Finite Group Databasebeta

← #46781466

Subgroups — #46781466

Order 33664.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#30681960C211yesmaximal, characteristic, complemented
4#30681685C211yesmaximal, characteristic, complemented
5#30681683C211yesmaximal, characteristic, complemented
6#30681682C211yesmaximal, characteristic, complemented
7#331×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9C2×#16862359—21no—
10#22554470C2211yescharacteristic
11#22554457—21no—
12#22554441—21no—
13#22554441C412yes—
14D4×Dic263—21no—
15D4×Dic263C412yes—
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—42no—
26#16862375—42no—
27C2×Dic526—21no—
28C2×C22⋊D263—22no—
29C22×Dic263—22no—
30C2×C4×D263C2×C411yescharacteristic
31C2×C4×D263D411yescharacteristic
32C2×C4×D263D411yescharacteristic
33#16862359—42no—
34C2×C263⋊C8—21no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263C2×C412yes—
38C22⋊Dic263—22no—
39C22⋊Dic263—22no—
40C4×Dic263C2×C411yescharacteristic
41C4×Dic263D411yescharacteristic
42C4×Dic263D411yescharacteristic
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×D4×C263C2×C412yes—
46C2×C8×C263—21no—
47C2×C8×C263—21no—
48C42×C263C2311yescharacteristic
49C22×D263C22⋊C411yescharacteristic
50Dic526—41no—
51Dic526—41no—
52C22⋊D263—44no—
53C2×Dic263—22no—
54C2×Dic263—44no—
55C2×Dic263C22⋊C411yescharacteristic
56C2×Dic263C22⋊C411yescharacteristic
57C2×Dic263C22⋊C411yescharacteristic
58C4×D263—21no—
59C4×D263—21no—
60C4×D263—21no—
61C4×D263—21no—
62C4×D263—41no—
63C263⋊C8—41no—
64C263⋊C8—41no—
65C23×C263—22no—
66D4×C263—42no—
67D4×C263—41no—
68D4×C263—41no—
69D4×C263—41no—
70D4×C263—41no—
71C2×C4×C263C22×C411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C8×C263—41no—
75C8×C263—41no—
76C22×C263—42no—
77C22×C263—42no—
78C22×C263—42no—
79C22×C263C2×C22⋊C411yescharacteristic
80C2×D263—21no—
81C2×D263—21no—
82C2×D263—21no—
83C4×C263—21no—
84C4×C263AGL(1,ℤ/8)11yescharacteristic
85C4×C263AGL(1,ℤ/8)11yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87C4×C263#13711yescharacteristic
88Dic263—21no—
89Dic263—21no—
90Dic263—21no—
91Dic263—42no—
92C2×C263—82no—
93C2×C263#41311yescharacteristic
94C2×C263#41711yescharacteristic
95C2×C263#41811yescharacteristic
96D263—41no—
97C263#155711yescharacteristic, complemented, Sylow
98#1557—2631nomaximal, Sylow
99#532—2631no—
100#432—2631no—
101#423—2631no—
102#332—2631no—
103#332—2631no—
104#331—2631no—
105#331D26311yescharacteristic, complemented
106C2×#41—5261no—
107C2×M16—5261no—
108C4⋊Q8—2631no—
109#127C2×D26311yescharacteristic
110#124—5261no—
111#121—2632no—
112#121—5261no—
113C4×D4—2632no—
114C4×D4—5261no—
115C2×C42—2631no—
116C4⋊C8—2631no—
117C4⋊C8—2631no—
118C4⋊C8—5261no—
119C4⋊C8C2×D26311yescharacteristic
120C4⋊C8C2×D26311yescharacteristic
121C22⋊C8—5261no—
122#97—5261no—
123#41—10522no—
124#41—10522no—
125C2×Q8—5261no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—5262no—
129C2×D4C4×D26312yes—
130C22×C4—2631no—
131C22×C4—2631no—
132C22×C4—2631no—
133C22×C4—5262no—
134M16—10522no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—5261no—
138C2×C8—5261no—
139C4⋊C4—2632no—
140C4⋊C4—5261no—
141C22⋊C4—5262no—
142C22⋊C4—5262no—
143C42—2631no—
144C42—2631no—
145C42—2631no—
146C42C22×D26311yescharacteristic
147C23—22no—
148C23—2631no—
149Q8—10521no—
150Q8—10521no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—10524no—
157C2×C4—2631no—
158C2×C4—2631no—
159C2×C4—2631no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—5261no—
163C2×C4—5261no—
164C2×C4—5262no—
165C2×C4—10521no—
166C2×C4—10524no—
167C2×C4C2×C4×D26311yescharacteristic
168C2×C4D4×D26311yescharacteristic
169C2×C4D4×D26311yescharacteristic
170C8—41no—
171C8—41no—
172C8—10521no—
173C8—10521no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—5261no—
178C22—5261no—
179C22—5261no—
180C22C22⋊C4×D26311yescharacteristic
181C4—21no—
182C4—5261no—
183C4—5261no—
184C4—5261no—
185C4—10522no—
186C4#2255449411yescharacteristic
187C4#2255449411yescharacteristic
188C4#2255449711yescharacteristic
189C4#2255449911yescharacteristic
190C2—82no—
191C2—10521no—
192C2#3068191911yescharacteristic
193C2#3068193611yescharacteristic
194C2#3068194111yescharacteristic
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#1557
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. #30681960C2semidirect
4. #30681685C2semidirect
5. #30681683C2semidirect
6. #30681682C2semidirect
7. #331×C263C2semidirect
97. C263#1557semidirect
105. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306824862
#306819942
#306819602
#306816852
#306816832
#306816822
#331×C2632
#1557263