Finite Group Databasebeta

← #46781153

Subgroups — #46781153

Order 33664.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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
2#30681991C211yesmaximal, characteristic, complemented
3#30681668C212yesmaximal, complemented
4#30681665C212yesmaximal, complemented
5#431×C263C211yesmaximal, characteristic, complemented
6#22554464—21no—
7#22554462C411yescharacteristic
8#22554458C411yescharacteristic
9#22554453—21no—
10#22554449C411yescharacteristic
11#22554444C411yescharacteristic
12C4×Dic526C2211yescharacteristic
13C4×D1052C2211yescharacteristic
14C4×C22⋊D263—21no—
15#22554427—21no—
16C4⋊(C263⋊C8)—21no—
17C22⋊(C263⋊C8)—21no—
18C4×C263⋊C8C2212yes—
19C2×C42×C263C2211yescharacteristic
20C4⋊C8×C263C2212yes—
21C22⋊C8×C263—21no—
22C4×C8×C263—21no—
23C2×Dic526C2×C411yescharacteristic
24C2×D1052C2×C411yescharacteristic
25C2×C22⋊D263—21no—
26C2×C4×D263—21no—
27C2×C263⋊C8—22no—
28C4⋊Dic263C2×C411yescharacteristic
29C4⋊Dic263C2×C411yescharacteristic
30Dic263⋊C4—21no—
31Dic263⋊C4—21no—
32Dic263⋊C4—21no—
33Dic263⋊C4—21no—
34C22⋊Dic263—21no—
35(C2×D263)⋊C4—21no—
36(C2×D263)⋊C4—21no—
37(C2×D263)⋊C4—21no—
38(C2×D263)⋊C4—21no—
39C4×Dic263—21no—
40C22×C4×C263C2×C411yescharacteristic
41C22×C4×C263D411yescharacteristic
42C22×C4×C263D411yescharacteristic
43C2×C8×C263—22no—
44C42×C263C2×C411yescharacteristic
45C42×C263D411yescharacteristic
46C42×C263D411yescharacteristic
47C42×C263C2311yescharacteristic
48C22×D263—21no—
49Dic526—22no—
50D1052—22no—
51C22⋊D263—42no—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C4×D263—42no—
56C263⋊C8—42no—
57C23×C263C22⋊C411yescharacteristic
58C2×C4×C263—22no—
59C2×C4×C263—22no—
60C2×C4×C263—41no—
61C2×C4×C263C22⋊C411yescharacteristic
62C2×C4×C263C22⋊C411yescharacteristic
63C2×C4×C263C22⋊C411yescharacteristic
64C2×C4×C263C22×C411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C8×C263—42no—
68C22×C263—21no—
69C22×C263—21no—
70C22×C263—21no—
71C22×C263C2×C22⋊C411yescharacteristic
72C2×D263—41no—
73C2×D263—41no—
74C2×D263—41no—
75C4×C263—21no—
76C4×C263—21no—
77C4×C263—21no—
78C4×C263—21no—
79C4×C263#13112yes—
80C4×C263#13512yes—
81Dic263—41no—
82Dic263—41no—
83Dic263—41no—
84C2×C263—41no—
85C2×C263#40811yescharacteristic
86C2×C263#41611yescharacteristic
87C2×C263#42111yescharacteristic
88D263—81no—
89C263#148211yescharacteristic, complemented, Sylow
90#1482—2631nomaximal, Sylow
91#529—2631no—
92#431—2631no—
93#431D26311yescharacteristic, complemented
94Q8⋊C8—2632no—
95D4⋊C8—2632no—
96#126—5261no—
97#125—2631no—
98#124—2631no—
99#123—5261no—
100C22⋊Q8—2631no—
101#121—2631no—
102C4×Q8—2631no—
103C4×D4—2631no—
104C4×D4—5261no—
105#117—5261no—
106C2×C42C2×D26311yescharacteristic
107C4⋊C8—5261no—
108C4⋊C8C2×D26312yes—
109C22⋊C8—21no—
110C22⋊C8—5261no—
111C4×C8—21no—
112C4×C8—2632no—
113C2×Q8—2631no—
114C2×D4—2631no—
115C2×D4—5261no—
116C22×C4—5261no—
117C22×C4C4×D26311yescharacteristic
118C22×C4C22⋊D26311yescharacteristic
119C22×C4D105211yescharacteristic
120C2×C8—22no—
121C2×C8—5262no—
122C4⋊C4—2631no—
123C4⋊C4—2631no—
124C4⋊C4—5261no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4—5261no—
128C22⋊C4—5261no—
129C22⋊C4—5261no—
130C22⋊C4—5261no—
131C22⋊C4—5261no—
132C22⋊C4—5261no—
133C42—5261no—
134C42C4×D26311yescharacteristic
135C42C22⋊D26311yescharacteristic
136C42D105211yescharacteristic
137C42C22×D26311yescharacteristic
138C23—5261no—
139C23(C2×D263)⋊C411yescharacteristic
140Q8—5262no—
141D4—5262no—
142D4—10522no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—5261no—
147C2×C4—5261no—
148C2×C4—5261no—
149C2×C4—10522no—
150C2×C4(C2×D263)⋊C411yescharacteristic
151C2×C4(C2×D263)⋊C411yescharacteristic
152C2×C4(C2×D263)⋊C411yescharacteristic
153C2×C4C2×C4×D26311yescharacteristic
154C2×C4C2×C22⋊D26311yescharacteristic
155C2×C4C2×D105211yescharacteristic
156C8—42no—
157C8—10522no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—10521no—
162C22—10521no—
163C22—10521no—
164C22C2×(C2×D263)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—10521no—
170C4—10521no—
171C4—10521no—
172C4#2255447612yes—
173C4#2255449012yes—
174C2—41no—
175C2—21041no—
176C2#3068190411yescharacteristic
177C2#3068193211yescharacteristic
178C2#3068195411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#431×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C4
cosocleC42×C263C23
hypercenter#431D263
hypocenterC263#1482
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #30681991C2semidirect
3. #30681668C2semidirect
4. #30681665C2semidirect
5. #431×C263C2semidirect
89. C263#1482semidirect
93. #431D263semidirect

Maximal subgroups

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

subgroupindex
#306824722
#306819912
#306816682
#306816652
#431×C2632
#1482263