Finite Group Databasebeta

← C2×D8×#10587739 #31797536

Subgroups — C2×D8×#10587739 #31797536

Order 17536.

616 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 178 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×#10587739C212yesmaximal, complemented
2D8×#10587739C218yesmaximal, direct product factor
3C2×#17984157C211yesmaximal, characteristic, complemented
4C2×#17984150C212yesmaximal, complemented
5C2×C8×#10587739C211yesmaximal, characteristic, complemented
6C2×D8×D137C211yesmaximal, characteristic
7C23×#10587739—22no—
8C2×#14555518C2211yescharacteristic
9D4×#10587739—24no—
10D4×#10587739C2218yescomplemented
11C2×C4⋊#10587739C2212yes—
12C2×C22⋊#10587739—22no—
13C2×C4×#10587739C2211yescharacteristic
14#17984157C2214yescomplemented
15#17984150C2218yescomplemented
16C8×#10587739C2214yescomplemented
17C2×D4×D137C2212yes—
18C2×D1096C411yescharacteristic, complemented
19C2×#14555495C412yescomplemented
20D8×D137C414yescomplemented
21D8×D137C2214yes—
22C2×C8×D137C2211yescharacteristic
23C2×D8×C137C411yescharacteristic, complemented
24C22×#10587739—28no—
25C22×#10587739—22no—
26C22×#10587739—48no—
27C22×#10587739D411yescharacteristic
28C22×#10587739D411yescharacteristic
29#14555518—21no—
30#14555518C2312yes—
31C2×#11764047—21no—
32C4⋊#10587739—22no—
33C4⋊#10587739C2314yes—
34C22⋊#10587739—28no—
35C4×#10587739D412yes—
36C4×#10587739C2312yes—
37C23×D137—22no—
38C2×D548C2×C412yescomplemented
39C2×C22⋊D137—22no—
40D4×D137—22no—
41D4×D137—22no—
42D4×D137C2×C414yescomplemented
43D4×D137C2314yes—
44C2×C4×D137C2311yescharacteristic
45D1096C2×C414yescomplemented
46#14555495C2×C418yescomplemented
47C2×#11764040C2×C411yescharacteristic, complemented
48C8×D137C2×C412yescomplemented
49C8×D137C2312yes—
50C2×D4×C137C2×C412yescomplemented
51D8×C137C2×C414yescomplemented
52C2×C8×C137C2×C411yescharacteristic, complemented
53C2×#10587739—22no—
54C2×#10587739—24no—
55C2×#10587739—44no—
56C2×#10587739—416no—
57C2×#10587739D814yesdirect product factor
58C2×#10587739C2×D412yes—
59C2×#10587739C2×D412yes—
60#11764047—22no—
61C22×D137—22no—
62C22×D137—24no—
63C22×D137—24no—
64C22×D137—44no—
65C22×D137—44no—
66C22×D137C2×D411yescharacteristic
67D548—22no—
68D548C22×C414yescomplemented
69C22⋊D137—24no—
70C22⋊D137—24no—
71C2×Dic137#4111yescharacteristic
72C4×D137C22×C411yescharacteristic
73C4×D137C2×D411yescharacteristic
74C4×D137#4111yescharacteristic
75C4×D137C2411yescharacteristic
76#11764040C22×C412yescomplemented
77C23×C137—22no—
78D4×C137—22no—
79D4×C137C22×C414yescomplemented
80C2×C4×C137C22×C411yescharacteristic
81C8×C137C22×C412yescomplemented
82C22×C137—24no—
83C22×C137—44no—
84C22×C137C4×D411yescharacteristic
85C2×D137—24no—
86C2×D137—44no—
87C2×D137—44no—
88C2×D137—44no—
89C2×D137—48no—
90C2×D137C4×D411yescharacteristic
91C2×D137C2×D812yes—
92C2×D137#13512yes—
93C2×D137C22×D411yescharacteristic
94#10587739—22no—
95#10587739—44no—
96#10587739C2×D814yesdirect product factor
97C4×C137C4×D411yescharacteristic
98C4×C137C23×C411yescharacteristic
99Dic137C4×D411yescharacteristic
100Dic137C2×#4111yescharacteristic
101C2×C137—44no—
102C2×C137C4×D812yescomplemented
103C2×C137C2×C4×D411yescharacteristic
104D137—44no—
105D137C4×D812yescomplemented
106D137C22×D811yescharacteristic
107D137C2×#13511yescharacteristic
108C137C2×C4×D811yescharacteristic, complemented, Sylow
109C2×C4×D8—1371nomaximal, Sylow
110C22×D8—1371no—
111C2×C4×D4—1372no—
112C4×D8—1378no—
113C2×#107—1371no—
114C2×#102—1372no—
115C2×C4×C8—1371no—
116C22×D4—1372no—
117C23×C4—2742no—
118C2×D8—1372no—
119C2×D8—1374no—
120C2×D8—1374no—
121C2×D8—1371no—
122C2×D8#1058773911yescharacteristic, direct product factor
123C22×C8—1371no—
124C22×C8—1371no—
125C4×D4—2744no—
126C4×D4—1378no—
127C2×C4⋊C4—1372no—
128C2×C22⋊C4—2742no—
129C2×C42—1371no—
130#107—1374no—
131#102—1378no—
132C4×C8—1374no—
133C24—2742no—
134C2×D4—2742no—
135C2×D4—2742no—
136C2×D4—2742no—
137C2×D4—1374no—
138C2×D4—1374no—
139C2×D4—1372no—
140C2×D4C2×#1058773912yescomplemented
141C22×C4—2742no—
142C22×C4—2748no—
143C22×C4—5488no—
144C22×C4—1371no—
145C22×C4—1371no—
146C22×C4—1371no—
147D8—1378no—
148D8—1374no—
149D8C2×#1058773914yesdirect product factor
150C2×C8—2741no—
151C2×C8—2741no—
152C2×C8—1372no—
153C2×C8—1371no—
154C2×C8—1372no—
155C2×C8—1372no—
156C2×C8C2×#1058773911yescharacteristic, complemented
157C4⋊C4—2742no—
158C4⋊C4—1374no—
159C22⋊C4—2748no—
160C42—1372no—
161C42—1372no—
162C23—22no—
163C23—2744no—
164C23—2744no—
165C23—2742no—
166C23—5484no—
167C23—5484no—
168C23—1371no—
169D4—22no—
170D4—2744no—
171D4—2744no—
172D4—2742no—
173D4—1374no—
174D4C22×#1058773914yescomplemented
175C2×C4—2742no—
176C2×C4—2744no—
177C2×C4—5484no—
178C2×C4—54816no—
179C2×C4—1372no—
180C2×C4—1372no—
181C2×C4—1374no—
182C2×C4—1371no—
183C2×C4—1371no—
184C2×C4—1371no—
185C2×C4—1371no—
186C2×C4—1371no—
187C2×C4C22×#1058773911yescharacteristic
188C8—2742no—
189C8—1372no—
190C8C22×#1058773912yescomplemented
191C22—24no—
192C22—44no—
193C22—2744no—
194C22—5484no—
195C22—5484no—
196C22—5488no—
197C22—5484no—
198C22—1372no—
199C22—1372no—
200C22—1371no—
201C22—1371no—
202C22D4×#1058773911yescharacteristic
203C4—2742no—
204C4—5484no—
205C4—1374no—
206C4—1371no—
207C4—1371no—
208C4D4×#1058773911yescharacteristic
209C4C23×#1058773911yescharacteristic
210C2—44no—
211C2—5484no—
212C2—1371no—
213C2—1371no—
214C2—1372no—
215C2D8×#1058773912yesdirect product factor
216C2C2×D4×#1058773911yescharacteristic
subgroupG/H
centerC22D4×#10587739
commutatorC4×C137C23×C4
FrattiniC4C23×#10587739
FittingC2×D8×C137C4
socleC22×C137C4×D4
prime radicalC2×D8×D137C2
cosocleC4×D137C24
hypercenterC2×D8#10587739
hypocenterC137C2×C4×D8
LCSG ▷ C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#10587739C2semidirect
2. D8×#10587739C2direct (N × H)
3. C2×#17984157C2semidirect
4. C2×#17984150C2semidirect
5. C2×C8×#10587739C2semidirect
10. D4×#10587739C22semidirect
14. #17984157C22semidirect
15. #17984150C22semidirect
16. C8×#10587739C22semidirect
18. C2×D1096C4semidirect
19. C2×#14555495C4semidirect
20. D8×D137C4semidirect
23. C2×D8×C137C4semidirect
38. C2×D548C2×C4semidirect
42. D4×D137C2×C4semidirect
45. D1096C2×C4semidirect
46. #14555495C2×C4semidirect
47. C2×#11764040C2×C4semidirect
48. C8×D137C2×C4semidirect
50. C2×D4×C137C2×C4semidirect
51. D8×C137C2×C4semidirect
52. C2×C8×C137C2×C4semidirect
57. C2×#10587739D8direct (N × H)
68. D548C22×C4semidirect
76. #11764040C22×C4semidirect
79. D4×C137C22×C4semidirect
81. C8×C137C22×C4semidirect
96. #10587739C2×D8direct (N × H)
102. C2×C137C4×D8semidirect
105. D137C4×D8semidirect
108. C137C2×C4×D8semidirect
122. C2×D8#10587739direct (N × H)
140. C2×D4C2×#10587739semidirect
149. D8C2×#10587739direct (N × H)
156. C2×C8C2×#10587739semidirect
174. D4C22×#10587739semidirect
190. C8C22×#10587739semidirect
215. C2D8×#10587739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#105877392
D8×#105877392
C2×#179841572
C2×#179841502
C2×C8×#105877392
C2×D8×D1372
C2×C4×D8137