Finite Group Databasebeta

← C2×C31×#1440 #21470596

Subgroups — C2×C31×#1440 #21470596

Order 7936.

4622 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C31C212yesmaximal
2C23×C22⋊C4×C31C211yesmaximal, characteristic
3C22×C31×#95C214yesmaximal, complemented
4C31×#1440C218yesmaximal, direct product factor
5C26×C31C2211yescharacteristic
6C24×C4×C31C2212yes—
7C24×C4×C31C2214yes—
8C22×C22⋊C4×C31—28no—
9C22×C22⋊C4×C31—28no—
10C22×C22⋊C4×C31—216no—
11C22×C22⋊C4×C31C418yescomplemented
12C22×C22⋊C4×C31C2218yes—
13C22×C22⋊C4×C31C2214yes—
14C2×C31×#95—216no—
15C2×C31×#95C22116yescomplemented
16C25×C31—28no—
17C25×C31—28no—
18C25×C31—28no—
19C25×C31C2×C414yes—
20C25×C31D418yes—
21C25×C31C2312yes—
22C25×C31C2311yescharacteristic
23C23×C4×C31—24no—
24C23×C4×C31—24no—
25C23×C4×C31—28no—
26C23×C4×C31—28no—
27C23×C4×C31—28no—
28C23×C4×C31—28no—
29C23×C4×C31—28no—
30C23×C4×C31—28no—
31C23×C4×C31—28no—
32C23×C4×C31—28no—
33C23×C4×C31C2×C418yes—
34C23×C4×C31D4116yes—
35C23×C4×C31C2314yes—
36C23×C4×C31C2318yes—
37C2×C22⋊C4×C31—264no—
38C2×C22⋊C4×C31—232no—
39C2×C22⋊C4×C31—216no—
40C2×C22⋊C4×C31—216no—
41C2×C22⋊C4×C31—232no—
42C2×C22⋊C4×C31C2×C4116yescomplemented
43C31×#95—232no—
44C24×C31—216no—
45C24×C31—232no—
46C24×C31—216no—
47C24×C31—232no—
48C24×C31—232no—
49C24×C31—216no—
50C24×C31—28no—
51C24×C31—28no—
52C24×C31—28no—
53C24×C31—416no—
54C24×C31—416no—
55C24×C31—416no—
56C24×C31—416no—
57C24×C31C22⋊C4116yes—
58C24×C31C22×C414yes—
59C24×C31C22×C412yes—
60C24×C31C2×D418yes—
61C24×C31C2×D414yes—
62C24×C31C2×D418yes—
63C24×C31#4118yes—
64C24×C31#4118yes—
65C24×C31C2411yescharacteristic
66C22×C4×C31—216no—
67C22×C4×C31—232no—
68C22×C4×C31—232no—
69C22×C4×C31—232no—
70C22×C4×C31—232no—
71C22×C4×C31—28no—
72C22×C4×C31—28no—
73C22×C4×C31—24no—
74C22×C4×C31—24no—
75C22×C4×C31—28no—
76C22×C4×C31—28no—
77C22×C4×C31—28no—
78C22×C4×C31—28no—
79C22×C4×C31—28no—
80C22×C4×C31—28no—
81C22×C4×C31—48no—
82C22×C4×C31—416no—
83C22×C4×C31—416no—
84C22×C4×C31—416no—
85C22×C4×C31—48no—
86C22×C4×C31—416no—
87C22×C4×C31—416no—
88C22×C4×C31C22×C418yes—
89C22×C4×C31C2×D4116yes—
90C22⋊C4×C31—264no—
91C22⋊C4×C31—232no—
92C2×#1440C3111yesmaximal, characteristic, direct product factor, Sylow
93C23×C31—28no—
94C23×C31—216no—
95C23×C31—28no—
96C23×C31—216no—
97C23×C31—216no—
98C23×C31—28no—
99C23×C31—232no—
100C23×C31—264no—
101C23×C31—48no—
102C23×C31—48no—
103C23×C31—48no—
104C23×C31—48no—
105C23×C31—464no—
106C23×C31—464no—
107C23×C31—464no—
108C23×C31C2×C22⋊C418yes—
109C23×C31C2×C22⋊C414yes—
110C23×C31#11718yes—
111C23×C31C4×D4116yes—
112C23×C31#12018yes—
113C23×C31#121116yes—
114C23×C31#121116yes—
115C23×C31#123116yes—
116C23×C31#12318yes—
117C23×C31#123116yes—
118C23×C31#124116yes—
119C23×C31#126116yes—
120C23×C31C23×C411yescharacteristic
121C23×C31C22×D412yes—
122C23×C31C22×D414yes—
123C23×C31C2×#4114yes—
124C23×C31C2×#4114yes—
125C2×C4×C31—28no—
126C2×C4×C31—216no—
127C2×C4×C31—216no—
128C2×C4×C31—216no—
129C2×C4×C31—216no—
130C2×C4×C31—44no—
131C2×C4×C31—48no—
132C2×C4×C31—48no—
133C2×C4×C31—48no—
134C2×C4×C31—48no—
135C2×C4×C31—44no—
136C2×C4×C31—48no—
137C2×C4×C31—432no—
138C2×C4×C31—464no—
139C23×C22⋊C4C2×C3112yes—
140C23×C22⋊C4C2×C3111yescharacteristic
141C22×#95C2×C3114yescomplemented
142#1440C2×C3118yesdirect product factor
143C22×C31—28no—
144C22×C31—216no—
145C22×C31—416no—
146C22×C31—416no—
147C22×C31—464no—
148C22×C31—416no—
149C22×C31#38118yes—
150C22×C31#386116yes—
151C22×C31#388132yes—
152C22×C31#394132yes—
153C22×C31#397132yes—
154C22×C31C22×C22⋊C411yescharacteristic
155C22×C31C2×#11712yes—
156C22×C31C2×C4×D414yes—
157C22×C31C2×#12012yes—
158C22×C31C2×#12114yes—
159C22×C31C2×#12114yes—
160C22×C31C2×#12314yes—
161C22×C31C2×#12314yes—
162C22×C31C2×#12312yes—
163C22×C31C2×#12414yes—
164C22×C31C2×#12614yes—
165C4×C31—416no—
166C4×C31—48no—
167C26C22×C3111yescharacteristic
168C24×C4C22×C3112yes—
169C24×C4C22×C3114yes—
170C22×C22⋊C4—28no—
171C22×C22⋊C4—28no—
172C22×C22⋊C4—216no—
173C22×C22⋊C4C4×C3118yescomplemented
174C22×C22⋊C4C22×C3118yes—
175C22×C22⋊C4C22×C3114yes—
176C2×#95—216no—
177C2×#95C22×C31116yescomplemented
178C2×C31—48no—
179C2×C31#1440116yesdirect product factor
180C2×C31C2×#38111yescharacteristic
181C2×C31C2×#38612yes—
182C2×C31C2×#38814yes—
183C2×C31C2×#39414yes—
184C2×C31C2×#39714yes—
185C25—28no—
186C25—28no—
187C25—28no—
188C25C2×C4×C3114yes—
189C25D4×C3118yes—
190C25C23×C3112yes—
191C25C23×C3111yescharacteristic
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—28no—
195C23×C4—28no—
196C23×C4—28no—
197C23×C4—28no—
198C23×C4—28no—
199C23×C4—28no—
200C23×C4—28no—
201C23×C4—28no—
202C23×C4C2×C4×C3118yes—
203C23×C4D4×C31116yes—
204C23×C4C23×C3114yes—
205C23×C4C23×C3118yes—
206C2×C22⋊C4—264no—
207C2×C22⋊C4—232no—
208C2×C22⋊C4—216no—
209C2×C22⋊C4—216no—
210C2×C22⋊C4—232no—
211C2×C22⋊C4C2×C4×C31116yescomplemented
212#95—232no—
213C31C2×#144011yescharacteristic, direct product factor, Sylow
214C24—216no—
215C24—232no—
216C24—216no—
217C24—232no—
218C24—232no—
219C24—216no—
220C24—28no—
221C24—28no—
222C24—28no—
223C24—416no—
224C24—416no—
225C24—416no—
226C24—416no—
227C24C22⋊C4×C31116yes—
228C24C22×C4×C3114yes—
229C24C22×C4×C3112yes—
230C24C2×D4×C3118yes—
231C24C2×D4×C3114yes—
232C24C2×D4×C3118yes—
233C24#41×C3118yes—
234C24#41×C3118yes—
235C24C24×C3111yescharacteristic
236C22×C4—216no—
237C22×C4—232no—
238C22×C4—232no—
239C22×C4—232no—
240C22×C4—232no—
241C22×C4—28no—
242C22×C4—28no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—28no—
246C22×C4—28no—
247C22×C4—28no—
248C22×C4—28no—
249C22×C4—28no—
250C22×C4—28no—
251C22×C4—48no—
252C22×C4—416no—
253C22×C4—416no—
254C22×C4—416no—
255C22×C4—48no—
256C22×C4—416no—
257C22×C4—416no—
258C22×C4C22×C4×C3118yes—
259C22×C4C2×D4×C31116yes—
260C22⋊C4—264no—
261C22⋊C4—232no—
262C23—28no—
263C23—216no—
264C23—28no—
265C23—216no—
266C23—216no—
267C23—28no—
268C23—232no—
269C23—264no—
270C23—464no—
271C23—48no—
272C23—48no—
273C23—48no—
274C23—48no—
275C23—464no—
276C23—464no—
277C23C2×C22⋊C4×C3118yes—
278C23C2×C22⋊C4×C3114yes—
279C23C31×#11718yes—
280C23C4×D4×C31116yes—
281C23C31×#12018yes—
282C23C31×#121116yes—
283C23C31×#121116yes—
284C23C31×#12318yes—
285C23C31×#123116yes—
286C23C31×#123116yes—
287C23C31×#124116yes—
288C23C31×#126116yes—
289C23C23×C4×C3111yescharacteristic
290C23C22×D4×C3112yes—
291C23C22×D4×C3114yes—
292C23C2×#41×C3114yes—
293C23C2×#41×C3114yes—
294C2×C4—28no—
295C2×C4—216no—
296C2×C4—216no—
297C2×C4—216no—
298C2×C4—216no—
299C2×C4—44no—
300C2×C4—48no—
301C2×C4—48no—
302C2×C4—48no—
303C2×C4—48no—
304C2×C4—44no—
305C2×C4—48no—
306C2×C4—432no—
307C2×C4—464no—
308C22—28no—
309C22—216no—
310C22—416no—
311C22—416no—
312C22—464no—
313C22—416no—
314C22C31×#38118yes—
315C22C31×#386116yes—
316C22C31×#388132yes—
317C22C31×#394132yes—
318C22C31×#397132yes—
319C22C22×C22⋊C4×C3111yescharacteristic
320C22C2×C31×#11712yes—
321C22C2×C4×D4×C3114yes—
322C22C2×C31×#12012yes—
323C22C2×C31×#12114yes—
324C22C2×C31×#12114yes—
325C22C2×C31×#12314yes—
326C22C2×C31×#12314yes—
327C22C2×C31×#12312yes—
328C22C2×C31×#12414yes—
329C22C2×C31×#12614yes—
330C4—416no—
331C4—48no—
332C2—48no—
333C2C31×#1440116yesdirect product factor
334C2C2×C31×#38111yescharacteristic
335C2C2×C31×#38612yes—
336C2C2×C31×#38814yes—
337C2C2×C31×#39414yes—
338C2C2×C31×#39714yes—
subgroupG/H
center, socleC25×C31C23
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C31×#95C2semidirect
4. C31×#1440C2direct (N × H)
11. C22×C22⋊C4×C31C4semidirect
15. C2×C31×#95C22semidirect
42. C2×C22⋊C4×C31C2×C4semidirect
92. C2×#1440C31direct (N × H)
141. C22×#95C2×C31semidirect
142. #1440C2×C31direct (N × H)
173. C22×C22⋊C4C4×C31semidirect
177. C2×#95C22×C31semidirect
179. C2×C31#1440direct (N × H)
211. C2×C22⋊C4C2×C4×C31semidirect
213. C31C2×#1440direct (N × H)
333. C2C31×#1440direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C22×C31×#952
C31×#14402
C2×#144031