Finite Group Databasebeta

← #46781456

Subgroups — #46781456

Order 33664.

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

normal subgroups only

This group has 198 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#30682493C211yesmaximal, characteristic
2#30681994C211yesmaximal, characteristic
3#30681990C211yesmaximal, characteristic
4#30681687C211yesmaximal, characteristic, complemented
5#30681685C211yesmaximal, characteristic, complemented
6#30681683C211yesmaximal, characteristic, complemented
7#333×C263C211yesmaximal, characteristic, complemented
8#22554470C2211yescharacteristic
9#22554461—21no—
10#22554450—21no—
11#22554446C412yes—
12Q8×Dic263C412yes—
13#22554435—21no—
14#22554428—21no—
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—
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×C4×D263C2×C411yescharacteristic
27C2×C4×D263D411yescharacteristic
28C2×C4×D263D411yescharacteristic
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—22no—
32C4⋊Dic263—21no—
33C4⋊Dic263C2×C412yes—
34Dic263⋊C4—22no—
35(C2×D263)⋊C4—22no—
36C4×Dic263—22no—
37C4×Dic263C2×C411yescharacteristic
38C4×Dic263D411yescharacteristic
39C4×Dic263D411yescharacteristic
40C2×Q8×C263C2×C412yes—
41C2×C8×C263—21no—
42C2×C8×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C42×C263C2311yescharacteristic
46C22×D263C22⋊C411yescharacteristic
47Dic526—41no—
48Dic526—41no—
49C2×Dic263—22no—
50C2×Dic263C22⋊C411yescharacteristic
51C2×Dic263C22⋊C411yescharacteristic
52C2×Dic263C22⋊C411yescharacteristic
53C4×D263—21no—
54C4×D263—21no—
55C4×D263—21no—
56C4×D263—21no—
57C4×D263—41no—
58C263⋊C8—41no—
59C263⋊C8—41no—
60Q8×C263—42no—
61C2×C4×C263—22no—
62C2×C4×C263C22×C411yescharacteristic
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263C2×D411yescharacteristic
65C8×C263—41no—
66C8×C263—41no—
67C22×C263C2×C22⋊C411yescharacteristic
68C2×D263—21no—
69C2×D263—21no—
70C2×D263—21no—
71C4×C263—21no—
72C4×C263—42no—
73C4×C263#13511yescharacteristic
74C4×C263#13511yescharacteristic
75C4×C263#13711yescharacteristic
76C4×C263#13711yescharacteristic
77Dic263—21no—
78Dic263—21no—
79Dic263—21no—
80Dic263—42no—
81C2×C263#41311yescharacteristic
82C2×C263#41611yescharacteristic
83C2×C263#41911yescharacteristic
84D263—41no—
85C263#155411yescharacteristic, complemented, Sylow
86#1554—2631nomaximal, Sylow
87#533—2631no—
88#432—2631no—
89#431—2631no—
90#333—2631no—
91#333D26311yescharacteristic, complemented
92#332—2631no—
93#332—2631no—
94C4⋊Q8—2631no—
95C4⋊Q8C2×D26311yescharacteristic
96#125—5261no—
97C22⋊Q8—2632no—
98C22⋊Q8—5261no—
99C4×Q8—2632no—
100C4×Q8—5261no—
101#117—5261no—
102C2×C42—2631no—
103C4⋊C8—2631no—
104C4⋊C8—2631no—
105C4⋊C8C2×D26311yescharacteristic
106C4⋊C8C2×D26311yescharacteristic
107C22⋊C8—5261no—
108C22⋊C8—5261no—
109#97—5261no—
110C4×C8—5261no—
111C2×Q8—5261no—
112C2×Q8C4×D26312yes—
113C22×C4—2631no—
114C22×C4—2631no—
115C22×C4—2631no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—5261no—
119C2×C8—5261no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—2632no—
123C4⋊C4—5262no—
124C4⋊C4—5262no—
125C4⋊C4—5261no—
126C22⋊C4—5262no—
127C42—2631no—
128C42—2631no—
129C42—2631no—
130C42—5262no—
131C42C22×D26311yescharacteristic
132C23—2631no—
133Q8—42no—
134Q8—10521no—
135Q8—10521no—
136C2×C4—22no—
137C2×C4—2631no—
138C2×C4—2631no—
139C2×C4—2631no—
140C2×C4—5261no—
141C2×C4—5261no—
142C2×C4—5261no—
143C2×C4—5261no—
144C2×C4—5262no—
145C2×C4—10521no—
146C2×C4C2×C4×D26311yescharacteristic
147C2×C4D4×D26311yescharacteristic
148C2×C4D4×D26311yescharacteristic
149C8—41no—
150C8—41no—
151C8—10521no—
152C8—10521no—
153C22—5261no—
154C22—5261no—
155C22—5261no—
156C22C22⋊C4×D26311yescharacteristic
157C4—21no—
158C4—42no—
159C4—5261no—
160C4—5261no—
161C4—5261no—
162C4—10522no—
163C4#2255449111yescharacteristic
164C4#2255449311yescharacteristic
165C4#2255449911yescharacteristic
166C4#2255450211yescharacteristic
167C2—10521no—
168C2#3068191911yescharacteristic
169C2#3068193311yescharacteristic
170C2#3068194511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#333×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×D263C22⋊C4
cosocleC42×C263C23
hypercenter#333D263
hypocenterC263#1554
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #30681687C2semidirect
5. #30681685C2semidirect
6. #30681683C2semidirect
7. #333×C263C2semidirect
85. C263#1554semidirect
91. #333D263semidirect

Maximal subgroups

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

subgroupindex
#306824932
#306819942
#306819902
#306816872
#306816852
#306816832
#333×C2632
#1554263