Finite Group Databasebeta

← #46781294

Subgroups — #46781294

Order 33664.

252 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 77 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#30681995C211yesmaximal, characteristic, complemented
2#30681806C211yesmaximal, characteristic, complemented
3#30681672C214yesmaximal, complemented
4#532×C263C211yesmaximal, characteristic
5C4⋊(C263⋊C8)—21no—
6C22⋊(C263⋊C8)C2212yes—
7#22554381—21no—
8C263⋊#95—21no—
9C263⋊#95—21no—
10C263⋊#95C2212yes—
11C2×#41×C263—21no—
12C4⋊Q8×C263C411yescharacteristic, complemented
13#127×C263C411yescharacteristic, complemented
14#124×C263—21no—
15#121×C263—21no—
16#121×C263C2212yes—
17C4×D4×C263—21no—
18C4×D4×C263C412yescomplemented
19C2×C42×C263C2211yescharacteristic
20C22×Dic263—22no—
21C2×C263⋊C8—22no—
22#41×C263—44no—
23C2×Q8×C263—21no—
24C2×D4×C263—22no—
25C2×D4×C263—21no—
26C2×D4×C263—21no—
27C2×D4×C263C2×C412yes—
28C22×C4×C263—22no—
29C22×C4×C263D411yescharacteristic
30C22×C4×C263D411yescharacteristic
31C22×C4×C263C2311yescharacteristic
32C4⋊C4×C263—21no—
33C4⋊C4×C263C2×C412yes—
34C22⋊C4×C263—22no—
35C22⋊C4×C263—22no—
36C42×C263C2×C411yescharacteristic
37C42×C263C2×C411yescharacteristic
38C42×C263D411yescharacteristic
39C42×C263D411yescharacteristic
40C2×Dic263—42no—
41C2×Dic263—42no—
42C2×Dic263—42no—
43C263⋊C8—42no—
44C23×C263—22no—
45C23×C263C2×D411yescharacteristic
46Q8×C263—42no—
47D4×C263—42no—
48D4×C263—42no—
49D4×C263—42no—
50D4×C263—44no—
51C2×C4×C263—22no—
52C2×C4×C263—22no—
53C2×C4×C263—41no—
54C2×C4×C263—41no—
55C2×C4×C263—44no—
56C2×C4×C263C22⋊C411yescharacteristic
57C2×C4×C263C22⋊C411yescharacteristic
58C2×C4×C263C22⋊C411yescharacteristic
59C2×C4×C263C22⋊C411yescharacteristic
60C2×C4×C263C22×C411yescharacteristic
61C2×C4×C263C2×D411yescharacteristic
62C22×C263—21no—
63C22×C263—21no—
64C22×C263—42no—
65C22×C263—42no—
66C22×C263—42no—
67C22×C263C2×C22⋊C411yescharacteristic
68C22×C263AGL(1,ℤ/8)12yes—
69C4×C263—21no—
70C4×C263—21no—
71C4×C263—21no—
72C4×C263—21no—
73C4×C263—21no—
74C4×C263—21no—
75C4×C263—42no—
76Dic263—82no—
77C2×C263—22no—
78C2×C263—82no—
79C2×C263#41011yescharacteristic
80C2×C263#41811yescharacteristic
81C2×C263#42111yescharacteristic
82C263#151411yescharacteristic, complemented, Sylow
83#1514—2631nomaximal, Sylow
84#532D26311yescharacteristic
85#432—2631no—
86#383—2631no—
87#327—2634no—
88C2×#41—21no—
89C4⋊Q8Dic26311yescharacteristic, complemented
90#127Dic26311yescharacteristic, complemented
91#124—21no—
92#121—21no—
93#121C2×D26312yes—
94C4×D4—21no—
95C4×D4Dic26312yescomplemented
96C2×C42C2×D26311yescharacteristic
97C4⋊C8—5261no—
98C22⋊C8—2632no—
99#97—5261no—
100#95—2632no—
101#95—5261no—
102#95—5261no—
103#41—44no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—21no—
107C2×D4—21no—
108C2×D4C2×Dic26312yes—
109C22×C4—22no—
110C22×C4—5262no—
111C22×C4C22⋊D26311yescharacteristic
112C22×C4C22⋊D26311yescharacteristic
113C22×C4C22×D26311yescharacteristic
114C2×C8—5262no—
115C4⋊C4—21no—
116C4⋊C4C2×Dic26312yes—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C42C2×Dic26311yescharacteristic
120C42C2×Dic26311yescharacteristic
121C42C22⋊D26311yescharacteristic
122C42C22⋊D26311yescharacteristic
123C23—22no—
124C23C2×C22⋊D26311yescharacteristic
125Q8—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—44no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—44no—
135C2×C4—10522no—
136C2×C4—10522no—
137C2×C4—10522no—
138C2×C4C22⋊Dic26311yescharacteristic
139C2×C4C22⋊Dic26311yescharacteristic
140C2×C4C22⋊Dic26311yescharacteristic
141C2×C4C22⋊Dic26311yescharacteristic
142C2×C4C22×Dic26311yescharacteristic
143C2×C4C2×C22⋊D26311yescharacteristic
144C8—10522no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22C2×C22⋊Dic26311yescharacteristic
151C22#2255449612yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—42no—
159C4—21042no—
160C2—22no—
161C2—82no—
162C2#3068191211yescharacteristic
163C2#3068194311yescharacteristic
164C2#3068195511yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting, prime radical#532×C263C2
socleC22×C263C2×C22⋊C4
cosocleC22×C4×C263C23
hypercenter#532D263
hypocenterC263#1514
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #30681995C2semidirect
2. #30681806C2semidirect
3. #30681672C2semidirect
12. C4⋊Q8×C263C4semidirect
13. #127×C263C4semidirect
18. C4×D4×C263C4semidirect
82. C263#1514semidirect
89. C4⋊Q8Dic263semidirect
90. #127Dic263semidirect
95. C4×D4Dic263semidirect

Maximal subgroups

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

subgroupindex
#306819952
#306818062
#306816722
#532×C2632
#1514263