Finite Group Databasebeta

← C31×#18462 #21475221

Subgroups — C31×#18462 #21475221

Order 7936.

1030 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×#3560C211yesmaximal, characteristic, complemented
2C31×#3217C211yesmaximal, characteristic, complemented
3C31×#3205C211yesmaximal, characteristic, complemented
4C31×#2818C211yesmaximal, characteristic, complemented
5C31×#1600C212yesmaximal, complemented
6C31×#1598C212yesmaximal, complemented
7C31×#1597C212yesmaximal, complemented
8C31×#1595C212yesmaximal, complemented
9C31×#1521C211yesmaximal, characteristic, complemented
10C31×#1514C211yesmaximal, characteristic, complemented
11C31×#1473C211yesmaximal, characteristic, complemented
12C31×#563—21no—
13C31×#560—21no—
14C31×#553—21no—
15C31×#553—21no—
16C31×#551—21no—
17C31×#547—21no—
18C31×#546—21no—
19C31×#546—21no—
20C31×#542—21no—
21C31×#539—21no—
22C31×#539C2211yescharacteristic
23C31×#538—21no—
24C31×#538—21no—
25C31×#538C2211yescharacteristic
26C31×#537C2211yescharacteristic
27C31×#534C2211yescharacteristic
28C31×#532C2211yescharacteristic
29C2×C31×#127C2211yescharacteristic, complemented
30C31×#529C2211yescharacteristic
31C2×C31×#126C2211yescharacteristic
32C31×#496—21no—
33C31×#493—21no—
34C31×#490—21no—
35C31×#486—21no—
36C31×#460—21no—
37C31×#459—21no—
38C31×#459—21no—
39C31×#459—21no—
40C31×#450C2212yescomplemented
41C31×#447C2212yes—
42C31×#447C2212yes—
43C31×#447C2212yescomplemented
44C31×#432C2211yescharacteristic, complemented
45C31×#431C2211yescharacteristic, complemented
46C31×#394—21no—
47C31×#394—21no—
48C31×#394C2212yescomplemented
49C31×#392—21no—
50C31×#392—21no—
51C31×#392C2212yes—
52C31×#383C2211yescharacteristic, complemented
53C31×#328C2212yescomplemented
54C31×#327C2212yes—
55C31×#327C2212yes—
56C31×#327C2212yescomplemented
57C31×#324C2212yescomplemented
58C31×#323C2212yes—
59C2×#41×C31—21no—
60C2×#41×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31—22no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31C2312yes—
66C2×SD16×C31—22no—
67C2×D8×C31—22no—
68C2×D8×C31—22no—
69C2×D8×C31—22no—
70C31×C4⋊Q8—21no—
71C31×C4⋊Q8D411yescharacteristic, complemented
72C31×#127—21no—
73C31×#127—21no—
74C31×#127—21no—
75C31×#127—21no—
76C31×#127D411yescharacteristic, complemented
77C31×#126—21no—
78C31×#126—21no—
79C31×#126—21no—
80C31×#126—21no—
81C31×#126—21no—
82C31×#126—21no—
83C31×#126—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#125—21no—
87C31×#125—21no—
88C31×#125D411yescharacteristic, complemented
89C31×#124—21no—
90C31×#124—21no—
91C31×#124—21no—
92C31×#124—21no—
93C31×#124D411yescharacteristic, complemented
94C31×#123—21no—
95C31×#123—21no—
96C31×#123—21no—
97C31×#123—21no—
98C31×#123—21no—
99C31×#123—21no—
100C31×#123—21no—
101C31×#123—21no—
102C31×#123—21no—
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×C22⋊Q8—21no—
107C31×C22⋊Q8—21no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8C2311yescharacteristic
114C31×#121—21no—
115C31×#121—21no—
116C31×#121—21no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121C2311yescharacteristic
127C31×#121C2311yescharacteristic
128C31×#121C2311yescharacteristic
129C31×#120—21no—
130C31×#120—21no—
131C31×#120—21no—
132C31×#120—21no—
133C31×#120—21no—
134C4×Q8×C31D411yescharacteristic, complemented
135C4×D4×C31—21no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31—21no—
140C4×D4×C31—21no—
141C4×D4×C31—21no—
142C4×D4×C31—21no—
143C4×D4×C31D411yescharacteristic, complemented
144C4×D4×C31D411yescharacteristic, complemented
145C4×D4×C31D411yescharacteristic, complemented
146C31×#117—21no—
147C31×#117—21no—
148C2×C4⋊C4×C31—21no—
149C2×C4⋊C4×C31D411yescharacteristic
150C2×C4⋊C4×C31D411yescharacteristic
151C2×C4⋊C4×C31C2311yescharacteristic
152C2×C22⋊C4×C31—21no—
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31—22no—
156C2×C22⋊C4×C31—22no—
157C2×C22⋊C4×C31D411yescharacteristic
158C2×C22⋊C4×C31D411yescharacteristic
159C2×C22⋊C4×C31C2311yescharacteristic
160C2×C42×C31C2311yescharacteristic
161C31×C4⋊C8—21no—
162C31×C4⋊C8—21no—
163C31×#102—22no—
164C31×#102—22no—
165C31×#102—22no—
166C31×#102—22no—
167C31×C22⋊C8C2312yes—
168C31×C22⋊C8C2312yes—
169C31×#97—21no—
170C4×C8×C31—21no—
171C31×#95—21no—
172C31×#95—21no—
173C31×#95C2312yes—
174C24×C31—21no—
175C24×C31—22no—
176C24×C31C2×D411yescharacteristic
177#41×C31—82no—
178#41×C31—82no—
179C2×Q8×C31—21no—
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—22no—
195C2×D4×C31—22no—
196C2×D4×C31—41no—
197C2×D4×C31—41no—
198C2×D4×C31—41no—
199C2×D4×C31—41no—
200C2×D4×C31—82no—
201C2×D4×C31—82no—
202C2×D4×C31—82no—
203C2×D4×C31—82no—
204C2×D4×C31—82no—
205C2×D4×C31—82no—
206C2×D4×C31—82no—
207C2×D4×C31C2×D411yescharacteristic
208C2×D4×C31C2×D411yescharacteristic
209C2×D4×C31C2×D411yescharacteristic
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—22no—
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2411yescharacteristic
225SD16×C31—82no—
226D8×C31—82no—
227D8×C31—82no—
228D8×C31—82no—
229C2×C8×C31—22no—
230C2×C8×C31—22no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
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—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31C2×D411yescharacteristic
249C4⋊C4×C31C2×D411yescharacteristic
250C4⋊C4×C31C2×D411yescharacteristic
251C4⋊C4×C31C2×D411yescharacteristic
252C22⋊C4×C31—21no—
253C22⋊C4×C31—21no—
254C22⋊C4×C31—21no—
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—82no—
278C22⋊C4×C31—82no—
279C22⋊C4×C31—82no—
280C42×C31—21no—
281C42×C31—21no—
282C42×C31—21no—
283C42×C31C2×D411yescharacteristic
284C42×C31C2×D411yescharacteristic
285C42×C31C2×D411yescharacteristic
286C42×C31C2×D411yescharacteristic
287#18462C3111yesmaximal, characteristic, direct product factor, Sylow
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—22no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—42no—
296C23×C31—42no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—81no—
303C23×C31—81no—
304C23×C31—81no—
305C23×C31C22×D411yescharacteristic
306Q8×C31—41no—
307Q8×C31—81no—
308Q8×C31—81no—
309D4×C31—41no—
310D4×C31—41no—
311D4×C31—41no—
312D4×C31—42no—
313D4×C31—42no—
314D4×C31—42no—
315D4×C31—42no—
316D4×C31—42no—
317D4×C31—42no—
318D4×C31—42no—
319D4×C31—81no—
320D4×C31—81no—
321D4×C31—82no—
322D4×C31—82no—
323D4×C31—82no—
324D4×C31—82no—
325D4×C31—81no—
326D4×C31—81no—
327D4×C31—81no—
328D4×C31—81no—
329D4×C31—81no—
330D4×C31—81no—
331D4×C31—81no—
332D4×C31—88no—
333C2×C4×C31—22no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—22no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
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—81no—
358C2×C4×C31#12011yescharacteristic
359C2×C4×C31#12011yescharacteristic
360C2×C4×C31#12011yescharacteristic
361C2×C4×C31#12011yescharacteristic
362C2×C4×C31C22×D411yescharacteristic
363C2×C4×C31C22×D411yescharacteristic
364C8×C31—42no—
365C8×C31—42no—
366#3560C2×C3111yescharacteristic, complemented
367#3217C2×C3111yescharacteristic, complemented
368#3205C2×C3111yescharacteristic, complemented
369#2818C2×C3111yescharacteristic, complemented
370#1600C2×C3112yescomplemented
371#1598C2×C3112yescomplemented
372#1597C2×C3112yescomplemented
373#1595C2×C3112yescomplemented
374#1521C2×C3111yescharacteristic, complemented
375#1514C2×C3111yescharacteristic, complemented
376#1473C2×C3111yescharacteristic, complemented
377C22×C31—21no—
378C22×C31—21no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—82no—
392C22×C31—82no—
393C22×C31—82no—
394C22×C31—82no—
395C22×C31—82no—
396C22×C31—82no—
397C22×C31—82no—
398C22×C31—82no—
399C22×C31—162no—
400C22×C31C2×#12011yescharacteristic
401C22×C31#57612yes—
402C4×C31—21no—
403C4×C31—21no—
404C4×C31—21no—
405C4×C31—21no—
406C4×C31—21no—
407C4×C31—21no—
408C4×C31—41no—
409C4×C31—41no—
410C4×C31—41no—
411C4×C31—41no—
412C4×C31—41no—
413C4×C31—41no—
414C4×C31—41no—
415C4×C31—41no—
416C4×C31—82no—
417#563—21no—
418#560—21no—
419#553—21no—
420#553—21no—
421#551—21no—
422#547—21no—
423#546—21no—
424#546—21no—
425#542—21no—
426#539—21no—
427#539C22×C3111yescharacteristic
428#538—21no—
429#538—21no—
430#538C22×C3111yescharacteristic
431#537C22×C3111yescharacteristic
432#534C22×C3111yescharacteristic
433#532C22×C3111yescharacteristic
434C2×#127C22×C3111yescharacteristic, complemented
435#529C22×C3111yescharacteristic
436C2×#126C22×C3111yescharacteristic
437#496—21no—
438#493—21no—
439#490—21no—
440#486—21no—
441#460—21no—
442#459—21no—
443#459—21no—
444#459—21no—
445#450C22×C3112yescomplemented
446#447C22×C3112yes—
447#447C22×C3112yes—
448#447C22×C3112yescomplemented
449#432C22×C3111yescharacteristic, complemented
450#431C22×C3111yescharacteristic, complemented
451#394—21no—
452#394—21no—
453#394C22×C3112yescomplemented
454#392—21no—
455#392—21no—
456#392C22×C3112yes—
457#383C22×C3111yescharacteristic, complemented
458#328C22×C3112yescomplemented
459#327C22×C3112yes—
460#327C22×C3112yes—
461#327C22×C3112yescomplemented
462#324C22×C3112yescomplemented
463#323C22×C3112yes—
464C2×C31—22no—
465C2×C31—81no—
466C2×C31—81no—
467C2×C31—81no—
468C2×C31—81no—
469C2×C31—162no—
470C2×C31#300811yescharacteristic
471C2×C31#302111yescharacteristic
472C2×C31#302711yescharacteristic
473C2×#41—21no—
474C2×#41—21no—
475C22×D4—21no—
476C22×D4—22no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4C23×C3112yes—
480C2×SD16—22no—
481C2×D8—22no—
482C2×D8—22no—
483C2×D8—22no—
484C4⋊Q8—21no—
485C4⋊Q8D4×C3111yescharacteristic, complemented
486#127—21no—
487#127—21no—
488#127—21no—
489#127—21no—
490#127D4×C3111yescharacteristic, complemented
491#126—21no—
492#126—21no—
493#126—21no—
494#126—21no—
495#126—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#125—21no—
501#125—21no—
502#125D4×C3111yescharacteristic, complemented
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C3111yescharacteristic, complemented
508#123—21no—
509#123—21no—
510#123—21no—
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8C23×C3111yescharacteristic
528#121—21no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121—21no—
539#121—21no—
540#121C23×C3111yescharacteristic
541#121C23×C3111yescharacteristic
542#121C23×C3111yescharacteristic
543#120—21no—
544#120—21no—
545#120—21no—
546#120—21no—
547#120—21no—
548C4×Q8D4×C3111yescharacteristic, complemented
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4D4×C3111yescharacteristic, complemented
558C4×D4D4×C3111yescharacteristic, complemented
559C4×D4D4×C3111yescharacteristic, complemented
560#117—21no—
561#117—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C3111yescharacteristic
564C2×C4⋊C4D4×C3111yescharacteristic
565C2×C4⋊C4C23×C3111yescharacteristic
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4D4×C3111yescharacteristic
572C2×C22⋊C4D4×C3111yescharacteristic
573C2×C22⋊C4C23×C3111yescharacteristic
574C2×C42C23×C3111yescharacteristic
575C4⋊C8—21no—
576C4⋊C8—21no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581C22⋊C8C23×C3112yes—
582C22⋊C8C23×C3112yes—
583#97—21no—
584C4×C8—21no—
585#95—21no—
586#95—21no—
587#95C23×C3112yes—
588C31#1846211yescharacteristic, direct product factor, Sylow
589C24—21no—
590C24—22no—
591C24C2×D4×C3111yescharacteristic
592#41—82no—
593#41—82no—
594C2×Q8—21no—
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—22no—
610C2×D4—22no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—82no—
616C2×D4—82no—
617C2×D4—82no—
618C2×D4—82no—
619C2×D4—82no—
620C2×D4—82no—
621C2×D4—82no—
622C2×D4C2×D4×C3111yescharacteristic
623C2×D4C2×D4×C3111yescharacteristic
624C2×D4C2×D4×C3111yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4C2×D4×C3111yescharacteristic
635C22×C4C2×D4×C3111yescharacteristic
636C22×C4C2×D4×C3111yescharacteristic
637C22×C4C2×D4×C3111yescharacteristic
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C24×C3111yescharacteristic
640SD16—82no—
641D8—82no—
642D8—82no—
643D8—82no—
644C2×C8—22no—
645C2×C8—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
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—21no—
662C4⋊C4—21no—
663C4⋊C4C2×D4×C3111yescharacteristic
664C4⋊C4C2×D4×C3111yescharacteristic
665C4⋊C4C2×D4×C3111yescharacteristic
666C4⋊C4C2×D4×C3111yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
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—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42C2×D4×C3111yescharacteristic
699C42C2×D4×C3111yescharacteristic
700C42C2×D4×C3111yescharacteristic
701C42C2×D4×C3111yescharacteristic
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23C22×D4×C3111yescharacteristic
720Q8—41no—
721Q8—81no—
722Q8—81no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—81no—
734D4—81no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—88no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
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—81no—
772C2×C4C31×#12011yescharacteristic
773C2×C4C31×#12011yescharacteristic
774C2×C4C31×#12011yescharacteristic
775C2×C4C31×#12011yescharacteristic
776C2×C4C22×D4×C3111yescharacteristic
777C2×C4C22×D4×C3111yescharacteristic
778C8—42no—
779C8—42no—
780C22—21no—
781C22—21no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—162no—
803C22C2×C31×#12011yescharacteristic
804C22C31×#57612yes—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—82no—
820C2—22no—
821C2—81no—
822C2—81no—
823C2—81no—
824C2—81no—
825C2—162no—
826C2C31×#300811yescharacteristic
827C2C31×#302111yescharacteristic
828C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3560C2semidirect
2. C31×#3217C2semidirect
3. C31×#3205C2semidirect
4. C31×#2818C2semidirect
5. C31×#1600C2semidirect
6. C31×#1598C2semidirect
7. C31×#1597C2semidirect
8. C31×#1595C2semidirect
9. C31×#1521C2semidirect
10. C31×#1514C2semidirect
11. C31×#1473C2semidirect
29. C2×C31×#127C22semidirect
40. C31×#450C22semidirect
43. C31×#447C22semidirect
44. C31×#432C22semidirect
45. C31×#431C22semidirect
48. C31×#394C22semidirect
52. C31×#383C22semidirect
53. C31×#328C22semidirect
56. C31×#327C22semidirect
57. C31×#324C22semidirect
71. C31×C4⋊Q8D4semidirect
76. C31×#127D4semidirect
88. C31×#125D4semidirect
93. C31×#124D4semidirect
134. C4×Q8×C31D4semidirect
143. C4×D4×C31D4semidirect
144. C4×D4×C31D4semidirect
145. C4×D4×C31D4semidirect
287. #18462C31direct (N × H)
366. #3560C2×C31semidirect
367. #3217C2×C31semidirect
368. #3205C2×C31semidirect
369. #2818C2×C31semidirect
370. #1600C2×C31semidirect
371. #1598C2×C31semidirect
372. #1597C2×C31semidirect
373. #1595C2×C31semidirect
374. #1521C2×C31semidirect
375. #1514C2×C31semidirect
376. #1473C2×C31semidirect
434. C2×#127C22×C31semidirect
445. #450C22×C31semidirect
448. #447C22×C31semidirect
449. #432C22×C31semidirect
450. #431C22×C31semidirect
453. #394C22×C31semidirect
457. #383C22×C31semidirect
458. #328C22×C31semidirect
461. #327C22×C31semidirect
462. #324C22×C31semidirect
485. C4⋊Q8D4×C31semidirect
490. #127D4×C31semidirect
502. #125D4×C31semidirect
507. #124D4×C31semidirect
548. C4×Q8D4×C31semidirect
557. C4×D4D4×C31semidirect
558. C4×D4D4×C31semidirect
559. C4×D4D4×C31semidirect
588. C31#18462direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35602
C31×#32172
C31×#32052
C31×#28182
C31×#16002
C31×#15982
C31×#15972
C31×#15952
C31×#15212
C31×#15142
C31×#14732
#1846231