Finite Group Databasebeta

← C31×#7581 #21464340

Subgroups — C31×#7581 #21464340

Order 7936.

424 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2295C211yesmaximal, characteristic
2C31×#1839C211yesmaximal, characteristic
3C31×#1744C211yesmaximal, characteristic
4C31×#1272C212yesmaximal
5C31×#1271C212yesmaximal
6C2×C4×Q8×C31C411yescharacteristic
7C2×C4×C8×C31—21no—
8C31×#391C411yescharacteristic
9C31×#391C2211yescharacteristic
10C31×#389C411yescharacteristic
11C31×#389C2211yescharacteristic
12C31×#387—21no—
13C31×#387—21no—
14C4×C4⋊C4×C31—21no—
15C4×C4⋊C4×C31C411yescharacteristic
16C31×#376—21no—
17C43×C31C2211yescharacteristic
18C31×#336—21no—
19C31×#336—21no—
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×C8×C31—22no—
25C22×C8×C31—22no—
26C4×Q8×C31—22no—
27C4×Q8×C31C814yescomplemented
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C42×C31—21no—
35C2×C42×C31—21no—
36C2×C42×C31C2×C411yescharacteristic
37C2×C42×C31C2×C411yescharacteristic
38C2×C42×C31D411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31C2311yescharacteristic
43C4×C8×C31—24no—
44C31×#95—21no—
45C31×#95—21no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C2×Q8×C31—21no—
52C2×Q8×C31—41no—
53C2×Q8×C31—41no—
54C2×Q8×C31C2×C812yes—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22×C411yescharacteristic
64C22×C4×C31C2×D411yescharacteristic
65C22×C4×C31C2×D411yescharacteristic
66C2×C8×C31—24no—
67C2×C8×C31—42no—
68C2×C8×C31—42no—
69C2×C8×C31—42no—
70C2×C8×C31—42no—
71C2×C8×C31—42no—
72C4⋊C4×C31—24no—
73C4⋊C4×C31—21no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—42no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31C2×C812yes—
79C42×C31—24no—
80C42×C31—22no—
81C42×C31—22no—
82C42×C31—22no—
83C42×C31—41no—
84C42×C31—41no—
85C42×C31—41no—
86C42×C31—42no—
87C42×C31C2×C812yes—
88C42×C31M1612yes—
89#7581C3111yesmaximal, characteristic, direct product factor, Sylow
90C23×C31C2×C22⋊C411yescharacteristic
91Q8×C31—42no—
92Q8×C31—42no—
93C2×C4×C31—21no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—22no—
106C2×C4×C31—22no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31C22⋊C812yes—
121C2×C4×C31C22⋊C812yes—
122C2×C4×C31#10412yes—
123C2×C4×C31C22×C811yescharacteristic
124C2×C4×C31C2×M1611yescharacteristic
125C2×C4×C31#13512yes—
126C2×C4×C31#13712yes—
127C8×C31—44no—
128C8×C31—82no—
129#2295C2×C3111yescharacteristic
130#1839C2×C3111yescharacteristic
131#1744C2×C3111yescharacteristic
132#1272C2×C3112yes—
133#1271C2×C3112yes—
134C22×C31C2×C22⋊C811yescharacteristic
135C22×C31#41011yescharacteristic
136C22×C31#41311yescharacteristic
137C22×C31#41611yescharacteristic
138C22×C31#41911yescharacteristic
139C22×C31C2×#10411yescharacteristic
140C22×C31#42111yescharacteristic
141C4×C31—21no—
142C4×C31—21no—
143C4×C31—22no—
144C4×C31—22no—
145C4×C31—22no—
146C4×C31—22no—
147C4×C31—22no—
148C4×C31—41no—
149C4×C31—42no—
150C4×C31—42no—
151C4×C31—81no—
152C4×C31—81no—
153C2×C4×Q8C4×C3111yescharacteristic
154C2×C4×C8—21no—
155#391C4×C3111yescharacteristic
156#391C22×C3111yescharacteristic
157#389C4×C3111yescharacteristic
158#389C22×C3111yescharacteristic
159#387—21no—
160#387—21no—
161C4×C4⋊C4—21no—
162C4×C4⋊C4C4×C3111yescharacteristic
163#376—21no—
164C43C22×C3111yescharacteristic
165#336—21no—
166#336—21no—
167#336—21no—
168#336C22×C3112yes—
169#336C22×C3112yes—
170C2×C31#145811yescharacteristic
171C2×C31#147611yescharacteristic
172C2×C31#147911yescharacteristic
173C2×C31#150611yescharacteristic
174C2×C31#152111yescharacteristic
175C2×C31#153211yescharacteristic
176C2×C31#155411yescharacteristic
177C22×Q8C2×C4×C3111yescharacteristic
178C22×C8—22no—
179C22×C8—22no—
180C4×Q8—22no—
181C4×Q8C8×C3114yescomplemented
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×C4×C3111yescharacteristic
186C2×C4⋊C4C2×C4×C3111yescharacteristic
187C2×C4⋊C4C2×C4×C3111yescharacteristic
188C2×C42—21no—
189C2×C42—21no—
190C2×C42C2×C4×C3111yescharacteristic
191C2×C42C2×C4×C3111yescharacteristic
192C2×C42D4×C3111yescharacteristic
193C2×C42D4×C3111yescharacteristic
194C2×C42D4×C3111yescharacteristic
195C2×C42D4×C3111yescharacteristic
196C2×C42C23×C3111yescharacteristic
197C4×C8—24no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205C31#758111yescharacteristic, direct product factor, Sylow
206C2×Q8—21no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8C2×C8×C3112yes—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C22⋊C4×C3111yescharacteristic
215C22×C4C22⋊C4×C3111yescharacteristic
216C22×C4C22⋊C4×C3111yescharacteristic
217C22×C4C22⋊C4×C3111yescharacteristic
218C22×C4C22×C4×C3111yescharacteristic
219C22×C4C2×D4×C3111yescharacteristic
220C22×C4C2×D4×C3111yescharacteristic
221C2×C8—24no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C4⋊C4—24no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4C2×C8×C3112yes—
234C42—24no—
235C42—22no—
236C42—22no—
237C42—22no—
238C42—41no—
239C42—41no—
240C42—41no—
241C42—42no—
242C42C2×C8×C3112yes—
243C42M16×C3112yes—
244C23C2×C22⋊C4×C3111yescharacteristic
245Q8—42no—
246Q8—42no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4C31×C22⋊C812yes—
275C2×C4C31×C22⋊C812yes—
276C2×C4C31×#10412yes—
277C2×C4C22×C8×C3111yescharacteristic
278C2×C4C2×M16×C3111yescharacteristic
279C2×C4C31×#13512yes—
280C2×C4C31×#13712yes—
281C8—44no—
282C8—82no—
283C22C2×C31×C22⋊C811yescharacteristic
284C22C31×#41011yescharacteristic
285C22C31×#41311yescharacteristic
286C22C31×#41611yescharacteristic
287C22C31×#41911yescharacteristic
288C22C2×C31×#10411yescharacteristic
289C22C31×#42111yescharacteristic
290C4—21no—
291C4—21no—
292C4—22no—
293C4—22no—
294C4—22no—
295C4—22no—
296C4—22no—
297C4—41no—
298C4—42no—
299C4—42no—
300C4—81no—
301C4—81no—
302C2C31×#145811yescharacteristic
303C2C31×#147611yescharacteristic
304C2C31×#147911yescharacteristic
305C2C31×#150611yescharacteristic
306C2C31×#152111yescharacteristic
307C2C31×#153211yescharacteristic
308C2C31×#155411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31C2×C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
27. C4×Q8×C31C8semidirect
89. #7581C31direct (N × H)
181. C4×Q8C8×C31semidirect
205. C31#7581direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22952
C31×#18392
C31×#17442
C31×#12722
C31×#12712
#758131