Finite Group Databasebeta

← #46781787

Subgroups — #46781787

Order 33664.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#30682567C211yesmaximal, characteristic
2#30682273C211yesmaximal, characteristic
3#30681876C211yesmaximal, characteristic
4#30681676C211yesmaximal, characteristic
5#30681675C211yesmaximal, characteristic
6#30681663C211yesmaximal, characteristic
7#484×C263C211yesmaximal, characteristic
8#22554469—21no—
9#22554468—21no—
10#22554460—21no—
11#22554460—21no—
12#22554449C2211yescharacteristic
13#22554447—21no—
14#22554426—21no—
15C2×Dic263⋊C4C2211yescharacteristic
16#22554403—21no—
17#22554393—21no—
18C22⋊(C263⋊C8)C2211yescharacteristic
19C263⋊#95—21no—
20C263⋊#95—21no—
21C263⋊#95C2211yescharacteristic
22C22⋊Q8×C263C2211yescharacteristic
23C2×C4⋊C4×C263C2211yescharacteristic
24#107×C263—21no—
25#103×C263—21no—
26C22⋊C8×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526D411yescharacteristic
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D411yescharacteristic
35Dic263⋊C4—21no—
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42C22⋊Dic263—21no—
43C4×Dic263—21no—
44C4×Dic263—21no—
45C2×Q8×C263D411yescharacteristic
46C22×C4×C263—21no—
47C22×C4×C263C2311yescharacteristic
48C2×C8×C263—21no—
49C4⋊C4×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263D411yescharacteristic
53C22⋊C4×C263—21no—
54Dic526—41no—
55Dic526—81no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—41no—
62C2×Dic263—41no—
63C2×Dic263—41no—
64C2×Dic263—41no—
65C2×Dic263Q1612yes—
66C263⋊C8—41no—
67C23×C263C2×D411yescharacteristic
68Q8×C263—41no—
69C2×C4×C263—21no—
70C2×C4×C263—21no—
71C2×C4×C263—41no—
72C2×C4×C263—42no—
73C2×C4×C263—41no—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C8×C263—41no—
77C22×C263—21no—
78C22×C263—21no—
79C22×C263#12011yescharacteristic
80C22×C263C2×Q1611yescharacteristic
81C22×C263#13711yescharacteristic
82C4×C263—21no—
83C4×C263—21no—
84C4×C263—41no—
85C4×C263—41no—
86C4×C263—81no—
87Dic263—22no—
88Dic263—41no—
89Dic263—41no—
90Dic263—41no—
91Dic263—81no—
92C2×C263—21no—
93C2×C263—21no—
94C2×C263#45111yescharacteristic
95C2×C263#45411yescharacteristic
96C2×C263#45811yescharacteristic
97C263#161711yescharacteristic, complemented, Sylow
98#1617—2631nomaximal, Sylow
99#544—2631no—
100#484—2631no—
101#484D26311yescharacteristic
102#400—2631no—
103#328—2631no—
104#328—2631no—
105#324—2631no—
106C4⋊Q8—5261no—
107C4⋊Q8—5261no—
108#125—5261no—
109#125—5261no—
110C22⋊Q8—2631no—
111C22⋊Q8—5261no—
112C22⋊Q8C2×D26311yescharacteristic
113#117—5261no—
114C2×C4⋊C4—2631no—
115C2×C4⋊C4C2×D26311yescharacteristic
116#107—21no—
117#107—5261no—
118#103—21no—
119#103—5261no—
120C22⋊C8—2631no—
121C22⋊C8C2×D26311yescharacteristic
122#95—2631no—
123#95—5261no—
124#95—5261no—
125C2×Q8—2631no—
126C2×Q8—5261no—
127C2×Q8C22⋊D26311yescharacteristic
128C22×C4—21no—
129C22×C4—2631no—
130C22×C4—2631no—
131C22×C4—5261no—
132C22×C4C22×D26311yescharacteristic
133C2×C8—21no—
134C2×C8—5261no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2631no—
139C4⋊C4—5261no—
140C4⋊C4—5261no—
141C4⋊C4—5261no—
142C4⋊C4—5261no—
143C4⋊C4—5261no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4C22⋊D26311yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—5261no—
150C42—5261no—
151C42—5261no—
152C23D4×D26311yescharacteristic
153Q8—41no—
154Q8—10521no—
155Q8—21041no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—2632no—
162C2×C4—5261no—
163C2×C4—5261no—
164C2×C4—5261no—
165C2×C4—5261no—
166C2×C4—5261no—
167C2×C4—10521no—
168C2×C4—10521no—
169C2×C4—10521no—
170C2×C4—10521no—
171C2×C4D4×D26311yescharacteristic
172C2×C4C2×C22⋊D26311yescharacteristic
173C8—41no—
174C8—10521no—
175C22—21no—
176C22—21no—
177C22#2255443811yescharacteristic
178C22Q16×D26311yescharacteristic
179C22#2255450211yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—5262no—
186C4—10521no—
187C4—10521no—
188C4—10521no—
189C4—21041no—
190C2—21no—
191C2—21no—
192C2#3068209211yescharacteristic
193C2#3068210911yescharacteristic
194C2#3068212711yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#484×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#484D263
hypocenterC263#1617
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C263#1617semidirect

Maximal subgroups

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

subgroupindex
#306825672
#306822732
#306818762
#306816762
#306816752
#306816632
#484×C2632
#1617263