Finite Group Databasebeta

← #46781814

Subgroups — #46781814

Order 33664.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682610C211yesmaximal, characteristic, complemented
2#30682315C211yesmaximal, characteristic, complemented
3#30682138C211yesmaximal, characteristic, complemented
4#30682134C211yesmaximal, characteristic, complemented
5#30681681C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862377—21no—
9C2×#16862363—21no—
10C2×D2104—21no—
11C2×D2104—22no—
12#22554467—21no—
13#22554467C2211yescharacteristic
14#22554467C2211yescharacteristic
15#22554445—22no—
16#22554445—21no—
17C4×D1052—21no—
18C4×D1052C2211yescharacteristic
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554392—21no—
21#22554390—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25#16862377—42no—
26#16862377—42no—
27C2×D1052—22no—
28C2×D1052—22no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052—21no—
33C2×D1052—21no—
34C2×D1052D411yescharacteristic
35C2×D1052D412yes—
36C2×C4×D263—22no—
37C2×C4×D263—21no—
38#16862363—42no—
39D2104—44no—
40D2104—42no—
41C2×C263⋊C8—21no—
42C4⋊Dic263D411yescharacteristic
43(C2×D263)⋊C4—22no—
44(C2×D263)⋊C4—21no—
45C2×Q8×C263D411yescharacteristic
46C2×C8×C263—21no—
47C2×C8×C263—21no—
48C4⋊C4×C263—21no—
49C4⋊C4×C263D411yescharacteristic
50C42×C263—21no—
51C42×C263C2311yescharacteristic
52C22×D263—21no—
53C22×D263—22no—
54C22×D263—41no—
55D1052—21no—
56D1052—21no—
57D1052—42no—
58D1052—44no—
59D1052—42no—
60D1052—41no—
61D1052—41no—
62D1052—41no—
63D1052—41no—
64D1052—41no—
65D1052—41no—
66D1052—41no—
67D1052—41no—
68D1052—82no—
69C2×Dic263—21no—
70C4×D263—44no—
71C4×D263—41no—
72C4×D263—41no—
73C263⋊C8—41no—
74Q8×C263—21no—
75Q8×C263D812yescomplemented
76C2×C4×C263—21no—
77C2×C4×C263—21no—
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C8×C263—22no—
82C8×C263—41no—
83C22×C263#12011yescharacteristic
84C2×D263—42no—
85C2×D263—41no—
86C2×D263—41no—
87C2×D263—42no—
88C2×D263—42no—
89C2×D263—41no—
90C2×D263—81no—
91C2×D263—81no—
92C2×D263—81no—
93C4×C263—22no—
94C4×C263—21no—
95C4×C263—41no—
96C4×C263C2×D811yescharacteristic
97C4×C263#13511yescharacteristic
98C4×C263AGL(1,ℤ/8)11yescharacteristic
99C4×C263AGL(1,ℤ/8)11yescharacteristic
100Dic263—41no—
101C2×C263#44711yescharacteristic
102C2×C263#44911yescharacteristic
103C2×C263#45311yescharacteristic
104D263—81no—
105D263—82no—
106D263—161no—
107C263#162111yescharacteristic, complemented, Sylow
108#1621—2631nomaximal, Sylow
109#550—2631no—
110#493—2631no—
111#460—2631no—
112#459—2631no—
113#331—2631no—
114Q8⋊C8D26311yescharacteristic, complemented
115D4⋊C8—2631no—
116C2×#41—5261no—
117C2×SD16—5261no—
118C2×D8—5261no—
119C2×D8—5262no—
120#127—2631no—
121#127—2631no—
122#127—5261no—
123#121—5262no—
124#121—5261no—
125C4×Q8C2×D26311yescharacteristic
126C4×D4—2631no—
127C4×D4—5261no—
128C4⋊C8—2631no—
129C4⋊C8C2×D26311yescharacteristic
130#102—5261no—
131#102—5261no—
132C4×C8C2×D26311yescharacteristic
133#41—10522no—
134#41—10522no—
135C2×Q8D105211yescharacteristic
136C2×D4—2631no—
137C2×D4—2632no—
138C2×D4—5262no—
139C2×D4—5262no—
140C2×D4—5261no—
141C2×D4—5261no—
142C2×D4—5261no—
143C2×D4—5261no—
144C2×D4—5261no—
145C22×C4—5262no—
146C22×C4—5261no—
147SD16—10522no—
148D8—10524no—
149D8—10522no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—5261no—
153C4⋊C4—21no—
154C4⋊C4—2631no—
155C4⋊C4D105211yescharacteristic
156C22⋊C4—5262no—
157C22⋊C4—5261no—
158C42—21no—
159C42C22×D26311yescharacteristic
160C23—5261no—
161C23—5262no—
162C23—10521no—
163Q8—21no—
164Q8D210412yescomplemented
165D4—5261no—
166D4—5261no—
167D4—10522no—
168D4—10524no—
169D4—10522no—
170D4—10521no—
171D4—10521no—
172D4—10521no—
173D4—10521no—
174D4—10521no—
175D4—10521no—
176D4—10521no—
177D4—10521no—
178D4—21042no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—5261no—
182C2×C4—10524no—
183C2×C4—10521no—
184C2×C4—10521no—
185C2×C4D4×D26311yescharacteristic
186C2×C4D4×D26311yescharacteristic
187C2×C4C2×D105211yescharacteristic
188C8—22no—
189C8—41no—
190C8—10521no—
191C22—10522no—
192C22—10521no—
193C22—10521no—
194C22—10522no—
195C22—10522no—
196C22—10521no—
197C22—21041no—
198C22—21041no—
199C22—21041no—
200C22#2255444011yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—10521no—
205C4C2×D210411yescharacteristic
206C4#2255449311yescharacteristic
207C4#2255449711yescharacteristic
208C4#2255449811yescharacteristic
209C2—21041no—
210C2—21042no—
211C2—42081no—
212C2#3068207411yescharacteristic
213C2#3068208611yescharacteristic
214C2#3068210711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263#120
hypercenterQ8⋊C8D263
hypocenterC263#1621
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. #30682610C2semidirect
2. #30682315C2semidirect
3. #30682138C2semidirect
4. #30682134C2semidirect
5. #30681681C2semidirect
6. #30681667C2semidirect
7. Q8⋊C8×C263C2semidirect
75. Q8×C263D8semidirect
107. C263#1621semidirect
114. Q8⋊C8D263semidirect
164. Q8D2104semidirect

Maximal subgroups

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

subgroupindex
#306826102
#306823152
#306821382
#306821342
#306816812
#306816672
Q8⋊C8×C2632
#1621263