Finite Group Databasebeta

← #46781815

Subgroups — #46781815

Order 33664.

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

normal subgroups only

This group has 278 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#30682609C211yesmaximal, characteristic, complemented
2#30682315C211yesmaximal, characteristic, complemented
3#30682139C211yesmaximal, characteristic, complemented
4#30682133C211yesmaximal, characteristic, complemented
5#30681681C211yesmaximal, characteristic, complemented
6#30681670C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862376—21no—
9C2×#16862365—21no—
10C2×D2104—22no—
11C2×#16862361—21no—
12#22554467C2211yescharacteristic
13#22554467C2211yescharacteristic
14#22554466—21no—
15#22554444—21no—
16#22554443—22no—
17C4×Dic526C2211yescharacteristic
18#22554432—21no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554392—21no—
21#22554390—21no—
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25#16862376—42no—
26#16862376—42no—
27C2×Dic526D411yescharacteristic
28C2×D1052—21no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052—21no—
33C2×D1052D412yes—
34C2×C22⋊D263—22no—
35C2×C22⋊D263—22no—
36C2×C4×D263—22no—
37#16862365—42no—
38D2104—44no—
39#16862361—42no—
40C2×C263⋊C8—21no—
41C4⋊Dic263D411yescharacteristic
42Dic263⋊C4—21no—
43(C2×D263)⋊C4—22no—
44C4×Dic263—21no—
45C2×D4×C263D411yescharacteristic
46C22×C4×C263—21no—
47C2×C8×C263—21no—
48C2×C8×C263—21no—
49C4⋊C4×C263D411yescharacteristic
50C22⋊C4×C263—21no—
51C42×C263C2311yescharacteristic
52C22×D263—22no—
53C22×D263—41no—
54Dic526—21no—
55Dic526D812yescomplemented
56D1052—42no—
57D1052—42no—
58D1052—41no—
59D1052—41no—
60D1052—41no—
61D1052—41no—
62D1052—41no—
63D1052—41no—
64D1052—41no—
65D1052—41no—
66C22⋊D263—44no—
67C22⋊D263—82no—
68C2×Dic263—21no—
69C2×Dic263—21no—
70C4×D263—44no—
71C263⋊C8—41no—
72C23×C263—21no—
73D4×C263—21no—
74D4×C263—21no—
75C2×C4×C263—21no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C8×C263—22no—
82C8×C263—41no—
83C22×C263—41no—
84C22×C263—41no—
85C22×C263—41no—
86C22×C263#12011yescharacteristic
87C2×D263—42no—
88C2×D263—42no—
89C2×D263—42no—
90C2×D263—81no—
91C2×D263—81no—
92C2×D263—81no—
93C4×C263—21no—
94C4×C263—41no—
95C4×C263C2×D811yescharacteristic
96C4×C263#13511yescharacteristic
97C4×C263AGL(1,ℤ/8)11yescharacteristic
98C4×C263AGL(1,ℤ/8)11yescharacteristic
99Dic263—22no—
100Dic263—41no—
101C2×C263—81no—
102C2×C263#44711yescharacteristic
103C2×C263#44911yescharacteristic
104C2×C263#45311yescharacteristic
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⋊C8—2631no—
115D4⋊C8D26311yescharacteristic, complemented
116C2×#41—5261no—
117C2×SD16—5261no—
118C2×D8—5262no—
119C2×D8—5261no—
120#127—2631no—
121#127—2631no—
122#127—5261no—
123#121—5262no—
124#121—5261no—
125C4×Q8—2631no—
126C4×D4—5261no—
127C4×D4C2×D26311yescharacteristic
128C4⋊C8—2631no—
129C4⋊C8C2×D26311yescharacteristic
130#102—5261no—
131#102—5261no—
132C4×C8C2×D26311yescharacteristic
133#41—10522no—
134#41—10522no—
135C2×Q8—2631no—
136C2×D4—2632no—
137C2×D4—5262no—
138C2×D4—5262no—
139C2×D4—5261no—
140C2×D4—5261no—
141C2×D4—5261no—
142C2×D4—5261no—
143C2×D4—5261no—
144C2×D4D105211yescharacteristic
145C22×C4—21no—
146C22×C4—5262no—
147SD16—10522no—
148D8—10524no—
149D8—10522no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—5261no—
153C4⋊C4—2631no—
154C4⋊C4—5261no—
155C4⋊C4D105211yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5262no—
158C42—5261no—
159C42C22×D26311yescharacteristic
160C23—21no—
161C23—5262no—
162C23—10521no—
163Q8—2632no—
164Q8—5261no—
165D4—21no—
166D4—21no—
167D4—10522no—
168D4—10522no—
169D4—10524no—
170D4—10521no—
171D4—10521no—
172D4—10521no—
173D4—10521no—
174D4—10521no—
175D4—10521no—
176D4—10521no—
177D4—10521no—
178D4—21042no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—5261no—
183C2×C4—5261no—
184C2×C4—10524no—
185C2×C4D4×D26311yescharacteristic
186C2×C4D4×D26311yescharacteristic
187C2×C4C2×D105211yescharacteristic
188C8—22no—
189C8—41no—
190C8—10521no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—10522no—
195C22—10522no—
196C22—10522no—
197C22—21041no—
198C22—21041no—
199C22—21041no—
200C22#2255444011yescharacteristic
201C4—21no—
202C4—41no—
203C4—5262no—
204C4—10521no—
205C4D8×D26311yescharacteristic
206C4#2255449211yescharacteristic
207C4#2255449711yescharacteristic
208C4#2255449811yescharacteristic
209C2—81no—
210C2—21042no—
211C2—42081no—
212C2#3068207311yescharacteristic
213C2#3068208511yescharacteristic
214C2#3068210711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
hypercenterD4⋊C8D263
hypocenterC263#1621
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #30682609C2semidirect
2. #30682315C2semidirect
3. #30682139C2semidirect
4. #30682133C2semidirect
5. #30681681C2semidirect
6. #30681670C2semidirect
7. D4⋊C8×C263C2semidirect
55. Dic526D8semidirect
107. C263#1621semidirect
115. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826092
#306823152
#306821392
#306821332
#306816812
#306816702
D4⋊C8×C2632
#1621263