Finite Group Databasebeta

← #46781213

Subgroups — #46781213

Order 33664.

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

normal subgroups only

This group has 216 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#30681962C211yesmaximal, characteristic, complemented
3#30681670C212yesmaximal, complemented
4#30681667C212yesmaximal, complemented
5#431×C263C211yesmaximal, characteristic, complemented
6C2×#16862360—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⋊C8)C2212yes—
19C2×C42×C263C2211yescharacteristic
20C4⋊C8×C263—21no—
21C22⋊C8×C263—21no—
22C4×C8×C263C2212yes—
23C2×Dic526C2×C411yescharacteristic
24C2×D1052C2×C411yescharacteristic
25C2×C22⋊D263—21no—
26C2×C4×D263—21no—
27#16862360—42no—
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—41no—
57C4×D263—41no—
58C263⋊C8—42no—
59C23×C263C22⋊C411yescharacteristic
60C2×C4×C263—22no—
61C2×C4×C263—21no—
62C2×C4×C263—21no—
63C2×C4×C263—41no—
64C2×C4×C263C22⋊C411yescharacteristic
65C2×C4×C263C22⋊C411yescharacteristic
66C2×C4×C263C22⋊C411yescharacteristic
67C2×C4×C263C22×C411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C8×C263—42no—
71C22×C263—21no—
72C22×C263—21no—
73C22×C263—21no—
74C22×C263C2×C22⋊C411yescharacteristic
75C2×D263—41no—
76C2×D263—41no—
77C2×D263—41no—
78C4×C263—21no—
79C4×C263—21no—
80C4×C263—21no—
81C4×C263—21no—
82C4×C263#13112yes—
83C4×C263AGL(1,ℤ/8)11yescharacteristic
84C4×C263#13711yescharacteristic
85Dic263—41no—
86Dic263—41no—
87Dic263—41no—
88C2×C263—41no—
89C2×C263#40811yescharacteristic
90C2×C263#41711yescharacteristic
91C2×C263#42111yescharacteristic
92D263—81no—
93C263#149511yescharacteristic, complemented, Sylow
94#1495—2631nomaximal, Sylow
95#529—2631no—
96#431D26311yescharacteristic, complemented
97#423—2631no—
98Q8⋊C8—2632no—
99D4⋊C8—2632no—
100C2×M16—5261no—
101#126—5261no—
102#125—2631no—
103#124—2631no—
104#123—5261no—
105C22⋊Q8—2631no—
106#121—2631no—
107C4×Q8—2631no—
108C4×D4—2631no—
109C4×D4—5261no—
110#117—5261no—
111C2×C42C2×D26311yescharacteristic
112C4⋊C8—21no—
113C4⋊C8—2632no—
114C4⋊C8—5261no—
115C22⋊C8—21no—
116C4×C8C2×D26312yes—
117C2×Q8—2631no—
118C2×D4—2631no—
119C2×D4—5261no—
120C22×C4—5261no—
121C22×C4C4×D26311yescharacteristic
122C22×C4C22⋊D26311yescharacteristic
123C22×C4D105211yescharacteristic
124M16—10522no—
125C2×C8—22no—
126C2×C8—5262no—
127C4⋊C4—2631no—
128C4⋊C4—2631no—
129C4⋊C4—5261no—
130C4⋊C4—5261no—
131C4⋊C4—5261no—
132C4⋊C4—5261no—
133C22⋊C4—5261no—
134C22⋊C4—5261no—
135C22⋊C4—5261no—
136C22⋊C4—5261no—
137C22⋊C4—5261no—
138C42—5261no—
139C42C4×D26311yescharacteristic
140C42C22⋊D26311yescharacteristic
141C42D105211yescharacteristic
142C42C22×D26311yescharacteristic
143C23—5261no—
144C23(C2×D263)⋊C411yescharacteristic
145Q8—5262no—
146D4—5262no—
147D4—10522no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—5261no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—10521no—
156C2×C4—10521no—
157C2×C4(C2×D263)⋊C411yescharacteristic
158C2×C4(C2×D263)⋊C411yescharacteristic
159C2×C4(C2×D263)⋊C411yescharacteristic
160C2×C4C2×C4×D26311yescharacteristic
161C2×C4C2×C22⋊D26311yescharacteristic
162C2×C4C2×D105211yescharacteristic
163C8—42no—
164C8—10522no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—10521no—
169C22—10521no—
170C22—10521no—
171C22C2×(C2×D263)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—10521no—
177C4—10521no—
178C4—10521no—
179C4#2255447612yes—
180C4#2255449811yescharacteristic
181C4#2255450311yescharacteristic
182C2—41no—
183C2—21041no—
184C2#3068190411yescharacteristic
185C2#3068194011yescharacteristic
186C2#3068195611yescharacteristic
subgroupG/H
centerC2×C4C2×D1052
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#431×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C4
cosocleC42×C263C23
hypercenter#431D263
hypocenterC263#1495
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. #30681962C2semidirect
3. #30681670C2semidirect
4. #30681667C2semidirect
5. #431×C263C2semidirect
93. C263#1495semidirect
96. #431D263semidirect

Maximal subgroups

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

subgroupindex
#306824722
#306819622
#306816702
#306816672
#431×C2632
#1495263