Finite Group Databasebeta

← C31×#33554 #21490313

Subgroups — C31×#33554 #21490313

Order 7936.

1112 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×#3538C211yesmaximal, characteristic, complemented
2C31×#3028C211yesmaximal, characteristic, complemented
3C31×#3025C211yesmaximal, characteristic
4C31×#3022C211yesmaximal, characteristic, complemented
5C31×#2201C214yesmaximal, complemented
6C31×#2197C214yesmaximal, complemented
7C31×#2129C211yesmaximal, characteristic, complemented
8C31×#2123C211yesmaximal, characteristic, complemented
9C31×#2120C211yesmaximal, characteristic, complemented
10C31×#585C2211yescharacteristic
11C2×C31×#137—21no—
12C31×#563—21no—
13C31×#563C2212yescomplemented
14C31×#552—21no—
15C31×#552—21no—
16C31×#551—21no—
17C31×#551C2212yescomplemented
18D4×Q8×C31—21no—
19D4×Q8×C31—21no—
20C31×#544—22no—
21C31×#541—21no—
22C31×#539—22no—
23C31×#536—21no—
24C31×#536C2211yescharacteristic
25C31×#536C2211yescharacteristic
26C31×#525—21no—
27C31×#525C2211yescharacteristic
28C2×C31×C22⋊Q8—21no—
29C31×#458—21no—
30C31×#458—22no—
31C31×#458C2214yes—
32C31×#458C2212yes—
33C31×B(4,𝔽2)—21no—
34C31×B(4,𝔽2)C2212yes—
35C31×#456—22no—
36C31×#455C2214yes—
37C31×#421—21no—
38C31×#413C2211yescharacteristic
39C31×#410—21no—
40C31×#410—21no—
41C31×#410C2211yescharacteristic
42C31×#410C2211yescharacteristic
43C31×#354C2214yescomplemented
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—42no—
57C2×#41×C31C2311yescharacteristic
58C22×Q8×C31—21no—
59C22×Q8×C31D411yescharacteristic, complemented
60C22×Q8×C31D411yescharacteristic, complemented
61C23×C4×C31D411yescharacteristic
62C31×#137—24no—
63C31×#137—42no—
64C2×Q16×C31—41no—
65C2×SD16×C31—41no—
66C2×M16×C31—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—22no—
69C31×C4⋊Q8—21no—
70C31×C4⋊Q8—22no—
71C31×C4⋊Q8—41no—
72C31×C4⋊Q8D412yescomplemented
73C31×#126—22no—
74C31×#126—22no—
75C31×#126—22no—
76C31×#126—22no—
77C31×#125—22no—
78C31×#125—22no—
79C31×#125—21no—
80C31×#125—22no—
81C31×#125—22no—
82C31×#124—21no—
83C31×#124—41no—
84C31×#124C2312yes—
85C31×#123—22no—
86C31×#123—21no—
87C31×#123—21no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—24no—
91C31×#123D411yescharacteristic
92C31×#123D412yescomplemented
93C31×#123C2311yescharacteristic
94C31×#123C2312yes—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8—21no—
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8—21no—
103C31×C22⋊Q8—21no—
104C31×C22⋊Q8—22no—
105C31×C22⋊Q8—21no—
106C31×C22⋊Q8—21no—
107C31×C22⋊Q8—22no—
108C31×C22⋊Q8—42no—
109C31×C22⋊Q8—41no—
110C31×#121—21no—
111C31×#121—41no—
112C31×#120—22no—
113C31×#120D411yescharacteristic
114C31×#120C2311yescharacteristic
115C4×Q8×C31—21no—
116C4×Q8×C31—21no—
117C4×D4×C31—22no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—22no—
121C4×D4×C31—42no—
122C31×#117—22no—
123C31×#117—22no—
124C31×#117—21no—
125C31×#117—21no—
126C31×#117D411yescharacteristic
127C31×#117D411yescharacteristic, complemented
128C31×#117D411yescharacteristic, complemented
129C2×C4⋊C4×C31—22no—
130C2×C4⋊C4×C31—21no—
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×C31C2×D411yescharacteristic
143#41×C31—22no—
144#41×C31—22no—
145#41×C31—41no—
146#41×C31—41no—
147#41×C31—42no—
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—42no—
154#41×C31—42no—
155#41×C31—42no—
156#41×C31—41no—
157#41×C31—41no—
158#41×C31—41no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—22no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—41no—
167C2×Q8×C31—41no—
168C2×Q8×C31—41no—
169C2×Q8×C31—41no—
170C2×Q8×C31—42no—
171C2×Q8×C31—81no—
172C2×Q8×C31—81no—
173C2×Q8×C31C2×D412yes—
174C2×Q8×C31C2×D411yescharacteristic
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—21no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—41no—
186C2×D4×C31—42no—
187C2×D4×C31C2×D411yescharacteristic
188C2×D4×C31C2×D411yescharacteristic
189C2×D4×C31C2411yescharacteristic
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—41no—
198C22×C4×C31—41no—
199C22×C4×C31—41no—
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D412yes—
204C22×C4×C31C2×D411yescharacteristic
205Q16×C31—44no—
206SD16×C31—44no—
207M16×C31—22no—
208M16×C31—41no—
209C2×C8×C31—41no—
210C4⋊C4×C31—22no—
211C4⋊C4×C31—22no—
212C4⋊C4×C31—22no—
213C4⋊C4×C31—22no—
214C4⋊C4×C31—22no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—22no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—41no—
229C4⋊C4×C31—41no—
230C4⋊C4×C31—42no—
231C4⋊C4×C31—44no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—21no—
235C22⋊C4×C31—21no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—21no—
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#33554C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—21no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—41no—
263C23×C31—42no—
264C23×C31—41no—
265C23×C31#12011yescharacteristic
266C23×C31C22×D411yescharacteristic
267C23×C31C22×D411yescharacteristic
268Q8×C31—22no—
269Q8×C31—41no—
270Q8×C31—42no—
271Q8×C31—41no—
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—41no—
285D4×C31—41no—
286D4×C31—42no—
287D4×C31—42no—
288D4×C31—42no—
289D4×C31—42no—
290D4×C31—42no—
291D4×C31—42no—
292D4×C31—41no—
293D4×C31—84no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—21no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—44no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—81no—
322C2×C4×C31—81no—
323C2×C4×C31—82no—
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31#12011yescharacteristic
326C2×C4×C31#12011yescharacteristic
327C2×C4×C31C22×D411yescharacteristic
328C8×C31—42no—
329#3538C2×C3111yescharacteristic, complemented
330#3028C2×C3111yescharacteristic, complemented
331#3025C2×C3111yescharacteristic
332#3022C2×C3111yescharacteristic, complemented
333#2201C2×C3114yescomplemented
334#2197C2×C3114yescomplemented
335#2129C2×C3111yescharacteristic, complemented
336#2123C2×C3111yescharacteristic, complemented
337#2120C2×C3111yescharacteristic, complemented
338C22×C31—22no—
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—41no—
343C22×C31—41no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—42no—
347C22×C31—41no—
348C22×C31—42no—
349C22×C31—81no—
350C22×C31—82no—
351C22×C31—82no—
352C22×C31—161no—
353C22×C31C2×#12011yescharacteristic
354C4×C31—21no—
355C4×C31—21no—
356C4×C31—21no—
357C4×C31—42no—
358C4×C31—42no—
359C4×C31—41no—
360C4×C31—41no—
361C4×C31—42no—
362C4×C31—41no—
363C4×C31—42no—
364C4×C31—42no—
365C4×C31—82no—
366C4×C31—82no—
367C4×C31B(4,𝔽2)11yescharacteristic
368C4×C31B(4,𝔽2)11yescharacteristic
369#585C22×C3111yescharacteristic
370C2×#137—21no—
371#563—21no—
372#563C22×C3112yescomplemented
373#552—21no—
374#552—21no—
375#551—21no—
376#551C22×C3112yescomplemented
377D4×Q8—21no—
378D4×Q8—21no—
379#544—22no—
380#541—21no—
381#539—22no—
382#536—21no—
383#536C22×C3111yescharacteristic
384#536C22×C3111yescharacteristic
385#525—21no—
386#525C22×C3111yescharacteristic
387C2×C22⋊Q8—21no—
388#458—21no—
389#458—22no—
390#458C22×C3114yes—
391#458C22×C3112yes—
392B(4,𝔽2)—21no—
393B(4,𝔽2)C22×C3112yes—
394#456—22no—
395#455C22×C3114yes—
396#421—21no—
397#413C22×C3111yescharacteristic
398#410—21no—
399#410—21no—
400#410C22×C3111yescharacteristic
401#410C22×C3111yescharacteristic
402#354C22×C3114yescomplemented
403#352C22×C3112yescomplemented
404#352C22×C3114yescomplemented
405AΣL(1,𝔽16)C22×C3112yescomplemented
406C2×C31—21no—
407C2×C31—41no—
408C2×C31—41no—
409C2×C31—42no—
410C2×C31—41no—
411C2×C31—82no—
412C2×C31C2×B(4,𝔽2)11yescharacteristic
4132−1+4—21no—
4142−1+4—41no—
415H(5,𝔽2)—21no—
416H(5,𝔽2)—21no—
417H(5,𝔽2)—41no—
418H(5,𝔽2)C23×C3112yes—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—42no—
423C2×#41C23×C3111yescharacteristic
424C22×Q8—21no—
425C22×Q8D4×C3111yescharacteristic, complemented
426C22×Q8D4×C3111yescharacteristic, complemented
427C23×C4D4×C3111yescharacteristic
428#137—24no—
429#137—42no—
430C2×Q16—41no—
431C2×SD16—41no—
432C2×M16—21no—
433C4⋊Q8—21no—
434C4⋊Q8—22no—
435C4⋊Q8—21no—
436C4⋊Q8—22no—
437C4⋊Q8—41no—
438C4⋊Q8D4×C3112yescomplemented
439#126—22no—
440#126—22no—
441#126—22no—
442#126—22no—
443#125—22no—
444#125—22no—
445#125—21no—
446#125—22no—
447#125—22no—
448#124—21no—
449#124—41no—
450#124C23×C3112yes—
451#123—22no—
452#123—21no—
453#123—21no—
454#123—22no—
455#123—22no—
456#123—24no—
457#123D4×C3111yescharacteristic
458#123D4×C3112yescomplemented
459#123C23×C3111yescharacteristic
460#123C23×C3112yes—
461C22⋊Q8—22no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—21no—
467C22⋊Q8—22no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—22no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—41no—
478#120—22no—
479#120D4×C3111yescharacteristic
480#120C23×C3111yescharacteristic
481C4×Q8—21no—
482C4×Q8—21no—
483C4×D4—22no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—22no—
487C4×D4—42no—
488#117—22no—
489#117—22no—
490#117—21no—
491#117—21no—
492#117D4×C3111yescharacteristic
493#117D4×C3111yescharacteristic, complemented
494#117D4×C3111yescharacteristic, complemented
495C2×C4⋊C4—22no—
496C2×C4⋊C4—21no—
497C2×C22⋊C4—22no—
498#104—24no—
499#101—21no—
500#100C23×C3112yes—
501#99—21no—
502#99—21no—
503#99—22no—
504#99—22no—
505#99—24no—
506#99C23×C3112yes—
507#99C23×C3112yes—
508C31#3355411yescharacteristic, direct product factor, Sylow
509C24C2×D4×C3111yescharacteristic
510#41—22no—
511#41—22no—
512#41—41no—
513#41—41no—
514#41—42no—
515#41—41no—
516#41—41no—
517#41—41no—
518#41—41no—
519#41—41no—
520#41—42no—
521#41—42no—
522#41—42no—
523#41—41no—
524#41—41no—
525#41—41no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—42no—
538C2×Q8—81no—
539C2×Q8—81no—
540C2×Q8C2×D4×C3112yes—
541C2×Q8C2×D4×C3111yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4C2×D4×C3111yescharacteristic
555C2×D4C2×D4×C3111yescharacteristic
556C2×D4C24×C3111yescharacteristic
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C2×D4×C3112yes—
571C22×C4C2×D4×C3111yescharacteristic
572Q16—44no—
573SD16—44no—
574M16—22no—
575M16—41no—
576C2×C8—41no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—42no—
598C4⋊C4—44no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—21no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—44no—
615C22⋊C4C2×D4×C3111yescharacteristic
616C22⋊C4C2×D4×C3111yescharacteristic
617C22⋊C4C2×D4×C3112yes—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—41no—
623C42—41no—
624C42C2×D4×C3112yes—
625C23—21no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23C31×#12011yescharacteristic
632C23C22×D4×C3111yescharacteristic
633C23C22×D4×C3111yescharacteristic
634Q8—22no—
635Q8—41no—
636Q8—42no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—81no—
645Q8—82no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—41no—
659D4—84no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—82no—
690C2×C4C31×#12011yescharacteristic
691C2×C4C31×#12011yescharacteristic
692C2×C4C31×#12011yescharacteristic
693C2×C4C22×D4×C3111yescharacteristic
694C8—42no—
695C22—22no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22—81no—
707C22—82no—
708C22—82no—
709C22—161no—
710C22C2×C31×#12011yescharacteristic
711C4—21no—
712C4—21no—
713C4—21no—
714C4—42no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—41no—
720C4—42no—
721C4—42no—
722C4—82no—
723C4—82no—
724C4C31×B(4,𝔽2)11yescharacteristic
725C4C31×B(4,𝔽2)11yescharacteristic
726C2—21no—
727C2—41no—
728C2—41no—
729C2—42no—
730C2—41no—
731C2—82no—
732C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C31C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C31
prime radicalC31×#3025C2
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×#3538C2semidirect
2. C31×#3028C2semidirect
4. C31×#3022C2semidirect
5. C31×#2201C2semidirect
6. C31×#2197C2semidirect
7. C31×#2129C2semidirect
8. C31×#2123C2semidirect
9. C31×#2120C2semidirect
13. C31×#563C22semidirect
17. C31×#551C22semidirect
43. C31×#354C22semidirect
44. C31×#352C22semidirect
45. C31×#352C22semidirect
46. C31×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C31D4semidirect
60. C22×Q8×C31D4semidirect
72. C31×C4⋊Q8D4semidirect
92. C31×#123D4semidirect
127. C31×#117D4semidirect
128. C31×#117D4semidirect
258. #33554C31direct (N × H)
329. #3538C2×C31semidirect
330. #3028C2×C31semidirect
332. #3022C2×C31semidirect
333. #2201C2×C31semidirect
334. #2197C2×C31semidirect
335. #2129C2×C31semidirect
336. #2123C2×C31semidirect
337. #2120C2×C31semidirect
372. #563C22×C31semidirect
376. #551C22×C31semidirect
402. #354C22×C31semidirect
403. #352C22×C31semidirect
404. #352C22×C31semidirect
405. AΣL(1,𝔽16)C22×C31semidirect
425. C22×Q8D4×C31semidirect
426. C22×Q8D4×C31semidirect
438. C4⋊Q8D4×C31semidirect
458. #123D4×C31semidirect
493. #117D4×C31semidirect
494. #117D4×C31semidirect
508. C31#33554direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35382
C31×#30282
C31×#30252
C31×#30222
C31×#22012
C31×#21972
C31×#21292
C31×#21232
C31×#21202
#3355431