Finite Group Databasebeta

← C31×#8548 #21465307

Subgroups — C31×#8548 #21465307

Order 7936.

1198 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C22×C31×#123C211yesmaximal, characteristic
2C31×#1783C212yesmaximal
3C31×#1463C214yesmaximal, complemented
4C23×D4×C31C2211yescharacteristic
5C24×C4×C31C411yescharacteristic
6C2×C31×#123—24no—
7C2×C31×#123—28no—
8C22×C4⋊C4×C31C2212yes—
9C22×C22⋊C4×C31C411yescharacteristic
10C22×C22⋊C4×C31C412yes—
11C2×C31×#100—24no—
12C31×#407C2214yes—
13C31×#324—28no—
14C25×C31C2×C411yescharacteristic
15C25×C31C2×C411yescharacteristic
16C22×D4×C31—24no—
17C22×D4×C31—44no—
18C22×D4×C31D414yes—
19C23×C4×C31—22no—
20C23×C4×C31—24no—
21C23×C4×C31—44no—
22C23×C4×C31C2×C412yes—
23C23×C4×C31C2×C412yes—
24C23×C4×C31C2311yescharacteristic
25C2×M16×C31—24no—
26C31×#123—232no—
27C2×C4⋊C4×C31—24no—
28C2×C4⋊C4×C31—24no—
29C2×C4⋊C4×C31D418yes—
30C2×C22⋊C4×C31—22no—
31C2×C22⋊C4×C31—24no—
32C2×C22⋊C4×C31—24no—
33C2×C22⋊C4×C31—24no—
34C2×C22⋊C4×C31—24no—
35C31×#100—48no—
36C31×C22⋊C8—28no—
37C24×C31—24no—
38C24×C31—22no—
39C24×C31—22no—
40C24×C31—42no—
41C24×C31—44no—
42C24×C31—44no—
43C24×C31C22⋊C412yes—
44C24×C31C22⋊C412yes—
45C24×C31C22×C411yescharacteristic
46C2×D4×C31—28no—
47C2×D4×C31—28no—
48C2×D4×C31—44no—
49C2×D4×C31—416no—
50C22×C4×C31—28no—
51C22×C4×C31—22no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—44no—
56C22×C4×C31—42no—
57C22×C4×C31—416no—
58C22×C4×C31—44no—
59C22×C4×C31—44no—
60C22×C4×C31—44no—
61C22×C4×C31C22⋊C414yes—
62C22×C4×C31C22⋊C414yes—
63C22×C4×C31C2×D412yes—
64C22×C4×C31C2×D414yes—
65M16×C31—48no—
66C2×C8×C31—44no—
67C4⋊C4×C31—216no—
68C22⋊C4×C31—28no—
69C22⋊C4×C31—216no—
70#8548C3111yesmaximal, characteristic, direct product factor, Sylow
71C23×C31—22no—
72C23×C31—24no—
73C23×C31—28no—
74C23×C31—22no—
75C23×C31—22no—
76C23×C31—22no—
77C23×C31—24no—
78C23×C31—44no—
79C23×C31—416no—
80C23×C31—44no—
81C23×C31—44no—
82C23×C31—44no—
83C23×C31—44no—
84C23×C31—44no—
85C23×C31—44no—
86C23×C31—88no—
87C23×C31#9914yes—
88C23×C31C2×C22⋊C411yescharacteristic
89C23×C31C2×C22⋊C412yes—
90D4×C31—416no—
91C2×C4×C31—24no—
92C2×C4×C31—24no—
93C2×C4×C31—24no—
94C2×C4×C31—28no—
95C2×C4×C31—44no—
96C2×C4×C31—44no—
97C2×C4×C31—44no—
98C2×C4×C31—44no—
99C2×C4×C31—416no—
100C2×C4×C31—44no—
101C2×C4×C31—44no—
102C2×C4×C31#12014yes—
103C8×C31—84no—
104C22×#123C2×C3111yescharacteristic
105#1783C2×C3112yes—
106#1463C2×C3114yescomplemented
107C22×C31—28no—
108C22×C31—22no—
109C22×C31—22no—
110C22×C31—22no—
111C22×C31—24no—
112C22×C31—44no—
113C22×C31—44no—
114C22×C31—416no—
115C22×C31—44no—
116C22×C31—42no—
117C22×C31—44no—
118C22×C31—84no—
119C22×C31—88no—
120C22×C31#37911yescharacteristic
121C22×C31C2×#9912yes—
122C22×C31#41314yes—
123C4×C31—24no—
124C4×C31—44no—
125C4×C31—44no—
126C23×D4C22×C3111yescharacteristic
127C24×C4C4×C3111yescharacteristic
128C2×#123—24no—
129C2×#123—28no—
130C22×C4⋊C4C22×C3112yes—
131C22×C22⋊C4C4×C3111yescharacteristic
132C22×C22⋊C4C4×C3112yes—
133C2×#100—24no—
134#407C22×C3114yes—
135#324—28no—
136C2×C31—22no—
137C2×C31—24no—
138C2×C31—44no—
139C2×C31—82no—
140C2×C31#178111yescharacteristic
141C2×C31#178512yes—
142C25C2×C4×C3111yescharacteristic
143C25C2×C4×C3111yescharacteristic
144C22×D4—24no—
145C22×D4—44no—
146C22×D4D4×C3114yes—
147C23×C4—22no—
148C23×C4—24no—
149C23×C4—44no—
150C23×C4C2×C4×C3112yes—
151C23×C4C2×C4×C3112yes—
152C23×C4C23×C3111yescharacteristic
153C2×M16—24no—
154#123—232no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4D4×C3118yes—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4—24no—
163#100—48no—
164C22⋊C8—28no—
165C31#854811yescharacteristic, direct product factor, Sylow
166C24—24no—
167C24—22no—
168C24—22no—
169C24—42no—
170C24—44no—
171C24—44no—
172C24C22⋊C4×C3112yes—
173C24C22⋊C4×C3112yes—
174C24C22×C4×C3111yescharacteristic
175C2×D4—28no—
176C2×D4—28no—
177C2×D4—44no—
178C2×D4—416no—
179C22×C4—28no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—44no—
185C22×C4—42no—
186C22×C4—416no—
187C22×C4—44no—
188C22×C4—44no—
189C22×C4—44no—
190C22×C4C22⋊C4×C3114yes—
191C22×C4C22⋊C4×C3114yes—
192C22×C4C2×D4×C3112yes—
193C22×C4C2×D4×C3114yes—
194M16—48no—
195C2×C8—44no—
196C4⋊C4—216no—
197C22⋊C4—28no—
198C22⋊C4—216no—
199C23—22no—
200C23—24no—
201C23—28no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—24no—
206C23—44no—
207C23—416no—
208C23—44no—
209C23—44no—
210C23—44no—
211C23—44no—
212C23—44no—
213C23—44no—
214C23—88no—
215C23C31×#9914yes—
216C23C2×C22⋊C4×C3111yescharacteristic
217C23C2×C22⋊C4×C3112yes—
218D4—416no—
219C2×C4—24no—
220C2×C4—28no—
221C2×C4—24no—
222C2×C4—24no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—416no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4C31×#12014yes—
231C8—84no—
232C22—28no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22—24no—
237C22—44no—
238C22—44no—
239C22—416no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—84no—
244C22—88no—
245C22C31×#37911yescharacteristic
246C22C2×C31×#9912yes—
247C22C31×#41314yes—
248C4—24no—
249C4—44no—
250C4—44no—
251C2—22no—
252C2—24no—
253C2—44no—
254C2—82no—
255C2C31×#178111yescharacteristic
256C2C31×#178512yes—
subgroupG/H
center, socleC22×C31#379
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1463C2semidirect
70. #8548C31direct (N × H)
106. #1463C2×C31semidirect
165. C31#8548direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C31×#17832
C31×#14632
#854831