Finite Group Databasebeta

← C31×#9910 #21466669

Subgroups — C31×#9910 #21466669

Order 7936.

640 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2851C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C4×C31×#95C211yesmaximal, characteristic
4C31×#1294C212yesmaximal
5C31×#1294C212yesmaximal
6C2×C31×#125C411yescharacteristic, complemented
7C22×C42×C31—21no—
8C22×C42×C31C2211yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C22⋊C8C2212yes—
11C31×#389C411yescharacteristic, complemented
12C31×#389C411yescharacteristic, complemented
13C31×#387—21no—
14C31×#387—21no—
15C31×#385—21no—
16C31×#385—21no—
17C31×#382C411yescharacteristic, complemented
18C31×#380C2211yescharacteristic
19C31×#380C2211yescharacteristic
20C2×C31×#95—21no—
21C2×C31×#95C2212yes—
22C31×#336—21no—
23C23×C4×C31—22no—
24C23×C4×C31D411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C22×C8×C31—22no—
28C31×#125—42no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C42×C31—24no—
40C2×C42×C31—42no—
41C2×C42×C31—42no—
42C2×C42×C31—42no—
43C2×C42×C31C2×C411yescharacteristic
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C31×C4⋊C8—42no—
48C31×C22⋊C8—24no—
49C31×#95—24no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—22no—
57C31×#95Q814yes—
58C24×C31C2×D411yescharacteristic
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—24no—
64C22×C4×C31—24no—
65C22×C4×C31—24no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—41no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—42no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22×C411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85C22×C4×C31C2×Q812yes—
86C22×C4×C31#4112yes—
87C2×C8×C31—42no—
88C2×C8×C31—42no—
89C2×C8×C31—42no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—41no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—42no—
96C4⋊C4×C31—42no—
97C4⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—41no—
100C22⋊C4×C31—41no—
101C42×C31—22no—
102C42×C31—22no—
103C42×C31—41no—
104C42×C31—41no—
105C42×C31—48no—
106#9910C3111yesmaximal, characteristic, direct product factor, Sylow
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31C2×C22⋊C411yescharacteristic
112C23×C31C22⋊Q812yes—
113C23×C31#13512yes—
114C23×C31AGL(1,ℤ/8)11yescharacteristic
115C23×C31#13711yescharacteristic
116C2×C4×C31—24no—
117C2×C4×C31—24no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—28no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—44no—
135C2×C4×C31—44no—
136C2×C4×C31—44no—
137C2×C4×C31—44no—
138C2×C4×C31—44no—
139C2×C4×C31—44no—
140C2×C4×C31—44no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31#9912yes—
154C2×C4×C31#10412yes—
155C2×C4×C31#10412yes—
156C2×C4×C31C4×Q812yes—
157C2×C4×C31#12411yescharacteristic
158C2×C4×C31C4⋊Q811yescharacteristic
159C8×C31—82no—
160#2851C2×C3111yescharacteristic
161#1797C2×C3111yescharacteristic
162C4×#95C2×C3111yescharacteristic
163#1294C2×C3112yes—
164#1294C2×C3112yes—
165C22×C31—22no—
166C22×C31—22no—
167C22×C31—22no—
168C22×C31—22no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—21no—
173C22×C31#39111yescharacteristic
174C22×C31C2×#9911yescharacteristic
175C22×C31#41011yescharacteristic
176C22×C31#41611yescharacteristic
177C22×C31#41711yescharacteristic
178C22×C31C2×#10411yescharacteristic
179C22×C31C2×#10411yescharacteristic
180C22×C31#47812yes—
181C22×C31#47912yes—
182C4×C31—21no—
183C4×C31—22no—
184C4×C31—21no—
185C4×C31—22no—
186C4×C31—22no—
187C4×C31—22no—
188C4×C31—48no—
189C4×C31—41no—
190C4×C31—81no—
191C4×C31—81no—
192C4×C31—81no—
193C4×C31—81no—
194C2×#125C4×C3111yescharacteristic, complemented
195C22×C42—21no—
196C22×C42C22×C3111yescharacteristic
197C2×C4⋊C8—21no—
198C2×C22⋊C8C22×C3112yes—
199#389C4×C3111yescharacteristic, complemented
200#389C4×C3111yescharacteristic, complemented
201#387—21no—
202#387—21no—
203#385—21no—
204#385—21no—
205#382C4×C3111yescharacteristic, complemented
206#380C22×C3111yescharacteristic
207#380C22×C3111yescharacteristic
208C2×#95—21no—
209C2×#95C22×C3112yes—
210#336—21no—
211C2×C31—22no—
212C2×C31—22no—
213C2×C31#150011yescharacteristic
214C2×C31#150111yescharacteristic
215C2×C31#150411yescharacteristic
216C2×C31#150911yescharacteristic
217C2×C31#198911yescharacteristic
218C2×C31#199411yescharacteristic
219C2×C31#199611yescharacteristic
220C23×C4—22no—
221C23×C4D4×C3111yescharacteristic
222C23×C4D4×C3111yescharacteristic
223C23×C4C23×C3111yescharacteristic
224C22×C8—22no—
225#125—42no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×C4×C3111yescharacteristic
231C2×C4⋊C4C2×C4×C3111yescharacteristic
232C2×C4⋊C4C2×C4×C3111yescharacteristic
233C2×C4⋊C4C2×C4×C3111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42—24no—
237C2×C42—42no—
238C2×C42—42no—
239C2×C42—42no—
240C2×C42C2×C4×C3111yescharacteristic
241C2×C42C2×C4×C3111yescharacteristic
242C2×C42D4×C3111yescharacteristic
243C2×C42D4×C3111yescharacteristic
244C4⋊C8—42no—
245C22⋊C8—24no—
246#95—24no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—22no—
254#95Q8×C3114yes—
255C31#991011yescharacteristic, direct product factor, Sylow
256C24C2×D4×C3111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4C22⋊C4×C3111yescharacteristic
278C22×C4C22⋊C4×C3111yescharacteristic
279C22×C4C22⋊C4×C3111yescharacteristic
280C22×C4C22⋊C4×C3111yescharacteristic
281C22×C4C22×C4×C3111yescharacteristic
282C22×C4C2×D4×C3111yescharacteristic
283C22×C4C2×Q8×C3112yes—
284C22×C4#41×C3112yes—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42—22no—
300C42—22no—
301C42—41no—
302C42—41no—
303C42—48no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23C2×C22⋊C4×C3111yescharacteristic
309C23C31×C22⋊Q812yes—
310C23C31×#13512yes—
311C23C31×AGL(1,ℤ/8)11yescharacteristic
312C23C31×#13711yescharacteristic
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—28no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4C31×#9912yes—
351C2×C4C31×#10412yes—
352C2×C4C31×#10412yes—
353C2×C4C4×Q8×C3112yes—
354C2×C4C31×#12411yescharacteristic
355C2×C4C31×C4⋊Q811yescharacteristic
356C8—82no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22C31×#39111yescharacteristic
366C22C2×C31×#9911yescharacteristic
367C22C31×#41011yescharacteristic
368C22C31×#41611yescharacteristic
369C22C31×#41711yescharacteristic
370C22C2×C31×#10411yescharacteristic
371C22C2×C31×#10411yescharacteristic
372C22C31×#47812yes—
373C22C31×#47912yes—
374C4—21no—
375C4—22no—
376C4—21no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—48no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2C31×#150011yescharacteristic
389C2C31×#150111yescharacteristic
390C2C31×#150411yescharacteristic
391C2C31×#150911yescharacteristic
392C2C31×#198911yescharacteristic
393C2C31×#199411yescharacteristic
394C2C31×#199611yescharacteristic
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
6. C2×C31×#125C4semidirect
11. C31×#389C4semidirect
12. C31×#389C4semidirect
17. C31×#382C4semidirect
106. #9910C31direct (N × H)
194. C2×#125C4×C31semidirect
199. #389C4×C31semidirect
200. #389C4×C31semidirect
205. #382C4×C31semidirect
255. C31#9910direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28512
C31×#17972
C4×C31×#952
C31×#12942
#991031