Finite Group Databasebeta

← C31×#14623 #21471382

Subgroups — C31×#14623 #21471382

Order 7936.

1910 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic, complemented
3C2×C31×#388C211yesmaximal, characteristic, complemented
4C31×#1442C211yesmaximal, characteristic, complemented
5C31×#1440C212yesmaximal, complemented
6C31×#1439C211yesmaximal, characteristic, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1434C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C42×C31C2211yescharacteristic
26C31×#392C418yescomplemented
27C31×#390—24no—
28C31×#388—24no—
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C25×C31C2311yescharacteristic
39C25×C31C2312yes—
40C22×D4×C31—22no—
41C22×D4×C31—22no—
42C22×D4×C31—42no—
43C22×D4×C31—42no—
44C22×D4×C31—42no—
45C22×D4×C31—42no—
46C22×D4×C31—42no—
47C22×D4×C31—42no—
48C22×D4×C31—42no—
49C22×D4×C31—42no—
50C22×D4×C31C2×C414yes—
51C22×D4×C31C2×C418yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2312yes—
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2312yes—
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2312yes—
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—42no—
64C2×C4⋊C4×C31—42no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
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×C31—42no—
80C2×C22⋊C4×C31—42no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31C2×C414yes—
89C2×C22⋊C4×C31C2×C418yes—
90C2×C42×C31—42no—
91C2×C42×C31D414yescomplemented
92C31×#95—22no—
93C31×#95—22no—
94C31×#95—22no—
95C31×#95—42no—
96C31×#95—42no—
97C31×#95—42no—
98C31×#95—42no—
99C31×#95—42no—
100C31×#95C2×C414yes—
101C24×C31—21no—
102C24×C31—22no—
103C24×C31—21no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—22no—
108C24×C31—21no—
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—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31—21no—
124C24×C31—22no—
125C24×C31C22×C412yes—
126C24×C31C22×C414yes—
127C24×C31C2411yescharacteristic
128C2×D4×C31—28no—
129C2×D4×C31—48no—
130C2×D4×C31—48no—
131C2×D4×C31—48no—
132C2×D4×C31—48no—
133C2×D4×C31—44no—
134C2×D4×C31—44no—
135C2×D4×C31—48no—
136C2×D4×C31—48no—
137C2×D4×C31—48no—
138C2×D4×C31—48no—
139C2×D4×C31—48no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
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—22no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—21no—
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—21no—
177C22×C4×C31—21no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—21no—
184C22×C4×C31C22×C414yes—
185C22×C4×C31C22×C412yes—
186C22×C4×C31C22×C412yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2×D412yes—
190C22×C4×C31#4112yes—
191C4⋊C4×C31—44no—
192C4⋊C4×C31—44no—
193C22⋊C4×C31—28no—
194C22⋊C4×C31—48no—
195C22⋊C4×C31—44no—
196C22⋊C4×C31—48no—
197C22⋊C4×C31—48no—
198C22⋊C4×C31—44no—
199C22⋊C4×C31—48no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31—48no—
202C42×C31—44no—
203#14623C3111yesmaximal, characteristic, direct product factor, Sylow
204C23×C31—22no—
205C23×C31—24no—
206C23×C31—24no—
207C23×C31—24no—
208C23×C31—22no—
209C23×C31—24no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—22no—
215C23×C31—24no—
216C23×C31—41no—
217C23×C31—42no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31—41no—
221C23×C31—42no—
222C23×C31—41no—
223C23×C31—41no—
224C23×C31—41no—
225C23×C31—42no—
226C23×C31—41no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—41no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—41no—
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—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—42no—
261C23×C31—42no—
262C23×C31C23×C411yescharacteristic
263C23×C31C22×D411yescharacteristic
264C23×C31C2×#4111yescharacteristic
265C23×C31H(5,𝔽2)12yes—
266C23×C31H(5,𝔽2)12yes—
267C23×C31H(5,𝔽2)12yes—
268C23×C31H(5,𝔽2)12yes—
269C23×C31H(5,𝔽2)11yescharacteristic
270C23×C31H(5,𝔽2)11yescharacteristic
271C23×C31H(5,𝔽2)11yescharacteristic
272C23×C312−1+411yescharacteristic
273D4×C31—416no—
274D4×C31—432no—
275C2×C4×C31—24no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—24no—
279C2×C4×C31—22no—
280C2×C4×C31—24no—
281C2×C4×C31—24no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—41no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—41no—
305C2×C4×C31—42no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
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×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×C31C4×D414yes—
326C2×#392C2×C3111yescharacteristic
327C2×#390C2×C3111yescharacteristic, complemented
328C2×#388C2×C3111yescharacteristic, complemented
329#1442C2×C3111yescharacteristic, complemented
330#1440C2×C3112yescomplemented
331#1439C2×C3111yescharacteristic, complemented
332#1439C2×C3112yescomplemented
333#1438C2×C3112yescomplemented
334#1438C2×C3112yescomplemented
335#1438C2×C3111yescharacteristic, complemented
336#1434C2×C3111yescharacteristic, complemented
337C22×C31—44no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—44no—
341C22×C31—42no—
342C22×C31—44no—
343C22×C31—44no—
344C22×C31—44no—
345C22×C31—44no—
346C22×C31—44no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—82no—
350C22×C31—81no—
351C22×C31—81no—
352C22×C31—82no—
353C22×C31—82no—
354C22×C31—82no—
355C22×C31—82no—
356C22×C31—82no—
357C22×C31—82no—
358C22×C31—82no—
359C22×C31—81no—
360C22×C31—82no—
361C22×C31—81no—
362C22×C31—82no—
363C22×C31C2×C4×D411yescharacteristic
364C22×C31#51812yes—
365C22×C31#51811yescharacteristic
366C22×C31#51812yes—
367C22×C31#52011yescharacteristic
368C22×C31#53411yescharacteristic
369C22×C31#53511yescharacteristic
370C22×C31#53511yescharacteristic
371C22×C31#53511yescharacteristic
372C22×C31#53511yescharacteristic
373C22×C31#53711yescharacteristic
374C22×C31#53812yes—
375C22×C31#54011yescharacteristic
376C22×C31#54012yes—
377C22×C31#54211yescharacteristic
378C22×C31#56012yes—
379C22×C31#56012yes—
380C22×C31#56012yes—
381C22×C31#56012yes—
382C22×C31#56012yes—
383C22×C31H(3,𝔽4)12yes—
384C22×C31#56212yes—
385C22×C31#56212yes—
386C4×C31—24no—
387C4×C31—42no—
388C4×C31—44no—
389C4×C31—42no—
390C4×C31—42no—
391C4×C31—82no—
392C4×C31—81no—
393C4×C31—82no—
394C4×C31—81no—
395C23×D4C22×C3111yescharacteristic
396C23×D4C22×C3112yes—
397C22×C4⋊C4C22×C3111yescharacteristic
398C22×C4⋊C4C22×C3111yescharacteristic
399C22×C22⋊C4C22×C3111yescharacteristic
400C22×C22⋊C4C22×C3111yescharacteristic
401C22×C22⋊C4C22×C3111yescharacteristic
402C22×C22⋊C4C22×C3112yes—
403C22×C22⋊C4C22×C3112yes—
404C22×C22⋊C4C22×C3112yes—
405C22×C22⋊C4C22×C3112yes—
406C22×C22⋊C4C22×C3112yes—
407C22×C22⋊C4C22×C3112yes—
408C22×C42C22×C3111yescharacteristic
409#392C4×C3118yescomplemented
410#390—24no—
411#388—24no—
412C2×#95C22×C3111yescharacteristic
413C2×#95C22×C3111yescharacteristic
414C2×#95C22×C3111yescharacteristic
415C2×#95C22×C3112yes—
416C2×#95C22×C3112yes—
417C2×#95C22×C3112yes—
418C2×#95C22×C3112yes—
419C2×#95C22×C3112yes—
420C2×#95C22×C3111yescharacteristic
421C2×C31—84no—
422C2×C31—82no—
423C2×C31#232111yescharacteristic
424C2×C31#232411yescharacteristic
425C2×C31#232811yescharacteristic
426C2×C31#237512yes—
427C2×C31#237712yes—
428C2×C31#281311yescharacteristic
429C2×C31#281511yescharacteristic
430C2×C31#281811yescharacteristic
431C2×C31#281911yescharacteristic
432C2×C31#282812yes—
433C2×C31#282912yes—
434C25C23×C3111yescharacteristic
435C25C23×C3112yes—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—42no—
439C22×D4—42no—
440C22×D4—42no—
441C22×D4—42no—
442C22×D4—42no—
443C22×D4—42no—
444C22×D4—42no—
445C22×D4—42no—
446C22×D4C2×C4×C3114yes—
447C22×D4C2×C4×C3118yes—
448C23×C4C23×C3111yescharacteristic
449C23×C4C23×C3112yes—
450C23×C4C23×C3111yescharacteristic
451C23×C4C23×C3112yes—
452C23×C4C23×C3111yescharacteristic
453C23×C4C23×C3112yes—
454C23×C4C23×C3111yescharacteristic
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
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×C3114yes—
485C2×C22⋊C4C2×C4×C3118yes—
486C2×C42—42no—
487C2×C42D4×C3114yescomplemented
488#95—22no—
489#95—22no—
490#95—22no—
491#95—42no—
492#95—42no—
493#95—42no—
494#95—42no—
495#95—42no—
496#95C2×C4×C3114yes—
497C31#1462311yescharacteristic, direct product factor, Sylow
498C24—21no—
499C24—22no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—22no—
522C24C22×C4×C3112yes—
523C24C22×C4×C3114yes—
524C24C24×C3111yescharacteristic
525C2×D4—28no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—48no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
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—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
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—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4C22×C4×C3114yes—
582C22×C4C22×C4×C3112yes—
583C22×C4C22×C4×C3112yes—
584C22×C4C2×D4×C3112yes—
585C22×C4C2×D4×C3112yes—
586C22×C4C2×D4×C3112yes—
587C22×C4#41×C3112yes—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C22⋊C4—28no—
591C22⋊C4—48no—
592C22⋊C4—44no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—44no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C42—44no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—41no—
619C23—41no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23C23×C4×C3111yescharacteristic
659C23C22×D4×C3111yescharacteristic
660C23C2×#41×C3111yescharacteristic
661C23C31×H(5,𝔽2)12yes—
662C23C31×H(5,𝔽2)12yes—
663C23C31×H(5,𝔽2)12yes—
664C23C31×H(5,𝔽2)12yes—
665C23C31×H(5,𝔽2)11yescharacteristic
666C23C31×H(5,𝔽2)11yescharacteristic
667C23C31×H(5,𝔽2)11yescharacteristic
668C23C31×2−1+411yescharacteristic
669D4—416no—
670D4—432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
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—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4C4×D4×C3114yes—
722C22—44no—
723C22—42no—
724C22—42no—
725C22—44no—
726C22—42no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—81no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22—81no—
743C22—82no—
744C22—81no—
745C22—82no—
746C22—82no—
747C22—81no—
748C22C2×C4×D4×C3111yescharacteristic
749C22C31×#51812yes—
750C22C31×#51811yescharacteristic
751C22C31×#51812yes—
752C22C31×#52011yescharacteristic
753C22C31×#53411yescharacteristic
754C22C31×#53511yescharacteristic
755C22C31×#53511yescharacteristic
756C22C31×#53511yescharacteristic
757C22C31×#53511yescharacteristic
758C22C31×#53711yescharacteristic
759C22C31×#53812yes—
760C22C31×#54011yescharacteristic
761C22C31×#54012yes—
762C22C31×#54211yescharacteristic
763C22C31×#56012yes—
764C22C31×#56012yes—
765C22C31×#56012yes—
766C22C31×#56012yes—
767C22C31×#56012yes—
768C22C31×H(3,𝔽4)12yes—
769C22C31×#56212yes—
770C22C31×#56212yes—
771C4—24no—
772C4—42no—
773C4—44no—
774C4—42no—
775C4—42no—
776C4—81no—
777C4—82no—
778C4—81no—
779C4—82no—
780C2—84no—
781C2—82no—
782C2C31×#232111yescharacteristic
783C2C31×#232411yescharacteristic
784C2C31×#232811yescharacteristic
785C2C31×#237512yes—
786C2C31×#237712yes—
787C2C31×#281311yescharacteristic
788C2C31×#281511yescharacteristic
789C2C31×#281811yescharacteristic
790C2C31×#281911yescharacteristic
791C2C31×#282812yes—
792C2C31×#282912yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#390C2semidirect
3. C2×C31×#388C2semidirect
4. C31×#1442C2semidirect
5. C31×#1440C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×#1434C2semidirect
26. C31×#392C4semidirect
91. C2×C42×C31D4semidirect
203. #14623C31direct (N × H)
327. C2×#390C2×C31semidirect
328. C2×#388C2×C31semidirect
329. #1442C2×C31semidirect
330. #1440C2×C31semidirect
331. #1439C2×C31semidirect
332. #1439C2×C31semidirect
333. #1438C2×C31semidirect
334. #1438C2×C31semidirect
335. #1438C2×C31semidirect
336. #1434C2×C31semidirect
409. #392C4×C31semidirect
487. C2×C42D4×C31semidirect
497. C31#14623direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C31×#14422
C31×#14402
C31×#14392
C31×#14382
C31×#14342
#1462331