Finite Group Databasebeta

← #10596299

Subgroups — #10596299

Order 576.

990 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 235 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
1C2×C32×#41C211yesmaximal, characteristic, complemented
2C22×C4×C3⋊D3C211yesmaximal, characteristic, complemented
3#64155C212yesmaximal, complemented
4#64147C212yesmaximal, complemented
5#64146C212yesmaximal, complemented
6#64144C212yesmaximal, complemented
7C4×#638C214yesmaximal, complemented
8#64135C211yesmaximal, characteristic, complemented
9#5828—34nomaximal
10C23×C3⋊D3C2211yescharacteristic
11C32×#41—24no—
12C2×C32×Q8C2211yescharacteristic, complemented
13C2×C32×D4C2212yes—
14C2×C32×D4C2211yescharacteristic, complemented
15C22×C32×C4C2211yescharacteristic
16C22×C32×C4C2212yescomplemented
17C2×#638C2214yes—
18C22×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊D3—24no—
20C2×C4×C3⋊D3C2212yes—
21C2×C4×C3⋊D3C2212yes—
22#3757C2212yes—
23#3757C2214yescomplemented
24#3752C2214yes—
25C4⋊(C3⋊Dic3)C2212yescomplemented
26#3750C2214yescomplemented
27C4×C3⋊Dic3C2212yescomplemented
28C2×C3×#41D314yescomplemented
29C22×C4×D3—34no—
30#946—38no—
31#938—38no—
32#937—38no—
33#935—38no—
34C4×#67—316no—
35#926—34no—
36C23×C32C2312yes—
37C23×C32C2311yescharacteristic
38C22×C3⋊D3—22no—
39C22×C3⋊D3—24no—
40C22×C3⋊D3C2312yes—
41C32×Q8—22no—
42C32×D4—24no—
43C32×D4—22no—
44C2×C32×C4—24no—
45C2×C32×C4D414yescomplemented
46C2×C32×C4C2312yes—
47C2×C32×C4C2311yescharacteristic
48C2×C32×C4C2311yescharacteristic
49#638—28no—
50C2×C3⋊Dic3—22no—
51C2×C3⋊Dic3C2314yes—
52C2×C3⋊Dic3C2312yes—
53C4×C3⋊D3—24no—
54C4×C3⋊D3—24no—
55#525—91noSylow
56C23×D3—34no—
57C3×#41—216no—
58C2×C3×Q8C2×D314yescomplemented
59C2×C3×D4C2×D318yes—
60C2×C3×D4C2×D314yescomplemented
61C22×C3×C4C2×D314yes—
62C22×C3×C4C2×D318yescomplemented
63C2×#67—316no—
64C22×Dic3—34no—
65C2×C4×D3—38no—
66C2×C4×D3—38no—
67C2×C4×D3—616no—
68#217—38no—
69#217—316no—
70(C2×D3)⋊C4—316no—
71C4⋊Dic3—38no—
72Dic3⋊C4—316no—
73C4×Dic3—38no—
74C22×C32—22no—
75C22×C32—22no—
76C22×C32—24no—
77C22×C32C2×D412yes—
78C22×C32C2411yescharacteristic
79C2×C3⋊D3—28no—
80C2×C3⋊D3—22no—
81C2×C3⋊D3—22no—
82C2×C3⋊D3#4114yescomplemented
83C32×C4—22no—
84C32×C4C2×D412yes—
85C32×C4C2×D412yes—
86C3⋊Dic3—22no—
87C3⋊Dic3—24no—
88C2×#41C3⋊D311yescharacteristic, complemented
89C23×C4—91no—
90#123—92no—
91C22⋊Q8—92no—
92#121—92no—
93#120—92no—
94C4×D4—94no—
95#117—91no—
96C23×C3C22×D318yes—
97C23×C3C22×D314yes—
98C22×D3—38no—
99C22×D3—616no—
100C22×D3—68no—
101C3×Q8—28no—
102C3×D4—216no—
103C3×D4—28no—
104C2×C3×C4—216no—
105C2×C3×C4#67116yescomplemented
106C2×C3×C4C22×D318yes—
107C2×C3×C4C22×D314yes—
108C2×C3×C4C22×D314yes—
109#67—632no—
110C2×Dic3—316no—
111C2×Dic3—38no—
112C2×Dic3—68no—
113C4×D3—616no—
114C4×D3—616no—
115C2×C32—22no—
116C2×C32—42no—
117C2×C32C22×D411yescharacteristic
118C2×C32C2×#4112yes—
119C3⋊D3—24no—
120C24—91no—
121#41—24no—
122C2×Q8C2×C3⋊D311yescharacteristic, complemented
123C2×D4—94no—
124C2×D4C2×C3⋊D312yes—
125C2×D4C2×C3⋊D311yescharacteristic, complemented
126C22×C4—91no—
127C22×C4—92no—
128C22×C4—92no—
129C22×C4—184no—
130C22×C4C2×C3⋊D311yescharacteristic
131C22×C4C2×C3⋊D312yescomplemented
132C4⋊C4—92no—
133C4⋊C4—94no—
134C22⋊C4—92no—
135C22⋊C4—94no—
136C22⋊C4—94no—
137C42—92no—
138C22×C3—28no—
139C22×C3—216no—
140C22×C3—28no—
141C22×C3C2×#6718yes—
142C22×C3C23×D314yes—
143C2×D3—316no—
144C2×D3—632no—
145C2×D3—68no—
146C2×D3—68no—
147C3×C4—28no—
148C3×C4C2×#6718yes—
149C3×C4C2×#6718yes—
150Dic3—616no—
151Dic3—68no—
152C32#52511yescharacteristic, complemented, Sylow
153C23—92no—
154C23—184no—
155C23—182no—
156C23C22×C3⋊D312yes—
157C23C22×C3⋊D311yescharacteristic
158Q8—22no—
159D4—24no—
160D4—22no—
161D4—188no—
162C2×C4—24no—
163C2×C4—94no—
164C2×C4—92no—
165C2×C4—182no—
166C2×C4—184no—
167C2×C4—184no—
168C2×C4#63814yescomplemented
169C2×C4C22×C3⋊D312yes—
170C2×C4C22×C3⋊D311yescharacteristic
171C2×C4C22×C3⋊D311yescharacteristic
172C2×C3—28no—
173C2×C3—48no—
174C2×C3D3×#4118yes—
175C2×C3C22×#6714yes—
176D3—616no—
177C22—22no—
178C22—24no—
179C22—22no—
180C22—94no—
181C22—188no—
182C22—182no—
183C22—182no—
184C22C2×#63812yes—
185C22C23×C3⋊D311yescharacteristic
186C4—22no—
187C4—184no—
188C4—182no—
189C4C2×#63812yes—
190C4C2×#63812yes—
191C3#582814yescomplemented
192C2—22no—
193C2—42no—
194C2—184no—
195C2#41×C3⋊D312yes—
196C2C22×#63811yescharacteristic
subgroupG/H
centerC2×C4C22×C3⋊D3
commutator, socle, cosocleC22×C32C24
FrattiniC22C23×C3⋊D3
FittingC2×C32×#41C2
hypercenterC2×#41C3⋊D3
hypocenterC32#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C32×#41C2semidirect
2. C22×C4×C3⋊D3C2semidirect
3. #64155C2semidirect
4. #64147C2semidirect
5. #64146C2semidirect
6. #64144C2semidirect
7. C4×#638C2semidirect
8. #64135C2semidirect
12. C2×C32×Q8C22semidirect
14. C2×C32×D4C22semidirect
16. C22×C32×C4C22semidirect
23. #3757C22semidirect
25. C4⋊(C3⋊Dic3)C22semidirect
26. #3750C22semidirect
27. C4×C3⋊Dic3C22semidirect
28. C2×C3×#41D3semidirect
45. C2×C32×C4D4semidirect
58. C2×C3×Q8C2×D3semidirect
60. C2×C3×D4C2×D3semidirect
62. C22×C3×C4C2×D3semidirect
82. C2×C3⋊D3#41semidirect
88. C2×#41C3⋊D3semidirect
105. C2×C3×C4#67semidirect
122. C2×Q8C2×C3⋊D3semidirect
125. C2×D4C2×C3⋊D3semidirect
131. C22×C4C2×C3⋊D3semidirect
152. C32#525semidirect
168. C2×C4#638semidirect
191. C3#5828semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#412
C22×C4×C3⋊D32
#641552
#641472
#641462
#641442
C4×#6382
#641352
#58283