Finite Group Databasebeta

← C31×#7316 #21464075

Subgroups — C31×#7316 #21464075

Order 7936.

620 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C31×#1783C211yesmaximal, characteristic
2C31×#1781C212yesmaximal
3C23×D4×C31C2211yescharacteristic
4C2×C31×#100—22no—
5C2×C31×#99—22no—
6C2×C31×#99—22no—
7C31×#407C412yescomplemented
8C31×#379C414yescomplemented
9C25×C31C2×C412yes—
10C22×D4×C31—42no—
11C22×D4×C31—44no—
12C22×D4×C31D412yes—
13C22×D4×C31D411yescharacteristic
14C22×D4×C31Q811yescharacteristic
15C23×C4×C31C2×C411yescharacteristic
16C2×M16×C31—22no—
17C2×C22⋊C4×C31—24no—
18C2×C22⋊C4×C31—44no—
19C31×#100—44no—
20C31×#99—44no—
21C31×#99—44no—
22C31×C22⋊C8—42no—
23C24×C31—24no—
24C24×C31—42no—
25C24×C31—42no—
26C24×C31—84no—
27C24×C31C4211yescharacteristic
28C24×C31C22⋊C412yes—
29C24×C31C4⋊C412yes—
30C2×D4×C31—24no—
31C2×D4×C31—24no—
32C2×D4×C31—24no—
33C2×D4×C31—42no—
34C2×D4×C31—41no—
35C2×D4×C31—41no—
36C2×D4×C31—42no—
37C2×D4×C31—416no—
38C22×C4×C31—22no—
39C22×C4×C31—42no—
40C22×C4×C31—44no—
41C22×C4×C31C22⋊C411yescharacteristic
42C22×C4×C31C4⋊C411yescharacteristic
43M16×C31—44no—
44C2×C8×C31—42no—
45C22⋊C4×C31—44no—
46C22⋊C4×C31—44no—
47C22⋊C4×C31—88no—
48#7316C3111yesmaximal, characteristic, direct product factor, Sylow
49C23×C31—21no—
50C23×C31—22no—
51C23×C31—22no—
52C23×C31—22no—
53C23×C31—22no—
54C23×C31—22no—
55C23×C31—22no—
56C23×C31—42no—
57C23×C31—48no—
58C23×C31—48no—
59C23×C31—84no—
60C23×C31—84no—
61C23×C31—82no—
62C23×C31—82no—
63C23×C31—84no—
64C23×C31—84no—
65C23×C31—84no—
66C23×C31#9511yescharacteristic
67C23×C31#9914yes—
68D4×C31—48no—
69D4×C31—44no—
70D4×C31—44no—
71C2×C4×C31—22no—
72C2×C4×C31—21no—
73C2×C4×C31—22no—
74C2×C4×C31—44no—
75C2×C4×C31—84no—
76C2×C4×C31—88no—
77C2×C4×C31#9912yes—
78C8×C31—82no—
79#1783C2×C3111yescharacteristic
80#1781C2×C3112yes—
81C22×C31—24no—
82C22×C31—22no—
83C22×C31—24no—
84C22×C31—41no—
85C22×C31—44no—
86C22×C31—42no—
87C22×C31—41no—
88C22×C31—44no—
89C22×C31—41no—
90C22×C31—42no—
91C22×C31—82no—
92C22×C31—82no—
93C22×C31—82no—
94C22×C31—82no—
95C22×C31—816no—
96C22×C31#34212yes—
97C22×C31#34211yescharacteristic
98C4×C31—22no—
99C4×C31—41no—
100C4×C31—164no—
101C23×D4C22×C3111yescharacteristic
102C2×#100—22no—
103C2×#99—22no—
104C2×#99—22no—
105#407C4×C3112yescomplemented
106#379C4×C3114yescomplemented
107C2×C31—22no—
108C2×C31—21no—
109C2×C31—44no—
110C2×C31—42no—
111C2×C31—82no—
112C2×C31#130411yescharacteristic
113C25C2×C4×C3112yes—
114C22×D4—42no—
115C22×D4—44no—
116C22×D4D4×C3112yes—
117C22×D4D4×C3111yescharacteristic
118C22×D4Q8×C3111yescharacteristic
119C23×C4C2×C4×C3111yescharacteristic
120C2×M16—22no—
121C2×C22⋊C4—24no—
122C2×C22⋊C4—44no—
123#100—44no—
124#99—44no—
125#99—44no—
126C22⋊C8—42no—
127C31#731611yescharacteristic, direct product factor, Sylow
128C24—24no—
129C24—42no—
130C24—42no—
131C24—84no—
132C24C42×C3111yescharacteristic
133C24C22⋊C4×C3112yes—
134C24C4⋊C4×C3112yes—
135C2×D4—24no—
136C2×D4—24no—
137C2×D4—24no—
138C2×D4—42no—
139C2×D4—41no—
140C2×D4—41no—
141C2×D4—42no—
142C2×D4—416no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—44no—
146C22×C4C22⋊C4×C3111yescharacteristic
147C22×C4C4⋊C4×C3111yescharacteristic
148M16—44no—
149C2×C8—42no—
150C22⋊C4—44no—
151C22⋊C4—44no—
152C22⋊C4—88no—
153C23—21no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—42no—
161C23—48no—
162C23—48no—
163C23—84no—
164C23—84no—
165C23—82no—
166C23—82no—
167C23—84no—
168C23—84no—
169C23—84no—
170C23C31×#9511yescharacteristic
171C23C31×#9914yes—
172D4—48no—
173D4—44no—
174D4—44no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—84no—
180C2×C4—88no—
181C2×C4C31×#9912yes—
182C8—82no—
183C22—24no—
184C22—22no—
185C22—24no—
186C22—41no—
187C22—44no—
188C22—42no—
189C22—41no—
190C22—44no—
191C22—41no—
192C22—42no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22—82no—
197C22—816no—
198C22C31×#34212yes—
199C22C31×#34211yescharacteristic
200C4—22no—
201C4—41no—
202C4—164no—
203C2—22no—
204C2—21no—
205C2—44no—
206C2—42no—
207C2—82no—
208C2C31×#130411yescharacteristic
subgroupG/H
center, socleC2×C31#1304
commutatorC24C42×C31
Frattini, cosocleC23×D4C22×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C23×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
7. C31×#407C4semidirect
8. C31×#379C4semidirect
48. #7316C31direct (N × H)
105. #407C4×C31semidirect
106. #379C4×C31semidirect
127. C31#7316direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17832
C31×#17812
#731631