Finite Group Databasebeta

← C4×#11758530 #16848213

Subgroups — C4×#11758530 #16848213

Order 3968.

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×#11758530C211yesmaximal, characteristic
2C2×C4×C22⋊D31C213yesmaximal, complemented
3#14520928C213yesmaximal, complemented
4#14520922C213yesmaximal, complemented
5#14520905C211yesmaximal, characteristic, complemented
6C4×C22⋊Dic31C213yesmaximal, complemented
7C24×C4×C31C211yesmaximal, characteristic, complemented
8C25×C31C2211yescharacteristic
9C23×C4×C31—212no—
10C23×C4×C31C2213yes—
11C23×C4×C31C2213yes—
12C22×C22⋊D31C2213yes—
13C22×C4×D31C2211yescharacteristic, complemented
14#11758530C418yesdirect product factor
15C2×C22⋊Dic31C2213yes—
16C2×C22⋊Dic31C2213yes—
17C2×C22⋊Dic31C2213yes—
18C4×C22⋊D31—212no—
19C2×(C2×D31)⋊C4C2213yescomplemented
20C2×Dic31⋊C4C2213yescomplemented
21C2×C4×Dic31C2213yescomplemented
22C31⋊#95C2216yescomplemented
23C24×C31—26no—
24C24×C31—26no—
25C24×C31C2×C414yescomplemented
26C24×C31C2313yes—
27C23×D31C2311yescharacteristic
28C22×C4×C31—232no—
29C22×C4×C31—26no—
30C22×C4×C31—212no—
31C22×C4×C31—212no—
32C22×C4×C31D4112yescomplemented
33C22×C4×C31C2313yes—
34C22×C4×C31C2311yescharacteristic
35C2×C22⋊D31—26no—
36C2×C22⋊D31—26no—
37C2×C22⋊D31C2×C4112yescomplemented
38C22×Dic31C2313yes—
39C22×Dic31C2311yescharacteristic
40C22×Dic31C2313yes—
41C2×C4×D31—26no—
42C22⋊Dic31—26no—
43C22⋊Dic31—26no—
44C22⋊Dic31C2×C4112yescomplemented
45(C2×D31)⋊C4—26no—
46Dic31⋊C4—26no—
47C4×Dic31—26no—
48C23×C31—28no—
49C23×C31—224no—
50C23×C31—224no—
51C23×C31—26no—
52C23×C31—26no—
53C23×C31C22×C416yes—
54C23×C31C2×D416yes—
55C23×C31#4116yes—
56C23×C31C2411yescharacteristic
57C22×D31—23no—
58C22×D31—23no—
59C22×D31C22×C412yescomplemented
60C2×C4×C31—224no—
61C2×C4×C31—26no—
62C2×C4×C31—224no—
63C2×C4×C31C2×D416yes—
64C2×C4×C31C2×D416yes—
65C22⋊D31—224no—
66C2×Dic31—23no—
67C2×Dic31—23no—
68C2×Dic31—23no—
69C2×Dic31—23no—
70C2×Dic31—26no—
71C2×Dic31C22×C416yescomplemented
72C4×D31—44no—
73C4×#120—311nomaximal, Sylow
74C22×C31—232no—
75C22×C31—212no—
76C22×C31—26no—
77C22×C31—26no—
78C22×C31—212no—
79C22×C31C4×D4112yescomplemented
80C22×C31C23×C411yescharacteristic
81C22×C31C22×D413yes—
82C22×C31C2×#4113yes—
83C2×D31—26no—
84C2×D31—41no—
85C2×D31—43no—
86C4×C31—26no—
87C4×C31#12014yescomplemented
88Dic31—26no—
89Dic31—41no—
90Dic31—43no—
91C24×C4D3111yescharacteristic, complemented
92C2×#120—311no—
93C2×C4×D4—313no—
94#386—313no—
95#385—313no—
96#379—311no—
97C4×C22⋊C4—313no—
98C2×C31—212no—
99C2×C31C2×C4×D413yes—
100C2×C31C2×#12011yescharacteristic
101C2×C31#52513yes—
102D31—42no—
103C25C2×D3111yescharacteristic
104C22×D4—313no—
105C23×C4—212no—
106C23×C4—311no—
107C23×C4C2×D3113yes—
108C23×C4C2×D3113yes—
109#120—318no—
110C4×D4—6212no—
111C2×C4⋊C4—313no—
112C2×C22⋊C4—313no—
113C2×C22⋊C4—313no—
114C2×C22⋊C4—313no—
115C2×C22⋊C4—313no—
116C2×C42—313no—
117#95—316no—
118C31C4×#12011yescharacteristic, complemented, Sylow
119C24—26no—
120C24—26no—
121C24—311no—
122C24C4×D3114yescomplemented
123C24C22×D3113yes—
124C2×D4—3112no—
125C2×D4—626no—
126C2×D4—626no—
127C22×C4—232no—
128C22×C4—26no—
129C22×C4—212no—
130C22×C4—212no—
131C22×C4—313no—
132C22×C4—313no—
133C22×C4—311no—
134C22×C4—626no—
135C22×C4C22⋊D31112yescomplemented
136C22×C4C22×D3113yes—
137C22×C4C22×D3111yescharacteristic
138C4⋊C4—626no—
139C22⋊C4—3112no—
140C22⋊C4—626no—
141C22⋊C4—626no—
142C22⋊C4—626no—
143C42—626no—
144C23—28no—
145C23—224no—
146C23—224no—
147C23—26no—
148C23—26no—
149C23—312no—
150C23—623no—
151C23—623no—
152C23C2×C4×D3116yes—
153C23#9249516yes—
154C23C2×C22⋊D3116yes—
155C23C23×D3111yescharacteristic
156D4—6224no—
157C2×C4—224no—
158C2×C4—26no—
159C2×C4—224no—
160C2×C4—316no—
161C2×C4—623no—
162C2×C4—623no—
163C2×C4—626no—
164C2×C4—623no—
165C2×C4—623no—
166C2×C4—1244no—
167C2×C4C2×C22⋊D3116yes—
168C2×C4C2×C22⋊D3116yes—
169C22—232no—
170C22—212no—
171C22—26no—
172C22—212no—
173C22—26no—
174C22—626no—
175C22—1241no—
176C22—1243no—
177C22C4×C22⋊D31112yescomplemented
178C22C22×C4×D3111yescharacteristic
179C22C2×#9249513yes—
180C22C22×C22⋊D3113yes—
181C4—26no—
182C4—626no—
183C4—1241no—
184C4—1243no—
185C4#1175853014yesdirect product factor
186C2—212no—
187C2—1242no—
188C2C2×C4×C22⋊D3113yes—
189C2C2×#1175853011yescharacteristic
190C2#1452156013yes—
subgroupG/H
centerC22×C4C22×D31
commutatorC22×C31C23×C4
FrattiniC23C23×D31
FittingC24×C4×C31C2
socle, cosocleC23×C31C24
prime radicalC2×#11758530C2
hypercenterC24×C4D31
hypocenterC31C4×#120
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D31C2semidirect
3. #14520928C2semidirect
4. #14520922C2semidirect
5. #14520905C2semidirect
6. C4×C22⋊Dic31C2semidirect
7. C24×C4×C31C2semidirect
13. C22×C4×D31C22semidirect
14. #11758530C4direct (N × H)
19. C2×(C2×D31)⋊C4C22semidirect
20. C2×Dic31⋊C4C22semidirect
21. C2×C4×Dic31C22semidirect
22. C31⋊#95C22semidirect
25. C24×C31C2×C4semidirect
32. C22×C4×C31D4semidirect
37. C2×C22⋊D31C2×C4semidirect
44. C22⋊Dic31C2×C4semidirect
59. C22×D31C22×C4semidirect
71. C2×Dic31C22×C4semidirect
79. C22×C31C4×D4semidirect
87. C4×C31#120semidirect
91. C24×C4D31semidirect
118. C31C4×#120semidirect
122. C24C4×D31semidirect
135. C22×C4C22⋊D31semidirect
177. C22C4×C22⋊D31semidirect
185. C4#11758530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585302
C2×C4×C22⋊D312
#145209282
#145209222
#145209052
C4×C22⋊Dic312
C24×C4×C312
C4×#12031