Finite Group Databasebeta

← C31×#8762 #21465521

Subgroups — C31×#8762 #21465521

Order 7936.

472 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2353C211yesmaximal, characteristic
2C31×#1799C211yesmaximal, characteristic
3C31×#1459C211yesmaximal, characteristic
4C31×#1294C212yesmaximal, complemented
5C31×#1289C212yesmaximal, complemented
6C2×C4×D4×C31C2211yescharacteristic
7C2×C31×#99—21no—
8C2×C31×C22⋊C8C2212yes—
9C31×#388—21no—
10C31×#387—21no—
11C31×#386—21no—
12C31×#383C411yescharacteristic, complemented
13C31×#381C411yescharacteristic, complemented
14C31×#380C2212yes—
15C31×#380C2211yescharacteristic
16C4×C22⋊C4×C31—21no—
17C4×C22⋊C4×C31C411yescharacteristic, complemented
18C31×#376C411yescharacteristic, complemented
19C2×C31×#95C2211yescharacteristic
20C31×#342—21no—
21C31×#324—21no—
22C31×#323—21no—
23C22×D4×C31D411yescharacteristic
24C23×C4×C31—21no—
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C22×C8×C31—22no—
28C4×D4×C31—22no—
29C4×D4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C22⋊C4×C31—21no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31D411yescharacteristic
38C2×C22⋊C4×C31D411yescharacteristic
39C2×C42×C31—21no—
40C2×C42×C31—21no—
41C2×C42×C31C2×C411yescharacteristic
42C31×#99—42no—
43C31×C22⋊C8—22no—
44C31×C22⋊C8—22no—
45C31×#95—21no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—22no—
51C31×#95C2×C411yescharacteristic
52C31×#95C2×C411yescharacteristic
53C31×#95C2×C411yescharacteristic
54C31×#95C2×C411yescharacteristic
55C24×C31C22⋊C411yescharacteristic
56C24×C31C2×D411yescharacteristic
57C2×D4×C31—22no—
58C2×D4×C31—22no—
59C2×D4×C31—21no—
60C2×D4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—42no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—42no—
71C22×C4×C31—81no—
72C22×C4×C31—81no—
73C22×C4×C31—81no—
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22×C411yescharacteristic
78C22×C4×C31C2×D411yescharacteristic
79C22×C4×C31#4112yes—
80C22×C4×C31#4112yes—
81C2×C8×C31—42no—
82C2×C8×C31—82no—
83C4⋊C4×C31—22no—
84C4⋊C4×C31—81no—
85C4⋊C4×C31—82no—
86C22⋊C4×C31—22no—
87C22⋊C4×C31—22no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—42no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—81no—
93C42×C31—21no—
94C42×C31—21no—
95C42×C31—42no—
96C42×C31—81no—
97#8762C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31—21no—
99C23×C31—21no—
100C23×C31—21no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31—41no—
105C23×C31C2×C22⋊C411yescharacteristic
106C23×C31#12312yes—
107C23×C31#13512yes—
108C23×C31AGL(1,ℤ/8)11yescharacteristic
109C23×C31#13711yescharacteristic
110D4×C31—42no—
111D4×C31—42no—
112C2×C4×C31—22no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—41no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
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—81no—
136C2×C4×C31—81no—
137C2×C4×C31—82no—
138C2×C4×C31—82no—
139C2×C4×C31—82no—
140C2×C4×C31—82no—
141C2×C4×C31—82no—
142C2×C4×C31#11711yescharacteristic
143C2×C4×C31#11711yescharacteristic
144C2×C4×C31#12312yes—
145C8×C31—82no—
146#2353C2×C3111yescharacteristic
147#1799C2×C3111yescharacteristic
148#1459C2×C3111yescharacteristic
149#1294C2×C3112yescomplemented
150#1289C2×C3112yescomplemented
151C22×C31—21no—
152C22×C31—22no—
153C22×C31—21no—
154C22×C31—22no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—42no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—81no—
162C22×C31—81no—
163C22×C31#38111yescharacteristic
164C22×C31#41611yescharacteristic
165C22×C31#41711yescharacteristic
166C22×C31#48212yes—
167C22×C31#48512yes—
168C4×C31—22no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—42no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—81no—
176C4×C31—81no—
177C4×C31—81no—
178C4×C31—162no—
179C2×C4×D4C22×C3111yescharacteristic
180C2×#99—21no—
181C2×C22⋊C8C22×C3112yes—
182#388—21no—
183#387—21no—
184#386—21no—
185#383C4×C3111yescharacteristic, complemented
186#381C4×C3111yescharacteristic, complemented
187#380C22×C3112yes—
188#380C22×C3111yescharacteristic
189C4×C22⋊C4—21no—
190C4×C22⋊C4C4×C3111yescharacteristic, complemented
191#376C4×C3111yescharacteristic, complemented
192C2×#95C22×C3111yescharacteristic
193#342—21no—
194#324—21no—
195#323—21no—
196C2×C31—21no—
197C2×C31—21no—
198C2×C31—22no—
199C2×C31—22no—
200C2×C31—81no—
201C2×C31#182511yescharacteristic
202C2×C31#182711yescharacteristic
203C2×C31#182811yescharacteristic
204C22×D4D4×C3111yescharacteristic
205C23×C4—21no—
206C23×C4C2×C4×C3111yescharacteristic
207C23×C4C23×C3111yescharacteristic
208C22×C8—22no—
209C4×D4—22no—
210C4×D4—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4D4×C3111yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4D4×C3111yescharacteristic
219C2×C22⋊C4D4×C3111yescharacteristic
220C2×C42—21no—
221C2×C42—21no—
222C2×C42C2×C4×C3111yescharacteristic
223#99—42no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—22no—
232#95C2×C4×C3111yescharacteristic
233#95C2×C4×C3111yescharacteristic
234#95C2×C4×C3111yescharacteristic
235#95C2×C4×C3111yescharacteristic
236C31#876211yescharacteristic, direct product factor, Sylow
237C24C22⋊C4×C3111yescharacteristic
238C24C2×D4×C3111yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—42no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4C22⋊C4×C3111yescharacteristic
257C22×C4C22⋊C4×C3111yescharacteristic
258C22×C4C22⋊C4×C3111yescharacteristic
259C22×C4C22×C4×C3111yescharacteristic
260C22×C4C2×D4×C3111yescharacteristic
261C22×C4#41×C3112yes—
262C22×C4#41×C3112yes—
263C2×C8—42no—
264C2×C8—82no—
265C4⋊C4—22no—
266C4⋊C4—81no—
267C4⋊C4—82no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—81no—
275C42—21no—
276C42—21no—
277C42—42no—
278C42—81no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C2×C22⋊C4×C3111yescharacteristic
287C23C31×#12312yes—
288C23C31×#13512yes—
289C23C31×AGL(1,ℤ/8)11yescharacteristic
290C23C31×#13711yescharacteristic
291D4—42no—
292D4—42no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4C31×#11711yescharacteristic
324C2×C4C31×#11711yescharacteristic
325C2×C4C31×#12312yes—
326C8—82no—
327C22—21no—
328C22—22no—
329C22—21no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22C31×#38111yescharacteristic
340C22C31×#41611yescharacteristic
341C22C31×#41711yescharacteristic
342C22C31×#48212yes—
343C22C31×#48512yes—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—162no—
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—81no—
360C2C31×#182511yescharacteristic
361C2C31×#182711yescharacteristic
362C2C31×#182811yescharacteristic
subgroupG/H
center, socleC22×C31#381
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1294C2semidirect
5. C31×#1289C2semidirect
12. C31×#383C4semidirect
13. C31×#381C4semidirect
17. C4×C22⋊C4×C31C4semidirect
18. C31×#376C4semidirect
97. #8762C31direct (N × H)
149. #1294C2×C31semidirect
150. #1289C2×C31semidirect
185. #383C4×C31semidirect
186. #381C4×C31semidirect
190. C4×C22⋊C4C4×C31semidirect
191. #376C4×C31semidirect
236. C31#8762direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23532
C31×#17992
C31×#14592
C31×#12942
C31×#12892
#876231