Finite Group Databasebeta

← #11783600

Subgroups — #11783600

Order 1152.

1008 conjugacy classes of subgroups; only the 309 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 309 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
2C2×C32×C4×C8C211yesmaximal, characteristic, complemented
3C2×#63647C212yesmaximal
4C2×#63630C211yesmaximal, characteristic, complemented
5#10589416C212yesmaximal, complemented
6#69753—34nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C32×C8C2212yes—
9C2×C32×C42C2211yescharacteristic
10C2×#3752C412yes—
11C2×#3750C412yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2212yes—
14#64081—22no—
15#64081—22no—
16C32×C4×C8—22no—
17#63647C418yescomplemented
18#63630—22no—
19C2×#872—34no—
20C2×C3×C4×C8D314yescomplemented
21C2×(C2×D3)⋊C8—38no—
22C2×#803—34no—
23#4550—38no—
24C23×C3⋊D3C2×C411yescharacteristic
25C22×C32×C4C2×C412yes—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3C2×C414yes—
33C2×C32×C8—22no—
34C2×C32×C8—22no—
35C2×C32×C8C2×C414yes—
36C32×C42D412yes—
37C32×C42D412yes—
38#3752—24no—
39#3750—24no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3—21no—
42C2×C3⋊(C3⋊C8)—22no—
43C2×C3⋊(C3⋊C8)—22no—
44C2×C3⋊(C3⋊C8)C2×C414yes—
45#1750—91noSylow
46C22×C4×D3—34no—
47C22×C3×C8C2×D318yes—
48C2×C3×C42C2×D314yes—
49C2×(C2×D3)⋊C4—38no—
50C2×Dic3⋊C4—38no—
51C2×C4×Dic3—34no—
52C22×C3⋊C8—38no—
53#872—68no—
54#872—68no—
55C3×C4×C8—28no—
56(C2×D3)⋊C8—332no—
57#803—68no—
58C23×C32C22×C411yescharacteristic
59C22×C3⋊D3—21no—
60C22×C3⋊D3—21no—
61C22×C3⋊D3—24no—
62C22×C3⋊D3C4212yes—
63C2×C32×C4—24no—
64C2×C32×C4C22⋊C414yes—
65C2×C32×C4C22×C412yes—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4#4112yes—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—24no—
73C2×C3⋊Dic3C4212yes—
74C4×C3⋊D3—24no—
75C4×C3⋊D3—24no—
76C32×C8—24no—
77C3⋊(C3⋊C8)—24no—
78C2×#117—91no—
79C2×C22⋊C8—92no—
80C2×#97—91no—
81C2×C4×C8C3⋊D311yescharacteristic, complemented
82#336—92no—
83C23×D3—34no—
84C22×C3×C4C4×D318yes—
85C22×C3×C4C22×D314yes—
86C22×Dic3—34no—
87C22×Dic3—38no—
88C2×C4×D3—316no—
89C2×C4×D3—64no—
90C2×C4×D3—68no—
91C2×C4×D3—64no—
92C2×C3×C8—28no—
93C2×C3×C8—28no—
94C2×C3×C8C4×D3116yes—
95C3×C42D1218yes—
96C3×C42#6718yes—
97(C2×D3)⋊C4—616no—
98Dic3⋊C4—616no—
99C4×Dic3—64no—
100C4×Dic3—64no—
101C2×C3⋊C8—316no—
102C2×C3⋊C8—68no—
103C2×C3⋊C8—68no—
104C22×C32C2×C4211yescharacteristic
105C22×C32C2×C22⋊C411yescharacteristic
106C22×C32#11711yescharacteristic
107C22×C32#13114yes—
108C2×C3⋊D3—22no—
109C2×C3⋊D3—24no—
110C2×C3⋊D3—42no—
111C2×C3⋊D3—42no—
112C32×C4—24no—
113C32×C4C4×D412yes—
114C32×C4C4×D412yes—
115C3⋊Dic3—22no—
116C3⋊Dic3—42no—
117C23×C4—91no—
118C22×C8—92no—
119C22×C8C2×C3⋊D312yes—
120#117—182no—
121#117—182no—
122C2×C4⋊C4—92no—
123C2×C22⋊C4—92no—
124C2×C42—91no—
125C2×C42C2×C3⋊D311yescharacteristic
126C22⋊C8—98no—
127#97—182no—
128C4×C8—22no—
129C23×C3C2×C4×D314yes—
130C22×D3—38no—
131C22×D3—64no—
132C22×D3—616no—
133C22×D3—64no—
134C2×C3×C4—216no—
135C2×C3×C4(C2×D3)⋊C4116yes—
136C2×C3×C4C2×C4×D318yes—
137C2×C3×C4C2×D1214yes—
138C2×C3×C4#23518yes—
139C2×C3×C4C2×#6714yes—
140C2×Dic3—38no—
141C2×Dic3—64no—
142C2×Dic3—64no—
143C2×Dic3—616no—
144C2×Dic3—68no—
145C4×D3—616no—
146C4×D3—616no—
147C3×C8—216no—
148C3⋊C8—616no—
149C2×C32C4×C22⋊C411yescharacteristic
150C2×C32#40512yes—
151C2×C32#40812yes—
152C2×C32#43312yes—
153C3⋊D3—42no—
154C24—91no—
155C22×C4—91no—
156C22×C4—94no—
157C22×C4—92no—
158C22×C4—181no—
159C22×C4—182no—
160C22×C4—181no—
161C22×C4C4×C3⋊D312yes—
162C22×C4C22×C3⋊D311yescharacteristic
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—94no—
166C2×C8—182no—
167C2×C8—182no—
168C2×C8C4×C3⋊D314yes—
169C4⋊C4—184no—
170C22⋊C4—184no—
171C42—181no—
172C42—181no—
173C42C4⋊(C3⋊D3)12yes—
174C42#63812yes—
175C22×C3C42×D314yes—
176C22×C3#87214yes—
177C22×C3#901116yes—
178C22×C3C2×(C2×D3)⋊C414yes—
179C2×D3—68no—
180C2×D3—616no—
181C2×D3—128no—
182C2×D3—128no—
183C3×C4—216no—
184C3×C4C4×D1218yes—
185C3×C4C4×#6718yes—
186Dic3—68no—
187Dic3—128no—
188C32#175011yescharacteristic, complemented, Sylow
189C23—92no—
190C23—181no—
191C23—184no—
192C23—181no—
193C23C2×C4×C3⋊D311yescharacteristic
194C2×C4—24no—
195C2×C4—92no—
196C2×C4—181no—
197C2×C4—181no—
198C2×C4—184no—
199C2×C4—184no—
200C2×C4—184no—
201C2×C4—182no—
202C2×C4#375214yes—
203C2×C4C2×C4×C3⋊D312yes—
204C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
205C2×C4#382812yes—
206C2×C4C2×#63811yescharacteristic
207C8—24no—
208C8—184no—
209C2×C3#468918yes—
210C2×C3#469018yes—
211C2×C3C4×(C2×D3)⋊C414yes—
212C2×C3#511018yes—
213D3—128no—
214C22—182no—
215C22—184no—
216C22—362no—
217C22—362no—
218C22C42×C3⋊D311yescharacteristic
219C22#6408111yescharacteristic
220C22#6411014yes—
221C22C2×#375211yescharacteristic
222C4—24no—
223C4—182no—
224C4—362no—
225C4C4×C4⋊(C3⋊D3)12yes—
226C4C4×#63812yes—
227C3#6975314yescomplemented
228C2—362no—
229C2#1059238812yes—
230C2#1059238912yes—
231C2C4×#375211yescharacteristic
232C2#1059280912yes—
subgroupG/H
center, FrattiniC22×C4C22×C3⋊D3
commutatorC22×C32C2×C42
FittingC2×C32×C4×C8C2
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4×C8C3⋊D3
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4×C8C2semidirect
4. C2×#63630C2semidirect
5. #10589416C2semidirect
17. #63647C4semidirect
20. C2×C3×C4×C8D3semidirect
81. C2×C4×C8C3⋊D3semidirect
188. C32#1750semidirect
227. C3#69753semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C32×C4×C82
C2×#636472
C2×#636302
#105894162
#697533