Finite Group Databasebeta

← #46781997

Subgroups — #46781997

Order 33664.

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

normal subgroups only

This group has 234 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
2#30682341C211yesmaximal, characteristic, complemented
3#30682219C211yesmaximal, characteristic
4#30682149C211yesmaximal, characteristic, complemented
5#30681668C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic
7#332×C263C211yesmaximal, characteristic, complemented
8C2×Q8×D263—21no—
9C2×Dic1052—21no—
10#22554470C2211yescharacteristic
11#22554469—21no—
12#22554448—22no—
13#22554446—21no—
14C4×Dic526C2211yescharacteristic
15C4×D1052C2211yescharacteristic
16#22554432—21no—
17#22554404—21no—
18#22554403—22no—
19#22554395—21no—
20#22554392—21no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—22no—
26C2×Dic526—21no—
27C2×Dic526D411yescharacteristic
28Q8×D263—42no—
29Q8×D263—42no—
30C2×D1052D411yescharacteristic
31C2×C4×D263—22no—
32C2×C4×D263—21no—
33Dic1052—42no—
34C2×C263⋊C8—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263D411yescharacteristic
38C4⋊Dic263D411yescharacteristic
39Dic263⋊C4—22no—
40Dic263⋊C4—21no—
41(C2×D263)⋊C4—22no—
42(C2×D263)⋊C4—21no—
43C4×Dic263—21no—
44C2×Q8×C263—21no—
45C2×C8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263D412yes—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—21no—
52Dic526—44no—
53Dic526—41no—
54Dic526—41no—
55Dic526D812yes—
56D1052—21no—
57D1052Q1612yescomplemented
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—41no—
62C4×D263—44no—
63C4×D263—41no—
64C4×D263—41no—
65C263⋊C8—22no—
66Q8×C263—41no—
67Q8×C263—41no—
68C2×C4×C263—22no—
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C8×C263—41no—
73C8×C263—41no—
74C22×C263#12011yescharacteristic
75C2×D263—22no—
76C2×D263—41no—
77C2×D263—41no—
78C4×C263—21no—
79C4×C263—42no—
80C4×C263C2×D811yescharacteristic
81C4×C263C2×Q1611yescharacteristic
82C4×C263AGL(1,ℤ/8)11yescharacteristic
83C4×C263#13711yescharacteristic
84Dic263—22no—
85Dic263—41no—
86Dic263—41no—
87Dic263—81no—
88C2×C263#44711yescharacteristic
89C2×C263#45111yescharacteristic
90C2×C263#45611yescharacteristic
91D263—42no—
92C263#164911yescharacteristic, complemented, Sylow
93#1649—2631nomaximal, Sylow
94D4×Q8—2631no—
95#500—2631no—
96#474—2631no—
97#462—2631no—
98#332D26311yescharacteristic, complemented
99Q8⋊C8—2631no—
100D4⋊C8—2631no—
101C22×Q8—5261no—
102C2×Q16—5261no—
103C4⋊Q8—2631no—
104C4⋊Q8—5261no—
105C4⋊Q8C2×D26311yescharacteristic
106C22⋊Q8—5261no—
107C22⋊Q8—5262no—
108C4×Q8—2631no—
109C4×D4—2631no—
110C4×D4—5261no—
111#107—5261no—
112#107—5262no—
113C4⋊C8C2×D26311yescharacteristic
114C4⋊C8C2×D26311yescharacteristic
115#103—5261no—
116#102—5261no—
117C4×C8—2631no—
118C2×Q8—21no—
119C2×Q8—2631no—
120C2×Q8—5262no—
121C2×Q8—5261no—
122C2×Q8—10522no—
123C2×Q8—10522no—
124C2×D4—2631no—
125C22×C4—5262no—
126C22×C4—5261no—
127Q16—10522no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5261no—
131C4⋊C4—21no—
132C4⋊C4—2631no—
133C4⋊C4—2631no—
134C4⋊C4—5262no—
135C4⋊C4—5261no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C4⋊C4D105212yes—
139C22⋊C4—5262no—
140C22⋊C4—5261no—
141C42—5261no—
142C42C22×D26311yescharacteristic
143C23—5261no—
144Q8—41no—
145Q8—41no—
146Q8—2632no—
147Q8—5261no—
148Q8—10524no—
149Q8—10521no—
150Q8—10521no—
151D4—2632no—
152D4—5261no—
153C2×C4—22no—
154C2×C4—5261no—
155C2×C4—5261no—
156C2×C4—5261no—
157C2×C4—10524no—
158C2×C4—10521no—
159C2×C4—10521no—
160C2×C4—10521no—
161C2×C4D4×D26311yescharacteristic
162C2×C4D4×D26311yescharacteristic
163C2×C4C2×D105211yescharacteristic
164C8—41no—
165C8—41no—
166C8—5262no—
167C22—5262no—
168C22—10521no—
169C22—10521no—
170C22#2255444011yescharacteristic
171C4—21no—
172C4—42no—
173C4—5262no—
174C4—10521no—
175C4—10521no—
176C4—21041no—
177C4D8×D26311yescharacteristic
178C4Q16×D26311yescharacteristic
179C4#2255449711yescharacteristic
180C4#2255449911yescharacteristic
181C2—10522no—
182C2#3068207311yescharacteristic
183C2#3068209511yescharacteristic
184C2#3068212311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#332×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#332D263
hypocenterC263#1649
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #30682341C2semidirect
4. #30682149C2semidirect
5. #30681668C2semidirect
7. #332×C263C2semidirect
57. D1052Q16semidirect
92. C263#1649semidirect
98. #332D263semidirect

Maximal subgroups

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

subgroupindex
#306826032
#306823412
#306822192
#306821492
#306816682
#306816652
#332×C2632
#1649263