Finite Group Databasebeta

← C31×#7430 #21464189

Subgroups — C31×#7430 #21464189

Order 7936.

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

normal subgroups only

This group has 236 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×#2027C211yesmaximal, characteristic
2C31×#1393C211yesmaximal, characteristic
3C31×#1270C211yesmaximal, characteristic
4C31×#544C411yescharacteristic, complemented
5C31×#418—21no—
6C2×C31×#99—21no—
7C31×#390C2211yescharacteristic
8C31×#343C411yescharacteristic, complemented
9C31×#339—21no—
10C31×#336—21no—
11C22×D4×C31D411yescharacteristic
12C2×M16×C31—21no—
13C22×C8×C31—41no—
14C31×C4⋊Q8—41no—
15C31×#125—41no—
16C31×C22⋊Q8—41no—
17C31×#117—21no—
18C2×C4⋊C4×C31C2×C411yescharacteristic
19C2×C22⋊C4×C31—41no—
20C2×C22⋊C4×C31—41no—
21C2×C42×C31D411yescharacteristic
22C31×#102—41no—
23C31×#102—41no—
24C31×#99—22no—
25C31×#99—41no—
26C24×C31—21no—
27C2×Q8×C31—41no—
28C2×D4×C31—21no—
29C2×D4×C31—41no—
30C2×D4×C31—41no—
31C2×D4×C31SD1611yescharacteristic
32C2×D4×C31Q1611yescharacteristic
33C22×C4×C31—21no—
34C22×C4×C31—21no—
35C22×C4×C31—81no—
36C22×C4×C31C22⋊C411yescharacteristic
37M16×C31—41no—
38M16×C31—41no—
39C2×C8×C31—41no—
40C2×C8×C31—42no—
41C2×C8×C31—81no—
42C2×C8×C31—81no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31—21no—
45C4⋊C4×C31—41no—
46C4⋊C4×C31—42no—
47C4⋊C4×C31—41no—
48C22⋊C4×C31—41no—
49C22⋊C4×C31—42no—
50C22⋊C4×C31—81no—
51C22⋊C4×C31—81no—
52C22⋊C4×C31—81no—
53C42×C31—41no—
54C42×C31—41no—
55#7430C3111yesmaximal, characteristic, direct product factor, Sylow
56C23×C31—21no—
57C23×C31—21no—
58C23×C31—41no—
59C23×C31—41no—
60C23×C31—81no—
61C23×C31—81no—
62C23×C31#9911yescharacteristic
63Q8×C31—161no—
64D4×C31—41no—
65D4×C31—41no—
66D4×C31—81no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31—21no—
71C2×C4×C31—41no—
72C2×C4×C31—41no—
73C2×C4×C31—41no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—81no—
77C2×C4×C31—82no—
78C2×C4×C31—161no—
79C2×C4×C31—161no—
80C2×C4×C31#10311yescharacteristic
81C2×C4×C31#10411yescharacteristic
82C8×C31—81no—
83C8×C31—82no—
84#2027C2×C3111yescharacteristic
85#1393C2×C3111yescharacteristic
86#1270C2×C3111yescharacteristic
87C22×C31—21no—
88C22×C31—21no—
89C22×C31—41no—
90C22×C31—41no—
91C22×C31—81no—
92C22×C31—81no—
93C22×C31—81no—
94C22×C31—81no—
95C22×C31—161no—
96C22×C31#32811yescharacteristic
97C22×C31AΣL(1,𝔽16)11yescharacteristic
98C22×C31#35411yescharacteristic
99C4×C31—21no—
100C4×C31—21no—
101C4×C31—41no—
102C4×C31—41no—
103C4×C31—81no—
104C4×C31—81no—
105C4×C31—81no—
106C4×C31—162no—
107#544C4×C3111yescharacteristic, complemented
108#418—21no—
109C2×#99—21no—
110#390C22×C3111yescharacteristic
111#343C4×C3111yescharacteristic, complemented
112#339—21no—
113#336—21no—
114C2×C31—21no—
115C2×C31—21no—
116C2×C31—81no—
117C2×C31—81no—
118C2×C31#135111yescharacteristic
119C2×C31#140211yescharacteristic
120C2×C31#140411yescharacteristic
121C22×D4D4×C3111yescharacteristic
122C2×M16—21no—
123C22×C8—41no—
124C4⋊Q8—41no—
125#125—41no—
126C22⋊Q8—41no—
127#117—21no—
128C2×C4⋊C4C2×C4×C3111yescharacteristic
129C2×C22⋊C4—41no—
130C2×C22⋊C4—41no—
131C2×C42D4×C3111yescharacteristic
132#102—41no—
133#102—41no—
134#99—22no—
135#99—41no—
136C31#743011yescharacteristic, direct product factor, Sylow
137C24—21no—
138C2×Q8—41no—
139C2×D4—21no—
140C2×D4—41no—
141C2×D4—41no—
142C2×D4SD16×C3111yescharacteristic
143C2×D4Q16×C3111yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—81no—
147C22×C4C22⋊C4×C3111yescharacteristic
148M16—41no—
149M16—41no—
150C2×C8—41no—
151C2×C8—42no—
152C2×C8—81no—
153C2×C8—81no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C22⋊C4—41no—
160C22⋊C4—42no—
161C22⋊C4—81no—
162C22⋊C4—81no—
163C22⋊C4—81no—
164C42—41no—
165C42—41no—
166C23—21no—
167C23—21no—
168C23—41no—
169C23—41no—
170C23—81no—
171C23—81no—
172C23C31×#9911yescharacteristic
173Q8—161no—
174D4—41no—
175D4—41no—
176D4—81no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—81no—
187C2×C4—82no—
188C2×C4—161no—
189C2×C4—161no—
190C2×C4C31×#10311yescharacteristic
191C2×C4C31×#10411yescharacteristic
192C8—81no—
193C8—82no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—161no—
203C22C31×#32811yescharacteristic
204C22C31×AΣL(1,𝔽16)11yescharacteristic
205C22C31×#35411yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—81no—
212C4—81no—
213C4—162no—
214C2—21no—
215C2—21no—
216C2—81no—
217C2—81no—
218C2C31×#135111yescharacteristic
219C2C31×#140211yescharacteristic
220C2C31×#140411yescharacteristic
subgroupG/H
center, socleC22×C31AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C31
Frattini, cosocle#390C22×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C4⋊C4 ▷ 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. C31×#544C4semidirect
8. C31×#343C4semidirect
55. #7430C31direct (N × H)
107. #544C4×C31semidirect
111. #343C4×C31semidirect
136. C31#7430direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20272
C31×#13932
C31×#12702
#743031