Finite Group Databasebeta

← #46781449

Subgroups — #46781449

Order 33664.

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

normal subgroups only

This group has 242 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#30681990C211yesmaximal, characteristic, complemented
4#30681685C211yesmaximal, characteristic, complemented
5#30681683C211yesmaximal, characteristic, complemented
6#30681682C211yesmaximal, characteristic, complemented
7#331×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9#22554470C2211yescharacteristic
10#22554457—21no—
11#22554441—21no—
12#22554441C412yes—
13D4×Dic263—21no—
14D4×Dic263C412yes—
15C42×D263C2211yescharacteristic
16C4⋊(C263⋊C8)C2211yescharacteristic
17C4⋊(C263⋊C8)C2211yescharacteristic
18(C2×D263)⋊C8—21no—
19(C2×D263)⋊C8—21no—
20#22554380—21no—
21C8×Dic263—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
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263C2×C412yes—
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—41no—
50Dic526—41no—
51C22⋊D263—44no—
52C2×Dic263—22no—
53C2×Dic263—44no—
54C2×Dic263C22⋊C411yescharacteristic
55C2×Dic263C22⋊C411yescharacteristic
56C2×Dic263C22⋊C411yescharacteristic
57C4×D263—21no—
58C4×D263—21no—
59C4×D263—21no—
60C4×D263—21no—
61C4×D263—41no—
62C263⋊C8—41no—
63C263⋊C8—41no—
64C23×C263—22no—
65D4×C263—42no—
66D4×C263—41no—
67D4×C263—41no—
68D4×C263—41no—
69D4×C263—41no—
70C2×C4×C263C22×C411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C8×C263—41no—
74C8×C263—41no—
75C22×C263—42no—
76C22×C263—42no—
77C22×C263—42no—
78C22×C263C2×C22⋊C411yescharacteristic
79C2×D263—21no—
80C2×D263—21no—
81C2×D263—21no—
82C4×C263—21no—
83C4×C263#13511yescharacteristic
84C4×C263#13511yescharacteristic
85C4×C263AGL(1,ℤ/8)11yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87Dic263—21no—
88Dic263—21no—
89Dic263—21no—
90Dic263—42no—
91C2×C263—82no—
92C2×C263#41311yescharacteristic
93C2×C263#41611yescharacteristic
94C2×C263#41811yescharacteristic
95D263—41no—
96C263#155311yescharacteristic, complemented, Sylow
97#1553—2631nomaximal, Sylow
98#532—2631no—
99#432—2631no—
100#431—2631no—
101#332—2631no—
102#332—2631no—
103#331—2631no—
104#331D26311yescharacteristic, complemented
105C2×#41—5261no—
106C4⋊Q8—2631no—
107#127C2×D26311yescharacteristic
108#124—5261no—
109#121—2632no—
110#121—5261no—
111C4×D4—2632no—
112C4×D4—5261no—
113C2×C42—2631no—
114C4⋊C8—2631no—
115C4⋊C8—2631no—
116C4⋊C8C2×D26311yescharacteristic
117C4⋊C8C2×D26311yescharacteristic
118C22⋊C8—5261no—
119C22⋊C8—5261no—
120#97—5261no—
121C4×C8—5261no—
122#41—10522no—
123#41—10522no—
124C2×Q8—5261no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—5262no—
128C2×D4C4×D26312yes—
129C22×C4—2631no—
130C22×C4—2631no—
131C22×C4—2631no—
132C22×C4—5262no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5261no—
136C2×C8—5261no—
137C4⋊C4—2632no—
138C4⋊C4—5261no—
139C22⋊C4—5262no—
140C22⋊C4—5262no—
141C42—2631no—
142C42—2631no—
143C42—2631no—
144C42C22×D26311yescharacteristic
145C23—22no—
146C23—2631no—
147Q8—10521no—
148Q8—10521no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—10524no—
155C2×C4—2631no—
156C2×C4—2631no—
157C2×C4—2631no—
158C2×C4—5261no—
159C2×C4—5261no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—5262no—
163C2×C4—10521no—
164C2×C4—10524no—
165C2×C4C2×C4×D26311yescharacteristic
166C2×C4D4×D26311yescharacteristic
167C2×C4D4×D26311yescharacteristic
168C8—41no—
169C8—41no—
170C8—10521no—
171C8—10521no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—5261no—
176C22—5261no—
177C22—5261no—
178C22C22⋊C4×D26311yescharacteristic
179C4—21no—
180C4—5261no—
181C4—5261no—
182C4—5261no—
183C4—10522no—
184C4#2255448911yescharacteristic
185C4#2255449111yescharacteristic
186C4#2255449411yescharacteristic
187C4#2255449711yescharacteristic
188C2—82no—
189C2—10521no—
190C2#3068191911yescharacteristic
191C2#3068193111yescharacteristic
192C2#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#1553
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. #30681990C2semidirect
4. #30681685C2semidirect
5. #30681683C2semidirect
6. #30681682C2semidirect
7. #331×C263C2semidirect
96. C263#1553semidirect
104. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306824862
#306819942
#306819902
#306816852
#306816832
#306816822
#331×C2632
#1553263