Finite Group Databasebeta

← C31×#20579 #21477338

Subgroups — C31×#20579 #21477338

Order 7936.

5990 conjugacy classes of subgroups; only the 750 normal subgroups are shown.

normal subgroups only

This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 750 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
1C25×C4×C31C211yesmaximal, characteristic
2C2×C31×#407C216yesmaximal, complemented
3C31×#1779C218yesmaximal, complemented
4C26×C31C411yescharacteristic
5C24×C4×C31—224no—
6C24×C4×C31C413yes—
7C24×C4×C31C414yes—
8C24×C4×C31C2214yes—
9C24×C4×C31C2213yes—
10C22×M16×C31C2214yescomplemented
11C31×#407—224no—
12C2×C31×C22⋊C8C22124yescomplemented
13C25×C31—212no—
14C25×C31—216no—
15C25×C31C2×C413yes—
16C25×C31C2×C414yes—
17C23×C4×C31—2128no—
18C23×C4×C31—212no—
19C23×C4×C31—224no—
20C23×C4×C31—248no—
21C23×C4×C31—248no—
22C23×C4×C31—224no—
23C23×C4×C31C2×C4112yes—
24C23×C4×C31C2×C413yes—
25C23×C4×C31C2×C416yes—
26C23×C4×C31D4124yes—
27C23×C4×C31C2316yes—
28C23×C4×C31C2311yescharacteristic
29C2×M16×C31—224no—
30C22×C8×C31C2318yescomplemented
31C31×C22⋊C8—248no—
32C24×C31—232no—
33C24×C31—2192no—
34C24×C31—224no—
35C24×C31—212no—
36C24×C31—224no—
37C24×C31—224no—
38C24×C31C22⋊C4112yes—
39C24×C31M16116yescomplemented
40C24×C31C22×C411yescharacteristic
41C24×C31C22×C416yes—
42C22×C4×C31—296no—
43C22×C4×C31—2128no—
44C22×C4×C31—2128no—
45C22×C4×C31—224no—
46C22×C4×C31—212no—
47C22×C4×C31—248no—
48C22×C4×C31—224no—
49C22×C4×C31—296no—
50C22×C4×C31—224no—
51C22×C4×C31C22⋊C4112yes—
52C22×C4×C31C22⋊C4124yes—
53C22×C4×C31C22×C416yes—
54C22×C4×C31C22×C411yescharacteristic
55C22×C4×C31C2×D4124yes—
56C22×C4×C31C2×D4112yes—
57C22×C4×C31C2411yescharacteristic
58M16×C31—416no—
59C2×C8×C31—224no—
60#20579C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31—232no—
62C23×C31—2256no—
63C23×C31—296no—
64C23×C31—296no—
65C23×C31—212no—
66C23×C31—24no—
67C23×C31—212no—
68C23×C31—224no—
69C23×C31—248no—
70C23×C31—296no—
71C23×C31C2×C22⋊C416yes—
72C23×C31C2×C22⋊C4112yes—
73C23×C31C2×M16124yes—
74C23×C31C23×C411yescharacteristic
75C2×C4×C31—296no—
76C2×C4×C31—212no—
77C2×C4×C31—224no—
78C2×C4×C31—248no—
79C2×C4×C31—248no—
80C2×C4×C31C2×C22⋊C4112yes—
81C2×C4×C31C2×C22⋊C416yes—
82C2×C4×C31#120116yes—
83C2×C4×C31C22×D416yes—
84C8×C31—48no—
85C25×C4C2×C3111yescharacteristic
86C2×#407C2×C3116yescomplemented
87#1779C2×C3118yescomplemented
88C22×C31—296no—
89C22×C31—2128no—
90C22×C31—212no—
91C22×C31—212no—
92C22×C31—248no—
93C22×C31—212no—
94C22×C31#37914yes—
95C22×C31#407124yescomplemented
96C22×C31C22×C22⋊C413yes—
97C22×C31C22×M1614yes—
98C4×C31—212no—
99C4×C31#37914yes—
100C4×C31C2×#12014yes—
101C26C4×C3111yescharacteristic
102C24×C4—224no—
103C24×C4C4×C3113yes—
104C24×C4C4×C3114yes—
105C24×C4C22×C3114yes—
106C24×C4C22×C3113yes—
107C22×M16C22×C3114yescomplemented
108#407—224no—
109C2×C22⋊C8C22×C31124yescomplemented
110C2×C31—24no—
111C2×C31—224no—
112C2×C31C2×#37911yescharacteristic
113C2×C31C2×#40716yes—
114C25—212no—
115C25—216no—
116C25C2×C4×C3113yes—
117C25C2×C4×C3114yes—
118C23×C4—2128no—
119C23×C4—212no—
120C23×C4—224no—
121C23×C4—248no—
122C23×C4—248no—
123C23×C4—224no—
124C23×C4C2×C4×C31112yes—
125C23×C4C2×C4×C3113yes—
126C23×C4C2×C4×C3116yes—
127C23×C4D4×C31124yes—
128C23×C4C23×C3116yes—
129C23×C4C23×C3111yescharacteristic
130C2×M16—224no—
131C22×C8C23×C3118yescomplemented
132C22⋊C8—248no—
133C31#2057911yescharacteristic, direct product factor, Sylow
134C24—232no—
135C24—2192no—
136C24—224no—
137C24—212no—
138C24—224no—
139C24—224no—
140C24C22⋊C4×C31112yes—
141C24M16×C31116yescomplemented
142C24C22×C4×C3111yescharacteristic
143C24C22×C4×C3116yes—
144C22×C4—296no—
145C22×C4—2128no—
146C22×C4—2128no—
147C22×C4—224no—
148C22×C4—212no—
149C22×C4—248no—
150C22×C4—224no—
151C22×C4—296no—
152C22×C4—224no—
153C22×C4C22⋊C4×C31112yes—
154C22×C4C22⋊C4×C31124yes—
155C22×C4C22×C4×C3116yes—
156C22×C4C22×C4×C3111yescharacteristic
157C22×C4C2×D4×C31124yes—
158C22×C4C2×D4×C31112yes—
159C22×C4C24×C3111yescharacteristic
160M16—416no—
161C2×C8—224no—
162C23—232no—
163C23—2256no—
164C23—296no—
165C23—296no—
166C23—248no—
167C23—296no—
168C23—212no—
169C23—24no—
170C23—212no—
171C23—224no—
172C23C2×C22⋊C4×C31112yes—
173C23C2×C22⋊C4×C3116yes—
174C23C2×M16×C31124yes—
175C23C23×C4×C3111yescharacteristic
176C2×C4—296no—
177C2×C4—212no—
178C2×C4—224no—
179C2×C4—248no—
180C2×C4—248no—
181C2×C4C2×C22⋊C4×C31112yes—
182C2×C4C2×C22⋊C4×C3116yes—
183C2×C4C31×#120116yes—
184C2×C4C22×D4×C3116yes—
185C8—48no—
186C22—2128no—
187C22—296no—
188C22—212no—
189C22—212no—
190C22—248no—
191C22—212no—
192C22C31×#37914yes—
193C22C31×#407124yescomplemented
194C22C22×C22⋊C4×C3113yes—
195C22C22×M16×C3114yes—
196C4—212no—
197C4C31×#37914yes—
198C4C2×C31×#12014yes—
199C2—224no—
200C2—24no—
201C2C2×C31×#37911yescharacteristic
202C2C2×C31×#40716yes—
subgroupG/H
centerC22×C4×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC23×C31C23×C4
prime radicalC26×C31C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#407C2semidirect
3. C31×#1779C2semidirect
10. C22×M16×C31C22semidirect
12. C2×C31×C22⋊C8C22semidirect
30. C22×C8×C31C23semidirect
39. C24×C31M16semidirect
60. #20579C31direct (N × H)
86. C2×#407C2×C31semidirect
87. #1779C2×C31semidirect
95. C22×C31#407semidirect
107. C22×M16C22×C31semidirect
109. C2×C22⋊C8C22×C31semidirect
131. C22×C8C23×C31semidirect
133. C31#20579direct (N × H)
141. C24M16×C31semidirect
193. C22C31×#407semidirect

Maximal subgroups

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

subgroupindex
C25×C4×C312
C2×C31×#4072
C31×#17792
#2057931