Finite Group Databasebeta

← C31×#12587 #21469346

Subgroups — C31×#12587 #21469346

Order 7936.

794 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#413C212yesmaximal
2C31×#2311C211yesmaximal, characteristic
3C31×#1394C214yesmaximal, complemented
4C22×#41×C31C2211yescharacteristic
5C22×M16×C31—22no—
6C2×C31×#117C411yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic
8C31×#413—24no—
9C31×#413C418yescomplemented
10C2×C31×#101C2214yes—
11C2×C31×#100—22no—
12C31×#391C2212yes—
13C31×#390C412yes—
14C31×#386—22no—
15C31×#380—22no—
16C2×#41×C31—42no—
17C2×#41×C31—42no—
18C2×#41×C31C2×C414yes—
19C2×#41×C31D412yes—
20C2×#41×C31Q812yes—
21C22×Q8×C31C2311yescharacteristic
22C22×D4×C31C2×C411yescharacteristic
23C22×D4×C31D412yes—
24C23×C4×C31—21no—
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D412yes—
27C2×M16×C31—28no—
28C2×M16×C31—24no—
29C2×M16×C31—42no—
30C2×M16×C31—44no—
31C22×C8×C31—42no—
32C31×#117—42no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—42no—
36C2×C4⋊C4×C31C2×C412yes—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—24no—
39C2×C42×C31C2×C412yes—
40C31×#101—24no—
41C31×#101C2×C418yescomplemented
42C31×#100—28no—
43C31×#95—24no—
44C24×C31C22⋊C412yes—
45C24×C31C22⋊C411yescharacteristic
46#41×C31—44no—
47#41×C31—44no—
48#41×C31—44no—
49#41×C31—44no—
50C2×Q8×C31—41no—
51C2×Q8×C31—41no—
52C2×Q8×C31C22×C412yes—
53C2×Q8×C31C2×D411yescharacteristic
54C2×Q8×C31C2×Q811yescharacteristic
55C2×D4×C31—41no—
56C2×D4×C31—41no—
57C2×D4×C31—42no—
58C2×D4×C31—42no—
59C2×D4×C31C4212yes—
60C2×D4×C31C22⋊C414yes—
61C2×D4×C31C4⋊C412yes—
62C2×D4×C31C4⋊C414yes—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—24no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—42no—
71C22×C4×C31—82no—
72C22×C4×C31C4212yes—
73C22×C4×C31C22⋊C414yes—
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C4⋊C412yes—
76C22×C4×C31C4⋊C414yes—
77C22×C4×C31C22×C411yescharacteristic
78C22×C4×C31C2×D412yes—
79M16×C31—28no—
80M16×C31—44no—
81M16×C31—48no—
82C2×C8×C31—44no—
83C2×C8×C31—48no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—84no—
89C42×C31—42no—
90#12587C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—21no—
92C23×C31—21no—
93C23×C31—22no—
94C23×C31—22no—
95C23×C31—41no—
96C23×C31—41no—
97C23×C31—42no—
98C23×C31—42no—
99C23×C31#9512yes—
100C23×C31#9514yes—
101C23×C31C2×C22⋊C411yescharacteristic
102Q8×C31—42no—
103Q8×C31—41no—
104Q8×C31—41no—
105D4×C31—42no—
106D4×C31—44no—
107D4×C31—42no—
108D4×C31—44no—
109C2×C4×C31—21no—
110C2×C4×C31—22no—
111C2×C4×C31—21no—
112C2×C4×C31—22no—
113C2×C4×C31—24no—
114C2×C4×C31—24no—
115C2×C4×C31—24no—
116C2×C4×C31—24no—
117C2×C4×C31—24no—
118C2×C4×C31—24no—
119C2×C4×C31—42no—
120C2×C4×C31—44no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—42no—
124C2×C4×C31—84no—
125C2×C4×C31#9512yes—
126C2×C4×C31#9912yes—
127C2×C4×C31#9912yes—
128C2×C4×C31C2×C4211yescharacteristic
129C2×C4×C31C2×C22⋊C412yes—
130C2×C4×C31C2×C4⋊C411yescharacteristic
131C2×C4×C31C2×C4⋊C412yes—
132C8×C31—48no—
133C2×#413C2×C3112yes—
134#2311C2×C3111yescharacteristic
135#1394C2×C3114yescomplemented
136C22×C31—21no—
137C22×C31—21no—
138C22×C31—22no—
139C22×C31—24no—
140C22×C31—42no—
141C22×C31—44no—
142C22×C31—42no—
143C22×C31—41no—
144C22×C31—42no—
145C22×C31—41no—
146C22×C31—42no—
147C22×C31—82no—
148C22×C31C2×#9511yescharacteristic
149C22×C31C2×#9911yescharacteristic
150C22×C31C2×#9911yescharacteristic
151C4×C31—22no—
152C4×C31—21no—
153C4×C31—21no—
154C4×C31—22no—
155C4×C31—82no—
156C4×C31—82no—
157C4×C31#34214yes—
158C22×#41C22×C3111yescharacteristic
159C22×M16—22no—
160C2×#117C4×C3111yescharacteristic
161C22×C4⋊C4C4×C3111yescharacteristic
162#413—24no—
163#413C4×C3118yescomplemented
164C2×#101C22×C3114yes—
165C2×#100—22no—
166#391C22×C3112yes—
167#390C4×C3112yes—
168#386—22no—
169#380—22no—
170C2×C31—21no—
171C2×C31—21no—
172C2×C31—42no—
173C2×C31—44no—
174C2×C31C2×#34211yescharacteristic
175C2×C31#213411yescharacteristic
176C2×C31#213511yescharacteristic
177C2×#41—42no—
178C2×#41—42no—
179C2×#41C2×C4×C3114yes—
180C2×#41D4×C3112yes—
181C2×#41Q8×C3112yes—
182C22×Q8C23×C3111yescharacteristic
183C22×D4C2×C4×C3111yescharacteristic
184C22×D4D4×C3112yes—
185C23×C4—21no—
186C23×C4C2×C4×C3111yescharacteristic
187C23×C4D4×C3112yes—
188C2×M16—28no—
189C2×M16—24no—
190C2×M16—42no—
191C2×M16—44no—
192C22×C8—42no—
193#117—42no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4C2×C4×C3112yes—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—24no—
200C2×C42C2×C4×C3112yes—
201#101—24no—
202#101C2×C4×C3118yescomplemented
203#100—28no—
204#95—24no—
205C31#1258711yescharacteristic, direct product factor, Sylow
206C24C22⋊C4×C3112yes—
207C24C22⋊C4×C3111yescharacteristic
208#41—44no—
209#41—44no—
210#41—44no—
211#41—44no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8C22×C4×C3112yes—
215C2×Q8C2×D4×C3111yescharacteristic
216C2×Q8C2×Q8×C3111yescharacteristic
217C2×D4—41no—
218C2×D4—41no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4C42×C3112yes—
222C2×D4C22⋊C4×C3114yes—
223C2×D4C4⋊C4×C3112yes—
224C2×D4C4⋊C4×C3114yes—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—42no—
233C22×C4—82no—
234C22×C4C42×C3112yes—
235C22×C4C22⋊C4×C3114yes—
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C4⋊C4×C3112yes—
238C22×C4C4⋊C4×C3114yes—
239C22×C4C22×C4×C3111yescharacteristic
240C22×C4C2×D4×C3112yes—
241M16—28no—
242M16—44no—
243M16—48no—
244C2×C8—44no—
245C2×C8—48no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—84no—
251C42—42no—
252C23—21no—
253C23—21no—
254C23—22no—
255C23—22no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23C31×#9512yes—
261C23C31×#9514yes—
262C23C2×C22⋊C4×C3111yescharacteristic
263Q8—42no—
264Q8—41no—
265Q8—41no—
266D4—42no—
267D4—44no—
268D4—42no—
269D4—44no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—42no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—84no—
286C2×C4C31×#9512yes—
287C2×C4C31×#9912yes—
288C2×C4C31×#9912yes—
289C2×C4C2×C42×C3111yescharacteristic
290C2×C4C2×C22⋊C4×C3112yes—
291C2×C4C2×C4⋊C4×C3111yescharacteristic
292C2×C4C2×C4⋊C4×C3112yes—
293C8—48no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—24no—
298C22—42no—
299C22—44no—
300C22—42no—
301C22—41no—
302C22—42no—
303C22—41no—
304C22—42no—
305C22—82no—
306C22C2×C31×#9511yescharacteristic
307C22C2×C31×#9911yescharacteristic
308C22C2×C31×#9911yescharacteristic
309C4—22no—
310C4—21no—
311C4—21no—
312C4—22no—
313C4—82no—
314C4—82no—
315C4C31×#34214yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—44no—
320C2C2×C31×#34211yescharacteristic
321C2C31×#213411yescharacteristic
322C2C31×#213511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC2×C4C2×C42×C31
Frattini, cosocleC22×Q8C23×C31
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1394C2semidirect
9. C31×#413C4semidirect
41. C31×#101C2×C4semidirect
90. #12587C31direct (N × H)
135. #1394C2×C31semidirect
163. #413C4×C31semidirect
202. #101C2×C4×C31semidirect
205. C31#12587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4132
C31×#23112
C31×#13942
#1258731