Finite Group Databasebeta

← #46781439

Subgroups — #46781439

Order 33664.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#30682486C211yesmaximal, characteristic
2#30681994C211yesmaximal, characteristic, complemented
3C4⋊C8×D263C211yesmaximal, characteristic, complemented
4#30681686C211yesmaximal, characteristic, complemented
5#30681686C211yesmaximal, characteristic, complemented
6#30681682C211yesmaximal, characteristic, complemented
7#331×C263C211yesmaximal, characteristic, complemented
8C2×#16862375C412yes—
9C2×C8×D263—21no—
10#22554470C2211yescharacteristic
11#22554457C412yes—
12#22554441—21no—
13#22554441—21no—
14D4×Dic263—21no—
15D4×Dic263—21no—
16C42×D263C2211yescharacteristic
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19Dic263⋊C8—21no—
20(C2×D263)⋊C8—21no—
21#22554380—21no—
22#127×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25#16862375—44no—
26C2×Dic526C2×C412yes—
27C2×C22⋊D263—22no—
28C22×Dic263—22no—
29C2×C4×D263C2×C411yescharacteristic
30C2×C4×D263D411yescharacteristic
31C2×C4×D263D411yescharacteristic
32C2×C263⋊C8—21no—
33C2×C263⋊C8—21no—
34C8×D263—42no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C22⋊Dic263—22no—
38C22⋊Dic263—22no—
39C4×Dic263C2×C411yescharacteristic
40C4×Dic263D411yescharacteristic
41C4×Dic263D411yescharacteristic
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263C2×C412yes—
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C42×C263C2311yescharacteristic
48C22×D263C22⋊C411yescharacteristic
49Dic526—42no—
50C22⋊D263—44no—
51C2×Dic263—22no—
52C2×Dic263—44no—
53C2×Dic263C22⋊C411yescharacteristic
54C2×Dic263C22⋊C411yescharacteristic
55C2×Dic263C22⋊C411yescharacteristic
56C4×D263—22no—
57C4×D263—21no—
58C4×D263—21no—
59C4×D263—21no—
60C4×D263—21no—
61C263⋊C8—41no—
62C263⋊C8—41no—
63C23×C263—22no—
64D4×C263—42no—
65D4×C263—41no—
66D4×C263—41no—
67D4×C263—41no—
68D4×C263—41no—
69C2×C4×C263C22×C411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C8×C263—41no—
73C8×C263—41no—
74C22×C263—42no—
75C22×C263—42no—
76C22×C263—42no—
77C22×C263C2×C22⋊C411yescharacteristic
78C2×D263—21no—
79C2×D263—21no—
80C2×D263#10012yes—
81C4×C263—21no—
82C4×C263#13511yescharacteristic
83C4×C263#13511yescharacteristic
84C4×C263AGL(1,ℤ/8)11yescharacteristic
85C4×C263#13711yescharacteristic
86Dic263—21no—
87Dic263—21no—
88Dic263—21no—
89Dic263—42no—
90C2×C263—82no—
91C2×C263C2×#10011yescharacteristic
92C2×C263#41611yescharacteristic
93C2×C263#41711yescharacteristic
94D263—22no—
95C263#155111yescharacteristic, complemented, Sylow
96#1551—2631nomaximal, Sylow
97#532—2631no—
98#432—2631no—
99C2×C4⋊C8—2631no—
100#333—2631no—
101#333—2631no—
102#331—2631no—
103#331D26311yescharacteristic, complemented
104C2×#41—2632no—
105C22×C8—5261no—
106C4⋊Q8—2631no—
107#127C2×D26311yescharacteristic
108#124—2632no—
109#121—5261no—
110#121—5261no—
111C4×D4—5261no—
112C4×D4—5261no—
113C2×C42—2631no—
114C4⋊C8—2631no—
115C4⋊C8—2631no—
116C4⋊C8—5261no—
117C4⋊C8C2×D26311yescharacteristic
118C4⋊C8C2×D26311yescharacteristic
119C22⋊C8—5261no—
120#97—5261no—
121#41—10524no—
122C2×Q8—2632no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—5262no—
126C2×D4C4×D26312yes—
127C22×C4—2631no—
128C22×C4—2631no—
129C22×C4—2631no—
130C22×C4—5262no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—5261no—
134C2×C8—5261no—
135C2×C8—10522no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C22⋊C4—5262no—
139C22⋊C4—5262no—
140C42—2631no—
141C42—2631no—
142C42—2631no—
143C42C22×D26311yescharacteristic
144C23—22no—
145C23—2631no—
146Q8—10522no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—10524no—
153C2×C4—2631no—
154C2×C4—2631no—
155C2×C4—2631no—
156C2×C4—5262no—
157C2×C4—5261no—
158C2×C4—5261no—
159C2×C4—5261no—
160C2×C4—5261no—
161C2×C4—5262no—
162C2×C4—10524no—
163C2×C4C2×C4×D26311yescharacteristic
164C2×C4D4×D26311yescharacteristic
165C2×C4D4×D26311yescharacteristic
166C8—41no—
167C8—41no—
168C8—10521no—
169C8—10521no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—2632no—
174C22—5261no—
175C22—5261no—
176C22C22⋊C4×D26311yescharacteristic
177C4—21no—
178C4—5261no—
179C4—5261no—
180C4—5261no—
181C4—10522no—
182C4#2255448911yescharacteristic
183C4#2255449111yescharacteristic
184C4#2255449411yescharacteristic
185C4#2255449911yescharacteristic
186C2—82no—
187C2—5262no—
188C2#100×D26311yescharacteristic
189C2#3068193111yescharacteristic
190C2#3068193611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#331×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682486C2
cosocleC42×C263C23
hypercenter#331D263
hypocenterC263#1551
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #30681994C2semidirect
3. C4⋊C8×D263C2semidirect
4. #30681686C2semidirect
5. #30681686C2semidirect
6. #30681682C2semidirect
7. #331×C263C2semidirect
95. C263#1551semidirect
103. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306824862
#306819942
C4⋊C8×D2632
#306816862
#306816822
#331×C2632
#1551263