Finite Group Databasebeta

← C31×#8723 #21465482

Subgroups — C31×#8723 #21465482

Order 7936.

630 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 206 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×#384C211yesmaximal, characteristic
2C31×#1797C212yesmaximal
3C31×#1296C214yesmaximal, complemented
4C22×C4⋊C4×C31—22no—
5C22×C4⋊C4×C31C412yes—
6C22×C42×C31C2211yescharacteristic
7C2×C31×C4⋊C8C2214yes—
8C2×C31×C22⋊C8—22no—
9C31×#384—22no—
10C31×#384C412yes—
11C31×#384C2212yes—
12C31×#336—22no—
13C23×C4×C31—22no—
14C23×C4×C31C2×C411yescharacteristic
15C23×C4×C31D412yes—
16C22×C8×C31—24no—
17C2×C4⋊C4×C31—24no—
18C2×C4⋊C4×C31—22no—
19C2×C4⋊C4×C31—24no—
20C2×C4⋊C4×C31—44no—
21C2×C4⋊C4×C31—44no—
22C2×C4⋊C4×C31—44no—
23C2×C4⋊C4×C31C2×C414yes—
24C2×C42×C31—24no—
25C2×C42×C31C2×C411yescharacteristic
26C2×C42×C31D412yes—
27C2×C42×C31C2311yescharacteristic
28C31×C4⋊C8—28no—
29C31×C22⋊C8—44no—
30C24×C31C22⋊C411yescharacteristic
31C22×C4×C31—22no—
32C22×C4×C31—22no—
33C22×C4×C31—22no—
34C22×C4×C31—24no—
35C22×C4×C31—24no—
36C22×C4×C31—24no—
37C22×C4×C31—44no—
38C22×C4×C31—48no—
39C22×C4×C31C22⋊C411yescharacteristic
40C22×C4×C31C22⋊C412yes—
41C22×C4×C31D814yes—
42C22×C4×C31SD1614yes—
43C22×C4×C31C22×C411yescharacteristic
44C22×C4×C31C2×D412yes—
45C2×C8×C31—44no—
46C2×C8×C31—44no—
47C2×C8×C31—44no—
48C4⋊C4×C31—44no—
49C4⋊C4×C31—44no—
50C4⋊C4×C31—48no—
51C4⋊C4×C31—44no—
52C4⋊C4×C31—44no—
53C42×C31—22no—
54C42×C31—24no—
55C42×C31#4114yes—
56#8723C3111yesmaximal, characteristic, direct product factor, Sylow
57C23×C31—21no—
58C23×C31—21no—
59C23×C31—22no—
60C23×C31#10012yes—
61C23×C31#10214yes—
62C23×C31C2×C22⋊C411yescharacteristic
63C2×C4×C31—28no—
64C2×C4×C31—21no—
65C2×C4×C31—22no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—22no—
70C2×C4×C31—28no—
71C2×C4×C31—28no—
72C2×C4×C31—44no—
73C2×C4×C31—48no—
74C2×C4×C31—88no—
75C2×C4×C31#10112yes—
76C2×C4×C31#10214yes—
77C2×C4×C31#11712yes—
78C2×C4×C31#12314yes—
79C2×C4×C31C2×D812yes—
80C2×C4×C31C2×SD1612yes—
81C2×C4×C31#13714yes—
82C8×C31—84no—
83C2×#384C2×C3111yescharacteristic
84#1797C2×C3112yes—
85#1296C2×C3114yescomplemented
86C22×C31—24no—
87C22×C31—22no—
88C22×C31—22no—
89C22×C31—24no—
90C22×C31#33114yes—
91C22×C31#38111yescharacteristic
92C22×C31C2×#10011yescharacteristic
93C22×C31C2×#10111yescharacteristic
94C22×C31C2×#10212yes—
95C22×C31#41912yes—
96C4×C31—22no—
97C4×C31—22no—
98C4×C31—24no—
99C4×C31—84no—
100C4×C31#48014yes—
101C4×C31#48314yes—
102C22×C4⋊C4—22no—
103C22×C4⋊C4C4×C3112yes—
104C22×C42C22×C3111yescharacteristic
105C2×C4⋊C8C22×C3114yes—
106C2×C22⋊C8—22no—
107#384—22no—
108#384C4×C3112yes—
109#384C22×C3112yes—
110#336—22no—
111C2×C31—24no—
112C2×C31C2×#33111yescharacteristic
113C2×C31#154612yes—
114C2×C31#155811yescharacteristic
115C2×C31#182111yescharacteristic
116C2×C31#182312yes—
117C23×C4—22no—
118C23×C4C2×C4×C3111yescharacteristic
119C23×C4D4×C3112yes—
120C22×C8—24no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—44no—
125C2×C4⋊C4—44no—
126C2×C4⋊C4—44no—
127C2×C4⋊C4C2×C4×C3114yes—
128C2×C42—24no—
129C2×C42C2×C4×C3111yescharacteristic
130C2×C42D4×C3112yes—
131C2×C42C23×C3111yescharacteristic
132C4⋊C8—28no—
133C22⋊C8—44no—
134C31#872311yescharacteristic, direct product factor, Sylow
135C24C22⋊C4×C3111yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—24no—
142C22×C4—44no—
143C22×C4—48no—
144C22×C4C22⋊C4×C3111yescharacteristic
145C22×C4C22⋊C4×C3112yes—
146C22×C4D8×C3114yes—
147C22×C4SD16×C3114yes—
148C22×C4C22×C4×C3111yescharacteristic
149C22×C4C2×D4×C3112yes—
150C2×C8—44no—
151C2×C8—44no—
152C2×C8—44no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C4⋊C4—48no—
156C4⋊C4—44no—
157C4⋊C4—44no—
158C42—22no—
159C42—24no—
160C42#41×C3114yes—
161C23—21no—
162C23—22no—
163C23—21no—
164C23C31×#10012yes—
165C23C31×#10214yes—
166C23C2×C22⋊C4×C3111yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—28no—
175C2×C4—28no—
176C2×C4—44no—
177C2×C4—48no—
178C2×C4—88no—
179C2×C4C31×#10112yes—
180C2×C4C31×#10214yes—
181C2×C4C31×#11712yes—
182C2×C4C31×#12314yes—
183C2×C4C2×D8×C3112yes—
184C2×C4C2×SD16×C3112yes—
185C2×C4C31×#13714yes—
186C8—84no—
187C22—24no—
188C22—22no—
189C22—22no—
190C22—24no—
191C22C31×#33114yes—
192C22C31×#38111yescharacteristic
193C22C2×C31×#10011yescharacteristic
194C22C2×C31×#10111yescharacteristic
195C22C2×C31×#10212yes—
196C22C31×#41912yes—
197C4—22no—
198C4—22no—
199C4—24no—
200C4—84no—
201C4C31×#48014yes—
202C4C31×#48314yes—
203C2—24no—
204C2C2×C31×#33111yescharacteristic
205C2C31×#154612yes—
206C2C31×#155811yescharacteristic
207C2C31×#182111yescharacteristic
208C2C31×#182312yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1296C2semidirect
56. #8723C31direct (N × H)
85. #1296C2×C31semidirect
134. C31#8723direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3842
C31×#17972
C31×#12962
#872331