Finite Group Databasebeta

← C31×#16632 #21473391

Subgroups — C31×#16632 #21473391

Order 7936.

1966 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#397C211yesmaximal, characteristic, complemented
3C2×C31×#393C211yesmaximal, characteristic, complemented
4C2×C31×#386C211yesmaximal, characteristic
5C31×#1446C211yesmaximal, characteristic, complemented
6C31×#1445C211yesmaximal, characteristic, complemented
7C31×#1442C212yesmaximal, complemented
8C31×#1440C212yesmaximal, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C2×C31×C22⋊Q8—24no—
16C2×C31×C22⋊Q8—24no—
17C2×C31×C22⋊Q8—24no—
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C31×#397—24no—
28C31×#393—24no—
29C31×#386—24no—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C25×C31C2311yescharacteristic
42C25×C31C2311yescharacteristic
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—42no—
46C22×Q8×C31—42no—
47C22×Q8×C31D414yescomplemented
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31—42no—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—42no—
56C23×C4×C31—42no—
57C23×C4×C31D414yes—
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2312yes—
60C23×C4×C31C2312yes—
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2312yes—
63C23×C4×C31C2312yes—
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C31×C22⋊Q8—232no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31—24no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31D414yescomplemented
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—22no—
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×C22⋊C4×C31—42no—
93C31×#95—24no—
94C31×#95—22no—
95C31×#95—22no—
96C31×#95—22no—
97C31×#95—24no—
98C31×#95—22no—
99C31×#95—24no—
100C31×#95—42no—
101C31×#95—42no—
102C31×#95—42no—
103C31×#95—42no—
104C24×C31—21no—
105C24×C31—21no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—21no—
116C24×C31—21no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—21no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—21no—
123C24×C31C2×D412yes—
124C24×C31#4112yes—
125C24×C31#4114yes—
126C24×C31C2411yescharacteristic
127C2×Q8×C31—28no—
128C2×Q8×C31—48no—
129C2×Q8×C31—44no—
130C2×Q8×C31—44no—
131C2×Q8×C31—48no—
132C2×D4×C31—28no—
133C2×D4×C31—48no—
134C2×D4×C31—48no—
135C2×D4×C31—44no—
136C2×D4×C31—44no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—21no—
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—22no—
159C22×C4×C31—28no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
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—21no—
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—21no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—44no—
185C22×C4×C31—44no—
186C22×C4×C31—48no—
187C22×C4×C31—48no—
188C22×C4×C31C2×D414yes—
189C22×C4×C31C2×D414yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D412yes—
193C22×C4×C31C2×D412yes—
194C22×C4×C31#4112yes—
195C4⋊C4×C31—216no—
196C4⋊C4×C31—28no—
197C22⋊C4×C31—216no—
198C22⋊C4×C31—48no—
199C22⋊C4×C31—44no—
200C22⋊C4×C31—48no—
201C22⋊C4×C31—48no—
202C22⋊C4×C31—44no—
203C22⋊C4×C31—44no—
204#16632C3111yesmaximal, characteristic, direct product factor, Sylow
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—22no—
218C23×C31—24no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—24no—
222C23×C31—42no—
223C23×C31—42no—
224C23×C31—42no—
225C23×C31—42no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—42no—
236C23×C31—41no—
237C23×C31—42no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—41no—
244C23×C31—42no—
245C23×C31—42no—
246C23×C31—41no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31#12414yes—
251C23×C31C22×D411yescharacteristic
252C23×C31C22×D411yescharacteristic
253C23×C31C22×D411yescharacteristic
254C23×C31C2×#4111yescharacteristic
255C23×C31C2×#4111yescharacteristic
256C23×C31C2×#4112yes—
257C23×C31H(5,𝔽2)12yes—
258C23×C31H(5,𝔽2)12yes—
259C23×C31H(5,𝔽2)11yescharacteristic
260C23×C312−1+412yes—
261C23×C312−1+411yescharacteristic
262Q8×C31—416no—
263D4×C31—416no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—24no—
267C2×C4×C31—24no—
268C2×C4×C31—24no—
269C2×C4×C31—24no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—24no—
274C2×C4×C31—22no—
275C2×C4×C31—24no—
276C2×C4×C31—24no—
277C2×C4×C31—24no—
278C2×C4×C31—24no—
279C2×C4×C31—416no—
280C2×C4×C31—42no—
281C2×C4×C31—41no—
282C2×C4×C31—42no—
283C2×C4×C31—41no—
284C2×C4×C31—42no—
285C2×C4×C31—42no—
286C2×C4×C31—42no—
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—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
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#12014yes—
318C22×C22⋊Q8C2×C3111yescharacteristic, complemented
319C2×#397C2×C3111yescharacteristic, complemented
320C2×#393C2×C3111yescharacteristic, complemented
321C2×#386C2×C3111yescharacteristic
322#1446C2×C3111yescharacteristic, complemented
323#1445C2×C3111yescharacteristic, complemented
324#1442C2×C3112yescomplemented
325#1440C2×C3112yescomplemented
326#1439C2×C3112yescomplemented
327#1438C2×C3112yes—
328C22⋊#95C2×C3111yescharacteristic, complemented
329C22×C31—24no—
330C22×C31—24no—
331C22×C31—24no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—44no—
336C22×C31—44no—
337C22×C31—44no—
338C22×C31—44no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—42no—
342C22×C31—42no—
343C22×C31—44no—
344C22×C31—44no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31—82no—
349C22×C31—82no—
350C22×C31—81no—
351C22×C31C2×#12011yescharacteristic
352C22×C31#52511yescharacteristic
353C22×C31C2×#12411yescharacteristic
354C22×C31#53411yescharacteristic
355C22×C31#53411yescharacteristic
356C22×C31#53412yes—
357C22×C31#53512yes—
358C22×C31#53611yescharacteristic
359C22×C31#53711yescharacteristic
360C22×C31#53812yes—
361C22×C31#53912yes—
362C22×C31#53912yes—
363C22×C31#54212yes—
364C22×C31#54611yescharacteristic
365C22×C31#54711yescharacteristic
366C22×C31#54811yescharacteristic
367C22×C31#54812yes—
368C22×C31#54812yes—
369C22×C31#55011yescharacteristic
370C22×C31#55112yes—
371C22×C31#55112yes—
372C22×C31#56212yes—
373C22×C31#56312yes—
374C4×C31—24no—
375C4×C31—42no—
376C4×C31—42no—
377C4×C31—44no—
378C4×C31—44no—
379C4×C31—81no—
380C4×C31—81no—
381C4×C31—82no—
382C4×C31—82no—
383C23×Q8C22×C3111yescharacteristic
384C23×D4C22×C3111yescharacteristic
385C24×C4C22×C3111yescharacteristic
386C2×C22⋊Q8—24no—
387C2×C22⋊Q8—24no—
388C2×C22⋊Q8—24no—
389C22×C4⋊C4C22×C3112yes—
390C22×C4⋊C4C22×C3111yescharacteristic
391C22×C22⋊C4C22×C3111yescharacteristic
392C22×C22⋊C4C22×C3112yes—
393C22×C22⋊C4C22×C3111yescharacteristic
394C22×C22⋊C4C22×C3112yes—
395C22×C22⋊C4C22×C3112yes—
396C22×C22⋊C4C22×C3112yes—
397C22×C22⋊C4C22×C3111yescharacteristic
398#397—24no—
399#393—24no—
400#386—24no—
401C2×#95C22×C3111yescharacteristic
402C2×#95C22×C3112yes—
403C2×#95C22×C3111yescharacteristic
404C2×#95C22×C3112yes—
405C2×#95C22×C3112yes—
406C2×#95C22×C3111yescharacteristic
407C2×#95C22×C3111yescharacteristic
408C2×#95C22×C3112yes—
409C2×#95C22×C3112yes—
410C2×#95C22×C3112yes—
411C2×#95C22×C3112yes—
412C2×C31—44no—
413C2×C31—82no—
414C2×C31#240711yescharacteristic
415C2×C31#243611yescharacteristic
416C2×C31#256111yescharacteristic
417C2×C31#261311yescharacteristic
418C2×C31#263811yescharacteristic
419C2×C31#263911yescharacteristic
420C2×C31#269612yes—
421C2×C31#272312yes—
422C2×C31#272812yes—
423C2×C31#273012yes—
424C2×C31#281411yescharacteristic
425C25C23×C3111yescharacteristic
426C25C23×C3111yescharacteristic
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—42no—
430C22×Q8—42no—
431C22×Q8D4×C3114yescomplemented
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—24no—
435C22×D4—22no—
436C22×D4—42no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4D4×C3114yes—
442C23×C4C23×C3111yescharacteristic
443C23×C4C23×C3112yes—
444C23×C4C23×C3112yes—
445C23×C4C23×C3111yescharacteristic
446C23×C4C23×C3112yes—
447C23×C4C23×C3112yes—
448C23×C4C23×C3111yescharacteristic
449C23×C4C23×C3111yescharacteristic
450C23×C4C23×C3111yescharacteristic
451C22⋊Q8—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4D4×C3114yescomplemented
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477#95—22no—
478#95—22no—
479#95—24no—
480#95—22no—
481#95—24no—
482#95—22no—
483#95—24no—
484#95—42no—
485#95—42no—
486#95—42no—
487#95—42no—
488C31#1663211yescharacteristic, direct product factor, Sylow
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—22no—
506C24—22no—
507C24—21no—
508C24C2×D4×C3112yes—
509C24#41×C3112yes—
510C24#41×C3114yes—
511C24C24×C3111yescharacteristic
512C2×Q8—28no—
513C2×Q8—48no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—48no—
517C2×D4—28no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—44no—
521C2×D4—44no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—21no—
546C22×C4—21no—
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—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4C2×D4×C3114yes—
574C22×C4C2×D4×C3114yes—
575C22×C4C2×D4×C3112yes—
576C22×C4C2×D4×C3112yes—
577C22×C4C2×D4×C3112yes—
578C22×C4C2×D4×C3112yes—
579C22×C4#41×C3112yes—
580C4⋊C4—216no—
581C4⋊C4—28no—
582C22⋊C4—216no—
583C22⋊C4—48no—
584C22⋊C4—44no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23C31×#12414yes—
635C23C22×D4×C3111yescharacteristic
636C23C22×D4×C3111yescharacteristic
637C23C22×D4×C3111yescharacteristic
638C23C2×#41×C3111yescharacteristic
639C23C2×#41×C3111yescharacteristic
640C23C2×#41×C3112yes—
641C23C31×H(5,𝔽2)12yes—
642C23C31×H(5,𝔽2)12yes—
643C23C31×H(5,𝔽2)11yescharacteristic
644C23C31×2−1+412yes—
645C23C31×2−1+411yescharacteristic
646Q8—416no—
647D4—416no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—416no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
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—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
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×C4C31×#12014yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—82no—
722C22—82no—
723C22—81no—
724C22C2×C31×#12011yescharacteristic
725C22C31×#52511yescharacteristic
726C22C2×C31×#12411yescharacteristic
727C22C31×#53411yescharacteristic
728C22C31×#53412yes—
729C22C31×#53411yescharacteristic
730C22C31×#53512yes—
731C22C31×#53611yescharacteristic
732C22C31×#53711yescharacteristic
733C22C31×#53812yes—
734C22C31×#53912yes—
735C22C31×#53912yes—
736C22C31×#54212yes—
737C22C31×#54611yescharacteristic
738C22C31×#54711yescharacteristic
739C22C31×#54811yescharacteristic
740C22C31×#54812yes—
741C22C31×#54812yes—
742C22C31×#55011yescharacteristic
743C22C31×#55112yes—
744C22C31×#55112yes—
745C22C31×#56212yes—
746C22C31×#56312yes—
747C4—24no—
748C4—42no—
749C4—44no—
750C4—44no—
751C4—42no—
752C4—81no—
753C4—81no—
754C4—82no—
755C4—82no—
756C2—44no—
757C2—82no—
758C2C31×#240711yescharacteristic
759C2C31×#243611yescharacteristic
760C2C31×#256111yescharacteristic
761C2C31×#261311yescharacteristic
762C2C31×#263811yescharacteristic
763C2C31×#263911yescharacteristic
764C2C31×#269612yes—
765C2C31×#272312yes—
766C2C31×#272812yes—
767C2C31×#273012yes—
768C2C31×#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
1. C22×C31×C22⋊Q8C2semidirect
2. C2×C31×#397C2semidirect
3. C2×C31×#393C2semidirect
5. C31×#1446C2semidirect
6. C31×#1445C2semidirect
7. C31×#1442C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
11. C31×C22⋊#95C2semidirect
47. C22×Q8×C31D4semidirect
73. C2×C4⋊C4×C31D4semidirect
204. #16632C31direct (N × H)
318. C22×C22⋊Q8C2×C31semidirect
319. C2×#397C2×C31semidirect
320. C2×#393C2×C31semidirect
322. #1446C2×C31semidirect
323. #1445C2×C31semidirect
324. #1442C2×C31semidirect
325. #1440C2×C31semidirect
326. #1439C2×C31semidirect
328. C22⋊#95C2×C31semidirect
431. C22×Q8D4×C31semidirect
457. C2×C4⋊C4D4×C31semidirect
488. C31#16632direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3972
C2×C31×#3932
C2×C31×#3862
C31×#14462
C31×#14452
C31×#14422
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1663231