Finite Group Databasebeta

← C31×#17120 #21473879

Subgroups — C31×#17120 #21473879

Order 7936.

1094 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C212yesmaximal
2C2×C31×#398C212yesmaximal
3C31×#1445C211yesmaximal, characteristic
4C31×#1445C211yesmaximal, characteristic
5C31×#1444C212yesmaximal
6C31×#1443C212yesmaximal
7C31×#1442C212yesmaximal
8C31×#1442C211yesmaximal, characteristic
9C31×#1441C212yesmaximal
10C22×C4⋊C4×C31C2212yes—
11C22×C4⋊C4×C31C2212yes—
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C31×#400—28no—
17C31×#398—28no—
18C2×C31×#95C2212yes—
19C2×C31×#95C2212yes—
20C2×C31×#95C2212yes—
21C2×C31×#95C2212yes—
22C2×C31×#95C2212yes—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C23×C4×C31C2312yes—
34C23×C4×C31C2312yes—
35C23×C4×C31C2312yes—
36C23×C4×C31C2312yes—
37C23×C4×C31C2312yes—
38C23×C4×C31C2311yescharacteristic
39C23×C4×C31C2311yescharacteristic
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C2×C4⋊C4×C31—24no—
43C2×C4⋊C4×C31—24no—
44C2×C4⋊C4×C31—24no—
45C2×C4⋊C4×C31—24no—
46C2×C4⋊C4×C31—24no—
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—41no—
50C2×C4⋊C4×C31—41no—
51C2×C4⋊C4×C31—41no—
52C2×C4⋊C4×C31—42no—
53C2×C4⋊C4×C31—42no—
54C2×C4⋊C4×C31—42no—
55C2×C4⋊C4×C31—41no—
56C2×C4⋊C4×C31—41no—
57C2×C4⋊C4×C31—42no—
58C2×C4⋊C4×C31D414yes—
59C31×#95—24no—
60C31×#95—24no—
61C31×#95—24no—
62C31×#95—24no—
63C31×#95—24no—
64C31×#95—24no—
65C31×#95—24no—
66C31×#95—24no—
67C31×#95—24no—
68C31×#95—24no—
69C31×#95—41no—
70C31×#95—41no—
71C31×#95—42no—
72C31×#95—41no—
73C31×#95D414yes—
74C24×C31C2411yescharacteristic
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—22no—
79C22×C4×C31—22no—
80C22×C4×C31—22no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—21no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31C2×D412yes—
127C22×C4×C31C2×D412yes—
128C22×C4×C31C2×D414yes—
129C22×C4×C31C2×D414yes—
130C22×C4×C31#4112yes—
131C22×C4×C31#4114yes—
132C4⋊C4×C31—44no—
133C4⋊C4×C31—48no—
134C4⋊C4×C31—48no—
135C4⋊C4×C31—44no—
136C4⋊C4×C31—48no—
137C4⋊C4×C31—44no—
138#17120C3111yesmaximal, characteristic, direct product factor, Sylow
139C23×C31C22×D411yescharacteristic
140C23×C31C22×D411yescharacteristic
141C23×C31C2×#4111yescharacteristic
142C23×C31C2×#4112yes—
143C23×C31H(5,𝔽2)11yescharacteristic
144C23×C31H(5,𝔽2)11yescharacteristic
145C23×C31H(5,𝔽2)11yescharacteristic
146C23×C312−1+412yes—
147C23×C312−1+412yes—
148C23×C312−1+412yes—
149C23×C312−1+411yescharacteristic
150C2×C4×C31—24no—
151C2×C4×C31—22no—
152C2×C4×C31—24no—
153C2×C4×C31—24no—
154C2×C4×C31—22no—
155C2×C4×C31—22no—
156C2×C4×C31—24no—
157C2×C4×C31—24no—
158C2×C4×C31—24no—
159C2×C4×C31—24no—
160C2×C4×C31—24no—
161C2×C4×C31—24no—
162C2×C4×C31—24no—
163C2×C4×C31—24no—
164C2×C4×C31—24no—
165C2×C4×C31—42no—
166C2×C4×C31—42no—
167C2×C4×C31—42no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—42no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—42no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—42no—
182C2×C4×C31—42no—
183C2×C4×C31—41no—
184C2×C4×C31—42no—
185C2×C4×C31—41no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—42no—
191C2×C4×C31—42no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×#400C2×C3112yes—
208C2×#398C2×C3112yes—
209#1445C2×C3111yescharacteristic
210#1445C2×C3111yescharacteristic
211#1444C2×C3112yes—
212#1443C2×C3112yes—
213#1442C2×C3112yes—
214#1442C2×C3111yescharacteristic
215#1441C2×C3112yes—
216C22×C31#53411yescharacteristic
217C22×C31#53612yes—
218C22×C31#53612yes—
219C22×C31#53711yescharacteristic
220C22×C31#53811yescharacteristic
221C22×C31#53912yes—
222C22×C31#54112yes—
223C22×C31#54112yes—
224C22×C31#54212yes—
225C22×C31D4211yescharacteristic
226C22×C31#54712yes—
227C22×C31#54711yescharacteristic
228C22×C31#54812yes—
229C22×C31#55011yescharacteristic
230C22×C31#55111yescharacteristic
231C22×C31#55212yes—
232C22×C31#56211yescharacteristic
233C22×C31#56311yescharacteristic
234C22×C31#56311yescharacteristic
235C22×C31#56312yes—
236C22×C31#56311yescharacteristic
237C22×C31#56312yes—
238C22×C31#56412yes—
239C4×C31—42no—
240C4×C31—44no—
241C4×C31—44no—
242C4×C31—42no—
243C4×C31—44no—
244C4×C31—42no—
245C4×C31—82no—
246C4×C31—82no—
247C4×C31—82no—
248C22×C4⋊C4C22×C3112yes—
249C22×C4⋊C4C22×C3112yes—
250C22×C4⋊C4C22×C3111yescharacteristic
251C22×C4⋊C4C22×C3112yes—
252C22×C4⋊C4C22×C3111yescharacteristic
253C22×C4⋊C4C22×C3111yescharacteristic
254#400—28no—
255#398—28no—
256C2×#95C22×C3112yes—
257C2×#95C22×C3112yes—
258C2×#95C22×C3112yes—
259C2×#95C22×C3112yes—
260C2×#95C22×C3112yes—
261C2×#95C22×C3112yes—
262C2×#95C22×C3112yes—
263C2×#95C22×C3112yes—
264C2×#95C22×C3112yes—
265C2×#95C22×C3112yes—
266C2×#95C22×C3112yes—
267C2×#95C22×C3111yescharacteristic
268C2×#95C22×C3111yescharacteristic
269C2×#95C22×C3111yescharacteristic
270C2×#95C22×C3111yescharacteristic
271C2×C31#267412yes—
272C2×C31#268211yescharacteristic
273C2×C31#271912yes—
274C2×C31#272112yes—
275C2×C31#272211yescharacteristic
276C2×C31#272811yescharacteristic
277C2×C31#276411yescharacteristic
278C2×C31#281711yescharacteristic
279C2×C31#282211yescharacteristic
280C2×C31#283311yescharacteristic
281C2×C31#283912yes—
282C23×C4C23×C3112yes—
283C23×C4C23×C3112yes—
284C23×C4C23×C3112yes—
285C23×C4C23×C3112yes—
286C23×C4C23×C3112yes—
287C23×C4C23×C3111yescharacteristic
288C23×C4C23×C3111yescharacteristic
289C23×C4C23×C3112yes—
290C23×C4C23×C3111yescharacteristic
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4D4×C3114yes—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—41no—
319#95—41no—
320#95—42no—
321#95—41no—
322#95D4×C3114yes—
323C31#1712011yescharacteristic, direct product factor, Sylow
324C24C24×C3111yescharacteristic
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4C2×D4×C3112yes—
377C22×C4C2×D4×C3112yes—
378C22×C4C2×D4×C3114yes—
379C22×C4C2×D4×C3114yes—
380C22×C4#41×C3112yes—
381C22×C4#41×C3114yes—
382C4⋊C4—44no—
383C4⋊C4—48no—
384C4⋊C4—48no—
385C4⋊C4—44no—
386C4⋊C4—48no—
387C4⋊C4—44no—
388C23C22×D4×C3111yescharacteristic
389C23C22×D4×C3111yescharacteristic
390C23C2×#41×C3111yescharacteristic
391C23C2×#41×C3112yes—
392C23C31×H(5,𝔽2)11yescharacteristic
393C23C31×H(5,𝔽2)11yescharacteristic
394C23C31×H(5,𝔽2)11yescharacteristic
395C23C31×2−1+412yes—
396C23C31×2−1+412yes—
397C23C31×2−1+412yes—
398C23C31×2−1+411yescharacteristic
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C22C31×#53411yescharacteristic
457C22C31×#53612yes—
458C22C31×#53612yes—
459C22C31×#53711yescharacteristic
460C22C31×#53811yescharacteristic
461C22C31×#53912yes—
462C22C31×#54112yes—
463C22C31×#54112yes—
464C22C31×#54212yes—
465C22D42×C3111yescharacteristic
466C22C31×#54712yes—
467C22C31×#54711yescharacteristic
468C22C31×#54812yes—
469C22C31×#55011yescharacteristic
470C22C31×#55111yescharacteristic
471C22C31×#55212yes—
472C22C31×#56211yescharacteristic
473C22C31×#56311yescharacteristic
474C22C31×#56311yescharacteristic
475C22C31×#56312yes—
476C22C31×#56311yescharacteristic
477C22C31×#56312yes—
478C22C31×#56412yes—
479C4—44no—
480C4—44no—
481C4—42no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4—82no—
487C4—82no—
488C2C31×#267412yes—
489C2C31×#268211yescharacteristic
490C2C31×#271912yes—
491C2C31×#272112yes—
492C2C31×#272211yescharacteristic
493C2C31×#272811yescharacteristic
494C2C31×#276411yescharacteristic
495C2C31×#281711yescharacteristic
496C2C31×#282211yescharacteristic
497C2C31×#283311yescharacteristic
498C2C31×#283912yes—
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
138. #17120C31direct (N × H)
323. C31#17120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4002
C2×C31×#3982
C31×#14452
C31×#14442
C31×#14432
C31×#14422
C31×#14412
#1712031