Finite Group Databasebeta

← #46781244

Subgroups — #46781244

Order 33664.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#30682490C211yesmaximal, characteristic
2#30681988C211yesmaximal, characteristic
3#30681789C211yesmaximal, characteristic
4#30681676C211yesmaximal, characteristic
5#30681675C211yesmaximal, characteristic
6#30681674C211yesmaximal, characteristic
7#328×C263C211yesmaximal, characteristic
8#22554469C411yescharacteristic, complemented
9#22554468C411yescharacteristic, complemented
10#22554460—21no—
11#22554449C2211yescharacteristic
12#22554447—21no—
13Q8×Dic263C411yescharacteristic, complemented
14#22554435—21no—
15#22554435C411yescharacteristic, complemented
16#22554426—21no—
17C2×Dic263⋊C4—21no—
18C2×C4×Dic263—21no—
19C2×C4×Dic263C2211yescharacteristic
20Dic263⋊C8—21no—
21C22⋊(C263⋊C8)C2211yescharacteristic
22C8×Dic263—21no—
23C263⋊#95C2211yescharacteristic
24C22⋊Q8×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526C2×C411yescharacteristic
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263C2×C411yescharacteristic
35Dic263⋊C4—24no—
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41C22⋊Dic263—21no—
42C4×Dic263—21no—
43C4×Dic263—21no—
44C4×Dic263—42no—
45C4×Dic263C2×C411yescharacteristic
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263D411yescharacteristic
48C4×Dic263D411yescharacteristic
49C2×Q8×C263C2×C411yescharacteristic
50C22×C4×C263—21no—
51C22×C4×C263C2311yescharacteristic
52C2×C8×C263—21no—
53C4⋊C4×C263—21no—
54C4⋊C4×C263C2×C411yescharacteristic
55C22⋊C4×C263—21no—
56Dic526—42no—
57Dic526—41no—
58C2×Dic263—22no—
59C2×Dic263—22no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—41no—
63C2×Dic263—41no—
64C2×Dic263C22⋊C411yescharacteristic
65C2×Dic263C22⋊C411yescharacteristic
66C2×Dic263C22⋊C411yescharacteristic
67C2×Dic263C22⋊C411yescharacteristic
68C2×Dic263SD1612yes—
69C2×Dic263Q1612yes—
70C263⋊C8—41no—
71C23×C263C2×D411yescharacteristic
72Q8×C263—41no—
73C2×C4×C263—22no—
74C2×C4×C263—21no—
75C2×C4×C263—21no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263—41no—
79C2×C4×C263C22×C411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C8×C263—41no—
82C22×C263—21no—
83C22×C263—21no—
84C22×C263C2×C22⋊C411yescharacteristic
85C22×C263C2×SD1611yescharacteristic
86C22×C263C2×Q1611yescharacteristic
87C4×C263—21no—
88C4×C263—21no—
89C4×C263—42no—
90C4×C263—41no—
91C4×C263—41no—
92Dic263—21no—
93Dic263—42no—
94Dic263—41no—
95Dic263—41no—
96Dic263#10312yes—
97Dic263#10312yes—
98Dic263#10412yes—
99C2×C263—21no—
100C2×C263—21no—
101C2×C263#41011yescharacteristic
102C2×C263C2×#10311yescharacteristic
103C2×C263C2×#10411yescharacteristic
104C263#150311yescharacteristic, complemented, Sylow
105#1503—2631nomaximal, Sylow
106#533—2631no—
107#431—2631no—
108C4×C4⋊C4—2631no—
109#328—2631no—
110#328—2631no—
111#328—2631no—
112#328D26311yescharacteristic
113C4⋊Q8—2631no—
114C4⋊Q8—2631no—
115#125—5261no—
116C22⋊Q8—2631no—
117C22⋊Q8—5261no—
118C22⋊Q8C2×D26311yescharacteristic
119C4×Q8—2631no—
120C4×Q8—2631no—
121C4×Q8—5261no—
122#117—5261no—
123C2×C4⋊C4—5261no—
124C2×C42—2631no—
125C2×C42—5261no—
126C4⋊C8—5261no—
127C22⋊C8—2631no—
128C22⋊C8C2×D26311yescharacteristic
129C4×C8—5261no—
130#95—2631no—
131#95C2×D26311yescharacteristic
132C2×Q8—2631no—
133C2×Q8—5261no—
134C2×Q8C4×D26311yescharacteristic
135C22×C4—21no—
136C22×C4—2631no—
137C22×C4—2631no—
138C22×C4—5261no—
139C22×C4C22×D26311yescharacteristic
140C2×C8—21no—
141C2×C8—5261no—
142C4⋊C4—21no—
143C4⋊C4—2631no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C4⋊C4—5264no—
150C4⋊C4—5261no—
151C4⋊C4C4×D26311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5261no—
154C42—2631no—
155C42—2631no—
156C42—2631no—
157C42—2631no—
158C42—5261no—
159C42—5261no—
160C42—10522no—
161C23D4×D26311yescharacteristic
162Q8—41no—
163Q8—10521no—
164Q8—10522no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2631no—
172C2×C4—2631no—
173C2×C4—2631no—
174C2×C4—2632no—
175C2×C4—2632no—
176C2×C4—2631no—
177C2×C4—5262no—
178C2×C4—5262no—
179C2×C4—5261no—
180C2×C4—5261no—
181C2×C4—10521no—
182C2×C4—10521no—
183C2×C4C2×C4×D26311yescharacteristic
184C2×C4D4×D26311yescharacteristic
185C8—41no—
186C8—10521no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D26311yescharacteristic
190C22SD16×D26311yescharacteristic
191C22Q16×D26311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—2632no—
198C4—2632no—
199C4—2632no—
200C4—5261no—
201C4—10522no—
202C4—10521no—
203C4—10521no—
204C2—21no—
205C2—21no—
206C2#3068191011yescharacteristic
207C2#103×D26311yescharacteristic
208C2#104×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#328×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenter#328D263
hypocenterC263#1503
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #22554469C4semidirect
9. #22554468C4semidirect
13. Q8×Dic263C4semidirect
15. #22554435C4semidirect
104. C263#1503semidirect

Maximal subgroups

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

subgroupindex
#306824902
#306819882
#306817892
#306816762
#306816752
#306816742
#328×C2632
#1503263