Finite Group Databasebeta

← #46780744

Subgroups — #46780744

Order 33664.

222 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 37 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#30681705C211yesmaximal, characteristic, complemented
2#30681662C211yesmaximal, characteristic, complemented
3#392×C263C211yesmaximal, characteristic
4C2×C22⋊Dic263—21no—
5C22⋊(C263⋊C8)—21no—
6C22×D4×C263—21no—
7C22×D4×C263C411yescharacteristic, complemented
8C2×C22⋊C4×C263—21no—
9C2×C22⋊C4×C263C2211yescharacteristic
10#95×C263C411yescharacteristic, complemented
11C22×Dic263—41no—
12C2×C263⋊C8—41no—
13C22⋊Dic263—22no—
14C22⋊Dic263—41no—
15C24×C263—21no—
16C24×C263D411yescharacteristic
17C2×D4×C263—41no—
18C2×D4×C263—42no—
19C2×D4×C263—42no—
20C2×D4×C263—41no—
21C2×D4×C263—41no—
22C2×D4×C263—42no—
23C22×C4×C263—21no—
24C22×C4×C263C2×C411yescharacteristic
25C22×C4×C263D411yescharacteristic
26C22⋊C4×C263—41no—
27C22⋊C4×C263—42no—
28C2×Dic263—42no—
29C2×Dic263—81no—
30C2×Dic263—81no—
31C263⋊C8—81no—
32C23×C263—21no—
33C23×C263—21no—
34C23×C263—22no—
35C23×C263—41no—
36C23×C263—41no—
37C23×C263—41no—
38C23×C263—41no—
39C23×C263—41no—
40C23×C263—41no—
41C23×C263—41no—
42C23×C263—41no—
43C23×C263C22⋊C411yescharacteristic
44C23×C263D811yescharacteristic
45C23×C263SD1611yescharacteristic
46D4×C263—42no—
47D4×C263—44no—
48D4×C263—44no—
49D4×C263—42no—
50C2×C4×C263—22no—
51C2×C4×C263—21no—
52C2×C4×C263—21no—
53C2×C4×C263—41no—
54C2×C4×C263—41no—
55C2×C4×C263—41no—
56C2×C4×C263—41no—
57C22×C263—21no—
58C22×C263—21no—
59C22×C263—21no—
60C22×C263—21no—
61C22×C263—41no—
62C22×C263—41no—
63C22×C263—42no—
64C22×C263—42no—
65C22×C263—41no—
66C22×C263—41no—
67C22×C263—42no—
68C22×C263—81no—
69C22×C263—81no—
70C22×C263—81no—
71C22×C263—81no—
72C22×C263—81no—
73C22×C263#9911yescharacteristic
74C22×C263#10211yescharacteristic
75C22×C263#10411yescharacteristic
76C4×C263—42no—
77C4×C263—41no—
78C4×C263—41no—
79Dic263—82no—
80C2×C263—21no—
81C2×C263—21no—
82C2×C263—41no—
83C2×C263—41no—
84C2×C263—82no—
85C2×C263#32711yescharacteristic
86C2×C263AΣL(1,𝔽16)11yescharacteristic
87C2×C263#35311yescharacteristic
88C263#134311yescharacteristic, complemented, Sylow
89#1343—2631nomaximal, Sylow
90#392D26311yescharacteristic
91#342—2631no—
92#323—2631no—
93C22×D4—21no—
94C22×D4Dic26311yescharacteristic, complemented
95C2×C22⋊C4—21no—
96C2×C22⋊C4—5261no—
97C2×C22⋊C4C2×D26311yescharacteristic
98C22⋊C8—5261no—
99#95Dic26311yescharacteristic, complemented
100C24—21no—
101C24C22⋊D26311yescharacteristic
102C2×D4—41no—
103C2×D4—42no—
104C2×D4—42no—
105C2×D4—41no—
106C2×D4—41no—
107C2×D4—42no—
108C22×C4—21no—
109C22×C4—10521no—
110C22×C4C2×Dic26311yescharacteristic
111C22×C4C22⋊D26311yescharacteristic
112C2×C8—10521no—
113C22⋊C4—41no—
114C22⋊C4—42no—
115C22⋊C4—5262no—
116C22⋊C4—10521no—
117C23—21no—
118C23—21no—
119C23—22no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—41no—
125C23—41no—
126C23—41no—
127C23—41no—
128C23C22⋊Dic26311yescharacteristic
129C23#1686236111yescharacteristic
130C23#1686236411yescharacteristic
131D4—42no—
132D4—44no—
133D4—44no—
134D4—42no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—10522no—
143C2×C4—21041no—
144C2×C4—21041no—
145C8—21041no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22—21no—
150C22—41no—
151C22—41no—
152C22—42no—
153C22—42no—
154C22—41no—
155C22—41no—
156C22—42no—
157C22—81no—
158C22—81no—
159C22—81no—
160C22—81no—
161C22—81no—
162C22#2255438511yescharacteristic
163C22#2255439111yescharacteristic
164C22#2255439711yescharacteristic
165C4—42no—
166C4—41no—
167C4—41no—
168C4—21042no—
169C2—21no—
170C2—21no—
171C2—41no—
172C2—41no—
173C2—82no—
174C2#3068167211yescharacteristic
175C2#3068172511yescharacteristic
176C2#3068173111yescharacteristic
subgroupG/H
centerC22#22554385
commutatorC22×C4×C263C2×C4
FrattiniC2×C22⋊C4C2×D263
Fitting, prime radical#392×C263C2
socleC22×C263#99
cosocleC2×C22⋊C4×C263C22
hypercenter#392D263
hypocenterC263#1343
LCSG ▷ C22×C4×C263 ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #30681705C2semidirect
2. #30681662C2semidirect
7. C22×D4×C263C4semidirect
10. #95×C263C4semidirect
88. C263#1343semidirect
94. C22×D4Dic263semidirect
99. #95Dic263semidirect

Maximal subgroups

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

subgroupindex
#306817052
#306816622
#392×C2632
#1343263