Finite Group Databasebeta

← C31×#14507 #21471266

Subgroups — C31×#14507 #21471266

Order 7936.

1406 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#381C211yesmaximal, characteristic
2C31×#1443C212yesmaximal, complemented
3C31×#1442C212yesmaximal, complemented
4C31×#1439C212yesmaximal
5C31×#1437C211yesmaximal, characteristic
6C31×#1437C211yesmaximal, characteristic
7C31×#1436C212yesmaximal, complemented
8C31×#1434C212yesmaximal, complemented
9C31×C22⋊#95C212yesmaximal
10C24×C4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2212yes—
12C22×C22⋊C4×C31C2212yes—
13C22×C22⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2211yescharacteristic
16C22×C42×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C31×#381C418yescomplemented
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×#95C2211yescharacteristic
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C25×C31C2311yescharacteristic
33C23×C4×C31—24no—
34C23×C4×C31—42no—
35C23×C4×C31—41no—
36C23×C4×C31—41no—
37C23×C4×C31C2×C414yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2312yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C2×C4⋊C4×C31—24no—
47C2×C4⋊C4×C31—42no—
48C2×C4⋊C4×C31—42no—
49C2×C22⋊C4×C31—24no—
50C2×C22⋊C4×C31—24no—
51C2×C22⋊C4×C31—24no—
52C2×C22⋊C4×C31—24no—
53C2×C22⋊C4×C31—41no—
54C2×C22⋊C4×C31—41no—
55C2×C22⋊C4×C31—42no—
56C2×C22⋊C4×C31—42no—
57C2×C22⋊C4×C31—42no—
58C2×C22⋊C4×C31C2×C414yes—
59C2×C22⋊C4×C31C2×C414yes—
60C2×C42×C31—24no—
61C2×C42×C31—41no—
62C2×C42×C31—41no—
63C2×C42×C31—42no—
64C31×#95—24no—
65C31×#95—24no—
66C31×#95—42no—
67C31×#95—42no—
68C31×#95—42no—
69C31×#95—42no—
70C31×#95—42no—
71C31×#95—41no—
72C31×#95—41no—
73C31×#95—42no—
74C31×#95—42no—
75C31×#95C2×C418yes—
76C31×#95C2×C418yes—
77C24×C31—22no—
78C24×C31—22no—
79C24×C31—22no—
80C24×C31—22no—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—22no—
84C24×C31C22×C412yes—
85C24×C31#4114yes—
86C24×C31C2411yescharacteristic
87C22×C4×C31—28no—
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—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
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—21no—
113C22×C4×C31—21no—
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×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—44no—
135C22×C4×C31—44no—
136C22×C4×C31—48no—
137C22×C4×C31—48no—
138C22×C4×C31C22×C412yes—
139C22×C4×C31C22×C414yes—
140C22×C4×C31C22×C412yes—
141C22×C4×C31C22×C414yes—
142C22×C4×C31#4114yes—
143C22×C4×C31#4114yes—
144C4⋊C4×C31—48no—
145C22⋊C4×C31—44no—
146C22⋊C4×C31—44no—
147C22⋊C4×C31—48no—
148C22⋊C4×C31—48no—
149C42×C31—44no—
150C42×C31—44no—
151#14507C3111yesmaximal, characteristic, direct product factor, Sylow
152C23×C31—24no—
153C23×C31—22no—
154C23×C31—22no—
155C23×C31—24no—
156C23×C31—24no—
157C23×C31—24no—
158C23×C31—24no—
159C23×C31—24no—
160C23×C31—24no—
161C23×C31—24no—
162C23×C31—42no—
163C23×C31—42no—
164C23×C31—42no—
165C23×C31—42no—
166C23×C31—41no—
167C23×C31—42no—
168C23×C31—41no—
169C23×C31—41no—
170C23×C31—42no—
171C23×C31—41no—
172C23×C31#11714yes—
173C23×C31C23×C411yescharacteristic
174C23×C31C2×#4112yes—
175C23×C31C2×#4112yes—
176C23×C31C2×#4112yes—
177C23×C31H(5,𝔽2)12yes—
178C23×C31H(5,𝔽2)11yescharacteristic
179C23×C31H(5,𝔽2)11yescharacteristic
180C23×C31H(5,𝔽2)12yes—
181C23×C312−1+412yes—
182C2×C4×C31—24no—
183C2×C4×C31—24no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—416no—
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×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—41no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—41no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×#381C2×C3111yescharacteristic
236#1443C2×C3112yescomplemented
237#1442C2×C3112yescomplemented
238#1439C2×C3112yes—
239#1437C2×C3111yescharacteristic
240#1437C2×C3111yescharacteristic
241#1436C2×C3112yescomplemented
242#1434C2×C3112yescomplemented
243C22⋊#95C2×C3112yes—
244C22×C31—24no—
245C22×C31—28no—
246C22×C31—44no—
247C22×C31—42no—
248C22×C31—42no—
249C22×C31—44no—
250C22×C31—44no—
251C22×C31—44no—
252C22×C31—44no—
253C22×C31C2×#11711yescharacteristic
254C22×C31C4×#4112yes—
255C22×C31#51811yescharacteristic
256C22×C31#51811yescharacteristic
257C22×C31#52012yes—
258C22×C31#53812yes—
259C22×C31#53812yes—
260C22×C31#53812yes—
261C22×C31#53912yes—
262C22×C31#54012yes—
263C22×C31#54212yes—
264C22×C31#55112yes—
265C22×C31#55112yes—
266C22×C31#55111yescharacteristic
267C22×C31#55212yes—
268C22×C31#55212yes—
269C22×C31#55312yes—
270C22×C31#55911yescharacteristic
271C22×C31#56011yescharacteristic
272C22×C31#56212yes—
273C22×C31#56311yescharacteristic
274C4×C31—44no—
275C4×C31—44no—
276C4×C31—42no—
277C4×C31—42no—
278C4×C31—44no—
279C4×C31—44no—
280C4×C31—82no—
281C4×C31—82no—
282C24×C4C22×C3111yescharacteristic
283C22×C4⋊C4C22×C3112yes—
284C22×C22⋊C4C22×C3112yes—
285C22×C22⋊C4C22×C3112yes—
286C22×C22⋊C4C22×C3111yescharacteristic
287C22×C22⋊C4C22×C3111yescharacteristic
288C22×C42C22×C3111yescharacteristic
289C22×C42C22×C3111yescharacteristic
290#381C4×C3118yescomplemented
291C2×#95C22×C3112yes—
292C2×#95C22×C3112yes—
293C2×#95C22×C3112yes—
294C2×#95C22×C3112yes—
295C2×#95C22×C3112yes—
296C2×#95C22×C3112yes—
297C2×#95C22×C3112yes—
298C2×#95C22×C3112yes—
299C2×#95C22×C3111yescharacteristic
300C2×#95C22×C3111yescharacteristic
301C2×#95C22×C3112yes—
302C2×#95C22×C3112yes—
303C2×#95C22×C3112yes—
304C2×C31—44no—
305C2×C31#231211yescharacteristic
306C2×C31#233512yes—
307C2×C31#234312yes—
308C2×C31#237411yescharacteristic
309C2×C31#237611yescharacteristic
310C2×C31#274312yes—
311C2×C31#274912yes—
312C2×C31#275112yes—
313C2×C31#276512yes—
314C25C23×C3111yescharacteristic
315C23×C4—24no—
316C23×C4—42no—
317C23×C4—41no—
318C23×C4—41no—
319C23×C4C2×C4×C3114yes—
320C23×C4C23×C3112yes—
321C23×C4C23×C3112yes—
322C23×C4C23×C3112yes—
323C23×C4C23×C3111yescharacteristic
324C23×C4C23×C3111yescharacteristic
325C23×C4C23×C3112yes—
326C23×C4C23×C3112yes—
327C23×C4C23×C3112yes—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4C2×C4×C3114yes—
341C2×C22⋊C4C2×C4×C3114yes—
342C2×C42—24no—
343C2×C42—41no—
344C2×C42—41no—
345C2×C42—42no—
346#95—24no—
347#95—24no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—41no—
354#95—41no—
355#95—42no—
356#95—42no—
357#95C2×C4×C3118yes—
358#95C2×C4×C3118yes—
359C31#1450711yescharacteristic, direct product factor, Sylow
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—21no—
365C24—21no—
366C24—22no—
367C24C22×C4×C3112yes—
368C24#41×C3114yes—
369C24C24×C3111yescharacteristic
370C22×C4—28no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4C22×C4×C3112yes—
422C22×C4C22×C4×C3114yes—
423C22×C4C22×C4×C3112yes—
424C22×C4C22×C4×C3114yes—
425C22×C4#41×C3114yes—
426C22×C4#41×C3114yes—
427C4⋊C4—48no—
428C22⋊C4—44no—
429C22⋊C4—44no—
430C22⋊C4—48no—
431C22⋊C4—48no—
432C42—44no—
433C42—44no—
434C23—24no—
435C23—22no—
436C23—22no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—24no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—41no—
449C23—42no—
450C23—41no—
451C23—41no—
452C23—42no—
453C23—41no—
454C23C31×#11714yes—
455C23C23×C4×C3111yescharacteristic
456C23C2×#41×C3112yes—
457C23C2×#41×C3112yes—
458C23C2×#41×C3112yes—
459C23C31×H(5,𝔽2)12yes—
460C23C31×H(5,𝔽2)11yescharacteristic
461C23C31×H(5,𝔽2)11yescharacteristic
462C23C31×H(5,𝔽2)12yes—
463C23C31×2−1+412yes—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—416no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C22—24no—
518C22—28no—
519C22—44no—
520C22—42no—
521C22—42no—
522C22—44no—
523C22—44no—
524C22—44no—
525C22—44no—
526C22C2×C31×#11711yescharacteristic
527C22C4×#41×C3112yes—
528C22C31×#51811yescharacteristic
529C22C31×#51811yescharacteristic
530C22C31×#52012yes—
531C22C31×#53812yes—
532C22C31×#53812yes—
533C22C31×#53812yes—
534C22C31×#53912yes—
535C22C31×#54012yes—
536C22C31×#54212yes—
537C22C31×#55112yes—
538C22C31×#55112yes—
539C22C31×#55111yescharacteristic
540C22C31×#55212yes—
541C22C31×#55212yes—
542C22C31×#55312yes—
543C22C31×#55911yescharacteristic
544C22C31×#56011yescharacteristic
545C22C31×#56212yes—
546C22C31×#56311yescharacteristic
547C4—44no—
548C4—44no—
549C4—42no—
550C4—42no—
551C4—44no—
552C4—44no—
553C4—82no—
554C4—82no—
555C2—44no—
556C2C31×#231211yescharacteristic
557C2C31×#233512yes—
558C2C31×#234312yes—
559C2C31×#237411yescharacteristic
560C2C31×#237611yescharacteristic
561C2C31×#274312yes—
562C2C31×#274912yes—
563C2C31×#275112yes—
564C2C31×#276512yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1443C2semidirect
3. C31×#1442C2semidirect
7. C31×#1436C2semidirect
8. C31×#1434C2semidirect
18. C31×#381C4semidirect
151. #14507C31direct (N × H)
236. #1443C2×C31semidirect
237. #1442C2×C31semidirect
241. #1436C2×C31semidirect
242. #1434C2×C31semidirect
290. #381C4×C31semidirect
359. C31#14507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3812
C31×#14432
C31×#14422
C31×#14392
C31×#14372
C31×#14362
C31×#14342
C31×C22⋊#952
#1450731