Finite Group Databasebeta

← C31×#9892 #21466651

Subgroups — C31×#9892 #21466651

Order 7936.

432 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2864C211yesmaximal, characteristic
2C31×#1767C211yesmaximal, characteristic
3C4×C31×#97C211yesmaximal, characteristic
4C31×#1295C212yesmaximal
5C31×#1295C212yesmaximal
6C2×C31×C4⋊C8—21no—
7C2×C31×#97—21no—
8C2×C31×#97C2212yes—
9C2×C31×#97C2212yes—
10C2×C4×C8×C31—21no—
11C31×#389C411yescharacteristic
12C31×#389C411yescharacteristic
13C31×#389C411yescharacteristic
14C31×#389C411yescharacteristic
15C31×#387—21no—
16C31×#387—21no—
17C31×#387—21no—
18C31×#387—21no—
19C31×#382C2211yescharacteristic
20C31×#382C2211yescharacteristic
21C43×C31C2211yescharacteristic
22C31×#336—21no—
23C22×C8×C31—22no—
24C22×C8×C31—22no—
25C2×C4⋊C4×C31—21no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31C2×C411yescharacteristic
30C2×C4⋊C4×C31C2×C411yescharacteristic
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C42×C31C2×C411yescharacteristic
34C2×C42×C31C2×C411yescharacteristic
35C2×C42×C31D411yescharacteristic
36C2×C42×C31D411yescharacteristic
37C2×C42×C31D411yescharacteristic
38C2×C42×C31D411yescharacteristic
39C2×C42×C31C2311yescharacteristic
40C31×C4⋊C8—24no—
41C31×#97—24no—
42C31×#97—22no—
43C31×#97—24no—
44C31×#97Q814yes—
45C4×C8×C31—24no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22×C411yescharacteristic
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31C2×D411yescharacteristic
65C2×C8×C31—24no—
66C2×C8×C31—24no—
67C2×C8×C31—24no—
68C2×C8×C31—24no—
69C2×C8×C31—42no—
70C2×C8×C31—42no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—41no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—42no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—42no—
79C42×C31—22no—
80C42×C31—22no—
81C42×C31—22no—
82C42×C31—41no—
83C42×C31—41no—
84C42×C31—41no—
85C42×C31C2×Q812yes—
86C42×C31#4112yes—
87#9892C3111yesmaximal, characteristic, direct product factor, Sylow
88C23×C31C2×C22⋊C411yescharacteristic
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
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—41no—
105C2×C4×C31—41no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
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#10412yes—
117C2×C4×C31#10412yes—
118C2×C4×C31#10412yes—
119C2×C4×C31C4×Q812yes—
120C2×C4×C31C22⋊Q812yes—
121C2×C4×C31#12411yescharacteristic
122C2×C4×C31C4⋊Q811yescharacteristic
123C8×C31—28no—
124C8×C31—44no—
125#2864C2×C3111yescharacteristic
126#1767C2×C3111yescharacteristic
127C4×#97C2×C3111yescharacteristic
128#1295C2×C3112yes—
129#1295C2×C3112yes—
130C22×C31#39111yescharacteristic
131C22×C31#41311yescharacteristic
132C22×C31#41311yescharacteristic
133C22×C31C2×#10411yescharacteristic
134C22×C31C2×#10411yescharacteristic
135C22×C31C2×#10411yescharacteristic
136C22×C31#42111yescharacteristic
137C4×C31—21no—
138C4×C31—21no—
139C4×C31—22no—
140C4×C31—22no—
141C4×C31—22no—
142C4×C31—22no—
143C4×C31—22no—
144C4×C31—41no—
145C4×C31—81no—
146C4×C31—81no—
147C4×C31—81no—
148C4×C31—81no—
149C2×C4⋊C8—21no—
150C2×#97—21no—
151C2×#97C22×C3112yes—
152C2×#97C22×C3112yes—
153C2×C4×C8—21no—
154#389C4×C3111yescharacteristic
155#389C4×C3111yescharacteristic
156#389C4×C3111yescharacteristic
157#389C4×C3111yescharacteristic
158#387—21no—
159#387—21no—
160#387—21no—
161#387—21no—
162#382C22×C3111yescharacteristic
163#382C22×C3111yescharacteristic
164C43C22×C3111yescharacteristic
165#336—21no—
166C2×C31#152411yescharacteristic
167C2×C31#152411yescharacteristic
168C2×C31#152911yescharacteristic
169C2×C31#153211yescharacteristic
170C2×C31#198611yescharacteristic
171C2×C31#199411yescharacteristic
172C2×C31#199811yescharacteristic
173C22×C8—22no—
174C22×C8—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C2×C4×C3111yescharacteristic
180C2×C4⋊C4C2×C4×C3111yescharacteristic
181C2×C4⋊C4C2×C4×C3111yescharacteristic
182C2×C4⋊C4C2×C4×C3111yescharacteristic
183C2×C42C2×C4×C3111yescharacteristic
184C2×C42C2×C4×C3111yescharacteristic
185C2×C42D4×C3111yescharacteristic
186C2×C42D4×C3111yescharacteristic
187C2×C42D4×C3111yescharacteristic
188C2×C42D4×C3111yescharacteristic
189C2×C42C23×C3111yescharacteristic
190C4⋊C8—24no—
191#97—24no—
192#97—22no—
193#97—24no—
194#97Q8×C3114yes—
195C4×C8—24no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204C31#989211yescharacteristic, direct product factor, Sylow
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C22⋊C4×C3111yescharacteristic
210C22×C4C22⋊C4×C3111yescharacteristic
211C22×C4C22⋊C4×C3111yescharacteristic
212C22×C4C22⋊C4×C3111yescharacteristic
213C22×C4C22×C4×C3111yescharacteristic
214C22×C4C2×D4×C3111yescharacteristic
215C22×C4C2×D4×C3111yescharacteristic
216C2×C8—24no—
217C2×C8—24no—
218C2×C8—24no—
219C2×C8—24no—
220C2×C8—42no—
221C2×C8—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C42—22no—
231C42—22no—
232C42—22no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42C2×Q8×C3112yes—
237C42#41×C3112yes—
238C23C2×C22⋊C4×C3111yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4C31×#10412yes—
267C2×C4C31×#10412yes—
268C2×C4C31×#10412yes—
269C2×C4C4×Q8×C3112yes—
270C2×C4C31×C22⋊Q812yes—
271C2×C4C31×#12411yescharacteristic
272C2×C4C31×C4⋊Q811yescharacteristic
273C8—28no—
274C8—44no—
275C22C31×#39111yescharacteristic
276C22C31×#41311yescharacteristic
277C22C31×#41311yescharacteristic
278C22C2×C31×#10411yescharacteristic
279C22C2×C31×#10411yescharacteristic
280C22C2×C31×#10411yescharacteristic
281C22C31×#42111yescharacteristic
282C4—21no—
283C4—21no—
284C4—22no—
285C4—22no—
286C4—22no—
287C4—22no—
288C4—22no—
289C4—41no—
290C4—81no—
291C4—81no—
292C4—81no—
293C4—81no—
294C2C31×#152411yescharacteristic
295C2C31×#152411yescharacteristic
296C2C31×#152911yescharacteristic
297C2C31×#153211yescharacteristic
298C2C31×#198611yescharacteristic
299C2C31×#199411yescharacteristic
300C2C31×#199811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
87. #9892C31direct (N × H)
204. C31#9892direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28642
C31×#17672
C4×C31×#972
C31×#12952
#989231