Finite Group Databasebeta

← C31×#7310 #21464069

Subgroups — C31×#7310 #21464069

Order 7936.

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

normal subgroups only

This group has 650 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×#1781C211yesmaximal, characteristic
2C31×#1781C212yesmaximal
3C23×D4×C31C2211yescharacteristic
4C2×C31×#99—22no—
5C2×C31×#99—22no—
6C2×C31×#99C414yescomplemented
7C31×#379—22no—
8C31×#379C412yescomplemented
9C25×C31C2×C411yescharacteristic
10C25×C31D411yescharacteristic
11C22×D4×C31—44no—
12C22×D4×C31—42no—
13C22×D4×C31C2×C412yes—
14C22×D4×C31D412yes—
15C23×C4×C31Q811yescharacteristic
16C2×C22⋊C4×C31—22no—
17C2×C22⋊C4×C31—24no—
18C2×C22⋊C4×C31—44no—
19C2×C22⋊C4×C31—42no—
20C31×#99—44no—
21C31×#99—44no—
22C31×#99—44no—
23C24×C31—22no—
24C24×C31—24no—
25C24×C31—42no—
26C24×C31—41no—
27C24×C31—82no—
28C24×C31—82no—
29C24×C31C4211yescharacteristic
30C24×C31C22⋊C412yes—
31C24×C31C22⋊C411yescharacteristic
32C24×C31C4⋊C411yescharacteristic
33C2×D4×C31—24no—
34C2×D4×C31—24no—
35C2×D4×C31—24no—
36C2×D4×C31—42no—
37C2×D4×C31—42no—
38C2×D4×C31—42no—
39C2×D4×C31—416no—
40C22×C4×C31—42no—
41C22×C4×C31—41no—
42C22×C4×C31—44no—
43C22×C4×C31—42no—
44C22×C4×C31C4⋊C412yes—
45C22⋊C4×C31—44no—
46C22⋊C4×C31—44no—
47C22⋊C4×C31—44no—
48C22⋊C4×C31—88no—
49C22⋊C4×C31—84no—
50#7310C3111yesmaximal, characteristic, direct product factor, Sylow
51C23×C31—22no—
52C23×C31—21no—
53C23×C31—22no—
54C23×C31—22no—
55C23×C31—22no—
56C23×C31—21no—
57C23×C31—22no—
58C23×C31—42no—
59C23×C31—44no—
60C23×C31—44no—
61C23×C31—48no—
62C23×C31—44no—
63C23×C31—82no—
64C23×C31—84no—
65C23×C31—82no—
66C23×C31—81no—
67C23×C31—81no—
68C23×C31—82no—
69C23×C31—84no—
70C23×C31—82no—
71C23×C31—84no—
72C23×C31#9511yescharacteristic
73C23×C31#9914yes—
74C23×C31#9912yes—
75D4×C31—48no—
76D4×C31—48no—
77C2×C4×C31—22no—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—44no—
81C2×C4×C31—82no—
82C2×C4×C31—84no—
83C2×C4×C31—84no—
84C2×C4×C31—88no—
85#1781C2×C3112yes—
86#1781C2×C3111yescharacteristic
87C22×C31—22no—
88C22×C31—24no—
89C22×C31—24no—
90C22×C31—22no—
91C22×C31—41no—
92C22×C31—42no—
93C22×C31—44no—
94C22×C31—44no—
95C22×C31—41no—
96C22×C31—42no—
97C22×C31—42no—
98C22×C31—41no—
99C22×C31—41no—
100C22×C31—82no—
101C22×C31—82no—
102C22×C31—82no—
103C22×C31—88no—
104C22×C31—88no—
105C22×C31#34212yes—
106C22×C31#34211yescharacteristic
107C4×C31—42no—
108C4×C31—164no—
109C4×C31—162no—
110C23×D4C22×C3111yescharacteristic
111C2×#99—22no—
112C2×#99—22no—
113C2×#99C4×C3114yescomplemented
114#379—22no—
115#379C4×C3112yescomplemented
116C2×C31—21no—
117C2×C31—22no—
118C2×C31—44no—
119C2×C31—42no—
120C2×C31—42no—
121C2×C31—81no—
122C2×C31#130411yescharacteristic
123C25C2×C4×C3111yescharacteristic
124C25D4×C3111yescharacteristic
125C22×D4—44no—
126C22×D4—42no—
127C22×D4C2×C4×C3112yes—
128C22×D4D4×C3112yes—
129C23×C4Q8×C3111yescharacteristic
130C2×C22⋊C4—24no—
131C2×C22⋊C4—22no—
132C2×C22⋊C4—44no—
133C2×C22⋊C4—42no—
134#99—44no—
135#99—44no—
136#99—44no—
137C31#731011yescharacteristic, direct product factor, Sylow
138C24—22no—
139C24—24no—
140C24—42no—
141C24—41no—
142C24—82no—
143C24—82no—
144C24C42×C3111yescharacteristic
145C24C22⋊C4×C3112yes—
146C24C22⋊C4×C3111yescharacteristic
147C24C4⋊C4×C3111yescharacteristic
148C2×D4—24no—
149C2×D4—24no—
150C2×D4—24no—
151C2×D4—42no—
152C2×D4—42no—
153C2×D4—42no—
154C2×D4—416no—
155C22×C4—42no—
156C22×C4—41no—
157C22×C4—44no—
158C22×C4—42no—
159C22×C4C4⋊C4×C3112yes—
160C22⋊C4—44no—
161C22⋊C4—44no—
162C22⋊C4—44no—
163C22⋊C4—88no—
164C22⋊C4—84no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23—22no—
172C23—42no—
173C23—44no—
174C23—44no—
175C23—48no—
176C23—44no—
177C23—82no—
178C23—84no—
179C23—82no—
180C23—81no—
181C23—81no—
182C23—82no—
183C23—84no—
184C23—82no—
185C23—84no—
186C23C31×#9511yescharacteristic
187C23C31×#9914yes—
188C23C31×#9912yes—
189D4—48no—
190D4—48no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—82no—
196C2×C4—84no—
197C2×C4—84no—
198C2×C4—88no—
199C22—22no—
200C22—24no—
201C22—24no—
202C22—22no—
203C22—41no—
204C22—42no—
205C22—44no—
206C22—44no—
207C22—41no—
208C22—42no—
209C22—42no—
210C22—41no—
211C22—41no—
212C22—82no—
213C22—82no—
214C22—82no—
215C22—88no—
216C22—88no—
217C22C31×#34212yes—
218C22C31×#34211yescharacteristic
219C4—42no—
220C4—164no—
221C4—162no—
222C2—21no—
223C2—22no—
224C2—44no—
225C2—42no—
226C2—42no—
227C2—81no—
228C2C31×#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
6. C2×C31×#99C4semidirect
8. C31×#379C4semidirect
50. #7310C31direct (N × H)
113. C2×#99C4×C31semidirect
115. #379C4×C31semidirect
137. C31#7310direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17812
#731031