Finite Group Databasebeta

← #46781322

Subgroups — #46781322

Order 33664.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#30681674C212yesmaximal, complemented
4#30681671C212yesmaximal
5#383×C263C211yesmaximal, characteristic, complemented
6#22554464—21no—
7#22554462C411yescharacteristic, complemented
8#22554458C411yescharacteristic, complemented
9#22554453—21no—
10#22554449C2211yescharacteristic
11#22554444C2211yescharacteristic
12C4×Dic526C411yescharacteristic, complemented
13C4×D1052C411yescharacteristic, complemented
14C4×C22⋊D263—21no—
15#22554427—21no—
16C4⋊(C263⋊C8)—21no—
17C22⋊(C263⋊C8)C2212yes—
18C4×C263⋊C8—21no—
19C2×C42×C263C2211yescharacteristic
20#95×C263—21no—
21#95×C263—21no—
22#95×C263C2212yes—
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×C263—22no—
41C22×C4×C263D411yescharacteristic
42C22×C4×C263D411yescharacteristic
43C22×C4×C263C2311yescharacteristic
44C42×C263C2×C411yescharacteristic
45C42×C263C2×C411yescharacteristic
46C42×C263D411yescharacteristic
47C42×C263D411yescharacteristic
48C22×D263—21no—
49Dic526—41no—
50D1052—41no—
51C22⋊D263—42no—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C4×D263—42no—
56C263⋊C8—42no—
57C23×C263C2×D411yescharacteristic
58C2×C4×C263—22no—
59C2×C4×C263—41no—
60C2×C4×C263—41no—
61C2×C4×C263—42no—
62C2×C4×C263—42no—
63C2×C4×C263—42no—
64C2×C4×C263C22⋊C411yescharacteristic
65C2×C4×C263C22⋊C411yescharacteristic
66C2×C4×C263C22⋊C411yescharacteristic
67C2×C4×C263C22⋊C411yescharacteristic
68C2×C4×C263C22×C411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C22×C263—21no—
71C22×C263—21no—
72C22×C263C2×C22⋊C411yescharacteristic
73C22×C263#13512yes—
74C2×D263—41no—
75C2×D263—41no—
76C2×D263—41no—
77C4×C263—21no—
78C4×C263—21no—
79C4×C263—21no—
80C4×C263—21no—
81C4×C263—21no—
82C4×C263—21no—
83C4×C263—82no—
84Dic263—41no—
85Dic263—41no—
86Dic263—41no—
87C2×C263—22no—
88C2×C263#41011yescharacteristic
89C2×C263#41611yescharacteristic
90C2×C263#42111yescharacteristic
91D263—81no—
92C263#152111yescharacteristic, complemented, Sylow
93#1521—2631nomaximal, Sylow
94#529—2631no—
95#431—2631no—
96#383D26311yescharacteristic, complemented
97#328—2632no—
98#327—2632no—
99#126—5261no—
100#125—2631no—
101#124—2631no—
102#123—5261no—
103C22⋊Q8—2631no—
104#121—2631no—
105C4×Q8—2631no—
106C4×D4—2631no—
107C4×D4—5261no—
108#117—5261no—
109C2×C42C2×D26311yescharacteristic
110C4⋊C8—5261no—
111C22⋊C8—2632no—
112C4×C8—5261no—
113#95—21no—
114#95—21no—
115#95C2×D26312yes—
116C2×Q8—2631no—
117C2×D4—2631no—
118C2×D4—5261no—
119C22×C4—22no—
120C22×C4—5261no—
121C22×C4C22⋊D26311yescharacteristic
122C22×C4C22⋊D26311yescharacteristic
123C22×C4C22×D26311yescharacteristic
124C2×C8—5262no—
125C4⋊C4—2631no—
126C4⋊C4—2631no—
127C4⋊C4—5261no—
128C4⋊C4—5261no—
129C4⋊C4—5261no—
130C4⋊C4—5261no—
131C22⋊C4—5261no—
132C22⋊C4—5261no—
133C22⋊C4—5261no—
134C22⋊C4—5261no—
135C22⋊C4—5261no—
136C42—5261no—
137C42C4×D26311yescharacteristic
138C42C4×D26311yescharacteristic
139C42D105211yescharacteristic
140C42D105211yescharacteristic
141C23—5261no—
142C23C2×C22⋊D26311yescharacteristic
143Q8—10521no—
144D4—10521no—
145D4—10522no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—5261no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—10522no—
156C2×C4(C2×D263)⋊C411yescharacteristic
157C2×C4(C2×D263)⋊C411yescharacteristic
158C2×C4(C2×D263)⋊C411yescharacteristic
159C2×C4(C2×D263)⋊C411yescharacteristic
160C2×C4C2×C4×D26311yescharacteristic
161C2×C4C2×D105211yescharacteristic
162C8—10522no—
163C22—21no—
164C22—21no—
165C22—10521no—
166C22—10521no—
167C22—10521no—
168C22C2×(C2×D263)⋊C411yescharacteristic
169C22#2255449012yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—10521no—
178C4—10521no—
179C4—10521no—
180C2—22no—
181C2—21041no—
182C2#3068191111yescharacteristic
183C2#3068193211yescharacteristic
184C2#3068195611yescharacteristic
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#383×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C22
cosocleC22×C4×C263C23
hypercenter#383D263
hypocenterC263#1521
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #30681991C2semidirect
3. #30681674C2semidirect
5. #383×C263C2semidirect
7. #22554462C4semidirect
8. #22554458C4semidirect
12. C4×Dic526C4semidirect
13. C4×D1052C4semidirect
92. C263#1521semidirect
96. #383D263semidirect

Maximal subgroups

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

subgroupindex
#306824722
#306819912
#306816742
#306816712
#383×C2632
#1521263