Finite Group Databasebeta

← #46781154

Subgroups — #46781154

Order 33664.

212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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#30681990C211yesmaximal, characteristic, complemented
3#30681989C211yesmaximal, characteristic, complemented
4Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
5#30681667C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8#22554465—21no—
9#22554461C411yescharacteristic
10#22554459C411yescharacteristic
11#22554455—21no—
12#22554446C411yescharacteristic
13#22554445C411yescharacteristic
14C4×D1052—21no—
15C4×D1052C2211yescharacteristic
16#22554427—21no—
17C42×D263C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19Dic263⋊C8—21no—
20(C2×D263)⋊C8—21no—
21(C2×D263)⋊C8—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—
35C4⋊Dic263—21no—
36C4⋊Dic263C2×C411yescharacteristic
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44C4×Dic263C2×C411yescharacteristic
45C4×Dic263D411yescharacteristic
46C4×Dic263D411yescharacteristic
47C2×Q8×C263C2×C411yescharacteristic
48C2×C8×C263—21no—
49C2×C8×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263C2×C411yescharacteristic
52C42×C263—21no—
53C42×C263C2311yescharacteristic
54C22×D263—21no—
55C22×D263C22⋊C411yescharacteristic
56D1052—21no—
57D1052—21no—
58D1052—42no—
59C2×Dic263—21no—
60C2×Dic263C22⋊C411yescharacteristic
61C2×Dic263C22⋊C411yescharacteristic
62C2×Dic263C22⋊C411yescharacteristic
63C4×D263—21no—
64C4×D263—21no—
65C4×D263—21no—
66C4×D263—21no—
67C4×D263—41no—
68C4×D263—41no—
69C4×D263—41no—
70C263⋊C8—41no—
71C263⋊C8—41no—
72Q8×C263—21no—
73Q8×C263—21no—
74C2×C4×C263—21no—
75C2×C4×C263—21no—
76C2×C4×C263C22×C411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C2×C4×C263C2×D411yescharacteristic
79C8×C263—41no—
80C8×C263—41no—
81C22×C263C2×C22⋊C411yescharacteristic
82C2×D263—21no—
83C2×D263—21no—
84C2×D263—21no—
85C2×D263—41no—
86C2×D263—41no—
87C2×D263—41no—
88C4×C263—21no—
89C4×C263—41no—
90C4×C263—41no—
91C4×C263#13111yescharacteristic
92C4×C263#13111yescharacteristic
93C4×C263#13511yescharacteristic
94C4×C263#13511yescharacteristic
95Dic263—21no—
96Dic263—21no—
97Dic263—21no—
98Dic263—41no—
99C2×C263#40811yescharacteristic
100C2×C263#41611yescharacteristic
101C2×C263#42111yescharacteristic
102D263—41no—
103D263—81no—
104C263#148211yescharacteristic, complemented, Sylow
105#1482—2631nomaximal, Sylow
106#529—2631no—
107#431—2631no—
108#431—2631no—
109Q8⋊C8—2631no—
110Q8⋊C8D26311yescharacteristic, complemented
111D4⋊C8—2631no—
112D4⋊C8—2631no—
113#126—5261no—
114#125—2631no—
115#124—2631no—
116#123—5261no—
117C22⋊Q8—2631no—
118#121—2631no—
119C4×Q8C2×D26311yescharacteristic
120C4×D4—2631no—
121C4×D4—5261no—
122#117—5261no—
123C2×C42—2631no—
124C4⋊C8—2631no—
125C4⋊C8—5261no—
126C4⋊C8C2×D26311yescharacteristic
127C22⋊C8—5261no—
128C22⋊C8—5261no—
129C4×C8—2631no—
130C4×C8—5261no—
131C4×C8C2×D26311yescharacteristic
132C2×Q8C4×D26311yescharacteristic
133C2×D4—2631no—
134C2×D4—5261no—
135C22×C4—2631no—
136C22×C4—2631no—
137C22×C4—2631no—
138C22×C4—5261no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—5261no—
142C2×C8—5261no—
143C4⋊C4—21no—
144C4⋊C4—2631no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4—5261no—
148C4⋊C4C4×D26311yescharacteristic
149C22⋊C4—5261no—
150C22⋊C4—5261no—
151C22⋊C4—5261no—
152C22⋊C4—5261no—
153C22⋊C4—5261no—
154C42—21no—
155C42—2631no—
156C42—2631no—
157C42—2631no—
158C42C22×D26311yescharacteristic
159C23—2631no—
160C23—5261no—
161Q8—21no—
162Q8—21no—
163D4—5261no—
164D4—5261no—
165D4—10522no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—2631no—
169C2×C4—2631no—
170C2×C4—2631no—
171C2×C4—5261no—
172C2×C4—5261no—
173C2×C4—5261no—
174C2×C4—5261no—
175C2×C4—5261no—
176C2×C4—10521no—
177C2×C4—10521no—
178C2×C4—10521no—
179C2×C4C2×C4×D26311yescharacteristic
180C2×C4D4×D26311yescharacteristic
181C2×C4D4×D26311yescharacteristic
182C8—41no—
183C8—41no—
184C8—10521no—
185C8—10521no—
186C22—5261no—
187C22—5261no—
188C22—5261no—
189C22—10521no—
190C22—10521no—
191C22—10521no—
192C22C22⋊C4×D26311yescharacteristic
193C4—21no—
194C4—41no—
195C4—41no—
196C4—5261no—
197C4—5261no—
198C4—5261no—
199C4—10521no—
200C4#2255447611yescharacteristic
201C4#2255447811yescharacteristic
202C4#2255449111yescharacteristic
203C4#2255449311yescharacteristic
204C2—10521no—
205C2—21041no—
206C2#3068190311yescharacteristic
207C2#3068193311yescharacteristic
208C2#3068195311yescharacteristic
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#1482
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. #30681990C2semidirect
3. #30681989C2semidirect
4. Q8⋊(C263⋊C8)C2semidirect
5. #30681667C2semidirect
6. #30681665C2semidirect
7. Q8⋊C8×C263C2semidirect
104. C263#1482semidirect
110. Q8⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306824752
#306819902
#306819892
Q8⋊(C263⋊C8)2
#306816672
#306816652
Q8⋊C8×C2632
#1482263