Finite Group Databasebeta

← C31×#18419 #21475178

Subgroups — C31×#18419 #21475178

Order 7936.

1062 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3537C211yesmaximal, characteristic
2C31×#3193C211yesmaximal, characteristic, complemented
3C31×#3190C211yesmaximal, characteristic, complemented
4C31×#2639C211yesmaximal, characteristic, complemented
5C31×#1612C212yesmaximal, complemented
6C31×#1607C212yesmaximal, complemented
7C31×#1606C212yesmaximal, complemented
8C31×#1601C212yesmaximal, complemented
9C31×#1504C211yesmaximal, characteristic, complemented
10C2×C31×#327C211yesmaximal, characteristic, complemented
11C31×#1471C211yesmaximal, characteristic, complemented
12C31×#560—22no—
13C31×#553—21no—
14C31×#553—21no—
15D42×C31—22no—
16D42×C31—21no—
17D42×C31—21no—
18C31×#540—21no—
19C31×#538—21no—
20C31×#538C2212yes—
21C31×#535—21no—
22C31×#534—21no—
23C31×#534C2212yes—
24C31×#525C2211yescharacteristic
25C2×C31×C22⋊Q8C2211yescharacteristic, complemented
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C31×#485—21no—
29C31×#484—21no—
30C31×#483C2211yescharacteristic, complemented
31C31×#480C2211yescharacteristic, complemented
32C31×#480C2212yescomplemented
33C31×#468—22no—
34C31×#467—21no—
35C31×#465—21no—
36C31×#452—21no—
37C31×#451C2211yescharacteristic, complemented
38C31×#450—21no—
39C31×#448C2211yescharacteristic, complemented
40C31×#448C2212yescomplemented
41C31×#407C2211yescharacteristic, complemented
42C2×C31×C22⋊C8C2211yescharacteristic, complemented
43C31×#400—21no—
44C31×#397C2212yescomplemented
45C31×#394—21no—
46C31×#393C2212yescomplemented
47C31×#386—22no—
48C2×C31×#95C2211yescharacteristic, complemented
49C31×#328C2212yescomplemented
50C31×#327C2212yescomplemented
51C31×#327C2212yescomplemented
52C31×#327C2212yescomplemented
53C31×#323C2212yescomplemented
54C31×#323C2212yescomplemented
55C2×#41×C31D411yescharacteristic
56C22×Q8×C31C2311yescharacteristic
57C22×D4×C31—22no—
58C22×D4×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31—22no—
61C22×D4×C31D412yes—
62C22×D4×C31D411yescharacteristic
63C22×D4×C31D411yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31C2311yescharacteristic
66C2×Q16×C31—21no—
67C2×SD16×C31—22no—
68C2×SD16×C31—21no—
69C2×M16×C31—21no—
70C22×C8×C31—21no—
71C31×#127—22no—
72C31×#127—21no—
73C31×#126—22no—
74C31×#126—22no—
75C31×#125—21no—
76C31×#124—22no—
77C31×#123—22no—
78C31×#123—21no—
79C31×#123—22no—
80C31×#123—22no—
81C31×#123—22no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8D411yescharacteristic
87C31×C22⋊Q8C2311yescharacteristic
88C31×#121—22no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—21no—
99C31×#121—21no—
100C31×#121—21no—
101C31×#121—22no—
102C31×#121D411yescharacteristic
103C31×#121D412yes—
104C31×#121C2312yes—
105C31×#121C2311yescharacteristic
106C31×#120—22no—
107C31×#120—22no—
108C31×#120—22no—
109C31×#120—21no—
110C31×#120—22no—
111C31×#120—22no—
112C31×#120—22no—
113C4×D4×C31—22no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31—22no—
119C31×#117—21no—
120C31×#117D411yescharacteristic
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31D411yescharacteristic
123C2×C4⋊C4×C31D411yescharacteristic
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31C2312yes—
130C31×#107—21no—
131C31×#107—22no—
132C31×#106—21no—
133C31×#103—21no—
134C31×#103—21no—
135C31×#103—22no—
136C31×#103—21no—
137C31×#102—22no—
138C31×#102—21no—
139C31×C22⋊C8—21no—
140C31×C22⋊C8—21no—
141C31×C22⋊C8C2311yescharacteristic
142C31×C22⋊C8C2311yescharacteristic
143C31×C22⋊C8C2312yes—
144C31×#95—22no—
145C31×#95—21no—
146C31×#95—22no—
147C31×#95C2312yes—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31C2×D411yescharacteristic
151C24×C31C2×D412yes—
152#41×C31—81no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—81no—
156C2×Q8×C31C2×D411yescharacteristic
157C2×D4×C31—22no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—21no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—44no—
173C2×D4×C31—81no—
174C2×D4×C31—82no—
175C2×D4×C31—81no—
176C2×D4×C31—81no—
177C2×D4×C31—81no—
178C2×D4×C31—82no—
179C2×D4×C31—82no—
180C2×D4×C31—84no—
181C2×D4×C31C2×D411yescharacteristic
182C2×D4×C31C2×D412yes—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—42no—
191C22×C4×C31—81no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31C2×D412yes—
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2411yescharacteristic
201Q16×C31—81no—
202SD16×C31—81no—
203SD16×C31—82no—
204M16×C31—81no—
205C2×C8×C31—21no—
206C2×C8×C31—22no—
207C2×C8×C31—21no—
208C2×C8×C31—81no—
209C4⋊C4×C31—22no—
210C4⋊C4×C31—22no—
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—41no—
219C4⋊C4×C31—41no—
220C4⋊C4×C31C2×D411yescharacteristic
221C4⋊C4×C31C2×D412yes—
222C4⋊C4×C31C2×D411yescharacteristic
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—21no—
229C22⋊C4×C31—21no—
230C22⋊C4×C31—21no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—21no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—41no—
238C22⋊C4×C31—41no—
239C22⋊C4×C31—82no—
240C22⋊C4×C31—82no—
241C42×C31—22no—
242C42×C31—21no—
243#18419C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—21no—
250C23×C31—22no—
251C23×C31—22no—
252C23×C31—41no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—81no—
257C23×C31—81no—
258C23×C31—82no—
259C23×C31—82no—
260C23×C31—82no—
261C23×C31#12011yescharacteristic
262C23×C31#12011yescharacteristic
263C23×C31C22×D411yescharacteristic
264Q8×C31—41no—
265Q8×C31—42no—
266Q8×C31—41no—
267Q8×C31—41no—
268D4×C31—42no—
269D4×C31—41no—
270D4×C31—42no—
271D4×C31—42no—
272D4×C31—42no—
273D4×C31—41no—
274D4×C31—42no—
275D4×C31—41no—
276D4×C31—44no—
277D4×C31—42no—
278D4×C31—81no—
279D4×C31—82no—
280D4×C31—82no—
281D4×C31—81no—
282D4×C31—82no—
283D4×C31—82no—
284D4×C31—82no—
285D4×C31—82no—
286D4×C31—82no—
287C2×C4×C31—21no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—42no—
307C2×C4×C31—41no—
308C2×C4×C31—81no—
309C2×C4×C31—82no—
310C2×C4×C31—82no—
311C2×C4×C31—84no—
312C2×C4×C31#12011yescharacteristic
313C2×C4×C31#12011yescharacteristic
314C2×C4×C31C22×D411yescharacteristic
315C2×C4×C31C22×D411yescharacteristic
316C8×C31—41no—
317C8×C31—41no—
318C8×C31—42no—
319#3537C2×C3111yescharacteristic
320#3193C2×C3111yescharacteristic, complemented
321#3190C2×C3111yescharacteristic, complemented
322#2639C2×C3111yescharacteristic, complemented
323#1612C2×C3112yescomplemented
324#1607C2×C3112yescomplemented
325#1606C2×C3112yescomplemented
326#1601C2×C3112yescomplemented
327#1504C2×C3111yescharacteristic, complemented
328C2×#327C2×C3111yescharacteristic, complemented
329#1471C2×C3111yescharacteristic, complemented
330C22×C31—21no—
331C22×C31—21no—
332C22×C31—21no—
333C22×C31—21no—
334C22×C31—21no—
335C22×C31—21no—
336C22×C31—21no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—41no—
342C22×C31—42no—
343C22×C31—42no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—82no—
349C22×C31—82no—
350C22×C31—162no—
351C22×C31—164no—
352C22×C31#45512yes—
353C22×C31C2×#12011yescharacteristic
354C22×C31#57611yescharacteristic
355C22×C31#57711yescharacteristic
356C4×C31—21no—
357C4×C31—21no—
358C4×C31—21no—
359C4×C31—21no—
360C4×C31—42no—
361C4×C31—41no—
362C4×C31—42no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31—82no—
366C4×C31—81no—
367C4×C31—81no—
368#560—22no—
369#553—21no—
370#553—21no—
371D42—22no—
372D42—21no—
373D42—21no—
374#540—21no—
375#538—21no—
376#538C22×C3112yes—
377#535—21no—
378#534—21no—
379#534C22×C3112yes—
380#525C22×C3111yescharacteristic
381C2×C22⋊Q8C22×C3111yescharacteristic, complemented
382C2×#121C22×C3111yescharacteristic
383C2×#121C22×C3111yescharacteristic
384#485—21no—
385#484—21no—
386#483C22×C3111yescharacteristic, complemented
387#480C22×C3111yescharacteristic, complemented
388#480C22×C3112yescomplemented
389#468—22no—
390#467—21no—
391#465—21no—
392#452—21no—
393#451C22×C3111yescharacteristic, complemented
394#450—21no—
395#448C22×C3111yescharacteristic, complemented
396#448C22×C3112yescomplemented
397#407C22×C3111yescharacteristic, complemented
398C2×C22⋊C8C22×C3111yescharacteristic, complemented
399#400—21no—
400#397C22×C3112yescomplemented
401#394—21no—
402#393C22×C3112yescomplemented
403#386—22no—
404C2×#95C22×C3111yescharacteristic, complemented
405#328C22×C3112yescomplemented
406#327C22×C3112yescomplemented
407#327C22×C3112yescomplemented
408#327C22×C3112yescomplemented
409#323C22×C3112yescomplemented
410#323C22×C3112yescomplemented
411C2×C31—21no—
412C2×C31—21no—
413C2×C31—22no—
414C2×C31—41no—
415C2×C31—82no—
416C2×C31—82no—
417C2×C31—81no—
418C2×C31#301211yescharacteristic
419C2×C31C2×#45511yescharacteristic
420C2×C31#302611yescharacteristic
421C2×#41D4×C3111yescharacteristic
422C22×Q8C23×C3111yescharacteristic
423C22×D4—22no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—22no—
427C22×D4D4×C3112yes—
428C22×D4D4×C3111yescharacteristic
429C22×D4D4×C3111yescharacteristic
430C23×C4—21no—
431C23×C4C23×C3111yescharacteristic
432C2×Q16—21no—
433C2×SD16—22no—
434C2×SD16—21no—
435C2×M16—21no—
436C22×C8—21no—
437#127—22no—
438#127—21no—
439#126—22no—
440#126—22no—
441#125—21no—
442#124—22no—
443#123—22no—
444#123—21no—
445#123—22no—
446#123—22no—
447#123—22no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8D4×C3111yescharacteristic
453C22⋊Q8C23×C3111yescharacteristic
454#121—22no—
455#121—21no—
456#121—21no—
457#121—22no—
458#121—22no—
459#121—22no—
460#121—22no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—22no—
468#121D4×C3112yes—
469#121D4×C3111yescharacteristic
470#121C23×C3112yes—
471#121C23×C3111yescharacteristic
472#120—22no—
473#120—22no—
474#120—22no—
475#120—21no—
476#120—22no—
477#120—22no—
478#120—22no—
479C4×D4—22no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—22no—
485#117—21no—
486#117D4×C3111yescharacteristic
487C2×C4⋊C4—21no—
488C2×C4⋊C4D4×C3111yescharacteristic
489C2×C4⋊C4D4×C3111yescharacteristic
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4C23×C3112yes—
496#107—21no—
497#107—22no—
498#106—21no—
499#103—21no—
500#103—21no—
501#103—22no—
502#103—21no—
503#102—22no—
504#102—21no—
505C22⋊C8—21no—
506C22⋊C8—21no—
507C22⋊C8C23×C3111yescharacteristic
508C22⋊C8C23×C3111yescharacteristic
509C22⋊C8C23×C3112yes—
510#95—21no—
511#95—22no—
512#95—22no—
513#95C23×C3112yes—
514C31#1841911yescharacteristic, direct product factor, Sylow
515C24—22no—
516C24—21no—
517C24C2×D4×C3111yescharacteristic
518C24C2×D4×C3112yes—
519#41—81no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—81no—
523C2×Q8C2×D4×C3111yescharacteristic
524C2×D4—22no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—44no—
540C2×D4—81no—
541C2×D4—82no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—82no—
546C2×D4—82no—
547C2×D4—84no—
548C2×D4C2×D4×C3111yescharacteristic
549C2×D4C2×D4×C3112yes—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—81no—
561C22×C4C2×D4×C3112yes—
562C22×C4C2×D4×C3111yescharacteristic
563C22×C4C2×D4×C3111yescharacteristic
564C22×C4C2×D4×C3111yescharacteristic
565C22×C4C2×D4×C3111yescharacteristic
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C24×C3111yescharacteristic
568Q16—81no—
569SD16—81no—
570SD16—82no—
571M16—81no—
572C2×C8—21no—
573C2×C8—22no—
574C2×C8—21no—
575C2×C8—81no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4C2×D4×C3111yescharacteristic
588C4⋊C4C2×D4×C3112yes—
589C4⋊C4C2×D4×C3111yescharacteristic
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—21no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—82no—
607C22⋊C4—82no—
608C42—22no—
609C42—21no—
610C23—22no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—22no—
615C23—21no—
616C23—22no—
617C23—22no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—81no—
623C23—81no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23C31×#12011yescharacteristic
628C23C31×#12011yescharacteristic
629C23C22×D4×C3111yescharacteristic
630Q8—41no—
631Q8—42no—
632Q8—41no—
633Q8—41no—
634D4—42no—
635D4—41no—
636D4—42no—
637D4—42no—
638D4—44no—
639D4—42no—
640D4—42no—
641D4—41no—
642D4—42no—
643D4—41no—
644D4—81no—
645D4—82no—
646D4—82no—
647D4—81no—
648D4—82no—
649D4—82no—
650D4—82no—
651D4—82no—
652D4—82no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—81no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4—84no—
678C2×C4C31×#12011yescharacteristic
679C2×C4C31×#12011yescharacteristic
680C2×C4C22×D4×C3111yescharacteristic
681C2×C4C22×D4×C3111yescharacteristic
682C8—41no—
683C8—41no—
684C8—42no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—82no—
704C22—82no—
705C22—162no—
706C22—164no—
707C22C31×#45512yes—
708C22C2×C31×#12011yescharacteristic
709C22C31×#57611yescharacteristic
710C22C31×#57711yescharacteristic
711C4—21no—
712C4—21no—
713C4—21no—
714C4—21no—
715C4—42no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—82no—
721C4—81no—
722C4—81no—
723C2—21no—
724C2—21no—
725C2—22no—
726C2—41no—
727C2—82no—
728C2—82no—
729C2—81no—
730C2C31×#301211yescharacteristic
731C2C2×C31×#45511yescharacteristic
732C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3537C2
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×#3193C2semidirect
3. C31×#3190C2semidirect
4. C31×#2639C2semidirect
5. C31×#1612C2semidirect
6. C31×#1607C2semidirect
7. C31×#1606C2semidirect
8. C31×#1601C2semidirect
9. C31×#1504C2semidirect
10. C2×C31×#327C2semidirect
11. C31×#1471C2semidirect
25. C2×C31×C22⋊Q8C22semidirect
30. C31×#483C22semidirect
31. C31×#480C22semidirect
32. C31×#480C22semidirect
37. C31×#451C22semidirect
39. C31×#448C22semidirect
40. C31×#448C22semidirect
41. C31×#407C22semidirect
42. C2×C31×C22⋊C8C22semidirect
44. C31×#397C22semidirect
46. C31×#393C22semidirect
48. C2×C31×#95C22semidirect
49. C31×#328C22semidirect
50. C31×#327C22semidirect
51. C31×#327C22semidirect
52. C31×#327C22semidirect
53. C31×#323C22semidirect
54. C31×#323C22semidirect
243. #18419C31direct (N × H)
320. #3193C2×C31semidirect
321. #3190C2×C31semidirect
322. #2639C2×C31semidirect
323. #1612C2×C31semidirect
324. #1607C2×C31semidirect
325. #1606C2×C31semidirect
326. #1601C2×C31semidirect
327. #1504C2×C31semidirect
328. C2×#327C2×C31semidirect
329. #1471C2×C31semidirect
381. C2×C22⋊Q8C22×C31semidirect
386. #483C22×C31semidirect
387. #480C22×C31semidirect
388. #480C22×C31semidirect
393. #451C22×C31semidirect
395. #448C22×C31semidirect
396. #448C22×C31semidirect
397. #407C22×C31semidirect
398. C2×C22⋊C8C22×C31semidirect
400. #397C22×C31semidirect
402. #393C22×C31semidirect
404. C2×#95C22×C31semidirect
405. #328C22×C31semidirect
406. #327C22×C31semidirect
407. #327C22×C31semidirect
408. #327C22×C31semidirect
409. #323C22×C31semidirect
410. #323C22×C31semidirect
514. C31#18419direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35372
C31×#31932
C31×#31902
C31×#26392
C31×#16122
C31×#16072
C31×#16062
C31×#16012
C31×#15042
C2×C31×#3272
C31×#14712
#1841931