Finite Group Databasebeta

← C31×#8702 #21465461

Subgroups — C31×#8702 #21465461

Order 7936.

786 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 150 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×C31×#381C211yesmaximal, characteristic
2C31×#1779C212yesmaximal
3C31×#1280C214yesmaximal, complemented
4C24×C4×C31C2211yescharacteristic
5C22×C22⋊C4×C31C412yes—
6C2×C31×C22⋊C8—24no—
7C2×C31×C22⋊C8C2214yes—
8C31×#381—24no—
9C2×C31×#95C412yes—
10C2×C31×#95C2212yes—
11C25×C31C2×C411yescharacteristic
12C23×C4×C31—24no—
13C23×C4×C31—44no—
14C23×C4×C31C2×C414yes—
15C23×C4×C31C2×C411yescharacteristic
16C23×C4×C31D414yes—
17C23×C4×C31C2311yescharacteristic
18C22×C8×C31—24no—
19C2×C22⋊C4×C31—22no—
20C2×C22⋊C4×C31—22no—
21C2×C22⋊C4×C31—44no—
22C31×C22⋊C8—28no—
23C31×C22⋊C8—48no—
24C31×#95—24no—
25C31×#95—24no—
26C24×C31—24no—
27C24×C31—22no—
28C24×C31—24no—
29C24×C31—42no—
30C24×C31C22⋊C412yes—
31C24×C31C22×C411yescharacteristic
32C22×C4×C31—28no—
33C22×C4×C31—22no—
34C22×C4×C31—28no—
35C22×C4×C31—24no—
36C22×C4×C31—28no—
37C22×C4×C31—42no—
38C22×C4×C31—44no—
39C22×C4×C31—42no—
40C22×C4×C31—416no—
41C22×C4×C31—44no—
42C22×C4×C31—44no—
43C22×C4×C31C22⋊C412yes—
44C22×C4×C31C2×D412yes—
45C22×C4×C31#4114yes—
46C2×C8×C31—48no—
47C2×C8×C31—44no—
48C22⋊C4×C31—44no—
49C22⋊C4×C31—44no—
50#8702C3111yesmaximal, characteristic, direct product factor, Sylow
51C23×C31—22no—
52C23×C31—22no—
53C23×C31—28no—
54C23×C31—22no—
55C23×C31—24no—
56C23×C31—22no—
57C23×C31—24no—
58C23×C31—416no—
59C23×C31—44no—
60C23×C31—44no—
61C23×C31#9914yes—
62C23×C31C2×C22⋊C411yescharacteristic
63C23×C31#11712yes—
64C23×C31#13114yes—
65C2×C4×C31—24no—
66C2×C4×C31—22no—
67C2×C4×C31—24no—
68C2×C4×C31—44no—
69C2×C4×C31—416no—
70C2×C4×C31—44no—
71C2×C4×C31—44no—
72C2×C4×C31—44no—
73C2×C4×C31—44no—
74C2×C4×C31—88no—
75C2×C4×C31#12314yes—
76C8×C31—84no—
77C2×#381C2×C3111yescharacteristic
78#1779C2×C3112yes—
79#1280C2×C3114yescomplemented
80C22×C31—22no—
81C22×C31—22no—
82C22×C31—28no—
83C22×C31—24no—
84C22×C31—28no—
85C22×C31—416no—
86C22×C31—42no—
87C22×C31—42no—
88C22×C31—44no—
89C22×C31#38111yescharacteristic
90C22×C31#40812yes—
91C22×C31C2×#9912yes—
92C22×C31#41312yes—
93C22×C31#43314yes—
94C4×C31—24no—
95C4×C31—42no—
96C4×C31—84no—
97C24×C4C22×C3111yescharacteristic
98C22×C22⋊C4C4×C3112yes—
99C2×C22⋊C8—24no—
100C2×C22⋊C8C22×C3114yes—
101#381—24no—
102C2×#95C4×C3112yes—
103C2×#95C22×C3112yes—
104C2×C31—24no—
105C2×C31—44no—
106C2×C31#146814yes—
107C2×C31#181811yescharacteristic
108C2×C31#181911yescharacteristic
109C2×C31#182211yescharacteristic
110C25C2×C4×C3111yescharacteristic
111C23×C4—24no—
112C23×C4—44no—
113C23×C4C2×C4×C3114yes—
114C23×C4C2×C4×C3111yescharacteristic
115C23×C4D4×C3114yes—
116C23×C4C23×C3111yescharacteristic
117C22×C8—24no—
118C2×C22⋊C4—22no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4—44no—
121C22⋊C8—28no—
122C22⋊C8—48no—
123#95—24no—
124#95—24no—
125C31#870211yescharacteristic, direct product factor, Sylow
126C24—24no—
127C24—22no—
128C24—24no—
129C24—42no—
130C24C22⋊C4×C3112yes—
131C24C22×C4×C3111yescharacteristic
132C22×C4—28no—
133C22×C4—22no—
134C22×C4—28no—
135C22×C4—24no—
136C22×C4—28no—
137C22×C4—42no—
138C22×C4—44no—
139C22×C4—42no—
140C22×C4—416no—
141C22×C4—44no—
142C22×C4—44no—
143C22×C4C22⋊C4×C3112yes—
144C22×C4C2×D4×C3112yes—
145C22×C4#41×C3114yes—
146C2×C8—48no—
147C2×C8—44no—
148C22⋊C4—44no—
149C22⋊C4—44no—
150C23—22no—
151C23—22no—
152C23—28no—
153C23—24no—
154C23—22no—
155C23—24no—
156C23—22no—
157C23—416no—
158C23—44no—
159C23—44no—
160C23C31×#9914yes—
161C23C2×C22⋊C4×C3111yescharacteristic
162C23C31×#11712yes—
163C23C31×#13114yes—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—44no—
168C2×C4—416no—
169C2×C4—44no—
170C2×C4—44no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—88no—
174C2×C4C31×#12314yes—
175C8—84no—
176C22—22no—
177C22—22no—
178C22—28no—
179C22—24no—
180C22—28no—
181C22—416no—
182C22—42no—
183C22—42no—
184C22—44no—
185C22C31×#38111yescharacteristic
186C22C31×#40812yes—
187C22C2×C31×#9912yes—
188C22C31×#41312yes—
189C22C31×#43314yes—
190C4—24no—
191C4—42no—
192C4—84no—
193C2—24no—
194C2—44no—
195C2C31×#146814yes—
196C2C31×#181811yescharacteristic
197C2C31×#181911yescharacteristic
198C2C31×#182211yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1280C2semidirect
50. #8702C31direct (N × H)
79. #1280C2×C31semidirect
125. C31#8702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3812
C31×#17792
C31×#12802
#870231