Finite Group Databasebeta

← #11801921

Subgroups — #11801921

Order 1152.

1572 conjugacy classes of subgroups; only the 393 normal subgroups are shown.

normal subgroups only

This group has 1572 conjugacy classes of subgroups — too many to draw. Only its 393 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×#64081C211yesmaximal, characteristic
2C32×#376C211yesmaximal, characteristic, complemented
3C4×#3752C212yesmaximal
4C4×#3750C212yesmaximal, complemented
5C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592368C214yesmaximal
7#10592351C214yesmaximal, complemented
8#73385—34nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C42C2212yes—
11C2×C32×C42C2211yescharacteristic
12C2×#3752C2214yes—
13C2×#3752C2212yes—
14C2×#3750C2214yes—
15C2×#3750C2212yes—
16C2×C4×C3⋊Dic3C2214yes—
17C2×C4×C3⋊Dic3C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64081C418yescomplemented
20C32×#95C2214yes—
21#63658C2214yes—
22#63658C2214yes—
23C2×#872—34no—
24C3×#376D314yescomplemented
25C4×(C2×D3)⋊C4—38no—
26C4×Dic3⋊C4—38no—
27C42×Dic3—34no—
28#4669—316no—
29#4652—316no—
30C23×C3⋊D3C2311yescharacteristic
31C22×C32×C4C2314yes—
32C22×C32×C4C2312yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3⋊Dic3C2312yes—
36C22×C3⋊Dic3C2314yes—
37C2×C4×C3⋊D3—24no—
38C2×C4×C3⋊D3C2×C414yes—
39C32×C42—24no—
40C32×C42C2×C414yes—
41#3752—28no—
42#3752C2×C418yes—
43#3750—28no—
44#3750C2×C418yes—
45C4×C3⋊Dic3—24no—
46C4×C3⋊Dic3—28no—
47C4×C3⋊Dic3C2×C414yes—
48#2298—91noSylow
49C22×C4×D3—34no—
50C2×C3×C42C2×D318yes—
51C2×C3×C42C2×D314yes—
52C2×(C2×D3)⋊C4—38no—
53C2×(C2×D3)⋊C4—316no—
54C2×Dic3⋊C4—38no—
55C2×Dic3⋊C4—316no—
56C2×C4×Dic3—34no—
57C2×C4×Dic3—316no—
58C2×C4×Dic3—38no—
59#872—332no—
60C3×#95C2×D3116yes—
61C3⋊#95—316no—
62C3⋊#95—316no—
63C23×C32C2411yescharacteristic
64C22×C3⋊D3—24no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3C22×C412yes—
67C2×C32×C4—24no—
68C2×C32×C4—24no—
69C2×C32×C4—24no—
70C2×C32×C4—24no—
71C2×C32×C4C22×C414yes—
72C2×C32×C4C22×C412yes—
73C2×C32×C4#4114yes—
74C2×C3⋊Dic3—24no—
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3—24no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3C22×C414yes—
79C2×C3⋊Dic3C22×C412yes—
80C2×C3⋊Dic3#4118yes—
81C4×C3⋊D3—28no—
82C2×#117—91no—
83#388—94no—
84#387—94no—
85C4×C4⋊C4—92no—
86C4×C22⋊C4—92no—
87#376C3⋊D311yescharacteristic, complemented
88C43—91no—
89C23×D3—34no—
90C22×C3×C4C22×D3116yes—
91C22×C3×C4C22×D318yes—
92C22×C3×C4C22×D314yes—
93C22×Dic3—34no—
94C22×Dic3—316no—
95C22×Dic3—38no—
96C2×C4×D3—316no—
97C2×C4×D3—616no—
98C3×C42—216no—
99C3×C42C4×D3116yes—
100(C2×D3)⋊C4—332no—
101(C2×D3)⋊C4—632no—
102Dic3⋊C4—332no—
103Dic3⋊C4—632no—
104C4×Dic3—316no—
105C4×Dic3—632no—
106C4×Dic3—616no—
107C22×C32C23×C411yescharacteristic
108C22×C32C2×#4112yes—
109C22×C32C2×#4114yes—
110C2×C3⋊D3—22no—
111C2×C3⋊D3—24no—
112C2×C3⋊D3—44no—
113C32×C4—24no—
114C32×C4—44no—
115C32×C4#11714yes—
116C3⋊Dic3—22no—
117C3⋊Dic3—24no—
118C3⋊Dic3—28no—
119C23×C4—91no—
120#117—98no—
121C2×C4⋊C4—92no—
122C2×C4⋊C4—94no—
123C2×C22⋊C4—92no—
124C2×C22⋊C4—94no—
125C2×C42—91no—
126C2×C42—94no—
127C2×C42—92no—
128C2×C42C2×C3⋊D312yes—
129C2×C42C2×C3⋊D311yescharacteristic
130#95—94no—
131#95—94no—
132#95C2×C3⋊D314yes—
133C23×C3C23×D314yes—
134C22×D3—38no—
135C22×D3—68no—
136C22×D3—616no—
137C2×C3×C4—216no—
138C2×C3×C4—216no—
139C2×C3×C4—216no—
140C2×C3×C4—216no—
141C2×C3×C4C2×C4×D3116yes—
142C2×C3×C4C2×C4×D318yes—
143C2×C3×C4#235116yes—
144C2×Dic3—316no—
145C2×Dic3—38no—
146C2×Dic3—332no—
147C2×Dic3—616no—
148C2×Dic3—68no—
149C2×Dic3—616no—
150C2×Dic3—616no—
151C4×D3—632no—
152C2×C32C2×#11711yescharacteristic
153C2×C32C4×#4112yes—
154C2×C32#52914yes—
155C3⋊D3—42no—
156C24—91no—
157C22×C4—91no—
158C22×C4—94no—
159C22×C4—92no—
160C22×C4—94no—
161C22×C4—184no—
162C22×C4C22×C3⋊D314yes—
163C22×C4C22×C3⋊D312yes—
164C22×C4C22×C3⋊D311yescharacteristic
165C4⋊C4—98no—
166C4⋊C4—188no—
167C22⋊C4—98no—
168C22⋊C4—188no—
169C42—24no—
170C42—94no—
171C42—188no—
172C42—184no—
173C42C4×C3⋊D314yes—
174C22×C3C22×C4×D314yes—
175C22×C3C2×#23518yes—
176C22×C3D3×#41116yes—
177C2×D3—68no—
178C2×D3—616no—
179C2×D3—1216no—
180C3×C4—216no—
181C3×C4—416no—
182C3×C4#872116yes—
183Dic3—68no—
184Dic3—616no—
185Dic3—632no—
186C32#229811yescharacteristic, complemented, Sylow
187C23—92no—
188C23—182no—
189C23—184no—
190C23C23×C3⋊D311yescharacteristic
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—24no—
194C2×C4—24no—
195C2×C4—94no—
196C2×C4—92no—
197C2×C4—98no—
198C2×C4—184no—
199C2×C4—182no—
200C2×C4—184no—
201C2×C4—184no—
202C2×C4—188no—
203C2×C4C2×C4×C3⋊D314yes—
204C2×C4C2×C4×C3⋊D312yes—
205C2×C4#382814yes—
206C2×C3C2×#87214yes—
207C2×C3#552218yes—
208C2×C3#5528116yes—
209D3—128no—
210C22—182no—
211C22—184no—
212C22—364no—
213C22C22×C4×C3⋊D311yescharacteristic
214C22C2×#382812yes—
215C22#41×C3⋊D314yes—
216C4—24no—
217C4—44no—
218C4—182no—
219C4—184no—
220C4—188no—
221C4#6408114yes—
222C3#7338514yescomplemented
223C2—362no—
224C2C2×#6408111yescharacteristic
225C2#1059599312yes—
226C2#1059599914yes—
subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC32×#376C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#376C3⋊D3
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C32×#376C2semidirect
4. C4×#3750C2semidirect
5. C42×C3⋊Dic3C2semidirect
7. #10592351C2semidirect
19. #64081C4semidirect
24. C3×#376D3semidirect
87. #376C3⋊D3semidirect
186. C32#2298semidirect
222. C3#73385semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C32×#3762
C4×#37522
C4×#37502
C42×C3⋊Dic32
#105923682
#105923512
#733853