Finite Group Databasebeta

← #46781205

Subgroups — #46781205

Order 33664.

230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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#30682472C211yesmaximal, characteristic
2C2×C4×C263⋊C8C211yesmaximal, characteristic, complemented
3#30681668C212yesmaximal, complemented
4#30681665C212yesmaximal, complemented
5#432×C263C211yesmaximal, characteristic, complemented
6C22×C263⋊C8—21no—
7#22554464—21no—
8#22554462C411yescharacteristic
9#22554458C411yescharacteristic
10#22554453—21no—
11#22554449C411yescharacteristic
12#22554444C411yescharacteristic
13C4×Dic526C2211yescharacteristic
14C4×D1052C2211yescharacteristic
15C4×C22⋊D263—21no—
16#22554427—21no—
17C4×C263⋊C8—21no—
18C4×C263⋊C8C2212yes—
19C2×C42×C263C2211yescharacteristic
20C4⋊C8×C263C2212yes—
21C22⋊C8×C263—21no—
22#97×C263—21no—
23C2×Dic526C2×C411yescharacteristic
24C2×D1052C2×C411yescharacteristic
25C2×C22⋊D263—21no—
26C2×C4×D263—21no—
27C2×C263⋊C8—24no—
28C2×C263⋊C8—22no—
29C4⋊Dic263C2×C411yescharacteristic
30C4⋊Dic263C2×C411yescharacteristic
31Dic263⋊C4—21no—
32Dic263⋊C4—21no—
33Dic263⋊C4—21no—
34Dic263⋊C4—21no—
35C22⋊Dic263—21no—
36(C2×D263)⋊C4—21no—
37(C2×D263)⋊C4—21no—
38(C2×D263)⋊C4—21no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—21no—
41C22×C4×C263C2×C411yescharacteristic
42C22×C4×C263D411yescharacteristic
43C22×C4×C263D411yescharacteristic
44C2×C8×C263—22no—
45C42×C263C2×C411yescharacteristic
46C42×C263D411yescharacteristic
47C42×C263D411yescharacteristic
48C42×C263C2311yescharacteristic
49C22×D263—21no—
50Dic526—22no—
51D1052—22no—
52C22⋊D263—42no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C4×D263—42no—
57C263⋊C8—24no—
58C23×C263C22⋊C411yescharacteristic
59C2×C4×C263—22no—
60C2×C4×C263—22no—
61C2×C4×C263—22no—
62C2×C4×C263C22⋊C411yescharacteristic
63C2×C4×C263C22⋊C411yescharacteristic
64C2×C4×C263C22⋊C411yescharacteristic
65C2×C4×C263C22×C411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C2×C4×C263C2×D411yescharacteristic
68C8×C263—42no—
69C22×C263—21no—
70C22×C263—21no—
71C22×C263#10412yes—
72C22×C263C2×C22⋊C411yescharacteristic
73C2×D263—41no—
74C2×D263—41no—
75C2×D263—41no—
76C4×C263—21no—
77C4×C263—21no—
78C4×C263—21no—
79C4×C263—21no—
80C4×C263#13112yes—
81C4×C263#13512yes—
82Dic263—41no—
83Dic263—41no—
84Dic263—41no—
85C2×C263—22no—
86C2×C263#40811yescharacteristic
87C2×C263#41611yescharacteristic
88C2×C263C2×#10411yescharacteristic
89D263—81no—
90C263#149411yescharacteristic, complemented, Sylow
91#1494—2631nomaximal, Sylow
92#529—2631no—
93#432D26311yescharacteristic, complemented
94C2×C4×C8—2631no—
95Q8⋊C8—2632no—
96D4⋊C8—2632no—
97C22×C8—5261no—
98#126—5261no—
99#125—2631no—
100#124—2631no—
101#123—5261no—
102C22⋊Q8—2631no—
103#121—2631no—
104C4×Q8—2631no—
105C4×D4—2631no—
106C4×D4—5261no—
107#117—5261no—
108C2×C42C2×D26311yescharacteristic
109C4⋊C8C2×D26312yes—
110C22⋊C8—21no—
111#97—21no—
112C4×C8—2632no—
113C4×C8—5261no—
114C2×Q8—2631no—
115C2×D4—2631no—
116C2×D4—5261no—
117C22×C4—5261no—
118C22×C4C4×D26311yescharacteristic
119C22×C4C22⋊D26311yescharacteristic
120C22×C4D105211yescharacteristic
121C2×C8—22no—
122C2×C8—5264no—
123C2×C8—5262no—
124C4⋊C4—2631no—
125C4⋊C4—2631no—
126C4⋊C4—5261no—
127C4⋊C4—5261no—
128C4⋊C4—5261no—
129C4⋊C4—5261no—
130C22⋊C4—5261no—
131C22⋊C4—5261no—
132C22⋊C4—5261no—
133C22⋊C4—5261no—
134C22⋊C4—5261no—
135C42—5261no—
136C42C4×D26311yescharacteristic
137C42C22⋊D26311yescharacteristic
138C42D105211yescharacteristic
139C42C22×D26311yescharacteristic
140C23—5261no—
141C23(C2×D263)⋊C411yescharacteristic
142Q8—5262no—
143D4—5262no—
144D4—10522no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—5261no—
149C2×C4—5261no—
150C2×C4—5261no—
151C2×C4—10522no—
152C2×C4(C2×D263)⋊C411yescharacteristic
153C2×C4(C2×D263)⋊C411yescharacteristic
154C2×C4(C2×D263)⋊C411yescharacteristic
155C2×C4C2×C4×D26311yescharacteristic
156C2×C4C2×C22⋊D26311yescharacteristic
157C2×C4C2×D105211yescharacteristic
158C8—42no—
159C8—5264no—
160C22—21no—
161C22—21no—
162C22—10521no—
163C22—10521no—
164C22—10521no—
165C22#2255439612yes—
166C22C2×(C2×D263)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—10521no—
172C4—10521no—
173C4—10521no—
174C4#2255447812yes—
175C4#2255449012yes—
176C2—22no—
177C2—21041no—
178C2#3068190611yescharacteristic
179C2#3068193211yescharacteristic
180C2C2×#2255439611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#432×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C4
cosocleC42×C263C23
hypercenter#432D263
hypocenterC263#1494
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×C263⋊C8C2semidirect
3. #30681668C2semidirect
4. #30681665C2semidirect
5. #432×C263C2semidirect
90. C263#1494semidirect
93. #432D263semidirect

Maximal subgroups

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

subgroupindex
#306824722
C2×C4×C263⋊C82
#306816682
#306816652
#432×C2632
#1494263