Finite Group Databasebeta

← #120×#90673 #28407037

Subgroups — #120×#90673 #28407037

Order 14464.

1224 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 210 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
1C24×#90673C211yesmaximal, characteristic, complemented
2C2×D4×#90673C213yesmaximal, complemented
3#20299546C213yesmaximal, complemented
4#20299545C213yesmaximal, complemented
5#20299539C211yesmaximal, characteristic, complemented
6C22⋊C4×#90673C213yesmaximal, complemented
7#120×D113C211yesmaximal, characteristic
8C23×#90673—212no—
9C23×#90673C2213yes—
10C23×#90673C2213yes—
11C23×#90673C2211yescharacteristic, complemented
12D4×#90673—212no—
13C2×C4⋊#90673C2213yescomplemented
14C2×C22⋊#90673C2213yes—
15C2×C22⋊#90673C2213yes—
16C2×C22⋊#90673C2213yescomplemented
17C2×C4×#90673C2213yescomplemented
18(C2×#90673)⋊C4C2216yescomplemented
19C24×D113C2211yescharacteristic
20C2×D4×D113C2213yes—
21#16813592C413yescomplemented
22#16813591C411yescharacteristic, complemented
23#16813590C413yescomplemented
24C22⋊C4×D113C2213yes—
25#120×C113C411yescharacteristic, complemented
26C22×#90673—232no—
27C22×#90673—26no—
28C22×#90673—212no—
29C22×#90673—212no—
30C22×#90673—26no—
31C22×#90673D4112yescomplemented
32C22×#90673C2313yes—
33C22×#90673C2311yescharacteristic
34C22×#90673C2313yes—
35C22×#90673C2311yescharacteristic
36C4⋊#90673—26no—
37C22⋊#90673—26no—
38C22⋊#90673—26no—
39C22⋊#90673—26no—
40C4×#90673—26no—
41C23×D113—26no—
42C23×D113—26no—
43C23×D113C2×C413yescomplemented
44C23×D113C2311yescharacteristic
45C23×D113C2313yes—
46C2×D452C2×C413yescomplemented
47C2×C22⋊D113C2×C413yescomplemented
48C2×C22⋊D113C2×C413yescomplemented
49D4×D113—26no—
50D4×D113—26no—
51C2×C4×D113C2313yes—
52C22⋊Dic113C2×C413yescomplemented
53#14268624C2×C416yescomplemented
54C24×C113C2×C411yescharacteristic, complemented
55C2×D4×C113C2×C413yescomplemented
56C22⋊C4×C113C2×C413yescomplemented
57C23×C113—26no—
58C23×C113C22×C413yes—
59C23×C113C22×C411yescharacteristic, complemented
60C22×D113—224no—
61C22×D113—28no—
62C22×D113—26no—
63C22×D113—212no—
64C22×D113—26no—
65C22×D113—26no—
66C22×D113—23no—
67C22×D113—23no—
68C22×D113C22×C413yes—
69C22×D113C22×C411yescharacteristic, complemented
70C22×D113C2×D416yes—
71C22×D113#4116yes—
72C22×D113C2411yescharacteristic
73C2×#90673—224no—
74C2×#90673—26no—
75C2×#90673—224no—
76C2×#90673—23no—
77C2×#90673—23no—
78C2×#90673—26no—
79C2×#90673—44no—
80C2×#90673C2×D416yes—
81C2×#90673C2×D416yes—
82D4×C113—26no—
83C2×C4×C113C22×C413yescomplemented
84C22⋊D113—26no—
85C22⋊D113—26no—
86C2×Dic113C22×C413yescomplemented
87D452—26no—
88C4×D113—23no—
89C4×D113—23no—
90C22×C113—28no—
91C22×C113—26no—
92C22×C113—23no—
93C22×C113C4×D416yescomplemented
94C22×C113C23×C411yescharacteristic
95C2×D113—224no—
96C2×D113—26no—
97C2×D113—26no—
98C2×D113—26no—
99C2×D113—212no—
100C2×D113—23no—
101C2×D113—41no—
102C2×D113—43no—
103C2×D113C4×D416yescomplemented
104C2×D113C22×D413yes—
105C2×D113C2×#4113yes—
106#90673—26no—
107#90673—41no—
108#90673—43no—
109#90673#12014yesdirect product factor
110C4×C113—23no—
111Dic113—23no—
112C2×C113—26no—
113C2×C113—41no—
114C2×C113C2×C4×D413yes—
115D113—26no—
116D113—41no—
117D113C2×#12011yescharacteristic
118D113#52513yes—
119C4×#120—1131nomaximal, Sylow
120C113C4×#12011yescharacteristic, complemented, Sylow
121C24×C4—1131no—
122C2×#120—1131no—
123C2×C4×D4—1133no—
124#386—1133no—
125#385—1133no—
126#379—1131no—
127C4×C22⋊C4—1133no—
128C25—1131no—
129C22×D4—1133no—
130C23×C4—1133no—
131C23×C4—1131no—
132C23×C4—1133no—
133C23×C4—22612no—
134#120—1131no—
135#120—1133no—
136#120—1133no—
137#120#9067311yescharacteristic, direct product factor
138C4×D4—22612no—
139C2×C4⋊C4—1133no—
140C2×C22⋊C4—1133no—
141C2×C22⋊C4—1133no—
142C2×C22⋊C4—1133no—
143C2×C22⋊C4—1133no—
144C2×C42—1133no—
145#95—1136no—
146C24—1133no—
147C24—1133no—
148C24—1131no—
149C24—2266no—
150C24—2266no—
151C24C2×#9067311yescharacteristic, complemented
152C2×D4—1133no—
153C2×D4—1133no—
154C2×D4—1133no—
155C2×D4—2266no—
156C2×D4—2266no—
157C2×D4C2×#9067313yescomplemented
158C22×C4—1131no—
159C22×C4—1133no—
160C22×C4—11312no—
161C22×C4—1133no—
162C22×C4—1133no—
163C22×C4—1131no—
164C22×C4—2266no—
165C22×C4—22612no—
166C22×C4—22612no—
167C22×C4—2266no—
168C22×C4—22632no—
169C4⋊C4—2266no—
170C22⋊C4—1133no—
171C22⋊C4—1136no—
172C22⋊C4—2266no—
173C22⋊C4—2266no—
174C22⋊C4—2266no—
175C22⋊C4C2×#9067313yescomplemented
176C42—2266no—
177C23—26no—
178C23—1131no—
179C23—1136no—
180C23—1136no—
181C23—1133no—
182C23—1131no—
183C23—2263no—
184C23—2263no—
185C23—2266no—
186C23—2266no—
187C23—22612no—
188C23—2268no—
189C23—22624no—
190C23—2266no—
191C23C22×#9067313yes—
192C23C22×#9067311yescharacteristic, complemented
193D4—26no—
194D4—2266no—
195D4—2266no—
196D4—2266no—
197C2×C4—1136no—
198C2×C4—1136no—
199C2×C4—1133no—
200C2×C4—4524no—
201C2×C4—2263no—
202C2×C4—2263no—
203C2×C4—22624no—
204C2×C4—2263no—
205C2×C4—2263no—
206C2×C4—2266no—
207C2×C4—2266no—
208C2×C4—22624no—
209C2×C4C22×#9067313yescomplemented
210C22—28no—
211C22—26no—
212C22—23no—
213C22—1133no—
214C22—1133no—
215C22—1136no—
216C22—4521no—
217C22—4523no—
218C22—2266no—
219C22—2266no—
220C22—22612no—
221C22—22624no—
222C22—2263no—
223C22—2266no—
224C22D4×#9067316yescomplemented
225C22C23×#9067311yescharacteristic
226C4—23no—
227C4—1134no—
228C4—4521no—
229C4—4523no—
230C4—2266no—
231C4—2263no—
232C2—26no—
233C2—41no—
234C2—1131no—
235C2—1133no—
236C2—4521no—
237C2—2266no—
238C2C2×D4×#9067313yes—
subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
Fitting#120×C113C4
prime radical#120×D113C2
cosocleC22×D113C24
hypercenter#120#90673
hypocenterC113C4×#120
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×#90673C2semidirect
2. C2×D4×#90673C2semidirect
3. #20299546C2semidirect
4. #20299545C2semidirect
5. #20299539C2semidirect
6. C22⋊C4×#90673C2semidirect
11. C23×#90673C22semidirect
13. C2×C4⋊#90673C22semidirect
16. C2×C22⋊#90673C22semidirect
17. C2×C4×#90673C22semidirect
18. (C2×#90673)⋊C4C22semidirect
21. #16813592C4semidirect
22. #16813591C4semidirect
23. #16813590C4semidirect
25. #120×C113C4semidirect
31. C22×#90673D4semidirect
43. C23×D113C2×C4semidirect
46. C2×D452C2×C4semidirect
47. C2×C22⋊D113C2×C4semidirect
48. C2×C22⋊D113C2×C4semidirect
52. C22⋊Dic113C2×C4semidirect
53. #14268624C2×C4semidirect
54. C24×C113C2×C4semidirect
55. C2×D4×C113C2×C4semidirect
56. C22⋊C4×C113C2×C4semidirect
59. C23×C113C22×C4semidirect
69. C22×D113C22×C4semidirect
83. C2×C4×C113C22×C4semidirect
86. C2×Dic113C22×C4semidirect
93. C22×C113C4×D4semidirect
103. C2×D113C4×D4semidirect
109. #90673#120direct (N × H)
120. C113C4×#120semidirect
137. #120#90673direct (N × H)
151. C24C2×#90673semidirect
157. C2×D4C2×#90673semidirect
175. C22⋊C4C2×#90673semidirect
192. C23C22×#90673semidirect
209. C2×C4C22×#90673semidirect
224. C22D4×#90673semidirect

Maximal subgroups

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

subgroupindex
C24×#906732
C2×D4×#906732
#202995462
#202995452
#202995392
C22⋊C4×#906732
#120×D1132
C4×#120113