Finite Group Databasebeta

← #46781421

Subgroups — #46781421

Order 33664.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#30681960C211yesmaximal, characteristic, complemented
3C4⋊C8×D263C211yesmaximal, 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—
10C2×C8×D263—21no—
11#22554470C2211yescharacteristic
12#22554457—21no—
13#22554441—21no—
14#22554441C412yes—
15D4×Dic263—21no—
16D4×Dic263C412yes—
17C42×D263C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19C4⋊(C263⋊C8)C2211yescharacteristic
20Dic263⋊C8—21no—
21Dic263⋊C8—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—
36C8×D263—42no—
37C4⋊Dic263—21no—
38C4⋊Dic263C2×C412yes—
39C22⋊Dic263—22no—
40C22⋊Dic263—22no—
41C4×Dic263C2×C411yescharacteristic
42C4×Dic263D411yescharacteristic
43C4×Dic263D411yescharacteristic
44C2×D4×C263—21no—
45C2×D4×C263—21no—
46C2×D4×C263C2×C412yes—
47C2×C8×C263—21no—
48C2×C8×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263C22⋊C411yescharacteristic
51Dic526—41no—
52Dic526—41no—
53C22⋊D263—44no—
54C2×Dic263—22no—
55C2×Dic263—44no—
56C2×Dic263C22⋊C411yescharacteristic
57C2×Dic263C22⋊C411yescharacteristic
58C2×Dic263C22⋊C411yescharacteristic
59C4×D263—21no—
60C4×D263—21no—
61C4×D263—41no—
62C4×D263D812yes—
63C4×D263SD1612yes—
64C263⋊C8—41no—
65C263⋊C8—41no—
66C23×C263—22no—
67D4×C263—42no—
68D4×C263—41no—
69D4×C263—41no—
70D4×C263—41no—
71D4×C263—41no—
72C2×C4×C263C22×C411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C8×C263—41no—
76C8×C263—41no—
77C22×C263—42no—
78C22×C263—42no—
79C22×C263—42no—
80C22×C263C2×C22⋊C411yescharacteristic
81C2×D263—21no—
82C2×D263—21no—
83C2×D263#10212yes—
84C4×C263—21no—
85C4×C263C2×D811yescharacteristic
86C4×C263C2×SD1611yescharacteristic
87C4×C263AGL(1,ℤ/8)11yescharacteristic
88C4×C263#13711yescharacteristic
89Dic263—21no—
90Dic263—21no—
91Dic263—42no—
92Dic263#10212yes—
93C2×C263—82no—
94C2×C263#41311yescharacteristic
95C2×C263C2×#10211yescharacteristic
96C2×C263#41711yescharacteristic
97D263—22no—
98C263#154711yescharacteristic, complemented, Sylow
99#1547—2631nomaximal, Sylow
100#532—2631no—
101#423—2631no—
102C2×C4⋊C8—2631no—
103#332—2631no—
104#332—2631no—
105#331—2631no—
106#331D26311yescharacteristic, complemented
107C2×#41—5261no—
108C2×M16—5261no—
109C22×C8—5261no—
110C4⋊Q8—2631no—
111#127C2×D26311yescharacteristic
112#124—5261no—
113#121—2632no—
114#121—5261no—
115C4×D4—2632no—
116C4×D4—5261no—
117C2×C42—2631no—
118C4⋊C8—2631no—
119C4⋊C8—2631no—
120C4⋊C8—5261no—
121C4⋊C8—5261no—
122C4⋊C8C2×D26311yescharacteristic
123C4⋊C8C2×D26311yescharacteristic
124#41—10522no—
125#41—10522no—
126C2×Q8—5261no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—5262no—
130C2×D4C4×D26312yes—
131C22×C4—2631no—
132C22×C4—2631no—
133C22×C4—2631no—
134C22×C4—5262no—
135M16—10522no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—5261no—
139C2×C8—5261no—
140C2×C8—10522no—
141C4⋊C4—2632no—
142C4⋊C4—5261no—
143C22⋊C4—5262no—
144C22⋊C4—5262no—
145C42—2631no—
146C42—2631no—
147C42—2631no—
148C42C22×D26311yescharacteristic
149C23—22no—
150C23—2631no—
151Q8—10521no—
152Q8—10521no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—10524no—
159C2×C4—2631no—
160C2×C4—2632no—
161C2×C4—2632no—
162C2×C4—2631no—
163C2×C4—2631no—
164C2×C4—5261no—
165C2×C4—5261no—
166C2×C4—5262no—
167C2×C4—10521no—
168C2×C4—10524no—
169C2×C4C2×C4×D26311yescharacteristic
170C2×C4D4×D26311yescharacteristic
171C2×C4D4×D26311yescharacteristic
172C8—41no—
173C8—41no—
174C8—10521no—
175C8—10521no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—2632no—
180C22—5261no—
181C22—5261no—
182C22C22⋊C4×D26311yescharacteristic
183C4—21no—
184C4—2632no—
185C4—5261no—
186C4—5261no—
187C4—10522no—
188C4D8×D26311yescharacteristic
189C4SD16×D26311yescharacteristic
190C4#2255449411yescharacteristic
191C4#2255449911yescharacteristic
192C2—82no—
193C2—5262no—
194C2#3068191911yescharacteristic
195C2#102×D26311yescharacteristic
196C2#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#1547
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. #30681960C2semidirect
3. C4⋊C8×D263C2semidirect
4. #30681685C2semidirect
5. #30681683C2semidirect
6. #30681682C2semidirect
7. #331×C263C2semidirect
98. C263#1547semidirect
106. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306824862
#306819602
C4⋊C8×D2632
#306816852
#306816832
#306816822
#331×C2632
#1547263