Finite Group Databasebeta

← C31×#9913 #21466672

Subgroups — C31×#9913 #21466672

Order 7936.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2851C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C31×#1434C211yesmaximal, characteristic
4C31×#1294C212yesmaximal
5C31×#1294C212yesmaximal
6C2×C31×#125C411yescharacteristic, complemented
7C22×C42×C31C2211yescharacteristic
8C2×C31×C4⋊C8—21no—
9C2×C31×C22⋊C8C2212yes—
10C31×#389C411yescharacteristic, complemented
11C31×#389C411yescharacteristic, complemented
12C31×#387—21no—
13C31×#387—21no—
14C31×#385—21no—
15C31×#385—21no—
16C31×#382C411yescharacteristic, complemented
17C31×#380C2211yescharacteristic
18C31×#380C2211yescharacteristic
19C2×C31×#95—21no—
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—42no—
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31C2×C411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C31×C4⋊C8—42no—
45C31×C22⋊C8—24no—
46C31×#95—21no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—22no—
53C31×#95—42no—
54C31×#95—42no—
55C31×#95Q814yes—
56C24×C31C2×D411yescharacteristic
57C22×C4×C31—22no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—22no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—24no—
66C22×C4×C31—41no—
67C22×C4×C31—41no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—41no—
71C22×C4×C31—42no—
72C22×C4×C31—42no—
73C22×C4×C31—42no—
74C22×C4×C31—42no—
75C22×C4×C31—42no—
76C22×C4×C31—42no—
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22×C411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83C22×C4×C31C2×Q812yes—
84C22×C4×C31#4112yes—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C2×C8×C31—42no—
88C4⋊C4×C31—42no—
89C4⋊C4×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—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—41no—
99C42×C31—22no—
100C42×C31—22no—
101C42×C31—41no—
102C42×C31—41no—
103#9913C3111yesmaximal, characteristic, direct product factor, Sylow
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31C2×C22⋊C411yescharacteristic
109C23×C31C22⋊Q812yes—
110C23×C31#13512yes—
111C23×C31AGL(1,ℤ/8)11yescharacteristic
112C23×C31#13711yescharacteristic
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—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31—44no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—44no—
134C2×C4×C31—44no—
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—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—44no—
148C2×C4×C31—82no—
149C2×C4×C31—82no—
150C2×C4×C31—82no—
151C2×C4×C31—82no—
152C2×C4×C31#9912yes—
153C2×C4×C31C4×Q812yes—
154C2×C4×C31#12411yescharacteristic
155C2×C4×C31C4⋊Q811yescharacteristic
156C8×C31—82no—
157#2851C2×C3111yescharacteristic
158#1797C2×C3111yescharacteristic
159#1434C2×C3111yescharacteristic
160#1294C2×C3112yes—
161#1294C2×C3112yes—
162C22×C31—22no—
163C22×C31—22no—
164C22×C31—21no—
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—22no—
169C22×C31—22no—
170C22×C31#39111yescharacteristic
171C22×C31C2×#9911yescharacteristic
172C22×C31#41011yescharacteristic
173C22×C31#41611yescharacteristic
174C22×C31#41711yescharacteristic
175C22×C31#42111yescharacteristic
176C22×C31#42111yescharacteristic
177C22×C31#47812yes—
178C22×C31#47912yes—
179C4×C31—21no—
180C4×C31—22no—
181C4×C31—21no—
182C4×C31—22no—
183C4×C31—41no—
184C4×C31—41no—
185C4×C31—41no—
186C4×C31—84no—
187C4×C31—81no—
188C4×C31—81no—
189C4×C31—81no—
190C4×C31—81no—
191C2×#125C4×C3111yescharacteristic, complemented
192C22×C42C22×C3111yescharacteristic
193C2×C4⋊C8—21no—
194C2×C22⋊C8C22×C3112yes—
195#389C4×C3111yescharacteristic, complemented
196#389C4×C3111yescharacteristic, complemented
197#387—21no—
198#387—21no—
199#385—21no—
200#385—21no—
201#382C4×C3111yescharacteristic, complemented
202#380C22×C3111yescharacteristic
203#380C22×C3111yescharacteristic
204C2×#95—21no—
205C2×#95—21no—
206C2×#95C22×C3112yes—
207#336—21no—
208C2×C31—22no—
209C2×C31—22no—
210C2×C31#151211yescharacteristic
211C2×C31#151311yescharacteristic
212C2×C31#151611yescharacteristic
213C2×C31#152111yescharacteristic
214C2×C31#198911yescharacteristic
215C2×C31#199511yescharacteristic
216C2×C31#199611yescharacteristic
217C23×C4—22no—
218C23×C4D4×C3111yescharacteristic
219C23×C4D4×C3111yescharacteristic
220C23×C4C23×C3111yescharacteristic
221C22×C8—22no—
222#125—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×C4×C3111yescharacteristic
228C2×C4⋊C4C2×C4×C3111yescharacteristic
229C2×C4⋊C4C2×C4×C3111yescharacteristic
230C2×C4⋊C4C2×C4×C3111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—42no—
234C2×C42C2×C4×C3111yescharacteristic
235C2×C42C2×C4×C3111yescharacteristic
236C2×C42D4×C3111yescharacteristic
237C2×C42D4×C3111yescharacteristic
238C4⋊C8—42no—
239C22⋊C8—24no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—22no—
247#95—42no—
248#95—42no—
249#95Q8×C3114yes—
250C31#991311yescharacteristic, direct product factor, Sylow
251C24C2×D4×C3111yescharacteristic
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—24no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C22⋊C4×C3111yescharacteristic
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C22⋊C4×C3111yescharacteristic
275C22×C4C22⋊C4×C3111yescharacteristic
276C22×C4C22×C4×C3111yescharacteristic
277C22×C4C2×D4×C3111yescharacteristic
278C22×C4C2×Q8×C3112yes—
279C22×C4#41×C3112yes—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23C2×C22⋊C4×C3111yescharacteristic
303C23C31×C22⋊Q812yes—
304C23C31×#13512yes—
305C23C31×AGL(1,ℤ/8)11yescharacteristic
306C23C31×#13711yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—44no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4C31×#9912yes—
347C2×C4C4×Q8×C3112yes—
348C2×C4C31×#12411yescharacteristic
349C2×C4C31×C4⋊Q811yescharacteristic
350C8—82no—
351C22—22no—
352C22—22no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22C31×#39111yescharacteristic
360C22C2×C31×#9911yescharacteristic
361C22C31×#41011yescharacteristic
362C22C31×#41611yescharacteristic
363C22C31×#41711yescharacteristic
364C22C31×#42111yescharacteristic
365C22C31×#42111yescharacteristic
366C22C31×#47812yes—
367C22C31×#47912yes—
368C4—21no—
369C4—22no—
370C4—21no—
371C4—22no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—84no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C2—22no—
381C2—22no—
382C2C31×#151211yescharacteristic
383C2C31×#151311yescharacteristic
384C2C31×#151611yescharacteristic
385C2C31×#152111yescharacteristic
386C2C31×#198911yescharacteristic
387C2C31×#199511yescharacteristic
388C2C31×#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
10. C31×#389C4semidirect
11. C31×#389C4semidirect
16. C31×#382C4semidirect
103. #9913C31direct (N × H)
191. C2×#125C4×C31semidirect
195. #389C4×C31semidirect
196. #389C4×C31semidirect
201. #382C4×C31semidirect
250. C31#9913direct (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
C31×#14342
C31×#12942
#991331