Finite Group Databasebeta

← C31×#16662 #21473421

Subgroups — C31×#16662 #21473421

Order 7936.

1930 conjugacy classes of subgroups.

The subgroup lattice has 808 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
4C2×C31×#383C211yesmaximal, characteristic, complemented
5C31×#1442C211yesmaximal, characteristic, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1439C211yesmaximal, characteristic, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1438C212yesmaximal, 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×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C42×C31C2211yescharacteristic
26C31×#392—24no—
27C31×#390—24no—
28C31×#388—24no—
29C31×#383—24no—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2211yescharacteristic
39C25×C31C2311yescharacteristic
40C25×C31C2312yes—
41C22×D4×C31—24no—
42C22×D4×C31—24no—
43C22×D4×C31—24no—
44C22×D4×C31—22no—
45C22×D4×C31—24no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—42no—
49C22×D4×C31—42no—
50C22×D4×C31—42no—
51C22×D4×C31—42no—
52C22×D4×C31—42no—
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2312yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2312yes—
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—42no—
65C2×C4⋊C4×C31—42no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
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×C31—42no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—42no—
91C2×C22⋊C4×C31—42no—
92C2×C42×C31—22no—
93C2×C42×C31—22no—
94C2×C42×C31D414yescomplemented
95C31×#95—24no—
96C31×#95—24no—
97C31×#95—22no—
98C31×#95—22no—
99C31×#95—22no—
100C31×#95—42no—
101C31×#95—42no—
102C31×#95—42no—
103C31×#95D414yes—
104C24×C31—21no—
105C24×C31—22no—
106C24×C31—21no—
107C24×C31—22no—
108C24×C31—21no—
109C24×C31—21no—
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—21no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—21no—
128C24×C31#4112yes—
129C24×C31#4114yes—
130C24×C31C2411yescharacteristic
131C2×D4×C31—28no—
132C2×D4×C31—48no—
133C2×D4×C31—48no—
134C2×D4×C31—48no—
135C2×D4×C31—48no—
136C2×D4×C31—44no—
137C2×D4×C31—48no—
138C2×D4×C31—48no—
139C2×D4×C31—48no—
140C2×D4×C31—48no—
141C2×D4×C31—48no—
142C2×D4×C31—44no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
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—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—22no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—21no—
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—21no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31C2×D414yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D412yes—
193C22×C4×C31C2×D412yes—
194C22×C4×C31#4112yes—
195C22×C4×C31#4112yes—
196C4⋊C4×C31—44no—
197C4⋊C4×C31—44no—
198C22⋊C4×C31—28no—
199C22⋊C4×C31—48no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31—44no—
202C22⋊C4×C31—48no—
203C22⋊C4×C31—48no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—48no—
206C22⋊C4×C31—44no—
207C42×C31—28no—
208#16662C3111yesmaximal, characteristic, direct product factor, Sylow
209C23×C31—22no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—22no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—22no—
221C23×C31—41no—
222C23×C31—42no—
223C23×C31—41no—
224C23×C31—42no—
225C23×C31—42no—
226C23×C31—42no—
227C23×C31—41no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—42no—
235C23×C31—41no—
236C23×C31—42no—
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—41no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—41no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31C22×D411yescharacteristic
268C23×C31C22×D411yescharacteristic
269C23×C31C2×#4111yescharacteristic
270C23×C31C2×#4112yes—
271C23×C31C2×#4111yescharacteristic
272C23×C31C2×#4111yescharacteristic
273C23×C31H(5,𝔽2)12yes—
274C23×C31H(5,𝔽2)12yes—
275C23×C31H(5,𝔽2)12yes—
276C23×C31H(5,𝔽2)11yescharacteristic
277C23×C31H(5,𝔽2)11yescharacteristic
278D4×C31—416no—
279D4×C31—432no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
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—22no—
291C2×C4×C31—24no—
292C2×C4×C31—24no—
293C2×C4×C31—24no—
294C2×C4×C31—24no—
295C2×C4×C31—41no—
296C2×C4×C31—42no—
297C2×C4×C31—41no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—42no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—42no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
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—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×C4×C31#12114yes—
333C2×#392C2×C3111yescharacteristic
334C2×#390C2×C3111yescharacteristic, complemented
335C2×#388C2×C3111yescharacteristic, complemented
336C2×#383C2×C3111yescharacteristic, complemented
337#1442C2×C3111yescharacteristic, complemented
338#1440C2×C3112yescomplemented
339#1439C2×C3111yescharacteristic, complemented
340#1439C2×C3112yescomplemented
341#1438C2×C3112yescomplemented
342#1438C2×C3111yescharacteristic, complemented
343#1438C2×C3112yescomplemented
344C22×C31—42no—
345C22×C31—44no—
346C22×C31—42no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—42no—
350C22×C31—44no—
351C22×C31—44no—
352C22×C31—44no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—82no—
357C22×C31—81no—
358C22×C31—81no—
359C22×C31—82no—
360C22×C31—82no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—82no—
364C22×C31—82no—
365C22×C31—82no—
366C22×C31—82no—
367C22×C31—82no—
368C22×C31—82no—
369C22×C31—82no—
370C22×C31C2×#12111yescharacteristic
371C22×C31#52511yescharacteristic
372C22×C31#52511yescharacteristic
373C22×C31#53511yescharacteristic
374C22×C31#53511yescharacteristic
375C22×C31#53511yescharacteristic
376C22×C31#53511yescharacteristic
377C22×C31#53512yes—
378C22×C31#53812yes—
379C22×C31#53812yes—
380C22×C31#53812yes—
381C22×C31#53812yes—
382C22×C31#54012yes—
383C22×C31#54612yes—
384C22×C31#54611yescharacteristic
385C22×C31#55011yescharacteristic
386C22×C31#55112yes—
387C22×C31#55112yes—
388C22×C31#55312yes—
389C22×C31#55311yescharacteristic
390C22×C31#55511yescharacteristic
391C22×C31#56012yes—
392C22×C31#56012yes—
393C4×C31—24no—
394C4×C31—42no—
395C4×C31—42no—
396C4×C31—42no—
397C4×C31—44no—
398C4×C31—82no—
399C4×C31—81no—
400C4×C31—81no—
401C4×C31—82no—
402C23×D4C22×C3111yescharacteristic
403C23×D4C22×C3112yes—
404C22×C4⋊C4C22×C3111yescharacteristic
405C22×C4⋊C4C22×C3111yescharacteristic
406C22×C22⋊C4C22×C3111yescharacteristic
407C22×C22⋊C4C22×C3111yescharacteristic
408C22×C22⋊C4C22×C3112yes—
409C22×C22⋊C4C22×C3112yes—
410C22×C22⋊C4C22×C3112yes—
411C22×C22⋊C4C22×C3111yescharacteristic
412C22×C22⋊C4C22×C3112yes—
413C22×C22⋊C4C22×C3112yes—
414C22×C22⋊C4C22×C3112yes—
415C22×C42C22×C3111yescharacteristic
416#392—24no—
417#390—24no—
418#388—24no—
419#383—24no—
420C2×#95C22×C3111yescharacteristic
421C2×#95C22×C3112yes—
422C2×#95C22×C3112yes—
423C2×#95C22×C3111yescharacteristic
424C2×#95C22×C3111yescharacteristic
425C2×#95C22×C3112yes—
426C2×#95C22×C3112yes—
427C2×#95C22×C3112yes—
428C2×#95C22×C3111yescharacteristic
429C2×C31—84no—
430C2×C31—82no—
431C2×C31#241111yescharacteristic
432C2×C31#241411yescharacteristic
433C2×C31#259811yescharacteristic
434C2×C31#261911yescharacteristic
435C2×C31#263111yescharacteristic
436C2×C31#263111yescharacteristic
437C2×C31#268512yes—
438C2×C31#271412yes—
439C2×C31#274912yes—
440C2×C31#275612yes—
441C2×C31#281811yescharacteristic
442C25C23×C3111yescharacteristic
443C25C23×C3112yes—
444C22×D4—24no—
445C22×D4—24no—
446C22×D4—24no—
447C22×D4—22no—
448C22×D4—24no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—42no—
452C22×D4—42no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4—42no—
456C23×C4C23×C3111yescharacteristic
457C23×C4C23×C3112yes—
458C23×C4C23×C3112yes—
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3111yescharacteristic
462C23×C4C23×C3112yes—
463C23×C4C23×C3111yescharacteristic
464C23×C4C23×C3111yescharacteristic
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42D4×C3114yescomplemented
498#95—24no—
499#95—24no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—42no—
504#95—42no—
505#95—42no—
506#95D4×C3114yes—
507C31#1666211yescharacteristic, direct product factor, Sylow
508C24—21no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—21no—
532C24#41×C3112yes—
533C24#41×C3114yes—
534C24C24×C3111yescharacteristic
535C2×D4—28no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—48no—
539C2×D4—48no—
540C2×D4—44no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—44no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
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—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4C2×D4×C3114yes—
594C22×C4C2×D4×C3112yes—
595C22×C4C2×D4×C3112yes—
596C22×C4C2×D4×C3112yes—
597C22×C4C2×D4×C3112yes—
598C22×C4#41×C3112yes—
599C22×C4#41×C3112yes—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C22⋊C4—28no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—44no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—44no—
611C42—28no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—41no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—41no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—41no—
636C23—42no—
637C23—41no—
638C23—41no—
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—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23C22×D4×C3111yescharacteristic
671C23C22×D4×C3111yescharacteristic
672C23C2×#41×C3111yescharacteristic
673C23C2×#41×C3112yes—
674C23C2×#41×C3111yescharacteristic
675C23C2×#41×C3111yescharacteristic
676C23C31×H(5,𝔽2)12yes—
677C23C31×H(5,𝔽2)12yes—
678C23C31×H(5,𝔽2)12yes—
679C23C31×H(5,𝔽2)11yescharacteristic
680C23C31×H(5,𝔽2)11yescharacteristic
681D4—416no—
682D4—432no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
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—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C31×#12114yes—
736C22—42no—
737C22—44no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—81no—
749C22—82no—
750C22—82no—
751C22—81no—
752C22—81no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—81no—
762C22C2×C31×#12111yescharacteristic
763C22C31×#52511yescharacteristic
764C22C31×#52511yescharacteristic
765C22C31×#53511yescharacteristic
766C22C31×#53511yescharacteristic
767C22C31×#53512yes—
768C22C31×#53511yescharacteristic
769C22C31×#53511yescharacteristic
770C22C31×#53812yes—
771C22C31×#53812yes—
772C22C31×#53812yes—
773C22C31×#53812yes—
774C22C31×#54012yes—
775C22C31×#54612yes—
776C22C31×#54611yescharacteristic
777C22C31×#55011yescharacteristic
778C22C31×#55112yes—
779C22C31×#55112yes—
780C22C31×#55312yes—
781C22C31×#55311yescharacteristic
782C22C31×#55511yescharacteristic
783C22C31×#56012yes—
784C22C31×#56012yes—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—44no—
790C4—81no—
791C4—81no—
792C4—82no—
793C4—82no—
794C2—84no—
795C2—82no—
796C2C31×#241111yescharacteristic
797C2C31×#241411yescharacteristic
798C2C31×#259811yescharacteristic
799C2C31×#261911yescharacteristic
800C2C31×#263111yescharacteristic
801C2C31×#263111yescharacteristic
802C2C31×#268512yes—
803C2C31×#271412yes—
804C2C31×#274912yes—
805C2C31×#275612yes—
806C2C31×#281811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ 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. C2×C31×#383C2semidirect
5. C31×#1442C2semidirect
6. C31×#1440C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×#1438C2semidirect
94. C2×C42×C31D4semidirect
208. #16662C31direct (N × H)
334. C2×#390C2×C31semidirect
335. C2×#388C2×C31semidirect
336. C2×#383C2×C31semidirect
337. #1442C2×C31semidirect
338. #1440C2×C31semidirect
339. #1439C2×C31semidirect
340. #1439C2×C31semidirect
341. #1438C2×C31semidirect
342. #1438C2×C31semidirect
343. #1438C2×C31semidirect
497. C2×C42D4×C31semidirect
507. C31#16662direct (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
C2×C31×#3832
C31×#14422
C31×#14402
C31×#14392
C31×#14382
#1666231