Finite Group Databasebeta

← #46783879

Subgroups — #46783879

Order 33664.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#30682500C211yesmaximal, characteristic
2C2×#22554454C212yesmaximal, complemented
3C2×#22554384C212yesmaximal, complemented
4#30681799C211yesmaximal, characteristic, complemented
5#342×C263C211yesmaximal, characteristic, complemented
6C22×C22⋊D263C2212yes—
7C23×Dic263C2211yescharacteristic
8#22554454—22no—
9#22554454—24no—
10#22554454—24no—
11#22554444—22no—
12#22554440—22no—
13C2×C4⋊Dic263—22no—
14C2×C22⋊Dic263C2211yescharacteristic
15C2×(C2×D263)⋊C4—22no—
16#22554384—24no—
17C263⋊#95—22no—
18C2×C22⋊C4×C263C2211yescharacteristic
19C2×C22⋊C4×C263C2212yes—
20C23×D263D412yes—
21C2×D1052—22no—
22C2×C22⋊D263—22no—
23C2×C22⋊D263—22no—
24C2×C22⋊D263—22no—
25C2×C22⋊D263—22no—
26C2×C22⋊D263—22no—
27C2×C22⋊D263—22no—
28C22×Dic263—21no—
29C22×Dic263—22no—
30C22×Dic263—22no—
31C22×Dic263—21no—
32C22×Dic263—21no—
33C22×Dic263D412yes—
34C22×Dic263D412yescomplemented
35C4⋊Dic263—28no—
36C4⋊Dic263—22no—
37C22⋊Dic263—22no—
38(C2×D263)⋊C4—28no—
39(C2×D263)⋊C4—24no—
40C24×C263C2311yescharacteristic
41C22×C4×C263—22no—
42C22×C4×C263D412yes—
43C22⋊C4×C263—22no—
44C22⋊C4×C263—22no—
45C22⋊C4×C263D414yescomplemented
46C22×D263—22no—
47C22×D263—22no—
48C22×D263—22no—
49C22×D263—44no—
50D1052—82no—
51C22⋊D263—42no—
52C22⋊D263—42no—
53C22⋊D263—42no—
54C22⋊D263—42no—
55C2×Dic263—24no—
56C2×Dic263—22no—
57C2×Dic263—22no—
58C2×Dic263—22no—
59C2×Dic263—22no—
60C2×Dic263—41no—
61C2×Dic263—42no—
62C2×Dic263—41no—
63C2×Dic263—42no—
64C2×Dic263—41no—
65C23×C263—42no—
66C23×C263C2×D412yes—
67C23×C263C2×D411yescharacteristic
68C23×C263C2×D411yescharacteristic
69C23×C263C2×D412yes—
70C23×C263#4111yescharacteristic
71C2×C4×C263—22no—
72C2×C4×C263—24no—
73C2×C4×C263—44no—
74C2×C4×C263—42no—
75C22×C263—22no—
76C22×C263—24no—
77C22×C263—41no—
78C22×C263—42no—
79C22×C263—41no—
80C22×C263#12012yes—
81C22×C263#12011yescharacteristic
82C22×C263#12111yescharacteristic
83C22×C263#12112yes—
84C22×C263#12711yescharacteristic
85C2×D263—44no—
86C2×D263—42no—
87C2×D263—44no—
88C2×D263—82no—
89C4×C263—44no—
90C4×C263—42no—
91Dic263—42no—
92Dic263—42no—
93Dic263—81no—
94C2×C263—21no—
95C2×C263—22no—
96C2×C263—22no—
97C2×C263—21no—
98C2×C263#39211yescharacteristic
99C2×C263#45812yes—
100D263—82no—
101C263#202211yescharacteristic, complemented, Sylow
102#2022—2631nomaximal, Sylow
103#534—2631no—
104C2×#123—2632no—
105C2×#99—2632no—
106#381—2631no—
107#342D26311yescharacteristic, complemented
108C22×D4—2632no—
109C23×C4—2631no—
110#123—5264no—
111#123—5262no—
112#123—5264no—
113#121—5262no—
114#120—5262no—
115C2×C4⋊C4—5262no—
116C2×C22⋊C4—2631no—
117C2×C22⋊C4—5262no—
118C2×C22⋊C4C2×D26311yescharacteristic
119C2×C22⋊C4C2×D26312yes—
120#99—5264no—
121#95—5262no—
122C24—2632no—
123C24C22×D26311yescharacteristic
124C2×D4—5262no—
125C2×D4—5262no—
126C2×D4—5262no—
127C2×D4—5262no—
128C2×D4—5262no—
129C2×D4—5262no—
130C2×D4—5262no—
131C22×C4—22no—
132C22×C4—2632no—
133C22×C4—2632no—
134C22×C4—5262no—
135C22×C4—5261no—
136C22×C4—5262no—
137C22×C4—5261no—
138C22×C4—5261no—
139C22×C4D105212yes—
140C4⋊C4—5268no—
141C4⋊C4—5262no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—5268no—
145C22⋊C4—5264no—
146C22⋊C4—5262no—
147C22⋊C4D105214yescomplemented
148C23—42no—
149C23—5262no—
150C23—5262no—
151C23—5262no—
152C23—10524no—
153C23D4×D26312yes—
154C23D4×D26311yescharacteristic
155C23C2×D105211yescharacteristic
156C23C2×D105212yes—
157C23#1686237711yescharacteristic
158D4—10522no—
159D4—10522no—
160D4—10522no—
161D4—10522no—
162D4—21042no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—5264no—
168C2×C4—5262no—
169C2×C4—5262no—
170C2×C4—5262no—
171C2×C4—5262no—
172C2×C4—10521no—
173C2×C4—10522no—
174C2×C4—10521no—
175C2×C4—10522no—
176C2×C4—10521no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—10524no—
183C22—10524no—
184C22—10522no—
185C22—21042no—
186C22#2255444012yes—
187C22#2255444011yescharacteristic
188C22#2255444511yescharacteristic
189C22#2255444512yes—
190C22#2255446711yescharacteristic
191C4—44no—
192C4—42no—
193C4—10522no—
194C4—10522no—
195C4—21041no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—21042no—
201C2#3068184811yescharacteristic
202C2#3068212912yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC24×C263C23
FrattiniC24C22×D263
Fitting#342×C263C2
socleC22×C263#120
prime radical#30682500C2
hypercenter#342D263
hypocenterC263#2022
LCSG ▷ C24×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#22554454C2semidirect
3. C2×#22554384C2semidirect
4. #30681799C2semidirect
5. #342×C263C2semidirect
34. C22×Dic263D4semidirect
45. C22⋊C4×C263D4semidirect
101. C263#2022semidirect
107. #342D263semidirect
147. C22⋊C4D1052semidirect

Maximal subgroups

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

subgroupindex
#306825002
C2×#225544542
C2×#225543842
#306817992
#342×C2632
#2022263