Finite Group Databasebeta

← #46781822

Subgroups — #46781822

Order 33664.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682648C211yesmaximal, characteristic, complemented
2#30682311C211yesmaximal, characteristic, complemented
3#30682138C211yesmaximal, characteristic, complemented
4#30682134C211yesmaximal, characteristic
5#30681686C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—22no—
9C2×#16862363—21no—
10C2×D2104—21no—
11#22554470C2211yescharacteristic
12#22554467C2211yescharacteristic
13#22554462—21no—
14#22554448—22no—
15#22554446—21no—
16C4×D1052—21no—
17C4×D1052C2211yescharacteristic
18C4⋊C4×D263—21no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554392—21no—
21#22554390—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526D412yes—
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052D411yescharacteristic
30C2×C4×D263—22no—
31C2×C4×D263—21no—
32#16862365—44no—
33#16862363—42no—
34D2104—42no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263D411yescharacteristic
39Dic263⋊C4—22no—
40Dic263⋊C4—22no—
41(C2×D263)⋊C4—22no—
42(C2×D263)⋊C4—21no—
43C2×Q8×C263D411yescharacteristic
44C2×C8×C263—21no—
45C2×C8×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C42×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51C22×D263—41no—
52Dic526—42no—
53D1052—21no—
54D1052—42no—
55D1052—41no—
56D1052—41no—
57D1052—41no—
58D1052—41no—
59D1052SD1612yescomplemented
60C2×Dic263—21no—
61C2×Dic263—22no—
62C4×D263—41no—
63C4×D263—41no—
64C4×D263—82no—
65C263⋊C8—41no—
66Q8×C263—21no—
67Q8×C263—21no—
68C2×C4×C263—21no—
69C2×C4×C263—21no—
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C8×C263—22no—
74C8×C263—41no—
75C22×C263#12011yescharacteristic
76C2×D263—22no—
77C2×D263—41no—
78C2×D263—41no—
79C2×D263—81no—
80C2×D263—81no—
81C2×D263—81no—
82C4×C263—21no—
83C4×C263—41no—
84C4×C263—41no—
85C4×C263C2×SD1611yescharacteristic
86C4×C263#13511yescharacteristic
87C4×C263AGL(1,ℤ/8)11yescharacteristic
88C4×C263#13711yescharacteristic
89Dic263—41no—
90Dic263—42no—
91C2×C263#44811yescharacteristic
92C2×C263#44911yescharacteristic
93C2×C263#45311yescharacteristic
94D263—42no—
95D263—161no—
96C263#162211yescharacteristic, complemented, Sylow
97#1622—2631nomaximal, Sylow
98#554—2631no—
99#492—2631no—
100#460—2631no—
101#459—2631no—
102#333—2631no—
103Q8⋊C8D26311yescharacteristic, complemented
104D4⋊C8—2631no—
105C2×SD16—5262no—
106C2×SD16—5261no—
107C2×D8—5261no—
108C4⋊Q8—2631no—
109#127—2631no—
110#125—5261no—
111C22⋊Q8—5262no—
112C22⋊Q8—5261no—
113C4×Q8C2×D26311yescharacteristic
114C4×D4—2631no—
115C4×D4—5261no—
116C2×C4⋊C4—5261no—
117C4⋊C8—2631no—
118C4⋊C8C2×D26311yescharacteristic
119#102—5261no—
120#102—5261no—
121C4×C8C2×D26311yescharacteristic
122C2×Q8—2632no—
123C2×Q8D105211yescharacteristic
124C2×D4—2631no—
125C2×D4—5261no—
126C2×D4—5261no—
127C2×D4—5261no—
128C22×C4—5262no—
129C22×C4—5261no—
130SD16—10524no—
131SD16—10522no—
132D8—10522no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5261no—
136C4⋊C4—21no—
137C4⋊C4—2631no—
138C4⋊C4—5262no—
139C4⋊C4—5262no—
140C4⋊C4—5261no—
141C4⋊C4—5261no—
142C4⋊C4D105211yescharacteristic
143C22⋊C4—5262no—
144C22⋊C4—5261no—
145C42—21no—
146C42C22×D26311yescharacteristic
147C23—5261no—
148C23—10521no—
149Q8—21no—
150Q8—21no—
151Q8—10522no—
152D4—2632no—
153D4—5261no—
154D4—10522no—
155D4—10521no—
156D4—10521no—
157D4—10521no—
158D4—10521no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—5261no—
162C2×C4—5262no—
163C2×C4—10521no—
164C2×C4—10521no—
165C2×C4—21042no—
166C2×C4D4×D26311yescharacteristic
167C2×C4D4×D26311yescharacteristic
168C2×C4C2×D105211yescharacteristic
169C8—22no—
170C8—41no—
171C8—10521no—
172C22—5262no—
173C22—10521no—
174C22—10521no—
175C22—21041no—
176C22—21041no—
177C22—21041no—
178C22#2255444011yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—10521no—
183C4—10522no—
184C4SD16×D26311yescharacteristic
185C4#2255449211yescharacteristic
186C4#2255449811yescharacteristic
187C4#2255450211yescharacteristic
188C2—10522no—
189C2—42081no—
190C2#3068207811yescharacteristic
191C2#3068208511yescharacteristic
192C2#3068210711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263#120
prime radical#30682134C2
hypercenterQ8⋊C8D263
hypocenterC263#1622
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #30682648C2semidirect
2. #30682311C2semidirect
3. #30682138C2semidirect
5. #30681686C2semidirect
6. #30681667C2semidirect
7. Q8⋊C8×C263C2semidirect
59. D1052SD16semidirect
96. C263#1622semidirect
103. Q8⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826482
#306823112
#306821382
#306821342
#306816862
#306816672
Q8⋊C8×C2632
#1622263