Finite Group Databasebeta

← C31×#8703 #21465462

Subgroups — C31×#8703 #21465462

Order 7936.

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

normal subgroups only

This group has 530 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×#382C211yesmaximal, characteristic
2C31×#1817C212yesmaximal
3C31×#1280C214yesmaximal
4C22×C4⋊C4×C31C412yes—
5C22×C42×C31C2211yescharacteristic
6C2×C31×C22⋊C8C2214yes—
7C31×#382—22no—
8C31×#382—22no—
9C2×C31×#95C412yes—
10C2×C31×#95C2212yes—
11C31×#336—22no—
12C31×#336—22no—
13C23×C4×C31C2×C411yescharacteristic
14C23×C4×C31C2×C411yescharacteristic
15C23×C4×C31C2×C414yes—
16C23×C4×C31C2311yescharacteristic
17C22×C8×C31—24no—
18C2×C4⋊C4×C31—22no—
19C2×C4⋊C4×C31—22no—
20C2×C4⋊C4×C31—44no—
21C2×C42×C31—24no—
22C2×C42×C31D412yes—
23C2×C42×C31D412yes—
24C31×C22⋊C8—28no—
25C31×#95—24no—
26C31×#95—24no—
27C24×C31C22×C411yescharacteristic
28C22×C4×C31—22no—
29C22×C4×C31—22no—
30C22×C4×C31—22no—
31C22×C4×C31—22no—
32C22×C4×C31—24no—
33C22×C4×C31—24no—
34C22×C4×C31—28no—
35C22×C4×C31—42no—
36C22×C4×C31—44no—
37C22×C4×C31—44no—
38C22×C4×C31C22⋊C412yes—
39C22×C4×C31C22⋊C411yescharacteristic
40C22×C4×C31C22⋊C411yescharacteristic
41C22×C4×C31C2×D412yes—
42C22×C4×C31#4114yes—
43C2×C8×C31—48no—
44C2×C8×C31—44no—
45C4⋊C4×C31—44no—
46C4⋊C4×C31—44no—
47C42×C31—24no—
48C42×C31—24no—
49#8703C3111yesmaximal, characteristic, direct product factor, Sylow
50C23×C31—22no—
51C23×C31—21no—
52C23×C31—21no—
53C23×C31C2×C22⋊C411yescharacteristic
54C23×C31#11712yes—
55C23×C31#13114yes—
56C2×C4×C31—28no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—24no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—22no—
63C2×C4×C31—24no—
64C2×C4×C31—44no—
65C2×C4×C31—44no—
66C2×C4×C31—44no—
67C2×C4×C31—44no—
68C2×C4×C31—44no—
69C2×C4×C31—88no—
70C2×C4×C31#10012yes—
71C2×C4×C31#10112yes—
72C2×C4×C31#12314yes—
73C8×C31—84no—
74C2×#382C2×C3111yescharacteristic
75#1817C2×C3112yes—
76#1280C2×C3114yes—
77C22×C31—22no—
78C22×C31—22no—
79C22×C31—24no—
80C22×C31—24no—
81C22×C31#38111yescharacteristic
82C22×C31#40812yes—
83C22×C31#41012yes—
84C22×C31C2×#10011yescharacteristic
85C22×C31C2×#10111yescharacteristic
86C22×C31#43314yes—
87C4×C31—24no—
88C4×C31—22no—
89C4×C31—22no—
90C4×C31—42no—
91C4×C31—84no—
92C22×C4⋊C4C4×C3112yes—
93C22×C42C22×C3111yescharacteristic
94C2×C22⋊C8C22×C3114yes—
95#382—22no—
96#382—22no—
97C2×#95C4×C3112yes—
98C2×#95C22×C3112yes—
99#336—22no—
100#336—22no—
101C2×C31—24no—
102C2×C31#146912yes—
103C2×C31#147012yes—
104C2×C31#181811yescharacteristic
105C2×C31#182011yescharacteristic
106C2×C31#182111yescharacteristic
107C23×C4C2×C4×C3111yescharacteristic
108C23×C4C2×C4×C3111yescharacteristic
109C23×C4C2×C4×C3114yes—
110C23×C4C23×C3111yescharacteristic
111C22×C8—24no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—44no—
115C2×C42—24no—
116C2×C42D4×C3112yes—
117C2×C42D4×C3112yes—
118C22⋊C8—28no—
119#95—24no—
120#95—24no—
121C31#870311yescharacteristic, direct product factor, Sylow
122C24C22×C4×C3111yescharacteristic
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—24no—
128C22×C4—24no—
129C22×C4—28no—
130C22×C4—42no—
131C22×C4—44no—
132C22×C4—44no—
133C22×C4C22⋊C4×C3112yes—
134C22×C4C22⋊C4×C3111yescharacteristic
135C22×C4C22⋊C4×C3111yescharacteristic
136C22×C4C2×D4×C3112yes—
137C22×C4#41×C3114yes—
138C2×C8—48no—
139C2×C8—44no—
140C4⋊C4—44no—
141C4⋊C4—44no—
142C42—24no—
143C42—24no—
144C23—22no—
145C23—21no—
146C23—21no—
147C23C2×C22⋊C4×C3111yescharacteristic
148C23C31×#11712yes—
149C23C31×#13114yes—
150C2×C4—28no—
151C2×C4—24no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—44no—
161C2×C4—44no—
162C2×C4—44no—
163C2×C4—88no—
164C2×C4C31×#10012yes—
165C2×C4C31×#10112yes—
166C2×C4C31×#12314yes—
167C8—84no—
168C22—22no—
169C22—22no—
170C22—24no—
171C22—24no—
172C22C31×#38111yescharacteristic
173C22C31×#40812yes—
174C22C31×#41012yes—
175C22C2×C31×#10011yescharacteristic
176C22C2×C31×#10111yescharacteristic
177C22C31×#43314yes—
178C4—24no—
179C4—22no—
180C4—22no—
181C4—42no—
182C4—84no—
183C2—24no—
184C2C31×#146912yes—
185C2C31×#147012yes—
186C2C31×#181811yescharacteristic
187C2C31×#182011yescharacteristic
188C2C31×#182111yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
49. #8703C31direct (N × H)
121. C31#8703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3822
C31×#18172
C31×#12802
#870331