Finite Group Databasebeta

← C31×#17144 #21473903

Subgroups — C31×#17144 #21473903

Order 7936.

1074 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C211yesmaximal, characteristic
2C2×C31×#395C211yesmaximal, characteristic
3C31×#1446C212yesmaximal
4C31×#1445C211yesmaximal, characteristic
5C31×#1443C212yesmaximal
6C31×#1443C212yesmaximal
7C31×#1443C212yesmaximal
8C31×#1442C212yesmaximal
9C31×#1441C212yesmaximal
10C23×Q8×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2212yes—
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C31×#400—24no—
15C31×#395—24no—
16C2×C31×#95C2211yescharacteristic
17C2×C31×#95C2212yes—
18C2×C31×#95C2211yescharacteristic
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×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C22×Q8×C31—22no—
34C22×Q8×C31—24no—
35C22×Q8×C31—42no—
36C22×Q8×C31—41no—
37C22×Q8×C31—41no—
38C23×C4×C31C2312yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2312yes—
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—24no—
50C2×C4⋊C4×C31—41no—
51C2×C4⋊C4×C31—41no—
52C2×C4⋊C4×C31—42no—
53C2×C4⋊C4×C31—41no—
54C2×C4⋊C4×C31—41no—
55C2×C4⋊C4×C31D414yes—
56C31×#95—22no—
57C31×#95—24no—
58C31×#95—22no—
59C31×#95—24no—
60C31×#95—24no—
61C31×#95—24no—
62C31×#95—24no—
63C31×#95—24no—
64C31×#95—24no—
65C31×#95—42no—
66C31×#95—42no—
67C31×#95—41no—
68C31×#95—41no—
69C31×#95—42no—
70C31×#95—42no—
71C31×#95—42no—
72C31×#95—42no—
73C24×C31C2411yescharacteristic
74C2×Q8×C31—48no—
75C2×Q8×C31—44no—
76C2×Q8×C31—44no—
77C2×Q8×C31—48no—
78C2×Q8×C31—44no—
79C22×C4×C31—22no—
80C22×C4×C31—22no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31—22no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—22no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
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×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31C2×D412yes—
132C22×C4×C31C2×D412yes—
133C22×C4×C31C2×D412yes—
134C22×C4×C31#4114yes—
135C22×C4×C31#4114yes—
136C4⋊C4×C31—44no—
137C4⋊C4×C31—48no—
138C4⋊C4×C31—44no—
139#17144C3111yesmaximal, characteristic, direct product factor, Sylow
140C23×C31C22×D411yescharacteristic
141C23×C31C2×#4112yes—
142C23×C31C2×#4112yes—
143C23×C31H(5,𝔽2)11yescharacteristic
144C23×C31H(5,𝔽2)11yescharacteristic
145C23×C31H(5,𝔽2)12yes—
146C23×C312−1+412yes—
147C23×C312−1+412yes—
148C23×C312−1+412yes—
149Q8×C31—416no—
150C2×C4×C31—22no—
151C2×C4×C31—22no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—24no—
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—42no—
164C2×C4×C31—42no—
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—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—42no—
176C2×C4×C31—42no—
177C2×C4×C31—42no—
178C2×C4×C31—42no—
179C2×C4×C31—42no—
180C2×C4×C31—42no—
181C2×C4×C31—42no—
182C2×C4×C31—42no—
183C2×C4×C31—42no—
184C2×C4×C31—42no—
185C2×C4×C31—42no—
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×C3111yescharacteristic
208C2×#395C2×C3111yescharacteristic
209#1446C2×C3112yes—
210#1445C2×C3111yescharacteristic
211#1443C2×C3112yes—
212#1443C2×C3112yes—
213#1443C2×C3112yes—
214#1442C2×C3112yes—
215#1441C2×C3112yes—
216C22×C31#53411yescharacteristic
217C22×C31#53611yescharacteristic
218C22×C31#53611yescharacteristic
219C22×C31#53812yes—
220C22×C31#53912yes—
221C22×C31#54112yes—
222C22×C31#54112yes—
223C22×C31#54212yes—
224C22×C31#54212yes—
225C22×C31#54612yes—
226C22×C31#54812yes—
227C22×C31#55111yescharacteristic
228C22×C31#55212yes—
229C22×C31#55511yescharacteristic
230C22×C31#55612yes—
231C22×C31#56011yescharacteristic
232C22×C31#56312yes—
233C22×C31#56312yes—
234C22×C31#56311yescharacteristic
235C22×C31#56312yes—
236C22×C31#56312yes—
237C4×C31—42no—
238C4×C31—44no—
239C4×C31—42no—
240C4×C31—42no—
241C4×C31—44no—
242C4×C31—82no—
243C4×C31—82no—
244C4×C31—82no—
245C4×C31—82no—
246C23×Q8C22×C3111yescharacteristic
247C22×C4⋊C4C22×C3112yes—
248C22×C4⋊C4C22×C3111yescharacteristic
249C22×C4⋊C4C22×C3111yescharacteristic
250#400—24no—
251#395—24no—
252C2×#95C22×C3111yescharacteristic
253C2×#95C22×C3112yes—
254C2×#95C22×C3111yescharacteristic
255C2×#95C22×C3112yes—
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×C3111yescharacteristic
267C2×#95C22×C3111yescharacteristic
268C2×#95C22×C3112yes—
269C2×C31#269012yes—
270C2×C31#269711yescharacteristic
271C2×C31#271612yes—
272C2×C31#273111yescharacteristic
273C2×C31#275812yes—
274C2×C31#277512yes—
275C2×C31#281711yescharacteristic
276C2×C31#283312yes—
277C2×C31#283812yes—
278C22×Q8—22no—
279C22×Q8—24no—
280C22×Q8—42no—
281C22×Q8—41no—
282C22×Q8—41no—
283C23×C4C23×C3112yes—
284C23×C4C23×C3112yes—
285C23×C4C23×C3112yes—
286C23×C4C23×C3112yes—
287C23×C4C23×C3111yescharacteristic
288C23×C4C23×C3111yescharacteristic
289C23×C4C23×C3111yescharacteristic
290C23×C4C23×C3112yes—
291C23×C4C23×C3112yes—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4D4×C3114yes—
301#95—22no—
302#95—24no—
303#95—22no—
304#95—24no—
305#95—24no—
306#95—24no—
307#95—24no—
308#95—24no—
309#95—24no—
310#95—42no—
311#95—42no—
312#95—41no—
313#95—41no—
314#95—42no—
315#95—42no—
316#95—42no—
317#95—42no—
318C31#1714411yescharacteristic, direct product factor, Sylow
319C24C24×C3111yescharacteristic
320C2×Q8—48no—
321C2×Q8—44no—
322C2×Q8—44no—
323C2×Q8—48no—
324C2×Q8—44no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
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×C4—22no—
377C22×C4C2×D4×C3112yes—
378C22×C4C2×D4×C3112yes—
379C22×C4C2×D4×C3112yes—
380C22×C4#41×C3114yes—
381C22×C4#41×C3114yes—
382C4⋊C4—44no—
383C4⋊C4—48no—
384C4⋊C4—44no—
385C23C22×D4×C3111yescharacteristic
386C23C2×#41×C3112yes—
387C23C2×#41×C3112yes—
388C23C31×H(5,𝔽2)11yescharacteristic
389C23C31×H(5,𝔽2)11yescharacteristic
390C23C31×H(5,𝔽2)12yes—
391C23C31×2−1+412yes—
392C23C31×2−1+412yes—
393C23C31×2−1+412yes—
394Q8—416no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
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—
452C22C31×#53411yescharacteristic
453C22C31×#53611yescharacteristic
454C22C31×#53611yescharacteristic
455C22C31×#53812yes—
456C22C31×#53912yes—
457C22C31×#54112yes—
458C22C31×#54112yes—
459C22C31×#54212yes—
460C22C31×#54212yes—
461C22C31×#54612yes—
462C22C31×#54812yes—
463C22C31×#55111yescharacteristic
464C22C31×#55212yes—
465C22C31×#55511yescharacteristic
466C22C31×#55612yes—
467C22C31×#56011yescharacteristic
468C22C31×#56311yescharacteristic
469C22C31×#56312yes—
470C22C31×#56312yes—
471C22C31×#56312yes—
472C22C31×#56312yes—
473C4—44no—
474C4—42no—
475C4—44no—
476C4—42no—
477C4—42no—
478C4—82no—
479C4—82no—
480C4—82no—
481C4—82no—
482C2C31×#269012yes—
483C2C31×#269711yescharacteristic
484C2C31×#271612yes—
485C2C31×#273111yescharacteristic
486C2C31×#275812yes—
487C2C31×#277512yes—
488C2C31×#281711yescharacteristic
489C2C31×#283312yes—
490C2C31×#283812yes—
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
139. #17144C31direct (N × H)
318. C31#17144direct (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×#3952
C31×#14462
C31×#14452
C31×#14432
C31×#14422
C31×#14412
#1714431