Finite Group Databasebeta

← C31×#16359 #21473118

Subgroups — C31×#16359 #21473118

Order 7936.

1902 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C2×C31×#398C211yesmaximal, characteristic, complemented
3C2×C31×#397C211yesmaximal, characteristic, complemented
4C2×C31×#380C211yesmaximal, characteristic, complemented
5C31×#1442C212yesmaximal, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1438C212yesmaximal
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C2×C31×#123—24no—
15C2×C31×#123—24no—
16C2×C31×#123—24no—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2212yes—
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C31×#398—24no—
30C31×#397—24no—
31C31×#380—24no—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C25×C31C2311yescharacteristic
42C25×C31C2311yescharacteristic
43C22×D4×C31—22no—
44C22×D4×C31—22no—
45C22×D4×C31—24no—
46C22×D4×C31—22no—
47C22×D4×C31—42no—
48C23×C4×C31—24no—
49C23×C4×C31—22no—
50C23×C4×C31—22no—
51C23×C4×C31—42no—
52C23×C4×C31D414yes—
53C23×C4×C31C2312yes—
54C23×C4×C31C2312yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2312yes—
61C23×C4×C31C2311yescharacteristic
62C31×#123—232no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—42no—
74C2×C4⋊C4×C31—42no—
75C2×C4⋊C4×C31—42no—
76C2×C4⋊C4×C31D414yes—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—42no—
91C2×C22⋊C4×C31—42no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31—42no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31—42no—
96C2×C22⋊C4×C31—42no—
97C2×C22⋊C4×C31D414yes—
98C31×#95—22no—
99C31×#95—24no—
100C31×#95—22no—
101C31×#95—24no—
102C31×#95—24no—
103C31×#95—24no—
104C31×#95—42no—
105C31×#95—42no—
106C31×#95—42no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—22no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—21no—
116C24×C31—21no—
117C24×C31—21no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—21no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31—22no—
124C24×C31—21no—
125C24×C31—22no—
126C24×C31C2×D412yes—
127C24×C31C2×D412yes—
128C24×C31#4114yes—
129C24×C31C2411yescharacteristic
130C2×D4×C31—28no—
131C2×D4×C31—48no—
132C2×D4×C31—48no—
133C2×D4×C31—44no—
134C2×D4×C31—44no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—28no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
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—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—28no—
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×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—44no—
185C22×C4×C31—48no—
186C22×C4×C31—48no—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2×D412yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D412yes—
193C22×C4×C31C2×D412yes—
194C22×C4×C31#4114yes—
195C4⋊C4×C31—28no—
196C4⋊C4×C31—28no—
197C4⋊C4×C31—44no—
198C4⋊C4×C31—48no—
199C4⋊C4×C31—44no—
200C22⋊C4×C31—28no—
201C22⋊C4×C31—28no—
202C22⋊C4×C31—28no—
203C22⋊C4×C31—48no—
204C22⋊C4×C31—48no—
205C22⋊C4×C31—48no—
206C22⋊C4×C31—48no—
207#16359C3111yesmaximal, characteristic, direct product factor, Sylow
208C23×C31—22no—
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—22no—
213C23×C31—22no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—41no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
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#12314yes—
254C23×C31C22×D411yescharacteristic
255C23×C31C22×D411yescharacteristic
256C23×C31C22×D411yescharacteristic
257C23×C31C2×#4112yes—
258C23×C31C2×#4112yes—
259C23×C31H(5,𝔽2)12yes—
260C23×C31H(5,𝔽2)11yescharacteristic
261C23×C31H(5,𝔽2)11yescharacteristic
262C23×C31H(5,𝔽2)11yescharacteristic
263C23×C312−1+412yes—
264C23×C312−1+411yescharacteristic
265D4×C31—416no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—24no—
269C2×C4×C31—24no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—24no—
279C2×C4×C31—24no—
280C2×C4×C31—24no—
281C2×C4×C31—24no—
282C2×C4×C31—24no—
283C2×C4×C31—416no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—42no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
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—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—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×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31#12014yes—
322C22×#123C2×C3111yescharacteristic
323C2×#398C2×C3111yescharacteristic, complemented
324C2×#397C2×C3111yescharacteristic, complemented
325C2×#380C2×C3111yescharacteristic, complemented
326#1442C2×C3112yescomplemented
327#1441C2×C3111yescharacteristic, complemented
328#1439C2×C3112yescomplemented
329#1439C2×C3112yescomplemented
330#1439C2×C3111yescharacteristic, complemented
331#1438C2×C3112yes—
332C22⋊#95C2×C3111yescharacteristic, complemented
333C22×C31—24no—
334C22×C31—24no—
335C22×C31—24no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—44no—
340C22×C31—44no—
341C22×C31—44no—
342C22×C31—44no—
343C22×C31—42no—
344C22×C31—42no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—44no—
348C22×C31—44no—
349C22×C31—81no—
350C22×C31—81no—
351C22×C31—82no—
352C22×C31—82no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31C2×#12011yescharacteristic
356C22×C31C2×#12311yescharacteristic
357C22×C31#53211yescharacteristic
358C22×C31#53411yescharacteristic
359C22×C31#53511yescharacteristic
360C22×C31#53511yescharacteristic
361C22×C31#53511yescharacteristic
362C22×C31#53611yescharacteristic
363C22×C31#53711yescharacteristic
364C22×C31#53711yescharacteristic
365C22×C31#53711yescharacteristic
366C22×C31#53812yes—
367C22×C31#53912yes—
368C22×C31#53912yes—
369C22×C31#54012yes—
370C22×C31#54612yes—
371C22×C31#54612yes—
372C22×C31#54712yes—
373C22×C31#54812yes—
374C22×C31#55112yes—
375C22×C31#55212yes—
376C22×C31#56212yes—
377C22×C31#56312yes—
378C4×C31—24no—
379C4×C31—42no—
380C4×C31—42no—
381C4×C31—42no—
382C4×C31—42no—
383C4×C31—44no—
384C4×C31—82no—
385C4×C31—82no—
386C4×C31—82no—
387C23×D4C22×C3111yescharacteristic
388C24×C4C22×C3111yescharacteristic
389C2×#123—24no—
390C2×#123—24no—
391C2×#123—24no—
392C22×C4⋊C4C22×C3111yescharacteristic
393C22×C4⋊C4C22×C3111yescharacteristic
394C22×C4⋊C4C22×C3111yescharacteristic
395C22×C4⋊C4C22×C3112yes—
396C22×C4⋊C4C22×C3111yescharacteristic
397C22×C22⋊C4C22×C3111yescharacteristic
398C22×C22⋊C4C22×C3111yescharacteristic
399C22×C22⋊C4C22×C3112yes—
400C22×C22⋊C4C22×C3111yescharacteristic
401C22×C22⋊C4C22×C3112yes—
402C22×C22⋊C4C22×C3112yes—
403C22×C22⋊C4C22×C3112yes—
404#398—24no—
405#397—24no—
406#380—24no—
407C2×#95C22×C3111yescharacteristic
408C2×#95C22×C3112yes—
409C2×#95C22×C3111yescharacteristic
410C2×#95C22×C3112yes—
411C2×#95C22×C3112yes—
412C2×#95C22×C3112yes—
413C2×#95C22×C3112yes—
414C2×#95C22×C3112yes—
415C2×#95C22×C3112yes—
416C2×C31—44no—
417C2×C31—82no—
418C2×C31#240511yescharacteristic
419C2×C31#243211yescharacteristic
420C2×C31#249811yescharacteristic
421C2×C31#261511yescharacteristic
422C2×C31#262311yescharacteristic
423C2×C31#266111yescharacteristic
424C2×C31#269512yes—
425C2×C31#269612yes—
426C2×C31#270612yes—
427C2×C31#270712yes—
428C2×C31#281411yescharacteristic
429C25C23×C3111yescharacteristic
430C25C23×C3111yescharacteristic
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—24no—
434C22×D4—22no—
435C22×D4—42no—
436C23×C4—24no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—42no—
440C23×C4D4×C3114yes—
441C23×C4C23×C3112yes—
442C23×C4C23×C3112yes—
443C23×C4C23×C3112yes—
444C23×C4C23×C3111yescharacteristic
445C23×C4C23×C3111yescharacteristic
446C23×C4C23×C3111yescharacteristic
447C23×C4C23×C3111yescharacteristic
448C23×C4C23×C3112yes—
449C23×C4C23×C3111yescharacteristic
450#123—232no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4D4×C3114yes—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
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⋊C4—42no—
485C2×C22⋊C4D4×C3114yes—
486#95—24no—
487#95—22no—
488#95—24no—
489#95—22no—
490#95—24no—
491#95—24no—
492#95—42no—
493#95—42no—
494#95—42no—
495C31#1635911yescharacteristic, direct product factor, Sylow
496C24—21no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—21no—
514C24—22no—
515C24C2×D4×C3112yes—
516C24C2×D4×C3112yes—
517C24#41×C3114yes—
518C24C24×C3111yescharacteristic
519C2×D4—28no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—44no—
523C2×D4—44no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—28no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—28no—
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×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—44no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4C2×D4×C3112yes—
577C22×C4C2×D4×C3112yes—
578C22×C4C2×D4×C3112yes—
579C22×C4C2×D4×C3112yes—
580C22×C4C2×D4×C3112yes—
581C22×C4C2×D4×C3112yes—
582C22×C4C2×D4×C3112yes—
583C22×C4#41×C3114yes—
584C4⋊C4—28no—
585C4⋊C4—28no—
586C4⋊C4—44no—
587C4⋊C4—48no—
588C4⋊C4—44no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23C31×#12314yes—
642C23C22×D4×C3111yescharacteristic
643C23C22×D4×C3111yescharacteristic
644C23C22×D4×C3111yescharacteristic
645C23C2×#41×C3112yes—
646C23C2×#41×C3112yes—
647C23C31×H(5,𝔽2)12yes—
648C23C31×H(5,𝔽2)11yescharacteristic
649C23C31×H(5,𝔽2)11yescharacteristic
650C23C31×H(5,𝔽2)11yescharacteristic
651C23C31×2−1+412yes—
652C23C31×2−1+411yescharacteristic
653D4—416no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—416no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
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—
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×C4C31×#12014yes—
710C22—24no—
711C22—24no—
712C22—24no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—44no—
726C22—81no—
727C22—81no—
728C22—82no—
729C22—82no—
730C22—81no—
731C22—81no—
732C22C2×C31×#12011yescharacteristic
733C22C2×C31×#12311yescharacteristic
734C22C31×#53211yescharacteristic
735C22C31×#53411yescharacteristic
736C22C31×#53511yescharacteristic
737C22C31×#53511yescharacteristic
738C22C31×#53511yescharacteristic
739C22C31×#53611yescharacteristic
740C22C31×#53711yescharacteristic
741C22C31×#53711yescharacteristic
742C22C31×#53711yescharacteristic
743C22C31×#53812yes—
744C22C31×#53912yes—
745C22C31×#53912yes—
746C22C31×#54012yes—
747C22C31×#54612yes—
748C22C31×#54612yes—
749C22C31×#54712yes—
750C22C31×#54812yes—
751C22C31×#55112yes—
752C22C31×#55212yes—
753C22C31×#56212yes—
754C22C31×#56312yes—
755C4—24no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—44no—
761C4—82no—
762C4—82no—
763C4—82no—
764C2—44no—
765C2—82no—
766C2C31×#240511yescharacteristic
767C2C31×#243211yescharacteristic
768C2C31×#249811yescharacteristic
769C2C31×#261511yescharacteristic
770C2C31×#262311yescharacteristic
771C2C31×#266111yescharacteristic
772C2C31×#269512yes—
773C2C31×#269612yes—
774C2C31×#270612yes—
775C2C31×#270712yes—
776C2C31×#281411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#398C2semidirect
3. C2×C31×#397C2semidirect
4. C2×C31×#380C2semidirect
5. C31×#1442C2semidirect
6. C31×#1441C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
11. C31×C22⋊#95C2semidirect
207. #16359C31direct (N × H)
323. C2×#398C2×C31semidirect
324. C2×#397C2×C31semidirect
325. C2×#380C2×C31semidirect
326. #1442C2×C31semidirect
327. #1441C2×C31semidirect
328. #1439C2×C31semidirect
329. #1439C2×C31semidirect
330. #1439C2×C31semidirect
332. C22⋊#95C2×C31semidirect
495. C31#16359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C2×C31×#3982
C2×C31×#3972
C2×C31×#3802
C31×#14422
C31×#14412
C31×#14392
C31×#14382
C31×C22⋊#952
#1635931