Finite Group Databasebeta

← C2×D8×#87938 #27187879

Subgroups — C2×D8×#87938 #27187879

Order 12928.

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×#87938C212yesmaximal, complemented
2D8×#87938C218yesmaximal, direct product factor
3C2×#15692324C211yesmaximal, characteristic, complemented
4C2×#15692317C212yesmaximal, complemented
5C2×C8×#87938C211yesmaximal, characteristic, complemented
6C2×D8×D101C211yesmaximal, characteristic
7C23×#87938—22no—
8C2×D101⋊C8C2211yescharacteristic
9D4×#87938—24no—
10D4×#87938C2218yescomplemented
11C2×C4⋊#87938C2212yes—
12C2×C22⋊#87938—22no—
13C2×C4×#87938C2211yescharacteristic
14#15692324C2214yescomplemented
15#15692317C2218yescomplemented
16C8×#87938C2214yescomplemented
17C2×D4×D101C2212yes—
18C2×D808C411yescharacteristic, complemented
19C2×#13108059C412yescomplemented
20D8×D101C414yescomplemented
21D8×D101C2214yes—
22C2×C8×D101C2211yescharacteristic
23C2×D8×C101C411yescharacteristic, complemented
24C22×#87938—22no—
25C22×#87938—28no—
26C22×#87938—48no—
27C22×#87938D411yescharacteristic
28C22×#87938D411yescharacteristic
29D101⋊C8—21no—
30D101⋊C8C2312yes—
31C2×#11717581—21no—
32C4⋊#87938—22no—
33C4⋊#87938C2314yes—
34C22⋊#87938—28no—
35C4×#87938D412yes—
36C4×#87938C2312yes—
37C23×D101—22no—
38C2×D404C2×C412yescomplemented
39C2×C22⋊D101—22no—
40D4×D101—22no—
41D4×D101—22no—
42D4×D101C2×C414yescomplemented
43D4×D101C2314yes—
44C2×C4×D101C2311yescharacteristic
45D808C2×C414yescomplemented
46#13108059C2×C418yescomplemented
47C2×#11717579C2×C411yescharacteristic, complemented
48C8×D101C2×C412yescomplemented
49C8×D101C2312yes—
50C2×D4×C101C2×C412yescomplemented
51D8×C101C2×C414yescomplemented
52C2×C8×C101C2×C411yescharacteristic, complemented
53C23×C101—22no—
54C22×D101—22no—
55C22×D101—24no—
56C22×D101—24no—
57C22×D101—44no—
58C22×D101—44no—
59C22×D101C2×D411yescharacteristic
60C2×#87938—22no—
61C2×#87938—24no—
62C2×#87938—44no—
63C2×#87938—416no—
64C2×#87938D814yesdirect product factor
65C2×#87938C2×D412yes—
66C2×#87938C2×D412yes—
67D4×C101—22no—
68D4×C101C22×C414yescomplemented
69C2×C4×C101C22×C411yescharacteristic
70C22⋊D101—24no—
71C22⋊D101—24no—
72C2×Dic101#4111yescharacteristic
73D404—22no—
74D404C22×C414yescomplemented
75C4×D101C22×C411yescharacteristic
76C4×D101C2×D411yescharacteristic
77C4×D101#4111yescharacteristic
78C4×D101C2411yescharacteristic
79#11717581—22no—
80C8×C101C22×C412yescomplemented
81#11717579C22×C412yescomplemented
82C22×C101—24no—
83C22×C101—44no—
84C22×C101C4×D411yescharacteristic
85C2×D101—24no—
86C2×D101—44no—
87C2×D101—44no—
88C2×D101—44no—
89C2×D101—48no—
90C2×D101C4×D411yescharacteristic
91C2×D101C2×D812yes—
92C2×D101#13512yes—
93C2×D101C22×D411yescharacteristic
94#87938—22no—
95#87938—44no—
96#87938C2×D814yesdirect product factor
97C4×C101C4×D411yescharacteristic
98C4×C101C23×C411yescharacteristic
99Dic101C4×D411yescharacteristic
100Dic101C2×#4111yescharacteristic
101C2×C101—44no—
102C2×C101C4×D812yescomplemented
103C2×C101C2×C4×D411yescharacteristic
104D101—44no—
105D101C4×D812yescomplemented
106D101C22×D811yescharacteristic
107D101C2×#13511yescharacteristic
108C2×C4×D8—1011nomaximal, Sylow
109C101C2×C4×D811yescharacteristic, complemented, Sylow
110C22×D8—1011no—
111C2×C4×D4—1012no—
112C4×D8—1018no—
113C2×#107—1011no—
114C2×#102—1012no—
115C2×C4×C8—1011no—
116C22×D4—1012no—
117C23×C4—2022no—
118C2×D8—1012no—
119C2×D8—1014no—
120C2×D8—1014no—
121C2×D8—1011no—
122C2×D8#8793811yescharacteristic, direct product factor
123C22×C8—1011no—
124C22×C8—1011no—
125C4×D4—1018no—
126C4×D4—2024no—
127C2×C4⋊C4—1012no—
128C2×C22⋊C4—2022no—
129C2×C42—1011no—
130#107—1014no—
131#102—1018no—
132C4×C8—1014no—
133C24—2022no—
134C2×D4—1014no—
135C2×D4—1014no—
136C2×D4—1012no—
137C2×D4—2022no—
138C2×D4—2022no—
139C2×D4—2022no—
140C2×D4C2×#8793812yescomplemented
141C22×C4—1011no—
142C22×C4—1011no—
143C22×C4—1011no—
144C22×C4—4048no—
145C22×C4—2028no—
146C22×C4—2022no—
147D8—1018no—
148D8—1014no—
149D8C2×#8793814yesdirect product factor
150C2×C8—1011no—
151C2×C8—1012no—
152C2×C8—1012no—
153C2×C8—1012no—
154C2×C8—2021no—
155C2×C8—2021no—
156C2×C8C2×#8793811yescharacteristic, complemented
157C4⋊C4—1014no—
158C4⋊C4—2022no—
159C22⋊C4—2028no—
160C42—1012no—
161C42—1012no—
162C23—22no—
163C23—1011no—
164C23—4044no—
165C23—4044no—
166C23—2024no—
167C23—2024no—
168C23—2022no—
169D4—22no—
170D4—1014no—
171D4—2024no—
172D4—2024no—
173D4—2022no—
174D4C22×#8793814yescomplemented
175C2×C4—1012no—
176C2×C4—1014no—
177C2×C4—1011no—
178C2×C4—1011no—
179C2×C4—1011no—
180C2×C4—1011no—
181C2×C4—1011no—
182C2×C4—1012no—
183C2×C4—40416no—
184C2×C4—4044no—
185C2×C4—2024no—
186C2×C4—2022no—
187C2×C4C22×#8793811yescharacteristic
188C8—1012no—
189C8—2022no—
190C8C22×#8793812yescomplemented
191C22—24no—
192C22—44no—
193C22—1011no—
194C22—1011no—
195C22—1012no—
196C22—1012no—
197C22—4044no—
198C22—4044no—
199C22—4048no—
200C22—4044no—
201C22—2024no—
202C22D4×#8793811yescharacteristic
203C4—1014no—
204C4—1011no—
205C4—1011no—
206C4—4044no—
207C4—2022no—
208C4D4×#8793811yescharacteristic
209C4C23×#8793811yescharacteristic
210C2—44no—
211C2—1011no—
212C2—1011no—
213C2—1012no—
214C2—4044no—
215C2D8×#8793812yesdirect product factor
216C2C2×D4×#8793811yescharacteristic
subgroupG/H
centerC22D4×#87938
commutatorC4×C101C23×C4
FrattiniC4C23×#87938
FittingC2×D8×C101C4
socleC22×C101C4×D4
prime radicalC2×D8×D101C2
cosocleC4×D101C24
hypercenterC2×D8#87938
hypocenterC101C2×C4×D8
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#87938C2semidirect
2. D8×#87938C2direct (N × H)
3. C2×#15692324C2semidirect
4. C2×#15692317C2semidirect
5. C2×C8×#87938C2semidirect
10. D4×#87938C22semidirect
14. #15692324C22semidirect
15. #15692317C22semidirect
16. C8×#87938C22semidirect
18. C2×D808C4semidirect
19. C2×#13108059C4semidirect
20. D8×D101C4semidirect
23. C2×D8×C101C4semidirect
38. C2×D404C2×C4semidirect
42. D4×D101C2×C4semidirect
45. D808C2×C4semidirect
46. #13108059C2×C4semidirect
47. C2×#11717579C2×C4semidirect
48. C8×D101C2×C4semidirect
50. C2×D4×C101C2×C4semidirect
51. D8×C101C2×C4semidirect
52. C2×C8×C101C2×C4semidirect
64. C2×#87938D8direct (N × H)
68. D4×C101C22×C4semidirect
74. D404C22×C4semidirect
80. C8×C101C22×C4semidirect
81. #11717579C22×C4semidirect
96. #87938C2×D8direct (N × H)
102. C2×C101C4×D8semidirect
105. D101C4×D8semidirect
109. C101C2×C4×D8semidirect
122. C2×D8#87938direct (N × H)
140. C2×D4C2×#87938semidirect
149. D8C2×#87938direct (N × H)
156. C2×C8C2×#87938semidirect
174. D4C22×#87938semidirect
190. C8C22×#87938semidirect
215. C2D8×#87938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#879382
D8×#879382
C2×#156923242
C2×#156923172
C2×C8×#879382
C2×D8×D1012
C2×C4×D8101