Finite Group Databasebeta

← #46781206

Subgroups — #46781206

Order 33664.

230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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#30682475C211yesmaximal, characteristic
2#30681994C211yesmaximal, characteristic, complemented
3C4×C8×D263C211yesmaximal, characteristic, complemented
4Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
5#30681667C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×C8×D263—21no—
9#22554465—21no—
10#22554461C411yescharacteristic
11#22554459C411yescharacteristic
12#22554455—21no—
13#22554446C411yescharacteristic
14#22554445C411yescharacteristic
15C4×D1052—21no—
16C4×D1052C2211yescharacteristic
17#22554427—21no—
18C42×D263C2211yescharacteristic
19C4⋊(C263⋊C8)C2211yescharacteristic
20(C2×D263)⋊C8—21no—
21#22554380—21no—
22C4×C263⋊C8C2211yescharacteristic
23C8×Dic263—21no—
24C4×Q8×C263C2211yescharacteristic
25C4⋊C8×C263C2211yescharacteristic
26C4×C8×C263C2211yescharacteristic
27C2×D1052—21no—
28C2×D1052C2×C411yescharacteristic
29C2×C4×D263—21no—
30C2×C4×D263C2×C411yescharacteristic
31C2×C4×D263D411yescharacteristic
32C2×C4×D263D411yescharacteristic
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C8×D263—24no—
36C4⋊Dic263—21no—
37C4⋊Dic263C2×C411yescharacteristic
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40(C2×D263)⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45C4×Dic263C2×C411yescharacteristic
46C4×Dic263D411yescharacteristic
47C4×Dic263D411yescharacteristic
48C2×Q8×C263C2×C411yescharacteristic
49C2×C8×C263—21no—
50C2×C8×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263C2×C411yescharacteristic
53C42×C263—21no—
54C42×C263C2311yescharacteristic
55C22×D263—21no—
56C22×D263C22⋊C411yescharacteristic
57D1052—21no—
58D1052—21no—
59D1052—42no—
60C2×Dic263—21no—
61C2×Dic263C22⋊C411yescharacteristic
62C2×Dic263C22⋊C411yescharacteristic
63C2×Dic263C22⋊C411yescharacteristic
64C4×D263—22no—
65C4×D263—21no—
66C4×D263—21no—
67C4×D263—21no—
68C4×D263—21no—
69C4×D263—41no—
70C4×D263—41no—
71C263⋊C8—22no—
72C263⋊C8—41no—
73Q8×C263—21no—
74Q8×C263—21no—
75C2×C4×C263—21no—
76C2×C4×C263—21no—
77C2×C4×C263C22×C411yescharacteristic
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C8×C263—22no—
81C8×C263—41no—
82C22×C263C2×C22⋊C411yescharacteristic
83C2×D263—21no—
84C2×D263—21no—
85C2×D263—41no—
86C2×D263—41no—
87C2×D263—41no—
88C2×D263#10412yes—
89C4×C263—21no—
90C4×C263—41no—
91C4×C263—41no—
92C4×C263#13111yescharacteristic
93C4×C263#13111yescharacteristic
94C4×C263#13511yescharacteristic
95C4×C263#13511yescharacteristic
96Dic263—21no—
97Dic263—21no—
98Dic263—21no—
99Dic263—41no—
100C2×C263#40811yescharacteristic
101C2×C263#41611yescharacteristic
102C2×C263C2×#10411yescharacteristic
103D263—22no—
104D263—81no—
105C263#149411yescharacteristic, complemented, Sylow
106#1494—2631nomaximal, Sylow
107#529—2631no—
108#432—2631no—
109C2×C4×C8—2631no—
110Q8⋊C8—2631no—
111Q8⋊C8D26311yescharacteristic, complemented
112D4⋊C8—2631no—
113D4⋊C8—2631no—
114C22×C8—5261no—
115#126—5261no—
116#125—2631no—
117#124—2631no—
118#123—5261no—
119C22⋊Q8—2631no—
120#121—2631no—
121C4×Q8C2×D26311yescharacteristic
122C4×D4—2631no—
123C4×D4—5261no—
124#117—5261no—
125C2×C42—2631no—
126C4⋊C8—2631no—
127C4⋊C8C2×D26311yescharacteristic
128C22⋊C8—5261no—
129#97—5261no—
130C4×C8—2631no—
131C4×C8—5261no—
132C4×C8C2×D26311yescharacteristic
133C2×Q8C4×D26311yescharacteristic
134C2×D4—2631no—
135C2×D4—5261no—
136C22×C4—2631no—
137C22×C4—2631no—
138C22×C4—2631no—
139C22×C4—5261no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—5264no—
143C2×C8—5261no—
144C2×C8—5261no—
145C4⋊C4—21no—
146C4⋊C4—2631no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C4⋊C4—5261no—
150C4⋊C4C4×D26311yescharacteristic
151C22⋊C4—5261no—
152C22⋊C4—5261no—
153C22⋊C4—5261no—
154C22⋊C4—5261no—
155C22⋊C4—5261no—
156C42—21no—
157C42—2631no—
158C42—2631no—
159C42—2631no—
160C42C22×D26311yescharacteristic
161C23—2631no—
162C23—5261no—
163Q8—21no—
164Q8—21no—
165D4—5261no—
166D4—5261no—
167D4—10522no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—2631no—
171C2×C4—2631no—
172C2×C4—2631no—
173C2×C4—5262no—
174C2×C4—5261no—
175C2×C4—5261no—
176C2×C4—5261no—
177C2×C4—5261no—
178C2×C4—5261no—
179C2×C4—10521no—
180C2×C4—10521no—
181C2×C4C2×C4×D26311yescharacteristic
182C2×C4D4×D26311yescharacteristic
183C2×C4D4×D26311yescharacteristic
184C8—22no—
185C8—41no—
186C8—5262no—
187C8—10521no—
188C22—2632no—
189C22—5261no—
190C22—5261no—
191C22—10521no—
192C22—10521no—
193C22—10521no—
194C22C22⋊C4×D26311yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—5261no—
199C4—5261no—
200C4—5261no—
201C4—10521no—
202C4#2255447611yescharacteristic
203C4#2255447811yescharacteristic
204C4#2255449111yescharacteristic
205C4#2255449311yescharacteristic
206C2—5262no—
207C2—21041no—
208C2#3068190311yescharacteristic
209C2#3068193311yescharacteristic
210C2#104×D26311yescharacteristic
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554445C4
cosocleC42×C263C23
hypercenterQ8⋊C8D263
hypocenterC263#1494
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #30681994C2semidirect
3. C4×C8×D263C2semidirect
4. Q8⋊(C263⋊C8)C2semidirect
5. #30681667C2semidirect
6. #30681665C2semidirect
7. Q8⋊C8×C263C2semidirect
105. C263#1494semidirect
111. Q8⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306824752
#306819942
C4×C8×D2632
Q8⋊(C263⋊C8)2
#306816672
#306816652
Q8⋊C8×C2632
#1494263