Finite Group Databasebeta

← C31×#8752 #21465511

Subgroups — C31×#8752 #21465511

Order 7936.

754 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2308C211yesmaximal, characteristic
2C31×#1783C212yesmaximal
3C31×#1306C214yesmaximal, complemented
4C23×D4×C31C2211yescharacteristic
5C22×C22⋊C4×C31C412yes—
6C2×C31×#100—24no—
7C31×#407C2214yes—
8C31×#386—24no—
9C31×#381C2212yes—
10C31×#379C412yes—
11C25×C31C2×C411yescharacteristic
12C25×C31C2×C411yescharacteristic
13C22×D4×C31—24no—
14C22×D4×C31—44no—
15C22×D4×C31D414yes—
16C23×C4×C31—22no—
17C23×C4×C31C2311yescharacteristic
18C2×M16×C31—24no—
19C2×C22⋊C4×C31—22no—
20C2×C22⋊C4×C31—24no—
21C2×C22⋊C4×C31—44no—
22C2×C22⋊C4×C31C2×C414yes—
23C31×#100—48no—
24C31×C22⋊C8—28no—
25C31×#95—24no—
26C24×C31—24no—
27C24×C31—22no—
28C24×C31—22no—
29C24×C31—42no—
30C24×C31—82no—
31C24×C31—82no—
32C24×C31C22⋊C412yes—
33C24×C31C22⋊C412yes—
34C24×C31C22×C411yescharacteristic
35C2×D4×C31—28no—
36C2×D4×C31—28no—
37C2×D4×C31—44no—
38C2×D4×C31—416no—
39C22×C4×C31—24no—
40C22×C4×C31—42no—
41C22×C4×C31—44no—
42C22×C4×C31—84no—
43C22×C4×C31C2×D412yes—
44C22×C4×C31#4114yes—
45M16×C31—48no—
46C2×C8×C31—44no—
47C22⋊C4×C31—44no—
48C22⋊C4×C31—44no—
49C22⋊C4×C31—84no—
50#8752C3111yesmaximal, characteristic, direct product factor, Sylow
51C23×C31—28no—
52C23×C31—22no—
53C23×C31—22no—
54C23×C31—22no—
55C23×C31—22no—
56C23×C31—24no—
57C23×C31—42no—
58C23×C31—44no—
59C23×C31—44no—
60C23×C31—44no—
61C23×C31—84no—
62C23×C31—84no—
63C23×C31—88no—
64C23×C31—88no—
65C23×C31#9914yes—
66C23×C31C2×C22⋊C411yescharacteristic
67C23×C31#11712yes—
68D4×C31—416no—
69C2×C4×C31—24no—
70C2×C4×C31—44no—
71C2×C4×C31—48no—
72C2×C4×C31—44no—
73C2×C4×C31—88no—
74C2×C4×C31#12314yes—
75C8×C31—84no—
76#2308C2×C3111yescharacteristic
77#1783C2×C3112yes—
78#1306C2×C3114yescomplemented
79C22×C31—22no—
80C22×C31—22no—
81C22×C31—24no—
82C22×C31—24no—
83C22×C31—44no—
84C22×C31—44no—
85C22×C31—44no—
86C22×C31—44no—
87C22×C31—42no—
88C22×C31—44no—
89C22×C31—84no—
90C22×C31—88no—
91C22×C31—88no—
92C22×C31#38111yescharacteristic
93C22×C31C2×#9912yes—
94C4×C31—24no—
95C4×C31—84no—
96C23×D4C22×C3111yescharacteristic
97C22×C22⋊C4C4×C3112yes—
98C2×#100—24no—
99#407C22×C3114yes—
100#386—24no—
101#381C22×C3112yes—
102#379C4×C3112yes—
103C2×C31—22no—
104C2×C31—42no—
105C2×C31—44no—
106C2×C31—82no—
107C2×C31#181911yescharacteristic
108C2×C31#182912yes—
109C25C2×C4×C3111yescharacteristic
110C25C2×C4×C3111yescharacteristic
111C22×D4—24no—
112C22×D4—44no—
113C22×D4D4×C3114yes—
114C23×C4—22no—
115C23×C4C23×C3111yescharacteristic
116C2×M16—24no—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—24no—
119C2×C22⋊C4—44no—
120C2×C22⋊C4C2×C4×C3114yes—
121#100—48no—
122C22⋊C8—28no—
123#95—24no—
124C31#875211yescharacteristic, direct product factor, Sylow
125C24—24no—
126C24—22no—
127C24—22no—
128C24—42no—
129C24—82no—
130C24—82no—
131C24C22⋊C4×C3112yes—
132C24C22⋊C4×C3112yes—
133C24C22×C4×C3111yescharacteristic
134C2×D4—28no—
135C2×D4—28no—
136C2×D4—44no—
137C2×D4—416no—
138C22×C4—24no—
139C22×C4—42no—
140C22×C4—44no—
141C22×C4—84no—
142C22×C4C2×D4×C3112yes—
143C22×C4#41×C3114yes—
144M16—48no—
145C2×C8—44no—
146C22⋊C4—44no—
147C22⋊C4—44no—
148C22⋊C4—84no—
149C23—28no—
150C23—22no—
151C23—22no—
152C23—22no—
153C23—22no—
154C23—24no—
155C23—42no—
156C23—44no—
157C23—44no—
158C23—44no—
159C23—84no—
160C23—84no—
161C23—88no—
162C23—88no—
163C23C31×#9914yes—
164C23C2×C22⋊C4×C3111yescharacteristic
165C23C31×#11712yes—
166D4—416no—
167C2×C4—24no—
168C2×C4—44no—
169C2×C4—48no—
170C2×C4—44no—
171C2×C4—88no—
172C2×C4C31×#12314yes—
173C8—84no—
174C22—22no—
175C22—22no—
176C22—24no—
177C22—24no—
178C22—44no—
179C22—44no—
180C22—44no—
181C22—44no—
182C22—42no—
183C22—44no—
184C22—84no—
185C22—88no—
186C22—88no—
187C22C31×#38111yescharacteristic
188C22C2×C31×#9912yes—
189C4—24no—
190C4—84no—
191C2—22no—
192C2—42no—
193C2—44no—
194C2—82no—
195C2C31×#181911yescharacteristic
196C2C31×#182912yes—
subgroupG/H
center, socleC22×C31#381
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1306C2semidirect
50. #8752C31direct (N × H)
78. #1306C2×C31semidirect
124. C31#8752direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23082
C31×#17832
C31×#13062
#875231