Finite Group Databasebeta

← C2×D8×#3866 #18011343

Subgroups — C2×D8×#3866 #18011343

Order 4736.

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×#3866C212yesmaximal, complemented
2D8×#3866C218yesmaximal, direct product factor
3C2×#11924605C211yesmaximal, characteristic, complemented
4C2×#11924598C212yesmaximal, complemented
5C2×C8×#3866C211yesmaximal, characteristic, complemented
6C2×D8×D37C211yesmaximal, characteristic
7C23×#3866—22no—
8C2×D37⋊C8C2211yescharacteristic
9D4×#3866—24no—
10D4×#3866C2218yescomplemented
11C2×C4⋊#3866C2212yes—
12C2×C22⋊#3866—22no—
13C2×C4×#3866C2211yescharacteristic
14#11924605C2214yescomplemented
15#11924598C2218yescomplemented
16C8×#3866C2214yescomplemented
17C2×D4×D37C2212yes—
18C2×D296C411yescharacteristic, complemented
19C2×#10596939C412yescomplemented
20D8×D37C414yescomplemented
21D8×D37C2214yes—
22C2×C8×D37C2211yescharacteristic
23C2×D8×C37C411yescharacteristic, complemented
24C23×D37—22no—
25C22×#3866—22no—
26C22×#3866—28no—
27C22×#3866—48no—
28C22×#3866D411yescharacteristic
29C22×#3866D411yescharacteristic
30C2×D4×C37C2×C412yescomplemented
31C2×C22⋊D37—22no—
32D4×D37—22no—
33D4×D37—22no—
34D4×D37C2×C414yescomplemented
35D4×D37C2314yes—
36C2×D148C2×C412yescomplemented
37C2×C4×D37C2311yescharacteristic
38C22⋊#3866—28no—
39C2×#64438—21no—
40C4⋊#3866—22no—
41C4⋊#3866C2314yes—
42C4×#3866D412yes—
43C4×#3866C2312yes—
44D37⋊C8—21no—
45D37⋊C8C2312yes—
46D8×C37C2×C414yescomplemented
47C2×C8×C37C2×C411yescharacteristic, complemented
48#10596939C2×C418yescomplemented
49C2×#64436C2×C411yescharacteristic, complemented
50D296C2×C414yescomplemented
51C8×D37C2×C412yescomplemented
52C8×D37C2312yes—
53C23×C37—22no—
54C22×D37—22no—
55C22×D37—24no—
56C22×D37—24no—
57C22×D37—44no—
58C22×D37—44no—
59C22×D37C2×D411yescharacteristic
60C2×#3866—22no—
61C2×#3866—24no—
62C2×#3866—44no—
63C2×#3866—416no—
64C2×#3866D814yesdirect product factor
65C2×#3866C2×D412yes—
66C2×#3866C2×D412yes—
67D4×C37—22no—
68D4×C37C22×C414yescomplemented
69C2×C4×C37C22×C411yescharacteristic
70C22⋊D37—24no—
71C22⋊D37—24no—
72C2×Dic37#4111yescharacteristic
73D148—22no—
74D148C22×C414yescomplemented
75C4×D37C22×C411yescharacteristic
76C4×D37C2×D411yescharacteristic
77C4×D37#4111yescharacteristic
78C4×D37C2411yescharacteristic
79#64438—22no—
80C8×C37C22×C412yescomplemented
81#64436C22×C412yescomplemented
82C22×C37—24no—
83C22×C37—44no—
84C22×C37C4×D411yescharacteristic
85C2×D37—24no—
86C2×D37—44no—
87C2×D37—44no—
88C2×D37—44no—
89C2×D37—48no—
90C2×D37C4×D411yescharacteristic
91C2×D37C2×D812yes—
92C2×D37#13512yes—
93C2×D37C22×D411yescharacteristic
94#3866—22no—
95#3866—44no—
96#3866C2×D814yesdirect product factor
97C4×C37C4×D411yescharacteristic
98C4×C37C23×C411yescharacteristic
99Dic37C4×D411yescharacteristic
100Dic37C2×#4111yescharacteristic
101C2×C4×D8—371nomaximal, Sylow
102C2×C37—44no—
103C2×C37C4×D812yescomplemented
104C2×C37C2×C4×D411yescharacteristic
105D37—44no—
106D37C4×D812yescomplemented
107D37C22×D811yescharacteristic
108D37C2×#13511yescharacteristic
109C22×D8—371no—
110C2×C4×D4—372no—
111C4×D8—378no—
112C2×#107—371no—
113C2×#102—372no—
114C2×C4×C8—371no—
115C37C2×C4×D811yescharacteristic, complemented, Sylow
116C22×D4—372no—
117C23×C4—742no—
118C2×D8—372no—
119C2×D8—374no—
120C2×D8—374no—
121C2×D8—371no—
122C2×D8#386611yescharacteristic, direct product factor
123C22×C8—371no—
124C22×C8—371no—
125C4×D4—378no—
126C4×D4—744no—
127C2×C4⋊C4—372no—
128C2×C22⋊C4—742no—
129C2×C42—371no—
130#107—374no—
131#102—378no—
132C4×C8—374no—
133C24—742no—
134C2×D4—374no—
135C2×D4—374no—
136C2×D4—372no—
137C2×D4—742no—
138C2×D4—742no—
139C2×D4—742no—
140C2×D4C2×#386612yescomplemented
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—748no—
145C22×C4—742no—
146C22×C4—1488no—
147D8—378no—
148D8—374no—
149D8C2×#386614yesdirect product factor
150C2×C8—371no—
151C2×C8—372no—
152C2×C8—372no—
153C2×C8—372no—
154C2×C8—741no—
155C2×C8—741no—
156C2×C8C2×#386611yescharacteristic, complemented
157C4⋊C4—374no—
158C4⋊C4—742no—
159C22⋊C4—748no—
160C42—372no—
161C42—372no—
162C23—22no—
163C23—371no—
164C23—744no—
165C23—744no—
166C23—742no—
167C23—1484no—
168C23—1484no—
169D4—22no—
170D4—374no—
171D4—744no—
172D4—744no—
173D4—742no—
174D4C22×#386614yescomplemented
175C2×C4—372no—
176C2×C4—374no—
177C2×C4—371no—
178C2×C4—371no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—372no—
183C2×C4—742no—
184C2×C4—744no—
185C2×C4—14816no—
186C2×C4—1484no—
187C2×C4C22×#386611yescharacteristic
188C8—372no—
189C8—742no—
190C8C22×#386612yescomplemented
191C22—24no—
192C22—44no—
193C22—372no—
194C22—372no—
195C22—371no—
196C22—371no—
197C22—744no—
198C22—1484no—
199C22—1484no—
200C22—1488no—
201C22—1484no—
202C22D4×#386611yescharacteristic
203C4—374no—
204C4—371no—
205C4—371no—
206C4—742no—
207C4—1484no—
208C4D4×#386611yescharacteristic
209C4C23×#386611yescharacteristic
210C2—44no—
211C2—371no—
212C2—371no—
213C2—372no—
214C2—1484no—
215C2D8×#386612yesdirect product factor
216C2C2×D4×#386611yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC4×C37C23×C4
FrattiniC4C23×#3866
FittingC2×D8×C37C4
socleC22×C37C4×D4
prime radicalC2×D8×D37C2
cosocleC4×D37C24
hypercenterC2×D8#3866
hypocenterC37C2×C4×D8
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#3866C2semidirect
2. D8×#3866C2direct (N × H)
3. C2×#11924605C2semidirect
4. C2×#11924598C2semidirect
5. C2×C8×#3866C2semidirect
10. D4×#3866C22semidirect
14. #11924605C22semidirect
15. #11924598C22semidirect
16. C8×#3866C22semidirect
18. C2×D296C4semidirect
19. C2×#10596939C4semidirect
20. D8×D37C4semidirect
23. C2×D8×C37C4semidirect
30. C2×D4×C37C2×C4semidirect
34. D4×D37C2×C4semidirect
36. C2×D148C2×C4semidirect
46. D8×C37C2×C4semidirect
47. C2×C8×C37C2×C4semidirect
48. #10596939C2×C4semidirect
49. C2×#64436C2×C4semidirect
50. D296C2×C4semidirect
51. C8×D37C2×C4semidirect
64. C2×#3866D8direct (N × H)
68. D4×C37C22×C4semidirect
74. D148C22×C4semidirect
80. C8×C37C22×C4semidirect
81. #64436C22×C4semidirect
96. #3866C2×D8direct (N × H)
103. C2×C37C4×D8semidirect
106. D37C4×D8semidirect
115. C37C2×C4×D8semidirect
122. C2×D8#3866direct (N × H)
140. C2×D4C2×#3866semidirect
149. D8C2×#3866direct (N × H)
156. C2×C8C2×#3866semidirect
174. D4C22×#3866semidirect
190. C8C22×#3866semidirect
215. C2D8×#3866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#38662
D8×#38662
C2×#119246052
C2×#119245982
C2×C8×#38662
C2×D8×D372
C2×C4×D837