Finite Group Databasebeta

← C31×#9893 #21466652

Subgroups — C31×#9893 #21466652

Order 7936.

388 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2864C211yesmaximal, characteristic
2C31×#1767C211yesmaximal, characteristic
3C31×#1745C211yesmaximal, characteristic
4C31×#1295C212yesmaximal
5C31×#1295C212yesmaximal
6C2×C31×C4⋊C8—21no—
7C2×C31×#97C2212yes—
8C2×C31×#97C2212yes—
9C31×#389C411yescharacteristic
10C31×#389C411yescharacteristic
11C31×#389C411yescharacteristic
12C31×#389C411yescharacteristic
13C31×#387—21no—
14C31×#387—21no—
15C31×#387—21no—
16C31×#387—21no—
17C31×#382C2211yescharacteristic
18C31×#382C2211yescharacteristic
19C43×C31C2211yescharacteristic
20C31×#336—21no—
21C31×#336—21no—
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—22no—
42C31×#97—24no—
43C31×#97Q814yes—
44C31×#95—21no—
45C31×#95—21no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C22×C4×C31—21no—
53C22×C4×C31—21no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31C22⋊C411yescharacteristic
57C22×C4×C31C22⋊C411yescharacteristic
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22×C411yescharacteristic
61C22×C4×C31C2×D411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63C2×C8×C31—24no—
64C2×C8×C31—24no—
65C2×C8×C31—42no—
66C2×C8×C31—42no—
67C2×C8×C31—42no—
68C2×C8×C31—42no—
69C4⋊C4×C31—42no—
70C4⋊C4×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—
77C42×C31—22no—
78C42×C31—41no—
79C42×C31—41no—
80C42×C31—41no—
81C42×C31—41no—
82C42×C31—41no—
83C42×C31C2×Q812yes—
84C42×C31#4112yes—
85#9893C3111yesmaximal, characteristic, direct product factor, Sylow
86C23×C31C2×C22⋊C411yescharacteristic
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—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×C31C4×Q812yes—
118C2×C4×C31C22⋊Q812yes—
119C2×C4×C31#12411yescharacteristic
120C2×C4×C31C4⋊Q811yescharacteristic
121C8×C31—44no—
122C8×C31—44no—
123#2864C2×C3111yescharacteristic
124#1767C2×C3111yescharacteristic
125#1745C2×C3111yescharacteristic
126#1295C2×C3112yes—
127#1295C2×C3112yes—
128C22×C31#39111yescharacteristic
129C22×C31#41311yescharacteristic
130C22×C31#41311yescharacteristic
131C22×C31C2×#10411yescharacteristic
132C22×C31#42111yescharacteristic
133C22×C31#42111yescharacteristic
134C22×C31#42111yescharacteristic
135C4×C31—21no—
136C4×C31—21no—
137C4×C31—22no—
138C4×C31—22no—
139C4×C31—22no—
140C4×C31—41no—
141C4×C31—41no—
142C4×C31—41no—
143C4×C31—81no—
144C4×C31—81no—
145C4×C31—81no—
146C4×C31—81no—
147C2×C4⋊C8—21no—
148C2×#97C22×C3112yes—
149C2×#97C22×C3112yes—
150#389C4×C3111yescharacteristic
151#389C4×C3111yescharacteristic
152#389C4×C3111yescharacteristic
153#389C4×C3111yescharacteristic
154#387—21no—
155#387—21no—
156#387—21no—
157#387—21no—
158#382C22×C3111yescharacteristic
159#382C22×C3111yescharacteristic
160C43C22×C3111yescharacteristic
161#336—21no—
162#336—21no—
163#336—21no—
164C2×C31#152911yescharacteristic
165C2×C31#153211yescharacteristic
166C2×C31#153511yescharacteristic
167C2×C31#153511yescharacteristic
168C2×C31#198611yescharacteristic
169C2×C31#199511yescharacteristic
170C2×C31#199811yescharacteristic
171C22×C8—22no—
172C22×C8—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4C2×C4×C3111yescharacteristic
178C2×C4⋊C4C2×C4×C3111yescharacteristic
179C2×C4⋊C4C2×C4×C3111yescharacteristic
180C2×C4⋊C4C2×C4×C3111yescharacteristic
181C2×C42C2×C4×C3111yescharacteristic
182C2×C42C2×C4×C3111yescharacteristic
183C2×C42D4×C3111yescharacteristic
184C2×C42D4×C3111yescharacteristic
185C2×C42D4×C3111yescharacteristic
186C2×C42D4×C3111yescharacteristic
187C2×C42C23×C3111yescharacteristic
188C4⋊C8—24no—
189#97—22no—
190#97—24no—
191#97Q8×C3114yes—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200C31#989311yescharacteristic, direct product factor, Sylow
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4C22⋊C4×C3111yescharacteristic
206C22×C4C22⋊C4×C3111yescharacteristic
207C22×C4C22⋊C4×C3111yescharacteristic
208C22×C4C22⋊C4×C3111yescharacteristic
209C22×C4C22×C4×C3111yescharacteristic
210C22×C4C2×D4×C3111yescharacteristic
211C22×C4C2×D4×C3111yescharacteristic
212C2×C8—24no—
213C2×C8—24no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C42—22no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—41no—
232C42C2×Q8×C3112yes—
233C42#41×C3112yes—
234C23C2×C22⋊C4×C3111yescharacteristic
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—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
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×C4C31×#10412yes—
265C2×C4C4×Q8×C3112yes—
266C2×C4C31×C22⋊Q812yes—
267C2×C4C31×#12411yescharacteristic
268C2×C4C31×C4⋊Q811yescharacteristic
269C8—44no—
270C8—44no—
271C22C31×#39111yescharacteristic
272C22C31×#41311yescharacteristic
273C22C31×#41311yescharacteristic
274C22C2×C31×#10411yescharacteristic
275C22C31×#42111yescharacteristic
276C22C31×#42111yescharacteristic
277C22C31×#42111yescharacteristic
278C4—21no—
279C4—21no—
280C4—22no—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—81no—
287C4—81no—
288C4—81no—
289C4—81no—
290C2C31×#152911yescharacteristic
291C2C31×#153211yescharacteristic
292C2C31×#153511yescharacteristic
293C2C31×#153511yescharacteristic
294C2C31×#198611yescharacteristic
295C2C31×#199511yescharacteristic
296C2C31×#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
85. #9893C31direct (N × H)
200. C31#9893direct (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
C31×#17452
C31×#12952
#989331