Finite Group Databasebeta

← C4×#16813591 #28393076

Subgroups — C4×#16813591 #28393076

Order 14464.

1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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×#16813591C211yesmaximal, characteristic
2C2×C4×C22⋊D113C213yesmaximal, complemented
3#20298477C213yesmaximal, complemented
4#20298471C213yesmaximal, complemented
5#20298454C211yesmaximal, characteristic, complemented
6C4×C22⋊Dic113C213yesmaximal, complemented
7C24×C4×C113C211yesmaximal, characteristic, complemented
8C22×C22⋊D113C2213yes—
9C22×C4×D113C2211yescharacteristic, complemented
10#16813591C418yesdirect product factor
11C4×C22⋊D113—212no—
12C2×#14268626C2213yescomplemented
13C2×C22⋊Dic113C2213yes—
14C2×C22⋊Dic113C2213yes—
15C2×C22⋊Dic113C2213yes—
16C2×#14268624C2213yescomplemented
17C2×C4×Dic113C2213yescomplemented
18#16813529C2216yescomplemented
19C25×C113C2211yescharacteristic
20C23×C4×C113—212no—
21C23×C4×C113C2213yes—
22C23×C4×C113C2213yes—
23C23×D113C2311yescharacteristic
24C2×C22⋊D113—26no—
25C2×C22⋊D113—26no—
26C2×C22⋊D113C2×C4112yescomplemented
27C22×Dic113C2313yes—
28C22×Dic113C2311yescharacteristic
29C22×Dic113C2313yes—
30C2×C4×D113—26no—
31#14268626—26no—
32C22⋊Dic113—26no—
33C22⋊Dic113—26no—
34C22⋊Dic113C2×C4112yescomplemented
35#14268624—26no—
36C4×Dic113—26no—
37C24×C113—26no—
38C24×C113—26no—
39C24×C113C2×C414yescomplemented
40C24×C113C2313yes—
41C22×C4×C113—232no—
42C22×C4×C113—26no—
43C22×C4×C113—212no—
44C22×C4×C113—212no—
45C22×C4×C113D4112yescomplemented
46C22×C4×C113C2313yes—
47C22×C4×C113C2311yescharacteristic
48C23×C113—28no—
49C23×C113—224no—
50C23×C113—224no—
51C23×C113—26no—
52C23×C113—26no—
53C23×C113C22×C416yes—
54C23×C113C2×D416yes—
55C23×C113#4116yes—
56C23×C113C2411yescharacteristic
57C22×D113—23no—
58C22×D113—23no—
59C22×D113C22×C412yescomplemented
60C2×C4×C113—224no—
61C2×C4×C113—26no—
62C2×C4×C113—224no—
63C2×C4×C113C2×D416yes—
64C2×C4×C113C2×D416yes—
65C22⋊D113—224no—
66C2×Dic113—23no—
67C2×Dic113—23no—
68C2×Dic113—23no—
69C2×Dic113—23no—
70C2×Dic113—26no—
71C2×Dic113C22×C416yescomplemented
72C4×D113—44no—
73C22×C113—232no—
74C22×C113—212no—
75C22×C113—26no—
76C22×C113—26no—
77C22×C113—212no—
78C22×C113C4×D4112yescomplemented
79C22×C113C23×C411yescharacteristic
80C22×C113C22×D413yes—
81C22×C113C2×#4113yes—
82C2×D113—26no—
83C2×D113—41no—
84C2×D113—43no—
85C4×C113—26no—
86C4×C113#12014yescomplemented
87Dic113—26no—
88Dic113—41no—
89Dic113—43no—
90C2×C113—212no—
91C2×C113C2×C4×D413yes—
92C2×C113C2×#12011yescharacteristic
93C2×C113#52513yes—
94D113—42no—
95C4×#120—1131nomaximal, Sylow
96C113C4×#12011yescharacteristic, complemented, Sylow
97C24×C4D11311yescharacteristic, complemented
98C2×#120—1131no—
99C2×C4×D4—1133no—
100#386—1133no—
101#385—1133no—
102#379—1131no—
103C4×C22⋊C4—1133no—
104C25C2×D11311yescharacteristic
105C22×D4—1133no—
106C23×C4—212no—
107C23×C4—1131no—
108C23×C4C2×D11313yes—
109C23×C4C2×D11313yes—
110#120—1138no—
111C4×D4—22612no—
112C2×C4⋊C4—1133no—
113C2×C22⋊C4—1133no—
114C2×C22⋊C4—1133no—
115C2×C22⋊C4—1133no—
116C2×C22⋊C4—1133no—
117C2×C42—1133no—
118#95—1136no—
119C24—26no—
120C24—26no—
121C24—1131no—
122C24C4×D11314yescomplemented
123C24C22×D11313yes—
124C2×D4—11312no—
125C2×D4—2266no—
126C2×D4—2266no—
127C22×C4—232no—
128C22×C4—26no—
129C22×C4—212no—
130C22×C4—212no—
131C22×C4—1133no—
132C22×C4—1133no—
133C22×C4—1131no—
134C22×C4—2266no—
135C22×C4C22⋊D113112yescomplemented
136C22×C4C22×D11313yes—
137C22×C4C22×D11311yescharacteristic
138C4⋊C4—2266no—
139C22⋊C4—11312no—
140C22⋊C4—2266no—
141C22⋊C4—2266no—
142C22⋊C4—2266no—
143C42—2266no—
144C23—28no—
145C23—224no—
146C23—224no—
147C23—26no—
148C23—26no—
149C23—1132no—
150C23—2263no—
151C23—2263no—
152C23C2×C4×D11316yes—
153C23C2×C22⋊D11316yes—
154C23#1426864716yes—
155C23C23×D11311yescharacteristic
156D4—22624no—
157C2×C4—224no—
158C2×C4—26no—
159C2×C4—224no—
160C2×C4—1136no—
161C2×C4—4524no—
162C2×C4—2263no—
163C2×C4—2263no—
164C2×C4—2266no—
165C2×C4—2263no—
166C2×C4—2263no—
167C2×C4C2×C22⋊D11316yes—
168C2×C4C2×C22⋊D11316yes—
169C22—232no—
170C22—212no—
171C22—26no—
172C22—26no—
173C22—212no—
174C22—4521no—
175C22—4523no—
176C22—2266no—
177C22C4×C22⋊D113112yescomplemented
178C22C22×C4×D11311yescharacteristic
179C22C22×C22⋊D11313yes—
180C22C2×#1426864713yes—
181C4—26no—
182C4—4521no—
183C4—4523no—
184C4—2266no—
185C4#1681359114yesdirect product factor
186C2—212no—
187C2—4522no—
188C2C2×C4×C22⋊D11313yes—
189C2C2×#1681359111yescharacteristic
190C2#2029910913yes—
subgroupG/H
centerC22×C4C22×D113
commutatorC22×C113C23×C4
FrattiniC23C23×D113
FittingC24×C4×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813591C2
hypercenterC24×C4D113
hypocenterC113C4×#120
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D113C2semidirect
3. #20298477C2semidirect
4. #20298471C2semidirect
5. #20298454C2semidirect
6. C4×C22⋊Dic113C2semidirect
7. C24×C4×C113C2semidirect
9. C22×C4×D113C22semidirect
10. #16813591C4direct (N × H)
12. C2×#14268626C22semidirect
16. C2×#14268624C22semidirect
17. C2×C4×Dic113C22semidirect
18. #16813529C22semidirect
26. C2×C22⋊D113C2×C4semidirect
34. C22⋊Dic113C2×C4semidirect
39. C24×C113C2×C4semidirect
45. C22×C4×C113D4semidirect
59. C22×D113C22×C4semidirect
71. C2×Dic113C22×C4semidirect
78. C22×C113C4×D4semidirect
86. C4×C113#120semidirect
96. C113C4×#120semidirect
97. C24×C4D113semidirect
122. C24C4×D113semidirect
135. C22×C4C22⋊D113semidirect
177. C22C4×C22⋊D113semidirect
185. C4#16813591direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168135912
C2×C4×C22⋊D1132
#202984772
#202984712
#202984542
C4×C22⋊Dic1132
C24×C4×C1132
C4×#120113