Finite Group Databasebeta

← C2×D8×#595 #14545531

Subgroups — C2×D8×#595 #14545531

Order 2176.

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×#595C212yesmaximal, complemented
2D8×#595C218yesmaximal, direct product factor
3C2×#10587534C211yesmaximal, characteristic, complemented
4C2×#10587547C212yesmaximal, complemented
5C2×C8×#595C211yesmaximal, characteristic, complemented
6C2×D8×D17C211yesmaximal, characteristic
7C23×#595—22no—
8C2×D4×D17C2212yes—
9C2×C22⋊#595—22no—
10D4×#595—24no—
11D4×#595C2218yescomplemented
12C2×C4⋊#595C2212yes—
13C2×C4×#595C2211yescharacteristic
14C2×#63242C2211yescharacteristic
15C2×D8×C17C411yescharacteristic, complemented
16C2×#63228C412yescomplemented
17D8×D17C414yescomplemented
18D8×D17C2214yes—
19C2×D136C411yescharacteristic, complemented
20C2×C8×D17C2211yescharacteristic
21#10587547C2218yescomplemented
22#10587534C2214yescomplemented
23C8×#595C2214yescomplemented
24C23×D17—22no—
25C22×#595—22no—
26C22×#595—28no—
27C22×#595—48no—
28C22×#595D411yescharacteristic
29C22×#595D411yescharacteristic
30C2×D4×C17C2×C412yescomplemented
31C2×C22⋊D17—22no—
32D4×D17—22no—
33D4×D17—22no—
34D4×D17C2×C414yescomplemented
35D4×D17C2314yes—
36C2×D68C2×C412yescomplemented
37C2×C4×D17C2311yescharacteristic
38C22⋊#595—28no—
39C2×#3624—21no—
40C4⋊#595—22no—
41C4⋊#595C2314yes—
42C4×#595D412yes—
43C4×#595C2312yes—
44#63242—21no—
45#63242C2312yes—
46D8×C17C2×C414yescomplemented
47C2×C8×C17C2×C411yescharacteristic, complemented
48#63228C2×C418yescomplemented
49C2×#3622C2×C411yescharacteristic, complemented
50D136C2×C414yescomplemented
51C8×D17C2×C412yescomplemented
52C8×D17C2312yes—
53C23×C17—22no—
54C22×D17—22no—
55C22×D17—24no—
56C22×D17—24no—
57C22×D17—44no—
58C22×D17—44no—
59C22×D17C2×D411yescharacteristic
60C2×#595—22no—
61C2×#595—24no—
62C2×#595—44no—
63C2×#595—416no—
64C2×#595D814yesdirect product factor
65C2×#595C2×D412yes—
66C2×#595C2×D412yes—
67D4×C17—22no—
68D4×C17C22×C414yescomplemented
69C2×C4×C17C22×C411yescharacteristic
70C22⋊D17—24no—
71C22⋊D17—24no—
72C2×Dic17#4111yescharacteristic
73D68—22no—
74D68C22×C414yescomplemented
75C4×D17C22×C411yescharacteristic
76C4×D17C2×D411yescharacteristic
77C4×D17#4111yescharacteristic
78C4×D17C2411yescharacteristic
79#3624—22no—
80C8×C17C22×C412yescomplemented
81#3622C22×C412yescomplemented
82C2×C4×D8—171nomaximal, Sylow
83C22×C17—24no—
84C22×C17—44no—
85C22×C17C4×D411yescharacteristic
86C2×D17—24no—
87C2×D17—44no—
88C2×D17—44no—
89C2×D17—44no—
90C2×D17—48no—
91C2×D17C4×D411yescharacteristic
92C2×D17C2×D812yes—
93C2×D17#13512yes—
94C2×D17C22×D411yescharacteristic
95#595—22no—
96#595—44no—
97#595C2×D814yesdirect product factor
98C4×C17C4×D411yescharacteristic
99C4×C17C23×C411yescharacteristic
100Dic17C4×D411yescharacteristic
101Dic17C2×#4111yescharacteristic
102C22×D8—171no—
103C2×C4×D4—172no—
104C4×D8—178no—
105C2×#107—171no—
106C2×#102—172no—
107C2×C4×C8—171no—
108C2×C17—44no—
109C2×C17C4×D812yescomplemented
110C2×C17C2×C4×D411yescharacteristic
111D17—44no—
112D17C4×D812yescomplemented
113D17C22×D811yescharacteristic
114D17C2×#13511yescharacteristic
115C22×D4—172no—
116C23×C4—342no—
117C2×D8—172no—
118C2×D8—174no—
119C2×D8—174no—
120C2×D8—171no—
121C2×D8#59511yescharacteristic, direct product factor
122C22×C8—171no—
123C22×C8—171no—
124C4×D4—178no—
125C4×D4—344no—
126C2×C4⋊C4—172no—
127C2×C22⋊C4—342no—
128C2×C42—171no—
129#107—174no—
130#102—178no—
131C4×C8—174no—
132C17C2×C4×D811yescharacteristic, complemented, Sylow
133C24—342no—
134C2×D4—174no—
135C2×D4—174no—
136C2×D4—172no—
137C2×D4—342no—
138C2×D4—342no—
139C2×D4—342no—
140C2×D4C2×#59512yescomplemented
141C22×C4—171no—
142C22×C4—171no—
143C22×C4—171no—
144C22×C4—348no—
145C22×C4—342no—
146C22×C4—688no—
147D8—178no—
148D8—174no—
149D8C2×#59514yesdirect product factor
150C2×C8—171no—
151C2×C8—172no—
152C2×C8—172no—
153C2×C8—172no—
154C2×C8—341no—
155C2×C8—341no—
156C2×C8C2×#59511yescharacteristic, complemented
157C4⋊C4—174no—
158C4⋊C4—342no—
159C22⋊C4—348no—
160C42—172no—
161C42—172no—
162C23—22no—
163C23—171no—
164C23—344no—
165C23—344no—
166C23—342no—
167C23—684no—
168C23—684no—
169D4—22no—
170D4—174no—
171D4—344no—
172D4—344no—
173D4—342no—
174D4C22×#59514yescomplemented
175C2×C4—172no—
176C2×C4—174no—
177C2×C4—171no—
178C2×C4—171no—
179C2×C4—171no—
180C2×C4—171no—
181C2×C4—171no—
182C2×C4—172no—
183C2×C4—342no—
184C2×C4—344no—
185C2×C4—6816no—
186C2×C4—684no—
187C2×C4C22×#59511yescharacteristic
188C8—172no—
189C8—342no—
190C8C22×#59512yescomplemented
191C22—24no—
192C22—44no—
193C22—172no—
194C22—172no—
195C22—171no—
196C22—171no—
197C22—344no—
198C22—684no—
199C22—684no—
200C22—688no—
201C22—684no—
202C22D4×#59511yescharacteristic
203C4—174no—
204C4—171no—
205C4—171no—
206C4—342no—
207C4—684no—
208C4D4×#59511yescharacteristic
209C4C23×#59511yescharacteristic
210C2—44no—
211C2—171no—
212C2—171no—
213C2—172no—
214C2—684no—
215C2D8×#59512yesdirect product factor
216C2C2×D4×#59511yescharacteristic
subgroupG/H
centerC22D4×#595
commutatorC4×C17C23×C4
FrattiniC4C23×#595
FittingC2×D8×C17C4
socleC22×C17C4×D4
prime radicalC2×D8×D17C2
cosocleC4×D17C24
hypercenterC2×D8#595
hypocenterC17C2×C4×D8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#595C2semidirect
2. D8×#595C2direct (N × H)
3. C2×#10587534C2semidirect
4. C2×#10587547C2semidirect
5. C2×C8×#595C2semidirect
11. D4×#595C22semidirect
15. C2×D8×C17C4semidirect
16. C2×#63228C4semidirect
17. D8×D17C4semidirect
19. C2×D136C4semidirect
21. #10587547C22semidirect
22. #10587534C22semidirect
23. C8×#595C22semidirect
30. C2×D4×C17C2×C4semidirect
34. D4×D17C2×C4semidirect
36. C2×D68C2×C4semidirect
46. D8×C17C2×C4semidirect
47. C2×C8×C17C2×C4semidirect
48. #63228C2×C4semidirect
49. C2×#3622C2×C4semidirect
50. D136C2×C4semidirect
51. C8×D17C2×C4semidirect
64. C2×#595D8direct (N × H)
68. D4×C17C22×C4semidirect
74. D68C22×C4semidirect
80. C8×C17C22×C4semidirect
81. #3622C22×C4semidirect
97. #595C2×D8direct (N × H)
109. C2×C17C4×D8semidirect
112. D17C4×D8semidirect
121. C2×D8#595direct (N × H)
132. C17C2×C4×D8semidirect
140. C2×D4C2×#595semidirect
149. D8C2×#595direct (N × H)
156. C2×C8C2×#595semidirect
174. D4C22×#595semidirect
190. C8C22×#595semidirect
215. C2D8×#595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#5952
D8×#5952
C2×#105875342
C2×#105875472
C2×C8×#5952
C2×D8×D172
C2×C4×D817