Finite Group Databasebeta

← C2×D4×#3633 #14546023

Subgroups — C2×D4×#3633 #14546023

Order 2176.

616 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 215 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
1C23×#3633C212yesmaximal, complemented
2D4×#3633C218yesmaximal, direct product factor
3C2×C4⋊#3633C211yesmaximal, characteristic, complemented
4C2×C22⋊#3633C212yesmaximal, complemented
5C2×C4×#3633C211yesmaximal, characteristic, complemented
6C2×D4×#595C211yesmaximal, characteristic
7C23×#595C2212yes—
8C22×#3633—28no—
9C22×#3633C2211yescharacteristic
10C22×#3633C2212yes—
11C22×#3633C2211yescharacteristic
12C22×#3633C2218yescomplemented
13C2×D4×D17C411yescharacteristic
14C2×C22⋊#595C412yes—
15D4×#595C414yes—
16D4×#595C2214yes—
17C2×C4⋊#595C411yescharacteristic
18C2×C4×#595C2211yescharacteristic
19C22⋊#3633C2218yescomplemented
20C4⋊#3633C2214yescomplemented
21C4×#3633C2214yescomplemented
22C23×D17C2×C412yes—
23C22×#595—24no—
24C22×#595—24no—
25C22×#595C2×C411yescharacteristic
26C22×#595C2×C412yes—
27C22×#595C2×C414yes—
28C22×#595C2314yes—
29C22×#595C2311yescharacteristic
30C2×#3633—24no—
31C2×#3633—22no—
32C2×#3633—216no—
33C2×#3633D414yesdirect product factor
34C2×#3633C2312yes—
35C2×#3633C2314yes—
36C2×#3633C2312yes—
37C2×D4×C17C811yescharacteristic, complemented
38C2×C22⋊D17C812yescomplemented
39D4×D17C814yescomplemented
40D4×D17C2×C414yes—
41C2×D68C811yescharacteristic, complemented
42C2×C4×D17C2×C411yescharacteristic
43C22⋊#595C2×C418yes—
44C4⋊#595C2×C414yes—
45C4×#595C2×C412yes—
46C4×#595C2312yes—
47C23×C17C2×C812yescomplemented
48C22×D17—24no—
49C22×D17—24no—
50C22×D17C2×C814yescomplemented
51C22×D17C2×C812yescomplemented
52C22×D17C22×C414yes—
53C22×D17C22×C411yescharacteristic
54C2×#595—24no—
55C2×#595—22no—
56C2×#595—28no—
57C2×#595—24no—
58C2×#595—24no—
59C2×#595C22×C412yes—
60C2×#595C22×C414yes—
61C2×#595C22×C411yescharacteristic
62C2×#595C2×D412yes—
63C2×#595#4112yes—
64C2×#595C2411yescharacteristic
65#3633—24no—
66#3633—22no—
67#3633C2×D414yesdirect product factor
68D4×C17C2×C814yescomplemented
69C2×C4×C17C2×C811yescharacteristic, complemented
70C22⋊D17C2×C818yescomplemented
71C2×Dic17C2×C811yescharacteristic, complemented
72D68C2×C814yescomplemented
73C4×D17C2×C812yescomplemented
74C4×D17C22×C412yes—
75C2×C8×D4—171nomaximal, Sylow
76C22×C17—24no—
77C22×C17C22×C811yescharacteristic
78C22×C17C22×C814yescomplemented
79C2×D17—24no—
80C2×D17—24no—
81C2×D17—24no—
82C2×D17—28no—
83C2×D17C4×D412yes—
84C2×D17C22×C811yescharacteristic
85C2×D17C22×C814yescomplemented
86C2×D17#13112yes—
87C2×D17C23×C411yescharacteristic
88#595—24no—
89#595—22no—
90#595C4×D412yes—
91#595C22×D411yescharacteristic
92#595C2×#4111yescharacteristic
93C4×C17C22×C812yescomplemented
94Dic17C22×C812yescomplemented
95C23×C8—172no—
96C2×C4×D4—171no—
97C8×D4—178no—
98C2×C4⋊C8—171no—
99C2×C22⋊C8—172no—
100C2×C4×C8—171no—
101C2×C17—24no—
102C2×C17C8×D412yescomplemented
103C2×C17C23×C811yescharacteristic
104D17—24no—
105D17C8×D412yescomplemented
106D17C2×C4×D411yescharacteristic
107D17C2×#13111yescharacteristic
108C22×D4—171no—
109C23×C4—172no—
110C22×C8—171no—
111C22×C8—172no—
112C22×C8—178no—
113C22×C8—171no—
114C22×C8—348no—
115C4×D4—174no—
116C4×D4—174no—
117C2×C4⋊C4—171no—
118C2×C22⋊C4—172no—
119C2×C42—171no—
120C4⋊C8—174no—
121C22⋊C8—178no—
122C4×C8—174no—
123C17C2×C8×D411yescharacteristic, complemented, Sylow
124C24—172no—
125C2×D4—172no—
126C2×D4—174no—
127C2×D4—174no—
128C2×D4—171no—
129C2×D4#363311yescharacteristic, direct product factor
130C22×C4—171no—
131C22×C4—171no—
132C22×C4—171no—
133C22×C4—172no—
134C22×C4—174no—
135C22×C4—174no—
136C22×C4—344no—
137C22×C4—344no—
138C2×C8—174no—
139C2×C8—172no—
140C2×C8—172no—
141C2×C8—174no—
142C2×C8—3416no—
143C2×C8—342no—
144C2×C8—344no—
145C4⋊C4—174no—
146C22⋊C4—178no—
147C42—172no—
148C42—172no—
149C23—171no—
150C23—172no—
151C23—174no—
152C23—174no—
153C23—344no—
154C23—344no—
155C23C2×#363312yescomplemented
156D4—178no—
157D4—174no—
158D4C2×#363314yesdirect product factor
159C2×C4—171no—
160C2×C4—171no—
161C2×C4—172no—
162C2×C4—172no—
163C2×C4—171no—
164C2×C4—172no—
165C2×C4—172no—
166C2×C4—172no—
167C2×C4—174no—
168C2×C4—344no—
169C2×C4—344no—
170C2×C4—348no—
171C2×C4—344no—
172C2×C4—342no—
173C2×C4C2×#363311yescharacteristic, complemented
174C8—174no—
175C8—344no—
176C8—342no—
177C22—24no—
178C22—172no—
179C22—172no—
180C22—171no—
181C22—171no—
182C22—174no—
183C22—344no—
184C22—344no—
185C22—348no—
186C22—344no—
187C22C22×#363311yescharacteristic
188C22C22×#363314yescomplemented
189C4—171no—
190C4—171no—
191C4—172no—
192C4—172no—
193C4—344no—
194C4—342no—
195C4C22×#363312yescomplemented
196C2—24no—
197C2—171no—
198C2—171no—
199C2—172no—
200C2—344no—
201C2D4×#363312yesdirect product factor
202C2C23×#363311yescharacteristic
subgroupG/H
centerC22C22×#3633
commutatorC2×C17C23×C8
FrattiniC2C23×#3633
FittingC2×D4×C17C8
socleC22×C17C22×C8
prime radicalC2×D4×D17C4
cosocleC2×#595C24
hypercenterC2×D4#3633
hypocenterC17C2×C8×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#3633C2semidirect
2. D4×#3633C2direct (N × H)
3. C2×C4⋊#3633C2semidirect
4. C2×C22⋊#3633C2semidirect
5. C2×C4×#3633C2semidirect
12. C22×#3633C22semidirect
19. C22⋊#3633C22semidirect
20. C4⋊#3633C22semidirect
21. C4×#3633C22semidirect
33. C2×#3633D4direct (N × H)
37. C2×D4×C17C8semidirect
38. C2×C22⋊D17C8semidirect
39. D4×D17C8semidirect
41. C2×D68C8semidirect
47. C23×C17C2×C8semidirect
50. C22×D17C2×C8semidirect
51. C22×D17C2×C8semidirect
67. #3633C2×D4direct (N × H)
68. D4×C17C2×C8semidirect
69. C2×C4×C17C2×C8semidirect
70. C22⋊D17C2×C8semidirect
71. C2×Dic17C2×C8semidirect
72. D68C2×C8semidirect
73. C4×D17C2×C8semidirect
78. C22×C17C22×C8semidirect
85. C2×D17C22×C8semidirect
93. C4×C17C22×C8semidirect
94. Dic17C22×C8semidirect
102. C2×C17C8×D4semidirect
105. D17C8×D4semidirect
123. C17C2×C8×D4semidirect
129. C2×D4#3633direct (N × H)
155. C23C2×#3633semidirect
158. D4C2×#3633direct (N × H)
173. C2×C4C2×#3633semidirect
188. C22C22×#3633semidirect
195. C4C22×#3633semidirect
201. C2D4×#3633direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#36332
D4×#36332
C2×C4⋊#36332
C2×C22⋊#36332
C2×C4×#36332
C2×D4×#5952
C2×C8×D417