Finite Group Databasebeta

← #46781920

Subgroups — #46781920

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#30682662C211yesmaximal, characteristic
2#30682290C211yesmaximal, characteristic, complemented
3#30682234C211yesmaximal, characteristic, complemented
4#30682229C211yesmaximal, characteristic
5#30681668C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic
7#332×C263C211yesmaximal, characteristic, complemented
8#22554470C2211yescharacteristic
9#22554465—22no—
10#22554459—21no—
11#22554450—21no—
12Q8×Dic263—21no—
13C4×Dic526C2211yescharacteristic
14C4×D1052C2211yescharacteristic
15#22554428—21no—
16#22554404—21no—
17#22554402—21no—
18#22554395—21no—
19#22554393—22no—
20#22554392—21no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526D411yescharacteristic
27C2×D1052D411yescharacteristic
28C2×C4×D263—21no—
29C2×C263⋊C8—21no—
30C4⋊Dic263—22no—
31C4⋊Dic263—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263D411yescharacteristic
34C4⋊Dic263D411yescharacteristic
35Dic263⋊C4—21no—
36(C2×D263)⋊C4—22no—
37(C2×D263)⋊C4—22no—
38(C2×D263)⋊C4—21no—
39C4×Dic263—22no—
40C4×Dic263—21no—
41C2×Q8×C263—21no—
42C2×C8×C263—21no—
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D412yes—
46C42×C263C2311yescharacteristic
47C22×D263—21no—
48Dic526—21no—
49Dic526—21no—
50Dic526—42no—
51D1052—21no—
52D1052—21no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—41no—
57C4×D263—41no—
58C4×D263—41no—
59C263⋊C8—41no—
60Q8×C263—41no—
61Q8×C263—41no—
62C2×C4×C263—22no—
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C8×C263—41no—
67C8×C263—41no—
68C22×C263#12011yescharacteristic
69C2×D263—41no—
70C2×D263—41no—
71C2×D263—41no—
72C4×C263—21no—
73C4×C263—42no—
74C4×C263#13511yescharacteristic
75C4×C263#13511yescharacteristic
76C4×C263#13711yescharacteristic
77C4×C263#13711yescharacteristic
78Dic263—41no—
79Dic263—41no—
80Dic263—41no—
81Dic263—81no—
82C2×C263#45211yescharacteristic
83C2×C263#45211yescharacteristic
84C2×C263#45411yescharacteristic
85D263—81no—
86C263#163811yescharacteristic, complemented, Sylow
87#1638—2631nomaximal, Sylow
88#556—2631no—
89#487—2631no—
90#477—2631no—
91#476—2631no—
92#332D26311yescharacteristic, complemented
93Q8⋊C8—2631no—
94D4⋊C8—2631no—
95C4⋊Q8—2631no—
96C4⋊Q8C2×D26311yescharacteristic
97#126—5262no—
98#124—5261no—
99C22⋊Q8—5261no—
100C4×Q8—2631no—
101C4×Q8—5261no—
102C4×D4—2631no—
103#117—5261no—
104#107—5261no—
105#106—5261no—
106C4⋊C8C2×D26311yescharacteristic
107C4⋊C8C2×D26311yescharacteristic
108#103—5261no—
109#103—5262no—
110#102—5261no—
111C4×C8—2631no—
112C2×Q8—21no—
113C2×Q8—2631no—
114C2×Q8—5261no—
115C2×D4—2631no—
116C22×C4—5261no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—5261no—
120C4⋊C4—21no—
121C4⋊C4—2631no—
122C4⋊C4—2631no—
123C4⋊C4—5262no—
124C4⋊C4—5261no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4D105212yes—
128C22⋊C4—5262no—
129C22⋊C4—5262no—
130C22⋊C4—5261no—
131C42—5262no—
132C42—5261no—
133C42C22×D26311yescharacteristic
134C23—5261no—
135Q8—41no—
136Q8—41no—
137Q8—5261no—
138Q8—5261no—
139Q8—10522no—
140D4—5261no—
141D4—5261no—
142C2×C4—22no—
143C2×C4—5261no—
144C2×C4—5261no—
145C2×C4—5261no—
146C2×C4—10521no—
147C2×C4—10521no—
148C2×C4—10521no—
149C2×C4D4×D26311yescharacteristic
150C2×C4D4×D26311yescharacteristic
151C2×C4C2×D105211yescharacteristic
152C8—41no—
153C8—41no—
154C8—10521no—
155C22—10521no—
156C22—10521no—
157C22—10521no—
158C22#2255444011yescharacteristic
159C4—21no—
160C4—42no—
161C4—10521no—
162C4—10521no—
163C4—10521no—
164C4—21041no—
165C4#2255448911yescharacteristic
166C4#2255449111yescharacteristic
167C4#2255449911yescharacteristic
168C4#2255450211yescharacteristic
169C2—21041no—
170C2#3068210111yescharacteristic
171C2#3068210311yescharacteristic
172C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#332×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#332D263
hypocenterC263#1638
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. #30682290C2semidirect
3. #30682234C2semidirect
5. #30681668C2semidirect
7. #332×C263C2semidirect
86. C263#1638semidirect
92. #332D263semidirect

Maximal subgroups

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

subgroupindex
#306826622
#306822902
#306822342
#306822292
#306816682
#306816652
#332×C2632
#1638263