Finite Group Databasebeta

← #46782023

Subgroups — #46782023

Order 33664.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682666C211yesmaximal, characteristic
2#30682334C211yesmaximal, characteristic
3#30682145C211yesmaximal, characteristic
4#30681685C211yesmaximal, characteristic
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic
6#30681668C211yesmaximal, characteristic
7#475×C263C211yesmaximal, characteristic
8C2×#16862366—21no—
9#22554470C2211yescharacteristic
10#22554468—21no—
11#22554462—21no—
12#22554460—22no—
13C4×Dic526—21no—
14C4×Dic526C2211yescharacteristic
15#22554435—21no—
16#22554401—22no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18#22554394—21no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×Q8×C263C2211yescharacteristic
22#106×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#103×C263—21no—
25C2×Dic526—21no—
26C2×Dic526D411yescharacteristic
27#16862366—42no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263D411yescharacteristic
32C4⋊Dic263D412yes—
33Dic263⋊C4—22no—
34Dic263⋊C4—22no—
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—41no—
50Dic526—41no—
51Dic526SD1612yes—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—22no—
55C263⋊C8—22no—
56C263⋊C8—41no—
57Q8×C263—21no—
58Q8×C263—21no—
59Q8×C263—41no—
60Q8×C263—41no—
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—21no—
70C4×C263—41no—
71C4×C263—41no—
72C4×C263—81no—
73C4×C263C2×SD1611yescharacteristic
74C4×C263#13511yescharacteristic
75C4×C263#13711yescharacteristic
76C4×C263#13711yescharacteristic
77Dic263—22no—
78Dic263—42no—
79Dic263—41no—
80C2×C263#44811yescharacteristic
81C2×C263#45211yescharacteristic
82C2×C263#45611yescharacteristic
83C263#165311yescharacteristic, complemented, Sylow
84#1653—2631nomaximal, Sylow
85#557—2631no—
86#498—2631no—
87#475D26311yescharacteristic
88#462—2631no—
89#332—2631no—
90Q8⋊C8—2631no—
91Q8⋊C8—2631no—
92C2×Q16—5261no—
93C4⋊Q8—2631no—
94C4⋊Q8—5261no—
95C4⋊Q8C2×D26311yescharacteristic
96#125—5261no—
97#125—5262no—
98C4×Q8—2631no—
99C4×Q8—5261no—
100C4×Q8—5261no—
101C4×Q8C2×D26311yescharacteristic
102#106—21no—
103#106—5262no—
104C4⋊C8—2631no—
105C4⋊C8C2×D26311yescharacteristic
106#103—21no—
107#103—5261no—
108C4×C8—2631no—
109C2×Q8—21no—
110C2×Q8—2631no—
111C2×Q8—5261no—
112C2×Q8C22⋊D26311yescharacteristic
113Q16—10522no—
114C2×C8—21no—
115C2×C8—5261no—
116C2×C8—5261no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—2631no—
121C4⋊C4—2632no—
122C4⋊C4—5262no—
123C4⋊C4—5262no—
124C4⋊C4—5262no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4C22⋊D26311yescharacteristic
128C42—21no—
129C42—5262no—
130C42—5261no—
131C42C22×D26311yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—41no—
135Q8—41no—
136Q8—2632no—
137Q8—5261no—
138Q8—10521no—
139Q8—10521no—
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—5262no—
151C8—10521no—
152C22#2255443811yescharacteristic
153C4—21no—
154C4—41no—
155C4—41no—
156C4—81no—
157C4—5262no—
158C4—10521no—
159C4—10522no—
160C4SD16×D26311yescharacteristic
161C4#2255449011yescharacteristic
162C4#2255449911yescharacteristic
163C4#2255450111yescharacteristic
164C2#3068207511yescharacteristic
165C2#3068209811yescharacteristic
166C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#475×C263C2
socle, prime radicalC22×C263#120
hypercenter#475D263
hypocenterC263#1653
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
83. C263#1653semidirect

Maximal subgroups

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

subgroupindex
#306826662
#306823342
#306821452
#306816852
Q8⋊(C263⋊C8)2
#306816682
#475×C2632
#1653263