Finite Group Databasebeta

← C31×#7693 #21464452

Subgroups — C31×#7693 #21464452

Order 7936.

390 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2863C211yesmaximal, characteristic
2C31×#1745C211yesmaximal, characteristic
3C31×#1744C211yesmaximal, characteristic
4C31×#1272C212yesmaximal
5C31×#1271C212yesmaximal
6C2×C31×#97—21no—
7C2×C4×C8×C31—21no—
8C31×#391C411yescharacteristic
9C31×#391C411yescharacteristic
10C31×#391C2211yescharacteristic
11C31×#389C411yescharacteristic
12C31×#389C411yescharacteristic
13C31×#389C2211yescharacteristic
14C31×#387—21no—
15C31×#387—21no—
16C31×#387—21no—
17C31×#383—21no—
18C43×C31C2211yescharacteristic
19C31×#336—21no—
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×C8×C31—22no—
25C22×C8×C31—22no—
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×C42×C31C2×C411yescharacteristic
33C2×C42×C31C2×C411yescharacteristic
34C2×C42×C31D411yescharacteristic
35C2×C42×C31D411yescharacteristic
36C2×C42×C31D411yescharacteristic
37C2×C42×C31D411yescharacteristic
38C2×C42×C31C2311yescharacteristic
39C31×#97—24no—
40C4×C8×C31—24no—
41C31×#95—21no—
42C31×#95—21no—
43C31×#95—21no—
44C31×#95—21no—
45C31×#95—21no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C2×Q8×C31—22no—
51C2×Q8×C31—41no—
52C2×Q8×C31—41no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31C22⋊C411yescharacteristic
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22×C411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63C22×C4×C31C2×D411yescharacteristic
64C2×C8×C31—24no—
65C2×C8×C31—24no—
66C2×C8×C31—42no—
67C2×C8×C31—42no—
68C2×C8×C31—42no—
69C2×C8×C31—42no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—42no—
75C4⋊C4×C31—42no—
76C42×C31—22no—
77C42×C31—22no—
78C42×C31—22no—
79C42×C31—22no—
80C42×C31—22no—
81C42×C31—41no—
82C42×C31—41no—
83#7693C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31C2×C22⋊C411yescharacteristic
85Q8×C31—82no—
86C2×C4×C31—21no—
87C2×C4×C31—21no—
88C2×C4×C31—21no—
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—41no—
103C2×C4×C31—41no—
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#10412yes—
115C2×C4×C31#10412yes—
116C2×C4×C31#13112yes—
117C2×C4×C31#13512yes—
118C2×C4×C31#13712yes—
119C8×C31—44no—
120C8×C31—44no—
121#2863C2×C3111yescharacteristic
122#1745C2×C3111yescharacteristic
123#1744C2×C3111yescharacteristic
124#1272C2×C3112yes—
125#1271C2×C3112yes—
126C22×C31#40811yescharacteristic
127C22×C31#41011yescharacteristic
128C22×C31#41311yescharacteristic
129C22×C31#41611yescharacteristic
130C22×C31#41911yescharacteristic
131C22×C31C2×#10411yescharacteristic
132C22×C31C2×#10411yescharacteristic
133C4×C31—22no—
134C4×C31—22no—
135C4×C31—22no—
136C4×C31—22no—
137C4×C31—22no—
138C4×C31—41no—
139C4×C31—41no—
140C4×C31—81no—
141C4×C31—81no—
142C4×C31—81no—
143C4×C31—81no—
144C2×#97—21no—
145C2×C4×C8—21no—
146#391C4×C3111yescharacteristic
147#391C4×C3111yescharacteristic
148#391C22×C3111yescharacteristic
149#389C4×C3111yescharacteristic
150#389C4×C3111yescharacteristic
151#389C22×C3111yescharacteristic
152#387—21no—
153#387—21no—
154#387—21no—
155#383—21no—
156C43C22×C3111yescharacteristic
157#336—21no—
158#336—21no—
159#336C22×C3112yes—
160#336C22×C3112yes—
161C2×C31#147311yescharacteristic
162C2×C31#148511yescharacteristic
163C2×C31#149411yescharacteristic
164C2×C31#150011yescharacteristic
165C2×C31#150611yescharacteristic
166C2×C31#152411yescharacteristic
167C2×C31#155411yescharacteristic
168C22×Q8C2×C4×C3111yescharacteristic
169C22×C8—22no—
170C22×C8—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×C4×C3111yescharacteristic
175C2×C4⋊C4C2×C4×C3111yescharacteristic
176C2×C4⋊C4C2×C4×C3111yescharacteristic
177C2×C42C2×C4×C3111yescharacteristic
178C2×C42C2×C4×C3111yescharacteristic
179C2×C42D4×C3111yescharacteristic
180C2×C42D4×C3111yescharacteristic
181C2×C42D4×C3111yescharacteristic
182C2×C42D4×C3111yescharacteristic
183C2×C42C23×C3111yescharacteristic
184#97—24no—
185C4×C8—24no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195C31#769311yescharacteristic, direct product factor, Sylow
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4C22⋊C4×C3111yescharacteristic
204C22×C4C22⋊C4×C3111yescharacteristic
205C22×C4C22⋊C4×C3111yescharacteristic
206C22×C4C22⋊C4×C3111yescharacteristic
207C22×C4C22×C4×C3111yescharacteristic
208C22×C4C2×D4×C3111yescharacteristic
209C22×C4C2×D4×C3111yescharacteristic
210C2×C8—24no—
211C2×C8—24no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—22no—
226C42—22no—
227C42—41no—
228C42—41no—
229C23C2×C22⋊C4×C3111yescharacteristic
230Q8—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
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—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4C31×#10412yes—
260C2×C4C31×#10412yes—
261C2×C4C31×#13112yes—
262C2×C4C31×#13512yes—
263C2×C4C31×#13712yes—
264C8—44no—
265C8—44no—
266C22C31×#40811yescharacteristic
267C22C31×#41011yescharacteristic
268C22C31×#41311yescharacteristic
269C22C31×#41611yescharacteristic
270C22C31×#41911yescharacteristic
271C22C2×C31×#10411yescharacteristic
272C22C2×C31×#10411yescharacteristic
273C4—22no—
274C4—22no—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—41no—
279C4—41no—
280C4—81no—
281C4—81no—
282C4—81no—
283C4—81no—
284C2C31×#147311yescharacteristic
285C2C31×#148511yescharacteristic
286C2C31×#149411yescharacteristic
287C2C31×#150011yescharacteristic
288C2C31×#150611yescharacteristic
289C2C31×#152411yescharacteristic
290C2C31×#155411yescharacteristic
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
83. #7693C31direct (N × H)
195. C31#7693direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28632
C31×#17452
C31×#17442
C31×#12722
C31×#12712
#769331