Finite Group Databasebeta

← C2×C31×#1461 #21474107

Subgroups — C2×C31×#1461 #21474107

Order 7936.

1282 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
1C22×C4×Q8×C31C211yesmaximal, characteristic
2C2×C31×#431C212yesmaximal
3C31×#1461C218yesmaximal, direct product factor
4C2×C31×#324C214yesmaximal
5C23×Q8×C31C411yescharacteristic
6C2×C4×Q8×C31—22no—
7C2×C4×Q8×C31—24no—
8C2×C4×Q8×C31—22no—
9C2×C4×Q8×C31C414yes—
10C2×C4×Q8×C31C2214yes—
11C22×C4⋊C4×C31C411yescharacteristic
12C22×C4⋊C4×C31C2212yes—
13C22×C42×C31C412yes—
14C22×C42×C31C2211yescharacteristic
15C31×#431—24no—
16C31×#431C2218yes—
17C2×C31×C4⋊C8—22no—
18C2×C31×C22⋊C8C2214yes—
19C2×C4×C8×C31—22no—
20C31×#324C22116yes—
21C22×Q8×C31—22no—
22C22×Q8×C31—22no—
23C22×Q8×C31—24no—
24C22×Q8×C31C818yescomplemented
25C22×Q8×C31C2×C414yes—
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C412yes—
28C23×C4×C31C2×C412yes—
29C23×C4×C31C2×C411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—24no—
32C4×Q8×C31—28no—
33C4×Q8×C31—28no—
34C4×Q8×C31—28no—
35C4×Q8×C31—28no—
36C2×C4⋊C4×C31—22no—
37C2×C4⋊C4×C31—22no—
38C2×C4⋊C4×C31—24no—
39C2×C4⋊C4×C31—24no—
40C2×C4⋊C4×C31C2×C414yes—
41C2×C4⋊C4×C31C2×C414yes—
42C2×C4⋊C4×C31C2314yes—
43C2×C42×C31—22no—
44C2×C42×C31—24no—
45C2×C42×C31—22no—
46C2×C42×C31C2×C418yes—
47C2×C42×C31C2×C412yes—
48C2×C42×C31D412yes—
49C2×C42×C31D414yes—
50C2×C42×C31D412yes—
51C2×C42×C31C2312yes—
52C31×C4⋊C8—28no—
53C31×C22⋊C8—24no—
54C31×C22⋊C8C2318yes—
55C4×C8×C31—28no—
56C24×C31C22×C411yescharacteristic
57C2×Q8×C31—216no—
58C2×Q8×C31—216no—
59C2×Q8×C31—28no—
60C2×Q8×C31—28no—
61C2×Q8×C31C2×C8116yescomplemented
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—24no—
65C22×C4×C31—24no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—42no—
69C22×C4×C31—44no—
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C412yes—
72C22×C4×C31C22⋊C412yes—
73C22×C4×C31C22⋊C412yes—
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C2×C818yes—
76C22×C4×C31C2×C814yes—
77C22×C4×C31M1614yes—
78C22×C4×C31C22×C412yes—
79C22×C4×C31C22×C414yes—
80C22×C4×C31C22×C414yes—
81C22×C4×C31C22×C411yescharacteristic
82C22×C4×C31C22×C412yes—
83C22×C4×C31C2×D412yes—
84C22×C4×C31C2×D412yes—
85C22×C4×C31C2411yescharacteristic
86C2×C8×C31—28no—
87C2×C8×C31—48no—
88C4⋊C4×C31—28no—
89C4⋊C4×C31—28no—
90C4⋊C4×C31—28no—
91C42×C31—28no—
92C42×C31—28no—
93C42×C31C22⋊C414yes—
94C42×C31C22⋊C414yes—
95C42×C31C2×D414yes—
96C42×C31C2×D414yes—
97C2×#1461C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31—22no—
99C23×C31—22no—
100C23×C31C2×C22⋊C411yescharacteristic
101C23×C31C2×C22⋊C411yescharacteristic
102C23×C31C22×C812yes—
103C23×C31C2×M1612yes—
104C23×C31C23×C411yescharacteristic
105Q8×C31—232no—
106C2×C4×C31—24no—
107C2×C4×C31—24no—
108C2×C4×C31—28no—
109C2×C4×C31—28no—
110C2×C4×C31—24no—
111C2×C4×C31—22no—
112C2×C4×C31—24no—
113C2×C4×C31—24no—
114C2×C4×C31—24no—
115C2×C4×C31—41no—
116C2×C4×C31—42no—
117C2×C4×C31—41no—
118C2×C4×C31—44no—
119C2×C4×C31—44no—
120C2×C4×C31—44no—
121C2×C4×C31C22⋊C818yes—
122C2×C4×C31C22⋊C818yes—
123C2×C4×C31#10114yes—
124C2×C4×C31C2×C22⋊C412yes—
125C2×C4×C31C2×C22⋊C412yes—
126C2×C4×C31C2×C22⋊C414yes—
127C2×C4×C31C2×C22⋊C412yes—
128C2×C4×C31C22×C818yes—
129C2×C4×C31C22×C814yes—
130C2×C4×C31C2×M1614yes—
131C2×C4×C31C22×D412yes—
132C8×C31—48no—
133C22×C4×Q8C2×C3111yescharacteristic
134C2×#431C2×C3112yes—
135#1461C2×C3118yesdirect product factor
136C2×#324C2×C3114yes—
137C22×C31—21no—
138C22×C31—21no—
139C22×C31—21no—
140C22×C31—21no—
141C22×C31—24no—
142C22×C31—24no—
143C22×C31C2×C22⋊C812yes—
144C22×C31C2×C22⋊C812yes—
145C22×C31#41012yes—
146C22×C31C2×#10112yes—
147C22×C31C22×C22⋊C411yescharacteristic
148C22×C31C23×C811yescharacteristic
149C22×C31C22×M1611yescharacteristic
150C4×C31—28no—
151C4×C31—22no—
152C4×C31—22no—
153C4×C31—22no—
154C4×C31—44no—
155C4×C31C2×C22⋊C818yes—
156C4×C31C2×#10114yes—
157C23×Q8C4×C3111yescharacteristic
158C2×C4×Q8—22no—
159C2×C4×Q8—22no—
160C2×C4×Q8—24no—
161C2×C4×Q8C4×C3114yes—
162C2×C4×Q8C22×C3114yes—
163C22×C4⋊C4C4×C3111yescharacteristic
164C22×C4⋊C4C22×C3112yes—
165C22×C42C4×C3112yes—
166C22×C42C22×C3111yescharacteristic
167#431—24no—
168#431C22×C3118yes—
169C2×C4⋊C8—22no—
170C2×C22⋊C8C22×C3114yes—
171C2×C4×C8—22no—
172#324C22×C31116yes—
173C2×C31—21no—
174C2×C31—21no—
175C2×C31—22no—
176C2×C31#146114yesdirect product factor
177C2×C31C22×C22⋊C811yescharacteristic
178C2×C31C2×#41011yescharacteristic
179C2×C31C22×#10111yescharacteristic
180C22×Q8—22no—
181C22×Q8—22no—
182C22×Q8—24no—
183C22×Q8C8×C3118yescomplemented
184C22×Q8C2×C4×C3114yes—
185C23×C4C2×C4×C3111yescharacteristic
186C23×C4C2×C4×C3112yes—
187C23×C4C2×C4×C3112yes—
188C23×C4C2×C4×C3111yescharacteristic
189C23×C4C23×C3111yescharacteristic
190C22×C8—24no—
191C4×Q8—28no—
192C4×Q8—28no—
193C4×Q8—28no—
194C4×Q8—28no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4C2×C4×C3114yes—
200C2×C4⋊C4C2×C4×C3114yes—
201C2×C4⋊C4C23×C3114yes—
202C2×C42—22no—
203C2×C42—24no—
204C2×C42—22no—
205C2×C42C2×C4×C3118yes—
206C2×C42C2×C4×C3112yes—
207C2×C42D4×C3112yes—
208C2×C42D4×C3112yes—
209C2×C42D4×C3114yes—
210C2×C42C23×C3112yes—
211C4⋊C8—28no—
212C22⋊C8—24no—
213C22⋊C8C23×C3118yes—
214C4×C8—28no—
215C31C2×#146111yescharacteristic, direct product factor, Sylow
216C24C22×C4×C3111yescharacteristic
217C2×Q8—216no—
218C2×Q8—216no—
219C2×Q8—28no—
220C2×Q8—28no—
221C2×Q8C2×C8×C31116yescomplemented
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—44no—
230C22×C4C22⋊C4×C3111yescharacteristic
231C22×C4C22⋊C4×C3112yes—
232C22×C4C22⋊C4×C3112yes—
233C22×C4C22⋊C4×C3112yes—
234C22×C4C22⋊C4×C3111yescharacteristic
235C22×C4C2×C8×C3118yes—
236C22×C4C2×C8×C3114yes—
237C22×C4M16×C3114yes—
238C22×C4C22×C4×C3112yes—
239C22×C4C22×C4×C3114yes—
240C22×C4C22×C4×C3114yes—
241C22×C4C22×C4×C3111yescharacteristic
242C22×C4C22×C4×C3112yes—
243C22×C4C2×D4×C3112yes—
244C22×C4C2×D4×C3112yes—
245C22×C4C24×C3111yescharacteristic
246C2×C8—28no—
247C2×C8—48no—
248C4⋊C4—28no—
249C4⋊C4—28no—
250C4⋊C4—28no—
251C42—28no—
252C42—28no—
253C42C22⋊C4×C3114yes—
254C42C22⋊C4×C3114yes—
255C42C2×D4×C3114yes—
256C42C2×D4×C3114yes—
257C23—22no—
258C23—22no—
259C23C2×C22⋊C4×C3111yescharacteristic
260C23C2×C22⋊C4×C3111yescharacteristic
261C23C22×C8×C3112yes—
262C23C2×M16×C3112yes—
263C23C23×C4×C3111yescharacteristic
264Q8—232no—
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—24no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4C31×C22⋊C818yes—
281C2×C4C31×C22⋊C818yes—
282C2×C4C31×#10114yes—
283C2×C4C2×C22⋊C4×C3112yes—
284C2×C4C2×C22⋊C4×C3112yes—
285C2×C4C2×C22⋊C4×C3114yes—
286C2×C4C2×C22⋊C4×C3112yes—
287C2×C4C22×C8×C3118yes—
288C2×C4C22×C8×C3114yes—
289C2×C4C2×M16×C3114yes—
290C2×C4C22×D4×C3112yes—
291C8—48no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—24no—
297C22—24no—
298C22C2×C31×C22⋊C812yes—
299C22C2×C31×C22⋊C812yes—
300C22C31×#41012yes—
301C22C2×C31×#10112yes—
302C22C22×C22⋊C4×C3111yescharacteristic
303C22C23×C8×C3111yescharacteristic
304C22C22×M16×C3111yescharacteristic
305C4—28no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—44no—
310C4C2×C31×C22⋊C818yes—
311C4C2×C31×#10114yes—
312C2—22no—
313C2—21no—
314C2—21no—
315C2C31×#146114yesdirect product factor
316C2C22×C31×C22⋊C811yescharacteristic
317C2C2×C31×#41011yescharacteristic
318C2C22×C31×#10111yescharacteristic
subgroupG/H
centerC22×C4×C31C22⋊C4
commutatorC22C23×C8×C31
Frattini, cosocleC22×C4C24×C31
socleC23×C31C2×C22⋊C4
prime radicalC24×C31C22×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1461C2direct (N × H)
24. C22×Q8×C31C8semidirect
61. C2×Q8×C31C2×C8semidirect
97. C2×#1461C31direct (N × H)
135. #1461C2×C31direct (N × H)
176. C2×C31#1461direct (N × H)
183. C22×Q8C8×C31semidirect
215. C31C2×#1461direct (N × H)
221. C2×Q8C2×C8×C31semidirect
315. C2C31×#1461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C2×C31×#4312
C31×#14612
C2×C31×#3242
C2×#146131