Finite Group Databasebeta

← C31×#19095 #21475854

Subgroups — C31×#19095 #21475854

Order 7936.

834 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3568C211yesmaximal, characteristic
2C31×#3239C211yesmaximal, characteristic, complemented
3C31×#3238C211yesmaximal, characteristic, complemented
4C31×#3218C211yesmaximal, characteristic, complemented
5C31×#1664C212yesmaximal, complemented
6C31×#1664C212yesmaximal, complemented
7C31×#1660C212yesmaximal, complemented
8C31×#1659C212yesmaximal, complemented
9C31×#1535C211yesmaximal, characteristic, complemented
10C31×#1535C211yesmaximal, characteristic, complemented
11C31×#1535C211yesmaximal, characteristic, complemented
12C31×#563C2211yescharacteristic
13C31×#563C2211yescharacteristic
14C31×#563C2211yescharacteristic
15C31×H(3,𝔽4)C2211yescharacteristic
16C31×#556—21no—
17C31×#556—21no—
18C31×#556—21no—
19C31×#551—21no—
20C31×#551—21no—
21C31×#551—21no—
22C31×#542—21no—
23C31×#542—21no—
24C31×#542—21no—
25C31×#538—21no—
26C31×#538—21no—
27C31×#538—21no—
28C2×C31×C4⋊Q8C2211yescharacteristic, complemented
29C31×#529C2211yescharacteristic
30C31×#529C2211yescharacteristic
31C31×#529C2211yescharacteristic
32C31×#501C2212yescomplemented
33C31×#501C2212yescomplemented
34C31×#497C2212yes—
35C31×#491C2212yescomplemented
36C31×#489C2212yes—
37C31×#489C2212yes—
38C31×#484—21no—
39C31×#483—21no—
40C31×#481—21no—
41C31×#480—21no—
42C31×#477—21no—
43C31×#476—21no—
44C31×#475—21no—
45C31×#474—21no—
46C31×#462—21no—
47C31×#461—21no—
48C31×#451—21no—
49C31×#448—21no—
50C31×#432C2211yescharacteristic, complemented
51C31×#432C2211yescharacteristic, complemented
52C31×#432C2211yescharacteristic, complemented
53C31×#330C2212yescomplemented
54C31×#330C2212yescomplemented
55C31×#330C2212yescomplemented
56C31×#329C2212yes—
57C31×#329C2212yes—
58C31×#329C2212yes—
59C22×Q8×C31—21no—
60C2×Q16×C31—22no—
61C2×SD16×C31—22no—
62C31×C4⋊Q8—21no—
63C31×C4⋊Q8—21no—
64C31×C4⋊Q8—21no—
65C31×C4⋊Q8—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8C2312yes—
69C31×#126—21no—
70C31×#126—21no—
71C31×#126—21no—
72C31×#126—21no—
73C31×#126—21no—
74C31×#126—21no—
75C31×#126—21no—
76C31×#126—21no—
77C31×#126—21no—
78C31×#126—21no—
79C31×#126—21no—
80C31×#126—21no—
81C31×#126—21no—
82C31×#125C2311yescharacteristic
83C31×#125C2311yescharacteristic
84C31×#125C2311yescharacteristic
85C31×#124—21no—
86C31×#124—21no—
87C31×#124—21no—
88C31×#124—21no—
89C31×#124—21no—
90C31×#124—21no—
91C31×#124—21no—
92C31×#124—21no—
93C31×#124—21no—
94C31×#124C2311yescharacteristic
95C31×#124C2311yescharacteristic
96C31×#124C2311yescharacteristic
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⋊Q8—21no—
114C31×C22⋊Q8—21no—
115C31×C22⋊Q8D411yescharacteristic
116C31×C22⋊Q8D411yescharacteristic
117C31×C22⋊Q8D411yescharacteristic
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121D411yescharacteristic
122C31×#121D411yescharacteristic
123C31×#121D411yescharacteristic
124C31×#120—21no—
125C31×#120—21no—
126C31×#120—21no—
127C31×#120—21no—
128C4×Q8×C31—21no—
129C4×Q8×C31—21no—
130C4×Q8×C31—21no—
131C4×Q8×C31D411yescharacteristic
132C4×Q8×C31D411yescharacteristic
133C4×Q8×C31D411yescharacteristic
134C4×D4×C31—21no—
135C4×D4×C31—21no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31—21no—
140C4×D4×C31D411yescharacteristic
141C4×D4×C31D411yescharacteristic
142C4×D4×C31D411yescharacteristic
143C31×#117—21no—
144C31×#117—21no—
145C31×#117—21no—
146C31×#117—21no—
147C31×#117—21no—
148C31×#117—21no—
149C2×C4⋊C4×C31—21no—
150C2×C4⋊C4×C31—21no—
151C2×C22⋊C4×C31—21no—
152C2×C22⋊C4×C31—21no—
153C2×C22⋊C4×C31—21no—
154C2×C42×C31C2311yescharacteristic
155C31×#107—22no—
156C31×#107—22no—
157C31×#106—22no—
158C31×#106—22no—
159C31×C4⋊C8—21no—
160C31×C4⋊C8—21no—
161C31×C4⋊C8—21no—
162C31×#103—22no—
163C31×#103—22no—
164C31×#103—22no—
165C31×#103—22no—
166C31×#102—22no—
167C31×#102—22no—
168C31×C22⋊C8—21no—
169C31×C22⋊C8—21no—
170C31×C22⋊C8—21no—
171C31×#97C2312yes—
172C31×#97C2312yes—
173C31×#97C2312yes—
174C24×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—22no—
179C2×Q8×C31—41no—
180C2×Q8×C31—82no—
181C2×Q8×C31C2×D411yescharacteristic
182C2×Q8×C31C2×D411yescharacteristic
183C2×Q8×C31C2×D411yescharacteristic
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×C31C2×D411yescharacteristic
191C2×D4×C31C2×D411yescharacteristic
192C2×D4×C31C2×D411yescharacteristic
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—41no—
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203Q16×C31—82no—
204SD16×C31—82no—
205C2×C8×C31—22no—
206C2×C8×C31—22no—
207C2×C8×C31—22no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—41no—
229C4⋊C4×C31—41no—
230C4⋊C4×C31C2×D411yescharacteristic
231C4⋊C4×C31C2×D411yescharacteristic
232C4⋊C4×C31C2×D411yescharacteristic
233C4⋊C4×C31C2×D411yescharacteristic
234C4⋊C4×C31C2×D411yescharacteristic
235C4⋊C4×C31C2×D411yescharacteristic
236C22⋊C4×C31—21no—
237C22⋊C4×C31—21no—
238C22⋊C4×C31—21no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
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—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—21no—
266C42×C31—21no—
267C42×C31—21no—
268C42×C31—21no—
269C42×C31—21no—
270C42×C31C2×D411yescharacteristic
271C42×C31C2×D411yescharacteristic
272C42×C31C2×D411yescharacteristic
273C42×C31C2411yescharacteristic
274#19095C3111yesmaximal, characteristic, direct product factor, Sylow
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—81no—
279C23×C31—81no—
280C23×C31—81no—
281C23×C31#12011yescharacteristic
282Q8×C31—41no—
283Q8×C31—41no—
284Q8×C31—41no—
285Q8×C31—42no—
286Q8×C31—42no—
287Q8×C31—82no—
288Q8×C31—81no—
289Q8×C31—81no—
290Q8×C31—81no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—81no—
295D4×C31—81no—
296D4×C31—81no—
297D4×C31—81no—
298D4×C31—81no—
299D4×C31—81no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—42no—
313C2×C4×C31—81no—
314C2×C4×C31—81no—
315C2×C4×C31—81no—
316C2×C4×C31—81no—
317C2×C4×C31—81no—
318C2×C4×C31—81no—
319C2×C4×C31—82no—
320C2×C4×C31#12011yescharacteristic
321C2×C4×C31#12011yescharacteristic
322C2×C4×C31#12011yescharacteristic
323C2×C4×C31C22×D411yescharacteristic
324C2×C4×C31C22×D411yescharacteristic
325C2×C4×C31C22×D411yescharacteristic
326C8×C31—42no—
327C8×C31—42no—
328C8×C31—42no—
329#3568C2×C3111yescharacteristic
330#3239C2×C3111yescharacteristic, complemented
331#3238C2×C3111yescharacteristic, complemented
332#3218C2×C3111yescharacteristic, complemented
333#1664C2×C3112yescomplemented
334#1664C2×C3112yescomplemented
335#1660C2×C3112yescomplemented
336#1659C2×C3112yescomplemented
337#1535C2×C3111yescharacteristic, complemented
338#1535C2×C3111yescharacteristic, complemented
339#1535C2×C3111yescharacteristic, complemented
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—41no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—162no—
353C22×C31C2×#12011yescharacteristic
354C4×C31—21no—
355C4×C31—21no—
356C4×C31—21no—
357C4×C31—21no—
358C4×C31—21no—
359C4×C31—21no—
360C4×C31—41no—
361C4×C31—41no—
362C4×C31—41no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31—41no—
366C4×C31—41no—
367C4×C31—41no—
368C4×C31—41no—
369C4×C31—82no—
370#563C22×C3111yescharacteristic
371#563C22×C3111yescharacteristic
372#563C22×C3111yescharacteristic
373H(3,𝔽4)C22×C3111yescharacteristic
374#556—21no—
375#556—21no—
376#556—21no—
377#551—21no—
378#551—21no—
379#551—21no—
380#542—21no—
381#542—21no—
382#542—21no—
383#538—21no—
384#538—21no—
385#538—21no—
386C2×C4⋊Q8C22×C3111yescharacteristic, complemented
387#529C22×C3111yescharacteristic
388#529C22×C3111yescharacteristic
389#529C22×C3111yescharacteristic
390#501C22×C3112yescomplemented
391#501C22×C3112yescomplemented
392#497C22×C3112yes—
393#491C22×C3112yescomplemented
394#489C22×C3112yes—
395#489C22×C3112yes—
396#484—21no—
397#483—21no—
398#481—21no—
399#480—21no—
400#477—21no—
401#476—21no—
402#475—21no—
403#474—21no—
404#462—21no—
405#461—21no—
406#451—21no—
407#448—21no—
408#432C22×C3111yescharacteristic, complemented
409#432C22×C3111yescharacteristic, complemented
410#432C22×C3111yescharacteristic, complemented
411#330C22×C3112yescomplemented
412#330C22×C3112yescomplemented
413#330C22×C3112yescomplemented
414#329C22×C3112yes—
415#329C22×C3112yes—
416#329C22×C3112yes—
417C2×C31—41no—
418C2×C31—81no—
419C2×C31—81no—
420C2×C31—81no—
421C2×C31#302111yescharacteristic
422C2×C31#302211yescharacteristic
423C2×C31#302211yescharacteristic
424C22×Q8—21no—
425C2×Q16—22no—
426C2×SD16—22no—
427C4⋊Q8—21no—
428C4⋊Q8—21no—
429C4⋊Q8—21no—
430C4⋊Q8—21no—
431C4⋊Q8—21no—
432C4⋊Q8—21no—
433C4⋊Q8C23×C3112yes—
434#126—21no—
435#126—21no—
436#126—21no—
437#126—21no—
438#126—21no—
439#126—21no—
440#126—21no—
441#126—21no—
442#126—21no—
443#126—21no—
444#126—21no—
445#126—21no—
446#126—21no—
447#125C23×C3111yescharacteristic
448#125C23×C3111yescharacteristic
449#125C23×C3111yescharacteristic
450#124—21no—
451#124—21no—
452#124—21no—
453#124—21no—
454#124—21no—
455#124—21no—
456#124—21no—
457#124—21no—
458#124—21no—
459#124C23×C3111yescharacteristic
460#124C23×C3111yescharacteristic
461#124C23×C3111yescharacteristic
462#123—21no—
463#123—21no—
464#123—21no—
465#123—21no—
466#123—21no—
467#123—21no—
468#123—21no—
469#123—21no—
470#123—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8D4×C3111yescharacteristic
481C22⋊Q8D4×C3111yescharacteristic
482C22⋊Q8D4×C3111yescharacteristic
483#121—21no—
484#121—21no—
485#121—21no—
486#121D4×C3111yescharacteristic
487#121D4×C3111yescharacteristic
488#121D4×C3111yescharacteristic
489#120—21no—
490#120—21no—
491#120—21no—
492#120—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8D4×C3111yescharacteristic
497C4×Q8D4×C3111yescharacteristic
498C4×Q8D4×C3111yescharacteristic
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4D4×C3111yescharacteristic
506C4×D4D4×C3111yescharacteristic
507C4×D4D4×C3111yescharacteristic
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C42C23×C3111yescharacteristic
520#107—22no—
521#107—22no—
522#106—22no—
523#106—22no—
524C4⋊C8—21no—
525C4⋊C8—21no—
526C4⋊C8—21no—
527#103—22no—
528#103—22no—
529#103—22no—
530#103—22no—
531#102—22no—
532#102—22no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536#97C23×C3112yes—
537#97C23×C3112yes—
538#97C23×C3112yes—
539C31#1909511yescharacteristic, direct product factor, Sylow
540C24—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—41no—
546C2×Q8—82no—
547C2×Q8C2×D4×C3111yescharacteristic
548C2×Q8C2×D4×C3111yescharacteristic
549C2×Q8C2×D4×C3111yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4C2×D4×C3111yescharacteristic
557C2×D4C2×D4×C3111yescharacteristic
558C2×D4C2×D4×C3111yescharacteristic
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—41no—
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569Q16—82no—
570SD16—82no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4C2×D4×C3111yescharacteristic
597C4⋊C4C2×D4×C3111yescharacteristic
598C4⋊C4C2×D4×C3111yescharacteristic
599C4⋊C4C2×D4×C3111yescharacteristic
600C4⋊C4C2×D4×C3111yescharacteristic
601C4⋊C4C2×D4×C3111yescharacteristic
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42C2×D4×C3111yescharacteristic
637C42C2×D4×C3111yescharacteristic
638C42C2×D4×C3111yescharacteristic
639C42C24×C3111yescharacteristic
640C23—21no—
641C23—21no—
642C23—21no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23C31×#12011yescharacteristic
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—42no—
651Q8—42no—
652Q8—82no—
653Q8—81no—
654Q8—81no—
655Q8—81no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—81no—
660D4—81no—
661D4—81no—
662D4—81no—
663D4—81no—
664D4—81no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4C31×#12011yescharacteristic
686C2×C4C31×#12011yescharacteristic
687C2×C4C31×#12011yescharacteristic
688C2×C4C22×D4×C3111yescharacteristic
689C2×C4C22×D4×C3111yescharacteristic
690C2×C4C22×D4×C3111yescharacteristic
691C8—42no—
692C8—42no—
693C8—42no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—162no—
707C22C2×C31×#12011yescharacteristic
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—21no—
713C4—21no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—82no—
724C2—41no—
725C2—81no—
726C2—81no—
727C2—81no—
728C2C31×#302111yescharacteristic
729C2C31×#302211yescharacteristic
730C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3568C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3239C2semidirect
3. C31×#3238C2semidirect
4. C31×#3218C2semidirect
5. C31×#1664C2semidirect
6. C31×#1664C2semidirect
7. C31×#1660C2semidirect
8. C31×#1659C2semidirect
9. C31×#1535C2semidirect
10. C31×#1535C2semidirect
11. C31×#1535C2semidirect
28. C2×C31×C4⋊Q8C22semidirect
32. C31×#501C22semidirect
33. C31×#501C22semidirect
35. C31×#491C22semidirect
50. C31×#432C22semidirect
51. C31×#432C22semidirect
52. C31×#432C22semidirect
53. C31×#330C22semidirect
54. C31×#330C22semidirect
55. C31×#330C22semidirect
274. #19095C31direct (N × H)
330. #3239C2×C31semidirect
331. #3238C2×C31semidirect
332. #3218C2×C31semidirect
333. #1664C2×C31semidirect
334. #1664C2×C31semidirect
335. #1660C2×C31semidirect
336. #1659C2×C31semidirect
337. #1535C2×C31semidirect
338. #1535C2×C31semidirect
339. #1535C2×C31semidirect
386. C2×C4⋊Q8C22×C31semidirect
390. #501C22×C31semidirect
391. #501C22×C31semidirect
393. #491C22×C31semidirect
408. #432C22×C31semidirect
409. #432C22×C31semidirect
410. #432C22×C31semidirect
411. #330C22×C31semidirect
412. #330C22×C31semidirect
413. #330C22×C31semidirect
539. C31#19095direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35682
C31×#32392
C31×#32382
C31×#32182
C31×#16642
C31×#16602
C31×#16592
C31×#15352
#1909531