Finite Group Databasebeta

← C31×#18168 #21474927

Subgroups — C31×#18168 #21474927

Order 7936.

1244 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic, complemented
2C31×#3007C211yesmaximal, characteristic, complemented
3C31×#3006C211yesmaximal, characteristic, complemented
4C31×#2388C211yesmaximal, characteristic, complemented
5C31×#1606C212yesmaximal, complemented
6C31×#1603C212yesmaximal, complemented
7C31×#1600C212yesmaximal, complemented
8C31×#1597C212yesmaximal, complemented
9C31×#1508C211yesmaximal, characteristic, complemented
10C31×#1507C211yesmaximal, characteristic, complemented
11C31×#1465C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C2×C31×#137—21no—
14C2×C31×AGL(1,ℤ/8)—21no—
15C31×#553—22no—
16C31×#553—21no—
17C31×#552—21no—
18C31×#551—22no—
19C31×#548—21no—
20C31×#546—21no—
21C31×#539C2212yes—
22C31×#538C2212yes—
23C31×#534—21no—
24C31×#529—21no—
25C31×#525—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C31×#518—21no—
29C2×C4×D4×C31—21no—
30C2×C4×D4×C31C2211yescharacteristic
31C31×#452—22no—
32C31×#451C2212yescomplemented
33C31×#450C2212yescomplemented
34C31×#449—22no—
35C31×#448C2212yes—
36C31×#447C2212yes—
37C31×#417—21no—
38C31×#417—21no—
39C31×#407C2211yescharacteristic
40C31×#407C2211yescharacteristic
41C31×#395C2211yescharacteristic, complemented
42C31×#394—21no—
43C31×#394C2211yescharacteristic, complemented
44C31×#393C2211yescharacteristic, complemented
45C31×#392—21no—
46C31×#392C2211yescharacteristic, complemented
47C4×C22⋊C4×C31—21no—
48C4×C22⋊C4×C31C2211yescharacteristic
49C31×#328C2212yescomplemented
50C31×#328C2212yescomplemented
51C31×#327C2212yes—
52C31×#327C2212yes—
53C31×#324C2212yescomplemented
54C31×#323C2212yescomplemented
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—21no—
60C2×#41×C31—44no—
61C22×Q8×C31D411yescharacteristic, complemented
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31D411yescharacteristic
67C22×D4×C31D411yescharacteristic, complemented
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31D411yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C31×#137—44no—
73C31×AGL(1,ℤ/8)—44no—
74C2×Q16×C31—22no—
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×D8×C31—22no—
78C2×M16×C31—21no—
79C2×M16×C31—21no—
80C31×#126—22no—
81C31×#126—22no—
82C31×#126—22no—
83C31×#125—21no—
84C31×#125—22no—
85C31×#124—21no—
86C31×#124—22no—
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—22no—
91C31×#123—22no—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8D412yescomplemented
97C31×C22⋊Q8C2312yes—
98C31×#121—21no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121D412yescomplemented
105C31×#121C2312yes—
106C31×#120—22no—
107C31×#120—22no—
108C4×Q8×C31—21no—
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C4×D4×C31—22no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—22no—
118C4×D4×C31—22no—
119C4×D4×C31—44no—
120C31×#117—22no—
121C31×#117—21no—
122C31×#117—22no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31D411yescharacteristic, complemented
126C2×C4⋊C4×C31D411yescharacteristic, complemented
127C2×C4⋊C4×C31C2311yescharacteristic
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31D411yescharacteristic
137C2×C22⋊C4×C31C2311yescharacteristic
138C2×C42×C31—21no—
139C2×C42×C31D411yescharacteristic
140C31×#103—22no—
141C31×#103—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×C22⋊C8—21no—
145C31×C22⋊C8—21no—
146C31×C22⋊C8C2312yes—
147C31×C22⋊C8C2312yes—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95C2311yescharacteristic
151C31×#95C2311yescharacteristic
152C24×C31—21no—
153C24×C31—21no—
154C24×C31C2×D411yescharacteristic
155C24×C31C2×D411yescharacteristic
156#41×C31—24no—
157#41×C31—24no—
158#41×C31—42no—
159#41×C31—42no—
160#41×C31—42no—
161#41×C31—42no—
162#41×C31—42no—
163#41×C31—42no—
164#41×C31—82no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—42no—
169C2×Q8×C31—42no—
170C2×Q8×C31C2×D412yes—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—41no—
181C2×D4×C31—41no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—41no—
192C2×D4×C31—41no—
193C2×D4×C31C2×D412yes—
194C22×C4×C31—24no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—42no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31—41no—
209C22×C4×C31—41no—
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2411yescharacteristic
219Q16×C31—44no—
220SD16×C31—44no—
221SD16×C31—44no—
222D8×C31—44no—
223M16×C31—42no—
224M16×C31—42no—
225C2×C8×C31—22no—
226C2×C8×C31—22no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—22no—
229C4⋊C4×C31—22no—
230C4⋊C4×C31—22no—
231C4⋊C4×C31—22no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—22no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31C2×D412yes—
239C4⋊C4×C31C2×D412yes—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—21no—
253C22⋊C4×C31—21no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C42×C31—22no—
260C42×C31—22no—
261C42×C31—21no—
262C42×C31—21no—
263C42×C31—42no—
264#18168C3111yesmaximal, characteristic, direct product factor, Sylow
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—22no—
268C23×C31—21no—
269C23×C31—22no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—42no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—81no—
284C23×C31—81no—
285C23×C31#12011yescharacteristic
286C23×C31#12011yescharacteristic
287C23×C31C22×D411yescharacteristic
288Q8×C31—22no—
289Q8×C31—22no—
290Q8×C31—42no—
291Q8×C31—41no—
292Q8×C31—41no—
293Q8×C31—42no—
294D4×C31—22no—
295D4×C31—22no—
296D4×C31—42no—
297D4×C31—41no—
298D4×C31—41no—
299D4×C31—42no—
300D4×C31—42no—
301D4×C31—44no—
302D4×C31—44no—
303D4×C31—44no—
304D4×C31—48no—
305D4×C31—42no—
306D4×C31—42no—
307D4×C31—42no—
308D4×C31—82no—
309D4×C31—82no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—22no—
320C2×C4×C31—22no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—44no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—42no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—44no—
333C2×C4×C31—42no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—81no—
340C2×C4×C31—81no—
341C2×C4×C31—81no—
342C2×C4×C31—82no—
343C2×C4×C31—82no—
344C2×C4×C31#12011yescharacteristic
345C2×C4×C31#12011yescharacteristic
346C2×C4×C31C22×D411yescharacteristic
347C2×C4×C31C22×D411yescharacteristic
348C8×C31—42no—
349C8×C31—42no—
350#3505C2×C3111yescharacteristic, complemented
351#3007C2×C3111yescharacteristic, complemented
352#3006C2×C3111yescharacteristic, complemented
353#2388C2×C3111yescharacteristic, complemented
354#1606C2×C3112yescomplemented
355#1603C2×C3112yescomplemented
356#1600C2×C3112yescomplemented
357#1597C2×C3112yescomplemented
358#1508C2×C3111yescharacteristic, complemented
359#1507C2×C3111yescharacteristic, complemented
360#1465C2×C3111yescharacteristic, complemented
361C22×C31—21no—
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—21no—
365C22×C31—21no—
366C22×C31—21no—
367C22×C31—21no—
368C22×C31—21no—
369C22×C31—42no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—41no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—41no—
376C22×C31—42no—
377C22×C31—41no—
378C22×C31—42no—
379C22×C31—81no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—162no—
387C22×C31C2×#12011yescharacteristic
388C22×C31#57511yescharacteristic
389C22×C31#57511yescharacteristic
390C4×C31—21no—
391C4×C31—21no—
392C4×C31—21no—
393C4×C31—42no—
394C4×C31—41no—
395C4×C31—42no—
396C4×C31—41no—
397C4×C31—42no—
398C4×C31—42no—
399C4×C31—41no—
400C4×C31—42no—
401C4×C31—81no—
402C4×C31B(4,𝔽2)12yes—
403C22×#41C22×C3111yescharacteristic
404C2×#137—21no—
405C2×AGL(1,ℤ/8)—21no—
406#553—22no—
407#553—21no—
408#552—21no—
409#551—22no—
410#548—21no—
411#546—21no—
412#539C22×C3112yes—
413#538C22×C3112yes—
414#534—21no—
415#529—21no—
416#525—21no—
417C2×C22⋊Q8C22×C3111yescharacteristic
418C2×#121C22×C3111yescharacteristic
419#518—21no—
420C2×C4×D4—21no—
421C2×C4×D4C22×C3111yescharacteristic
422#452—22no—
423#451C22×C3112yescomplemented
424#450C22×C3112yescomplemented
425#449—22no—
426#448C22×C3112yes—
427#447C22×C3112yes—
428#417—21no—
429#417—21no—
430#407C22×C3111yescharacteristic
431#407C22×C3111yescharacteristic
432#395C22×C3111yescharacteristic, complemented
433#394—21no—
434#394C22×C3111yescharacteristic, complemented
435#393C22×C3111yescharacteristic, complemented
436#392—21no—
437#392C22×C3111yescharacteristic, complemented
438C4×C22⋊C4—21no—
439C4×C22⋊C4C22×C3111yescharacteristic
440#328C22×C3112yescomplemented
441#328C22×C3112yescomplemented
442#327C22×C3112yes—
443#327C22×C3112yes—
444#324C22×C3112yescomplemented
445#323C22×C3112yescomplemented
446C2×C31—21no—
447C2×C31—21no—
448C2×C31—41no—
449C2×C31—41no—
450C2×C31—81no—
451C2×C31—82no—
452C2×C31—82no—
453C2×C31#300511yescharacteristic
454C2×C31#301811yescharacteristic
455C2×C31C2×B(4,𝔽2)11yescharacteristic
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—44no—
462C22×Q8D4×C3111yescharacteristic, complemented
463C22×Q8C23×C3111yescharacteristic
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4D4×C3111yescharacteristic
468C22×D4D4×C3111yescharacteristic, complemented
469C22×D4C23×C3111yescharacteristic
470C23×C4—21no—
471C23×C4D4×C3111yescharacteristic
472C23×C4C23×C3111yescharacteristic
473#137—44no—
474AGL(1,ℤ/8)—44no—
475C2×Q16—22no—
476C2×SD16—22no—
477C2×SD16—22no—
478C2×D8—22no—
479C2×M16—21no—
480C2×M16—21no—
481#126—22no—
482#126—22no—
483#126—22no—
484#125—21no—
485#125—22no—
486#124—21no—
487#124—22no—
488#123—22no—
489#123—22no—
490#123—22no—
491#123—22no—
492#123—22no—
493C22⋊Q8—21no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C3112yescomplemented
498C22⋊Q8C23×C3112yes—
499#121—21no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—21no—
505#121D4×C3112yescomplemented
506#121C23×C3112yes—
507#120—22no—
508#120—22no—
509C4×Q8—21no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—44no—
521#117—22no—
522#117—21no—
523#117—22no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4D4×C3111yescharacteristic, complemented
527C2×C4⋊C4D4×C3111yescharacteristic, complemented
528C2×C4⋊C4C23×C3111yescharacteristic
529C2×C22⋊C4—22no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4D4×C3111yescharacteristic
538C2×C22⋊C4C23×C3111yescharacteristic
539C2×C42—21no—
540C2×C42D4×C3111yescharacteristic
541#103—22no—
542#103—22no—
543#102—22no—
544#102—22no—
545C22⋊C8—21no—
546C22⋊C8—21no—
547C22⋊C8C23×C3112yes—
548C22⋊C8C23×C3112yes—
549#95—21no—
550#95—21no—
551#95C23×C3111yescharacteristic
552#95C23×C3111yescharacteristic
553C31#1816811yescharacteristic, direct product factor, Sylow
554C24—21no—
555C24—21no—
556C24C2×D4×C3111yescharacteristic
557C24C2×D4×C3111yescharacteristic
558#41—24no—
559#41—24no—
560#41—42no—
561#41—42no—
562#41—42no—
563#41—42no—
564#41—42no—
565#41—42no—
566#41—82no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8C2×D4×C3112yes—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C2×D4×C3112yes—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4C2×D4×C3111yescharacteristic
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4C2×D4×C3111yescharacteristic
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C24×C3111yescharacteristic
621Q16—44no—
622SD16—44no—
623SD16—44no—
624D8—44no—
625M16—42no—
626M16—42no—
627C2×C8—22no—
628C2×C8—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—42no—
640C4⋊C4C2×D4×C3112yes—
641C4⋊C4C2×D4×C3112yes—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C42—22no—
662C42—22no—
663C42—21no—
664C42—21no—
665C42—42no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—81no—
685C23—81no—
686C23C31×#12011yescharacteristic
687C23C31×#12011yescharacteristic
688C23C22×D4×C3111yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—42no—
692Q8—41no—
693Q8—41no—
694Q8—42no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—41no—
699D4—41no—
700D4—42no—
701D4—42no—
702D4—44no—
703D4—44no—
704D4—44no—
705D4—48no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—82no—
710D4—82no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—82no—
744C2×C4—82no—
745C2×C4C31×#12011yescharacteristic
746C2×C4C31×#12011yescharacteristic
747C2×C4C22×D4×C3111yescharacteristic
748C2×C4C22×D4×C3111yescharacteristic
749C8—42no—
750C8—42no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—162no—
777C22C2×C31×#12011yescharacteristic
778C22C31×#57511yescharacteristic
779C22C31×#57511yescharacteristic
780C4—21no—
781C4—21no—
782C4—21no—
783C4—42no—
784C4—41no—
785C4—42no—
786C4—41no—
787C4—42no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4C31×B(4,𝔽2)12yes—
793C2—21no—
794C2—21no—
795C2—41no—
796C2—41no—
797C2—81no—
798C2—82no—
799C2—82no—
800C2C31×#300511yescharacteristic
801C2C31×#301811yescharacteristic
802C2C2×C31×B(4,𝔽2)11yescharacteristic
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×#3007C2semidirect
3. C31×#3006C2semidirect
4. C31×#2388C2semidirect
5. C31×#1606C2semidirect
6. C31×#1603C2semidirect
7. C31×#1600C2semidirect
8. C31×#1597C2semidirect
9. C31×#1508C2semidirect
10. C31×#1507C2semidirect
11. C31×#1465C2semidirect
32. C31×#451C22semidirect
33. C31×#450C22semidirect
41. C31×#395C22semidirect
43. C31×#394C22semidirect
44. C31×#393C22semidirect
46. C31×#392C22semidirect
49. C31×#328C22semidirect
50. C31×#328C22semidirect
53. C31×#324C22semidirect
54. C31×#323C22semidirect
61. C22×Q8×C31D4semidirect
67. C22×D4×C31D4semidirect
96. C31×C22⋊Q8D4semidirect
104. C31×#121D4semidirect
125. C2×C4⋊C4×C31D4semidirect
126. C2×C4⋊C4×C31D4semidirect
264. #18168C31direct (N × H)
350. #3505C2×C31semidirect
351. #3007C2×C31semidirect
352. #3006C2×C31semidirect
353. #2388C2×C31semidirect
354. #1606C2×C31semidirect
355. #1603C2×C31semidirect
356. #1600C2×C31semidirect
357. #1597C2×C31semidirect
358. #1508C2×C31semidirect
359. #1507C2×C31semidirect
360. #1465C2×C31semidirect
423. #451C22×C31semidirect
424. #450C22×C31semidirect
432. #395C22×C31semidirect
434. #394C22×C31semidirect
435. #393C22×C31semidirect
437. #392C22×C31semidirect
440. #328C22×C31semidirect
441. #328C22×C31semidirect
444. #324C22×C31semidirect
445. #323C22×C31semidirect
462. C22×Q8D4×C31semidirect
468. C22×D4D4×C31semidirect
497. C22⋊Q8D4×C31semidirect
505. #121D4×C31semidirect
526. C2×C4⋊C4D4×C31semidirect
527. C2×C4⋊C4D4×C31semidirect
553. C31#18168direct (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×#30072
C31×#30062
C31×#23882
C31×#16062
C31×#16032
C31×#16002
C31×#15972
C31×#15082
C31×#15072
C31×#14652
#1816831