Finite Group Databasebeta

← C31×#18233 #21474992

Subgroups — C31×#18233 #21474992

Order 7936.

1002 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3534C211yesmaximal, characteristic
2C31×#3092C211yesmaximal, characteristic, complemented
3C2×C31×#481C211yesmaximal, characteristic, complemented
4C31×#2623C211yesmaximal, characteristic, complemented
5C31×#1618C212yesmaximal, complemented
6C31×#1616C212yesmaximal, complemented
7C31×#1615C212yesmaximal, complemented
8C31×#1613C212yesmaximal, complemented
9C31×#1516C211yesmaximal, characteristic, complemented
10C31×#1510C211yesmaximal, characteristic, complemented
11C31×#1468C211yesmaximal, characteristic, complemented
12C31×#562—21no—
13C31×#560—21no—
14C31×#553—21no—
15C31×#551—21no—
16C31×#546—21no—
17C31×#546—21no—
18C31×#546—21no—
19D42×C31—21no—
20C31×#540—21no—
21C31×#539—21no—
22C31×#539C2211yescharacteristic
23C31×#538—21no—
24C31×#538C2211yescharacteristic
25C31×#537C2211yescharacteristic
26C31×#534—21no—
27C31×#534C2211yescharacteristic
28C31×#525C2211yescharacteristic
29C2×C31×#123C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic, complemented
32C31×#484C2212yescomplemented
33C31×#483—21no—
34C31×#481—21no—
35C31×#481—21no—
36C31×#481C2212yes—
37C31×#481C2212yescomplemented
38C31×#481C2212yescomplemented
39C31×#480—21no—
40C31×#428—21no—
41C2×C31×#106—21no—
42C31×#417—21no—
43C2×C31×#102—21no—
44C31×#407C2211yescharacteristic, complemented
45C2×C31×C22⋊C8C2211yescharacteristic, complemented
46C31×#400C2212yescomplemented
47C31×#399C2212yescomplemented
48C31×#398—21no—
49C31×#397—21no—
50C31×#386—21no—
51C31×#385—21no—
52C31×#381C2211yescharacteristic, complemented
53C31×#328C2212yescomplemented
54C31×#327C2212yes—
55C31×#327C2212yescomplemented
56C31×#327C2212yescomplemented
57C31×#324C2212yescomplemented
58C31×#323C2212yescomplemented
59C2×#41×C31—21no—
60C2×#41×C31D411yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31D411yescharacteristic
65C22×D4×C31D411yescharacteristic
66C23×C4×C31—21no—
67C23×C4×C31C2311yescharacteristic
68C2×M16×C31—21no—
69C22×C8×C31—21no—
70C31×#127—21no—
71C31×#126—21no—
72C31×#126—21no—
73C31×#126—21no—
74C31×#126—21no—
75C31×#125—21no—
76C31×#125—21no—
77C31×#124—21no—
78C31×#124—21no—
79C31×#124—21no—
80C31×#123—21no—
81C31×#123—21no—
82C31×#123—21no—
83C31×#123—21no—
84C31×#123—21no—
85C31×#123—21no—
86C31×#123—21no—
87C31×#123—21no—
88C31×#123—21no—
89C31×#123—21no—
90C31×#123—21no—
91C31×#123—21no—
92C31×#123—21no—
93C31×#123—21no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8D411yescharacteristic
100C31×C22⋊Q8C2311yescharacteristic
101C31×#121—21no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121—21no—
109C31×#121—21no—
110C31×#121—21no—
111C31×#121—21no—
112C31×#121—21no—
113C31×#121—21no—
114C31×#121—21no—
115C31×#121—21no—
116C31×#121D411yescharacteristic
117C31×#121D411yescharacteristic
118C31×#121D411yescharacteristic
119C31×#121C2311yescharacteristic
120C31×#121C2311yescharacteristic
121C31×#121C2311yescharacteristic
122C31×#120—21no—
123C31×#120—21no—
124C31×#120—21no—
125C31×#120—21no—
126C31×#120—21no—
127C31×#120—21no—
128C31×#120—21no—
129C31×#120—21no—
130C4×D4×C31—21no—
131C4×D4×C31—21no—
132C4×D4×C31—21no—
133C4×D4×C31—21no—
134C4×D4×C31—21no—
135C4×D4×C31—21no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C31×#117—21no—
139C31×#117D411yescharacteristic
140C2×C4⋊C4×C31—21no—
141C2×C4⋊C4×C31—21no—
142C2×C4⋊C4×C31—21no—
143C2×C4⋊C4×C31—21no—
144C2×C4⋊C4×C31—21no—
145C2×C4⋊C4×C31—22no—
146C2×C4⋊C4×C31D411yescharacteristic
147C2×C4⋊C4×C31D411yescharacteristic
148C2×C4⋊C4×C31C2312yes—
149C2×C4⋊C4×C31C2311yescharacteristic
150C2×C22⋊C4×C31—21no—
151C2×C22⋊C4×C31—21no—
152C2×C22⋊C4×C31—21no—
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31D411yescharacteristic
156C2×C22⋊C4×C31D411yescharacteristic
157C2×C22⋊C4×C31C2311yescharacteristic
158C31×#107—22no—
159C31×#106—22no—
160C31×#106—22no—
161C31×#106—22no—
162C31×#103—22no—
163C31×#102—22no—
164C31×#102—22no—
165C31×#102—22no—
166C31×C22⋊C8—21no—
167C31×C22⋊C8—21no—
168C31×C22⋊C8C2312yes—
169C31×C22⋊C8C2312yes—
170C31×#95—21no—
171C31×#95—22no—
172C31×#95—22no—
173C31×#95C2312yes—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31C2×D411yescharacteristic
177C24×C31C2×D411yescharacteristic
178#41×C31—42no—
179#41×C31—82no—
180C2×Q8×C31—21no—
181C2×Q8×C31C2×D411yescharacteristic
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—42no—
200C2×D4×C31—42no—
201C2×D4×C31—82no—
202C2×D4×C31—82no—
203C2×D4×C31—82no—
204C2×D4×C31C2×D411yescharacteristic
205C2×D4×C31C2×D411yescharacteristic
206C2×D4×C31C2×D411yescharacteristic
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—42no—
217C22×C4×C31—41no—
218C22×C4×C31—41no—
219C22×C4×C31—82no—
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2411yescharacteristic
229M16×C31—42no—
230C2×C8×C31—22no—
231C2×C8×C31—22no—
232C2×C8×C31—42no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—22no—
248C4⋊C4×C31—41no—
249C4⋊C4×C31—41no—
250C4⋊C4×C31—82no—
251C4⋊C4×C31C2×D411yescharacteristic
252C4⋊C4×C31C2×D411yescharacteristic
253C4⋊C4×C31C2×D411yescharacteristic
254C4⋊C4×C31C2×D411yescharacteristic
255C22⋊C4×C31—21no—
256C22⋊C4×C31—21no—
257C22⋊C4×C31—21no—
258C22⋊C4×C31—21no—
259C22⋊C4×C31—21no—
260C22⋊C4×C31—21no—
261C22⋊C4×C31—21no—
262C22⋊C4×C31—21no—
263C22⋊C4×C31—21no—
264C22⋊C4×C31—21no—
265C22⋊C4×C31—21no—
266C22⋊C4×C31—21no—
267C22⋊C4×C31—21no—
268C22⋊C4×C31—21no—
269C22⋊C4×C31—21no—
270C22⋊C4×C31—21no—
271C22⋊C4×C31—21no—
272C22⋊C4×C31—21no—
273C22⋊C4×C31—21no—
274C22⋊C4×C31—21no—
275C22⋊C4×C31—21no—
276C22⋊C4×C31—21no—
277C22⋊C4×C31—21no—
278C22⋊C4×C31—21no—
279C22⋊C4×C31—21no—
280C22⋊C4×C31—42no—
281C22⋊C4×C31—82no—
282C42×C31—21no—
283C42×C31—21no—
284C42×C31—21no—
285#18233C3111yesmaximal, characteristic, direct product factor, Sylow
286C23×C31—22no—
287C23×C31—22no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—22no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—42no—
297C23×C31—81no—
298C23×C31—81no—
299C23×C31—81no—
300C23×C31—81no—
301C23×C31—81no—
302C23×C31#12011yescharacteristic
303C23×C31#12011yescharacteristic
304C23×C31C22×D411yescharacteristic
305Q8×C31—41no—
306Q8×C31—81no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31—41no—
310D4×C31—42no—
311D4×C31—42no—
312D4×C31—42no—
313D4×C31—42no—
314D4×C31—42no—
315D4×C31—81no—
316D4×C31—81no—
317D4×C31—81no—
318D4×C31—81no—
319D4×C31—81no—
320D4×C31—81no—
321D4×C31—81no—
322D4×C31—81no—
323D4×C31—81no—
324D4×C31—81no—
325D4×C31—81no—
326D4×C31—81no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—22no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
347C2×C4×C31—42no—
348C2×C4×C31—42no—
349C2×C4×C31—42no—
350C2×C4×C31—81no—
351C2×C4×C31—81no—
352C2×C4×C31—81no—
353C2×C4×C31—81no—
354C2×C4×C31—81no—
355C2×C4×C31—81no—
356C2×C4×C31—81no—
357C2×C4×C31—82no—
358C2×C4×C31—82no—
359C2×C4×C31#12011yescharacteristic
360C2×C4×C31#12011yescharacteristic
361C2×C4×C31C22×D411yescharacteristic
362C2×C4×C31C22×D411yescharacteristic
363C8×C31—42no—
364C8×C31—42no—
365#3534C2×C3111yescharacteristic
366#3092C2×C3111yescharacteristic, complemented
367C2×#481C2×C3111yescharacteristic, complemented
368#2623C2×C3111yescharacteristic, complemented
369#1618C2×C3112yescomplemented
370#1616C2×C3112yescomplemented
371#1615C2×C3112yescomplemented
372#1613C2×C3112yescomplemented
373#1516C2×C3111yescharacteristic, complemented
374#1510C2×C3111yescharacteristic, complemented
375#1468C2×C3111yescharacteristic, complemented
376C22×C31—21no—
377C22×C31—21no—
378C22×C31—21no—
379C22×C31—21no—
380C22×C31—21no—
381C22×C31—21no—
382C22×C31—21no—
383C22×C31—44no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—41no—
396C22×C31—82no—
397C22×C31—162no—
398C22×C31—162no—
399C22×C31#45812yes—
400C22×C31C2×#12011yescharacteristic
401C22×C31#57712yes—
402C4×C31—21no—
403C4×C31—21no—
404C4×C31—21no—
405C4×C31—21no—
406C4×C31—41no—
407C4×C31—41no—
408C4×C31—41no—
409C4×C31—41no—
410C4×C31—41no—
411C4×C31—41no—
412C4×C31—41no—
413C4×C31—41no—
414C4×C31—82no—
415C4×C31—82no—
416#562—21no—
417#560—21no—
418#553—21no—
419#551—21no—
420#546—21no—
421#546—21no—
422#546—21no—
423D42—21no—
424#540—21no—
425#539—21no—
426#539C22×C3111yescharacteristic
427#538—21no—
428#538C22×C3111yescharacteristic
429#537C22×C3111yescharacteristic
430#534—21no—
431#534C22×C3111yescharacteristic
432#525C22×C3111yescharacteristic
433C2×#123C22×C3111yescharacteristic
434C2×#121C22×C3111yescharacteristic
435C22×C4⋊C4C22×C3111yescharacteristic, complemented
436#484C22×C3112yescomplemented
437#483—21no—
438#481—21no—
439#481—21no—
440#481C22×C3112yes—
441#481C22×C3112yescomplemented
442#481C22×C3112yescomplemented
443#480—21no—
444#428—21no—
445C2×#106—21no—
446#417—21no—
447C2×#102—21no—
448#407C22×C3111yescharacteristic, complemented
449C2×C22⋊C8C22×C3111yescharacteristic, complemented
450#400C22×C3112yescomplemented
451#399C22×C3112yescomplemented
452#398—21no—
453#397—21no—
454#386—21no—
455#385—21no—
456#381C22×C3111yescharacteristic, complemented
457#328C22×C3112yescomplemented
458#327C22×C3112yes—
459#327C22×C3112yescomplemented
460#327C22×C3112yescomplemented
461#324C22×C3112yescomplemented
462#323C22×C3112yescomplemented
463C2×C31—22no—
464C2×C31—22no—
465C2×C31—41no—
466C2×C31—81no—
467C2×C31—81no—
468C2×C31—81no—
469C2×C31—81no—
470C2×C31#300911yescharacteristic
471C2×C31#302111yescharacteristic
472C2×C31C2×#45811yescharacteristic
473C2×#41—21no—
474C2×#41D4×C3111yescharacteristic
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C3111yescharacteristic
479C22×D4D4×C3111yescharacteristic
480C23×C4—21no—
481C23×C4C23×C3111yescharacteristic
482C2×M16—21no—
483C22×C8—21no—
484#127—21no—
485#126—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#125—21no—
490#125—21no—
491#124—21no—
492#124—21no—
493#124—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123—21no—
499#123—21no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—21no—
505#123—21no—
506#123—21no—
507#123—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8D4×C3111yescharacteristic
514C22⋊Q8C23×C3111yescharacteristic
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C3111yescharacteristic
531#121D4×C3111yescharacteristic
532#121D4×C3111yescharacteristic
533#121C23×C3111yescharacteristic
534#121C23×C3111yescharacteristic
535#121C23×C3111yescharacteristic
536#120—21no—
537#120—21no—
538#120—21no—
539#120—21no—
540#120—21no—
541#120—21no—
542#120—21no—
543#120—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552#117—21no—
553#117D4×C3111yescharacteristic
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4D4×C3111yescharacteristic
561C2×C4⋊C4D4×C3111yescharacteristic
562C2×C4⋊C4C23×C3112yes—
563C2×C4⋊C4C23×C3111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4D4×C3111yescharacteristic
570C2×C22⋊C4D4×C3111yescharacteristic
571C2×C22⋊C4C23×C3111yescharacteristic
572#107—22no—
573#106—22no—
574#106—22no—
575#106—22no—
576#103—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8C23×C3112yes—
583C22⋊C8C23×C3112yes—
584#95—21no—
585#95—22no—
586#95—22no—
587#95C23×C3112yes—
588C31#1823311yescharacteristic, direct product factor, Sylow
589C24—21no—
590C24—21no—
591C24C2×D4×C3111yescharacteristic
592C24C2×D4×C3111yescharacteristic
593#41—42no—
594#41—82no—
595C2×Q8—21no—
596C2×Q8C2×D4×C3111yescharacteristic
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—82no—
617C2×D4—82no—
618C2×D4—82no—
619C2×D4C2×D4×C3111yescharacteristic
620C2×D4C2×D4×C3111yescharacteristic
621C2×D4C2×D4×C3111yescharacteristic
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—42no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—82no—
635C22×C4C2×D4×C3111yescharacteristic
636C22×C4C2×D4×C3111yescharacteristic
637C22×C4C2×D4×C3111yescharacteristic
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C24×C3111yescharacteristic
644M16—42no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—42no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—82no—
666C4⋊C4C2×D4×C3111yescharacteristic
667C4⋊C4C2×D4×C3111yescharacteristic
668C4⋊C4C2×D4×C3111yescharacteristic
669C4⋊C4C2×D4×C3111yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—42no—
696C22⋊C4—82no—
697C42—21no—
698C42—21no—
699C42—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23C31×#12011yescharacteristic
717C23C31×#12011yescharacteristic
718C23C22×D4×C3111yescharacteristic
719Q8—41no—
720Q8—81no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4C31×#12011yescharacteristic
774C2×C4C31×#12011yescharacteristic
775C2×C4C22×D4×C3111yescharacteristic
776C2×C4C22×D4×C3111yescharacteristic
777C8—42no—
778C8—42no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—44no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—82no—
800C22—162no—
801C22—162no—
802C22C31×#45812yes—
803C22C2×C31×#12011yescharacteristic
804C22C31×#57712yes—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—82no—
818C4—82no—
819C2—22no—
820C2—22no—
821C2—41no—
822C2—81no—
823C2—81no—
824C2—81no—
825C2—81no—
826C2C31×#300911yescharacteristic
827C2C31×#302111yescharacteristic
828C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3534C2
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
2. C31×#3092C2semidirect
3. C2×C31×#481C2semidirect
4. C31×#2623C2semidirect
5. C31×#1618C2semidirect
6. C31×#1616C2semidirect
7. C31×#1615C2semidirect
8. C31×#1613C2semidirect
9. C31×#1516C2semidirect
10. C31×#1510C2semidirect
11. C31×#1468C2semidirect
31. C22×C4⋊C4×C31C22semidirect
32. C31×#484C22semidirect
37. C31×#481C22semidirect
38. C31×#481C22semidirect
44. C31×#407C22semidirect
45. C2×C31×C22⋊C8C22semidirect
46. C31×#400C22semidirect
47. C31×#399C22semidirect
52. C31×#381C22semidirect
53. C31×#328C22semidirect
55. C31×#327C22semidirect
56. C31×#327C22semidirect
57. C31×#324C22semidirect
58. C31×#323C22semidirect
285. #18233C31direct (N × H)
366. #3092C2×C31semidirect
367. C2×#481C2×C31semidirect
368. #2623C2×C31semidirect
369. #1618C2×C31semidirect
370. #1616C2×C31semidirect
371. #1615C2×C31semidirect
372. #1613C2×C31semidirect
373. #1516C2×C31semidirect
374. #1510C2×C31semidirect
375. #1468C2×C31semidirect
435. C22×C4⋊C4C22×C31semidirect
436. #484C22×C31semidirect
441. #481C22×C31semidirect
442. #481C22×C31semidirect
448. #407C22×C31semidirect
449. C2×C22⋊C8C22×C31semidirect
450. #400C22×C31semidirect
451. #399C22×C31semidirect
456. #381C22×C31semidirect
457. #328C22×C31semidirect
459. #327C22×C31semidirect
460. #327C22×C31semidirect
461. #324C22×C31semidirect
462. #323C22×C31semidirect
588. C31#18233direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35342
C31×#30922
C2×C31×#4812
C31×#26232
C31×#16182
C31×#16162
C31×#16152
C31×#16132
C31×#15162
C31×#15102
C31×#14682
#1823331