Finite Group Databasebeta

← C31×#14365 #21471124

Subgroups — C31×#14365 #21471124

Order 7936.

2854 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#388C212yesmaximal, complemented
2C2×C31×#379C212yesmaximal
3C2×C31×#379C211yesmaximal, characteristic
4C31×#1440C212yesmaximal, complemented
5C31×#1439C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1437C211yesmaximal, characteristic, complemented
8C31×#1437C211yesmaximal, characteristic, complemented
9C31×#1437C212yesmaximal, complemented
10C26×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2212yescomplemented
12C22×C22⋊C4×C31C2212yes—
13C22×C22⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31C2211yescharacteristic, complemented
23C22×C42×C31C2211yescharacteristic, complemented
24C31×#388—28no—
25C31×#379—28no—
26C31×#379C418yescomplemented
27C2×C31×#95C2212yescomplemented
28C2×C31×#95C2212yescomplemented
29C2×C31×#95C2212yescomplemented
30C2×C31×#95C2211yescharacteristic, complemented
31C2×C31×#95C2212yescomplemented
32C2×C31×#95C2211yescharacteristic, complemented
33C2×C31×#95C2212yescomplemented
34C25×C31—24no—
35C25×C31—24no—
36C25×C31—24no—
37C25×C31—41no—
38C25×C31—41no—
39C25×C31—42no—
40C25×C31—42no—
41C25×C31—42no—
42C25×C31C2×C414yes—
43C25×C31C2312yes—
44C25×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—42no—
54C2×C4⋊C4×C31—42no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—24no—
57C2×C22⋊C4×C31—24no—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—24no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—42no—
67C2×C22⋊C4×C31—41no—
68C2×C22⋊C4×C31—41no—
69C2×C22⋊C4×C31—42no—
70C2×C22⋊C4×C31—42no—
71C2×C22⋊C4×C31—42no—
72C2×C22⋊C4×C31—42no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—42no—
75C2×C22⋊C4×C31—42no—
76C2×C22⋊C4×C31—42no—
77C2×C22⋊C4×C31—42no—
78C2×C22⋊C4×C31—42no—
79C2×C22⋊C4×C31C2×C418yes—
80C2×C22⋊C4×C31C2×C414yes—
81C2×C22⋊C4×C31C2×C414yes—
82C2×C22⋊C4×C31C2×C418yes—
83C2×C22⋊C4×C31D418yes—
84C2×C42×C31—24no—
85C2×C42×C31—41no—
86C2×C42×C31—42no—
87C2×C42×C31—41no—
88C31×#95—24no—
89C31×#95—24no—
90C31×#95—42no—
91C31×#95—42no—
92C31×#95—41no—
93C31×#95—41no—
94C31×#95—42no—
95C24×C31—22no—
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—21no—
103C24×C31—21no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—22no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—28no—
115C24×C31—216no—
116C24×C31—44no—
117C24×C31—48no—
118C24×C31—44no—
119C24×C31—44no—
120C24×C31—48no—
121C24×C31—48no—
122C24×C31—48no—
123C24×C31—48no—
124C24×C31—48no—
125C24×C31—44no—
126C24×C31—48no—
127C24×C31—48no—
128C24×C31—48no—
129C24×C31—48no—
130C24×C31—48no—
131C24×C31—48no—
132C24×C31—48no—
133C24×C31—44no—
134C24×C31—44no—
135C24×C31C22×C412yes—
136C24×C31C22×C414yes—
137C24×C31C2×D414yes—
138C24×C31#4114yes—
139C24×C31#4114yes—
140C24×C31C2411yescharacteristic
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—21no—
152C22×C4×C31—22no—
153C22×C4×C31—21no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31C22×C412yes—
182C22×C4×C31C22×C414yes—
183C22×C4×C31C22×C412yes—
184C22×C4×C31C2×D414yes—
185C22×C4×C31C2×D414yes—
186C4⋊C4×C31—48no—
187C22⋊C4×C31—216no—
188C22⋊C4×C31—44no—
189C22⋊C4×C31—48no—
190C22⋊C4×C31—44no—
191C22⋊C4×C31—48no—
192C22⋊C4×C31—48no—
193C22⋊C4×C31—48no—
194C22⋊C4×C31—48no—
195C22⋊C4×C31—48no—
196C22⋊C4×C31—48no—
197C42×C31—44no—
198C42×C31—44no—
199#14365C3111yesmaximal, characteristic, direct product factor, Sylow
200C23×C31—24no—
201C23×C31—24no—
202C23×C31—24no—
203C23×C31—22no—
204C23×C31—22no—
205C23×C31—24no—
206C23×C31—24no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—24no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—432no—
229C23×C31—416no—
230C23×C31—416no—
231C23×C31—432no—
232C23×C31—416no—
233C23×C31—432no—
234C23×C31—432no—
235C23×C31—432no—
236C23×C31—432no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—42no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—41no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—41no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—41no—
261C23×C31—42no—
262C23×C31—41no—
263C23×C31#11714yes—
264C23×C31C4×D418yes—
265C23×C31C23×C411yescharacteristic
266C23×C31C22×D412yes—
267C23×C31C2×#4112yes—
268C23×C31C2×#4112yes—
269C23×C31H(5,𝔽2)12yes—
270C23×C31H(5,𝔽2)12yes—
271C23×C31H(5,𝔽2)12yes—
272C23×C31H(5,𝔽2)11yescharacteristic
273C23×C31H(5,𝔽2)11yescharacteristic
274C2×C4×C31—24no—
275C2×C4×C31—24no—
276C2×C4×C31—24no—
277C2×C4×C31—24no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—24no—
281C2×C4×C31—24no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—24no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—41no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—41no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—41no—
302C2×C4×C31—42no—
303C2×C4×C31—41no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×#388C2×C3112yescomplemented
320C2×#379C2×C3112yes—
321C2×#379C2×C3111yescharacteristic
322#1440C2×C3112yescomplemented
323#1439C2×C3112yescomplemented
324#1439C2×C3112yescomplemented
325#1437C2×C3111yescharacteristic, complemented
326#1437C2×C3111yescharacteristic, complemented
327#1437C2×C3112yescomplemented
328C22×C31—24no—
329C22×C31—28no—
330C22×C31—28no—
331C22×C31—28no—
332C22×C31—28no—
333C22×C31—464no—
334C22×C31—44no—
335C22×C31—44no—
336C22×C31—44no—
337C22×C31—44no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—44no—
341C22×C31—44no—
342C22×C31—44no—
343C22×C31—44no—
344C22×C31—44no—
345C22×C31—44no—
346C22×C31—44no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—44no—
350C22×C31—44no—
351C22×C31—44no—
352C22×C31—44no—
353C22×C31C2×#11711yescharacteristic
354C22×C31C2×C4×D412yes—
355C22×C31#51811yescharacteristic
356C22×C31#51811yescharacteristic
357C22×C31#51812yes—
358C22×C31#53412yes—
359C22×C31#53512yes—
360C22×C31#53812yes—
361C22×C31#53812yes—
362C22×C31#53812yes—
363C22×C31#53812yes—
364C22×C31D4211yescharacteristic
365C22×C31#54612yes—
366C22×C31#54612yes—
367C22×C31#54612yes—
368C22×C31#55112yes—
369C22×C31#55112yes—
370C22×C31#55111yescharacteristic
371C22×C31#56012yes—
372C22×C31#56011yescharacteristic
373C22×C31H(3,𝔽4)11yescharacteristic
374C4×C31—44no—
375C4×C31—42no—
376C4×C31—42no—
377C4×C31—44no—
378C4×C31—44no—
379C4×C31—82no—
380C4×C31—82no—
381C26C22×C3111yescharacteristic
382C22×C4⋊C4C22×C3112yescomplemented
383C22×C22⋊C4C22×C3112yes—
384C22×C22⋊C4C22×C3112yes—
385C22×C22⋊C4C22×C3112yes—
386C22×C22⋊C4C22×C3112yes—
387C22×C22⋊C4C22×C3112yes—
388C22×C22⋊C4C22×C3112yes—
389C22×C22⋊C4C22×C3111yescharacteristic
390C22×C22⋊C4C22×C3112yes—
391C22×C22⋊C4C22×C3111yescharacteristic
392C22×C22⋊C4C22×C3112yes—
393C22×C42C22×C3111yescharacteristic, complemented
394C22×C42C22×C3111yescharacteristic, complemented
395#388—28no—
396#379—28no—
397#379C4×C3118yescomplemented
398C2×#95C22×C3112yescomplemented
399C2×#95C22×C3112yescomplemented
400C2×#95C22×C3112yescomplemented
401C2×#95C22×C3111yescharacteristic, complemented
402C2×#95C22×C3112yescomplemented
403C2×#95C22×C3111yescharacteristic, complemented
404C2×#95C22×C3112yescomplemented
405C2×C31—44no—
406C2×C31—48no—
407C2×C31#231211yescharacteristic
408C2×C31#232112yes—
409C2×C31#234212yes—
410C2×C31#235811yescharacteristic
411C2×C31#237511yescharacteristic
412C2×C31#267812yes—
413C2×C31#268412yes—
414C2×C31#268512yes—
415C2×C31#273512yes—
416C25—24no—
417C25—24no—
418C25—24no—
419C25—41no—
420C25—41no—
421C25—42no—
422C25—42no—
423C25—42no—
424C25C2×C4×C3114yes—
425C25C23×C3112yes—
426C25C23×C3111yescharacteristic
427C23×C4C23×C3112yes—
428C23×C4C23×C3112yes—
429C23×C4C23×C3112yes—
430C23×C4C23×C3111yescharacteristic
431C23×C4C23×C3111yescharacteristic
432C23×C4C23×C3112yes—
433C23×C4C23×C3112yes—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4—41no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4C2×C4×C3118yes—
462C2×C22⋊C4C2×C4×C3114yes—
463C2×C22⋊C4C2×C4×C3114yes—
464C2×C22⋊C4C2×C4×C3118yes—
465C2×C22⋊C4D4×C3118yes—
466C2×C42—24no—
467C2×C42—41no—
468C2×C42—42no—
469C2×C42—41no—
470#95—24no—
471#95—24no—
472#95—42no—
473#95—42no—
474#95—41no—
475#95—41no—
476#95—42no—
477C31#1436511yescharacteristic, direct product factor, Sylow
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—28no—
498C24—216no—
499C24—44no—
500C24—48no—
501C24—44no—
502C24—44no—
503C24—48no—
504C24—48no—
505C24—48no—
506C24—48no—
507C24—48no—
508C24—44no—
509C24—48no—
510C24—48no—
511C24—48no—
512C24—48no—
513C24—48no—
514C24—48no—
515C24—48no—
516C24—44no—
517C24—44no—
518C24C22×C4×C3112yes—
519C24C22×C4×C3114yes—
520C24C2×D4×C3114yes—
521C24#41×C3114yes—
522C24#41×C3114yes—
523C24C24×C3111yescharacteristic
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4C22×C4×C3112yes—
565C22×C4C22×C4×C3114yes—
566C22×C4C22×C4×C3112yes—
567C22×C4C2×D4×C3114yes—
568C22×C4C2×D4×C3114yes—
569C4⋊C4—48no—
570C22⋊C4—216no—
571C22⋊C4—44no—
572C22⋊C4—48no—
573C22⋊C4—44no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C42—44no—
581C42—44no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—432no—
611C23—416no—
612C23—416no—
613C23—432no—
614C23—416no—
615C23—432no—
616C23—432no—
617C23—432no—
618C23—432no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—41no—
643C23—42no—
644C23—41no—
645C23C31×#11714yes—
646C23C4×D4×C3118yes—
647C23C23×C4×C3111yescharacteristic
648C23C22×D4×C3112yes—
649C23C2×#41×C3112yes—
650C23C2×#41×C3112yes—
651C23C31×H(5,𝔽2)12yes—
652C23C31×H(5,𝔽2)12yes—
653C23C31×H(5,𝔽2)12yes—
654C23C31×H(5,𝔽2)11yescharacteristic
655C23C31×H(5,𝔽2)11yescharacteristic
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C22—24no—
702C22—28no—
703C22—28no—
704C22—28no—
705C22—28no—
706C22—464no—
707C22—44no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—42no—
712C22—42no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22C2×C31×#11711yescharacteristic
727C22C2×C4×D4×C3112yes—
728C22C31×#51811yescharacteristic
729C22C31×#51811yescharacteristic
730C22C31×#51812yes—
731C22C31×#53412yes—
732C22C31×#53512yes—
733C22C31×#53812yes—
734C22C31×#53812yes—
735C22C31×#53812yes—
736C22C31×#53812yes—
737C22D42×C3111yescharacteristic
738C22C31×#54612yes—
739C22C31×#54612yes—
740C22C31×#54612yes—
741C22C31×#55112yes—
742C22C31×#55112yes—
743C22C31×#55111yescharacteristic
744C22C31×#56012yes—
745C22C31×#56011yescharacteristic
746C22C31×H(3,𝔽4)11yescharacteristic
747C4—44no—
748C4—42no—
749C4—42no—
750C4—44no—
751C4—44no—
752C4—82no—
753C4—82no—
754C2—44no—
755C2—48no—
756C2C31×#231211yescharacteristic
757C2C31×#232112yes—
758C2C31×#234212yes—
759C2C31×#235811yescharacteristic
760C2C31×#237511yescharacteristic
761C2C31×#267812yes—
762C2C31×#268412yes—
763C2C31×#268512yes—
764C2C31×#273512yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#388C2semidirect
4. C31×#1440C2semidirect
5. C31×#1439C2semidirect
6. C31×#1439C2semidirect
7. C31×#1437C2semidirect
8. C31×#1437C2semidirect
9. C31×#1437C2semidirect
11. C22×C4⋊C4×C31C22semidirect
22. C22×C42×C31C22semidirect
23. C22×C42×C31C22semidirect
26. C31×#379C4semidirect
27. C2×C31×#95C22semidirect
28. C2×C31×#95C22semidirect
29. C2×C31×#95C22semidirect
30. C2×C31×#95C22semidirect
31. C2×C31×#95C22semidirect
32. C2×C31×#95C22semidirect
33. C2×C31×#95C22semidirect
199. #14365C31direct (N × H)
319. C2×#388C2×C31semidirect
322. #1440C2×C31semidirect
323. #1439C2×C31semidirect
324. #1439C2×C31semidirect
325. #1437C2×C31semidirect
326. #1437C2×C31semidirect
327. #1437C2×C31semidirect
382. C22×C4⋊C4C22×C31semidirect
393. C22×C42C22×C31semidirect
394. C22×C42C22×C31semidirect
397. #379C4×C31semidirect
398. C2×#95C22×C31semidirect
399. C2×#95C22×C31semidirect
400. C2×#95C22×C31semidirect
401. C2×#95C22×C31semidirect
402. C2×#95C22×C31semidirect
403. C2×#95C22×C31semidirect
404. C2×#95C22×C31semidirect
477. C31#14365direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3882
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14372
#1436531