Finite Group Databasebeta

← #46782004

Subgroups — #46782004

Order 33664.

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

normal subgroups only

This group has 200 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#30682341C211yesmaximal, characteristic, complemented
3#30682224C211yesmaximal, characteristic, complemented
4#30682144C211yesmaximal, characteristic
5#30681668C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic
7#332×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—21no—
9#22554470C2211yescharacteristic
10#22554465—22no—
11#22554459—21no—
12#22554450—21no—
13Q8×Dic263—21no—
14C4×Dic526C2211yescharacteristic
15C4×D1052C2211yescharacteristic
16#22554428—21no—
17#22554403—22no—
18#22554402—21no—
19#22554395—21no—
20#22554395—21no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526D411yescharacteristic
27C2×D1052D411yescharacteristic
28C2×C4×D263—21no—
29#16862365—42no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—22no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D411yescharacteristic
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—21no—
37(C2×D263)⋊C4—22no—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—22no—
41C4×Dic263—21no—
42C2×Q8×C263—21no—
43C2×C8×C263—21no—
44C2×C8×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263D412yes—
47C42×C263C2311yescharacteristic
48C22×D263—21no—
49Dic526—21no—
50Dic526—21no—
51Dic526—41no—
52Dic526—41no—
53D1052—21no—
54D1052—21no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—41no—
59C4×D263—41no—
60C4×D263—41no—
61C263⋊C8—22no—
62Q8×C263—41no—
63Q8×C263—41no—
64C2×C4×C263—22no—
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C2×C4×C263C2×D411yescharacteristic
68C8×C263—41no—
69C8×C263—41no—
70C22×C263#12011yescharacteristic
71C2×D263—41no—
72C2×D263—41no—
73C2×D263—41no—
74C4×C263—21no—
75C4×C263—42no—
76C4×C263#13511yescharacteristic
77C4×C263#13511yescharacteristic
78C4×C263AGL(1,ℤ/8)11yescharacteristic
79C4×C263#13711yescharacteristic
80Dic263—41no—
81Dic263—41no—
82Dic263—41no—
83Dic263—81no—
84C2×C263#44911yescharacteristic
85C2×C263#45211yescharacteristic
86C2×C263#45611yescharacteristic
87D263—81no—
88C263#165011yescharacteristic, complemented, Sylow
89#1650—2631nomaximal, Sylow
90#556—2631no—
91#500—2631no—
92#475—2631no—
93#461—2631no—
94#332D26311yescharacteristic, complemented
95Q8⋊C8—2631no—
96D4⋊C8—2631no—
97C2×SD16—5261no—
98C4⋊Q8—2631no—
99C4⋊Q8C2×D26311yescharacteristic
100#126—5262no—
101#124—5261no—
102C22⋊Q8—5261no—
103C4×Q8—2631no—
104C4×Q8—5261no—
105C4×D4—2631no—
106#117—5261no—
107#107—5262no—
108#106—5261no—
109C4⋊C8C2×D26311yescharacteristic
110C4⋊C8C2×D26311yescharacteristic
111#103—5261no—
112#103—5261no—
113C4×C8—2631no—
114C2×Q8—21no—
115C2×Q8—2631no—
116C2×Q8—5261no—
117C2×D4—2631no—
118C22×C4—5261no—
119SD16—10522no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5261no—
123C4⋊C4—21no—
124C4⋊C4—2631no—
125C4⋊C4—2631no—
126C4⋊C4—5262no—
127C4⋊C4—5261no—
128C4⋊C4—5261no—
129C4⋊C4—5261no—
130C4⋊C4D105212yes—
131C22⋊C4—5262no—
132C22⋊C4—5262no—
133C22⋊C4—5261no—
134C42—5262no—
135C42—5261no—
136C42C22×D26311yescharacteristic
137C23—5261no—
138Q8—41no—
139Q8—41no—
140Q8—5261no—
141Q8—5261no—
142Q8—10521no—
143Q8—10521no—
144D4—5261no—
145D4—5261no—
146C2×C4—22no—
147C2×C4—5261no—
148C2×C4—5261no—
149C2×C4—5261no—
150C2×C4—10521no—
151C2×C4—10521no—
152C2×C4—10521no—
153C2×C4D4×D26311yescharacteristic
154C2×C4D4×D26311yescharacteristic
155C2×C4C2×D105211yescharacteristic
156C8—41no—
157C8—41no—
158C8—5262no—
159C22—10521no—
160C22—10521no—
161C22—10521no—
162C22#2255444011yescharacteristic
163C4—21no—
164C4—42no—
165C4—10521no—
166C4—10521no—
167C4—10521no—
168C4—21041no—
169C4#2255449111yescharacteristic
170C4#2255449111yescharacteristic
171C4#2255449411yescharacteristic
172C4#2255450211yescharacteristic
173C2—21041no—
174C2#3068208411yescharacteristic
175C2#3068210311yescharacteristic
176C2#3068212311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#332×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#332D263
hypocenterC263#1650
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
3. #30682224C2semidirect
5. #30681668C2semidirect
7. #332×C263C2semidirect
88. C263#1650semidirect
94. #332D263semidirect

Maximal subgroups

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

subgroupindex
#306826622
#306823412
#306822242
#306821442
#306816682
#306816652
#332×C2632
#1650263