Finite Group Databasebeta

← C31×#14366 #21471125

Subgroups — C31×#14366 #21471125

Order 7936.

2854 conjugacy classes of subgroups.

The subgroup lattice has 804 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×#1439C211yesmaximal, characteristic, complemented
6C31×#1439C211yesmaximal, characteristic, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1437C212yesmaximal, complemented
9C31×#1437C212yesmaximal, complemented
10C26×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2211yescharacteristic, complemented
12C22×C4⋊C4×C31C2211yescharacteristic, complemented
13C22×C22⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C42×C31C2212yescomplemented
24C31×#388—28no—
25C31×#379—28no—
26C31×#379C418yescomplemented
27C2×C31×#95C2212yescomplemented
28C2×C31×#95C2212yescomplemented
29C2×C31×#95C2211yescharacteristic, complemented
30C2×C31×#95C2212yescomplemented
31C2×C31×#95C2212yescomplemented
32C2×C31×#95C2212yescomplemented
33C2×C31×#95C2211yescharacteristic, complemented
34C25×C31—24no—
35C25×C31—22no—
36C25×C31—22no—
37C25×C31—24no—
38C25×C31—41no—
39C25×C31—41no—
40C25×C31—42no—
41C25×C31—42no—
42C25×C31—41no—
43C25×C31—41no—
44C25×C31C2×C414yes—
45C25×C31C2312yes—
46C25×C31C2311yescharacteristic
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2311yescharacteristic
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2312yes—
53C23×C4×C31C2312yes—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—41no—
56C2×C4⋊C4×C31—42no—
57C2×C4⋊C4×C31—41no—
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—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—41no—
70C2×C22⋊C4×C31—41no—
71C2×C22⋊C4×C31—42no—
72C2×C22⋊C4×C31—42no—
73C2×C22⋊C4×C31—41no—
74C2×C22⋊C4×C31—41no—
75C2×C22⋊C4×C31—42no—
76C2×C22⋊C4×C31—42no—
77C2×C22⋊C4×C31—42no—
78C2×C22⋊C4×C31—42no—
79C2×C22⋊C4×C31—42no—
80C2×C22⋊C4×C31—42no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31C2×C418yes—
84C2×C22⋊C4×C31C2×C414yes—
85C2×C22⋊C4×C31C2×C414yes—
86C2×C22⋊C4×C31C2×C418yes—
87C2×C22⋊C4×C31D418yes—
88C2×C42×C31—24no—
89C2×C42×C31—42no—
90C2×C42×C31—42no—
91C31×#95—24no—
92C31×#95—24no—
93C31×#95—41no—
94C31×#95—42no—
95C31×#95—42no—
96C31×#95—42no—
97C31×#95—41no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—22no—
103C24×C31—22no—
104C24×C31—21no—
105C24×C31—21no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—28no—
119C24×C31—216no—
120C24×C31—44no—
121C24×C31—48no—
122C24×C31—44no—
123C24×C31—44no—
124C24×C31—48no—
125C24×C31—48no—
126C24×C31—48no—
127C24×C31—48no—
128C24×C31—48no—
129C24×C31—44no—
130C24×C31—48no—
131C24×C31—48no—
132C24×C31—44no—
133C24×C31—44no—
134C24×C31—44no—
135C24×C31—44no—
136C24×C31—48no—
137C24×C31—48no—
138C24×C31—44no—
139C24×C31—48no—
140C24×C31—44no—
141C24×C31C22×C412yes—
142C24×C31C22×C414yes—
143C24×C31C2×D414yes—
144C24×C31#4112yes—
145C24×C31#4112yes—
146C24×C31#4114yes—
147C24×C31C2411yescharacteristic
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—22no—
160C22×C4×C31—21no—
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—21no—
171C22×C4×C31—22no—
172C22×C4×C31—21no—
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×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31C22×C412yes—
189C22×C4×C31C22×C414yes—
190C22×C4×C31C22×C412yes—
191C22×C4×C31C2×D414yes—
192C22×C4×C31C2×D414yes—
193C4⋊C4×C31—44no—
194C4⋊C4×C31—44no—
195C22⋊C4×C31—216no—
196C22⋊C4×C31—44no—
197C22⋊C4×C31—48no—
198C22⋊C4×C31—44no—
199C22⋊C4×C31—48no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31—48no—
202C22⋊C4×C31—48no—
203C22⋊C4×C31—48no—
204C22⋊C4×C31—48no—
205C42×C31—48no—
206#14366C3111yesmaximal, characteristic, direct product factor, Sylow
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—24no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—24no—
233C23×C31—24no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—432no—
238C23×C31—416no—
239C23×C31—416no—
240C23×C31—432no—
241C23×C31—416no—
242C23×C31—416no—
243C23×C31—416no—
244C23×C31—432no—
245C23×C31—432no—
246C23×C31—416no—
247C23×C31—416no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—41no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—41no—
267C23×C31—42no—
268C23×C31—41no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—41no—
274C23×C31#11714yes—
275C23×C31C4×D418yes—
276C23×C31C23×C411yescharacteristic
277C23×C31C22×D412yes—
278C23×C31C2×#4111yescharacteristic
279C23×C31C2×#4111yescharacteristic
280C23×C31C2×#4112yes—
281C23×C31H(5,𝔽2)11yescharacteristic
282C23×C31H(5,𝔽2)12yes—
283C23×C31H(5,𝔽2)11yescharacteristic
284C23×C31H(5,𝔽2)12yes—
285C23×C31H(5,𝔽2)11yescharacteristic
286C23×C31H(5,𝔽2)11yescharacteristic
287C2×C4×C31—24no—
288C2×C4×C31—24no—
289C2×C4×C31—24no—
290C2×C4×C31—24no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—24no—
294C2×C4×C31—24no—
295C2×C4×C31—24no—
296C2×C4×C31—24no—
297C2×C4×C31—24no—
298C2×C4×C31—24no—
299C2×C4×C31—24no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—41no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—41no—
312C2×C4×C31—42no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×#388C2×C3112yescomplemented
333C2×#379C2×C3112yes—
334C2×#379C2×C3111yescharacteristic
335#1440C2×C3112yescomplemented
336#1439C2×C3111yescharacteristic, complemented
337#1439C2×C3111yescharacteristic, complemented
338#1439C2×C3112yescomplemented
339#1437C2×C3112yescomplemented
340#1437C2×C3112yescomplemented
341C22×C31—24no—
342C22×C31—28no—
343C22×C31—28no—
344C22×C31—28no—
345C22×C31—28no—
346C22×C31—464no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—44no—
350C22×C31—44no—
351C22×C31—42no—
352C22×C31—42no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—42no—
356C22×C31—44no—
357C22×C31—42no—
358C22×C31—44no—
359C22×C31—44no—
360C22×C31—44no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—42no—
365C22×C31—44no—
366C22×C31—42no—
367C22×C31—44no—
368C22×C31C2×#11711yescharacteristic
369C22×C31C2×C4×D412yes—
370C22×C31#51811yescharacteristic
371C22×C31#51811yescharacteristic
372C22×C31#51812yes—
373C22×C31#53412yes—
374C22×C31#53512yes—
375C22×C31#53811yescharacteristic
376C22×C31#53811yescharacteristic
377C22×C31#53811yescharacteristic
378C22×C31#53811yescharacteristic
379C22×C31#53812yes—
380C22×C31#53812yes—
381C22×C31D4211yescharacteristic
382C22×C31#54612yes—
383C22×C31#54612yes—
384C22×C31#54612yes—
385C22×C31#55112yes—
386C22×C31#55112yes—
387C22×C31#55111yescharacteristic
388C22×C31#56011yescharacteristic
389C22×C31#56012yes—
390C22×C31H(3,𝔽4)11yescharacteristic
391C4×C31—44no—
392C4×C31—42no—
393C4×C31—42no—
394C4×C31—44no—
395C4×C31—44no—
396C4×C31—82no—
397C4×C31—82no—
398C26C22×C3111yescharacteristic
399C22×C4⋊C4C22×C3111yescharacteristic, complemented
400C22×C4⋊C4C22×C3111yescharacteristic, complemented
401C22×C22⋊C4C22×C3112yes—
402C22×C22⋊C4C22×C3112yes—
403C22×C22⋊C4C22×C3112yes—
404C22×C22⋊C4C22×C3112yes—
405C22×C22⋊C4C22×C3112yes—
406C22×C22⋊C4C22×C3112yes—
407C22×C22⋊C4C22×C3111yescharacteristic
408C22×C22⋊C4C22×C3112yes—
409C22×C22⋊C4C22×C3111yescharacteristic
410C22×C22⋊C4C22×C3112yes—
411C22×C42C22×C3112yescomplemented
412#388—28no—
413#379—28no—
414#379C4×C3118yescomplemented
415C2×#95C22×C3112yescomplemented
416C2×#95C22×C3112yescomplemented
417C2×#95C22×C3111yescharacteristic, complemented
418C2×#95C22×C3112yescomplemented
419C2×#95C22×C3112yescomplemented
420C2×#95C22×C3112yescomplemented
421C2×#95C22×C3111yescharacteristic, complemented
422C2×C31—44no—
423C2×C31—48no—
424C2×C31#231211yescharacteristic
425C2×C31#232112yes—
426C2×C31#234212yes—
427C2×C31#235811yescharacteristic
428C2×C31#237511yescharacteristic
429C2×C31#266811yescharacteristic
430C2×C31#267011yescharacteristic
431C2×C31#268512yes—
432C2×C31#269712yes—
433C2×C31#273511yescharacteristic
434C2×C31#273611yescharacteristic
435C25—24no—
436C25—22no—
437C25—22no—
438C25—24no—
439C25—41no—
440C25—41no—
441C25—42no—
442C25—42no—
443C25—41no—
444C25—41no—
445C25C2×C4×C3114yes—
446C25C23×C3112yes—
447C25C23×C3111yescharacteristic
448C23×C4C23×C3112yes—
449C23×C4C23×C3112yes—
450C23×C4C23×C3111yescharacteristic
451C23×C4C23×C3111yescharacteristic
452C23×C4C23×C3112yes—
453C23×C4C23×C3112yes—
454C23×C4C23×C3112yes—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—41no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4—41no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—41no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4C2×C4×C3118yes—
485C2×C22⋊C4C2×C4×C3114yes—
486C2×C22⋊C4C2×C4×C3114yes—
487C2×C22⋊C4C2×C4×C3118yes—
488C2×C22⋊C4D4×C3118yes—
489C2×C42—24no—
490C2×C42—42no—
491C2×C42—42no—
492#95—24no—
493#95—24no—
494#95—41no—
495#95—42no—
496#95—42no—
497#95—42no—
498#95—41no—
499C31#1436611yescharacteristic, direct product factor, Sylow
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—28no—
521C24—216no—
522C24—44no—
523C24—48no—
524C24—44no—
525C24—44no—
526C24—48no—
527C24—48no—
528C24—48no—
529C24—48no—
530C24—48no—
531C24—44no—
532C24—48no—
533C24—48no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—48no—
539C24—48no—
540C24—44no—
541C24—48no—
542C24—44no—
543C24C22×C4×C3112yes—
544C24C22×C4×C3114yes—
545C24C2×D4×C3114yes—
546C24#41×C3112yes—
547C24#41×C3112yes—
548C24#41×C3114yes—
549C24C24×C3111yescharacteristic
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—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4C22×C4×C3112yes—
591C22×C4C22×C4×C3114yes—
592C22×C4C22×C4×C3112yes—
593C22×C4C2×D4×C3114yes—
594C22×C4C2×D4×C3114yes—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C22⋊C4—216no—
598C22⋊C4—44no—
599C22⋊C4—48no—
600C22⋊C4—44no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C42—48no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—432no—
639C23—416no—
640C23—416no—
641C23—432no—
642C23—416no—
643C23—416no—
644C23—416no—
645C23—432no—
646C23—432no—
647C23—416no—
648C23—416no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23C31×#11714yes—
676C23C4×D4×C3118yes—
677C23C23×C4×C3111yescharacteristic
678C23C22×D4×C3112yes—
679C23C2×#41×C3111yescharacteristic
680C23C2×#41×C3111yescharacteristic
681C23C2×#41×C3112yes—
682C23C31×H(5,𝔽2)11yescharacteristic
683C23C31×H(5,𝔽2)12yes—
684C23C31×H(5,𝔽2)11yescharacteristic
685C23C31×H(5,𝔽2)12yes—
686C23C31×H(5,𝔽2)11yescharacteristic
687C23C31×H(5,𝔽2)11yescharacteristic
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C22—24no—
734C22—28no—
735C22—28no—
736C22—28no—
737C22—28no—
738C22—464no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—42no—
745C22—44no—
746C22—44no—
747C22—42no—
748C22—44no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—44no—
760C22C2×C31×#11711yescharacteristic
761C22C2×C4×D4×C3112yes—
762C22C31×#51811yescharacteristic
763C22C31×#51811yescharacteristic
764C22C31×#51812yes—
765C22C31×#53412yes—
766C22C31×#53512yes—
767C22C31×#53811yescharacteristic
768C22C31×#53811yescharacteristic
769C22C31×#53811yescharacteristic
770C22C31×#53811yescharacteristic
771C22C31×#53812yes—
772C22C31×#53812yes—
773C22D42×C3111yescharacteristic
774C22C31×#54612yes—
775C22C31×#54612yes—
776C22C31×#54612yes—
777C22C31×#55112yes—
778C22C31×#55112yes—
779C22C31×#55111yescharacteristic
780C22C31×#56011yescharacteristic
781C22C31×#56012yes—
782C22C31×H(3,𝔽4)11yescharacteristic
783C4—44no—
784C4—42no—
785C4—42no—
786C4—44no—
787C4—44no—
788C4—82no—
789C4—82no—
790C2—44no—
791C2—48no—
792C2C31×#231211yescharacteristic
793C2C31×#232112yes—
794C2C31×#234212yes—
795C2C31×#235811yescharacteristic
796C2C31×#237511yescharacteristic
797C2C31×#266811yescharacteristic
798C2C31×#267011yescharacteristic
799C2C31×#268512yes—
800C2C31×#269712yes—
801C2C31×#273511yescharacteristic
802C2C31×#273611yescharacteristic
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×#1439C2semidirect
8. C31×#1437C2semidirect
9. C31×#1437C2semidirect
11. C22×C4⋊C4×C31C22semidirect
12. C22×C4⋊C4×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
206. #14366C31direct (N × H)
332. C2×#388C2×C31semidirect
335. #1440C2×C31semidirect
336. #1439C2×C31semidirect
337. #1439C2×C31semidirect
338. #1439C2×C31semidirect
339. #1437C2×C31semidirect
340. #1437C2×C31semidirect
399. C22×C4⋊C4C22×C31semidirect
400. C22×C4⋊C4C22×C31semidirect
411. C22×C42C22×C31semidirect
414. #379C4×C31semidirect
415. C2×#95C22×C31semidirect
416. C2×#95C22×C31semidirect
417. C2×#95C22×C31semidirect
418. C2×#95C22×C31semidirect
419. C2×#95C22×C31semidirect
420. C2×#95C22×C31semidirect
421. C2×#95C22×C31semidirect
499. C31#14366direct (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
#1436631