Finite Group Databasebeta

← #46782942

Subgroups — #46782942

Order 33664.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C22×C4⋊Dic263C211yesmaximal, characteristic
2C2×#22554402C212yesmaximal, complemented
3#30681798C211yesmaximal, characteristic
4#30681701C212yesmaximal, complemented
5C2×C22⋊C8×C263C211yesmaximal, characteristic
6C23×Dic263—21no—
7C2×C4⋊Dic263—24no—
8C2×C4⋊Dic263—21no—
9C2×C4⋊Dic263C2211yescharacteristic
10C2×C4⋊Dic263C2211yescharacteristic
11C2×C4⋊Dic263C2212yes—
12C2×C22⋊Dic263—21no—
13#22554402—24no—
14C263⋊#95—21no—
15C23×C4×C263C2211yescharacteristic
16C22×C8×C263C2212yes—
17C22⋊C8×C263C414yescomplemented
18C22×Dic263—24no—
19C22×Dic263—22no—
20C22×Dic263—21no—
21C22×Dic263—21no—
22C22×Dic263—42no—
23C22×Dic263—42no—
24C4⋊Dic263—24no—
25C4⋊Dic263—22no—
26C4⋊Dic263—22no—
27C4⋊Dic263—22no—
28C4⋊Dic263D414yes—
29C22⋊Dic263—42no—
30C24×C263D411yescharacteristic
31C22×C4×C263—22no—
32C22×C4×C263—22no—
33C22×C4×C263C2×C412yes—
34C22×C4×C263D411yescharacteristic
35C22×C4×C263Q812yes—
36C22×C4×C263C2311yescharacteristic
37C2×C8×C263—22no—
38C2×C8×C263—22no—
39C2×C8×C263C2×C414yescomplemented
40C2×Dic263—24no—
41C2×Dic263—48no—
42C2×Dic263—42no—
43C2×Dic263—42no—
44C2×Dic263—41no—
45C2×Dic263—41no—
46C2×Dic263—41no—
47C2×Dic263—41no—
48C2×Dic263—41no—
49C2×Dic263—41no—
50C23×C263—21no—
51C23×C263—21no—
52C23×C263—21no—
53C23×C263—21no—
54C23×C263C4⋊C412yes—
55C23×C263SD1612yes—
56C23×C263SD1612yes—
57C23×C263C2×D411yescharacteristic
58C2×C4×C263—21no—
59C2×C4×C263—21no—
60C2×C4×C263—24no—
61C2×C4×C263—24no—
62C2×C4×C263C4⋊C412yes—
63C2×C4×C263C22×C411yescharacteristic
64C2×C4×C263C2×D412yes—
65C2×C4×C263C2×Q811yescharacteristic
66C2×C4×C263#4112yes—
67C8×C263—24no—
68C22×C263—22no—
69C22×C263—22no—
70C22×C263—22no—
71C22×C263—22no—
72C22×C263—22no—
73C22×C263—22no—
74C22×C263#10614yescomplemented
75C22×C263C2×C4⋊C411yescharacteristic
76C22×C263#12011yescharacteristic
77C22×C263#12311yescharacteristic
78C22×C263C2×SD1611yescharacteristic
79C22×C263C2×SD1611yescharacteristic
80C22×C263AGL(1,ℤ/8)11yescharacteristic
81C22×C263#13711yescharacteristic
82C4×C263—22no—
83C4×C263C4×D412yes—
84C4×C263C22⋊Q812yes—
85Dic263—44no—
86Dic263—81no—
87Dic263—81no—
88C2×C263—24no—
89C2×C263#38511yescharacteristic
90C2×C263C2×#10611yescharacteristic
91C2×C263#42811yescharacteristic
92C2×C263#44811yescharacteristic
93C2×C263#45011yescharacteristic
94C2×C263#48111yescharacteristic
95C2×C263#48311yescharacteristic
96C263#185311yescharacteristic, complemented, Sylow
97#1853—2631nomaximal, Sylow
98C22×C4⋊C4—2631no—
99C2×#106—2632no—
100C2×C22⋊C8D26311yescharacteristic
101#380—2631no—
102#340—2632no—
103C23×C4—5261no—
104C23×C4C2×D26311yescharacteristic
105C22×C8C2×D26312yes—
106C2×C4⋊C4—2632no—
107C2×C4⋊C4—2631no—
108C2×C4⋊C4—2631no—
109C2×C4⋊C4—5264no—
110C2×C4⋊C4—5261no—
111C2×C22⋊C4—5261no—
112#106—5264no—
113C22⋊C8Dic26314yescomplemented
114#95—5261no—
115C24D105211yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—5264no—
119C22×C4—5262no—
120C22×C4—5261no—
121C22×C4—5261no—
122C22×C4—10522no—
123C22×C4—10522no—
124C22×C4C2×Dic26312yes—
125C22×C4D105211yescharacteristic
126C22×C4Dic52612yes—
127C22×C4C22×D26311yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×Dic26314yescomplemented
131C4⋊C4—2634no—
132C4⋊C4—5264no—
133C4⋊C4—5262no—
134C4⋊C4—5262no—
135C4⋊C4—5262no—
136C22⋊C4—10522no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23C4⋊Dic26312yes—
142C23#1686236512yes—
143C23#1686236512yes—
144C23C2×D105211yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—5264no—
150C2×C4—10528no—
151C2×C4—10522no—
152C2×C4—10522no—
153C2×C4—10521no—
154C2×C4—10521no—
155C2×C4—10521no—
156C2×C4—10521no—
157C2×C4—10521no—
158C2×C4—10521no—
159C2×C4C4⋊Dic26312yes—
160C2×C4C22×Dic26311yescharacteristic
161C2×C4D4×D26312yes—
162C2×C4C2×Dic52611yescharacteristic
163C2×C4#1686237512yes—
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#2255440214yescomplemented
172C22C2×C4⋊Dic26311yescharacteristic
173C22#2255444011yescharacteristic
174C22#2255445411yescharacteristic
175C22C2×#1686236511yescharacteristic
176C22C2×#1686236511yescharacteristic
177C22#2255449811yescharacteristic
178C22#2255450311yescharacteristic
179C4—22no—
180C4—10524no—
181C4—21041no—
182C4—21041no—
183C4D4×Dic26312yes—
184C4#2255444712yes—
185C2—24no—
186C2#3068181311yescharacteristic
187C2C2×#2255440211yescharacteristic
188C2#3068198011yescharacteristic
189C2#3068207911yescharacteristic
190C2#3068209111yescharacteristic
191C2#3068225711yescharacteristic
192C2#3068226911yescharacteristic
subgroupG/H
centerC23C2×D1052
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×C22⋊C8×C263C2
socleC23×C263C2×D4
prime radicalC24×C263D4
cosocleC22×C4×C263C23
hypercenterC2×C22⋊C8D263
hypocenterC263#1853
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#22554402C2semidirect
4. #30681701C2semidirect
17. C22⋊C8×C263C4semidirect
39. C2×C8×C263C2×C4semidirect
74. C22×C263#106semidirect
96. C263#1853semidirect
113. C22⋊C8Dic263semidirect
130. C2×C8C2×Dic263semidirect
171. C22#22554402semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic2632
C2×#225544022
#306817982
#306817012
C2×C22⋊C8×C2632
#1853263