Finite Group Databasebeta

← C2×D8×#89137 #28379779

Subgroups — C2×D8×#89137 #28379779

Order 13952.

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×#89137C212yesmaximal, complemented
2D8×#89137C218yesmaximal, direct product factor
3C2×#16812768C211yesmaximal, characteristic, complemented
4C2×#16812761C212yesmaximal, complemented
5C2×C8×#89137C211yesmaximal, characteristic, complemented
6C2×D8×D109C211yesmaximal, characteristic
7C23×#89137—22no—
8C2×D109⋊C8C2211yescharacteristic
9D4×#89137—24no—
10D4×#89137C2218yescomplemented
11C2×C4⋊#89137C2212yes—
12C2×C22⋊#89137—22no—
13C2×C4×#89137C2211yescharacteristic
14#16812768C2214yescomplemented
15#16812761C2218yescomplemented
16C8×#89137C2214yescomplemented
17C2×D4×D109C2212yes—
18C2×D872C411yescharacteristic, complemented
19C2×#13182014C412yescomplemented
20D8×D109C414yescomplemented
21D8×D109C2214yes—
22C2×C8×D109C2211yescharacteristic
23C2×D8×C109C411yescharacteristic, complemented
24C22×#89137—22no—
25C22×#89137—28no—
26C22×#89137—48no—
27C22×#89137D411yescharacteristic
28C22×#89137D411yescharacteristic
29D109⋊C8—21no—
30D109⋊C8C2312yes—
31C2×#11724786—21no—
32C4⋊#89137—22no—
33C4⋊#89137C2314yes—
34C22⋊#89137—28no—
35C4×#89137D412yes—
36C4×#89137C2312yes—
37C23×D109—22no—
38C2×D436C2×C412yescomplemented
39C2×C22⋊D109—22no—
40D4×D109—22no—
41D4×D109—22no—
42D4×D109C2×C414yescomplemented
43D4×D109C2314yes—
44C2×C4×D109C2311yescharacteristic
45D872C2×C414yescomplemented
46#13182014C2×C418yescomplemented
47C2×#11724784C2×C411yescharacteristic, complemented
48C8×D109C2×C412yescomplemented
49C8×D109C2312yes—
50C2×D4×C109C2×C412yescomplemented
51D8×C109C2×C414yescomplemented
52C2×C8×C109C2×C411yescharacteristic, complemented
53C23×C109—22no—
54C22×D109—22no—
55C22×D109—24no—
56C22×D109—24no—
57C22×D109—44no—
58C22×D109—44no—
59C22×D109C2×D411yescharacteristic
60C2×#89137—22no—
61C2×#89137—24no—
62C2×#89137—44no—
63C2×#89137—416no—
64C2×#89137D814yesdirect product factor
65C2×#89137C2×D412yes—
66C2×#89137C2×D412yes—
67D4×C109—22no—
68D4×C109C22×C414yescomplemented
69C2×C4×C109C22×C411yescharacteristic
70C22⋊D109—24no—
71C22⋊D109—24no—
72C2×Dic109#4111yescharacteristic
73D436—22no—
74D436C22×C414yescomplemented
75C4×D109C22×C411yescharacteristic
76C4×D109C2×D411yescharacteristic
77C4×D109#4111yescharacteristic
78C4×D109C2411yescharacteristic
79#11724786—22no—
80C8×C109C22×C412yescomplemented
81#11724784C22×C412yescomplemented
82C22×C109—24no—
83C22×C109—44no—
84C22×C109C4×D411yescharacteristic
85C2×D109—24no—
86C2×D109—44no—
87C2×D109—44no—
88C2×D109—44no—
89C2×D109—48no—
90C2×D109C4×D411yescharacteristic
91C2×D109C2×D812yes—
92C2×D109#13512yes—
93C2×D109C22×D411yescharacteristic
94#89137—22no—
95#89137—44no—
96#89137C2×D814yesdirect product factor
97C4×C109C4×D411yescharacteristic
98C4×C109C23×C411yescharacteristic
99Dic109C4×D411yescharacteristic
100Dic109C2×#4111yescharacteristic
101C2×C109—44no—
102C2×C109C4×D812yescomplemented
103C2×C109C2×C4×D411yescharacteristic
104D109—44no—
105D109C4×D812yescomplemented
106D109C22×D811yescharacteristic
107D109C2×#13511yescharacteristic
108C2×C4×D8—1091nomaximal, Sylow
109C109C2×C4×D811yescharacteristic, complemented, Sylow
110C22×D8—1091no—
111C2×C4×D4—1092no—
112C4×D8—1098no—
113C2×#107—1091no—
114C2×#102—1092no—
115C2×C4×C8—1091no—
116C22×D4—1092no—
117C23×C4—2182no—
118C2×D8—1092no—
119C2×D8—1094no—
120C2×D8—1094no—
121C2×D8—1091no—
122C2×D8#8913711yescharacteristic, direct product factor
123C22×C8—1091no—
124C22×C8—1091no—
125C4×D4—1098no—
126C4×D4—2184no—
127C2×C4⋊C4—1092no—
128C2×C22⋊C4—2182no—
129C2×C42—1091no—
130#107—1094no—
131#102—1098no—
132C4×C8—1094no—
133C24—2182no—
134C2×D4—1094no—
135C2×D4—1094no—
136C2×D4—1092no—
137C2×D4—2182no—
138C2×D4—2182no—
139C2×D4—2182no—
140C2×D4C2×#8913712yescomplemented
141C22×C4—1091no—
142C22×C4—1091no—
143C22×C4—1091no—
144C22×C4—4368no—
145C22×C4—2188no—
146C22×C4—2182no—
147D8—1098no—
148D8—1094no—
149D8C2×#8913714yesdirect product factor
150C2×C8—1091no—
151C2×C8—1092no—
152C2×C8—1092no—
153C2×C8—1092no—
154C2×C8—2181no—
155C2×C8—2181no—
156C2×C8C2×#8913711yescharacteristic, complemented
157C4⋊C4—1094no—
158C4⋊C4—2182no—
159C22⋊C4—2188no—
160C42—1092no—
161C42—1092no—
162C23—22no—
163C23—1091no—
164C23—4364no—
165C23—4364no—
166C23—2184no—
167C23—2184no—
168C23—2182no—
169D4—22no—
170D4—1094no—
171D4—2184no—
172D4—2184no—
173D4—2182no—
174D4C22×#8913714yescomplemented
175C2×C4—1092no—
176C2×C4—1094no—
177C2×C4—1091no—
178C2×C4—1091no—
179C2×C4—1091no—
180C2×C4—1091no—
181C2×C4—1091no—
182C2×C4—1092no—
183C2×C4—43616no—
184C2×C4—4364no—
185C2×C4—2184no—
186C2×C4—2182no—
187C2×C4C22×#8913711yescharacteristic
188C8—1092no—
189C8—2182no—
190C8C22×#8913712yescomplemented
191C22—24no—
192C22—44no—
193C22—1092no—
194C22—1092no—
195C22—1091no—
196C22—1091no—
197C22—4364no—
198C22—4364no—
199C22—4368no—
200C22—4364no—
201C22—2184no—
202C22D4×#8913711yescharacteristic
203C4—1094no—
204C4—1091no—
205C4—1091no—
206C4—4364no—
207C4—2182no—
208C4D4×#8913711yescharacteristic
209C4C23×#8913711yescharacteristic
210C2—44no—
211C2—1091no—
212C2—1091no—
213C2—1092no—
214C2—4364no—
215C2D8×#8913712yesdirect product factor
216C2C2×D4×#8913711yescharacteristic
subgroupG/H
centerC22D4×#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
FittingC2×D8×C109C4
socleC22×C109C4×D4
prime radicalC2×D8×D109C2
cosocleC4×D109C24
hypercenterC2×D8#89137
hypocenterC109C2×C4×D8
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#89137C2semidirect
2. D8×#89137C2direct (N × H)
3. C2×#16812768C2semidirect
4. C2×#16812761C2semidirect
5. C2×C8×#89137C2semidirect
10. D4×#89137C22semidirect
14. #16812768C22semidirect
15. #16812761C22semidirect
16. C8×#89137C22semidirect
18. C2×D872C4semidirect
19. C2×#13182014C4semidirect
20. D8×D109C4semidirect
23. C2×D8×C109C4semidirect
38. C2×D436C2×C4semidirect
42. D4×D109C2×C4semidirect
45. D872C2×C4semidirect
46. #13182014C2×C4semidirect
47. C2×#11724784C2×C4semidirect
48. C8×D109C2×C4semidirect
50. C2×D4×C109C2×C4semidirect
51. D8×C109C2×C4semidirect
52. C2×C8×C109C2×C4semidirect
64. C2×#89137D8direct (N × H)
68. D4×C109C22×C4semidirect
74. D436C22×C4semidirect
80. C8×C109C22×C4semidirect
81. #11724784C22×C4semidirect
96. #89137C2×D8direct (N × H)
102. C2×C109C4×D8semidirect
105. D109C4×D8semidirect
109. C109C2×C4×D8semidirect
122. C2×D8#89137direct (N × H)
140. C2×D4C2×#89137semidirect
149. D8C2×#89137direct (N × H)
156. C2×C8C2×#89137semidirect
174. D4C22×#89137semidirect
190. C8C22×#89137semidirect
215. C2D8×#89137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#891372
D8×#891372
C2×#168127682
C2×#168127612
C2×C8×#891372
C2×D8×D1092
C2×C4×D8109