Finite Group Databasebeta

← C2×D4×#11764049 #31798028

Subgroups — C2×D4×#11764049 #31798028

Order 17536.

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×#11764049C212yesmaximal, complemented
2D4×#11764049C218yesmaximal, direct product factor
3C2×C4⋊#11764049C211yesmaximal, characteristic, complemented
4C2×C22⋊#11764049C212yesmaximal, complemented
5C2×C4×#11764049C211yesmaximal, characteristic, complemented
6C2×D4×#10587739C211yesmaximal, characteristic
7C22×#11764049—28no—
8C22×#11764049C2211yescharacteristic
9C22×#11764049C2212yes—
10C22×#11764049C2211yescharacteristic
11C22×#11764049C2218yescomplemented
12C4⋊#11764049C2214yescomplemented
13C22⋊#11764049C2218yescomplemented
14C4×#11764049C2214yescomplemented
15C23×#10587739C2212yes—
16D4×#10587739C414yes—
17D4×#10587739C2214yes—
18C2×C4⋊#10587739C411yescharacteristic
19C2×C22⋊#10587739C412yes—
20C2×C4×#10587739C2211yescharacteristic
21C2×D4×D137C411yescharacteristic
22C2×#11764049—216no—
23C2×#11764049—24no—
24C2×#11764049—22no—
25C2×#11764049D414yesdirect product factor
26C2×#11764049C2312yes—
27C2×#11764049C2314yes—
28C2×#11764049C2312yes—
29C22×#10587739—24no—
30C22×#10587739—24no—
31C22×#10587739C2×C411yescharacteristic
32C22×#10587739C2×C412yes—
33C22×#10587739C2×C414yes—
34C22×#10587739C2314yes—
35C22×#10587739C2311yescharacteristic
36C4⋊#10587739C2×C414yes—
37C22⋊#10587739C2×C418yes—
38C4×#10587739C2×C412yes—
39C4×#10587739C2312yes—
40C23×D137C2×C412yes—
41C2×D548C811yescharacteristic, complemented
42C2×C22⋊D137C812yescomplemented
43D4×D137C814yescomplemented
44D4×D137C2×C414yes—
45C2×C4×D137C2×C411yescharacteristic
46C2×D4×C137C811yescharacteristic, complemented
47#11764049—24no—
48#11764049—22no—
49#11764049C2×D414yesdirect product factor
50C2×#10587739—24no—
51C2×#10587739—22no—
52C2×#10587739—28no—
53C2×#10587739—24no—
54C2×#10587739—24no—
55C2×#10587739C22×C412yes—
56C2×#10587739C22×C414yes—
57C2×#10587739C22×C411yescharacteristic
58C2×#10587739C2×D412yes—
59C2×#10587739#4112yes—
60C2×#10587739C2411yescharacteristic
61C22×D137—24no—
62C22×D137—24no—
63C22×D137C2×C814yescomplemented
64C22×D137C2×C812yescomplemented
65C22×D137C22×C414yes—
66C22×D137C22×C411yescharacteristic
67D548C2×C814yescomplemented
68C22⋊D137C2×C818yescomplemented
69C2×Dic137C2×C811yescharacteristic, complemented
70C4×D137C2×C812yescomplemented
71C4×D137C22×C412yes—
72C23×C137C2×C812yescomplemented
73D4×C137C2×C814yescomplemented
74C2×C4×C137C2×C811yescharacteristic, complemented
75C22×C137—24no—
76C22×C137C22×C811yescharacteristic
77C22×C137C22×C814yescomplemented
78C2×D137—24no—
79C2×D137—24no—
80C2×D137—24no—
81C2×D137—28no—
82C2×D137C4×D412yes—
83C2×D137C22×C811yescharacteristic
84C2×D137C22×C814yescomplemented
85C2×D137#13112yes—
86C2×D137C23×C411yescharacteristic
87#10587739—24no—
88#10587739—22no—
89#10587739C4×D412yes—
90#10587739C22×D411yescharacteristic
91#10587739C2×#4111yescharacteristic
92C4×C137C22×C812yescomplemented
93Dic137C22×C812yescomplemented
94C2×C137—24no—
95C2×C137C8×D412yescomplemented
96C2×C137C23×C811yescharacteristic
97D137—24no—
98D137C8×D412yescomplemented
99D137C2×C4×D411yescharacteristic
100D137C2×#13111yescharacteristic
101C137C2×C8×D411yescharacteristic, complemented, Sylow
102C2×C8×D4—1371nomaximal, Sylow
103C23×C8—1372no—
104C2×C4×D4—1371no—
105C8×D4—1378no—
106C2×C4⋊C8—1371no—
107C2×C22⋊C8—1372no—
108C2×C4×C8—1371no—
109C22×D4—1371no—
110C23×C4—1372no—
111C22×C8—2748no—
112C22×C8—1372no—
113C22×C8—1378no—
114C22×C8—1371no—
115C22×C8—1371no—
116C4×D4—1374no—
117C4×D4—1374no—
118C2×C4⋊C4—1371no—
119C2×C22⋊C4—1372no—
120C2×C42—1371no—
121C4⋊C8—1374no—
122C22⋊C8—1378no—
123C4×C8—1374no—
124C24—1372no—
125C2×D4—1372no—
126C2×D4—1374no—
127C2×D4—1374no—
128C2×D4—1371no—
129C2×D4#1176404911yescharacteristic, direct product factor
130C22×C4—2744no—
131C22×C4—2744no—
132C22×C4—1374no—
133C22×C4—1371no—
134C22×C4—1372no—
135C22×C4—1374no—
136C22×C4—1371no—
137C22×C4—1371no—
138C2×C8—2744no—
139C2×C8—2742no—
140C2×C8—27416no—
141C2×C8—1372no—
142C2×C8—1374no—
143C2×C8—1372no—
144C2×C8—1374no—
145C4⋊C4—1374no—
146C22⋊C4—1378no—
147C42—1372no—
148C42—1372no—
149C23—2744no—
150C23—2744no—
151C23—1372no—
152C23—1374no—
153C23—1374no—
154C23—1371no—
155C23C2×#1176404912yescomplemented
156D4—1378no—
157D4—1374no—
158D4C2×#1176404914yesdirect product factor
159C2×C4—2744no—
160C2×C4—2742no—
161C2×C4—2744no—
162C2×C4—2744no—
163C2×C4—2748no—
164C2×C4—1372no—
165C2×C4—1374no—
166C2×C4—1371no—
167C2×C4—1371no—
168C2×C4—1372no—
169C2×C4—1372no—
170C2×C4—1371no—
171C2×C4—1372no—
172C2×C4—1372no—
173C2×C4C2×#1176404911yescharacteristic, complemented
174C8—2744no—
175C8—2742no—
176C8—1374no—
177C22—24no—
178C22—2744no—
179C22—2744no—
180C22—2748no—
181C22—2744no—
182C22—1374no—
183C22—1372no—
184C22—1372no—
185C22—1371no—
186C22—1371no—
187C22C22×#1176404911yescharacteristic
188C22C22×#1176404914yescomplemented
189C4—2744no—
190C4—2742no—
191C4—1371no—
192C4—1371no—
193C4—1372no—
194C4—1372no—
195C4C22×#1176404912yescomplemented
196C2—24no—
197C2—2744no—
198C2—1371no—
199C2—1371no—
200C2—1372no—
201C2D4×#1176404912yesdirect product factor
202C2C23×#1176404911yescharacteristic
subgroupG/H
centerC22C22×#11764049
commutatorC2×C137C23×C8
FrattiniC2C23×#11764049
FittingC2×D4×C137C8
socleC22×C137C22×C8
prime radicalC2×D4×D137C4
cosocleC2×#10587739C24
hypercenterC2×D4#11764049
hypocenterC137C2×C8×D4
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#11764049C2semidirect
2. D4×#11764049C2direct (N × H)
3. C2×C4⋊#11764049C2semidirect
4. C2×C22⋊#11764049C2semidirect
5. C2×C4×#11764049C2semidirect
11. C22×#11764049C22semidirect
12. C4⋊#11764049C22semidirect
13. C22⋊#11764049C22semidirect
14. C4×#11764049C22semidirect
25. C2×#11764049D4direct (N × H)
41. C2×D548C8semidirect
42. C2×C22⋊D137C8semidirect
43. D4×D137C8semidirect
46. C2×D4×C137C8semidirect
49. #11764049C2×D4direct (N × H)
63. C22×D137C2×C8semidirect
64. C22×D137C2×C8semidirect
67. D548C2×C8semidirect
68. C22⋊D137C2×C8semidirect
69. C2×Dic137C2×C8semidirect
70. C4×D137C2×C8semidirect
72. C23×C137C2×C8semidirect
73. D4×C137C2×C8semidirect
74. C2×C4×C137C2×C8semidirect
77. C22×C137C22×C8semidirect
84. C2×D137C22×C8semidirect
92. C4×C137C22×C8semidirect
93. Dic137C22×C8semidirect
95. C2×C137C8×D4semidirect
98. D137C8×D4semidirect
101. C137C2×C8×D4semidirect
129. C2×D4#11764049direct (N × H)
155. C23C2×#11764049semidirect
158. D4C2×#11764049direct (N × H)
173. C2×C4C2×#11764049semidirect
188. C22C22×#11764049semidirect
195. C4C22×#11764049semidirect
201. C2D4×#11764049direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117640492
D4×#117640492
C2×C4⋊#117640492
C2×C22⋊#117640492
C2×C4×#117640492
C2×D4×#105877392
C2×C8×D4137