Finite Group Databasebeta

← C31×#8102 #21464861

Subgroups — C31×#8102 #21464861

Order 7936.

994 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2280C212yesmaximal
2C31×#2280C211yesmaximal, characteristic
3C31×#1304C214yesmaximal
4C24×C4×C31C2211yescharacteristic
5C2×C31×#117—22no—
6C2×C31×#117C412yescomplemented
7C31×#381—22no—
8C31×#381C412yescomplemented
9C31×#380—22no—
10C31×#380—22no—
11C31×#380C414yescomplemented
12C31×#379C2214yes—
13C31×#379C2212yes—
14C4×C22⋊C4×C31—22no—
15C4×C22⋊C4×C31—22no—
16C4×C22⋊C4×C31C414yescomplemented
17C25×C31C2311yescharacteristic
18C23×C4×C31—44no—
19C23×C4×C31C2×C411yescharacteristic
20C23×C4×C31C2×C412yes—
21C23×C4×C31C2×C412yes—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D412yes—
24C23×C4×C31D412yes—
25C23×C4×C31D412yes—
26C23×C4×C31Q812yes—
27C31×#117—48no—
28C31×#117—44no—
29C2×C4⋊C4×C31—24no—
30C2×C4⋊C4×C31—22no—
31C2×C22⋊C4×C31—24no—
32C2×C22⋊C4×C31—24no—
33C2×C22⋊C4×C31—24no—
34C2×C22⋊C4×C31C2×C414yes—
35C2×C22⋊C4×C31C2×C418yes—
36C2×C42×C31—24no—
37C2×C42×C31—22no—
38C31×#95—24no—
39C31×#95—24no—
40C31×#95—24no—
41C24×C31—42no—
42C24×C31—44no—
43C24×C31C22×C411yescharacteristic
44C24×C31C22×C412yes—
45C24×C31C2×D412yes—
46C24×C31C2×D411yescharacteristic
47C24×C31C2×Q811yescharacteristic
48C22×C4×C31—24no—
49C22×C4×C31—28no—
50C22×C4×C31—28no—
51C22×C4×C31—24no—
52C22×C4×C31—44no—
53C22×C4×C31—44no—
54C22×C4×C31—44no—
55C22×C4×C31—44no—
56C22×C4×C31—42no—
57C22×C4×C31—44no—
58C22×C4×C31C4212yes—
59C22×C4×C31C4211yescharacteristic
60C22×C4×C31C4211yescharacteristic
61C22×C4×C31C22⋊C412yes—
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22⋊C412yes—
64C22×C4×C31C22⋊C412yes—
65C22×C4×C31C22⋊C412yes—
66C22×C4×C31C22⋊C412yes—
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C4⋊C412yes—
69C22×C4×C31C4⋊C412yes—
70C22×C4×C31C4⋊C412yes—
71C22×C4×C31C4⋊C412yes—
72C22×C4×C31C4⋊C412yes—
73C22×C4×C31C4⋊C412yes—
74C4⋊C4×C31—48no—
75C4⋊C4×C31—44no—
76C22⋊C4×C31—48no—
77C22⋊C4×C31—48no—
78C22⋊C4×C31—48no—
79C22⋊C4×C31—48no—
80C22⋊C4×C31—44no—
81C42×C31—44no—
82C42×C31—48no—
83#8102C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31—22no—
85C23×C31—24no—
86C23×C31—24no—
87C23×C31—24no—
88C23×C31—24no—
89C23×C31—42no—
90C23×C31—41no—
91C23×C31—41no—
92C23×C31—42no—
93C23×C31—42no—
94C23×C31—42no—
95C23×C31—42no—
96C23×C31—416no—
97C23×C31C2×C4211yescharacteristic
98C23×C31C2×C22⋊C411yescharacteristic
99C23×C31C2×C22⋊C412yes—
100C23×C31C2×C4⋊C411yescharacteristic
101C23×C31C2×C4⋊C412yes—
102C2×C4×C31—22no—
103C2×C4×C31—24no—
104C2×C4×C31—24no—
105C2×C4×C31—24no—
106C2×C4×C31—24no—
107C2×C4×C31—24no—
108C2×C4×C31—24no—
109C2×C4×C31—24no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—42no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—48no—
118C2×C4×C31—48no—
119C2×C4×C31—48no—
120C2×C4×C31—44no—
121C2×C4×C31—48no—
122C2×C4×C31#9512yes—
123C2×C4×C31#9512yes—
124C2×C4×C31#9512yes—
125C2×C4×C31#9512yes—
126C2×C4×C31#9914yes—
127#2280C2×C3112yes—
128#2280C2×C3111yescharacteristic
129#1304C2×C3114yes—
130C22×C31—22no—
131C22×C31—22no—
132C22×C31—22no—
133C22×C31—21no—
134C22×C31—21no—
135C22×C31—22no—
136C22×C31—22no—
137C22×C31—22no—
138C22×C31—22no—
139C22×C31—22no—
140C22×C31—48no—
141C22×C31—44no—
142C22×C31—44no—
143C22×C31—48no—
144C22×C31—44no—
145C22×C31C2×#9511yescharacteristic
146C22×C31C2×#9912yes—
147C22×C31#41014yes—
148C4×C31—22no—
149C4×C31—22no—
150C4×C31—22no—
151C4×C31—84no—
152C4×C31—88no—
153C4×C31#34214yes—
154C24×C4C22×C3111yescharacteristic
155C2×#117—22no—
156C2×#117C4×C3112yescomplemented
157#381—22no—
158#381C4×C3112yescomplemented
159#380—22no—
160#380—22no—
161#380C4×C3114yescomplemented
162#379C22×C3114yes—
163#379C22×C3112yes—
164C4×C22⋊C4—22no—
165C4×C22⋊C4—22no—
166C4×C22⋊C4C4×C3114yescomplemented
167C2×C31—22no—
168C2×C31—24no—
169C2×C31—41no—
170C2×C31—41no—
171C2×C31—42no—
172C2×C31C2×#34211yescharacteristic
173C2×C31#174012yes—
174C25C23×C3111yescharacteristic
175C23×C4—44no—
176C23×C4C2×C4×C3111yescharacteristic
177C23×C4C2×C4×C3112yes—
178C23×C4C2×C4×C3112yes—
179C23×C4C2×C4×C3111yescharacteristic
180C23×C4D4×C3112yes—
181C23×C4D4×C3112yes—
182C23×C4D4×C3112yes—
183C23×C4Q8×C3112yes—
184#117—48no—
185#117—44no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—22no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—24no—
191C2×C22⋊C4C2×C4×C3114yes—
192C2×C22⋊C4C2×C4×C3118yes—
193C2×C42—24no—
194C2×C42—22no—
195#95—24no—
196#95—24no—
197#95—24no—
198C31#810211yescharacteristic, direct product factor, Sylow
199C24—42no—
200C24—44no—
201C24C22×C4×C3111yescharacteristic
202C24C22×C4×C3112yes—
203C24C2×D4×C3112yes—
204C24C2×D4×C3111yescharacteristic
205C24C2×Q8×C3111yescharacteristic
206C22×C4—24no—
207C22×C4—28no—
208C22×C4—28no—
209C22×C4—24no—
210C22×C4—44no—
211C22×C4—44no—
212C22×C4—44no—
213C22×C4—44no—
214C22×C4—42no—
215C22×C4—44no—
216C22×C4C42×C3112yes—
217C22×C4C42×C3111yescharacteristic
218C22×C4C42×C3111yescharacteristic
219C22×C4C22⋊C4×C3112yes—
220C22×C4C22⋊C4×C3111yescharacteristic
221C22×C4C22⋊C4×C3112yes—
222C22×C4C22⋊C4×C3112yes—
223C22×C4C22⋊C4×C3112yes—
224C22×C4C22⋊C4×C3112yes—
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C4⋊C4×C3112yes—
227C22×C4C4⋊C4×C3112yes—
228C22×C4C4⋊C4×C3112yes—
229C22×C4C4⋊C4×C3112yes—
230C22×C4C4⋊C4×C3112yes—
231C22×C4C4⋊C4×C3112yes—
232C4⋊C4—48no—
233C4⋊C4—44no—
234C22⋊C4—48no—
235C22⋊C4—48no—
236C22⋊C4—48no—
237C22⋊C4—48no—
238C22⋊C4—44no—
239C42—44no—
240C42—48no—
241C23—22no—
242C23—24no—
243C23—24no—
244C23—24no—
245C23—24no—
246C23—42no—
247C23—41no—
248C23—41no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—416no—
254C23C2×C42×C3111yescharacteristic
255C23C2×C22⋊C4×C3111yescharacteristic
256C23C2×C22⋊C4×C3112yes—
257C23C2×C4⋊C4×C3111yescharacteristic
258C23C2×C4⋊C4×C3112yes—
259C2×C4—22no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—48no—
275C2×C4—48no—
276C2×C4—48no—
277C2×C4—44no—
278C2×C4—48no—
279C2×C4C31×#9512yes—
280C2×C4C31×#9512yes—
281C2×C4C31×#9512yes—
282C2×C4C31×#9512yes—
283C2×C4C31×#9914yes—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—48no—
295C22—44no—
296C22—44no—
297C22—48no—
298C22—44no—
299C22C2×C31×#9511yescharacteristic
300C22C2×C31×#9912yes—
301C22C31×#41014yes—
302C4—22no—
303C4—22no—
304C4—22no—
305C4—84no—
306C4—88no—
307C4C31×#34214yes—
308C2—22no—
309C2—24no—
310C2—41no—
311C2—41no—
312C2—42no—
313C2C2×C31×#34211yescharacteristic
314C2C31×#174012yes—
subgroupG/H
center, socleC22×C31C2×#95
commutatorC23C2×C42×C31
Frattini, cosocleC25C23×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C31×#117C4semidirect
8. C31×#381C4semidirect
11. C31×#380C4semidirect
16. C4×C22⋊C4×C31C4semidirect
83. #8102C31direct (N × H)
156. C2×#117C4×C31semidirect
158. #381C4×C31semidirect
161. #380C4×C31semidirect
166. C4×C22⋊C4C4×C31semidirect
198. C31#8102direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22802
C31×#13042
#810231