Finite Group Databasebeta

← C31×#12583 #21469342

Subgroups — C31×#12583 #21469342

Order 7936.

826 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#410C212yesmaximal
2C31×#2311C211yesmaximal, characteristic
3C31×#1393C214yesmaximal, complemented
4C22×#41×C31C2211yescharacteristic
5C2×C31×#117—22no—
6C2×C31×#117C411yescharacteristic, complemented
7C22×C4⋊C4×C31C411yescharacteristic, complemented
8C31×#410—24no—
9C31×#410C418yescomplemented
10C2×C31×#99—22no—
11C2×C31×#99C2214yes—
12C31×#391C412yescomplemented
13C31×#390C2212yes—
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×C31C2×C411yescharacteristic
22C22×D4×C31D412yes—
23C22×D4×C31C2311yescharacteristic
24C23×C4×C31—21no—
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D412yes—
27C31×#117—28no—
28C31×#117—44no—
29C31×#117—42no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—42no—
33C2×C4⋊C4×C31—42no—
34C2×C4⋊C4×C31C2×C412yes—
35C2×C22⋊C4×C31—24no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—24no—
38C2×C42×C31—42no—
39C2×C42×C31C2×C412yes—
40C31×#99—28no—
41C31×#99—24no—
42C31×#99C2×C418yescomplemented
43C31×#95—24no—
44C24×C31C22⋊C411yescharacteristic
45C24×C31C2×D412yes—
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×C31C4212yes—
53C2×Q8×C31C4⋊C412yes—
54C2×D4×C31—42no—
55C2×D4×C31—42no—
56C2×D4×C31—41no—
57C2×D4×C31—41no—
58C2×D4×C31C22⋊C414yes—
59C2×D4×C31C4⋊C414yes—
60C2×D4×C31C22×C412yes—
61C2×D4×C31C2×D411yescharacteristic
62C2×D4×C31C2×Q811yescharacteristic
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—24no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—44no—
71C22×C4×C31—42no—
72C22×C4×C31—82no—
73C22×C4×C31C4212yes—
74C22×C4×C31C22⋊C412yes—
75C22×C4×C31C22⋊C414yes—
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C4⋊C414yes—
78C22×C4×C31C4⋊C412yes—
79C22×C4×C31C22×C411yescharacteristic
80C4⋊C4×C31—48no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—42no—
84C22⋊C4×C31—28no—
85C22⋊C4×C31—44no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—84no—
88C42×C31—48no—
89C42×C31—42no—
90#12583C3111yesmaximal, 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×C31C2×C22⋊C411yescharacteristic
101C23×C31C2×C22⋊C412yes—
102C23×C31C2×C4⋊C412yes—
103Q8×C31—42no—
104Q8×C31—42no—
105D4×C31—44no—
106D4×C31—44no—
107D4×C31—42no—
108D4×C31—41no—
109D4×C31—41no—
110C2×C4×C31—21no—
111C2×C4×C31—22no—
112C2×C4×C31—21no—
113C2×C4×C31—22no—
114C2×C4×C31—24no—
115C2×C4×C31—24no—
116C2×C4×C31—24no—
117C2×C4×C31—24no—
118C2×C4×C31—24no—
119C2×C4×C31—24no—
120C2×C4×C31—48no—
121C2×C4×C31—42no—
122C2×C4×C31—44no—
123C2×C4×C31—42no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—84no—
127C2×C4×C31—84no—
128C2×C4×C31—84no—
129C2×C4×C31#9514yes—
130C2×C4×C31#9512yes—
131C2×C4×C31#9912yes—
132C2×C4×C31#9912yes—
133C2×C4×C31C2×C4211yescharacteristic
134C2×C4×C31C2×C4⋊C411yescharacteristic
135C2×#410C2×C3112yes—
136#2311C2×C3111yescharacteristic
137#1393C2×C3114yescomplemented
138C22×C31—21no—
139C22×C31—21no—
140C22×C31—22no—
141C22×C31—22no—
142C22×C31—22no—
143C22×C31—42no—
144C22×C31—42no—
145C22×C31—42no—
146C22×C31—42no—
147C22×C31—41no—
148C22×C31—42no—
149C22×C31—42no—
150C22×C31—41no—
151C22×C31—82no—
152C22×C31C2×#9511yescharacteristic
153C22×C31C2×#9911yescharacteristic
154C22×C31C2×#9911yescharacteristic
155C4×C31—24no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—82no—
159C4×C31—88no—
160C4×C31—82no—
161C4×C31#34214yes—
162C22×#41C22×C3111yescharacteristic
163C2×#117—22no—
164C2×#117C4×C3111yescharacteristic, complemented
165C22×C4⋊C4C4×C3111yescharacteristic, complemented
166#410—24no—
167#410C4×C3118yescomplemented
168C2×#99—22no—
169C2×#99C22×C3114yes—
170#391C4×C3112yescomplemented
171#390C22×C3112yes—
172#386—22no—
173#380—22no—
174C2×C31—21no—
175C2×C31—21no—
176C2×C31—42no—
177C2×C31—42no—
178C2×C31—42no—
179C2×C31C2×#34211yescharacteristic
180C2×C31#212811yescharacteristic
181C2×C31#212911yescharacteristic
182C2×#41—42no—
183C2×#41—42no—
184C2×#41C2×C4×C3114yes—
185C2×#41D4×C3112yes—
186C2×#41Q8×C3112yes—
187C22×Q8C2×C4×C3111yescharacteristic
188C22×D4D4×C3112yes—
189C22×D4C23×C3111yescharacteristic
190C23×C4—21no—
191C23×C4C2×C4×C3111yescharacteristic
192C23×C4D4×C3112yes—
193#117—28no—
194#117—44no—
195#117—42no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4C2×C4×C3112yes—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—24no—
204C2×C42—42no—
205C2×C42C2×C4×C3112yes—
206#99—28no—
207#99—24no—
208#99C2×C4×C3118yescomplemented
209#95—24no—
210C31#1258311yescharacteristic, direct product factor, Sylow
211C24C22⋊C4×C3111yescharacteristic
212C24C2×D4×C3112yes—
213#41—44no—
214#41—44no—
215#41—44no—
216#41—44no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8C42×C3112yes—
220C2×Q8C4⋊C4×C3112yes—
221C2×D4—42no—
222C2×D4—42no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4C22⋊C4×C3114yes—
226C2×D4C4⋊C4×C3114yes—
227C2×D4C22×C4×C3112yes—
228C2×D4C2×D4×C3111yescharacteristic
229C2×D4C2×Q8×C3111yescharacteristic
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—44no—
238C22×C4—42no—
239C22×C4—82no—
240C22×C4C42×C3112yes—
241C22×C4C22⋊C4×C3112yes—
242C22×C4C22⋊C4×C3114yes—
243C22×C4C22⋊C4×C3111yescharacteristic
244C22×C4C4⋊C4×C3114yes—
245C22×C4C4⋊C4×C3112yes—
246C22×C4C22×C4×C3111yescharacteristic
247C4⋊C4—42no—
248C4⋊C4—48no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C22⋊C4—28no—
252C22⋊C4—44no—
253C22⋊C4—42no—
254C22⋊C4—84no—
255C42—42no—
256C42—48no—
257C23—21no—
258C23—21no—
259C23—22no—
260C23—22no—
261C23—41no—
262C23—41no—
263C23—42no—
264C23—42no—
265C23C31×#9512yes—
266C23C2×C22⋊C4×C3111yescharacteristic
267C23C2×C22⋊C4×C3112yes—
268C23C2×C4⋊C4×C3112yes—
269Q8—42no—
270Q8—42no—
271D4—44no—
272D4—44no—
273D4—42no—
274D4—41no—
275D4—41no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—48no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—84no—
293C2×C4—84no—
294C2×C4—84no—
295C2×C4C31×#9514yes—
296C2×C4C31×#9512yes—
297C2×C4C31×#9912yes—
298C2×C4C31×#9912yes—
299C2×C4C2×C42×C3111yescharacteristic
300C2×C4C2×C4⋊C4×C3111yescharacteristic
301C22—21no—
302C22—21no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—42no—
310C22—41no—
311C22—42no—
312C22—42no—
313C22—41no—
314C22—82no—
315C22C2×C31×#9511yescharacteristic
316C22C2×C31×#9911yescharacteristic
317C22C2×C31×#9911yescharacteristic
318C4—24no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—88no—
323C4—82no—
324C4C31×#34214yes—
325C2—21no—
326C2—21no—
327C2—42no—
328C2—42no—
329C2—42no—
330C2C2×C31×#34211yescharacteristic
331C2C31×#212811yescharacteristic
332C2C31×#212911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC2×C4C2×C42×C31
Frattini, cosocleC22×D4C23×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×#1393C2semidirect
6. C2×C31×#117C4semidirect
7. C22×C4⋊C4×C31C4semidirect
9. C31×#410C4semidirect
12. C31×#391C4semidirect
42. C31×#99C2×C4semidirect
90. #12583C31direct (N × H)
137. #1393C2×C31semidirect
164. C2×#117C4×C31semidirect
165. C22×C4⋊C4C4×C31semidirect
167. #410C4×C31semidirect
170. #391C4×C31semidirect
208. #99C2×C4×C31semidirect
210. C31#12583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4102
C31×#23112
C31×#13932
#1258331