Finite Group Databasebeta

← C2×#20261776 #27158489

Subgroups — C2×#20261776 #27158489

Order 12416.

608 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 170 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×D4×#87604C212yesmaximal, complemented
2#20261776C218yesmaximal, direct product factor
3C2×#15690878C211yesmaximal, characteristic, complemented
4C2×#15690872C212yesmaximal, complemented
5C2×#15690864C211yesmaximal, characteristic, complemented
6C2×D8×D97C211yesmaximal, characteristic
7C23×#87604—22no—
8C2×#13095519C2211yescharacteristic
9D4×#87604—24no—
10D4×#87604C2218yescomplemented
11C2×C4⋊#87604C2212yes—
12C2×C22⋊#87604—22no—
13C2×C4×#87604C2211yescharacteristic
14#15690878C2214yescomplemented
15#15690872C2218yescomplemented
16#15690864C2214yescomplemented
17C2×D4×D97C2212yes—
18C2×D776C411yescharacteristic, complemented
19C2×#13095496C412yescomplemented
20D8×D97C414yescomplemented
21D8×D97C2214yes—
22C2×C8×D97C2211yescharacteristic
23C2×D8×C97C411yescharacteristic, complemented
24C22×#87604—22no—
25C22×#87604—28no—
26C22×#87604—48no—
27C22×#87604D412yes—
28#13095519—21no—
29#13095519C2312yes—
30C2×#11715897—21no—
31C4⋊#87604—22no—
32C4⋊#87604C2314yes—
33C22⋊#87604—28no—
34C4×#87604D412yes—
35C4×#87604C2312yes—
36C23×D97—22no—
37C2×D388C2×C412yescomplemented
38C2×C22⋊D97—22no—
39D4×D97—22no—
40D4×D97—22no—
41D4×D97C2×C414yescomplemented
42D4×D97C2314yes—
43C2×C4×D97C2311yescharacteristic
44D776C2×C414yescomplemented
45#13095496C2×C418yescomplemented
46C2×#11715895C2×C411yescharacteristic, complemented
47C8×D97C2×C412yescomplemented
48C8×D97C2312yes—
49C2×D4×C97C2×C412yescomplemented
50D8×C97C2×C414yescomplemented
51C2×C8×C97C2×C411yescharacteristic, complemented
52C23×C97—22no—
53C22×D97—22no—
54C22×D97—24no—
55C22×D97—24no—
56C22×D97—44no—
57C22×D97—44no—
58C22×D97C2×D411yescharacteristic
59C2×#87604—24no—
60C2×#87604—24no—
61C2×#87604—416no—
62C2×#87604—44no—
63C2×#87604C2×D414yes—
64D4×C97—22no—
65D4×C97C22×C414yescomplemented
66C2×C4×C97C22×C411yescharacteristic
67C22⋊D97—24no—
68C22⋊D97—24no—
69C2×Dic97#4111yescharacteristic
70D388—22no—
71D388C22×C414yescomplemented
72C4×D97C22×C411yescharacteristic
73C4×D97C2×D411yescharacteristic
74C4×D97#4111yescharacteristic
75C4×D97C2411yescharacteristic
76#11715897—22no—
77C8×C97C22×C412yescomplemented
78#11715895C22×C412yescomplemented
79C22×C97—24no—
80C22×C97—44no—
81C22×C97C4×D411yescharacteristic
82C2×D97—24no—
83C2×D97—44no—
84C2×D97—44no—
85C2×D97—44no—
86C2×D97—48no—
87C2×D97C4×D411yescharacteristic
88C2×D97AGL(1,ℤ/8)14yes—
89C2×D97C22×D411yescharacteristic
90#87604—24no—
91#87604—44no—
92C4×C97C4×D411yescharacteristic
93C4×C97C23×C411yescharacteristic
94Dic97C4×D411yescharacteristic
95Dic97C2×#4111yescharacteristic
96C2×C97—44no—
97C2×C97#44212yescomplemented
98C2×C97C2×C4×D411yescharacteristic
99D97—44no—
100D97#44212yescomplemented
101D97C2×AGL(1,ℤ/8)12yes—
102C2×#442—971nomaximal, Sylow
103C97C2×#44211yescharacteristic, complemented, Sylow
104C22×D8—971no—
105C2×C4×D4—972no—
106#442—978no—
107C2×#106—971no—
108C2×#102—972no—
109C2×#97—971no—
110C22×D4—972no—
111C23×C4—1942no—
112C2×D8—972no—
113C2×D8—974no—
114C2×D8—974no—
115C2×D8—971no—
116C2×D8#8760411yescharacteristic, complemented
117C22×C8—971no—
118C22×C8—971no—
119C4×D4—978no—
120C4×D4—1944no—
121C2×C4⋊C4—972no—
122C2×C22⋊C4—1942no—
123C2×C42—971no—
124#106—974no—
125#102—978no—
126#97—974no—
127C24—1942no—
128C2×D4—974no—
129C2×D4—974no—
130C2×D4—972no—
131C2×D4—1942no—
132C2×D4—1942no—
133C2×D4—1942no—
134C2×D4C2×#8760412yescomplemented
135C22×C4—971no—
136C22×C4—972no—
137C22×C4—3888no—
138C22×C4—1948no—
139C22×C4—1942no—
140D8—978no—
141D8—974no—
142D8C2×#8760414yescomplemented
143C2×C8—971no—
144C2×C8—972no—
145C2×C8—972no—
146C2×C8—972no—
147C2×C8—1941no—
148C2×C8—1941no—
149C2×C8C2×#8760411yescharacteristic, complemented
150C4⋊C4—974no—
151C4⋊C4—1942no—
152C22⋊C4—1948no—
153C42—972no—
154C42—972no—
155C23—22no—
156C23—971no—
157C23—3884no—
158C23—3884no—
159C23—1944no—
160C23—1944no—
161C23—1942no—
162D4—22no—
163D4—974no—
164D4—1944no—
165D4—1944no—
166D4—1942no—
167D4C22×#8760414yescomplemented
168C2×C4—971no—
169C2×C4—971no—
170C2×C4—971no—
171C2×C4—971no—
172C2×C4—971no—
173C2×C4—974no—
174C2×C4—3884no—
175C2×C4—38816no—
176C2×C4—1944no—
177C2×C4—1944no—
178C2×C4C22×#8760411yescharacteristic
179C8—972no—
180C8—1942no—
181C8C22×#8760412yescomplemented
182C22—24no—
183C22—44no—
184C22—974no—
185C22—971no—
186C22—971no—
187C22—3884no—
188C22—3884no—
189C22—3888no—
190C22—3884no—
191C22—1944no—
192C22D4×#8760411yescharacteristic
193C4—971no—
194C4—971no—
195C4—3884no—
196C4—1944no—
197C4D4×#8760411yescharacteristic
198C4C23×#8760411yescharacteristic
199C2—44no—
200C2—972no—
201C2—972no—
202C2—3884no—
203C2#2026177612yesdirect product factor
204C2C2×D4×#8760411yescharacteristic
subgroupG/H
centerC22D4×#87604
commutatorC4×C97C23×C4
FrattiniC4C23×#87604
FittingC2×D8×C97C4
socleC22×C97C4×D4
prime radicalC2×D8×D97C2
cosocleC4×D97C24
hypercenterC2×D8#87604
hypocenterC97C2×#442
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#87604C2semidirect
2. #20261776C2direct (N × H)
3. C2×#15690878C2semidirect
4. C2×#15690872C2semidirect
5. C2×#15690864C2semidirect
10. D4×#87604C22semidirect
14. #15690878C22semidirect
15. #15690872C22semidirect
16. #15690864C22semidirect
18. C2×D776C4semidirect
19. C2×#13095496C4semidirect
20. D8×D97C4semidirect
23. C2×D8×C97C4semidirect
37. C2×D388C2×C4semidirect
41. D4×D97C2×C4semidirect
44. D776C2×C4semidirect
45. #13095496C2×C4semidirect
46. C2×#11715895C2×C4semidirect
47. C8×D97C2×C4semidirect
49. C2×D4×C97C2×C4semidirect
50. D8×C97C2×C4semidirect
51. C2×C8×C97C2×C4semidirect
65. D4×C97C22×C4semidirect
71. D388C22×C4semidirect
77. C8×C97C22×C4semidirect
78. #11715895C22×C4semidirect
97. C2×C97#442semidirect
100. D97#442semidirect
103. C97C2×#442semidirect
116. C2×D8#87604semidirect
134. C2×D4C2×#87604semidirect
142. D8C2×#87604semidirect
149. C2×C8C2×#87604semidirect
167. D4C22×#87604semidirect
181. C8C22×#87604semidirect
203. C2#20261776direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#876042
#202617762
C2×#156908782
C2×#156908722
C2×#156908642
C2×D8×D972
C2×#44297