Finite Group Databasebeta

← C31×#33555 #21490314

Subgroups — C31×#33555 #21490314

Order 7936.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3540C211yesmaximal, characteristic, complemented
2C31×#3027C211yesmaximal, characteristic, complemented
3C31×#3025C211yesmaximal, characteristic, complemented
4C31×#3022C211yesmaximal, characteristic, complemented
5C31×#2199C214yesmaximal, complemented
6C31×#2197C214yesmaximal, complemented
7C31×#2129C211yesmaximal, characteristic, complemented
8C31×#2122C211yesmaximal, characteristic, complemented
9C31×#2120C211yesmaximal, characteristic, complemented
10C31×#585C2211yescharacteristic
11C2×C31×#137—21no—
12C31×H(3,𝔽4)C2212yescomplemented
13C31×#560—21no—
14C31×#559—21no—
15C31×#556—21no—
16C31×#555—21no—
17C31×#551C2212yescomplemented
18C31×#548—21no—
19C31×#546—21no—
20C31×#542—22no—
21C31×#542—21no—
22C31×#538—22no—
23C31×#536C2211yescharacteristic
24C31×#535—21no—
25C31×#535C2211yescharacteristic
26C31×#525—21no—
27C31×#525—21no—
28C31×#525C2211yescharacteristic
29C31×#458—21no—
30C31×#458C2212yes—
31C31×B(4,𝔽2)—21no—
32C31×B(4,𝔽2)—22no—
33C31×B(4,𝔽2)C2214yes—
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×AΣL(1,𝔽16)C2212yescomplemented
46C31×AΣL(1,𝔽16)C2214yescomplemented
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, complemented
62C31×#137—24no—
63C31×#137—42no—
64C2×Q16×C31—41no—
65C2×SD16×C31—41no—
66C2×M16×C31—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8D412yescomplemented
69C31×#127—21no—
70C31×#127—41no—
71C31×#126—22no—
72C31×#126—22no—
73C31×#126—22no—
74C31×#124—22no—
75C31×#124—21no—
76C31×#124—21no—
77C31×#124—22no—
78C31×#124—22no—
79C31×#124—22no—
80C31×#124—22no—
81C31×#124—41no—
82C31×#124C2312yes—
83C31×#123—22no—
84C31×#123—22no—
85C31×#123—21no—
86C31×#123—21no—
87C31×#123—22no—
88C31×#123—22no—
89C31×#123D411yescharacteristic, complemented
90C31×#123C2311yescharacteristic
91C31×C22⋊Q8—21no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—41no—
98C31×#121—21no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—42no—
106C31×#121—41no—
107C31×#120—22no—
108C31×#120—22no—
109C31×#120—22no—
110C31×#120—24no—
111C31×#120D411yescharacteristic, complemented
112C31×#120D412yescomplemented
113C31×#120C2311yescharacteristic
114C31×#120C2312yes—
115C4×Q8×C31—21no—
116C4×Q8×C31—22no—
117C4×D4×C31—22no—
118C4×D4×C31—22no—
119C4×D4×C31—21no—
120C4×D4×C31—22no—
121C4×D4×C31—21no—
122C4×D4×C31—21no—
123C4×D4×C31—42no—
124C31×#117—21no—
125C31×#117—22no—
126C31×#117—21no—
127C31×#117—21no—
128C31×#117D411yescharacteristic, complemented
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—24no—
138C31×#99—22no—
139C31×#99—22no—
140C31×#99C2312yes—
141C31×#99C2312yes—
142C24×C31C2×D412yes—
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—41no—
168C2×Q8×C31—41no—
169C2×Q8×C31—42no—
170C2×Q8×C31C2×D412yes—
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—21no—
182C2×D4×C31—22no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—41no—
186C2×D4×C31—41no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—41no—
191C2×D4×C31—42no—
192C2×D4×C31—44no—
193C2×D4×C31C2×D411yescharacteristic
194C2×D4×C31C2×D411yescharacteristic
195C2×D4×C31C2411yescharacteristic
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—41no—
204C22×C4×C31—41no—
205C22×C4×C31—41no—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210Q16×C31—44no—
211SD16×C31—44no—
212M16×C31—22no—
213M16×C31—41no—
214C2×C8×C31—41no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—41no—
226C4⋊C4×C31—41no—
227C4⋊C4×C31—42no—
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—21no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—44no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31C2×D412yes—
249C22⋊C4×C31C2×D411yescharacteristic
250C22⋊C4×C31C2×D411yescharacteristic
251C42×C31—22no—
252C42×C31—22no—
253C42×C31—21no—
254C42×C31—21no—
255C42×C31—41no—
256C42×C31—41no—
257C42×C31C2×D412yes—
258#33555C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—21no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—42no—
266C23×C31—81no—
267C23×C31—82no—
268C23×C31#12011yescharacteristic
269C23×C31C22×D411yescharacteristic
270C23×C31C22×D411yescharacteristic
271Q8×C31—22no—
272Q8×C31—41no—
273Q8×C31—42no—
274Q8×C31—41no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—41no—
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—41no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—81no—
294D4×C31—81no—
295D4×C31—82no—
296D4×C31—82no—
297D4×C31—82no—
298D4×C31—81no—
299D4×C31—82no—
300D4×C31—84no—
301D4×C31—164no—
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—22no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—22no—
312C2×C4×C31—21no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—41no—
320C2×C4×C31—42no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—81no—
327C2×C4×C31—81no—
328C2×C4×C31—82no—
329C2×C4×C31—82no—
330C2×C4×C31#12011yescharacteristic
331C2×C4×C31#12011yescharacteristic
332C2×C4×C31#12011yescharacteristic
333C2×C4×C31C22×D411yescharacteristic
334C8×C31—42no—
335#3540C2×C3111yescharacteristic, complemented
336#3027C2×C3111yescharacteristic, complemented
337#3025C2×C3111yescharacteristic, complemented
338#3022C2×C3111yescharacteristic, complemented
339#2199C2×C3114yescomplemented
340#2197C2×C3114yescomplemented
341#2129C2×C3111yescharacteristic, complemented
342#2122C2×C3111yescharacteristic, complemented
343#2120C2×C3111yescharacteristic, complemented
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—41no—
357C22×C31—42no—
358C22×C31—82no—
359C22×C31—82no—
360C22×C31—84no—
361C22×C31—81no—
362C22×C31—161no—
363C22×C31C2×#12011yescharacteristic
364C4×C31—21no—
365C4×C31—21no—
366C4×C31—21no—
367C4×C31—41no—
368C4×C31—42no—
369C4×C31—42no—
370C4×C31—41no—
371C4×C31—42no—
372C4×C31—41no—
373C4×C31—42no—
374C4×C31—82no—
375C4×C31—82no—
376C4×C31B(4,𝔽2)11yescharacteristic
377C4×C31B(4,𝔽2)11yescharacteristic
378#585C22×C3111yescharacteristic
379C2×#137—21no—
380H(3,𝔽4)C22×C3112yescomplemented
381#560—21no—
382#559—21no—
383#556—21no—
384#555—21no—
385#551C22×C3112yescomplemented
386#548—21no—
387#546—21no—
388#542—22no—
389#542—21no—
390#538—22no—
391#536C22×C3111yescharacteristic
392#535—21no—
393#535C22×C3111yescharacteristic
394#525—21no—
395#525—21no—
396#525C22×C3111yescharacteristic
397#458—21no—
398#458C22×C3112yes—
399B(4,𝔽2)—21no—
400B(4,𝔽2)—22no—
401B(4,𝔽2)C22×C3114yes—
402B(4,𝔽2)C22×C3112yes—
403#456—22no—
404#455C22×C3114yes—
405#421—21no—
406#413C22×C3111yescharacteristic
407#410—21no—
408#410—21no—
409#410C22×C3111yescharacteristic
410#410C22×C3111yescharacteristic
411#354C22×C3114yescomplemented
412#352C22×C3112yescomplemented
413AΣL(1,𝔽16)C22×C3112yescomplemented
414AΣL(1,𝔽16)C22×C3114yescomplemented
415C2×C31—21no—
416C2×C31—41no—
417C2×C31—41no—
418C2×C31—41no—
419C2×C31—81no—
420C2×C31—82no—
421C2×C31—82no—
422C2×C31C2×B(4,𝔽2)11yescharacteristic
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C3112yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C3111yescharacteristic
435C22×Q8D4×C3111yescharacteristic, complemented
436C22×D4D4×C3111yescharacteristic, complemented
437C23×C4D4×C3111yescharacteristic, complemented
438#137—24no—
439#137—42no—
440C2×Q16—41no—
441C2×SD16—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8D4×C3112yescomplemented
445#127—21no—
446#127—41no—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—21no—
453#124—22no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124C23×C3112yes—
459#123—22no—
460#123—22no—
461#123—21no—
462#123—21no—
463#123—22no—
464#123—22no—
465#123D4×C3111yescharacteristic, complemented
466#123C23×C3111yescharacteristic
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—21no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—41no—
474#121—21no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—42no—
482#121—41no—
483#120—22no—
484#120—22no—
485#120—22no—
486#120—24no—
487#120D4×C3111yescharacteristic, complemented
488#120D4×C3112yescomplemented
489#120C23×C3111yescharacteristic
490#120C23×C3112yes—
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—22no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C3111yescharacteristic, complemented
505#117D4×C3111yescharacteristic, complemented
506#117D4×C3111yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C3112yes—
511#99—21no—
512#99—21no—
513#99—24no—
514#99—22no—
515#99—22no—
516#99C23×C3112yes—
517#99C23×C3112yes—
518C31#3355511yescharacteristic, direct product factor, Sylow
519C24C2×D4×C3112yes—
520C24C2×D4×C3111yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C3112yes—
548C2×Q8C2×D4×C3111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C3111yescharacteristic
571C2×D4C2×D4×C3111yescharacteristic
572C2×D4C24×C3111yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C3112yes—
626C22⋊C4C2×D4×C3111yescharacteristic
627C22⋊C4C2×D4×C3111yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C3112yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23C31×#12011yescharacteristic
645C23C22×D4×C3111yescharacteristic
646C23C22×D4×C3111yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4C31×#12011yescharacteristic
707C2×C4C31×#12011yescharacteristic
708C2×C4C31×#12011yescharacteristic
709C2×C4C22×D4×C3111yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×C31×#12011yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4C31×B(4,𝔽2)11yescharacteristic
744C4C31×B(4,𝔽2)11yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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×#3027C2semidirect
3. C31×#3025C2semidirect
4. C31×#3022C2semidirect
5. C31×#2199C2semidirect
6. C31×#2197C2semidirect
7. C31×#2129C2semidirect
8. C31×#2122C2semidirect
9. C31×#2120C2semidirect
12. C31×H(3,𝔽4)C22semidirect
17. C31×#551C22semidirect
43. C31×#354C22semidirect
44. C31×#352C22semidirect
45. C31×AΣL(1,𝔽16)C22semidirect
46. C31×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C31D4semidirect
60. C22×D4×C31D4semidirect
61. C23×C4×C31D4semidirect
68. C31×C4⋊Q8D4semidirect
89. C31×#123D4semidirect
111. C31×#120D4semidirect
112. C31×#120D4semidirect
128. C31×#117D4semidirect
129. C31×#117D4semidirect
130. C31×#117D4semidirect
258. #33555C31direct (N × H)
335. #3540C2×C31semidirect
336. #3027C2×C31semidirect
337. #3025C2×C31semidirect
338. #3022C2×C31semidirect
339. #2199C2×C31semidirect
340. #2197C2×C31semidirect
341. #2129C2×C31semidirect
342. #2122C2×C31semidirect
343. #2120C2×C31semidirect
380. H(3,𝔽4)C22×C31semidirect
385. #551C22×C31semidirect
411. #354C22×C31semidirect
412. #352C22×C31semidirect
413. AΣL(1,𝔽16)C22×C31semidirect
414. AΣL(1,𝔽16)C22×C31semidirect
435. C22×Q8D4×C31semidirect
436. C22×D4D4×C31semidirect
437. C23×C4D4×C31semidirect
444. C4⋊Q8D4×C31semidirect
465. #123D4×C31semidirect
487. #120D4×C31semidirect
488. #120D4×C31semidirect
504. #117D4×C31semidirect
505. #117D4×C31semidirect
506. #117D4×C31semidirect
518. C31#33555direct (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×#30272
C31×#30252
C31×#30222
C31×#21992
C31×#21972
C31×#21292
C31×#21222
C31×#21202
#3355531