Finite Group Databasebeta

← #11858534

Subgroups — #11858534

Order 1152.

1428 conjugacy classes of subgroups.

The subgroup lattice has 231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#520C211yesmaximal, characteristic
2#10596298C211yesmaximal, characteristic
3C2×#64157C211yesmaximal, characteristic
4#10592697C213yesmaximal, complemented
5#10592694C213yesmaximal, complemented
6#10592663C213yesmaximal, complemented
7C2×#63635C213yesmaximal, complemented
8#82561—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C32×C4×Q8—21no—
11C32×C4×D4—23no—
12C32×#117C2213yes—
13C2×C32×C4⋊C4C2213yes—
14#64157C418yescomplemented
15Q8×C3⋊Dic3—21no—
16D4×C3⋊Dic3—23no—
17#64135C2213yes—
18C2×C4⋊(C3⋊Dic3)C2213yes—
19C2×#3748C2213yes—
20C22×C3⋊(C3⋊C8)C2213yes—
21#63635C2213yes—
22#63635C2216yes—
23#63635C2211yescharacteristic
24#63634C2213yes—
25#63634C2213yes—
26C3×#520D314yes—
27#5827—34no—
28C2×#948—34no—
29#4998—312no—
30#4995—312no—
31#4964—312no—
32C2×#808—312no—
33C32×#41C2×C414yes—
34C32×#41Q814yes—
35C2×C32×Q8D411yescharacteristic
36C2×C32×D4D413yes—
37C22×C32×C4—23no—
38C22×C32×C4C2313yes—
39C22×C3⋊Dic3—23no—
40C32×C4⋊C4—23no—
41C32×C4⋊C4C2311yescharacteristic
42C32×C4⋊C4C2313yes—
43C32×C22⋊C4—23no—
44C32×C42—23no—
45#3757—23no—
46C4⋊(C3⋊Dic3)—23no—
47C4⋊(C3⋊Dic3)C2313yes—
48C4⋊(C3⋊Dic3)C2311yescharacteristic
49C4×C3⋊Dic3—23no—
50#3748C2×C4112yescomplemented
51C2×C3⋊(C3⋊C8)C2×C4112yescomplemented
52C2×C3⋊(C3⋊C8)C2311yescharacteristic
53C2×C3⋊(C3⋊C8)C2313yes—
54#2912—91noSylow
55C2×C3×#41C2×D314yes—
56C3×C4×Q8—24no—
57C3×C4×D4—212no—
58C3×#117C2×D3112yes—
59C2×C3×C4⋊C4C2×D3112yes—
60#948—332no—
61Q8×Dic3—64no—
62D4×Dic3—612no—
63#926—312no—
64C2×C4⋊Dic3—312no—
65C2×#208—312no—
66C22×C3⋊C8—312no—
67#808—312no—
68#808—324no—
69#808—34no—
70#807—312no—
71#807—312no—
72C23×C32C2×D413yes—
73C32×Q8C4⋊C414yes—
74C32×D4C4⋊C4112yes—
75C2×C32×C4—21no—
76C2×C32×C4—23no—
77C2×C32×C4—83no—
78C2×C32×C4C22×C416yes—
79C2×C32×C4C2×D413yes—
80C2×C32×C4C2×Q816yes—
81C2×C32×C4C2411yescharacteristic
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—23no—
84C2×C3⋊Dic3—83no—
85C3⋊(C3⋊C8)C22×C412yes—
86C3⋊(C3⋊C8)C22×C416yes—
87C2×#131—91no—
88#520—91no—
89#520C3⋊D311yescharacteristic
90#428—93no—
91#428—93no—
92#427—93no—
93C2×#106—93no—
94C3×#41Dic6116yes—
95C3×#41C4×D3116yes—
96C2×C3×Q8#6714yes—
97C2×C3×D4#67112yes—
98C22×C3×C4—212no—
99C22×C3×C4C22×D3112yes—
100C22×Dic3—612no—
101C3×C4⋊C4—212no—
102C3×C4⋊C4C22×D314yes—
103C3×C4⋊C4C22×D3112yes—
104C3×C22⋊C4—212no—
105C3×C42—212no—
106#217—612no—
107C4⋊Dic3—34no—
108C4⋊Dic3—312no—
109C4⋊Dic3—612no—
110C4×Dic3—612no—
111#208—348no—
112C2×C3⋊C8—348no—
113C2×C3⋊C8—312no—
114C2×C3⋊C8—34no—
115C22×C32—23no—
116C22×C32—23no—
117C22×C32C2×C4⋊C416yes—
118C22×C32C22×D411yescharacteristic
119C32×C4—41no—
120C32×C4—43no—
121C32×C4C2×C4⋊C416yes—
122C32×C4C23×C411yescharacteristic
123C32×C4C22×Q811yescharacteristic
124C3⋊Dic3—41no—
125C3⋊Dic3—43no—
126C2×#41C2×C3⋊D311yescharacteristic
127#131—98no—
128C2×M16—93no—
129C22×C8—93no—
130C4×Q8—21no—
131C4×Q8—181no—
132C4×D4—23no—
133C4×D4—183no—
134#117—93no—
135#117C2×C3⋊D313yes—
136C2×C4⋊C4—93no—
137C2×C4⋊C4C2×C3⋊D313yes—
138#107—93no—
139#107—93no—
140#106—93no—
141#106—96no—
142#106—91no—
143C23×C3C2×#67112yes—
144C3×Q8Dic3⋊C4116yes—
145C3×D4Dic3⋊C4148yes—
146C2×C3×C4—24no—
147C2×C3×C4—212no—
148C2×C3×C4—812no—
149C2×C3×C4C2×Dic6124yes—
150C2×C3×C4C2×C4×D3124yes—
151C2×C3×C4C2×#67112yes—
152C2×C3×C4C23×D314yes—
153C2×Dic3—64no—
154C2×Dic3—612no—
155C2×Dic3—2412no—
156C3⋊C8—38no—
157C3⋊C8—324no—
158C2×C32—26no—
159C2×C32C22×C4⋊C411yescharacteristic
160C2×C32#57711yescharacteristic
161C2×C32#57711yescharacteristic
162#41#63414yes—
163#41C4×C3⋊D314yes—
164C2×Q8#63811yescharacteristic
165C2×D4#63813yes—
166C22×C4—23no—
167C22×C4—183no—
168C22×C4C22×C3⋊D313yes—
169M16—912no—
170C2×C8—91no—
171C2×C8—93no—
172C2×C8—912no—
173C4⋊C4—23no—
174C4⋊C4—93no—
175C4⋊C4—91no—
176C4⋊C4—183no—
177C4⋊C4C22×C3⋊D313yes—
178C4⋊C4C22×C3⋊D311yescharacteristic
179C22⋊C4—23no—
180C22⋊C4—183no—
181C42—23no—
182C42—183no—
183C22×C3—212no—
184C22×C3—212no—
185C22×C3C2×Dic3⋊C4124yes—
186C22×C3C22×#6714yes—
187C3×C4—412no—
188C3×C4—44no—
189C3×C4C2×Dic3⋊C4124yes—
190C3×C4C22×Dic614yes—
191C3×C4C22×C4×D314yes—
192Dic3—124no—
193Dic3—1212no—
194C32#291211yescharacteristic, complemented, Sylow
195C23C2×#63813yes—
196Q8#375014yes—
197D4#3750112yes—
198C2×C4—21no—
199C2×C4—23no—
200C2×C4—83no—
201C2×C4—181no—
202C2×C4—183no—
203C2×C4—723no—
204C2×C4C2×#63416yes—
205C2×C4C2×C4×C3⋊D316yes—
206C2×C4C2×#63813yes—
207C2×C4C23×C3⋊D311yescharacteristic
208C8—92no—
209C8—96no—
210C2×C3—224no—
211C2×C3C22×Dic3⋊C414yes—
212C2×C3#583614yes—
213C2×C3#583714yes—
214C22—23no—
215C22—23no—
216C22C2×#375016yes—
217C22C22×#63811yescharacteristic
218C4—43no—
219C4—41no—
220C4—361no—
221C4—363no—
222C4C2×#375016yes—
223C4C22×#63411yescharacteristic
224C4C22×C4×C3⋊D311yescharacteristic
225C3#8256114yescomplemented
226C2—26no—
227C2C22×#375011yescharacteristic
228C2#1059630711yescharacteristic
229C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#520C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
cosocleC2×C32×C4C24
hypercenter#520C3⋊D3
hypocenterC32#2912
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
4. #10592697C2semidirect
5. #10592694C2semidirect
6. #10592663C2semidirect
7. C2×#63635C2semidirect
14. #64157C4semidirect
50. #3748C2×C4semidirect
51. C2×C3⋊(C3⋊C8)C2×C4semidirect
194. C32#2912semidirect
225. C3#82561semidirect

Maximal subgroups

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

subgroupindex
C32×#5202
#105962982
C2×#641572
#105926972
#105926942
#105926632
C2×#636352
#825613