Finite Group Databasebeta

← C31×#8700 #21465459

Subgroups — C31×#8700 #21465459

Order 7936.

898 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 190 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
1C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
2C31×#1779C212yesmaximal
3C31×#1280C214yesmaximal, complemented
4C24×C4×C31C2211yescharacteristic
5C22×C22⋊C4×C31C411yescharacteristic
6C22×C22⋊C4×C31C411yescharacteristic
7C22×C42×C31C412yes—
8C2×C31×C22⋊C8—24no—
9C2×C31×C22⋊C8C2214yes—
10C4×C22⋊C4×C31—24no—
11C2×C31×#95C2212yes—
12C25×C31C2×C411yescharacteristic
13C23×C4×C31—24no—
14C23×C4×C31—44no—
15C23×C4×C31C2×C411yescharacteristic
16C23×C4×C31C2×C412yes—
17C23×C4×C31C2×C412yes—
18C23×C4×C31D414yes—
19C23×C4×C31C2311yescharacteristic
20C22×C8×C31—24no—
21C2×C22⋊C4×C31—22no—
22C2×C22⋊C4×C31—22no—
23C2×C22⋊C4×C31—22no—
24C2×C22⋊C4×C31—24no—
25C2×C22⋊C4×C31C814yescomplemented
26C2×C42×C31—22no—
27C2×C42×C31—22no—
28C2×C42×C31—44no—
29C31×C22⋊C8—28no—
30C31×C22⋊C8—48no—
31C31×#95—24no—
32C24×C31—22no—
33C24×C31—22no—
34C24×C31—42no—
35C24×C31—42no—
36C24×C31C22⋊C412yes—
37C24×C31C2×C812yes—
38C24×C31M1612yes—
39C24×C31C22×C411yescharacteristic
40C22×C4×C31—22no—
41C22×C4×C31—24no—
42C22×C4×C31—22no—
43C22×C4×C31—22no—
44C22×C4×C31—22no—
45C22×C4×C31—22no—
46C22×C4×C31—28no—
47C22×C4×C31—28no—
48C22×C4×C31—44no—
49C22×C4×C31—42no—
50C22×C4×C31—416no—
51C22×C4×C31—42no—
52C22×C4×C31—42no—
53C22×C4×C31—42no—
54C22×C4×C31—42no—
55C22×C4×C31C22⋊C412yes—
56C22×C4×C31C2×C814yes—
57C22×C4×C31M1614yes—
58C22×C4×C31C2×D412yes—
59C22×C4×C31#4114yes—
60C2×C8×C31—48no—
61C2×C8×C31—44no—
62C22⋊C4×C31—28no—
63C22⋊C4×C31—28no—
64C42×C31—44no—
65C42×C31—44no—
66#8700C3111yesmaximal, characteristic, direct product factor, Sylow
67C23×C31—22no—
68C23×C31—22no—
69C23×C31—22no—
70C23×C31—22no—
71C23×C31—24no—
72C23×C31—24no—
73C23×C31—24no—
74C23×C31—24no—
75C23×C31—44no—
76C23×C31—44no—
77C23×C31—44no—
78C23×C31—44no—
79C23×C31—44no—
80C23×C31—44no—
81C23×C31C22⋊C814yes—
82C23×C31C2×C22⋊C411yescharacteristic
83C23×C31#11712yes—
84C23×C31C22×C811yescharacteristic
85C23×C31C2×M1611yescharacteristic
86C23×C31C2×M1612yes—
87C2×C4×C31—28no—
88C2×C4×C31—22no—
89C2×C4×C31—22no—
90C2×C4×C31—24no—
91C2×C4×C31—24no—
92C2×C4×C31—24no—
93C2×C4×C31—44no—
94C2×C4×C31—416no—
95C2×C4×C31—44no—
96C2×C4×C31—44no—
97C2×C4×C31—42no—
98C2×C4×C31—42no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—44no—
102C2×C4×C31—44no—
103C2×C4×C31#9914yes—
104C2×C4×C31#12314yes—
105C8×C31—84no—
106C2×C4×C22⋊C4C2×C3111yescharacteristic
107#1779C2×C3112yes—
108#1280C2×C3114yescomplemented
109C22×C31—22no—
110C22×C31—22no—
111C22×C31—22no—
112C22×C31—22no—
113C22×C31—22no—
114C22×C31—22no—
115C22×C31—24no—
116C22×C31—28no—
117C22×C31—48no—
118C22×C31—48no—
119C22×C31—42no—
120C22×C31—42no—
121C22×C31—44no—
122C22×C31#38111yescharacteristic
123C22×C31C2×C22⋊C811yescharacteristic
124C22×C31#40711yescharacteristic
125C22×C31C2×#9912yes—
126C22×C31#41312yes—
127C22×C31#43112yes—
128C22×C31#43212yes—
129C4×C31—24no—
130C4×C31—24no—
131C4×C31—44no—
132C4×C31—44no—
133C24×C4C22×C3111yescharacteristic
134C22×C22⋊C4C4×C3111yescharacteristic
135C22×C22⋊C4C4×C3111yescharacteristic
136C22×C42C4×C3112yes—
137C2×C22⋊C8—24no—
138C2×C22⋊C8C22×C3114yes—
139C4×C22⋊C4—24no—
140C2×#95C22×C3112yes—
141C2×C31—22no—
142C2×C31—22no—
143C2×C31—44no—
144C2×C31#145912yes—
145C2×C31#146512yes—
146C2×C31#181711yescharacteristic
147C2×C31#181911yescharacteristic
148C2×C31#182211yescharacteristic
149C25C2×C4×C3111yescharacteristic
150C23×C4—24no—
151C23×C4—44no—
152C23×C4C2×C4×C3111yescharacteristic
153C23×C4C2×C4×C3112yes—
154C23×C4C2×C4×C3112yes—
155C23×C4D4×C3114yes—
156C23×C4C23×C3111yescharacteristic
157C22×C8—24no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4C8×C3114yescomplemented
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—44no—
166C22⋊C8—28no—
167C22⋊C8—48no—
168#95—24no—
169C31#870011yescharacteristic, direct product factor, Sylow
170C24—22no—
171C24—22no—
172C24—42no—
173C24—42no—
174C24C22⋊C4×C3112yes—
175C24C2×C8×C3112yes—
176C24M16×C3112yes—
177C24C22×C4×C3111yescharacteristic
178C22×C4—22no—
179C22×C4—24no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—28no—
185C22×C4—28no—
186C22×C4—44no—
187C22×C4—42no—
188C22×C4—416no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4C22⋊C4×C3112yes—
194C22×C4C2×C8×C3114yes—
195C22×C4M16×C3114yes—
196C22×C4C2×D4×C3112yes—
197C22×C4#41×C3114yes—
198C2×C8—48no—
199C2×C8—44no—
200C22⋊C4—28no—
201C22⋊C4—28no—
202C42—44no—
203C42—44no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—24no—
208C23—24no—
209C23—24no—
210C23—24no—
211C23—22no—
212C23—44no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—44no—
217C23—44no—
218C23C31×C22⋊C814yes—
219C23C2×C22⋊C4×C3111yescharacteristic
220C23C31×#11712yes—
221C23C22×C8×C3111yescharacteristic
222C23C2×M16×C3111yescharacteristic
223C23C2×M16×C3112yes—
224C2×C4—28no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—44no—
231C2×C4—416no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—44no—
240C2×C4C31×#9914yes—
241C2×C4C31×#12314yes—
242C8—84no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—24no—
250C22—28no—
251C22—48no—
252C22—48no—
253C22—42no—
254C22—42no—
255C22—44no—
256C22C31×#38111yescharacteristic
257C22C2×C31×C22⋊C811yescharacteristic
258C22C31×#40711yescharacteristic
259C22C2×C31×#9912yes—
260C22C31×#41312yes—
261C22C31×#43112yes—
262C22C31×#43212yes—
263C4—24no—
264C4—24no—
265C4—44no—
266C4—44no—
267C2—22no—
268C2—22no—
269C2—44no—
270C2C31×#145912yes—
271C2C31×#146512yes—
272C2C31×#181711yescharacteristic
273C2C31×#181911yescharacteristic
274C2C31×#182211yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C22×C8×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1280C2semidirect
25. C2×C22⋊C4×C31C8semidirect
66. #8700C31direct (N × H)
108. #1280C2×C31semidirect
162. C2×C22⋊C4C8×C31semidirect
169. C31#8700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C312
C31×#17792
C31×#12802
#870031