Finite Group Databasebeta

← #46781921

Subgroups — #46781921

Order 33664.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682658C211yesmaximal, characteristic
2#30682289C211yesmaximal, characteristic, complemented
3#30682234C211yesmaximal, characteristic, complemented
4#30682228C211yesmaximal, characteristic
5#30681683C211yesmaximal, characteristic, complemented
6#30681670C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic
8#22554470C2211yescharacteristic
9#22554470C2211yescharacteristic
10#22554463—22no—
11#22554457—21no—
12#22554449—21no—
13C4×Dic526C2211yescharacteristic
14#22554435—21no—
15#22554429—21no—
16#22554404—21no—
17#22554401—21no—
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554395—21no—
20#22554395—22no—
21#22554391—21no—
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526D411yescharacteristic
28C2×C263⋊C8—21no—
29C4⋊Dic263—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263—21no—
32C4⋊Dic263D412yes—
33C4⋊Dic263D411yescharacteristic
34Dic263⋊C4—22no—
35Dic263⋊C4—21no—
36C22⋊Dic263—22no—
37C22⋊Dic263—22no—
38C4×Dic263—22no—
39C4×Dic263—21no—
40C2×D4×C263D411yescharacteristic
41C22×C4×C263—21no—
42C2×C8×C263—21no—
43C2×C8×C263—21no—
44C4⋊C4×C263D411yescharacteristic
45C22⋊C4×C263—21no—
46C42×C263C2311yescharacteristic
47Dic526—21no—
48Dic526—21no—
49Dic526—41no—
50Dic526—41no—
51Dic526—42no—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—22no—
55C2×Dic263—41no—
56C263⋊C8—41no—
57C23×C263—21no—
58D4×C263—21no—
59D4×C263—21no—
60C2×C4×C263—21no—
61C2×C4×C263—41no—
62C2×C4×C263—41no—
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C8×C263—41no—
67C8×C263—41no—
68C22×C263—41no—
69C22×C263—41no—
70C22×C263—41no—
71C22×C263#12011yescharacteristic
72C4×C263—21no—
73C4×C263—41no—
74C4×C263#13511yescharacteristic
75C4×C263#13511yescharacteristic
76C4×C263#13711yescharacteristic
77C4×C263#13711yescharacteristic
78Dic263—41no—
79Dic263—42no—
80Dic263—41no—
81Dic263—81no—
82C2×C263—81no—
83C2×C263#45211yescharacteristic
84C2×C263#45211yescharacteristic
85C2×C263#45411yescharacteristic
86C263#163811yescharacteristic, complemented, Sylow
87#1638—2631nomaximal, Sylow
88#556—2631no—
89#487—2631no—
90#477—2631no—
91#476—2631no—
92#332—2631no—
93Q8⋊C8—2631no—
94D4⋊C8D26311yescharacteristic
95C4⋊Q8—2631no—
96C4⋊Q8—2631no—
97#126—5262no—
98#124—5261no—
99C22⋊Q8—5261no—
100C4×Q8—2631no—
101C4×Q8—5261no—
102C4×D4C2×D26311yescharacteristic
103#117—5261no—
104#107—5261no—
105#106—5261no—
106C4⋊C8—2631no—
107C4⋊C8C2×D26311yescharacteristic
108#103—5262no—
109#103—5261no—
110#102—5261no—
111C4×C8C2×D26311yescharacteristic
112C2×Q8—2631no—
113C2×Q8—5261no—
114C2×Q8—5261no—
115C2×D4D105211yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—5261no—
120C4⋊C4—2632no—
121C4⋊C4—2631no—
122C4⋊C4—5262no—
123C4⋊C4—5261no—
124C4⋊C4—5261no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4D105211yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—5262no—
130C22⋊C4—5262no—
131C42—5262no—
132C42—5261no—
133C42C22×D26311yescharacteristic
134C23—21no—
135Q8—5261no—
136Q8—5261no—
137Q8—10522no—
138Q8—10521no—
139Q8—10521no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—5261no—
146C2×C4—5262no—
147C2×C4—5261no—
148C2×C4—10521no—
149C2×C4D4×D26311yescharacteristic
150C2×C4D4×D26311yescharacteristic
151C2×C4C2×D105211yescharacteristic
152C8—41no—
153C8—41no—
154C8—10521no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2255444011yescharacteristic
159C4—21no—
160C4—41no—
161C4—10521no—
162C4—10521no—
163C4—10522no—
164C4—21041no—
165C4#2255448911yescharacteristic
166C4#2255449211yescharacteristic
167C4#2255449911yescharacteristic
168C4#2255450311yescharacteristic
169C2—81no—
170C2#3068210111yescharacteristic
171C2#3068210211yescharacteristic
172C2#3068211211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
prime radicalC2×D4×C263D4
hypercenterD4⋊C8D263
hypocenterC263#1638
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
2. #30682289C2semidirect
3. #30682234C2semidirect
5. #30681683C2semidirect
6. #30681670C2semidirect
86. C263#1638semidirect

Maximal subgroups

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

subgroupindex
#306826582
#306822892
#306822342
#306822282
#306816832
#306816702
D4⋊C8×C2632
#1638263