Finite Group Databasebeta

← C2×C31×#1280 #21464664

Subgroups — C2×C31×#1280 #21464664

Order 7936.

1390 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊C8C212yesmaximal
2C22×C31×#95C211yesmaximal, characteristic
3C31×#1280C214yesmaximal, direct product factor
4C24×C4×C31C412yes—
5C24×C4×C31C2211yescharacteristic
6C23×C8×C31—22no—
7C2×C31×C22⋊C8—22no—
8C2×C31×C22⋊C8—24no—
9C2×C31×C22⋊C8C418yescomplemented
10C2×C31×C22⋊C8C2214yes—
11C2×C31×#95—22no—
12C2×C31×#95—22no—
13C2×C31×#95C412yes—
14C2×C31×#95C2212yes—
15C25×C31C2×C411yescharacteristic
16C23×C4×C31—22no—
17C23×C4×C31—22no—
18C23×C4×C31—24no—
19C23×C4×C31—44no—
20C23×C4×C31—44no—
21C23×C4×C31—44no—
22C23×C4×C31C818yescomplemented
23C23×C4×C31C2×C414yes—
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C414yes—
26C23×C4×C31D412yes—
27C23×C4×C31D412yes—
28C23×C4×C31D412yes—
29C23×C4×C31Q812yes—
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—28no—
32C22×C8×C31—24no—
33C22×C8×C31—48no—
34C31×C22⋊C8—28no—
35C31×C22⋊C8—24no—
36C31×C22⋊C8C2×C418yescomplemented
37C31×#95—24no—
38C31×#95—24no—
39C24×C31—24no—
40C24×C31—22no—
41C24×C31—22no—
42C24×C31C4212yes—
43C24×C31C22⋊C411yescharacteristic
44C24×C31C22⋊C411yescharacteristic
45C24×C31C4⋊C412yes—
46C24×C31C2×C814yes—
47C24×C31M1614yes—
48C24×C31C22×C411yescharacteristic
49C22×C4×C31—28no—
50C22×C4×C31—28no—
51C22×C4×C31—28no—
52C22×C4×C31—24no—
53C22×C4×C31—24no—
54C22×C4×C31—48no—
55C22×C4×C31—42no—
56C22×C4×C31—44no—
57C22×C4×C31—44no—
58C22×C4×C31—44no—
59C22×C4×C31—42no—
60C22×C4×C31—416no—
61C22×C4×C31—44no—
62C22×C4×C31—44no—
63C22×C4×C31—44no—
64C22×C4×C31—44no—
65C22×C4×C31—416no—
66C22×C4×C31—44no—
67C22×C4×C31—44no—
68C22×C4×C31C4212yes—
69C22×C4×C31C22⋊C412yes—
70C22×C4×C31C22⋊C414yes—
71C22×C4×C31C22⋊C414yes—
72C22×C4×C31C4⋊C414yes—
73C22×C4×C31C4⋊C412yes—
74C22×C4×C31C4⋊C414yes—
75C22×C4×C31C2×C818yescomplemented
76C22×C4×C31C22×C412yes—
77C22×C4×C31C2×D412yes—
78C22×C4×C31C2×D411yescharacteristic
79C22×C4×C31C2×Q811yescharacteristic
80C2×C8×C31—28no—
81C2×C8×C31—416no—
82C2×C8×C31—48no—
83C2×#1280C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31—28no—
85C23×C31—28no—
86C23×C31—28no—
87C23×C31—28no—
88C23×C31—24no—
89C23×C31—24no—
90C23×C31—24no—
91C23×C31—24no—
92C23×C31—22no—
93C23×C31—22no—
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31#9512yes—
99C23×C31#9512yes—
100C23×C31C4×C814yes—
101C23×C31#9714yes—
102C23×C31C22⋊C814yes—
103C23×C31C22⋊C814yes—
104C23×C31#9914yes—
105C23×C31#10012yes—
106C23×C31#10112yes—
107C23×C31C4⋊C818yes—
108C23×C31C2×C4211yescharacteristic
109C23×C31C2×C22⋊C411yescharacteristic
110C23×C31C2×C4⋊C411yescharacteristic
111C23×C31C22×C812yes—
112C23×C31C2×M1612yes—
113C2×C4×C31—28no—
114C2×C4×C31—28no—
115C2×C4×C31—24no—
116C2×C4×C31—24no—
117C2×C4×C31—28no—
118C2×C4×C31—42no—
119C2×C4×C31—44no—
120C2×C4×C31—42no—
121C2×C4×C31—44no—
122C2×C4×C31—42no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—416no—
126C2×C4×C31—48no—
127C2×C4×C31—416no—
128C2×C4×C31—44no—
129C2×C4×C31—44no—
130C2×C4×C31—48no—
131C2×C4×C31#9514yes—
132C2×C4×C31C2×C22⋊C412yes—
133C2×C4×C31C2×C4⋊C412yes—
134C8×C31—48no—
135C22×C22⋊C8C2×C3112yes—
136C22×#95C2×C3111yescharacteristic
137#1280C2×C3114yesdirect product factor
138C22×C31—28no—
139C22×C31—28no—
140C22×C31—216no—
141C22×C31—24no—
142C22×C31—22no—
143C22×C31—22no—
144C22×C31—24no—
145C22×C31—22no—
146C22×C31—22no—
147C22×C31—22no—
148C22×C31—21no—
149C22×C31—21no—
150C22×C31—22no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31#32318yes—
154C22×C31#32418yes—
155C22×C31#33614yes—
156C22×C31#33614yes—
157C22×C31#34214yes—
158C22×C31#34314yes—
159C22×C31C2×#9511yescharacteristic
160C22×C31C2×C4×C811yescharacteristic
161C22×C31C2×#9711yescharacteristic
162C22×C31C2×C22⋊C812yes—
163C22×C31C2×#9912yes—
164C22×C31C2×#10011yescharacteristic
165C22×C31C2×#10111yescharacteristic
166C22×C31C2×C4⋊C812yes—
167C4×C31—22no—
168C4×C31—24no—
169C4×C31—22no—
170C4×C31—48no—
171C24×C4C4×C3112yes—
172C24×C4C22×C3111yescharacteristic
173C23×C8—22no—
174C2×C22⋊C8—22no—
175C2×C22⋊C8—24no—
176C2×C22⋊C8C4×C3118yescomplemented
177C2×C22⋊C8C22×C3114yes—
178C2×#95—22no—
179C2×#95—22no—
180C2×#95C4×C3112yes—
181C2×#95C22×C3112yes—
182C2×C31—24no—
183C2×C31—21no—
184C2×C31—21no—
185C2×C31—22no—
186C2×C31#128018yesdirect product factor
187C2×C31C2×#32312yes—
188C2×C31C2×#32412yes—
189C2×C31C2×#33611yescharacteristic
190C2×C31C2×#34211yescharacteristic
191C2×C31C2×#34311yescharacteristic
192C25C2×C4×C3111yescharacteristic
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—24no—
196C23×C4—44no—
197C23×C4—44no—
198C23×C4—44no—
199C23×C4C8×C3118yescomplemented
200C23×C4C2×C4×C3114yes—
201C23×C4C2×C4×C3111yescharacteristic
202C23×C4C2×C4×C3114yes—
203C23×C4D4×C3112yes—
204C23×C4D4×C3112yes—
205C23×C4D4×C3112yes—
206C23×C4Q8×C3112yes—
207C23×C4C23×C3111yescharacteristic
208C22×C8—28no—
209C22×C8—24no—
210C22×C8—48no—
211C22⋊C8—28no—
212C22⋊C8—24no—
213C22⋊C8C2×C4×C3118yescomplemented
214#95—24no—
215#95—24no—
216C31C2×#128011yescharacteristic, direct product factor, Sylow
217C24—24no—
218C24—22no—
219C24—22no—
220C24C42×C3112yes—
221C24C22⋊C4×C3111yescharacteristic
222C24C22⋊C4×C3111yescharacteristic
223C24C4⋊C4×C3112yes—
224C24C2×C8×C3114yes—
225C24M16×C3114yes—
226C24C22×C4×C3111yescharacteristic
227C22×C4—28no—
228C22×C4—28no—
229C22×C4—28no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—42no—
233C22×C4—48no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—44no—
237C22×C4—42no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—416no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—416no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4C42×C3112yes—
247C22×C4C22⋊C4×C3112yes—
248C22×C4C22⋊C4×C3114yes—
249C22×C4C22⋊C4×C3114yes—
250C22×C4C4⋊C4×C3114yes—
251C22×C4C4⋊C4×C3112yes—
252C22×C4C4⋊C4×C3114yes—
253C22×C4C2×C8×C3118yescomplemented
254C22×C4C22×C4×C3112yes—
255C22×C4C2×D4×C3112yes—
256C22×C4C2×D4×C3111yescharacteristic
257C22×C4C2×Q8×C3111yescharacteristic
258C2×C8—28no—
259C2×C8—48no—
260C2×C8—416no—
261C23—22no—
262C23—22no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—28no—
268C23—28no—
269C23—28no—
270C23—28no—
271C23—24no—
272C23—24no—
273C23—24no—
274C23—24no—
275C23C31×#9512yes—
276C23C31×#9512yes—
277C23C4×C8×C3114yes—
278C23C31×#9714yes—
279C23C31×C22⋊C814yes—
280C23C31×C22⋊C814yes—
281C23C31×#9914yes—
282C23C31×#10012yes—
283C23C31×#10112yes—
284C23C31×C4⋊C818yes—
285C23C2×C42×C3111yescharacteristic
286C23C2×C22⋊C4×C3111yescharacteristic
287C23C2×C4⋊C4×C3111yescharacteristic
288C23C22×C8×C3112yes—
289C23C2×M16×C3112yes—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—28no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—416no—
303C2×C4—48no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—416no—
307C2×C4—48no—
308C2×C4C31×#9514yes—
309C2×C4C2×C22⋊C4×C3112yes—
310C2×C4C2×C4⋊C4×C3112yes—
311C8—48no—
312C22—24no—
313C22—22no—
314C22—22no—
315C22—24no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—28no—
325C22—28no—
326C22—216no—
327C22C31×#32318yes—
328C22C31×#32418yes—
329C22C31×#33614yes—
330C22C31×#33614yes—
331C22C31×#34214yes—
332C22C31×#34314yes—
333C22C2×C31×#9511yescharacteristic
334C22C2×C4×C8×C3111yescharacteristic
335C22C2×C31×#9711yescharacteristic
336C22C2×C31×C22⋊C812yes—
337C22C2×C31×#9912yes—
338C22C2×C31×#10011yescharacteristic
339C22C2×C31×#10111yescharacteristic
340C22C2×C31×C4⋊C812yes—
341C4—22no—
342C4—24no—
343C4—22no—
344C4—48no—
345C2—21no—
346C2—21no—
347C2—22no—
348C2—24no—
349C2C31×#128018yesdirect product factor
350C2C2×C31×#32312yes—
351C2C2×C31×#32412yes—
352C2C2×C31×#33611yescharacteristic
353C2C2×C31×#34211yescharacteristic
354C2C2×C31×#34311yescharacteristic
subgroupG/H
center, socleC24×C31C22⋊C4
commutatorC22C2×C4×C8×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31C2×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1280C2direct (N × H)
9. C2×C31×C22⋊C8C4semidirect
22. C23×C4×C31C8semidirect
36. C31×C22⋊C8C2×C4semidirect
75. C22×C4×C31C2×C8semidirect
83. C2×#1280C31direct (N × H)
137. #1280C2×C31direct (N × H)
176. C2×C22⋊C8C4×C31semidirect
186. C2×C31#1280direct (N × H)
199. C23×C4C8×C31semidirect
213. C22⋊C8C2×C4×C31semidirect
216. C31C2×#1280direct (N × H)
253. C22×C4C2×C8×C31semidirect
349. C2C31×#1280direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊C82
C22×C31×#952
C31×#12802
C2×#128031