

subgroupindex
#306826492
#306823122
#306821392
#306821342
#306816682
#306816652
#333×C2632
#1622263