Finite Group Databasebeta

← #46781270

Subgroups — #46781270

Order 33664.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#30682472C211yesmaximal, characteristic
2#30681995C211yesmaximal, characteristic, complemented
3#30681674C212yesmaximal, complemented
4#30681671C212yesmaximal
5C4×C4⋊C4×C263C211yesmaximal, characteristic, complemented
6#22554464—21no—
7#22554462C411yescharacteristic, complemented
8#22554458C411yescharacteristic, complemented
9#22554453—21no—
10#22554449C2211yescharacteristic
11#22554444C2211yescharacteristic
12C4×Dic526C411yescharacteristic, complemented
13C4×D1052C411yescharacteristic, complemented
14C4×C22⋊D263—21no—
15#22554427—21no—
16C4⋊(C263⋊C8)—21no—
17C22⋊(C263⋊C8)C2212yes—
18#22554381—21no—
19C2×C4⋊C4×C263—21no—
20C2×C42×C263—21no—
21C2×C42×C263C2211yescharacteristic
22#95×C263C2212yes—
23C2×Dic526C2×C411yescharacteristic
24C2×D1052C2×C411yescharacteristic
25C2×C22⋊D263—21no—
26C2×C4×D263—21no—
27C2×C263⋊C8—22no—
28C4⋊Dic263C2×C411yescharacteristic
29C4⋊Dic263C2×C411yescharacteristic
30Dic263⋊C4—21no—
31Dic263⋊C4—21no—
32Dic263⋊C4—21no—
33Dic263⋊C4—21no—
34C22⋊Dic263—21no—
35(C2×D263)⋊C4—21no—
36(C2×D263)⋊C4—21no—
37(C2×D263)⋊C4—21no—
38(C2×D263)⋊C4—21no—
39C4×Dic263—21no—
40C22×C4×C263—22no—
41C22×C4×C263D411yescharacteristic
42C22×C4×C263D411yescharacteristic
43C22×C4×C263C2311yescharacteristic
44C4⋊C4×C263—24no—
45C42×C263—42no—
46C42×C263C2×C411yescharacteristic
47C42×C263C2×C411yescharacteristic
48C42×C263D411yescharacteristic
49C42×C263D411yescharacteristic
50C22×D263—21no—
51Dic526—41no—
52D1052—41no—
53C22⋊D263—41no—
54C22⋊D263—41no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C4×D263—42no—
59C263⋊C8—42no—
60C23×C263C2×D411yescharacteristic
61C2×C4×C263—21no—
62C2×C4×C263—21no—
63C2×C4×C263—22no—
64C2×C4×C263—24no—
65C2×C4×C263—41no—
66C2×C4×C263—42no—
67C2×C4×C263—42no—
68C2×C4×C263C22⋊C411yescharacteristic
69C2×C4×C263C22⋊C411yescharacteristic
70C2×C4×C263C22⋊C411yescharacteristic
71C2×C4×C263C22⋊C411yescharacteristic
72C2×C4×C263C22×C411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C22×C263—21no—
75C22×C263—21no—
76C22×C263C2×C22⋊C411yescharacteristic
77C22×C263AGL(1,ℤ/8)11yescharacteristic
78C22×C263#13711yescharacteristic
79C2×D263—41no—
80C2×D263—41no—
81C2×D263—41no—
82C4×C263—21no—
83C4×C263—21no—
84C4×C263—21no—
85C4×C263—21no—
86C4×C263—21no—
87C4×C263—44no—
88C4×C263#10412yes—
89Dic263—41no—
90Dic263—41no—
91Dic263—41no—
92C2×C263—21no—
93C2×C263—21no—
94C2×C263#41011yescharacteristic
95C2×C263#41711yescharacteristic
96C2×C263C2×#10411yescharacteristic
97D263—81no—
98C263#150911yescharacteristic, complemented, Sylow
99#1509—2631nomaximal, Sylow
100#529—2631no—
101#432—2631no—
102C4×C4⋊C4D26311yescharacteristic, complemented
103#328—2632no—
104#327—2632no—
105#126—5261no—
106#125—2631no—
107#124—2631no—
108#123—5261no—
109C22⋊Q8—2631no—
110#121—2631no—
111C4×Q8—2631no—
112C4×D4—2631no—
113C4×D4—5261no—
114#117—5261no—
115C2×C4⋊C4—21no—
116C2×C42—21no—
117C2×C42C2×D26311yescharacteristic
118C4⋊C8—5261no—
119C22⋊C8—2632no—
120#97—5261no—
121#95C2×D26312yes—
122C2×Q8—2631no—
123C2×D4—2631no—
124C2×D4—5261no—
125C22×C4—22no—
126C22×C4—5261no—
127C22×C4C22⋊D26311yescharacteristic
128C22×C4C22⋊D26311yescharacteristic
129C22×C4C22×D26311yescharacteristic
130C2×C8—5262no—
131C4⋊C4—24no—
132C4⋊C4—2631no—
133C4⋊C4—2631no—
134C4⋊C4—5261no—
135C4⋊C4—5261no—
136C4⋊C4—5261no—
137C4⋊C4—5261no—
138C22⋊C4—5261no—
139C22⋊C4—5261no—
140C22⋊C4—5261no—
141C22⋊C4—5261no—
142C22⋊C4—5261no—
143C42—42no—
144C42—5261no—
145C42C4×D26311yescharacteristic
146C42C4×D26311yescharacteristic
147C42D105211yescharacteristic
148C42D105211yescharacteristic
149C23—5261no—
150C23C2×C22⋊D26311yescharacteristic
151Q8—10521no—
152D4—10521no—
153D4—10521no—
154D4—10521no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—5261no—
163C2×C4—5261no—
164C2×C4—5261no—
165C2×C4—10522no—
166C2×C4(C2×D263)⋊C411yescharacteristic
167C2×C4(C2×D263)⋊C411yescharacteristic
168C2×C4(C2×D263)⋊C411yescharacteristic
169C2×C4(C2×D263)⋊C411yescharacteristic
170C2×C4C2×C4×D26311yescharacteristic
171C2×C4C2×D105211yescharacteristic
172C8—10522no—
173C22—21no—
174C22—21no—
175C22—10521no—
176C22—10521no—
177C22—10521no—
178C22C2×(C2×D263)⋊C411yescharacteristic
179C22#2255449611yescharacteristic
180C22#2255450111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—44no—
187C4—10521no—
188C4—10521no—
189C4—10521no—
190C4#2255439812yes—
191C2—21no—
192C2—21no—
193C2—21041no—
194C2#3068191111yescharacteristic
195C2#3068193711yescharacteristic
196C2C2×#2255439811yescharacteristic
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC4×C4⋊C4×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C22
cosocleC22×C4×C263C23
hypercenterC4×C4⋊C4D263
hypocenterC263#1509
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #30681995C2semidirect
3. #30681674C2semidirect
5. C4×C4⋊C4×C263C2semidirect
7. #22554462C4semidirect
8. #22554458C4semidirect
12. C4×Dic526C4semidirect
13. C4×D1052C4semidirect
98. C263#1509semidirect
102. C4×C4⋊C4D263semidirect

Maximal subgroups

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

subgroupindex
#306824722
#306819952
#306816742
#306816712
C4×C4⋊C4×C2632
#1509263