Finite Group Databasebeta

← C31×#7314 #21464073

Subgroups — C31×#7314 #21464073

Order 7936.

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

normal subgroups only

This group has 620 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×#1783C211yesmaximal, characteristic
2C31×#1781C212yesmaximal
3C23×D4×C31C2211yescharacteristic
4C2×C31×#100—22no—
5C2×C31×#99—22no—
6C2×C31×#99C414yescomplemented
7C31×#407C412yescomplemented
8C31×#379—22no—
9C25×C31D411yescharacteristic
10C25×C31Q811yescharacteristic
11C22×D4×C31—42no—
12C22×D4×C31—44no—
13C22×D4×C31C2×C412yes—
14C22×D4×C31D412yes—
15C23×C4×C31C2×C411yescharacteristic
16C2×M16×C31—22no—
17C2×C22⋊C4×C31—24no—
18C2×C22⋊C4×C31—44no—
19C31×#100—44no—
20C31×#99—44no—
21C31×#99—44no—
22C31×C22⋊C8—42no—
23C24×C31—24no—
24C24×C31—41no—
25C24×C31—41no—
26C24×C31—42no—
27C24×C31—82no—
28C24×C31—82no—
29C24×C31C22⋊C412yes—
30C24×C31C4⋊C411yescharacteristic
31C24×C31C4⋊C412yes—
32C2×D4×C31—24no—
33C2×D4×C31—24no—
34C2×D4×C31—24no—
35C2×D4×C31—42no—
36C2×D4×C31—42no—
37C2×D4×C31—42no—
38C2×D4×C31—416no—
39C22×C4×C31—22no—
40C22×C4×C31—42no—
41C22×C4×C31—44no—
42C22×C4×C31C4211yescharacteristic
43C22×C4×C31C22⋊C411yescharacteristic
44M16×C31—44no—
45C2×C8×C31—42no—
46C22⋊C4×C31—44no—
47C22⋊C4×C31—44no—
48C22⋊C4×C31—88no—
49#7314C3111yesmaximal, characteristic, direct product factor, Sylow
50C23×C31—21no—
51C23×C31—22no—
52C23×C31—22no—
53C23×C31—22no—
54C23×C31—22no—
55C23×C31—22no—
56C23×C31—22no—
57C23×C31—42no—
58C23×C31—44no—
59C23×C31—48no—
60C23×C31—44no—
61C23×C31—84no—
62C23×C31—82no—
63C23×C31—82no—
64C23×C31—82no—
65C23×C31—84no—
66C23×C31—82no—
67C23×C31—82no—
68C23×C31—84no—
69C23×C31—82no—
70C23×C31#9511yescharacteristic
71C23×C31#9914yes—
72D4×C31—48no—
73D4×C31—48no—
74C2×C4×C31—22no—
75C2×C4×C31—21no—
76C2×C4×C31—22no—
77C2×C4×C31—44no—
78C2×C4×C31—84no—
79C2×C4×C31—88no—
80C2×C4×C31#9912yes—
81C8×C31—82no—
82#1783C2×C3111yescharacteristic
83#1781C2×C3112yes—
84C22×C31—24no—
85C22×C31—22no—
86C22×C31—24no—
87C22×C31—41no—
88C22×C31—44no—
89C22×C31—44no—
90C22×C31—42no—
91C22×C31—41no—
92C22×C31—41no—
93C22×C31—42no—
94C22×C31—82no—
95C22×C31—82no—
96C22×C31—82no—
97C22×C31—82no—
98C22×C31—88no—
99C22×C31—88no—
100C22×C31#34212yes—
101C22×C31#34211yescharacteristic
102C4×C31—22no—
103C4×C31—41no—
104C4×C31—164no—
105C23×D4C22×C3111yescharacteristic
106C2×#100—22no—
107C2×#99—22no—
108C2×#99C4×C3114yescomplemented
109#407C4×C3112yescomplemented
110#379—22no—
111C2×C31—22no—
112C2×C31—21no—
113C2×C31—44no—
114C2×C31—42no—
115C2×C31—82no—
116C2×C31#130411yescharacteristic
117C25D4×C3111yescharacteristic
118C25Q8×C3111yescharacteristic
119C22×D4—42no—
120C22×D4—44no—
121C22×D4C2×C4×C3112yes—
122C22×D4D4×C3112yes—
123C23×C4C2×C4×C3111yescharacteristic
124C2×M16—22no—
125C2×C22⋊C4—24no—
126C2×C22⋊C4—44no—
127#100—44no—
128#99—44no—
129#99—44no—
130C22⋊C8—42no—
131C31#731411yescharacteristic, direct product factor, Sylow
132C24—24no—
133C24—41no—
134C24—41no—
135C24—42no—
136C24—82no—
137C24—82no—
138C24C22⋊C4×C3112yes—
139C24C4⋊C4×C3111yescharacteristic
140C24C4⋊C4×C3112yes—
141C2×D4—24no—
142C2×D4—24no—
143C2×D4—24no—
144C2×D4—42no—
145C2×D4—42no—
146C2×D4—42no—
147C2×D4—416no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—44no—
151C22×C4C42×C3111yescharacteristic
152C22×C4C22⋊C4×C3111yescharacteristic
153M16—44no—
154C2×C8—42no—
155C22⋊C4—44no—
156C22⋊C4—44no—
157C22⋊C4—88no—
158C23—21no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—22no—
163C23—22no—
164C23—22no—
165C23—42no—
166C23—44no—
167C23—48no—
168C23—44no—
169C23—84no—
170C23—82no—
171C23—82no—
172C23—82no—
173C23—84no—
174C23—82no—
175C23—82no—
176C23—84no—
177C23—82no—
178C23C31×#9511yescharacteristic
179C23C31×#9914yes—
180D4—48no—
181D4—48no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—44no—
186C2×C4—84no—
187C2×C4—88no—
188C2×C4C31×#9912yes—
189C8—82no—
190C22—24no—
191C22—22no—
192C22—24no—
193C22—41no—
194C22—44no—
195C22—44no—
196C22—42no—
197C22—41no—
198C22—41no—
199C22—42no—
200C22—82no—
201C22—82no—
202C22—82no—
203C22—82no—
204C22—88no—
205C22—88no—
206C22C31×#34212yes—
207C22C31×#34211yescharacteristic
208C4—22no—
209C4—41no—
210C4—164no—
211C2—22no—
212C2—21no—
213C2—44no—
214C2—42no—
215C2—82no—
216C2C31×#130411yescharacteristic
subgroupG/H
center, socleC2×C31#1304
commutatorC22×C4C42×C31
Frattini, cosocleC23×D4C22×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×C4 ▷ 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
7. C31×#407C4semidirect
49. #7314C31direct (N × H)
108. C2×#99C4×C31semidirect
109. #407C4×C31semidirect
131. C31#7314direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17832
C31×#17812
#731431