Finite Group Databasebeta

← C31×#33556 #21490315

Subgroups — C31×#33556 #21490315

Order 7936.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3540C211yesmaximal, characteristic, complemented
2C31×#3028C211yesmaximal, characteristic, complemented
3C31×#3025C211yesmaximal, characteristic, complemented
4C31×#3021C211yesmaximal, characteristic, complemented
5C31×#2200C214yesmaximal, complemented
6C31×#2198C214yesmaximal, complemented
7C31×#2128C211yesmaximal, characteristic, complemented
8C31×#2123C211yesmaximal, characteristic, complemented
9C31×#2120C211yesmaximal, characteristic, complemented
10C31×#585C2211yescharacteristic
11C2×C31×AGL(1,ℤ/8)—21no—
12C31×H(3,𝔽4)—21no—
13C31×#560C2212yescomplemented
14C31×#559C2212yescomplemented
15C31×#556—21no—
16C31×#555—21no—
17C31×#551—21no—
18C31×#548—21no—
19C31×#546—21no—
20C31×#542—22no—
21C31×#542—21no—
22C31×#538—22no—
23C31×#536—21no—
24C31×#536C2211yescharacteristic
25C31×#535C2211yescharacteristic
26C31×#525—21no—
27C31×#525—21no—
28C31×#525C2211yescharacteristic
29C31×#458—21no—
30C31×#458—22no—
31C31×#458C2212yescomplemented
32C31×#458C2214yescomplemented
33C31×B(4,𝔽2)—21no—
34C31×B(4,𝔽2)C2212yescomplemented
35C31×#454—22no—
36C31×#453C2214yes—
37C31×#421—21no—
38C31×#413C2211yescharacteristic
39C31×#410—21no—
40C31×#410—21no—
41C31×#410C2211yescharacteristic
42C31×#410C2211yescharacteristic
43C31×#353C2214yescomplemented
44C31×#352C2212yescomplemented
45C31×#352C2214yescomplemented
46C31×AΣL(1,𝔽16)C2212yescomplemented
47C31×2−1+4—21no—
48C31×2−1+4—41no—
49C31×H(5,𝔽2)—21no—
50C31×H(5,𝔽2)—21no—
51C31×H(5,𝔽2)—41no—
52C31×H(5,𝔽2)C2312yes—
53C2×#41×C31—21no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—42no—
58C2×#41×C31C2311yescharacteristic
59C22×Q8×C31D411yescharacteristic, complemented
60C22×D4×C31D411yescharacteristic, complemented
61C23×C4×C31D411yescharacteristic
62C31×AGL(1,ℤ/8)—24no—
63C31×AGL(1,ℤ/8)—42no—
64C2×SD16×C31—41no—
65C2×D8×C31—41no—
66C2×M16×C31—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8—41no—
70C31×#127C2312yes—
71C31×#126—22no—
72C31×#126—22no—
73C31×#126—22no—
74C31×#124—22no—
75C31×#124—21no—
76C31×#124—22no—
77C31×#124—22no—
78C31×#124—21no—
79C31×#124—22no—
80C31×#124—22no—
81C31×#124—41no—
82C31×#124D412yescomplemented
83C31×#123—22no—
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—22no—
87C31×#123—24no—
88C31×#123D411yescharacteristic
89C31×#123D412yescomplemented
90C31×#123C2311yescharacteristic
91C31×#123C2312yes—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—42no—
99C31×C22⋊Q8—41no—
100C31×#121—21no—
101C31×#121—21no—
102C31×#121—22no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—22no—
106C31×#121—22no—
107C31×#121—41no—
108C31×#120—22no—
109C31×#120—22no—
110C31×#120—21no—
111C31×#120—21no—
112C31×#120—22no—
113C31×#120D411yescharacteristic
114C31×#120C2311yescharacteristic
115C4×Q8×C31—21no—
116C4×Q8×C31—22no—
117C4×D4×C31—22no—
118C4×D4×C31—21no—
119C4×D4×C31—22no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31—22no—
123C4×D4×C31—42no—
124C31×#117—21no—
125C31×#117—22no—
126C31×#117—21no—
127C31×#117—21no—
128C31×#117D411yescharacteristic
129C31×#117D411yescharacteristic, complemented
130C31×#117D411yescharacteristic, complemented
131C2×C22⋊C4×C31—22no—
132C31×#104—24no—
133C31×#101—21no—
134C31×#100C2312yes—
135C31×#99—21no—
136C31×#99—21no—
137C31×#99—22no—
138C31×#99—22no—
139C31×#99—24no—
140C31×#99C2312yes—
141C31×#99C2312yes—
142C24×C31—21no—
143C24×C31C2×D411yescharacteristic
144#41×C31—22no—
145#41×C31—22no—
146#41×C31—41no—
147#41×C31—41no—
148#41×C31—42no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—41no—
154#41×C31—42no—
155#41×C31—42no—
156#41×C31—42no—
157#41×C31—41no—
158#41×C31—41no—
159#41×C31—41no—
160#41×C31—81no—
161#41×C31—81no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—22no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—41no—
169C2×Q8×C31—41no—
170C2×Q8×C31—42no—
171C2×Q8×C31C2×D411yescharacteristic
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—21no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—41no—
185C2×D4×C31—41no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—41no—
190C2×D4×C31—42no—
191C2×D4×C31C2×D411yescharacteristic
192C2×D4×C31C2×D411yescharacteristic
193C2×D4×C31C2×D412yes—
194C2×D4×C31C2411yescharacteristic
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—41no—
202C22×C4×C31—41no—
203C22×C4×C31—41no—
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D412yes—
209SD16×C31—44no—
210D8×C31—44no—
211M16×C31—22no—
212M16×C31—41no—
213C2×C8×C31—41no—
214C4⋊C4×C31—22no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—41no—
225C4⋊C4×C31—41no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—44no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—21no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—21no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—44no—
248C22⋊C4×C31C2×D411yescharacteristic
249C22⋊C4×C31C2×D411yescharacteristic
250C22⋊C4×C31C2×D412yes—
251C42×C31—22no—
252C42×C31—22no—
253C42×C31—21no—
254C42×C31—21no—
255C42×C31—41no—
256C42×C31—41no—
257C42×C31C2×D412yes—
258#33556C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—21no—
262C23×C31—22no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—81no—
266C23×C31—81no—
267C23×C31—82no—
268C23×C31#12011yescharacteristic
269C23×C31C22×D411yescharacteristic
270C23×C31C22×D411yescharacteristic
271Q8×C31—22no—
272Q8×C31—41no—
273Q8×C31—41no—
274Q8×C31—41no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—81no—
279Q8×C31—82no—
280D4×C31—22no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—42no—
285D4×C31—41no—
286D4×C31—41no—
287D4×C31—42no—
288D4×C31—42no—
289D4×C31—42no—
290D4×C31—42no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—81no—
295D4×C31—82no—
296D4×C31—82no—
297D4×C31—82no—
298D4×C31—81no—
299D4×C31—82no—
300D4×C31—84no—
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—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—21no—
313C2×C4×C31—22no—
314C2×C4×C31—21no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—41no—
319C2×C4×C31—42no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—81no—
327C2×C4×C31—82no—
328C2×C4×C31—82no—
329C2×C4×C31#12011yescharacteristic
330C2×C4×C31#12011yescharacteristic
331C2×C4×C31#12011yescharacteristic
332C2×C4×C31C22×D411yescharacteristic
333C8×C31—42no—
334#3540C2×C3111yescharacteristic, complemented
335#3028C2×C3111yescharacteristic, complemented
336#3025C2×C3111yescharacteristic, complemented
337#3021C2×C3111yescharacteristic, complemented
338#2200C2×C3114yescomplemented
339#2198C2×C3114yescomplemented
340#2128C2×C3111yescharacteristic, complemented
341#2123C2×C3111yescharacteristic, complemented
342#2120C2×C3111yescharacteristic, complemented
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—42no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—41no—
356C22×C31—42no—
357C22×C31—82no—
358C22×C31—82no—
359C22×C31—81no—
360C22×C31—161no—
361C22×C31—162no—
362C22×C31C2×#12011yescharacteristic
363C4×C31—21no—
364C4×C31—21no—
365C4×C31—21no—
366C4×C31—41no—
367C4×C31—42no—
368C4×C31—42no—
369C4×C31—41no—
370C4×C31—42no—
371C4×C31—41no—
372C4×C31—42no—
373C4×C31—82no—
374C4×C31—82no—
375C4×C31B(4,𝔽2)11yescharacteristic
376C4×C31B(4,𝔽2)11yescharacteristic
377#585C22×C3111yescharacteristic
378C2×AGL(1,ℤ/8)—21no—
379H(3,𝔽4)—21no—
380#560C22×C3112yescomplemented
381#559C22×C3112yescomplemented
382#556—21no—
383#555—21no—
384#551—21no—
385#548—21no—
386#546—21no—
387#542—22no—
388#542—21no—
389#538—22no—
390#536—21no—
391#536C22×C3111yescharacteristic
392#535C22×C3111yescharacteristic
393#525—21no—
394#525—21no—
395#525C22×C3111yescharacteristic
396#458—21no—
397#458—22no—
398#458C22×C3112yescomplemented
399#458C22×C3114yescomplemented
400B(4,𝔽2)—21no—
401B(4,𝔽2)C22×C3112yescomplemented
402#454—22no—
403#453C22×C3114yes—
404#421—21no—
405#413C22×C3111yescharacteristic
406#410—21no—
407#410—21no—
408#410C22×C3111yescharacteristic
409#410C22×C3111yescharacteristic
410#353C22×C3114yescomplemented
411#352C22×C3112yescomplemented
412#352C22×C3114yescomplemented
413AΣL(1,𝔽16)C22×C3112yescomplemented
414C2×C31—21no—
415C2×C31—41no—
416C2×C31—41no—
417C2×C31—41no—
418C2×C31—81no—
419C2×C31—82no—
420C2×C31—82no—
421C2×C31C2×B(4,𝔽2)11yescharacteristic
4222−1+4—21no—
4232−1+4—41no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—41no—
427H(5,𝔽2)C23×C3112yes—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—42no—
433C2×#41C23×C3111yescharacteristic
434C22×Q8D4×C3111yescharacteristic, complemented
435C22×D4D4×C3111yescharacteristic, complemented
436C23×C4D4×C3111yescharacteristic
437AGL(1,ℤ/8)—24no—
438AGL(1,ℤ/8)—42no—
439C2×SD16—41no—
440C2×D8—41no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—41no—
445#127C23×C3112yes—
446#126—22no—
447#126—22no—
448#126—22no—
449#124—22no—
450#124—21no—
451#124—22no—
452#124—22no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—41no—
457#124D4×C3112yescomplemented
458#123—22no—
459#123—22no—
460#123—22no—
461#123—22no—
462#123—24no—
463#123D4×C3111yescharacteristic
464#123D4×C3112yescomplemented
465#123C23×C3111yescharacteristic
466#123C23×C3112yes—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474C22⋊Q8—41no—
475#121—21no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—22no—
482#121—41no—
483#120—22no—
484#120—22no—
485#120—21no—
486#120—21no—
487#120—22no—
488#120D4×C3111yescharacteristic
489#120C23×C3111yescharacteristic
490C4×Q8—21no—
491C4×Q8—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—42no—
499#117—21no—
500#117—22no—
501#117—21no—
502#117—21no—
503#117D4×C3111yescharacteristic
504#117D4×C3111yescharacteristic, complemented
505#117D4×C3111yescharacteristic, complemented
506C2×C22⋊C4—22no—
507#104—24no—
508#101—21no—
509#100C23×C3112yes—
510#99—21no—
511#99—21no—
512#99—22no—
513#99—22no—
514#99—24no—
515#99C23×C3112yes—
516#99C23×C3112yes—
517C31#3355611yescharacteristic, direct product factor, Sylow
518C24—21no—
519C24C2×D4×C3111yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C3111yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C3111yescharacteristic
568C2×D4C2×D4×C3111yescharacteristic
569C2×D4C2×D4×C3112yes—
570C2×D4C24×C3111yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3112yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C3111yescharacteristic
625C22⋊C4C2×D4×C3111yescharacteristic
626C22⋊C4C2×D4×C3112yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C3112yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23C31×#12011yescharacteristic
644C23C22×D4×C3111yescharacteristic
645C23C22×D4×C3111yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—82no—
672D4—82no—
673D4—81no—
674D4—82no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4C31×#12011yescharacteristic
705C2×C4C31×#12011yescharacteristic
706C2×C4C31×#12011yescharacteristic
707C2×C4C22×D4×C3111yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×C31×#12011yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C31×B(4,𝔽2)11yescharacteristic
742C4C31×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C31C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C31
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3540C2semidirect
2. C31×#3028C2semidirect
3. C31×#3025C2semidirect
4. C31×#3021C2semidirect
5. C31×#2200C2semidirect
6. C31×#2198C2semidirect
7. C31×#2128C2semidirect
8. C31×#2123C2semidirect
9. C31×#2120C2semidirect
13. C31×#560C22semidirect
14. C31×#559C22semidirect
31. C31×#458C22semidirect
32. C31×#458C22semidirect
34. C31×B(4,𝔽2)C22semidirect
43. C31×#353C22semidirect
44. C31×#352C22semidirect
45. C31×#352C22semidirect
46. C31×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C31D4semidirect
60. C22×D4×C31D4semidirect
82. C31×#124D4semidirect
89. C31×#123D4semidirect
129. C31×#117D4semidirect
130. C31×#117D4semidirect
258. #33556C31direct (N × H)
334. #3540C2×C31semidirect
335. #3028C2×C31semidirect
336. #3025C2×C31semidirect
337. #3021C2×C31semidirect
338. #2200C2×C31semidirect
339. #2198C2×C31semidirect
340. #2128C2×C31semidirect
341. #2123C2×C31semidirect
342. #2120C2×C31semidirect
380. #560C22×C31semidirect
381. #559C22×C31semidirect
398. #458C22×C31semidirect
399. #458C22×C31semidirect
401. B(4,𝔽2)C22×C31semidirect
410. #353C22×C31semidirect
411. #352C22×C31semidirect
412. #352C22×C31semidirect
413. AΣL(1,𝔽16)C22×C31semidirect
434. C22×Q8D4×C31semidirect
435. C22×D4D4×C31semidirect
457. #124D4×C31semidirect
464. #123D4×C31semidirect
504. #117D4×C31semidirect
505. #117D4×C31semidirect
517. C31#33556direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35402
C31×#30282
C31×#30252
C31×#30212
C31×#22002
C31×#21982
C31×#21282
C31×#21232
C31×#21202
#3355631