Finite Group Databasebeta

← C31×#7562 #21464321

Subgroups — C31×#7562 #21464321

Order 7936.

462 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2295C211yesmaximal, characteristic
2C4×C31×C4⋊C8C211yesmaximal, characteristic
3C31×#1744C211yesmaximal, characteristic
4C31×#1272C212yesmaximal
5C31×#1271C212yesmaximal
6C2×C4×Q8×C31C411yescharacteristic
7C2×C31×C4⋊C8—21no—
8C2×C4×C8×C31—21no—
9C2×C4×C8×C31—21no—
10C31×#391C411yescharacteristic
11C31×#391C2211yescharacteristic
12C31×#389C411yescharacteristic
13C31×#389C2211yescharacteristic
14C31×#387—21no—
15C31×#387—21no—
16C4×C4⋊C4×C31—21no—
17C4×C4⋊C4×C31C411yescharacteristic
18C31×#376—21no—
19C43×C31C2211yescharacteristic
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
43C31×C4⋊C8—24no—
44C4×C8×C31—24no—
45C4×C8×C31—42no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C2×Q8×C31—21no—
54C2×Q8×C31—41no—
55C2×Q8×C31—41no—
56C2×Q8×C31C2×C812yes—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22×C411yescharacteristic
66C22×C4×C31C2×D411yescharacteristic
67C22×C4×C31C2×D411yescharacteristic
68C2×C8×C31—24no—
69C2×C8×C31—24no—
70C2×C8×C31—42no—
71C2×C8×C31—42no—
72C2×C8×C31—42no—
73C2×C8×C31—42no—
74C4⋊C4×C31—24no—
75C4⋊C4×C31—21no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—41no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—42no—
80C4⋊C4×C31C2×C812yes—
81C42×C31—24no—
82C42×C31—22no—
83C42×C31—22no—
84C42×C31—22no—
85C42×C31—41no—
86C42×C31—41no—
87C42×C31—42no—
88C42×C31C2×C812yes—
89C42×C31M1612yes—
90C42×C31SD1612yes—
91C42×C31Q1612yes—
92#7562C3111yesmaximal, characteristic, direct product factor, Sylow
93C23×C31C2×C22⋊C411yescharacteristic
94Q8×C31—42no—
95Q8×C31—42no—
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—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
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#10312yes—
123C2×C4×C31#10312yes—
124C2×C4×C31#10412yes—
125C2×C4×C31#10412yes—
126C2×C4×C31C22×C811yescharacteristic
127C2×C4×C31C2×M1611yescharacteristic
128C2×C4×C31C2×SD1611yescharacteristic
129C2×C4×C31C2×Q1611yescharacteristic
130C2×C4×C31#13512yes—
131C8×C31—44no—
132C8×C31—44no—
133#2295C2×C3111yescharacteristic
134C4×C4⋊C8C2×C3111yescharacteristic
135#1744C2×C3111yescharacteristic
136#1272C2×C3112yes—
137#1271C2×C3112yes—
138C22×C31C2×C22⋊C811yescharacteristic
139C22×C31#41011yescharacteristic
140C22×C31#41311yescharacteristic
141C22×C31C2×#10311yescharacteristic
142C22×C31#41611yescharacteristic
143C22×C31C2×#10411yescharacteristic
144C22×C31C2×#10411yescharacteristic
145C4×C31—22no—
146C4×C31—21no—
147C4×C31—21no—
148C4×C31—22no—
149C4×C31—22no—
150C4×C31—21no—
151C4×C31—21no—
152C4×C31—22no—
153C4×C31—42no—
154C4×C31—42no—
155C4×C31—81no—
156C4×C31—81no—
157C4×C31Q8⋊C814yes—
158C2×C4×Q8C4×C3111yescharacteristic
159C2×C4⋊C8—21no—
160C2×C4×C8—21no—
161C2×C4×C8—21no—
162#391C4×C3111yescharacteristic
163#391C22×C3111yescharacteristic
164#389C4×C3111yescharacteristic
165#389C22×C3111yescharacteristic
166#387—21no—
167#387—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4C4×C3111yescharacteristic
170#376—21no—
171C43C22×C3111yescharacteristic
172#336—21no—
173#336C22×C3112yes—
174#336C22×C3112yes—
175C2×C31#145811yescharacteristic
176C2×C31C2×Q8⋊C811yescharacteristic
177C2×C31#147611yescharacteristic
178C2×C31#150011yescharacteristic
179C2×C31#150311yescharacteristic
180C2×C31#152411yescharacteristic
181C2×C31#154211yescharacteristic
182C22×Q8C2×C4×C3111yescharacteristic
183C22×C8—22no—
184C22×C8—22no—
185C4×Q8—22no—
186C4×Q8C8×C3114yescomplemented
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C3111yescharacteristic
191C2×C4⋊C4C2×C4×C3111yescharacteristic
192C2×C4⋊C4C2×C4×C3111yescharacteristic
193C2×C42—21no—
194C2×C42—21no—
195C2×C42C2×C4×C3111yescharacteristic
196C2×C42C2×C4×C3111yescharacteristic
197C2×C42D4×C3111yescharacteristic
198C2×C42D4×C3111yescharacteristic
199C2×C42D4×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C2×C42C23×C3111yescharacteristic
202C4⋊C8—24no—
203C4×C8—24no—
204C4×C8—42no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212C31#756211yescharacteristic, direct product factor, Sylow
213C2×Q8—21no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8C2×C8×C3112yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4C22⋊C4×C3111yescharacteristic
222C22×C4C22⋊C4×C3111yescharacteristic
223C22×C4C22⋊C4×C3111yescharacteristic
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22×C4×C3111yescharacteristic
226C22×C4C2×D4×C3111yescharacteristic
227C22×C4C2×D4×C3111yescharacteristic
228C2×C8—24no—
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C4⋊C4—24no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4C2×C8×C3112yes—
241C42—24no—
242C42—22no—
243C42—22no—
244C42—22no—
245C42—41no—
246C42—41no—
247C42—42no—
248C42C2×C8×C3112yes—
249C42M16×C3112yes—
250C42SD16×C3112yes—
251C42Q16×C3112yes—
252C23C2×C22⋊C4×C3111yescharacteristic
253Q8—42no—
254Q8—42no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4C31×C22⋊C812yes—
280C2×C4C31×C22⋊C812yes—
281C2×C4C31×#10312yes—
282C2×C4C31×#10312yes—
283C2×C4C31×#10412yes—
284C2×C4C31×#10412yes—
285C2×C4C22×C8×C3111yescharacteristic
286C2×C4C2×M16×C3111yescharacteristic
287C2×C4C2×SD16×C3111yescharacteristic
288C2×C4C2×Q16×C3111yescharacteristic
289C2×C4C31×#13512yes—
290C8—44no—
291C8—44no—
292C22C2×C31×C22⋊C811yescharacteristic
293C22C31×#41011yescharacteristic
294C22C31×#41311yescharacteristic
295C22C2×C31×#10311yescharacteristic
296C22C31×#41611yescharacteristic
297C22C2×C31×#10411yescharacteristic
298C22C2×C31×#10411yescharacteristic
299C4—22no—
300C4—21no—
301C4—21no—
302C4—22no—
303C4—22no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—42no—
308C4—42no—
309C4—81no—
310C4—81no—
311C4C31×Q8⋊C814yes—
312C2C31×#145811yescharacteristic
313C2C2×C31×Q8⋊C811yescharacteristic
314C2C31×#147611yescharacteristic
315C2C31×#150011yescharacteristic
316C2C31×#150311yescharacteristic
317C2C31×#152411yescharacteristic
318C2C31×#154211yescharacteristic
subgroupG/H
centerC22×C4×C31C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
socle, prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
27. C4×Q8×C31C8semidirect
92. #7562C31direct (N × H)
186. C4×Q8C8×C31semidirect
212. C31#7562direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22952
C4×C31×C4⋊C82
C31×#17442
C31×#12722
C31×#12712
#756231