Finite Group Databasebeta

← C31×#7434 #21464193

Subgroups — C31×#7434 #21464193

Order 7936.

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

normal subgroups only

This group has 224 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×#2093C211yesmaximal, characteristic
2C31×#1393C211yesmaximal, characteristic
3C31×#1318C211yesmaximal, characteristic
4C2×C31×#107—21no—
5C2×C31×#102—21no—
6C2×C31×#99—21no—
7C31×#390C2211yescharacteristic
8C31×#384C411yescharacteristic, complemented
9C31×#336C411yescharacteristic, complemented
10C31×#324—21no—
11C22×D4×C31D411yescharacteristic
12C22×C8×C31—21no—
13C2×C4⋊C4×C31—21no—
14C2×C4⋊C4×C31—41no—
15C2×C4⋊C4×C31D411yescharacteristic
16C2×C22⋊C4×C31—41no—
17C2×C22⋊C4×C31—41no—
18C2×C42×C31C2×C411yescharacteristic
19C31×#107—42no—
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—22no—
36C2×C8×C31—41no—
37C2×C8×C31—41no—
38C2×C8×C31—81no—
39C4⋊C4×C31—41no—
40C4⋊C4×C31—41no—
41C4⋊C4×C31—41no—
42C4⋊C4×C31—82no—
43C22⋊C4×C31—42no—
44C22⋊C4×C31—82no—
45C22⋊C4×C31—81no—
46C42×C31—41no—
47#7434C3111yesmaximal, characteristic, direct product factor, Sylow
48C23×C31—21no—
49C23×C31—21no—
50C23×C31—41no—
51C23×C31—41no—
52C23×C31—81no—
53C23×C31—81no—
54C23×C31#9911yescharacteristic
55D4×C31—41no—
56D4×C31—41no—
57D4×C31—81no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—22no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31—81no—
65C2×C4×C31—82no—
66C2×C4×C31—82no—
67C2×C4×C31—81no—
68C2×C4×C31—161no—
69C2×C4×C31—161no—
70C2×C4×C31#10311yescharacteristic
71C2×C4×C31#10411yescharacteristic
72C8×C31—42no—
73C8×C31—161no—
74#2093C2×C3111yescharacteristic
75#1393C2×C3111yescharacteristic
76#1318C2×C3111yescharacteristic
77C22×C31—21no—
78C22×C31—21no—
79C22×C31—41no—
80C22×C31—41no—
81C22×C31—81no—
82C22×C31—81no—
83C22×C31—81no—
84C22×C31—81no—
85C22×C31—161no—
86C22×C31#32811yescharacteristic
87C22×C31#35211yescharacteristic
88C22×C31#35311yescharacteristic
89C4×C31—21no—
90C4×C31—21no—
91C4×C31—42no—
92C4×C31—81no—
93C4×C31—162no—
94C4×C31—161no—
95C2×#107—21no—
96C2×#102—21no—
97C2×#99—21no—
98#390C22×C3111yescharacteristic
99#384C4×C3111yescharacteristic, complemented
100#336C4×C3111yescharacteristic, complemented
101#324—21no—
102C2×C31—21no—
103C2×C31—21no—
104C2×C31—81no—
105C2×C31—81no—
106C2×C31#135211yescharacteristic
107C2×C31#140711yescharacteristic
108C2×C31#140811yescharacteristic
109C22×D4D4×C3111yescharacteristic
110C22×C8—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4D4×C3111yescharacteristic
114C2×C22⋊C4—41no—
115C2×C22⋊C4—41no—
116C2×C42C2×C4×C3111yescharacteristic
117#107—42no—
118#102—42no—
119#99—22no—
120#99—41no—
121C22⋊C8—41no—
122C31#743411yescharacteristic, direct product factor, Sylow
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4SD16×C3111yescharacteristic
128C2×D4Q16×C3111yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—81no—
133C22×C4C22⋊C4×C3111yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—81no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—82no—
142C22⋊C4—42no—
143C22⋊C4—82no—
144C22⋊C4—81no—
145C42—41no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23C31×#9911yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—82no—
165C2×C4—81no—
166C2×C4—161no—
167C2×C4—161no—
168C2×C4C31×#10311yescharacteristic
169C2×C4C31×#10411yescharacteristic
170C8—42no—
171C8—161no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22C31×#32811yescharacteristic
182C22C31×#35211yescharacteristic
183C22C31×#35311yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—162no—
189C4—161no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2C31×#135211yescharacteristic
195C2C31×#140711yescharacteristic
196C2C31×#140811yescharacteristic
subgroupG/H
center, socleC22×C31#353
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
8. C31×#384C4semidirect
9. C31×#336C4semidirect
47. #7434C31direct (N × H)
99. #384C4×C31semidirect
100. #336C4×C31semidirect
122. C31#7434direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20932
C31×#13932
C31×#13182
#743431