Finite Group Databasebeta

← #46781902

Subgroups — #46781902

Order 33664.

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

normal subgroups only

This group has 188 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#30682663C211yesmaximal, characteristic
2#30682230C211yesmaximal, characteristic
3#30682230C211yesmaximal, characteristic
4#30681684C211yesmaximal, characteristic
5#30681670C211yesmaximal, characteristic
6#30681670C211yesmaximal, characteristic
7#487×C263C211yesmaximal, characteristic
8#22554468—21no—
9#22554461—21no—
10#22554460—22no—
11Q8×Dic263—21no—
12C4×Dic526C2211yescharacteristic
13C4×Dic526C2211yescharacteristic
14#22554435—21no—
15#22554403—21no—
16#22554403—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554393—21no—
20#22554393—21no—
21C4⋊Q8×C263C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23#103×C263—22no—
24C4×C8×C263C2211yescharacteristic
25C2×Dic526D411yescharacteristic
26C2×Dic526D411yescharacteristic
27C2×C263⋊C8—21no—
28C2×C263⋊C8—21no—
29C4⋊Dic263—22no—
30C4⋊Dic263D411yescharacteristic
31C4⋊Dic263D411yescharacteristic
32Dic263⋊C4—22no—
33Dic263⋊C4—22no—
34Dic263⋊C4—21no—
35Dic263⋊C4—21no—
36C4×Dic263—22no—
37C4×Dic263—21no—
38C4×Dic263—21no—
39C2×Q8×C263—21no—
40C2×Q8×C263—21no—
41C2×C8×C263—21no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D412yes—
46C42×C263C2311yescharacteristic
47Dic526—21no—
48Dic526—21no—
49Dic526—21no—
50Dic526Q1612yes—
51C2×Dic263—21no—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C263⋊C8—41no—
56C263⋊C8—41no—
57Q8×C263—42no—
58Q8×C263—41no—
59Q8×C263—41no—
60C2×C4×C263—22no—
61C2×C4×C263—41no—
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263C2×D411yescharacteristic
65C8×C263—41no—
66C22×C263#12011yescharacteristic
67C4×C263—21no—
68C4×C263—42no—
69C4×C263—81no—
70C4×C263C2×Q1611yescharacteristic
71C4×C263#13511yescharacteristic
72C4×C263#13711yescharacteristic
73C4×C263#13711yescharacteristic
74Dic263—22no—
75Dic263—41no—
76Dic263—41no—
77Dic263—41no—
78C2×C263#45111yescharacteristic
79C2×C263#45211yescharacteristic
80C2×C263#45411yescharacteristic
81C263#163611yescharacteristic, complemented, Sylow
82#1636—2631nomaximal, Sylow
83#557—2631no—
84#487D26311yescharacteristic
85#477—2631no—
86#477—2631no—
87#332—2631no—
88Q8⋊C8—2631no—
89Q8⋊C8—2631no—
90C4⋊Q8—5261no—
91C4⋊Q8C2×D26311yescharacteristic
92C4⋊Q8C2×D26311yescharacteristic
93#125—5261no—
94#125—5262no—
95C4×Q8—2631no—
96C4×Q8—2631no—
97C4×Q8—5261no—
98C4×Q8—5261no—
99#107—5261no—
100#107—5261no—
101C4⋊C8—2631no—
102C4⋊C8—2631no—
103#103—22no—
104#103—5261no—
105#103—5261no—
106C4×C8C2×D26311yescharacteristic
107C2×Q8—21no—
108C2×Q8—21no—
109C2×Q8—2631no—
110C2×Q8—2631no—
111C2×C8—21no—
112C2×C8—5261no—
113C2×C8—5261no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—2631no—
118C4⋊C4—2631no—
119C4⋊C4—5262no—
120C4⋊C4—5262no—
121C4⋊C4—5262no—
122C4⋊C4—5261no—
123C4⋊C4—5261no—
124C4⋊C4C22⋊D26312yes—
125C42—5262no—
126C42—5261no—
127C42—5261no—
128C42C22×D26311yescharacteristic
129Q8—42no—
130Q8—41no—
131Q8—41no—
132Q8—2632no—
133Q8—5261no—
134Q8—5261no—
135Q8—5261no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—5261no—
139C2×C4—5261no—
140C2×C4—5261no—
141C2×C4—5261no—
142C2×C4D4×D26311yescharacteristic
143C2×C4D4×D26311yescharacteristic
144C2×C4C2×C22⋊D26311yescharacteristic
145C8—41no—
146C8—10521no—
147C8—10521no—
148C22#2255443811yescharacteristic
149C4—21no—
150C4—42no—
151C4—81no—
152C4—5262no—
153C4—10521no—
154C4—10521no—
155C4—10521no—
156C4Q16×D26311yescharacteristic
157C4#2255449111yescharacteristic
158C4#2255449911yescharacteristic
159C4#2255450211yescharacteristic
160C2#3068209211yescharacteristic
161C2#3068209711yescharacteristic
162C2#3068211011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#487×C263C2
socle, prime radicalC22×C263#120
hypercenter#487D263
hypocenterC263#1636
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
81. C263#1636semidirect

Maximal subgroups

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

subgroupindex
#306826632
#306822302
#306816842
#306816702
#487×C2632
#1636263