Finite Group Databasebeta

← #10595041

Subgroups — #10595041

Order 576.

518 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 128 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#64135C211yesmaximal, characteristic, complemented
2C3×#930C212yesmaximal, complemented
3#63970C214yesmaximal, complemented
4#63914C211yesmaximal, characteristic, complemented
5#63898C212yesmaximal, complemented
6#63891C214yesmaximal, complemented
7#63872C211yesmaximal, characteristic, complemented
8#5619—32nomaximal
9C22×C32×C4C2211yescharacteristic
10C2×C3×#67C2214yes—
11C2×C3×D12C2212yes—
12C2×#625C2214yes—
13C2×D3×Dic3C2214yes—
14#3757C2212yes—
15C4⋊(C3⋊Dic3)C2212yes—
16C4×C3⋊Dic3C2211yescharacteristic
17C4×C3⋊Dic3C2211yescharacteristic
18C3×(C2×D3)⋊C4C2214yes—
19C3×C4⋊Dic3C2212yes—
20Dic3⋊Dic3C2214yes—
21(C2×D3)⋊Dic3C2214yes—
22C3×#121—32no—
23#940—32no—
24#939—34no—
25#938—34no—
26D4×Dic3—32no—
27#930D312yescomplemented
28#926—32no—
29#926—61no—
30#893—32no—
31#890—32no—
32#886—34no—
33#883—34no—
34C23×C32C2311yescharacteristic
35C22×C3×D3C2314yes—
36C2×C32×C4—22no—
37C2×C32×C4C2311yescharacteristic
38C2×C32×C4C2311yescharacteristic
39C2×C3⋊Dic3C2312yes—
40C2×C3⋊Dic3C2312yes—
41C3×#67—44no—
42C2×C3×Dic3C2314yes—
43C3×D12—24no—
44#625—44no—
45D3×Dic3—44no—
46#540—91noSylow
47C2×C3×D4—34no—
48C2×C3×D4—32no—
49C22×C3×C4—21no—
50C22×C3×C4C2×D312yes—
51C2×#67—34no—
52C2×#67—34no—
53C2×#67C2×D314yes—
54C22×Dic3—34no—
55C2×D12C2×D312yes—
56C2×C4×D3—34no—
57C3×C4⋊C4—32no—
58C3×C22⋊C4—34no—
59#217—32no—
60#217—32no—
61#217—34no—
62#217—62no—
63(C2×D3)⋊C4—34no—
64(C2×D3)⋊C4C2×D314yes—
65C4⋊Dic3—32no—
66C4⋊Dic3—32no—
67C4⋊Dic3—34no—
68C4⋊Dic3—62no—
69C4⋊Dic3C2×D312yes—
70Dic3⋊C4—34no—
71C4×Dic3—32no—
72C4×Dic3—32no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C22×C32—21no—
76C22×C32—22no—
77C22×C32C2411yescharacteristic
78C2×C3×D3—24no—
79C2×C3×D3—24no—
80C2×C3×D3—24no—
81C32×C4—21no—
82C32×C4#4112yes—
83C3⋊Dic3—22no—
84C3⋊Dic3—22no—
85C3×Dic3—24no—
86#127—91no—
87#125—91no—
88#123—94no—
89#121—32no—
90#121—94no—
91C4×D4—92no—
92#117—91no—
93C23×C3—21no—
94C23×C3—34no—
95C23×C3C22×D312yes—
96C22×D3C22×D314yes—
97C3×D4—64no—
98C3×D4—124no—
99C2×C3×C4—24no—
100C2×C3×C4—24no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—34no—
104C2×C3×C4C22×D312yes—
105C2×C3×C4C22×D312yes—
106#67—44no—
107#67—124no—
108#67—124no—
109C2×Dic3—32no—
110C2×Dic3—32no—
111C2×Dic3—32no—
112C2×Dic3—32no—
113C2×Dic3—62no—
114C2×Dic3—62no—
115C2×Dic3—124no—
116C2×Dic3C22×D314yes—
117D12—24no—
118C4×D3—124no—
119C2×C32—41no—
120C2×C32C2×#4111yescharacteristic
121C2×C32H(5,𝔽2)12yes—
122C3×D3—44no—
123C2×D4—34no—
124C2×D4—32no—
125C2×D4—94no—
126C22×C4—94no—
127C22×C4D3211yescharacteristic
128C4⋊C4—32no—
129C4⋊C4—94no—
130C4⋊C4—92no—
131C22⋊C4—34no—
132C22⋊C4—94no—
133C22⋊C4—92no—
134C42—91no—
135C42—91no—
136C22×C3—22no—
137C22×C3—22no—
138C22×C3—22no—
139C22×C3—22no—
140C22×C3—21no—
141C22×C3—42no—
142C22×C3—64no—
143C22×C3—64no—
144C22×C3—64no—
145C22×C3C23×D312yes—
146C2×D3—24no—
147C2×D3—24no—
148C2×D3—24no—
149C3×C4—22no—
150C3×C4—22no—
151C3×C4—22no—
152C3×C4—64no—
153C3×C4#23714yes—
154Dic3—24no—
155Dic3—62no—
156Dic3—62no—
157Dic3—62no—
158Dic3—62no—
159Dic3—122no—
160Dic3—122no—
161C32#54011yescharacteristic, complemented, Sylow
162C23—34no—
163C23C2×D3211yescharacteristic
164D4—64no—
165D4—124no—
166D4—364no—
167C2×C4—22no—
168C2×C4—34no—
169C2×C4—92no—
170C2×C4—92no—
171C2×C4—364no—
172C2×C4C2×D3211yescharacteristic
173C2×C4C2×D3211yescharacteristic
174C2×C3—22no—
175C2×C3—21no—
176C2×C3—42no—
177C2×C3—42no—
178C2×C3—124no—
179C2×C3C2×#23712yes—
180C2×C3#100412yes—
181C2×C3#100912yes—
182D3—44no—
183C22—22no—
184C22—21no—
185C22—64no—
186C22—64no—
187C22—64no—
188C22C22×D3211yescharacteristic
189C4—21no—
190C4—64no—
191C4—182no—
192C4—182no—
193C4#380512yes—
194C3—21no—
195C3#561912yescomplemented
196C2—41no—
197C2—124no—
198C2#6430712yes—
199C2C2×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #64135C2semidirect
2. C3×#930C2semidirect
3. #63970C2semidirect
4. #63914C2semidirect
5. #63898C2semidirect
6. #63891C2semidirect
7. #63872C2semidirect
27. #930D3semidirect
161. C32#540semidirect
195. C3#5619semidirect

Maximal subgroups

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

subgroupindex
#641352
C3×#9302
#639702
#639142
#638982
#638912
#638722
#56193