Finite Group Databasebeta

← C31×#7428 #21464187

Subgroups — C31×#7428 #21464187

Order 7936.

226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2025C211yesmaximal, characteristic
2C31×#1393C211yesmaximal, characteristic
3C31×#1318C211yesmaximal, characteristic
4C2×C31×#125C411yescharacteristic, complemented
5C2×C31×#102—21no—
6C2×C31×#99—21no—
7C31×#390C2211yescharacteristic
8C31×#340—21no—
9C31×#336C411yescharacteristic, complemented
10C31×#324—21no—
11C22×D4×C31D411yescharacteristic
12C22×C8×C31—21no—
13C31×#125—42no—
14C2×C4⋊C4×C31—21no—
15C2×C4⋊C4×C31—41no—
16C2×C4⋊C4×C31D411yescharacteristic
17C2×C22⋊C4×C31—41no—
18C2×C22⋊C4×C31—41no—
19C2×C42×C31C2×C411yescharacteristic
20C31×#102—42no—
21C31×#99—22no—
22C31×#99—41no—
23C31×C22⋊C8—41no—
24C24×C31—21no—
25C2×D4×C31—21no—
26C2×D4×C31—41no—
27C2×D4×C31—41no—
28C2×D4×C31SD1611yescharacteristic
29C2×D4×C31Q1611yescharacteristic
30C22×C4×C31—21no—
31C22×C4×C31—21no—
32C22×C4×C31—41no—
33C22×C4×C31—81no—
34C22×C4×C31C22⋊C411yescharacteristic
35C2×C8×C31—41no—
36C2×C8×C31—41no—
37C2×C8×C31—41no—
38C2×C8×C31—81no—
39C4⋊C4×C31—22no—
40C4⋊C4×C31—41no—
41C4⋊C4×C31—41no—
42C4⋊C4×C31—42no—
43C4⋊C4×C31—42no—
44C22⋊C4×C31—42no—
45C22⋊C4×C31—82no—
46C22⋊C4×C31—81no—
47C42×C31—41no—
48#7428C3111yesmaximal, characteristic, direct product factor, Sylow
49C23×C31—21no—
50C23×C31—21no—
51C23×C31—41no—
52C23×C31—41no—
53C23×C31—81no—
54C23×C31—81no—
55C23×C31#9911yescharacteristic
56D4×C31—41no—
57D4×C31—41no—
58D4×C31—81no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31—42no—
65C2×C4×C31—41no—
66C2×C4×C31—81no—
67C2×C4×C31—81no—
68C2×C4×C31—81no—
69C2×C4×C31—82no—
70C2×C4×C31—161no—
71C2×C4×C31—161no—
72C2×C4×C31#10311yescharacteristic
73C2×C4×C31#10411yescharacteristic
74C8×C31—81no—
75C8×C31—161no—
76#2025C2×C3111yescharacteristic
77#1393C2×C3111yescharacteristic
78#1318C2×C3111yescharacteristic
79C22×C31—21no—
80C22×C31—21no—
81C22×C31—41no—
82C22×C31—41no—
83C22×C31—81no—
84C22×C31—81no—
85C22×C31—81no—
86C22×C31—81no—
87C22×C31—161no—
88C22×C31#32811yescharacteristic
89C22×C31AΣL(1,𝔽16)11yescharacteristic
90C22×C31#35411yescharacteristic
91C4×C31—21no—
92C4×C31—21no—
93C4×C31—81no—
94C4×C31—82no—
95C4×C31—81no—
96C4×C31—162no—
97C2×#125C4×C3111yescharacteristic, complemented
98C2×#102—21no—
99C2×#99—21no—
100#390C22×C3111yescharacteristic
101#340—21no—
102#336C4×C3111yescharacteristic, complemented
103#324—21no—
104C2×C31—21no—
105C2×C31—21no—
106C2×C31—81no—
107C2×C31—81no—
108C2×C31#135111yescharacteristic
109C2×C31#141211yescharacteristic
110C2×C31#141411yescharacteristic
111C22×D4D4×C3111yescharacteristic
112C22×C8—21no—
113#125—42no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4D4×C3111yescharacteristic
117C2×C22⋊C4—41no—
118C2×C22⋊C4—41no—
119C2×C42C2×C4×C3111yescharacteristic
120#102—42no—
121#99—22no—
122#99—41no—
123C22⋊C8—41no—
124C31#742811yescharacteristic, direct product factor, Sylow
125C24—21no—
126C2×D4—21no—
127C2×D4—41no—
128C2×D4—41no—
129C2×D4SD16×C3111yescharacteristic
130C2×D4Q16×C3111yescharacteristic
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—41no—
134C22×C4—81no—
135C22×C4C22⋊C4×C3111yescharacteristic
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—81no—
140C4⋊C4—22no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—42no—
144C4⋊C4—42no—
145C22⋊C4—42no—
146C22⋊C4—82no—
147C22⋊C4—81no—
148C42—41no—
149C23—21no—
150C23—21no—
151C23—41no—
152C23—41no—
153C23—81no—
154C23—81no—
155C23C31×#9911yescharacteristic
156D4—41no—
157D4—41no—
158D4—81no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—82no—
170C2×C4—161no—
171C2×C4—161no—
172C2×C4C31×#10311yescharacteristic
173C2×C4C31×#10411yescharacteristic
174C8—81no—
175C8—161no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22C31×#32811yescharacteristic
186C22C31×AΣL(1,𝔽16)11yescharacteristic
187C22C31×#35411yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—82no—
192C4—81no—
193C4—162no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2C31×#135111yescharacteristic
199C2C31×#141211yescharacteristic
200C2C31×#141411yescharacteristic
subgroupG/H
center, socleC22×C31#354
commutatorC2×C42C2×C4×C31
Frattini, cosocle#390C22×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#390 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#125C4semidirect
9. C31×#336C4semidirect
48. #7428C31direct (N × H)
97. C2×#125C4×C31semidirect
102. #336C4×C31semidirect
124. C31#7428direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20252
C31×#13932
C31×#13182
#742831