Finite Group Databasebeta

← #46781380

Subgroups — #46781380

Order 33664.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#30682487C211yesmaximal, characteristic
2#30681993C212yesmaximal, complemented
3#30681678C211yesmaximal, characteristic, complemented
4#30681677C212yesmaximal, complemented
5#329×C263C211yesmaximal, characteristic, complemented
6C2×#16862377C411yescharacteristic
7C2×#16862375C411yescharacteristic
8#22554468C411yescharacteristic
9#22554466C411yescharacteristic
10#22554458C2211yescharacteristic
11#22554443—22no—
12(C22⋊D263)⋊C4—22no—
13C42×D263C2211yescharacteristic
14Dic263⋊C8—22no—
15(C2×D263)⋊C8—22no—
16#22554381C2212yes—
17#124×C263C2211yescharacteristic
18#97×C263C2212yes—
19#16862377—42no—
20#16862375—42no—
21C2×Dic526C2×C411yescharacteristic
22C2×D1052—21no—
23C2×D1052C2×C411yescharacteristic
24C2×C22⋊D263—21no—
25C2×C22⋊D263—22no—
26C22×Dic263—21no—
27C2×C4×D263—21no—
28C2×C4×D263C2×C411yescharacteristic
29C2×C4×D263D412yes—
30C2×C263⋊C8—22no—
31Dic263⋊C4—22no—
32(C2×D263)⋊C4—22no—
33C4×Dic263C2×C411yescharacteristic
34C4×Dic263D412yes—
35C2×Q8×C263C2×C411yescharacteristic
36C2×D4×C263C2×C411yescharacteristic
37C2×C8×C263—22no—
38C22⋊C4×C263—22no—
39C42×C263C2311yescharacteristic
40C22×D263—21no—
41C22×D263C22⋊C411yescharacteristic
42Dic526—41no—
43D1052—41no—
44D1052—42no—
45C22⋊D263—44no—
46C22⋊D263—42no—
47C2×Dic263—21no—
48C2×Dic263—42no—
49C2×Dic263C22⋊C412yes—
50C2×Dic263C22⋊C411yescharacteristic
51C4×D263—22no—
52C4×D263—42no—
53C4×D263—42no—
54C263⋊C8—42no—
55C23×C263—21no—
56Q8×C263—41no—
57D4×C263—41no—
58C2×C4×C263—21no—
59C2×C4×C263C22×C411yescharacteristic
60C2×C4×C263C2×D412yes—
61C8×C263—42no—
62C22×C263—41no—
63C22×C263—42no—
64C22×C263C2×C22⋊C411yescharacteristic
65C2×D263—21no—
66C2×D263—22no—
67C2×D263—41no—
68C2×D263—42no—
69C4×C263—21no—
70C4×C263—22no—
71C4×C263—41no—
72Dic263—22no—
73Dic263—41no—
74Dic263#10012yes—
75C2×C263—81no—
76C2×C263C2×#10011yescharacteristic
77C2×C263#42112yes—
78D263—41no—
79D263—81no—
80C263#153611yescharacteristic, complemented, Sylow
81#1536—2631nomaximal, Sylow
82#532—2631no—
83#432—2632no—
84#329—2631no—
85#329—2632no—
86#329D26311yescharacteristic, complemented
87C2×#41—2631no—
88C2×#41—2631no—
89C4⋊Q8—2631no—
90#127—2631no—
91#124—2631no—
92#124C2×D26311yescharacteristic
93#121—5262no—
94C4×D4—5262no—
95C2×C42—2631no—
96C4⋊C8—5262no—
97C22⋊C8—5262no—
98#97—2632no—
99#97C2×D26312yes—
100#41—10522no—
101#41—10522no—
102C2×Q8—2631no—
103C2×Q8C4×D26311yescharacteristic
104C2×D4—2631no—
105C2×D4—5261no—
106C2×D4—5262no—
107C2×D4—5261no—
108C2×D4C4×D26311yescharacteristic
109C22×C4—2631no—
110C22×C4—2632no—
111C22×C4—5261no—
112C22×C4—5261no—
113C2×C8—22no—
114C2×C8—5262no—
115C4⋊C4—5262no—
116C22⋊C4—22no—
117C22⋊C4—5262no—
118C42—2631no—
119C42—2632no—
120C42C22×D26311yescharacteristic
121C23—21no—
122C23—2631no—
123C23—5261no—
124Q8—41no—
125Q8—10521no—
126D4—41no—
127D4—10521no—
128D4—10522no—
129D4—10524no—
130D4—10522no—
131C2×C4—21no—
132C2×C4—2631no—
133C2×C4—2632no—
134C2×C4—5262no—
135C2×C4—5261no—
136C2×C4—10522no—
137C2×C4—10522no—
138C2×C4—10522no—
139C2×C4C2×C4×D26311yescharacteristic
140C2×C4D4×D26312yes—
141C8—42no—
142C8—10522no—
143C22—41no—
144C22—42no—
145C22—5261no—
146C22—5262no—
147C22—10521no—
148C22—10522no—
149C22C22⋊C4×D26311yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2632no—
154C4—5262no—
155C4—10521no—
156C2—81no—
157C2—10521no—
158C2—21041no—
159C2#100×D26311yescharacteristic
160C2#3068195312yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682487C2
cosocleC42×C263C23
hypercenter#329D263
hypocenterC263#1536
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #30681993C2semidirect
3. #30681678C2semidirect
4. #30681677C2semidirect
5. #329×C263C2semidirect
80. C263#1536semidirect
86. #329D263semidirect

Maximal subgroups

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

subgroupindex
#306824872
#306819932
#306816782
#306816772
#329×C2632
#1536263