Finite Group Databasebeta

← #46781337

Subgroups — #46781337

Order 33664.

270 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 63 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#30681890C212yesmaximal, complemented
3#30681678C211yesmaximal, characteristic, complemented
4#30681677C212yesmaximal, complemented
5#329×C263C211yesmaximal, characteristic, complemented
6C2×#16862377C411yescharacteristic
7C2×#16862375C411yescharacteristic
8C2×#16862359—22no—
9#22554468C411yescharacteristic
10#22554466C411yescharacteristic
11#22554458C2211yescharacteristic
12#22554443—22no—
13(C22⋊D263)⋊C4—22no—
14C42×D263C2211yescharacteristic
15#22554381C2212yes—
16C8×Dic263—22no—
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—
30#16862359—28no—
31C2×C263⋊C8—22no—
32Dic263⋊C4—22no—
33(C2×D263)⋊C4—22no—
34C4×Dic263C2×C411yescharacteristic
35C4×Dic263D412yes—
36C2×Q8×C263C2×C411yescharacteristic
37C2×D4×C263C2×C411yescharacteristic
38C2×C8×C263—22no—
39C22⋊C4×C263—22no—
40C42×C263C2311yescharacteristic
41C22×D263—21no—
42C22×D263C22⋊C411yescharacteristic
43Dic526—41no—
44D1052—41no—
45D1052—42no—
46C22⋊D263—42no—
47C22⋊D263—44no—
48C2×Dic263—21no—
49C2×Dic263—42no—
50C2×Dic263C22⋊C411yescharacteristic
51C2×Dic263C22⋊C412yes—
52C4×D263—22no—
53C4×D263—24no—
54C4×D263—42no—
55C263⋊C8—24no—
56C23×C263—21no—
57Q8×C263—41no—
58D4×C263—41no—
59C2×C4×C263—21no—
60C2×C4×C263C22×C411yescharacteristic
61C2×C4×C263C2×D412yes—
62C8×C263—24no—
63C22×C263—41no—
64C22×C263—42no—
65C22×C263C2×C22⋊C411yescharacteristic
66C2×D263—21no—
67C2×D263—22no—
68C2×D263—41no—
69C2×D263—42no—
70C4×C263—21no—
71C4×C263—22no—
72C4×C263—41no—
73Dic263—41no—
74Dic263#10012yes—
75Dic263#10414yes—
76C2×C263—81no—
77C2×C263C2×#10011yescharacteristic
78C2×C263C2×#10412yes—
79D263—41no—
80D263—81no—
81C263#152511yescharacteristic, complemented, Sylow
82#1525—2631nomaximal, Sylow
83#532—2631no—
84C4×M16—2632no—
85#329—2631no—
86#329—2632no—
87#329D26311yescharacteristic, complemented
88C2×#41—2631no—
89C2×#41—2631no—
90C2×M16—5262no—
91C4⋊Q8—2631no—
92#127—2631no—
93#124—2631no—
94#124C2×D26311yescharacteristic
95#121—5262no—
96C4×D4—5262no—
97C2×C42—2631no—
98#97—2632no—
99#97C2×D26312yes—
100C4×C8—5262no—
101#41—10522no—
102#41—10522no—
103C2×Q8—2631no—
104C2×Q8C4×D26311yescharacteristic
105C2×D4—2631no—
106C2×D4—5261no—
107C2×D4—5262no—
108C2×D4—5261no—
109C2×D4C4×D26311yescharacteristic
110C22×C4—2631no—
111C22×C4—2632no—
112C22×C4—5261no—
113C22×C4—5261no—
114M16—5268no—
115C2×C8—22no—
116C2×C8—5262no—
117C4⋊C4—5262no—
118C22⋊C4—22no—
119C22⋊C4—5262no—
120C42—2631no—
121C42—2632no—
122C42C22×D26311yescharacteristic
123C23—21no—
124C23—2631no—
125C23—5261no—
126Q8—41no—
127Q8—10521no—
128D4—41no—
129D4—10521no—
130D4—10522no—
131D4—10524no—
132D4—10522no—
133C2×C4—21no—
134C2×C4—2632no—
135C2×C4—2631no—
136C2×C4—5264no—
137C2×C4—5262no—
138C2×C4—5261no—
139C2×C4—10522no—
140C2×C4—10522no—
141C2×C4C2×C4×D26311yescharacteristic
142C2×C4D4×D26312yes—
143C8—24no—
144C8—5264no—
145C22—41no—
146C22—42no—
147C22—5261no—
148C22—5262no—
149C22—10521no—
150C22—10522no—
151C22C22⋊C4×D26311yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—2632no—
156C4—2634no—
157C4—10521no—
158C2—81no—
159C2—10521no—
160C2—21041no—
161C2#100×D26311yescharacteristic
162C2#104×D26312yes—
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#1525
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. #30681890C2semidirect
3. #30681678C2semidirect
4. #30681677C2semidirect
5. #329×C263C2semidirect
81. C263#1525semidirect
87. #329D263semidirect

Maximal subgroups

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

subgroupindex
#306824872
#306818902
#306816782
#306816772
#329×C2632
#1525263