Finite Group Databasebeta

← C22×SD16×D31 #16860428

Subgroups — C22×SD16×D31 #16860428

Order 3968.

1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C22×Q8×D31C211yesmaximal, characteristic, complemented
2C22×D4×D31C211yesmaximal, characteristic
3C22×#92470C211yesmaximal, characteristic, complemented
4C22×#92480C211yesmaximal, characteristic, complemented
5C22×#92481C211yesmaximal, characteristic, complemented
6C2×SD16×D31C2124yesmaximal, direct product factor
7C22×C8×D31C211yesmaximal, characteristic, complemented
8C22×SD16×C31C211yesmaximal, characteristic, complemented
9C24×D31—21no—
10C22×Q8×C31C2211yescharacteristic, complemented
11C22×D4×C31C2211yescharacteristic
12C22×C22⋊D31—21no—
13C2×Q8×D31—26no—
14C2×Q8×D31C22112yescomplemented
15C2×D4×D31—26no—
16C2×D4×D31C22112yes—
17C22×D124C2211yescharacteristic
18C22×C4×D31—21no—
19C22×C4×D31C2211yescharacteristic
20C22×Dic62—21no—
21C22×Dic62C2211yescharacteristic, complemented
22C2×SD16×C31C22112yescomplemented
23C22×C8×C31C2211yescharacteristic, complemented
24C2×#92481C22112yescomplemented
25C2×#92480C22112yescomplemented
26C22×C31⋊C8C2211yescharacteristic, complemented
27SD16×D31C22164yesdirect product factor
28C2×#92470C22112yescomplemented
29C2×C8×D31C22112yescomplemented
30C24×C31—21no—
31C23×D31—21no—
32C23×D31—212no—
33C23×D31—48no—
34C23×D31D411yescharacteristic
35C2×Q8×C31—23no—
36C2×Q8×C31C2316yescomplemented
37C2×D4×C31—23no—
38C2×D4×C31C2316yes—
39C22×C4×C31—21no—
40C22×C4×C31C2311yescharacteristic
41C2×C22⋊D31—212no—
42C22×Dic31—21no—
43C22×Dic31D411yescharacteristic
44Q8×D31—224no—
45Q8×D31C23116yescomplemented
46D4×D31—224no—
47D4×D31C23116yes—
48C2×D124—23no—
49C2×D124C2316yes—
50C2×C4×D31—212no—
51C2×C4×D31D416yes—
52C2×C4×D31C2316yes—
53C2×Dic62—23no—
54C2×Dic62—212no—
55C2×Dic62C2316yescomplemented
56SD16×C31C23116yescomplemented
57C2×C8×C31C2316yescomplemented
58#92481C23116yescomplemented
59#92480C23116yescomplemented
60C2×C31⋊C8C2316yescomplemented
61#92470C23116yescomplemented
62C8×D31C23116yescomplemented
63C23×C31—26no—
64C23×C31—44no—
65C23×C31C2×D411yescharacteristic
66C22×D31—26no—
67C22×D31—216no—
68C22×D31—44no—
69C22×D31—448no—
70C22×D31SD1618yesdirect product factor
71C22×D31C2×D416yes—
72Q8×C31—26no—
73Q8×C31C2414yescomplemented
74D4×C31—26no—
75D4×C31C2414yes—
76C2×C4×C31—26no—
77C2×C4×C31C2×D413yes—
78C2×C4×C31C2413yes—
79C22⋊D31—216no—
80C2×Dic31—26no—
81C2×Dic31C2×D416yes—
82D124—26no—
83D124C2414yes—
84C4×D31—216no—
85C4×D31C2×D4112yes—
86C4×D31C2414yes—
87Dic62—26no—
88Dic62—216no—
89Dic62C2414yescomplemented
90C8×C31C2414yescomplemented
91C31⋊C8C2414yescomplemented
92C23×SD16—311nomaximal, Sylow
93C22×C31—24no—
94C22×C31—412no—
95C22×C31C2×SD1614yescomplemented
96C22×C31C22×D413yes—
97C2×D31—24no—
98C2×D31—412no—
99C2×D31—432no—
100C2×D31C2×SD16124yesdirect product factor
101C2×D31C22×D414yes—
102C4×C31—24no—
103C4×C31C22×D413yes—
104C4×C31C2511yescharacteristic
105Dic31—24no—
106Dic31C22×D414yes—
107C23×Q8—311no—
108C23×D4—311no—
109C22×SD16—311no—
110C22×SD16—311no—
111C22×SD16—3124no—
112C22×SD16—311no—
113C22×SD16D3111yescharacteristic, direct product factor
114C23×C8—311no—
115C2×C31—44no—
116C2×C31C22×SD1616yescomplemented
117C2×C31C23×D411yescharacteristic
118D31—44no—
119D31C22×SD1618yesdirect product factor
120C25—621no—
121C22×Q8—3112no—
122C22×Q8—311no—
123C22×Q8—621no—
124C22×Q8—626no—
125C22×Q8C2×D3111yescharacteristic, complemented
126C22×D4—3112no—
127C22×D4—311no—
128C22×D4—626no—
129C22×D4—621no—
130C22×D4C2×D3111yescharacteristic
131C23×C4—311no—
132C23×C4—621no—
133C2×SD16—3112no—
134C2×SD16—3112no—
135C2×SD16—3164no—
136C2×SD16—3112no—
137C2×SD16C2×D31112yesdirect product factor
138C22×C8—311no—
139C22×C8—3112no—
140C22×C8C2×D3111yescharacteristic, complemented
141C31C23×SD1611yescharacteristic, complemented, Sylow
142C24—21no—
143C24—311no—
144C24—6212no—
145C24—621no—
146C24—1248no—
147C2×Q8—23no—
148C2×Q8—3116no—
149C2×Q8—316no—
150C2×Q8—6212no—
151C2×Q8—6224no—
152C2×Q8—623no—
153C2×Q8C22×D3116yescomplemented
154C2×D4—23no—
155C2×D4—3116no—
156C2×D4—316no—
157C2×D4—6224no—
158C2×D4—6212no—
159C2×D4—623no—
160C2×D4C22×D3116yes—
161C22×C4—21no—
162C22×C4—311no—
163C22×C4—316no—
164C22×C4—316no—
165C22×C4—6212no—
166C22×C4—621no—
167C22×C4C22×D3111yescharacteristic
168SD16—3116no—
169SD16—3116no—
170SD16—3116no—
171SD16C22×D31116yesdirect product factor
172C2×C8—316no—
173C2×C8—3116no—
174C2×C8C22×D3116yescomplemented
175C23—26no—
176C23—44no—
177C23—318no—
178C23—316no—
179C23—6216no—
180C23—626no—
181C23—12448no—
182C23—1244no—
183C23D4×D3111yescharacteristic
184Q8—26no—
185Q8—314no—
186Q8—6216no—
187Q8—626no—
188Q8C23×D3114yescomplemented
189D4—26no—
190D4—314no—
191D4—6216no—
192D4—626no—
193D4C23×D3114yes—
194C2×C4—26no—
195C2×C4—316no—
196C2×C4—3112no—
197C2×C4—314no—
198C2×C4—6216no—
199C2×C4—626no—
200C2×C4D4×D3113yes—
201C2×C4C23×D3113yes—
202C8—314no—
203C8C23×D3114yescomplemented
204C22—24no—
205C22—412no—
206C22—314no—
207C22—3124no—
208C22—624no—
209C22—12432no—
210C22—12412no—
211C22SD16×D3114yesdirect product factor
212C22C2×D4×D3113yes—
213C4—24no—
214C4—314no—
215C4—624no—
216C4C2×D4×D3113yes—
217C4C24×D3111yescharacteristic
218C2—44no—
219C2—318no—
220C2—1244no—
221C2C2×SD16×D3116yesdirect product factor
222C2C22×D4×D3111yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
FittingC22×SD16×C31C2
socleC23×C31C2×D4
prime radicalC22×D4×D31C2
hypercenterC22×SD16D31
hypocenterC31C23×SD16
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D31C2semidirect
3. C22×#92470C2semidirect
4. C22×#92480C2semidirect
5. C22×#92481C2semidirect
6. C2×SD16×D31C2direct (N × H)
7. C22×C8×D31C2semidirect
8. C22×SD16×C31C2semidirect
10. C22×Q8×C31C22semidirect
14. C2×Q8×D31C22semidirect
21. C22×Dic62C22semidirect
22. C2×SD16×C31C22semidirect
23. C22×C8×C31C22semidirect
24. C2×#92481C22semidirect
25. C2×#92480C22semidirect
26. C22×C31⋊C8C22semidirect
27. SD16×D31C22direct (N × H)
28. C2×#92470C22semidirect
29. C2×C8×D31C22semidirect
36. C2×Q8×C31C23semidirect
45. Q8×D31C23semidirect
55. C2×Dic62C23semidirect
56. SD16×C31C23semidirect
57. C2×C8×C31C23semidirect
58. #92481C23semidirect
59. #92480C23semidirect
60. C2×C31⋊C8C23semidirect
61. #92470C23semidirect
62. C8×D31C23semidirect
70. C22×D31SD16direct (N × H)
73. Q8×C31C24semidirect
89. Dic62C24semidirect
90. C8×C31C24semidirect
91. C31⋊C8C24semidirect
95. C22×C31C2×SD16semidirect
100. C2×D31C2×SD16direct (N × H)
113. C22×SD16D31direct (N × H)
116. C2×C31C22×SD16semidirect
119. D31C22×SD16direct (N × H)
125. C22×Q8C2×D31semidirect
137. C2×SD16C2×D31direct (N × H)
140. C22×C8C2×D31semidirect
141. C31C23×SD16semidirect
153. C2×Q8C22×D31semidirect
171. SD16C22×D31direct (N × H)
174. C2×C8C22×D31semidirect
188. Q8C23×D31semidirect
203. C8C23×D31semidirect
211. C22SD16×D31direct (N × H)
221. C2C2×SD16×D31direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D312
C22×D4×D312
C22×#924702
C22×#924802
C22×#924812
C2×SD16×D312
C22×C8×D312
C22×SD16×C312
C23×SD1631