Finite Group Databasebeta

← #46781976

Subgroups — #46781976

Order 33664.

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

normal subgroups only

This group has 212 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#30682654C211yesmaximal, characteristic
2#30682288C211yesmaximal, characteristic, complemented
3#30682219C211yesmaximal, characteristic, complemented
4#30682144C211yesmaximal, characteristic, complemented
5#30681665C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#333×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—21no—
9#22554470C2211yescharacteristic
10#22554459—22no—
11#22554445—21no—
12#22554445—21no—
13C4×D1052C2211yescharacteristic
14C4×D1052C2211yescharacteristic
15#22554428—21no—
16#22554428—21no—
17#22554404—21no—
18#22554395—21no—
19#22554394—22no—
20#22554392—21no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×D1052—22no—
27C2×D1052D411yescharacteristic
28C2×D1052D411yescharacteristic
29C2×C4×D263—21no—
30C2×C4×D263—21no—
31#16862365—42no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36C4⋊Dic263D411yescharacteristic
37(C2×D263)⋊C4—22no—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41C4×Dic263—22no—
42C2×Q8×C263D412yes—
43C2×C8×C263—21no—
44C2×C8×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263—21no—
47C42×C263C2311yescharacteristic
48C22×D263—21no—
49C22×D263—21no—
50Dic526—41no—
51Dic526—41no—
52D1052—21no—
53D1052—21no—
54D1052—21no—
55D1052—21no—
56D1052—82no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—41no—
60C4×D263—41no—
61C4×D263—41no—
62C4×D263—41no—
63C4×D263—41no—
64C263⋊C8—41no—
65Q8×C263—42no—
66C2×C4×C263—22no—
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C8×C263—41no—
71C8×C263—41no—
72C22×C263#12011yescharacteristic
73C2×D263—41no—
74C2×D263—41no—
75C2×D263—41no—
76C2×D263—41no—
77C2×D263—41no—
78C2×D263—41no—
79C4×C263—21no—
80C4×C263—42no—
81C4×C263#13511yescharacteristic
82C4×C263#13511yescharacteristic
83C4×C263AGL(1,ℤ/8)11yescharacteristic
84C4×C263#13711yescharacteristic
85Dic263—41no—
86Dic263—41no—
87Dic263—81no—
88C2×C263#44911yescharacteristic
89C2×C263#45211yescharacteristic
90C2×C263#45511yescharacteristic
91D263—81no—
92D263—81no—
93C263#164611yescharacteristic, complemented, Sylow
94#1646—2631nomaximal, Sylow
95#555—2631no—
96#487—2631no—
97#474—2631no—
98#461—2631no—
99#333D26311yescharacteristic, complemented
100D4⋊C8—2631no—
101D4⋊C8—2631no—
102C2×SD16—5261no—
103C4⋊Q8—2631no—
104C4⋊Q8C2×D26311yescharacteristic
105#124—5262no—
106#121—5261no—
107#121—5261no—
108C4×D4—2631no—
109C4×D4—2631no—
110#117—5261no—
111#117—5261no—
112#107—5261no—
113C4⋊C8C2×D26311yescharacteristic
114C4⋊C8C2×D26311yescharacteristic
115#103—5261no—
116#103—5262no—
117#102—5261no—
118C4×C8—2631no—
119C2×Q8—5261no—
120C2×Q8D105212yes—
121C2×D4—2631no—
122C2×D4—2631no—
123C2×D4—5262no—
124C22×C4—5261no—
125C22×C4—5261no—
126SD16—10522no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5261no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2631no—
133C4⋊C4—2631no—
134C4⋊C4—5261no—
135C4⋊C4—5261no—
136C22⋊C4—5262no—
137C22⋊C4—5262no—
138C22⋊C4—5261no—
139C22⋊C4—5261no—
140C42—5262no—
141C42C22×D26311yescharacteristic
142C23—5261no—
143C23—5261no—
144Q8—42no—
145Q8—10521no—
146Q8—10521no—
147D4—5261no—
148D4—5261no—
149D4—5261no—
150D4—5261no—
151D4—21042no—
152C2×C4—22no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—10521no—
156C2×C4—10521no—
157C2×C4—10521no—
158C2×C4—10521no—
159C2×C4—10521no—
160C2×C4D4×D26311yescharacteristic
161C2×C4D4×D26311yescharacteristic
162C2×C4C2×D105211yescharacteristic
163C8—41no—
164C8—41no—
165C8—10521no—
166C22—10521no—
167C22—10521no—
168C22—10521no—
169C22—10521no—
170C22—10521no—
171C22—10521no—
172C22#2255444011yescharacteristic
173C4—21no—
174C4—42no—
175C4—10521no—
176C4—10521no—
177C4—21041no—
178C4#2255449111yescharacteristic
179C4#2255449311yescharacteristic
180C4#2255449711yescharacteristic
181C4#2255450211yescharacteristic
182C2—21041no—
183C2—21041no—
184C2#3068208611yescharacteristic
185C2#3068210311yescharacteristic
186C2#3068211811yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#333×C263C2
socleC22×C263#120
prime radical#30682654C2
hypercenter#333D263
hypocenterC263#1646
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #30682288C2semidirect
3. #30682219C2semidirect
4. #30682144C2semidirect
5. #30681665C2semidirect
6. #30681665C2semidirect
7. #333×C263C2semidirect
93. C263#1646semidirect
99. #333D263semidirect

Maximal subgroups

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

subgroupindex
#306826542
#306822882
#306822192
#306821442
#306816652
#333×C2632
#1646263