Finite Group Databasebeta

← #46781969

Subgroups — #46781969

Order 33664.

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

normal subgroups only

This group has 200 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#30682668C211yesmaximal, characteristic
2#30682288C211yesmaximal, characteristic
3#30682224C211yesmaximal, characteristic
4#30682149C211yesmaximal, characteristic
5#30681668C211yesmaximal, characteristic
6#30681668C211yesmaximal, characteristic
7#333×C263C211yesmaximal, characteristic
8C2×Dic1052—21no—
9#22554470C2211yescharacteristic
10#22554469—21no—
11#22554469—21no—
12#22554468—22no—
13C4×Dic526C2211yescharacteristic
14C4×Dic526C2211yescharacteristic
15#22554435—21no—
16#22554435—21no—
17#22554402—21no—
18#22554395—21no—
19#22554395—21no—
20#22554394—22no—
21C4×C263⋊C8C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—22no—
26C2×Dic526—21no—
27C2×Dic526D411yescharacteristic
28C2×Dic526D411yescharacteristic
29Dic1052—42no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263D411yescharacteristic
34C4⋊Dic263D411yescharacteristic
35Dic263⋊C4—22no—
36Dic263⋊C4—22no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39C4×Dic263—22no—
40C4×Dic263—21no—
41C4×Dic263—21no—
42C2×Q8×C263D412yes—
43C2×C8×C263—21no—
44C2×C8×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263—21no—
47C42×C263C2311yescharacteristic
48Dic526—21no—
49Dic526—21no—
50Dic526—41no—
51Dic526—41no—
52Dic526—82no—
53Dic526SD1612yes—
54Dic526Q1612yescomplemented
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—41no—
60C263⋊C8—41no—
61Q8×C263—42no—
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
69C4×C263—21no—
70C4×C263—42no—
71C4×C263C2×SD1611yescharacteristic
72C4×C263C2×Q1611yescharacteristic
73C4×C263#13711yescharacteristic
74C4×C263#13711yescharacteristic
75Dic263—22no—
76Dic263—22no—
77Dic263—41no—
78Dic263—41no—
79Dic263—81no—
80C2×C263#44811yescharacteristic
81C2×C263#45111yescharacteristic
82C2×C263#45511yescharacteristic
83C263#164511yescharacteristic, complemented, Sylow
84#1645—2631nomaximal, Sylow
85Q82—2631no—
86#487—2631no—
87#475—2631no—
88#462—2631no—
89#333D26311yescharacteristic
90Q8⋊C8—2631no—
91Q8⋊C8—2631no—
92C2×Q16—5261no—
93C4⋊Q8—2631no—
94C4⋊Q8—5261no—
95C4⋊Q8—5261no—
96C4⋊Q8—5262no—
97C4⋊Q8C2×D26311yescharacteristic
98C4×Q8—2631no—
99C4×Q8—2631no—
100C4×Q8—5261no—
101C4×Q8—5261no—
102#106—5261no—
103C4⋊C8C2×D26311yescharacteristic
104C4⋊C8C2×D26311yescharacteristic
105#103—5261no—
106#103—5261no—
107#103—5262no—
108C4×C8—2631no—
109C2×Q8—2631no—
110C2×Q8—2631no—
111C2×Q8—5262no—
112C2×Q8—5261no—
113C2×Q8D105212yes—
114Q16—10522no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—5261no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—2631no—
121C4⋊C4—2631no—
122C4⋊C4—5262no—
123C4⋊C4—5262no—
124C4⋊C4—5261no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4—5261no—
128C42—5262no—
129C42—5261no—
130C42—5261no—
131C42C22×D26311yescharacteristic
132Q8—42no—
133Q8—2632no—
134Q8—2632no—
135Q8—5261no—
136Q8—5261no—
137Q8—10521no—
138Q8—10521no—
139Q8—21042no—
140C2×C4—22no—
141C2×C4—5261no—
142C2×C4—5261no—
143C2×C4—5261no—
144C2×C4—5261no—
145C2×C4—10521no—
146C2×C4D4×D26311yescharacteristic
147C2×C4D4×D26311yescharacteristic
148C2×C4C2×D105211yescharacteristic
149C8—41no—
150C8—41no—
151C8—10521no—
152C22#2255444011yescharacteristic
153C4—21no—
154C4—42no—
155C4—5262no—
156C4—5262no—
157C4—10521no—
158C4—10521no—
159C4—21041no—
160C4SD16×D26311yescharacteristic
161C4Q16×D26311yescharacteristic
162C4#2255449911yescharacteristic
163C4#2255450211yescharacteristic
164C2#3068207811yescharacteristic
165C2#3068209511yescharacteristic
166C2#3068211811yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#333×C263C2
socle, prime radicalC22×C263#120
hypercenter#333D263
hypocenterC263#1645
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
54. Dic526Q16semidirect
83. C263#1645semidirect

Maximal subgroups

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

subgroupindex
#306826682
#306822882
#306822242
#306821492
#306816682
#333×C2632
#1645263