Finite Group Databasebeta

← C31×#8714 #21465473

Subgroups — C31×#8714 #21465473

Order 7936.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2283C211yesmaximal, characteristic
2C31×#1817C211yesmaximal, characteristic
3C31×#1434C211yesmaximal, characteristic
4C31×#1294C212yesmaximal
5C31×#1294C212yesmaximal
6C22×C42×C31C2211yescharacteristic
7C2×C31×C22⋊C8C2212yes—
8C31×#383—21no—
9C31×#382C411yescharacteristic, complemented
10C31×#382C411yescharacteristic, complemented
11C31×#381—21no—
12C31×#380C2211yescharacteristic
13C31×#380C2211yescharacteristic
14C4×C4⋊C4×C31C411yescharacteristic, complemented
15C4×C4⋊C4×C31C411yescharacteristic, complemented
16C4×C22⋊C4×C31—21no—
17C31×#376—21no—
18C2×C31×#95—21no—
19C2×C31×#95—21no—
20C2×C31×#95C2212yes—
21C31×#336—21no—
22C31×#336—21no—
23C23×C4×C31—22no—
24C23×C4×C31D411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C22×C8×C31—22no—
28C2×C4⋊C4×C31C2×C411yescharacteristic
29C2×C4⋊C4×C31C2×C411yescharacteristic
30C2×C4⋊C4×C31C2×C411yescharacteristic
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C22⋊C4×C31—21no—
33C2×C22⋊C4×C31—21no—
34C2×C42×C31—24no—
35C2×C42×C31—21no—
36C2×C42×C31—21no—
37C2×C42×C31C2×C411yescharacteristic
38C2×C42×C31C2×C411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C31×C22⋊C8—24no—
42C31×#95—24no—
43C31×#95—21no—
44C31×#95—21no—
45C31×#95—21no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—24no—
52C31×#95—42no—
53C24×C31C2×D411yescharacteristic
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—22no—
60C22×C4×C31—24no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—41no—
66C22×C4×C31—41no—
67C22×C4×C31—41no—
68C22×C4×C31—42no—
69C22×C4×C31—42no—
70C22×C4×C31—42no—
71C22×C4×C31—42no—
72C22×C4×C31—42no—
73C22×C4×C31—42no—
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22×C411yescharacteristic
79C22×C4×C31C2×D411yescharacteristic
80C22×C4×C31#4114yes—
81C2×C8×C31—42no—
82C2×C8×C31—42no—
83C2×C8×C31—42no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C42×C31—22no—
92C42×C31—22no—
93C42×C31—22no—
94C42×C31—22no—
95C42×C31—42no—
96C42×C31—42no—
97#8714C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31—21no—
99C23×C31—21no—
100C23×C31—21no—
101C23×C31—21no—
102C23×C31C2×C22⋊C411yescharacteristic
103C23×C31#12312yes—
104C23×C31#13512yes—
105C23×C31AGL(1,ℤ/8)11yescharacteristic
106C23×C31#13711yescharacteristic
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—44no—
123C2×C4×C31—44no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—44no—
127C2×C4×C31—44no—
128C2×C4×C31—44no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—82no—
142C2×C4×C31—82no—
143C2×C4×C31—82no—
144C2×C4×C31—82no—
145C2×C4×C31#10412yes—
146C2×C4×C31#11712yes—
147C2×C4×C31#12312yes—
148C8×C31—82no—
149#2283C2×C3111yescharacteristic
150#1817C2×C3111yescharacteristic
151#1434C2×C3111yescharacteristic
152#1294C2×C3112yes—
153#1294C2×C3112yes—
154C22×C31—22no—
155C22×C31—22no—
156C22×C31—22no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—22no—
162C22×C31#38111yescharacteristic
163C22×C31#41011yescharacteristic
164C22×C31#41011yescharacteristic
165C22×C31#41611yescharacteristic
166C22×C31#41711yescharacteristic
167C22×C31C2×#10411yescharacteristic
168C22×C31#42111yescharacteristic
169C22×C31#48212yes—
170C22×C31#48512yes—
171C4×C31—22no—
172C4×C31—22no—
173C4×C31—22no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31—41no—
177C4×C31—84no—
178C4×C31—81no—
179C4×C31—81no—
180C4×C31—81no—
181C4×C31—81no—
182C22×C42C22×C3111yescharacteristic
183C2×C22⋊C8C22×C3112yes—
184#383—21no—
185#382C4×C3111yescharacteristic, complemented
186#382C4×C3111yescharacteristic, complemented
187#381—21no—
188#380C22×C3111yescharacteristic
189#380C22×C3111yescharacteristic
190C4×C4⋊C4C4×C3111yescharacteristic, complemented
191C4×C4⋊C4C4×C3111yescharacteristic, complemented
192C4×C22⋊C4—21no—
193#376—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95C22×C3112yes—
197#336—21no—
198#336—21no—
199C2×C31—22no—
200C2×C31—22no—
201C2×C31#150011yescharacteristic
202C2×C31#150911yescharacteristic
203C2×C31#151211yescharacteristic
204C2×C31#152111yescharacteristic
205C2×C31#182011yescharacteristic
206C2×C31#182511yescharacteristic
207C2×C31#182611yescharacteristic
208C23×C4—22no—
209C23×C4D4×C3111yescharacteristic
210C23×C4D4×C3111yescharacteristic
211C23×C4C23×C3111yescharacteristic
212C22×C8—22no—
213C2×C4⋊C4C2×C4×C3111yescharacteristic
214C2×C4⋊C4C2×C4×C3111yescharacteristic
215C2×C4⋊C4C2×C4×C3111yescharacteristic
216C2×C4⋊C4C2×C4×C3111yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42—24no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42C2×C4×C3111yescharacteristic
223C2×C42C2×C4×C3111yescharacteristic
224C2×C42D4×C3111yescharacteristic
225C2×C42D4×C3111yescharacteristic
226C22⋊C8—24no—
227#95—24no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—24no—
237#95—42no—
238C31#871411yescharacteristic, direct product factor, Sylow
239C24C2×D4×C3111yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4C22⋊C4×C3111yescharacteristic
261C22×C4C22⋊C4×C3111yescharacteristic
262C22×C4C22⋊C4×C3111yescharacteristic
263C22×C4C22⋊C4×C3111yescharacteristic
264C22×C4C22×C4×C3111yescharacteristic
265C22×C4C2×D4×C3111yescharacteristic
266C22×C4#41×C3114yes—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C22⋊C4×C3111yescharacteristic
288C23C31×#12312yes—
289C23C31×#13512yes—
290C23C31×AGL(1,ℤ/8)11yescharacteristic
291C23C31×#13711yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4C31×#10412yes—
331C2×C4C31×#11712yes—
332C2×C4C31×#12312yes—
333C8—82no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22C31×#38111yescharacteristic
343C22C31×#41011yescharacteristic
344C22C31×#41011yescharacteristic
345C22C31×#41611yescharacteristic
346C22C31×#41711yescharacteristic
347C22C2×C31×#10411yescharacteristic
348C22C31×#42111yescharacteristic
349C22C31×#48212yes—
350C22C31×#48512yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—81no—
362C2—22no—
363C2—22no—
364C2C31×#150011yescharacteristic
365C2C31×#150911yescharacteristic
366C2C31×#151211yescharacteristic
367C2C31×#152111yescharacteristic
368C2C31×#182011yescharacteristic
369C2C31×#182511yescharacteristic
370C2C31×#182611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#382C4semidirect
10. C31×#382C4semidirect
14. C4×C4⋊C4×C31C4semidirect
15. C4×C4⋊C4×C31C4semidirect
97. #8714C31direct (N × H)
185. #382C4×C31semidirect
186. #382C4×C31semidirect
190. C4×C4⋊C4C4×C31semidirect
191. C4×C4⋊C4C4×C31semidirect
238. C31#8714direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22832
C31×#18172
C31×#14342
C31×#12942
#871431