Finite Group Databasebeta

← C31×#24026 #21480785

Subgroups — C31×#24026 #21480785

Order 7936.

1404 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3488C211yesmaximal, characteristic
2C31×#3092C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C31×#2501C211yesmaximal, characteristic, complemented
5C31×#2039C212yesmaximal, complemented
6C31×#2037C212yesmaximal, complemented
7C31×#1900C211yesmaximal, characteristic, complemented
8C31×#1871C211yesmaximal, characteristic, complemented
9C31×#1859C212yesmaximal, complemented
10C31×#1792C212yesmaximal, complemented
11C31×#1789C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic
14C22×M16×C31C2211yescharacteristic, complemented
15C31×#550—21no—
16C31×#548—21no—
17C31×#546—21no—
18C31×#546—22no—
19D42×C31—22no—
20D42×C31—21no—
21C31×#537—21no—
22C31×#537C2211yescharacteristic
23C31×#535—21no—
24C31×#535C2211yescharacteristic
25C31×#525—21no—
26C31×#525C2211yescharacteristic
27C2×C31×#123—22no—
28C2×C31×#121—21no—
29C2×C31×#121C2211yescharacteristic
30C31×#520C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic, complemented
32C31×#484—21no—
33C31×#483—21no—
34C31×#481—21no—
35C31×#480—21no—
36C31×#428C2212yescomplemented
37C2×C31×#104C2212yes—
38C2×C31×#104C2212yescomplemented
39C2×C31×#104C2212yescomplemented
40C31×#417—21no—
41C31×#417—21no—
42C31×#417C2212yes—
43C31×#417C2212yescomplemented
44C31×#417C2212yescomplemented
45C2×C31×#103—21no—
46C2×C31×#102—21no—
47C2×C31×#100C2212yescomplemented
48C31×#407C2211yescharacteristic, complemented
49C31×#399—22no—
50C31×#390C2212yescomplemented
51C31×#384C2212yescomplemented
52C4×C22⋊C4×C31C2211yescharacteristic, complemented
53C31×#343C2212yescomplemented
54C31×#339C2212yescomplemented
55C31×H(5,𝔽2)—24no—
56C31×H(5,𝔽2)—42no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—21no—
60C2×#41×C31—21no—
61C2×#41×C31—24no—
62C2×#41×C31—42no—
63C2×#41×C31D411yescharacteristic
64C2×#41×C31D411yescharacteristic
65C2×#41×C31C2311yescharacteristic
66C2×#41×C31C2311yescharacteristic
67C2×#41×C31C2311yescharacteristic
68C22×Q8×C31D411yescharacteristic
69C22×D4×C31—21no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31D411yescharacteristic
75C22×D4×C31D412yes—
76C22×D4×C31C2311yescharacteristic
77C23×C4×C31—21no—
78C23×C4×C31—21no—
79C23×C4×C31C2311yescharacteristic
80C2×M16×C31—21no—
81C2×M16×C31—42no—
82C2×M16×C31C2312yes—
83C2×M16×C31C2312yes—
84C22×C8×C31—21no—
85C31×#127—22no—
86C31×#127—21no—
87C31×#124—22no—
88C31×#124—21no—
89C31×#123—22no—
90C31×#123—21no—
91C31×#123—48no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8D411yescharacteristic
96C31×C22⋊Q8D411yescharacteristic
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121—22no—
109C31×#121—21no—
110C31×#121—21no—
111C31×#121D411yescharacteristic
112C31×#121D411yescharacteristic
113C31×#120—22no—
114C31×#120—22no—
115C31×#120—22no—
116C31×#120—21no—
117C31×#120—22no—
118C4×Q8×C31—21no—
119C4×D4×C31—22no—
120C4×D4×C31—22no—
121C4×D4×C31—21no—
122C4×D4×C31—22no—
123C4×D4×C31—21no—
124C4×D4×C31—21no—
125C31×#117—21no—
126C31×#117C2311yescharacteristic
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31—24no—
134C2×C4⋊C4×C31C2312yes—
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—24no—
139C2×C22⋊C4×C31D412yes—
140C2×C42×C31C2312yes—
141C31×#107—22no—
142C31×#106—22no—
143C31×#104—24no—
144C31×#104—42no—
145C31×#104—42no—
146C31×#103—22no—
147C31×#103—22no—
148C31×#103—22no—
149C31×#102—22no—
150C31×#102—22no—
151C31×#102—22no—
152C31×#100—42no—
153C31×C22⋊C8—21no—
154C31×C22⋊C8—21no—
155C31×#95—21no—
156C24×C31—22no—
157C24×C31—21no—
158C24×C31C2×D411yescharacteristic
159C24×C31C2×D412yes—
160#41×C31—22no—
161#41×C31—22no—
162#41×C31—22no—
163#41×C31—22no—
164#41×C31—22no—
165#41×C31—22no—
166#41×C31—22no—
167#41×C31—44no—
168#41×C31—41no—
169#41×C31—41no—
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—42no—
173#41×C31—42no—
174#41×C31#4114yes—
175C2×Q8×C31—21no—
176C2×Q8×C31—22no—
177C2×Q8×C31—41no—
178C2×Q8×C31C2×D411yescharacteristic
179C2×Q8×C31C2×D411yescharacteristic
180C2×Q8×C31C2×D411yescharacteristic
181C2×D4×C31—21no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—21no—
195C2×D4×C31—22no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—22no—
200C2×D4×C31—22no—
201C2×D4×C31—41no—
202C2×D4×C31—44no—
203C2×D4×C31—44no—
204C2×D4×C31—48no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—44no—
208C2×D4×C31—84no—
209C2×D4×C31C2×D411yescharacteristic
210C2×D4×C31C2×D411yescharacteristic
211C2×D4×C31C2×D411yescharacteristic
212C22×C4×C31—21no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—21no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—22no—
224C22×C4×C31—44no—
225C22×C4×C31—44no—
226C22×C4×C31—41no—
227C22×C4×C31—41no—
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2411yescharacteristic
235M16×C31—22no—
236M16×C31—22no—
237M16×C31—22no—
238M16×C31—22no—
239M16×C31—42no—
240C2×C8×C31—22no—
241C2×C8×C31—22no—
242C2×C8×C31—42no—
243C4⋊C4×C31—22no—
244C4⋊C4×C31—22no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—22no—
250C4⋊C4×C31—22no—
251C4⋊C4×C31—48no—
252C4⋊C4×C31—41no—
253C4⋊C4×C31—41no—
254C4⋊C4×C31C2×D411yescharacteristic
255C4⋊C4×C31C2×D411yescharacteristic
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—24no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—22no—
262C22⋊C4×C31—21no—
263C22⋊C4×C31—21no—
264C22⋊C4×C31—21no—
265C22⋊C4×C31—21no—
266C22⋊C4×C31—22no—
267C22⋊C4×C31—22no—
268C22⋊C4×C31—21no—
269C22⋊C4×C31—48no—
270C42×C31—22no—
271C42×C31—21no—
272C42×C31—22no—
273C42×C31—22no—
274#24026C3111yesmaximal, characteristic, direct product factor, Sylow
275C23×C31—21no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—22no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—24no—
282C23×C31—41no—
283C23×C31—42no—
284C23×C31—44no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—81no—
289C23×C31—82no—
290C23×C31—82no—
291C23×C31#12011yescharacteristic
292C23×C31#12011yescharacteristic
293C23×C31C22×D411yescharacteristic
294Q8×C31—21no—
295Q8×C31—21no—
296Q8×C31—21no—
297Q8×C31—22no—
298Q8×C31—42no—
299Q8×C31#12312yescomplemented
300D4×C31—24no—
301D4×C31—21no—
302D4×C31—21no—
303D4×C31—21no—
304D4×C31—22no—
305D4×C31—42no—
306D4×C31—42no—
307D4×C31—44no—
308D4×C31—42no—
309D4×C31—44no—
310D4×C31—42no—
311D4×C31—42no—
312D4×C31—44no—
313D4×C31—42no—
314D4×C31—41no—
315D4×C31—41no—
316D4×C31—42no—
317D4×C31—81no—
318D4×C31—82no—
319D4×C31—82no—
320D4×C31—82no—
321D4×C31—82no—
322D4×C31#12312yescomplemented
323C2×C4×C31—21no—
324C2×C4×C31—22no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—24no—
332C2×C4×C31—24no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—44no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—42no—
347C2×C4×C31—42no—
348C2×C4×C31—44no—
349C2×C4×C31—42no—
350C2×C4×C31—82no—
351C2×C4×C31—82no—
352C2×C4×C31—82no—
353C2×C4×C31#12011yescharacteristic
354C2×C4×C31#12011yescharacteristic
355C2×C4×C31C22×D411yescharacteristic
356C2×C4×C31C22×D411yescharacteristic
357C2×C4×C31C2×#4112yes—
358C2×C4×C31H(5,𝔽2)12yes—
359C8×C31—42no—
360C8×C31—42no—
361#3488C2×C3111yescharacteristic
362#3092C2×C3111yescharacteristic, complemented
363C2×#417C2×C3111yescharacteristic, complemented
364#2501C2×C3111yescharacteristic, complemented
365#2039C2×C3112yescomplemented
366#2037C2×C3112yescomplemented
367#1900C2×C3111yescharacteristic, complemented
368#1871C2×C3111yescharacteristic, complemented
369#1859C2×C3112yescomplemented
370#1792C2×C3112yescomplemented
371#1789C2×C3111yescharacteristic, complemented
372C22×C31—21no—
373C22×C31—21no—
374C22×C31—21no—
375C22×C31—21no—
376C22×C31—21no—
377C22×C31—22no—
378C22×C31—21no—
379C22×C31—21no—
380C22×C31—44no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—42no—
391C22×C31—41no—
392C22×C31—84no—
393C22×C31—84no—
394C22×C31—164no—
395C22×C31#45312yes—
396C22×C31C2×#12011yescharacteristic
397C22×C31#54612yes—
398C4×C31—21no—
399C4×C31—21no—
400C4×C31—22no—
401C4×C31—44no—
402C4×C31—41no—
403C4×C31—41no—
404C4×C31—42no—
405C4×C31—41no—
406C4×C31—41no—
407C4×C31—82no—
408C4×C31C2×#12311yescharacteristic
409C4×C31#53411yescharacteristic
410C4×C31#54612yes—
411C2×H(5,𝔽2)C22×C3111yescharacteristic
412C22×#41C22×C3111yescharacteristic
413C22×M16C22×C3111yescharacteristic, complemented
414#550—21no—
415#548—21no—
416#546—21no—
417#546—22no—
418D42—22no—
419D42—21no—
420#537—21no—
421#537C22×C3111yescharacteristic
422#535—21no—
423#535C22×C3111yescharacteristic
424#525—21no—
425#525C22×C3111yescharacteristic
426C2×#123—22no—
427C2×#121—21no—
428C2×#121C22×C3111yescharacteristic
429#520C22×C3111yescharacteristic
430C22×C4⋊C4C22×C3111yescharacteristic, complemented
431#484—21no—
432#483—21no—
433#481—21no—
434#480—21no—
435#428C22×C3112yescomplemented
436C2×#104C22×C3112yes—
437C2×#104C22×C3112yescomplemented
438C2×#104C22×C3112yescomplemented
439#417—21no—
440#417—21no—
441#417C22×C3112yes—
442#417C22×C3112yescomplemented
443#417C22×C3112yescomplemented
444C2×#103—21no—
445C2×#102—21no—
446C2×#100C22×C3112yescomplemented
447#407C22×C3111yescharacteristic, complemented
448#399—22no—
449#390C22×C3112yescomplemented
450#384C22×C3112yescomplemented
451C4×C22⋊C4C22×C3111yescharacteristic, complemented
452#343C22×C3112yescomplemented
453#339C22×C3112yescomplemented
454C2×C31—22no—
455C2×C31—22no—
456C2×C31—41no—
457C2×C31—42no—
458C2×C31—81no—
459C2×C31—82no—
460C2×C31—81no—
461C2×C31#240511yescharacteristic
462C2×C31C2×#45311yescharacteristic
463C2×C31#302211yescharacteristic
464H(5,𝔽2)—24no—
465H(5,𝔽2)—42no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—24no—
471C2×#41—42no—
472C2×#41D4×C3111yescharacteristic
473C2×#41D4×C3111yescharacteristic
474C2×#41C23×C3111yescharacteristic
475C2×#41C23×C3111yescharacteristic
476C2×#41C23×C3111yescharacteristic
477C22×Q8D4×C3111yescharacteristic
478C22×D4—21no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4D4×C3111yescharacteristic
484C22×D4D4×C3112yes—
485C22×D4C23×C3111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C3111yescharacteristic
489C2×M16—21no—
490C2×M16—42no—
491C2×M16C23×C3112yes—
492C2×M16C23×C3112yes—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#124—22no—
497#124—21no—
498#123—22no—
499#123—21no—
500#123—48no—
501C22⋊Q8—22no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C3111yescharacteristic
505C22⋊Q8D4×C3111yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—22no—
518#121—21no—
519#121—21no—
520#121D4×C3111yescharacteristic
521#121D4×C3111yescharacteristic
522#120—22no—
523#120—22no—
524#120—22no—
525#120—21no—
526#120—22no—
527C4×Q8—21no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—21no—
531C4×D4—22no—
532C4×D4—21no—
533C4×D4—21no—
534#117—21no—
535#117C23×C3111yescharacteristic
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4C23×C3112yes—
544C2×C4⋊C4C23×C3111yescharacteristic
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4D4×C3112yes—
549C2×C42C23×C3112yes—
550#107—22no—
551#106—22no—
552#104—24no—
553#104—42no—
554#104—42no—
555#103—22no—
556#103—22no—
557#103—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#100—42no—
562C22⋊C8—21no—
563C22⋊C8—21no—
564#95—21no—
565C31#2402611yescharacteristic, direct product factor, Sylow
566C24—22no—
567C24—21no—
568C24C2×D4×C3111yescharacteristic
569C24C2×D4×C3112yes—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—44no—
578#41—41no—
579#41—41no—
580#41—44no—
581#41—44no—
582#41—42no—
583#41—42no—
584#41#41×C3114yes—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—41no—
588C2×Q8C2×D4×C3111yescharacteristic
589C2×Q8C2×D4×C3111yescharacteristic
590C2×Q8C2×D4×C3111yescharacteristic
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—41no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—48no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—84no—
619C2×D4C2×D4×C3111yescharacteristic
620C2×D4C2×D4×C3111yescharacteristic
621C2×D4C2×D4×C3111yescharacteristic
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3112yes—
644C22×C4C24×C3111yescharacteristic
645M16—22no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—42no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—42no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—48no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4C2×D4×C3111yescharacteristic
665C4⋊C4C2×D4×C3111yescharacteristic
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—48no—
680C42—22no—
681C42—21no—
682C42—22no—
683C42—22no—
684C23—22no—
685C23—21no—
686C23—22no—
687C23—22no—
688C23—21no—
689C23—21no—
690C23—24no—
691C23—41no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23C31×#12011yescharacteristic
701C23C31×#12011yescharacteristic
702C23C22×D4×C3111yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—22no—
707Q8—42no—
708Q8C31×#12312yescomplemented
709D4—24no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—44no—
717D4—42no—
718D4—44no—
719D4—44no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—41no—
724D4—41no—
725D4—42no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4C31×#12312yescomplemented
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4C31×#12011yescharacteristic
763C2×C4C31×#12011yescharacteristic
764C2×C4C22×D4×C3111yescharacteristic
765C2×C4C22×D4×C3111yescharacteristic
766C2×C4C2×#41×C3112yes—
767C2×C4C31×H(5,𝔽2)12yes—
768C8—42no—
769C8—42no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—21no—
777C22—21no—
778C22—44no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—41no—
790C22—84no—
791C22—84no—
792C22—164no—
793C22C31×#45312yes—
794C22C2×C31×#12011yescharacteristic
795C22C31×#54612yes—
796C4—21no—
797C4—21no—
798C4—22no—
799C4—44no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—82no—
806C4C2×C31×#12311yescharacteristic
807C4C31×#53411yescharacteristic
808C4C31×#54612yes—
809C2—22no—
810C2—22no—
811C2—41no—
812C2—42no—
813C2—81no—
814C2—82no—
815C2—81no—
816C2C31×#240511yescharacteristic
817C2C2×C31×#45311yescharacteristic
818C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3092C2semidirect
3. C2×C31×#417C2semidirect
4. C31×#2501C2semidirect
5. C31×#2039C2semidirect
6. C31×#2037C2semidirect
7. C31×#1900C2semidirect
8. C31×#1871C2semidirect
9. C31×#1859C2semidirect
10. C31×#1792C2semidirect
11. C31×#1789C2semidirect
14. C22×M16×C31C22semidirect
31. C22×C4⋊C4×C31C22semidirect
36. C31×#428C22semidirect
38. C2×C31×#104C22semidirect
39. C2×C31×#104C22semidirect
43. C31×#417C22semidirect
44. C31×#417C22semidirect
47. C2×C31×#100C22semidirect
48. C31×#407C22semidirect
50. C31×#390C22semidirect
51. C31×#384C22semidirect
52. C4×C22⋊C4×C31C22semidirect
53. C31×#343C22semidirect
54. C31×#339C22semidirect
274. #24026C31direct (N × H)
299. Q8×C31#123semidirect
322. D4×C31#123semidirect
362. #3092C2×C31semidirect
363. C2×#417C2×C31semidirect
364. #2501C2×C31semidirect
365. #2039C2×C31semidirect
366. #2037C2×C31semidirect
367. #1900C2×C31semidirect
368. #1871C2×C31semidirect
369. #1859C2×C31semidirect
370. #1792C2×C31semidirect
371. #1789C2×C31semidirect
413. C22×M16C22×C31semidirect
430. C22×C4⋊C4C22×C31semidirect
435. #428C22×C31semidirect
437. C2×#104C22×C31semidirect
438. C2×#104C22×C31semidirect
442. #417C22×C31semidirect
443. #417C22×C31semidirect
446. C2×#100C22×C31semidirect
447. #407C22×C31semidirect
449. #390C22×C31semidirect
450. #384C22×C31semidirect
451. C4×C22⋊C4C22×C31semidirect
452. #343C22×C31semidirect
453. #339C22×C31semidirect
565. C31#24026direct (N × H)
708. Q8C31×#123semidirect
731. D4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C31×#34882
C31×#30922
C2×C31×#4172
C31×#25012
C31×#20392
C31×#20372
C31×#19002
C31×#18712
C31×#18592
C31×#17922
C31×#17892
#2402631