Finite Group Databasebeta

← C31×#11003 #21467762

Subgroups — C31×#11003 #21467762

Order 7936.

1292 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3449C211yesmaximal, characteristic
2C2×C31×#421C211yesmaximal, characteristic, complemented
3C2×C31×#421C211yesmaximal, characteristic, complemented
4C2×C31×#421C211yesmaximal, characteristic, complemented
5C31×#2896C211yesmaximal, characteristic, complemented
6C2×C31×#344C211yesmaximal, characteristic, complemented
7C31×#1740C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×#41×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C31×#537—22no—
13C31×#536—21no—
14C31×#536C412yescomplemented
15C31×#535—21no—
16C31×#535C412yescomplemented
17C31×#534—22no—
18C31×#532—22no—
19C31×#525—22no—
20C31×#525—22no—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C2×C31×#117C2211yescharacteristic
24C31×#421—22no—
25C31×#421—22no—
26C31×#421—22no—
27C31×#421—22no—
28C31×#421—22no—
29C31×#421—22no—
30C2×C31×#104—22no—
31C2×C31×#104—22no—
32C2×C31×#104—22no—
33C31×#419—21no—
34C31×#418—21no—
35C31×#417—22no—
36C31×#416—22no—
37C31×#344—22no—
38C31×#342—22no—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—21no—
49C2×#41×C31—21no—
50C2×#41×C31—21no—
51C2×#41×C31—21no—
52C2×#41×C31—21no—
53C2×#41×C31—21no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31C2×C412yes—
60C2×#41×C31D412yes—
61C2×#41×C31D412yes—
62C2×#41×C31D412yes—
63C22×Q8×C31C2×C411yescharacteristic
64C22×Q8×C31D411yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31C2×C411yescharacteristic
68C22×D4×C31D411yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31C2311yescharacteristic
72C2×M16×C31—21no—
73C2×M16×C31—21no—
74C2×M16×C31—21no—
75C2×M16×C31—21no—
76C2×M16×C31—21no—
77C2×M16×C31—21no—
78C2×M16×C31—21no—
79C2×M16×C31—21no—
80C2×M16×C31—21no—
81C2×M16×C31—21no—
82C2×M16×C31D412yescomplemented
83C2×M16×C31D412yescomplemented
84C22×C8×C31—21no—
85C22×C8×C31—21no—
86C31×C4⋊Q8—22no—
87C31×#127—22no—
88C31×#124—22no—
89C31×#124—22no—
90C31×#123—24no—
91C31×#123—24no—
92C31×C22⋊Q8—24no—
93C31×C22⋊Q8—24no—
94C31×#121—24no—
95C31×#121—28no—
96C31×#121—24no—
97C31×#120—24no—
98C31×#120—24no—
99C4×D4×C31—28no—
100C31×#117—21no—
101C31×#117—21no—
102C31×#117—21no—
103C31×#117—21no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117—21no—
108C31×#117—21no—
109C31×#117C2×C412yes—
110C31×#117D412yes—
111C31×#117D412yescomplemented
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31D412yes—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31D412yescomplemented
121C31×#104—28no—
122C31×#104—28no—
123C31×#104—28no—
124C31×#103—24no—
125C31×#102—24no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31C2×D411yescharacteristic
129#41×C31—22no—
130#41×C31—22no—
131#41×C31—22no—
132#41×C31—22no—
133#41×C31—22no—
134#41×C31—22no—
135#41×C31—22no—
136#41×C31—22no—
137#41×C31—22no—
138#41×C31—22no—
139#41×C31—22no—
140#41×C31—22no—
141#41×C31—22no—
142#41×C31—22no—
143#41×C31—22no—
144#41×C31—22no—
145#41×C31—41no—
146#41×C31—41no—
147#41×C31—41no—
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—41no—
154#41×C31—41no—
155#41×C31—41no—
156#41×C31—41no—
157#41×C31—41no—
158#41×C31—41no—
159#41×C31—41no—
160#41×C31—41no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31C22⋊C412yes—
172C2×Q8×C31C22⋊C412yes—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—28no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
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—41no—
189C2×D4×C31—41no—
190C2×D4×C31—41no—
191C2×D4×C31—41no—
192C2×D4×C31—41no—
193C2×D4×C31—41no—
194C2×D4×C31—41no—
195C2×D4×C31—41no—
196C2×D4×C31C22⋊C412yes—
197C2×D4×C31C22⋊C412yes—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—41no—
207C22×C4×C31—41no—
208C22×C4×C31—41no—
209C22×C4×C31—41no—
210C22×C4×C31—41no—
211C22×C4×C31—41no—
212C22×C4×C31—41no—
213C22×C4×C31—41no—
214C22×C4×C31—41no—
215C22×C4×C31C22×C411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31#4111yescharacteristic
226C22×C4×C31#4111yescharacteristic
227C22×C4×C31#4111yescharacteristic
228C22×C4×C31#4111yescharacteristic
229M16×C31—22no—
230M16×C31—22no—
231M16×C31—22no—
232M16×C31—22no—
233M16×C31—41no—
234M16×C31—41no—
235M16×C31—41no—
236M16×C31—41no—
237C2×C8×C31—22no—
238C2×C8×C31—22no—
239C2×C8×C31—41no—
240C2×C8×C31—41no—
241C2×C8×C31—41no—
242C2×C8×C31—41no—
243C4⋊C4×C31—28no—
244C4⋊C4×C31—22no—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—41no—
248C4⋊C4×C31—41no—
249C4⋊C4×C31—41no—
250C22⋊C4×C31—28no—
251C22⋊C4×C31—28no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—41no—
255C22⋊C4×C31—41no—
256C22⋊C4×C31—41no—
257C22⋊C4×C31C22⋊C414yes—
258C42×C31—22no—
259C42×C31—22no—
260C42×C31—22no—
261C42×C31—22no—
262C42×C31—22no—
263C42×C31—41no—
264#11003C3111yesmaximal, characteristic, direct product factor, Sylow
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—81no—
272C23×C31—82no—
273C23×C31—82no—
274C23×C31C2×C22⋊C411yescharacteristic
275C23×C31#12011yescharacteristic
276C23×C31#12011yescharacteristic
277C23×C31#12111yescharacteristic
278C23×C31#12111yescharacteristic
279C23×C31#12411yescharacteristic
280C23×C31#12711yescharacteristic
281Q8×C31—22no—
282Q8×C31—22no—
283Q8×C31—22no—
284Q8×C31—22no—
285Q8×C31—41no—
286Q8×C31—41no—
287Q8×C31—41no—
288Q8×C31—41no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—22no—
292D4×C31—22no—
293D4×C31—42no—
294D4×C31—42no—
295D4×C31—42no—
296D4×C31—42no—
297D4×C31—42no—
298D4×C31—42no—
299D4×C31—42no—
300D4×C31—42no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
304D4×C31—41no—
305D4×C31—88no—
306C2×C4×C31—24no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—82no—
324C2×C4×C31—82no—
325C2×C4×C31—82no—
326C2×C4×C31C2×C22⋊C411yescharacteristic
327C2×C4×C31C2×C22⋊C411yescharacteristic
328C2×C4×C31C4×D411yescharacteristic
329C2×C4×C31C4×D411yescharacteristic
330C2×C4×C31C4×D411yescharacteristic
331C2×C4×C31C4×D411yescharacteristic
332C2×C4×C31#12011yescharacteristic
333C2×C4×C31#12011yescharacteristic
334C2×C4×C31#12011yescharacteristic
335C2×C4×C31#12011yescharacteristic
336C2×C4×C31#12011yescharacteristic
337C2×C4×C31#12011yescharacteristic
338C2×C4×C31#12111yescharacteristic
339C2×C4×C31#12111yescharacteristic
340C2×C4×C31#12111yescharacteristic
341C2×C4×C31#12111yescharacteristic
342C2×C4×C31#12111yescharacteristic
343C2×C4×C31#12111yescharacteristic
344C2×C4×C31#12111yescharacteristic
345C2×C4×C31#12111yescharacteristic
346C2×C4×C31#12111yescharacteristic
347C2×C4×C31#12111yescharacteristic
348C2×C4×C31#12311yescharacteristic
349C2×C4×C31#12311yescharacteristic
350C2×C4×C31#12311yescharacteristic
351C2×C4×C31#12311yescharacteristic
352C2×C4×C31#12411yescharacteristic
353C2×C4×C31#12711yescharacteristic
354C8×C31—42no—
355C8×C31—42no—
356#3449C2×C3111yescharacteristic
357C2×#421C2×C3111yescharacteristic, complemented
358C2×#421C2×C3111yescharacteristic, complemented
359C2×#421C2×C3111yescharacteristic, complemented
360#2896C2×C3111yescharacteristic, complemented
361C2×#344C2×C3111yescharacteristic, complemented
362#1740C2×C3111yescharacteristic, complemented
363C22×C31—41no—
364C22×C31—41no—
365C22×C31—41no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—44no—
371C22×C31—44no—
372C22×C31—42no—
373C22×C31—42no—
374C22×C31—82no—
375C22×C31—82no—
376C22×C31—82no—
377C22×C31—82no—
378C22×C31#37911yescharacteristic
379C22×C31#39011yescharacteristic
380C22×C31#39011yescharacteristic
381C22×C31#39211yescharacteristic
382C22×C31#39211yescharacteristic
383C22×C31#39411yescharacteristic
384C22×C31#39411yescharacteristic
385C4×C31—44no—
386C4×C31—42no—
387C4×C31—42no—
388C4×C31—82no—
389C4×C31—82no—
390C4×C31#38611yescharacteristic
391C4×C31#38611yescharacteristic
392C4×C31#38611yescharacteristic
393C4×C31#38611yescharacteristic
394C4×C31#39211yescharacteristic
395C4×C31#39211yescharacteristic
396C4×C31#39411yescharacteristic
397C4×C31#39411yescharacteristic
398C22×#41C22×C3111yescharacteristic
399C22×#41C22×C3111yescharacteristic
400C22×M16C22×C3111yescharacteristic
401C22×M16C22×C3111yescharacteristic
402#537—22no—
403#536—21no—
404#536C4×C3112yescomplemented
405#535—21no—
406#535C4×C3112yescomplemented
407#534—22no—
408#532—22no—
409#525—22no—
410#525—22no—
411C2×#117C22×C3111yescharacteristic
412C2×#117C22×C3111yescharacteristic
413C2×#117C22×C3111yescharacteristic
414#421—22no—
415#421—22no—
416#421—22no—
417#421—22no—
418#421—22no—
419#421—22no—
420C2×#104—22no—
421C2×#104—22no—
422C2×#104—22no—
423#419—21no—
424#418—21no—
425#417—22no—
426#416—22no—
427#344—22no—
428#342—22no—
429C2×C31—21no—
430C2×C31—21no—
431C2×C31—21no—
432C2×C31—21no—
433C2×C31—21no—
434C2×C31—21no—
435C2×C31—21no—
436C2×C31—82no—
437C2×C31—82no—
438C2×C31#143811yescharacteristic
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C2×C4×C3112yes—
460C2×#41D4×C3112yes—
461C2×#41D4×C3112yes—
462C2×#41D4×C3112yes—
463C22×Q8C2×C4×C3111yescharacteristic
464C22×Q8D4×C3111yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4C2×C4×C3111yescharacteristic
468C22×D4D4×C3111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4C23×C3111yescharacteristic
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16D4×C3112yescomplemented
483C2×M16D4×C3112yescomplemented
484C22×C8—21no—
485C22×C8—21no—
486C4⋊Q8—22no—
487#127—22no—
488#124—22no—
489#124—22no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493C22⋊Q8—24no—
494#121—24no—
495#121—28no—
496#121—24no—
497#120—24no—
498#120—24no—
499C4×D4—28no—
500#117—21no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117C2×C4×C3112yes—
510#117D4×C3112yes—
511#117D4×C3112yescomplemented
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4D4×C3112yes—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42D4×C3112yescomplemented
521#104—28no—
522#104—28no—
523#104—28no—
524#103—24no—
525#102—24no—
526C31#1100311yescharacteristic, direct product factor, Sylow
527C24—21no—
528C24—21no—
529C24C2×D4×C3111yescharacteristic
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8C22⋊C4×C3112yes—
573C2×Q8C22⋊C4×C3112yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—28no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4C22⋊C4×C3112yes—
598C2×D4C22⋊C4×C3112yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4C22×C4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C2×D4×C3111yescharacteristic
621C22×C4C2×D4×C3111yescharacteristic
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3111yescharacteristic
625C22×C4C2×D4×C3111yescharacteristic
626C22×C4#41×C3111yescharacteristic
627C22×C4#41×C3111yescharacteristic
628C22×C4#41×C3111yescharacteristic
629C22×C4#41×C3111yescharacteristic
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—41no—
635M16—41no—
636M16—41no—
637M16—41no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C4⋊C4—28no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4C22⋊C4×C3114yes—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—41no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—81no—
672C23—82no—
673C23—82no—
674C23C2×C22⋊C4×C3111yescharacteristic
675C23C31×#12011yescharacteristic
676C23C31×#12011yescharacteristic
677C23C31×#12111yescharacteristic
678C23C31×#12111yescharacteristic
679C23C31×#12411yescharacteristic
680C23C31×#12711yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—88no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4C2×C22⋊C4×C3111yescharacteristic
727C2×C4C2×C22⋊C4×C3111yescharacteristic
728C2×C4C4×D4×C3111yescharacteristic
729C2×C4C4×D4×C3111yescharacteristic
730C2×C4C4×D4×C3111yescharacteristic
731C2×C4C4×D4×C3111yescharacteristic
732C2×C4C31×#12011yescharacteristic
733C2×C4C31×#12011yescharacteristic
734C2×C4C31×#12011yescharacteristic
735C2×C4C31×#12011yescharacteristic
736C2×C4C31×#12011yescharacteristic
737C2×C4C31×#12011yescharacteristic
738C2×C4C31×#12111yescharacteristic
739C2×C4C31×#12111yescharacteristic
740C2×C4C31×#12111yescharacteristic
741C2×C4C31×#12111yescharacteristic
742C2×C4C31×#12111yescharacteristic
743C2×C4C31×#12111yescharacteristic
744C2×C4C31×#12111yescharacteristic
745C2×C4C31×#12111yescharacteristic
746C2×C4C31×#12111yescharacteristic
747C2×C4C31×#12111yescharacteristic
748C2×C4C31×#12311yescharacteristic
749C2×C4C31×#12311yescharacteristic
750C2×C4C31×#12311yescharacteristic
751C2×C4C31×#12311yescharacteristic
752C2×C4C31×#12411yescharacteristic
753C2×C4C31×#12711yescharacteristic
754C8—42no—
755C8—42no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C31×#37911yescharacteristic
772C22C31×#39011yescharacteristic
773C22C31×#39011yescharacteristic
774C22C31×#39211yescharacteristic
775C22C31×#39211yescharacteristic
776C22C31×#39411yescharacteristic
777C22C31×#39411yescharacteristic
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—82no—
783C4C31×#38611yescharacteristic
784C4C31×#38611yescharacteristic
785C4C31×#38611yescharacteristic
786C4C31×#38611yescharacteristic
787C4C31×#39211yescharacteristic
788C4C31×#39211yescharacteristic
789C4C31×#39411yescharacteristic
790C4C31×#39411yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—82no—
799C2—82no—
800C2C31×#143811yescharacteristic
subgroupG/H
centerC4×C31#392
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
socleC2×C31#1438
prime radicalC31×#3449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#421C2semidirect
3. C2×C31×#421C2semidirect
4. C2×C31×#421C2semidirect
5. C31×#2896C2semidirect
6. C2×C31×#344C2semidirect
7. C31×#1740C2semidirect
14. C31×#536C4semidirect
16. C31×#535C4semidirect
82. C2×M16×C31D4semidirect
83. C2×M16×C31D4semidirect
111. C31×#117D4semidirect
120. C2×C42×C31D4semidirect
264. #11003C31direct (N × H)
357. C2×#421C2×C31semidirect
358. C2×#421C2×C31semidirect
359. C2×#421C2×C31semidirect
360. #2896C2×C31semidirect
361. C2×#344C2×C31semidirect
362. #1740C2×C31semidirect
404. #536C4×C31semidirect
406. #535C4×C31semidirect
482. C2×M16D4×C31semidirect
483. C2×M16D4×C31semidirect
511. #117D4×C31semidirect
520. C2×C42D4×C31semidirect
526. C31#11003direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34492
C2×C31×#4212
C31×#28962
C2×C31×#3442
C31×#17402
#1100331