Finite Group Databasebeta

← C2×D8×#1181 #16836239

Subgroups — C2×D8×#1181 #16836239

Order 3712.

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×#1181C212yesmaximal, complemented
2D8×#1181C218yesmaximal, direct product factor
3C2×#11745210C211yesmaximal, characteristic, complemented
4C2×#11745223C212yesmaximal, complemented
5C2×C8×#1181C211yesmaximal, characteristic, complemented
6C2×D8×D29C211yesmaximal, characteristic
7C23×#1181—22no—
8C2×D4×D29C2212yes—
9C2×C22⋊#1181—22no—
10D4×#1181—24no—
11D4×#1181C2218yescomplemented
12C2×C4⋊#1181C2212yes—
13C2×C4×#1181C2211yescharacteristic
14C2×D29⋊C8C2211yescharacteristic
15C2×D8×C29C411yescharacteristic, complemented
16C2×#90782C412yescomplemented
17D8×D29C414yescomplemented
18D8×D29C2214yes—
19C2×D232C411yescharacteristic, complemented
20C2×C8×D29C2211yescharacteristic
21#11745223C2218yescomplemented
22#11745210C2214yescomplemented
23C8×#1181C2214yescomplemented
24C23×D29—22no—
25C22×#1181—22no—
26C22×#1181—28no—
27C22×#1181—48no—
28C22×#1181D411yescharacteristic
29C22×#1181D411yescharacteristic
30C2×D4×C29C2×C412yescomplemented
31C2×C22⋊D29—22no—
32D4×D29—22no—
33D4×D29—22no—
34D4×D29C2×C414yescomplemented
35D4×D29C2314yes—
36C2×D116C2×C412yescomplemented
37C2×C4×D29C2311yescharacteristic
38C22⋊#1181—28no—
39C2×#6599—21no—
40C4⋊#1181—22no—
41C4⋊#1181C2314yes—
42C4×#1181D412yes—
43C4×#1181C2312yes—
44D29⋊C8—21no—
45D29⋊C8C2312yes—
46D8×C29C2×C414yescomplemented
47C2×C8×C29C2×C411yescharacteristic, complemented
48#90782C2×C418yescomplemented
49C2×#6597C2×C411yescharacteristic, complemented
50D232C2×C414yescomplemented
51C8×D29C2×C412yescomplemented
52C8×D29C2312yes—
53C23×C29—22no—
54C22×D29—22no—
55C22×D29—24no—
56C22×D29—24no—
57C22×D29—44no—
58C22×D29—44no—
59C22×D29C2×D411yescharacteristic
60C2×#1181—22no—
61C2×#1181—24no—
62C2×#1181—44no—
63C2×#1181—416no—
64C2×#1181D814yesdirect product factor
65C2×#1181C2×D412yes—
66C2×#1181C2×D412yes—
67D4×C29—22no—
68D4×C29C22×C414yescomplemented
69C2×C4×C29C22×C411yescharacteristic
70C22⋊D29—24no—
71C22⋊D29—24no—
72C2×Dic29#4111yescharacteristic
73D116—22no—
74D116C22×C414yescomplemented
75C4×D29C22×C411yescharacteristic
76C4×D29C2×D411yescharacteristic
77C4×D29#4111yescharacteristic
78C4×D29C2411yescharacteristic
79#6599—22no—
80C8×C29C22×C412yescomplemented
81#6597C22×C412yescomplemented
82C2×C4×D8—291nomaximal, Sylow
83C22×C29—24no—
84C22×C29—44no—
85C22×C29C4×D411yescharacteristic
86C2×D29—24no—
87C2×D29—44no—
88C2×D29—44no—
89C2×D29—44no—
90C2×D29—48no—
91C2×D29C4×D411yescharacteristic
92C2×D29C2×D812yes—
93C2×D29#13512yes—
94C2×D29C22×D411yescharacteristic
95#1181—22no—
96#1181—44no—
97#1181C2×D814yesdirect product factor
98C4×C29C4×D411yescharacteristic
99C4×C29C23×C411yescharacteristic
100Dic29C4×D411yescharacteristic
101Dic29C2×#4111yescharacteristic
102C22×D8—291no—
103C2×C4×D4—292no—
104C4×D8—298no—
105C2×#107—291no—
106C2×#102—292no—
107C2×C4×C8—291no—
108C2×C29—44no—
109C2×C29C4×D812yescomplemented
110C2×C29C2×C4×D411yescharacteristic
111D29—44no—
112D29C4×D812yescomplemented
113D29C22×D811yescharacteristic
114D29C2×#13511yescharacteristic
115C22×D4—292no—
116C23×C4—582no—
117C2×D8—292no—
118C2×D8—294no—
119C2×D8—294no—
120C2×D8—291no—
121C2×D8#118111yescharacteristic, direct product factor
122C22×C8—291no—
123C22×C8—291no—
124C4×D4—298no—
125C4×D4—584no—
126C2×C4⋊C4—292no—
127C2×C22⋊C4—582no—
128C2×C42—291no—
129#107—294no—
130#102—298no—
131C4×C8—294no—
132C29C2×C4×D811yescharacteristic, complemented, Sylow
133C24—582no—
134C2×D4—294no—
135C2×D4—294no—
136C2×D4—292no—
137C2×D4—582no—
138C2×D4—582no—
139C2×D4—582no—
140C2×D4C2×#118112yescomplemented
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—291no—
144C22×C4—588no—
145C22×C4—582no—
146C22×C4—1168no—
147D8—298no—
148D8—294no—
149D8C2×#118114yesdirect product factor
150C2×C8—291no—
151C2×C8—292no—
152C2×C8—292no—
153C2×C8—292no—
154C2×C8—581no—
155C2×C8—581no—
156C2×C8C2×#118111yescharacteristic, complemented
157C4⋊C4—294no—
158C4⋊C4—582no—
159C22⋊C4—588no—
160C42—292no—
161C42—292no—
162C23—22no—
163C23—291no—
164C23—584no—
165C23—584no—
166C23—582no—
167C23—1164no—
168C23—1164no—
169D4—22no—
170D4—294no—
171D4—584no—
172D4—584no—
173D4—582no—
174D4C22×#118114yescomplemented
175C2×C4—292no—
176C2×C4—294no—
177C2×C4—291no—
178C2×C4—291no—
179C2×C4—291no—
180C2×C4—291no—
181C2×C4—291no—
182C2×C4—292no—
183C2×C4—582no—
184C2×C4—584no—
185C2×C4—11616no—
186C2×C4—1164no—
187C2×C4C22×#118111yescharacteristic
188C8—292no—
189C8—582no—
190C8C22×#118112yescomplemented
191C22—24no—
192C22—44no—
193C22—292no—
194C22—292no—
195C22—291no—
196C22—291no—
197C22—584no—
198C22—1164no—
199C22—1164no—
200C22—1168no—
201C22—1164no—
202C22D4×#118111yescharacteristic
203C4—294no—
204C4—291no—
205C4—291no—
206C4—582no—
207C4—1164no—
208C4D4×#118111yescharacteristic
209C4C23×#118111yescharacteristic
210C2—44no—
211C2—291no—
212C2—291no—
213C2—292no—
214C2—1164no—
215C2D8×#118112yesdirect product factor
216C2C2×D4×#118111yescharacteristic
subgroupG/H
centerC22D4×#1181
commutatorC4×C29C23×C4
FrattiniC4C23×#1181
FittingC2×D8×C29C4
socleC22×C29C4×D4
prime radicalC2×D8×D29C2
cosocleC4×D29C24
hypercenterC2×D8#1181
hypocenterC29C2×C4×D8
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#1181C2semidirect
2. D8×#1181C2direct (N × H)
3. C2×#11745210C2semidirect
4. C2×#11745223C2semidirect
5. C2×C8×#1181C2semidirect
11. D4×#1181C22semidirect
15. C2×D8×C29C4semidirect
16. C2×#90782C4semidirect
17. D8×D29C4semidirect
19. C2×D232C4semidirect
21. #11745223C22semidirect
22. #11745210C22semidirect
23. C8×#1181C22semidirect
30. C2×D4×C29C2×C4semidirect
34. D4×D29C2×C4semidirect
36. C2×D116C2×C4semidirect
46. D8×C29C2×C4semidirect
47. C2×C8×C29C2×C4semidirect
48. #90782C2×C4semidirect
49. C2×#6597C2×C4semidirect
50. D232C2×C4semidirect
51. C8×D29C2×C4semidirect
64. C2×#1181D8direct (N × H)
68. D4×C29C22×C4semidirect
74. D116C22×C4semidirect
80. C8×C29C22×C4semidirect
81. #6597C22×C4semidirect
97. #1181C2×D8direct (N × H)
109. C2×C29C4×D8semidirect
112. D29C4×D8semidirect
121. C2×D8#1181direct (N × H)
132. C29C2×C4×D8semidirect
140. C2×D4C2×#1181semidirect
149. D8C2×#1181direct (N × H)
156. C2×C8C2×#1181semidirect
174. D4C22×#1181semidirect
190. C8C22×#1181semidirect
215. C2D8×#1181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#11812
D8×#11812
C2×#117452102
C2×#117452232
C2×C8×#11812
C2×D8×D292
C2×C4×D829