Finite Group Databasebeta

← C2×#20266218 #27187885

Subgroups — C2×#20266218 #27187885

Order 12928.

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×#87938C212yesmaximal, complemented
2#20266218C218yesmaximal, direct product factor
3C2×#15692323C211yesmaximal, characteristic, complemented
4C2×#15692317C212yesmaximal, complemented
5C2×#15692309C211yesmaximal, 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#15692323C2214yescomplemented
15#15692317C2218yescomplemented
16#15692309C2214yescomplemented
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×#87938D412yes—
28D101⋊C8—21no—
29D101⋊C8C2312yes—
30C2×#11717581—21no—
31C4⋊#87938—22no—
32C4⋊#87938C2314yes—
33C22⋊#87938—28no—
34C4×#87938D412yes—
35C4×#87938C2312yes—
36C23×D101—22no—
37C2×D404C2×C412yescomplemented
38C2×C22⋊D101—22no—
39D4×D101—22no—
40D4×D101—22no—
41D4×D101C2×C414yescomplemented
42D4×D101C2314yes—
43C2×C4×D101C2311yescharacteristic
44D808C2×C414yescomplemented
45#13108059C2×C418yescomplemented
46C2×#11717579C2×C411yescharacteristic, complemented
47C8×D101C2×C412yescomplemented
48C8×D101C2312yes—
49C2×D4×C101C2×C412yescomplemented
50D8×C101C2×C414yescomplemented
51C2×C8×C101C2×C411yescharacteristic, complemented
52C23×C101—22no—
53C22×D101—22no—
54C22×D101—24no—
55C22×D101—24no—
56C22×D101—44no—
57C22×D101—44no—
58C22×D101C2×D411yescharacteristic
59C2×#87938—24no—
60C2×#87938—24no—
61C2×#87938—416no—
62C2×#87938—44no—
63C2×#87938C2×D414yes—
64D4×C101—22no—
65D4×C101C22×C414yescomplemented
66C2×C4×C101C22×C411yescharacteristic
67C22⋊D101—24no—
68C22⋊D101—24no—
69C2×Dic101#4111yescharacteristic
70D404—22no—
71D404C22×C414yescomplemented
72C4×D101C22×C411yescharacteristic
73C4×D101C2×D411yescharacteristic
74C4×D101#4111yescharacteristic
75C4×D101C2411yescharacteristic
76#11717581—22no—
77C8×C101C22×C412yescomplemented
78#11717579C22×C412yescomplemented
79C22×C101—24no—
80C22×C101—44no—
81C22×C101C4×D411yescharacteristic
82C2×D101—24no—
83C2×D101—44no—
84C2×D101—44no—
85C2×D101—44no—
86C2×D101—48no—
87C2×D101C4×D411yescharacteristic
88C2×D101AGL(1,ℤ/8)14yes—
89C2×D101C22×D411yescharacteristic
90#87938—24no—
91#87938—44no—
92C4×C101C4×D411yescharacteristic
93C4×C101C23×C411yescharacteristic
94Dic101C4×D411yescharacteristic
95Dic101C2×#4111yescharacteristic
96C2×C101—44no—
97C2×C101#44212yescomplemented
98C2×C101C2×C4×D411yescharacteristic
99D101—44no—
100D101#44212yescomplemented
101D101C2×AGL(1,ℤ/8)12yes—
102C2×#442—1011nomaximal, Sylow
103C101C2×#44211yescharacteristic, complemented, Sylow
104C22×D8—1011no—
105C2×C4×D4—1012no—
106#442—1018no—
107C2×#106—1011no—
108C2×#102—1012no—
109C2×#97—1011no—
110C22×D4—1012no—
111C23×C4—2022no—
112C2×D8—1012no—
113C2×D8—1014no—
114C2×D8—1014no—
115C2×D8—1011no—
116C2×D8#8793811yescharacteristic, complemented
117C22×C8—1011no—
118C22×C8—1011no—
119C4×D4—1018no—
120C4×D4—2024no—
121C2×C4⋊C4—1012no—
122C2×C22⋊C4—2022no—
123C2×C42—1011no—
124#106—1014no—
125#102—1018no—
126#97—1014no—
127C24—2022no—
128C2×D4—1014no—
129C2×D4—1014no—
130C2×D4—1012no—
131C2×D4—2022no—
132C2×D4—2022no—
133C2×D4—2022no—
134C2×D4C2×#8793812yescomplemented
135C22×C4—1011no—
136C22×C4—1012no—
137C22×C4—4048no—
138C22×C4—2028no—
139C22×C4—2022no—
140D8—1018no—
141D8—1014no—
142D8C2×#8793814yescomplemented
143C2×C8—1011no—
144C2×C8—1012no—
145C2×C8—1012no—
146C2×C8—1012no—
147C2×C8—2021no—
148C2×C8—2021no—
149C2×C8C2×#8793811yescharacteristic, complemented
150C4⋊C4—1014no—
151C4⋊C4—2022no—
152C22⋊C4—2028no—
153C42—1012no—
154C42—1012no—
155C23—22no—
156C23—1011no—
157C23—4044no—
158C23—4044no—
159C23—2024no—
160C23—2024no—
161C23—2022no—
162D4—22no—
163D4—1014no—
164D4—2024no—
165D4—2024no—
166D4—2022no—
167D4C22×#8793814yescomplemented
168C2×C4—1011no—
169C2×C4—1011no—
170C2×C4—1011no—
171C2×C4—1011no—
172C2×C4—1011no—
173C2×C4—1014no—
174C2×C4—4044no—
175C2×C4—40416no—
176C2×C4—2024no—
177C2×C4—2024no—
178C2×C4C22×#8793811yescharacteristic
179C8—1012no—
180C8—2022no—
181C8C22×#8793812yescomplemented
182C22—24no—
183C22—44no—
184C22—1011no—
185C22—1011no—
186C22—1014no—
187C22—4044no—
188C22—4044no—
189C22—4048no—
190C22—4044no—
191C22—2024no—
192C22D4×#8793811yescharacteristic
193C4—1011no—
194C4—1011no—
195C4—4044no—
196C4—2024no—
197C4D4×#8793811yescharacteristic
198C4C23×#8793811yescharacteristic
199C2—44no—
200C2—1012no—
201C2—1012no—
202C2—4044no—
203C2#2026621812yesdirect product factor
204C2C2×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×#442
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. #20266218C2direct (N × H)
3. C2×#15692323C2semidirect
4. C2×#15692317C2semidirect
5. C2×#15692309C2semidirect
10. D4×#87938C22semidirect
14. #15692323C22semidirect
15. #15692317C22semidirect
16. #15692309C22semidirect
18. C2×D808C4semidirect
19. C2×#13108059C4semidirect
20. D8×D101C4semidirect
23. C2×D8×C101C4semidirect
37. C2×D404C2×C4semidirect
41. D4×D101C2×C4semidirect
44. D808C2×C4semidirect
45. #13108059C2×C4semidirect
46. C2×#11717579C2×C4semidirect
47. C8×D101C2×C4semidirect
49. C2×D4×C101C2×C4semidirect
50. D8×C101C2×C4semidirect
51. C2×C8×C101C2×C4semidirect
65. D4×C101C22×C4semidirect
71. D404C22×C4semidirect
77. C8×C101C22×C4semidirect
78. #11717579C22×C4semidirect
97. C2×C101#442semidirect
100. D101#442semidirect
103. C101C2×#442semidirect
116. C2×D8#87938semidirect
134. C2×D4C2×#87938semidirect
142. D8C2×#87938semidirect
149. C2×C8C2×#87938semidirect
167. D4C22×#87938semidirect
181. C8C22×#87938semidirect
203. C2#20266218direct (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
#202662182
C2×#156923232
C2×#156923172
C2×#156923092
C2×D8×D1012
C2×#442101