Finite Group Databasebeta

← C31×#18593 #21475352

Subgroups — C31×#18593 #21475352

Order 7936.

916 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3511C211yesmaximal, characteristic
2C31×#3254C211yesmaximal, characteristic, complemented
3C31×#3165C211yesmaximal, characteristic, complemented
4C31×#3107C211yesmaximal, characteristic, complemented
5C31×#1654C212yesmaximal, complemented
6C31×#1652C212yesmaximal, complemented
7C31×#1650C212yesmaximal, complemented
8C31×#1647C212yesmaximal, complemented
9C31×#1546C211yesmaximal, characteristic, complemented
10C31×#1489C211yesmaximal, characteristic, complemented
11C31×#1484C211yesmaximal, characteristic, complemented
12C31×#556C2212yes—
13C31×#555—21no—
14C31×#554—21no—
15C31×#553—22no—
16C31×#548—22no—
17C31×#547C2212yes—
18C31×#542—22no—
19C31×#537—21no—
20C31×#533—21no—
21C31×#533C2211yescharacteristic
22C31×#532—21no—
23C31×#532C2211yescharacteristic
24C2×C31×C4⋊Q8C2211yescharacteristic
25C31×#520—21no—
26C4×#41×C31C2211yescharacteristic
27C31×#501—22no—
28C31×#500C2212yes—
29C31×#498C2212yes—
30C31×#485—21no—
31C31×#477—21no—
32C31×#475C2211yescharacteristic
33C31×#474C2211yescharacteristic
34C31×#474C2212yes—
35C31×#468—22no—
36C31×#462C2211yescharacteristic
37C31×#461C2211yescharacteristic
38C31×#461C2212yes—
39C31×#460—21no—
40C31×#452—21no—
41C4×Q16×C31—21no—
42C4×SD16×C31—21no—
43C31×#431C2211yescharacteristic
44C31×#428—22no—
45C31×#423C2211yescharacteristic
46C4×M16×C31C2211yescharacteristic
47C31×#332C2212yes—
48C31×#332C2212yes—
49C31×Q8⋊C8C2212yes—
50C31×D4⋊C8C2212yes—
51C31×D4⋊C8C2212yes—
52C31×D4⋊C8C2212yes—
53C2×#41×C31—22no—
54C2×#41×C31—21no—
55C2×#41×C31D411yescharacteristic
56C22×Q8×C31—21no—
57C2×Q16×C31—21no—
58C2×SD16×C31—21no—
59C2×SD16×C31—22no—
60C2×M16×C31—21no—
61C2×M16×C31—21no—
62C31×C4⋊Q8—21no—
63C31×C4⋊Q8—21no—
64C31×C4⋊Q8D411yescharacteristic
65C31×C4⋊Q8D412yes—
66C31×C4⋊Q8C2311yescharacteristic
67C31×C4⋊Q8C2311yescharacteristic
68C31×C4⋊Q8C2312yes—
69C31×#127D411yescharacteristic
70C31×#126—24no—
71C31×#125—22no—
72C31×#125—21no—
73C31×#124—24no—
74C31×#124—22no—
75C31×#124—21no—
76C31×#123—24no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—24no—
79C31×C22⋊Q8—22no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×#121—22no—
84C31×#121—22no—
85C31×#121—24no—
86C31×#121—22no—
87C31×#121—21no—
88C31×#121D412yes—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×Q8×C31—21no—
92C4×Q8×C31—21no—
93C4×Q8×C31D411yescharacteristic
94C4×Q8×C31C2311yescharacteristic
95C4×D4×C31—22no—
96C4×D4×C31—24no—
97C4×D4×C31—22no—
98C4×D4×C31—21no—
99C4×D4×C31—21no—
100C4×D4×C31—21no—
101C4×D4×C31D411yescharacteristic
102C4×D4×C31C2311yescharacteristic
103C4×D4×C31C2312yes—
104C31×#117—22no—
105C31×#117—22no—
106C31×#117—21no—
107C31×#117—21no—
108C31×#117D411yescharacteristic
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31D412yes—
112C2×C42×C31—21no—
113C2×C42×C31C2311yescharacteristic
114C31×#107—24no—
115C31×#107—21no—
116C31×#107—22no—
117C31×#106—24no—
118C31×#106—21no—
119C31×C4⋊C8—21no—
120C31×C4⋊C8C2312yes—
121C31×C4⋊C8C2311yescharacteristic
122C31×C4⋊C8C2311yescharacteristic
123C31×#103—21no—
124C31×#103—21no—
125C31×#103—21no—
126C31×#103—22no—
127C31×#102—21no—
128C31×#102—22no—
129C31×C22⋊C8—21no—
130C31×#97—21no—
131C4×C8×C31—21no—
132C4×C8×C31C2312yes—
133#41×C31—41no—
134#41×C31—41no—
135#41×C31—42no—
136#41×C31—42no—
137#41×C31—82no—
138#41×C31—82no—
139C2×Q8×C31—21no—
140C2×Q8×C31—22no—
141C2×Q8×C31—22no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—81no—
145C2×Q8×C31—81no—
146C2×Q8×C31C2×D411yescharacteristic
147C2×D4×C31—21no—
148C2×D4×C31—22no—
149C2×D4×C31—24no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31C2×D411yescharacteristic
153C2×D4×C31C2×D412yes—
154C22×C4×C31—24no—
155C22×C4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—22no—
160C22×C4×C31C2×D411yescharacteristic
161C22×C4×C31C2×D411yescharacteristic
162C22×C4×C31C2×D411yescharacteristic
163Q16×C31—42no—
164SD16×C31—42no—
165SD16×C31—82no—
166M16×C31—24no—
167M16×C31—81no—
168C2×C8×C31—22no—
169C2×C8×C31—21no—
170C2×C8×C31—21no—
171C2×C8×C31—22no—
172C4⋊C4×C31—24no—
173C4⋊C4×C31—24no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—21no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—41no—
185C4⋊C4×C31—41no—
186C4⋊C4×C31C2×D411yescharacteristic
187C4⋊C4×C31C2×D411yescharacteristic
188C4⋊C4×C31C2×D412yes—
189C4⋊C4×C31C2×D414yes—
190C22⋊C4×C31—24no—
191C22⋊C4×C31—24no—
192C22⋊C4×C31—24no—
193C22⋊C4×C31—21no—
194C22⋊C4×C31—21no—
195C22⋊C4×C31—22no—
196C22⋊C4×C31—21no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—41no—
199C42×C31—24no—
200C42×C31—21no—
201C42×C31—21no—
202C42×C31—21no—
203C42×C31—41no—
204C42×C31C2×D411yescharacteristic
205C42×C31C2×D411yescharacteristic
206C42×C31C2×D411yescharacteristic
207C42×C31C2411yescharacteristic
208#18593C3111yesmaximal, characteristic, direct product factor, Sylow
209C23×C31—21no—
210C23×C31—22no—
211C23×C31#12011yescharacteristic
212Q8×C31—21no—
213Q8×C31—21no—
214Q8×C31—42no—
215Q8×C31—42no—
216Q8×C31—42no—
217Q8×C31—41no—
218Q8×C31—41no—
219Q8×C31—41no—
220Q8×C31—41no—
221Q8×C31—82no—
222D4×C31—21no—
223D4×C31—21no—
224D4×C31—22no—
225D4×C31—22no—
226D4×C31—42no—
227D4×C31—42no—
228D4×C31—44no—
229D4×C31—42no—
230D4×C31—84no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—22no—
236C2×C4×C31—21no—
237C2×C4×C31—21no—
238C2×C4×C31—22no—
239C2×C4×C31—21no—
240C2×C4×C31—24no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—42no—
244C2×C4×C31—41no—
245C2×C4×C31—41no—
246C2×C4×C31—42no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—82no—
250C2×C4×C31—84no—
251C2×C4×C31#12011yescharacteristic
252C2×C4×C31#12011yescharacteristic
253C2×C4×C31#12011yescharacteristic
254C2×C4×C31C22×D411yescharacteristic
255C2×C4×C31C22×D411yescharacteristic
256C2×C4×C31C22×D411yescharacteristic
257C8×C31—24no—
258C8×C31—41no—
259C8×C31—41no—
260C8×C31—42no—
261#3511C2×C3111yescharacteristic
262#3254C2×C3111yescharacteristic, complemented
263#3165C2×C3111yescharacteristic, complemented
264#3107C2×C3111yescharacteristic, complemented
265#1654C2×C3112yescomplemented
266#1652C2×C3112yescomplemented
267#1650C2×C3112yescomplemented
268#1647C2×C3112yescomplemented
269#1546C2×C3111yescharacteristic, complemented
270#1489C2×C3111yescharacteristic, complemented
271#1484C2×C3111yescharacteristic, complemented
272C22×C31—21no—
273C22×C31—21no—
274C22×C31—21no—
275C22×C31—41no—
276C22×C31—42no—
277C22×C31—41no—
278C22×C31—42no—
279C22×C31—41no—
280C22×C31—42no—
281C22×C31C2×#12011yescharacteristic
282C4×C31—21no—
283C4×C31—21no—
284C4×C31—21no—
285C4×C31—41no—
286C4×C31—42no—
287C4×C31—41no—
288C4×C31—44no—
289C4×C31—41no—
290C4×C31—81no—
291C4×C31—81no—
292C4×C31#45612yes—
293C4×C31#57511yescharacteristic
294C4×C31#57511yescharacteristic
295C4×C31#57611yescharacteristic
296C4×C31#57711yescharacteristic
297#556C22×C3112yes—
298#555—21no—
299#554—21no—
300#553—22no—
301#548—22no—
302#547C22×C3112yes—
303#542—22no—
304#537—21no—
305#533—21no—
306#533C22×C3111yescharacteristic
307#532—21no—
308#532C22×C3111yescharacteristic
309C2×C4⋊Q8C22×C3111yescharacteristic
310#520—21no—
311C4×#41C22×C3111yescharacteristic
312#501—22no—
313#500C22×C3112yes—
314#498C22×C3112yes—
315#485—21no—
316#477—21no—
317#475C22×C3111yescharacteristic
318#474C22×C3111yescharacteristic
319#474C22×C3112yes—
320#468—22no—
321#462C22×C3111yescharacteristic
322#461C22×C3111yescharacteristic
323#461C22×C3112yes—
324#460—21no—
325#452—21no—
326C4×Q16—21no—
327C4×SD16—21no—
328#431C22×C3111yescharacteristic
329#428—22no—
330#423C22×C3111yescharacteristic
331C4×M16C22×C3111yescharacteristic
332#332C22×C3112yes—
333#332C22×C3112yes—
334Q8⋊C8C22×C3112yes—
335D4⋊C8C22×C3112yes—
336D4⋊C8C22×C3112yes—
337D4⋊C8C22×C3112yes—
338C2×C31—41no—
339C2×C31—81no—
340C2×C31—82no—
341C2×C31#300511yescharacteristic
342C2×C31#301211yescharacteristic
343C2×C31C2×#45611yescharacteristic
344C2×#41—22no—
345C2×#41—21no—
346C2×#41D4×C3111yescharacteristic
347C22×Q8—21no—
348C2×Q16—21no—
349C2×SD16—21no—
350C2×SD16—22no—
351C2×M16—21no—
352C2×M16—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8D4×C3112yes—
356C4⋊Q8D4×C3111yescharacteristic
357C4⋊Q8C23×C3111yescharacteristic
358C4⋊Q8C23×C3111yescharacteristic
359C4⋊Q8C23×C3112yes—
360#127D4×C3111yescharacteristic
361#126—24no—
362#125—22no—
363#125—21no—
364#124—24no—
365#124—22no—
366#124—21no—
367#123—24no—
368C22⋊Q8—22no—
369C22⋊Q8—24no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374#121—22no—
375#121—22no—
376#121—24no—
377#121—22no—
378#121—21no—
379#121D4×C3112yes—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8D4×C3111yescharacteristic
385C4×Q8C23×C3111yescharacteristic
386C4×D4—22no—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4D4×C3111yescharacteristic
393C4×D4C23×C3111yescharacteristic
394C4×D4C23×C3112yes—
395#117—22no—
396#117—22no—
397#117—21no—
398#117—21no—
399#117D4×C3111yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4D4×C3112yes—
403C2×C42—21no—
404C2×C42C23×C3111yescharacteristic
405#107—24no—
406#107—21no—
407#107—22no—
408#106—24no—
409#106—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C3111yescharacteristic
412C4⋊C8C23×C3111yescharacteristic
413C4⋊C8C23×C3112yes—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—22no—
418#102—21no—
419#102—22no—
420C22⋊C8—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8C23×C3112yes—
424C31#1859311yescharacteristic, direct product factor, Sylow
425#41—41no—
426#41—41no—
427#41—42no—
428#41—42no—
429#41—82no—
430#41—82no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8C2×D4×C3111yescharacteristic
439C2×D4—21no—
440C2×D4—22no—
441C2×D4—24no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×D4×C3111yescharacteristic
445C2×D4C2×D4×C3112yes—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3111yescharacteristic
454C22×C4C2×D4×C3111yescharacteristic
455Q16—42no—
456SD16—42no—
457SD16—82no—
458M16—24no—
459M16—81no—
460C2×C8—22no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—22no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C3111yescharacteristic
479C4⋊C4C2×D4×C3111yescharacteristic
480C4⋊C4C2×D4×C3112yes—
481C4⋊C4C2×D4×C3114yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C42—24no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C2×D4×C3111yescharacteristic
497C42C2×D4×C3111yescharacteristic
498C42C2×D4×C3111yescharacteristic
499C42C24×C3111yescharacteristic
500C23—21no—
501C23—22no—
502C23C31×#12011yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—42no—
506Q8—42no—
507Q8—42no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—82no—
513D4—21no—
514D4—21no—
515D4—22no—
516D4—22no—
517D4—42no—
518D4—42no—
519D4—44no—
520D4—42no—
521D4—84no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—84no—
542C2×C4C31×#12011yescharacteristic
543C2×C4C31×#12011yescharacteristic
544C2×C4C31×#12011yescharacteristic
545C2×C4C22×D4×C3111yescharacteristic
546C2×C4C22×D4×C3111yescharacteristic
547C2×C4C22×D4×C3111yescharacteristic
548C8—24no—
549C8—41no—
550C8—41no—
551C8—42no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—42no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22C2×C31×#12011yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—44no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4C31×#45612yes—
573C4C31×#57511yescharacteristic
574C4C31×#57511yescharacteristic
575C4C31×#57611yescharacteristic
576C4C31×#57711yescharacteristic
577C2—41no—
578C2—81no—
579C2—82no—
580C2C31×#300511yescharacteristic
581C2C31×#301211yescharacteristic
582C2C2×C31×#45611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3511C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3254C2semidirect
3. C31×#3165C2semidirect
4. C31×#3107C2semidirect
5. C31×#1654C2semidirect
6. C31×#1652C2semidirect
7. C31×#1650C2semidirect
8. C31×#1647C2semidirect
9. C31×#1546C2semidirect
10. C31×#1489C2semidirect
11. C31×#1484C2semidirect
208. #18593C31direct (N × H)
262. #3254C2×C31semidirect
263. #3165C2×C31semidirect
264. #3107C2×C31semidirect
265. #1654C2×C31semidirect
266. #1652C2×C31semidirect
267. #1650C2×C31semidirect
268. #1647C2×C31semidirect
269. #1546C2×C31semidirect
270. #1489C2×C31semidirect
271. #1484C2×C31semidirect
424. C31#18593direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35112
C31×#32542
C31×#31652
C31×#31072
C31×#16542
C31×#16522
C31×#16502
C31×#16472
C31×#15462
C31×#14892
C31×#14842
#1859331