Finite Group Databasebeta

← C31×#24740 #21481499

Subgroups — C31×#24740 #21481499

Order 7936.

1030 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#463C211yesmaximal, characteristic
2C2×C31×#463C211yesmaximal, characteristic
3C2×C31×#461C211yesmaximal, characteristic, complemented
4C2×C31×#440C211yesmaximal, characteristic, complemented
5C31×#2545C211yesmaximal, characteristic, complemented
6D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2067C211yesmaximal, characteristic, complemented
9C31×#2043C211yesmaximal, characteristic, complemented
10C31×#2042C211yesmaximal, characteristic, complemented
11C31×#1959C211yesmaximal, characteristic, complemented
12C31×#1940C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1803C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C22×C4⋊C4×C31—21no—
27C31×#463—24no—
28C31×#463—24no—
29C31×#461—24no—
30C31×#440—24no—
31C2×C31×#107C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#97C2211yescharacteristic
46C31×#396—21no—
47C31×#396—21no—
48C31×#391C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#388—21no—
53C31×#388—21no—
54C31×#385—21no—
55C31×#385—21no—
56C31×#384C2211yescharacteristic
57C31×#380—21no—
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31D414yes—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×C4⋊Q8—22no—
84C31×C4⋊Q8—41no—
85C31×#124—22no—
86C31×#124—22no—
87C31×#124—22no—
88C31×#124—41no—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—41no—
95C4×D4×C31—41no—
96C4×D4×C31D414yes—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—44no—
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31D411yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#107—22no—
125C31×C4⋊C8—22no—
126C31×C4⋊C8—22no—
127C31×C4⋊C8—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—41no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—41no—
138C31×#97—22no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95D411yescharacteristic
144C31×#95D411yescharacteristic
145C24×C31—21no—
146C24×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31C2×D412yes—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31C2×D412yes—
169C2×D4×C31C2×D412yes—
170C2×D4×C31#4112yes—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—24no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—42no—
179C22×C4×C31—42no—
180C22×C4×C31—42no—
181C22×C4×C31—42no—
182C22×C4×C31—42no—
183C22×C4×C31—42no—
184C22×C4×C31—81no—
185C22×C4×C31—81no—
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2411yescharacteristic
193SD16×C31—28no—
194SD16×C31—44no—
195D8×C31—44no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31C2×D412yes—
208C4⋊C4×C31—22no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—41no—
217C4⋊C4×C31—42no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—42no—
220C4⋊C4×C31—42no—
221C4⋊C4×C31—42no—
222C4⋊C4×C31—42no—
223C4⋊C4×C31—81no—
224C4⋊C4×C31C2×D412yes—
225C22⋊C4×C31—24no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C42×C31—21no—
235C42×C31—21no—
236C42×C31—21no—
237C42×C31—21no—
238C42×C31—42no—
239C42×C31C2×D412yes—
240C42×C31#4112yes—
241#24740C3111yesmaximal, characteristic, direct product factor, Sylow
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31C22×D411yescharacteristic
257Q8×C31—22no—
258Q8×C31—22no—
259Q8×C31—41no—
260Q8×C31—41no—
261Q8×C31—41no—
262Q8×C31—41no—
263Q8×C31—41no—
264Q8×C31—41no—
265D4×C31—22no—
266D4×C31—22no—
267D4×C31—22no—
268D4×C31—41no—
269D4×C31—41no—
270D4×C31—41no—
271D4×C31—41no—
272D4×C31#12114yes—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—22no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—22no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—48no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—84no—
308C2×C4×C31—84no—
309C2×C4×C31#12112yes—
310C2×C4×C31#12112yes—
311C2×C4×C31AGL(1,ℤ/8)12yes—
312C2×C4×C31C22×D411yescharacteristic
313C2×C4×C31C22×D411yescharacteristic
314C2×C4×C31C2×#4111yescharacteristic
315C2×C4×C31C2×#4111yescharacteristic
316C2×C4×C31H(5,𝔽2)11yescharacteristic
317C2×C4×C312−1+411yescharacteristic
318C8×C31—22no—
319C8×C31—41no—
320C8×C31—41no—
321C8×C31—41no—
322C2×#463C2×C3111yescharacteristic
323C2×#463C2×C3111yescharacteristic
324C2×#461C2×C3111yescharacteristic, complemented
325C2×#440C2×C3111yescharacteristic, complemented
326#2545C2×C3111yescharacteristic, complemented
327D4×C4⋊C4C2×C3111yescharacteristic, complemented
328#2068C2×C3111yescharacteristic, complemented
329#2067C2×C3111yescharacteristic, complemented
330#2043C2×C3111yescharacteristic, complemented
331#2042C2×C3111yescharacteristic, complemented
332#1959C2×C3111yescharacteristic, complemented
333#1940C2×C3111yescharacteristic, complemented
334#1879C2×C3111yescharacteristic
335#1877C2×C3111yescharacteristic, complemented
336#1803C2×C3111yescharacteristic, complemented
337C22×C31—24no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—42no—
342C22×C31—42no—
343C22×C31—42no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31—81no—
349C22×C31—81no—
350C22×C31—81no—
351C22×C31C2×#12111yescharacteristic
352C22×C31D4211yescharacteristic
353C22×C31#54811yescharacteristic
354C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C31#57511yescharacteristic
356C22×C31#57711yescharacteristic
357C22×C31#57811yescharacteristic
358C4×C31—22no—
359C4×C31—22no—
360C4×C31—22no—
361C4×C31—42no—
362C4×C31—41no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31—42no—
366C4×C31—81no—
367C4×C31—81no—
368C4×C31—81no—
369C4×C31—81no—
370C4×C31C2×#12111yescharacteristic
371C4×C31#53711yescharacteristic
372C4×C31#54711yescharacteristic
373C4×C31#55311yescharacteristic
374C22×SD16C22×C3111yescharacteristic
375C22×SD16C22×C3111yescharacteristic
376C22×D8C22×C3111yescharacteristic
377C2×C4⋊Q8C22×C3111yescharacteristic
378C2×#124C22×C3111yescharacteristic
379C2×#124C22×C3111yescharacteristic
380C2×C4×Q8C22×C3111yescharacteristic
381C2×C4×D4C22×C3111yescharacteristic
382C2×C4×D4C22×C3111yescharacteristic
383C2×C4×D4C22×C3111yescharacteristic
384C22×C4⋊C4—21no—
385#463—24no—
386#463—24no—
387#461—24no—
388#440—24no—
389C2×#107C22×C3111yescharacteristic
390C2×C4⋊C8C22×C3111yescharacteristic
391C2×C4⋊C8C22×C3111yescharacteristic
392C2×C4⋊C8C22×C3111yescharacteristic
393C2×#103C22×C3111yescharacteristic
394C2×#103C22×C3111yescharacteristic
395C2×#103C22×C3111yescharacteristic
396C2×#103C22×C3111yescharacteristic
397C2×#103C22×C3111yescharacteristic
398C2×#103C22×C3111yescharacteristic
399C2×#102C22×C3111yescharacteristic
400C2×#102C22×C3111yescharacteristic
401C2×#102C22×C3111yescharacteristic
402C2×#102C22×C3111yescharacteristic
403C2×#97C22×C3111yescharacteristic
404#396—21no—
405#396—21no—
406#391C22×C3111yescharacteristic
407#390C22×C3111yescharacteristic
408#389C22×C3111yescharacteristic
409#389C22×C3111yescharacteristic
410#388—21no—
411#388—21no—
412#385—21no—
413#385—21no—
414#384C22×C3111yescharacteristic
415#380—21no—
416C4×C4⋊C4C22×C3111yescharacteristic
417#340C22×C3111yescharacteristic
418#340C22×C3111yescharacteristic
419#336C22×C3111yescharacteristic
420#336C22×C3111yescharacteristic
421C2×C31—44no—
422C2×C31—161no—
423C2×C31#241611yescharacteristic
424C2×C31#303611yescharacteristic
425C2×C31#304611yescharacteristic
426C2×C31#326511yescharacteristic
427C2×C31#326911yescharacteristic
428C2×C31#336711yescharacteristic
429C2×C31#337611yescharacteristic
430C22×Q8C23×C3111yescharacteristic
431C22×Q8C23×C3111yescharacteristic
432C22×D4C23×C3111yescharacteristic
433C22×D4C23×C3111yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16D4×C3114yes—
443C2×D8—22no—
444C2×D8—22no—
445C2×D8—22no—
446C22×C8C23×C3111yescharacteristic
447C22×C8C23×C3111yescharacteristic
448C22×C8C23×C3111yescharacteristic
449C22×C8C23×C3111yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8—41no—
452#124—22no—
453#124—22no—
454#124—22no—
455#124—41no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—41no—
462C4×D4—41no—
463C4×D4D4×C3114yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—44no—
472C2×C4⋊C4D4×C3111yescharacteristic
473C2×C4⋊C4D4×C3111yescharacteristic
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C4⋊C4C23×C3111yescharacteristic
476C2×C4⋊C4C23×C3111yescharacteristic
477C2×C4⋊C4C23×C3111yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42C23×C3111yescharacteristic
489C2×C42C23×C3111yescharacteristic
490C2×C42C23×C3111yescharacteristic
491#107—22no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495#103—22no—
496#103—22no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—41no—
501#102—22no—
502#102—22no—
503#102—22no—
504#102—41no—
505#97—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95D4×C3111yescharacteristic
511#95D4×C3111yescharacteristic
512C31#2474011yescharacteristic, direct product factor, Sylow
513C24—21no—
514C24—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8C2×D4×C3112yes—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4C2×D4×C3112yes—
537C2×D4C2×D4×C3112yes—
538C2×D4#41×C3112yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4C2×D4×C3111yescharacteristic
555C22×C4C2×D4×C3111yescharacteristic
556C22×C4C2×D4×C3111yescharacteristic
557C22×C4C2×D4×C3111yescharacteristic
558C22×C4C2×D4×C3111yescharacteristic
559C22×C4C2×D4×C3111yescharacteristic
560C22×C4C24×C3111yescharacteristic
561SD16—28no—
562SD16—44no—
563D8—44no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8C2×D4×C3112yes—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—41no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—81no—
592C4⋊C4C2×D4×C3112yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42C2×D4×C3112yes—
608C42#41×C3112yes—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23C22×D4×C3111yescharacteristic
624Q8—22no—
625Q8—22no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4C31×#12114yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—48no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4C31×#12112yes—
677C2×C4C31×#12112yes—
678C2×C4C31×AGL(1,ℤ/8)12yes—
679C2×C4C22×D4×C3111yescharacteristic
680C2×C4C22×D4×C3111yescharacteristic
681C2×C4C2×#41×C3111yescharacteristic
682C2×C4C2×#41×C3111yescharacteristic
683C2×C4C31×H(5,𝔽2)11yescharacteristic
684C2×C4C31×2−1+411yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C22—24no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22C2×C31×#12111yescharacteristic
704C22D42×C3111yescharacteristic
705C22C31×#54811yescharacteristic
706C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
707C22C31×#57511yescharacteristic
708C22C31×#57711yescharacteristic
709C22C31×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—42no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4C2×C31×#12111yescharacteristic
723C4C31×#53711yescharacteristic
724C4C31×#54711yescharacteristic
725C4C31×#55311yescharacteristic
726C2—44no—
727C2—161no—
728C2C31×#241611yescharacteristic
729C2C31×#303611yescharacteristic
730C2C31×#304611yescharacteristic
731C2C31×#326511yescharacteristic
732C2C31×#326911yescharacteristic
733C2C31×#336711yescharacteristic
734C2C31×#337611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#461C2semidirect
4. C2×C31×#440C2semidirect
5. C31×#2545C2semidirect
6. D4×C4⋊C4×C31C2semidirect
7. C31×#2068C2semidirect
8. C31×#2067C2semidirect
9. C31×#2043C2semidirect
10. C31×#2042C2semidirect
11. C31×#1959C2semidirect
12. C31×#1940C2semidirect
14. C31×#1877C2semidirect
15. C31×#1803C2semidirect
241. #24740C31direct (N × H)
324. C2×#461C2×C31semidirect
325. C2×#440C2×C31semidirect
326. #2545C2×C31semidirect
327. D4×C4⋊C4C2×C31semidirect
328. #2068C2×C31semidirect
329. #2067C2×C31semidirect
330. #2043C2×C31semidirect
331. #2042C2×C31semidirect
332. #1959C2×C31semidirect
333. #1940C2×C31semidirect
335. #1877C2×C31semidirect
336. #1803C2×C31semidirect
512. C31#24740direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C2×C31×#4612
C2×C31×#4402
C31×#25452
D4×C4⋊C4×C312
C31×#20682
C31×#20672
C31×#20432
C31×#20422
C31×#19592
C31×#19402
C31×#18792
C31×#18772
C31×#18032
#2474031