Finite Group Databasebeta

← #46781967

Subgroups — #46781967

Order 33664.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic526C211yesmaximal, characteristic
2#30682290C211yesmaximal, characteristic
3#30682145C211yesmaximal, characteristic
4#30681686C211yesmaximal, characteristic
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic
6#30681668C211yesmaximal, characteristic
7#475×C263C211yesmaximal, characteristic
8C2×#16862366—21no—
9#22554470—21no—
10#22554470C2211yescharacteristic
11#22554469—22no—
12#22554469—21no—
13Q8×Dic263—21no—
14C4×Dic526—21no—
15C4×Dic526C2211yescharacteristic
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554394—21no—
18#22554393—22no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×Q8×C263C2211yescharacteristic
22#106×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#103×C263—21no—
25C2×Dic526—22no—
26C2×Dic526D411yescharacteristic
27C2×Dic526D412yes—
28#16862366—42no—
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—22no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D411yescharacteristic
35Dic263⋊C4—22no—
36Dic263⋊C4—21no—
37C4×Dic263—22no—
38C4×Dic263—21no—
39C2×Q8×C263—21no—
40C2×Q8×C263D411yescharacteristic
41C2×C8×C263—21no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D411yescharacteristic
46C42×C263—21no—
47C42×C263C2311yescharacteristic
48Dic526—21no—
49Dic526—42no—
50Dic526—82no—
51Dic526SD1612yes—
52C2×Dic263—21no—
53C2×Dic263—22no—
54C2×Dic263—21no—
55C263⋊C8—41no—
56C263⋊C8—41no—
57Q8×C263—21no—
58Q8×C263—41no—
59Q8×C263—41no—
60Q8×C263Q1612yescomplemented
61C2×C4×C263—21no—
62C2×C4×C263—21no—
63C2×C4×C263—41no—
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C8×C263—41no—
68C22×C263#12011yescharacteristic
69C4×C263—22no—
70C4×C263—21no—
71C4×C263—41no—
72C4×C263—81no—
73C4×C263C2×SD1611yescharacteristic
74C4×C263C2×Q1611yescharacteristic
75C4×C263#13711yescharacteristic
76C4×C263#13711yescharacteristic
77Dic263—22no—
78Dic263—42no—
79Dic263—41no—
80C2×C263#44811yescharacteristic
81C2×C263#45111yescharacteristic
82C2×C263#45511yescharacteristic
83C263#164511yescharacteristic, complemented, Sylow
84#1645—2631nomaximal, Sylow
85Q82—2631no—
86#487—2631no—
87#475D26311yescharacteristic
88#462—2631no—
89#333—2631no—
90Q8⋊C8—2631no—
91Q8⋊C8—2631no—
92C2×Q16—5261no—
93C4⋊Q8—2631no—
94C4⋊Q8—5261no—
95C4⋊Q8—5262no—
96C4⋊Q8—5261no—
97C4⋊Q8C2×D26311yescharacteristic
98C4×Q8—2631no—
99C4×Q8—5261no—
100C4×Q8—5261no—
101C4×Q8C2×D26311yescharacteristic
102#106—21no—
103C4⋊C8—2631no—
104C4⋊C8C2×D26311yescharacteristic
105#103—21no—
106#103—5262no—
107#103—5261no—
108C4×C8—2631no—
109C2×Q8—21no—
110C2×Q8—2631no—
111C2×Q8—2632no—
112C2×Q8—5262no—
113C2×Q8C22⋊D26311yescharacteristic
114Q16—10522no—
115C2×C8—21no—
116C2×C8—5261no—
117C2×C8—5261no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—2631no—
122C4⋊C4—5262no—
123C4⋊C4—5262no—
124C4⋊C4—5261no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4C22⋊D26311yescharacteristic
128C42—21no—
129C42—5262no—
130C42—5261no—
131C42C22×D26311yescharacteristic
132Q8—21no—
133Q8—41no—
134Q8—41no—
135Q8—2632no—
136Q8—5261no—
137Q8—10522no—
138Q8—21042no—
139Q8#1686236612yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—5261no—
144C2×C4—5261no—
145C2×C4—5262no—
146C2×C4D4×D26311yescharacteristic
147C2×C4D4×D26311yescharacteristic
148C2×C4C2×C22⋊D26311yescharacteristic
149C8—41no—
150C8—10521no—
151C8—10521no—
152C22#2255443811yescharacteristic
153C4—21no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—5262no—
158C4—10522no—
159C4—10521no—
160C4SD16×D26311yescharacteristic
161C4C2×#1686236611yescharacteristic
162C4#2255449911yescharacteristic
163C4#2255450011yescharacteristic
164C2#3068207511yescharacteristic
165C2#3068209311yescharacteristic
166C2#3068211411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#475×C263C2
socle, prime radicalC22×C263#120
hypercenter#475D263
hypocenterC263#1645
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
60. Q8×C263Q16semidirect
83. C263#1645semidirect
139. Q8#16862366semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic5262
#306822902
#306821452
#306816862
Q8⋊(C263⋊C8)2
#306816682
#475×C2632
#1645263