Finite Group Databasebeta

← D4×#1113 #11724621

Subgroups — D4×#1113 #11724621

Order 864.

1122 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C22×#1113C212yesmaximal, complemented
2C3×D4×C3⋊D3C213yesmaximal, complemented
3#89049C216yesmaximal, complemented
4C4⋊#1113C213yesmaximal, complemented
5C4×#1113C211yesmaximal, characteristic, complemented
6D32×D4—33nomaximal
7C22×C3×C3⋊D3C2216yescomplemented
8C2×#1113—28no—
9C2×#1113C2211yescharacteristic
10C2×#1113C2216yescomplemented
11C33×D4C2211yescharacteristic, complemented
12C3×#638C2216yescomplemented
13C3×C4⋊(C3⋊D3)C2213yescomplemented
14C3×C4×C3⋊D3C2213yescomplemented
15#6295C2216yescomplemented
16#6294C2213yescomplemented
17C22×D32—36no—
18D4×C3⋊D3D313yescomplemented
19C3×D3×D4—36no—
20C3×D3×D4—63no—
21#3811—36no—
22D3×#67—312no—
23#3802—33no—
24D3×D12—36no—
25C4×D32—33no—
26C22×C33C2312yescomplemented
27C2×C3×C3⋊D3—212no—
28C2×C3×C3⋊D3C2313yes—
29C2×C3×C3⋊D3C2316yescomplemented
30#1113—212no—
31#1113D414yesdirect product factor
32C33×C4C2311yescharacteristic, complemented
33C3×C3⋊Dic3C2313yescomplemented
34C2×D3×D4—93no—
35C22×C3⋊D3C2×D316yescomplemented
36C22×C3×D3—312no—
37C22×C3×D3—66no—
38C2×D32—33no—
39C2×D32—36no—
40C2×D32—312no—
41C2×D32—624no—
42C32×D4—23no—
43C32×D4—41no—
44C32×D4C2×D313yescomplemented
45#638C2×D316yescomplemented
46C4⋊(C3⋊D3)C2×D313yescomplemented
47C4×C3⋊D3C2×D313yescomplemented
48C3×#67—312no—
49C3×#67—66no—
50C3×D12—36no—
51C3×D12—63no—
52C3×C4×D3—36no—
53C3×C4×D3—63no—
54#626—312no—
55#625—36no—
56#624—33no—
57D3×Dic3—36no—
58C2×C33—22no—
59C2×C33C2411yescharacteristic
60C3×C3⋊D3—26no—
61C3×C3⋊D3C2×D416yescomplemented
62C23×D3—96no—
63C2×C3×D4—93no—
64C2×#67—96no—
65D3×D4—36no—
66D3×D4—63no—
67D3×D4—96no—
68D3×D4—912no—
69C2×D12—93no—
70C2×C4×D3—93no—
71C22×C32—26no—
72C22×C32—42no—
73C22×C32C22×D316yescomplemented
74C2×C3⋊D3—212no—
75C2×C3⋊D3C22×D313yes—
76C2×C3⋊D3C22×D316yescomplemented
77C2×C3×D3—36no—
78C2×C3×D3—312no—
79C2×C3×D3—63no—
80C2×C3×D3—66no—
81C2×C3×D3—624no—
82C2×C3×D3—1212no—
83D32—312no—
84D32—624no—
85D32—612no—
86C32×C4—23no—
87C32×C4—41no—
88C32×C4C22×D313yescomplemented
89C3⋊Dic3C22×D313yescomplemented
90C3×Dic3—36no—
91C3×Dic3—63no—
92C22×D4—271noSylow
93C33C22×D411yescharacteristic, complemented, Sylow
94C23×C3—96no—
95C22×D3—312no—
96C22×D3—66no—
97C22×D3—93no—
98C22×D3—96no—
99C22×D3—912no—
100C22×D3—1824no—
101C3×D4—23no—
102C3×D4—41no—
103C3×D4—96no—
104C3×D4—93no—
105C3×D4D3213yescomplemented
106C2×C3×C4—93no—
107#67—312no—
108#67—66no—
109#67—912no—
110C2×Dic3—93no—
111D12—36no—
112D12—63no—
113D12—96no—
114C4×D3—36no—
115C4×D3—63no—
116C4×D3—96no—
117C2×C32—26no—
118C2×C32—23no—
119C2×C32—41no—
120C2×C32—46no—
121C2×C32—82no—
122C2×C32C23×D313yes—
123C3⋊D3—26no—
124C3⋊D3D3×D416yescomplemented
125C3×D3—312no—
126C3×D3—66no—
127C3×D3—612no—
128C3×D3—126no—
129C24—272no—
130C2×D4—93no—
131C2×D4—273no—
132C2×D4—276no—
133C22×C4—271no—
134C22×C3—26no—
135C22×C3—42no—
136C22×C3—93no—
137C22×C3—96no—
138C22×C3—1812no—
139C22×C3C2×D3216yescomplemented
140C2×D3—36no—
141C2×D3—312no—
142C2×D3—63no—
143C2×D3—66no—
144C2×D3—624no—
145C2×D3—912no—
146C2×D3—1212no—
147C2×D3—1824no—
148C2×D3—1812no—
149C3×C4—23no—
150C3×C4—41no—
151C3×C4—93no—
152C3×C4C2×D3213yescomplemented
153Dic3—36no—
154Dic3—63no—
155C32—23no—
156C32—41no—
157C32C2×D3×D413yescomplemented
158C23—96no—
159C23—271no—
160C23—276no—
161C23—548no—
162D4—96no—
163D4—93no—
164D4—276no—
165D4#111311yescharacteristic, direct product factor
166C2×C4—93no—
167C2×C4—273no—
168C2×C3—26no—
169C2×C3—23no—
170C2×C3—46no—
171C2×C3—41no—
172C2×C3—82no—
173C2×C3—96no—
174C2×C3—186no—
175C2×C3C22×D3213yes—
176D3—312no—
177D3—66no—
178D3—612no—
179D3—126no—
180C22—93no—
181C22—96no—
182C22—1812no—
183C22—274no—
184C22—5412no—
185C22C2×#111312yescomplemented
186C4—93no—
187C4C2×#111311yescharacteristic, complemented
188C3—23no—
189C3—41no—
190C3D32×D413yescomplemented
191C2—22no—
192C2—96no—
193C2—186no—
194C2C22×#111311yescharacteristic
subgroupG/H
center, FrattiniC2C22×#1113
commutator, socle, cosocleC2×C33C24
FittingC33×D4C22
hypercenterD4#1113
hypocenterC33C22×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×#1113C2semidirect
2. C3×D4×C3⋊D3C2semidirect
3. #89049C2semidirect
4. C4⋊#1113C2semidirect
5. C4×#1113C2semidirect
7. C22×C3×C3⋊D3C22semidirect
10. C2×#1113C22semidirect
11. C33×D4C22semidirect
12. C3×#638C22semidirect
13. C3×C4⋊(C3⋊D3)C22semidirect
14. C3×C4×C3⋊D3C22semidirect
15. #6295C22semidirect
16. #6294C22semidirect
18. D4×C3⋊D3D3semidirect
26. C22×C33C23semidirect
29. C2×C3×C3⋊D3C23semidirect
31. #1113D4direct (N × H)
32. C33×C4C23semidirect
33. C3×C3⋊Dic3C23semidirect
35. C22×C3⋊D3C2×D3semidirect
44. C32×D4C2×D3semidirect
45. #638C2×D3semidirect
46. C4⋊(C3⋊D3)C2×D3semidirect
47. C4×C3⋊D3C2×D3semidirect
61. C3×C3⋊D3C2×D4semidirect
73. C22×C32C22×D3semidirect
76. C2×C3⋊D3C22×D3semidirect
88. C32×C4C22×D3semidirect
89. C3⋊Dic3C22×D3semidirect
93. C33C22×D4semidirect
105. C3×D4D32semidirect
124. C3⋊D3D3×D4semidirect
139. C22×C3C2×D32semidirect
152. C3×C4C2×D32semidirect
157. C32C2×D3×D4semidirect
165. D4#1113direct (N × H)
185. C22C2×#1113semidirect
187. C4C2×#1113semidirect
190. C3D32×D4semidirect

Maximal subgroups

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

subgroupindex
C22×#11132
C3×D4×C3⋊D32
#890492
C4⋊#11132
C4×#11132
D32×D43