Finite Group Databasebeta

← C31×#18354 #21475113

Subgroups — C31×#18354 #21475113

Order 7936.

1022 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic, complemented
2C31×#3193C211yesmaximal, characteristic, complemented
3C31×#3192C211yesmaximal, characteristic, complemented
4C31×#2635C211yesmaximal, characteristic, complemented
5C31×#1618C212yesmaximal, complemented
6C31×#1615C212yesmaximal, complemented
7C31×#1600C212yesmaximal, complemented
8C31×#1597C212yesmaximal, complemented
9C31×#1511C211yesmaximal, characteristic, complemented
10C31×#1510C211yesmaximal, characteristic, complemented
11C31×#1465C211yesmaximal, characteristic, complemented
12C31×#553—22no—
13C31×#553—21no—
14C31×#552—21no—
15C31×#551—22no—
16C31×#548—21no—
17C31×#546—21no—
18C31×#539C2212yes—
19C31×#538C2212yes—
20C31×#534—21no—
21C31×#529—21no—
22C31×#525—21no—
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C31×#518—21no—
27C2×C4×D4×C31C2211yescharacteristic
28C31×#484C2212yescomplemented
29C31×#481—21no—
30C31×#481C2212yes—
31C31×#480—21no—
32C31×#469—22no—
33C31×#468—22no—
34C31×#450C2212yescomplemented
35C31×#448—21no—
36C31×#447—21no—
37C31×#447C2212yes—
38C31×#407C2211yescharacteristic
39C31×#407C2211yescharacteristic
40C31×#400C2211yescharacteristic, complemented
41C31×#399C2211yescharacteristic, complemented
42C31×#394—21no—
43C31×#394C2211yescharacteristic, complemented
44C31×#392—21no—
45C31×#392C2211yescharacteristic, complemented
46C31×#388—21no—
47C31×#386—21no—
48C31×#381C2211yescharacteristic
49C31×#328C2212yescomplemented
50C31×#328C2212yescomplemented
51C31×#327C2212yes—
52C31×#327C2212yes—
53C31×#324C2212yescomplemented
54C31×#323C2212yescomplemented
55C2×#41×C31—21no—
56C22×Q8×C31D411yescharacteristic, complemented
57C22×D4×C31—21no—
58C22×D4×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31D411yescharacteristic
61C22×D4×C31D411yescharacteristic, complemented
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31D411yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C2×SD16×C31—22no—
66C2×D8×C31—22no—
67C2×M16×C31—21no—
68C2×M16×C31—21no—
69C31×#126—22no—
70C31×#126—22no—
71C31×#126—22no—
72C31×#125—21no—
73C31×#125—22no—
74C31×#124—21no—
75C31×#124—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×#123—22no—
79C31×#123—22no—
80C31×#123—22no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8D412yescomplemented
86C31×C22⋊Q8C2312yes—
87C31×#121—21no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—21no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121D412yescomplemented
98C31×#121C2312yes—
99C31×#120—22no—
100C31×#120—22no—
101C4×Q8×C31—21no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—21no—
106C4×D4×C31—21no—
107C4×D4×C31—21no—
108C4×D4×C31—21no—
109C4×D4×C31—21no—
110C4×D4×C31—22no—
111C4×D4×C31—22no—
112C31×#117—22no—
113C31×#117—21no—
114C31×#117—22no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31D411yescharacteristic, complemented
118C2×C4⋊C4×C31D411yescharacteristic, complemented
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C22⋊C4×C31C2311yescharacteristic
132C2×C42×C31D411yescharacteristic
133C31×#107—22no—
134C31×#106—22no—
135C31×#103—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×C22⋊C8—21no—
140C31×C22⋊C8—21no—
141C31×C22⋊C8C2312yes—
142C31×C22⋊C8C2312yes—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95C2311yescharacteristic
147C31×#95C2311yescharacteristic
148C24×C31—21no—
149C24×C31—21no—
150C24×C31C2×D411yescharacteristic
151C24×C31C2×D411yescharacteristic
152#41×C31—82no—
153C2×Q8×C31—21no—
154C2×Q8×C31—81no—
155C2×Q8×C31C2×D412yes—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—41no—
166C2×D4×C31—41no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—41no—
171C2×D4×C31—41no—
172C2×D4×C31—81no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31—81no—
177C2×D4×C31—81no—
178C2×D4×C31C2×D412yes—
179C22×C4×C31—21no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—81no—
190C22×C4×C31—81no—
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2411yescharacteristic
200SD16×C31—82no—
201D8×C31—82no—
202M16×C31—81no—
203M16×C31—81no—
204C2×C8×C31—22no—
205C2×C8×C31—22no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31—22no—
209C4⋊C4×C31—22no—
210C4⋊C4×C31—22no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—22no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—81no—
219C4⋊C4×C31C2×D412yes—
220C4⋊C4×C31C2×D412yes—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—21no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—21no—
234C22⋊C4×C31—21no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—41no—
237C22⋊C4×C31—41no—
238C22⋊C4×C31—81no—
239C22⋊C4×C31—81no—
240C22⋊C4×C31—81no—
241C22⋊C4×C31—81no—
242C42×C31—22no—
243C42×C31—22no—
244C42×C31—21no—
245C42×C31—21no—
246#18354C3111yesmaximal, characteristic, direct product factor, Sylow
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—22no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—42no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—81no—
266C23×C31—81no—
267C23×C31#12011yescharacteristic
268C23×C31#12011yescharacteristic
269C23×C31C22×D411yescharacteristic
270Q8×C31—42no—
271Q8×C31—42no—
272D4×C31—42no—
273D4×C31—42no—
274D4×C31—42no—
275D4×C31—42no—
276D4×C31—42no—
277D4×C31—42no—
278D4×C31—44no—
279D4×C31—42no—
280D4×C31—42no—
281D4×C31—82no—
282D4×C31—82no—
283D4×C31—82no—
284D4×C31—82no—
285D4×C31—84no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—22no—
289C2×C4×C31—21no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—81no—
314C2×C4×C31—81no—
315C2×C4×C31—81no—
316C2×C4×C31—82no—
317C2×C4×C31—82no—
318C2×C4×C31#12011yescharacteristic
319C2×C4×C31#12011yescharacteristic
320C2×C4×C31C22×D411yescharacteristic
321C2×C4×C31C22×D411yescharacteristic
322C8×C31—42no—
323C8×C31—42no—
324#3505C2×C3111yescharacteristic, complemented
325#3193C2×C3111yescharacteristic, complemented
326#3192C2×C3111yescharacteristic, complemented
327#2635C2×C3111yescharacteristic, complemented
328#1618C2×C3112yescomplemented
329#1615C2×C3112yescomplemented
330#1600C2×C3112yescomplemented
331#1597C2×C3112yescomplemented
332#1511C2×C3111yescharacteristic, complemented
333#1510C2×C3111yescharacteristic, complemented
334#1465C2×C3111yescharacteristic, complemented
335C22×C31—21no—
336C22×C31—21no—
337C22×C31—21no—
338C22×C31—21no—
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—42no—
344C22×C31—41no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—42no—
350C22×C31—81no—
351C22×C31—81no—
352C22×C31—81no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—81no—
358C22×C31—81no—
359C22×C31—81no—
360C22×C31—162no—
361C22×C31C2×#12011yescharacteristic
362C22×C31#57511yescharacteristic
363C22×C31#57511yescharacteristic
364C4×C31—21no—
365C4×C31—21no—
366C4×C31—21no—
367C4×C31—21no—
368C4×C31—41no—
369C4×C31—42no—
370C4×C31—41no—
371C4×C31—42no—
372C4×C31—41no—
373C4×C31—42no—
374C4×C31—81no—
375C4×C31—81no—
376C4×C31—81no—
377#553—22no—
378#553—21no—
379#552—21no—
380#551—22no—
381#548—21no—
382#546—21no—
383#539C22×C3112yes—
384#538C22×C3112yes—
385#534—21no—
386#529—21no—
387#525—21no—
388C2×C22⋊Q8C22×C3111yescharacteristic
389C2×#121C22×C3111yescharacteristic
390C2×#121C22×C3111yescharacteristic
391#518—21no—
392C2×C4×D4C22×C3111yescharacteristic
393#484C22×C3112yescomplemented
394#481—21no—
395#481C22×C3112yes—
396#480—21no—
397#469—22no—
398#468—22no—
399#450C22×C3112yescomplemented
400#448—21no—
401#447—21no—
402#447C22×C3112yes—
403#407C22×C3111yescharacteristic
404#407C22×C3111yescharacteristic
405#400C22×C3111yescharacteristic, complemented
406#399C22×C3111yescharacteristic, complemented
407#394—21no—
408#394C22×C3111yescharacteristic, complemented
409#392—21no—
410#392C22×C3111yescharacteristic, complemented
411#388—21no—
412#386—21no—
413#381C22×C3111yescharacteristic
414#328C22×C3112yescomplemented
415#328C22×C3112yescomplemented
416#327C22×C3112yes—
417#327C22×C3112yes—
418#324C22×C3112yescomplemented
419#323C22×C3112yescomplemented
420C2×C31—21no—
421C2×C31—21no—
422C2×C31—41no—
423C2×C31—41no—
424C2×C31—81no—
425C2×C31—82no—
426C2×C31—161no—
427C2×C31#300511yescharacteristic
428C2×C31#302111yescharacteristic
429C2×C31#302611yescharacteristic
430C2×#41—21no—
431C22×Q8D4×C3111yescharacteristic, complemented
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4D4×C3111yescharacteristic
436C22×D4D4×C3111yescharacteristic, complemented
437C22×D4C23×C3111yescharacteristic
438C23×C4D4×C3111yescharacteristic
439C23×C4C23×C3111yescharacteristic
440C2×SD16—22no—
441C2×D8—22no—
442C2×M16—21no—
443C2×M16—21no—
444#126—22no—
445#126—22no—
446#126—22no—
447#125—21no—
448#125—22no—
449#124—21no—
450#124—22no—
451#123—22no—
452#123—22no—
453#123—22no—
454#123—22no—
455#123—22no—
456C22⋊Q8—21no—
457C22⋊Q8—22no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8D4×C3112yescomplemented
461C22⋊Q8C23×C3112yes—
462#121—21no—
463#121—22no—
464#121—22no—
465#121—22no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—21no—
472#121D4×C3112yescomplemented
473#121C23×C3112yes—
474#120—22no—
475#120—22no—
476C4×Q8—21no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—22no—
486C4×D4—22no—
487#117—22no—
488#117—21no—
489#117—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C3111yescharacteristic, complemented
493C2×C4⋊C4D4×C3111yescharacteristic, complemented
494C2×C4⋊C4C23×C3111yescharacteristic
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C3111yescharacteristic
506C2×C22⋊C4C23×C3111yescharacteristic
507C2×C42D4×C3111yescharacteristic
508#107—22no—
509#106—22no—
510#103—22no—
511#102—22no—
512#102—22no—
513#102—22no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516C22⋊C8C23×C3112yes—
517C22⋊C8C23×C3112yes—
518#95—21no—
519#95—21no—
520#95—21no—
521#95C23×C3111yescharacteristic
522#95C23×C3111yescharacteristic
523C31#1835411yescharacteristic, direct product factor, Sylow
524C24—21no—
525C24—21no—
526C24C2×D4×C3111yescharacteristic
527C24C2×D4×C3111yescharacteristic
528#41—82no—
529C2×Q8—21no—
530C2×Q8—81no—
531C2×Q8C2×D4×C3112yes—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4C2×D4×C3112yes—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C2×D4×C3111yescharacteristic
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4C2×D4×C3111yescharacteristic
573C22×C4C2×D4×C3111yescharacteristic
574C22×C4C2×D4×C3111yescharacteristic
575C22×C4C24×C3111yescharacteristic
576SD16—82no—
577D8—82no—
578M16—81no—
579M16—81no—
580C2×C8—22no—
581C2×C8—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—81no—
595C4⋊C4C2×D4×C3112yes—
596C4⋊C4C2×D4×C3112yes—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—21no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—42no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—21no—
627C23—21no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23C31×#12011yescharacteristic
643C23C31×#12011yescharacteristic
644C23C22×D4×C3111yescharacteristic
645Q8—42no—
646Q8—42no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—44no—
654D4—42no—
655D4—42no—
656D4—82no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—84no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4C31×#12011yescharacteristic
694C2×C4C31×#12011yescharacteristic
695C2×C4C22×D4×C3111yescharacteristic
696C2×C4C22×D4×C3111yescharacteristic
697C8—42no—
698C8—42no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—42no—
708C22—41no—
709C22—42no—
710C22—42no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—162no—
725C22C2×C31×#12011yescharacteristic
726C22C31×#57511yescharacteristic
727C22C31×#57511yescharacteristic
728C4—21no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—81no—
741C2—21no—
742C2—21no—
743C2—41no—
744C2—41no—
745C2—81no—
746C2—82no—
747C2—161no—
748C2C31×#300511yescharacteristic
749C2C31×#302111yescharacteristic
750C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3505C2semidirect
2. C31×#3193C2semidirect
3. C31×#3192C2semidirect
4. C31×#2635C2semidirect
5. C31×#1618C2semidirect
6. C31×#1615C2semidirect
7. C31×#1600C2semidirect
8. C31×#1597C2semidirect
9. C31×#1511C2semidirect
10. C31×#1510C2semidirect
11. C31×#1465C2semidirect
28. C31×#484C22semidirect
34. C31×#450C22semidirect
40. C31×#400C22semidirect
41. C31×#399C22semidirect
43. C31×#394C22semidirect
45. C31×#392C22semidirect
49. C31×#328C22semidirect
50. C31×#328C22semidirect
53. C31×#324C22semidirect
54. C31×#323C22semidirect
56. C22×Q8×C31D4semidirect
61. C22×D4×C31D4semidirect
85. C31×C22⋊Q8D4semidirect
97. C31×#121D4semidirect
117. C2×C4⋊C4×C31D4semidirect
118. C2×C4⋊C4×C31D4semidirect
246. #18354C31direct (N × H)
324. #3505C2×C31semidirect
325. #3193C2×C31semidirect
326. #3192C2×C31semidirect
327. #2635C2×C31semidirect
328. #1618C2×C31semidirect
329. #1615C2×C31semidirect
330. #1600C2×C31semidirect
331. #1597C2×C31semidirect
332. #1511C2×C31semidirect
333. #1510C2×C31semidirect
334. #1465C2×C31semidirect
393. #484C22×C31semidirect
399. #450C22×C31semidirect
405. #400C22×C31semidirect
406. #399C22×C31semidirect
408. #394C22×C31semidirect
410. #392C22×C31semidirect
414. #328C22×C31semidirect
415. #328C22×C31semidirect
418. #324C22×C31semidirect
419. #323C22×C31semidirect
431. C22×Q8D4×C31semidirect
436. C22×D4D4×C31semidirect
460. C22⋊Q8D4×C31semidirect
472. #121D4×C31semidirect
492. C2×C4⋊C4D4×C31semidirect
493. C2×C4⋊C4D4×C31semidirect
523. C31#18354direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35052
C31×#31932
C31×#31922
C31×#26352
C31×#16182
C31×#16152
C31×#16002
C31×#15972
C31×#15112
C31×#15102
C31×#14652
#1835431