Finite Group Databasebeta

← #46781851

Subgroups — #46781851

Order 33664.

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

normal subgroups only

This group has 250 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#30682603C211yesmaximal, characteristic, complemented
2#30682286C211yesmaximal, characteristic, complemented
3#30682139C211yesmaximal, characteristic, complemented
4#30682134C211yesmaximal, characteristic
5#30681668C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#332×C263C211yesmaximal, characteristic, complemented
8C2×Q8×D263—21no—
9C2×#16862365—21no—
10C2×D2104—21no—
11#22554469—21no—
12#22554467C2211yescharacteristic
13#22554448—22no—
14#22554446—21no—
15C4×Dic526C2211yescharacteristic
16C4×D1052C2211yescharacteristic
17#22554432—21no—
18#22554392—21no—
19#22554392—21no—
20#22554390—22no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—22no—
26C2×Dic526D411yescharacteristic
27Q8×D263—42no—
28Q8×D263—42no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052D411yescharacteristic
33C2×C4×D263—22no—
34C2×C4×D263—21no—
35#16862365—42no—
36D2104—42no—
37C2×C263⋊C8—21no—
38C4⋊Dic263D411yescharacteristic
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—22no—
41Dic263⋊C4—21no—
42(C2×D263)⋊C4—22no—
43(C2×D263)⋊C4—21no—
44C4×Dic263—21no—
45C2×Q8×C263—21no—
46C2×C8×C263—21no—
47C2×C8×C263—21no—
48C4⋊C4×C263—21no—
49C4⋊C4×C263D412yes—
50C42×C263C2311yescharacteristic
51C22×D263—21no—
52C22×D263—41no—
53Dic526—21no—
54Dic526—44no—
55Dic526D812yescomplemented
56D1052—21no—
57D1052—42no—
58D1052—41no—
59D1052—41no—
60D1052—41no—
61D1052—41no—
62D1052SD1612yescomplemented
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C4×D263—44no—
67C4×D263—41no—
68C4×D263—41no—
69C263⋊C8—41no—
70Q8×C263—41no—
71Q8×C263—41no—
72C2×C4×C263—22no—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C8×C263—41no—
77C8×C263—41no—
78C22×C263#12011yescharacteristic
79C2×D263—22no—
80C2×D263—41no—
81C2×D263—41no—
82C2×D263—81no—
83C2×D263—81no—
84C2×D263—81no—
85C4×C263—21no—
86C4×C263—42no—
87C4×C263C2×D811yescharacteristic
88C4×C263C2×SD1611yescharacteristic
89C4×C263AGL(1,ℤ/8)11yescharacteristic
90C4×C263#13711yescharacteristic
91Dic263—22no—
92Dic263—41no—
93Dic263—41no—
94C2×C263#44711yescharacteristic
95C2×C263#44811yescharacteristic
96C2×C263#45411yescharacteristic
97D263—42no—
98D263—161no—
99C263#162711yescharacteristic, complemented, Sylow
100#1627—2631nomaximal, Sylow
101D4×Q8—2631no—
102#486—2631no—
103#460—2631no—
104#459—2631no—
105#332D26311yescharacteristic, complemented
106Q8⋊C8—2631no—
107D4⋊C8—2631no—
108C22×Q8—5261no—
109C2×SD16—5261no—
110C2×D8—5261no—
111C4⋊Q8—5261no—
112C4⋊Q8C2×D26311yescharacteristic
113#127—2631no—
114C22⋊Q8—5261no—
115C22⋊Q8—5262no—
116C4×Q8—2631no—
117C4×D4—2631no—
118C4×D4—5261no—
119C4⋊C8C2×D26311yescharacteristic
120C4⋊C8C2×D26311yescharacteristic
121#102—5261no—
122#102—5261no—
123#102—5262no—
124C4×C8—2631no—
125C2×Q8—21no—
126C2×Q8—2631no—
127C2×Q8—5262no—
128C2×Q8—10522no—
129C2×Q8—10522no—
130C2×D4—2631no—
131C2×D4—5261no—
132C2×D4—5261no—
133C2×D4—5261no—
134C22×C4—5262no—
135C22×C4—5261no—
136SD16—10522no—
137D8—10522no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5261no—
141C4⋊C4—21no—
142C4⋊C4—2631no—
143C4⋊C4—2631no—
144C4⋊C4—5262no—
145C4⋊C4—5261no—
146C4⋊C4D105212yes—
147C22⋊C4—5262no—
148C22⋊C4—5261no—
149C42—5261no—
150C42C22×D26311yescharacteristic
151C23—5261no—
152C23—10521no—
153Q8—41no—
154Q8—41no—
155Q8—2632no—
156Q8—5261no—
157Q8—10524no—
158D4—2632no—
159D4—5261no—
160D4—10522no—
161D4—10521no—
162D4—10521no—
163D4—10521no—
164D4—10521no—
165C2×C4—22no—
166C2×C4—5261no—
167C2×C4—5261no—
168C2×C4—5261no—
169C2×C4—10524no—
170C2×C4—10521no—
171C2×C4—10521no—
172C2×C4D4×D26311yescharacteristic
173C2×C4D4×D26311yescharacteristic
174C2×C4C2×D105211yescharacteristic
175C8—41no—
176C8—41no—
177C8—10521no—
178C22—5262no—
179C22—10521no—
180C22—10521no—
181C22—21041no—
182C22—21041no—
183C22—21041no—
184C22#2255444011yescharacteristic
185C4—21no—
186C4—42no—
187C4—5262no—
188C4—10521no—
189C4—10521no—
190C4D8×D26311yescharacteristic
191C4SD16×D26311yescharacteristic
192C4#2255449711yescharacteristic
193C4#2255450211yescharacteristic
194C2—10522no—
195C2—42081no—
196C2#3068207311yescharacteristic
197C2#3068207811yescharacteristic
198C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#332×C263C2
socleC22×C263#120
prime radical#30682134C2
hypercenter#332D263
hypocenterC263#1627
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #30682603C2semidirect
2. #30682286C2semidirect
3. #30682139C2semidirect
5. #30681668C2semidirect
6. #30681665C2semidirect
7. #332×C263C2semidirect
55. Dic526D8semidirect
62. D1052SD16semidirect
99. C263#1627semidirect
105. #332D263semidirect

Maximal subgroups

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

subgroupindex
#306826032
#306822862
#306821392
#306821342
#306816682
#306816652
#332×C2632
#1627263