Finite Group Databasebeta

← C31×#24193 #21480952

Subgroups — C31×#24193 #21480952

Order 7936.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#556C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic
3C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2580C211yesmaximal, characteristic, complemented
5C31×#2043C211yesmaximal, characteristic, complemented
6C31×#2042C211yesmaximal, characteristic, complemented
7C31×#2013C211yesmaximal, characteristic, complemented
8C31×#2012C211yesmaximal, characteristic
9C31×#1984C211yesmaximal, characteristic, complemented
10C31×#1958C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic
13C31×#1865C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1805C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C31×#556—24no—
20C31×#556—24no—
21C2×C31×C4⋊Q8C2211yescharacteristic
22C2×C31×#126—21no—
23C2×C31×#126—21no—
24C2×C31×#124C2211yescharacteristic
25C2×C31×#124C2211yescharacteristic
26C2×C31×C22⋊Q8—21no—
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117—21no—
33C31×#463—24no—
34C4×SD16×C31—24no—
35C2×C31×#106C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C4×C8×C31C2211yescharacteristic
48C31×#399—21no—
49C31×#393—21no—
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#385—21no—
55C31×#385—21no—
56C31×#382C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
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×C31—41no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—41no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×C4⋊Q8—22no—
84C31×C4⋊Q8—22no—
85C31×#126—28no—
86C31×#126—28no—
87C31×#124—22no—
88C31×#124—22no—
89C31×#124—22no—
90C31×#124D414yes—
91C31×C22⋊Q8—28no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31—22no—
97C4×Q8×C31D414yes—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C31×#117—28no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31D411yescharacteristic
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C42×C31—21no—
127C2×C42×C31—21no—
128C2×C42×C31C2311yescharacteristic
129C2×C42×C31C2311yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C31×#106—22no—
132C31×C4⋊C8—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#103—41no—
138C31×#103—41no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C4×C8×C31—22no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31—21no—
150C2×Q8×C31—22no—
151C2×Q8×C31—22no—
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×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—41no—
163C2×Q8×C31C2×D412yes—
164C2×Q8×C31C2×D412yes—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31C2×D412yes—
176C2×D4×C31#4112yes—
177C22×C4×C31—24no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—42no—
187C22×C4×C31—81no—
188C22×C4×C31—81no—
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2411yescharacteristic
196SD16×C31—28no—
197SD16×C31—44no—
198D8×C31—44no—
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×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31#4112yes—
211C4⋊C4×C31—24no—
212C4⋊C4×C31—24no—
213C4⋊C4×C31—24no—
214C4⋊C4×C31—24no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—81no—
226C4⋊C4×C31—81no—
227C4⋊C4×C31C2×D412yes—
228C22⋊C4×C31—24no—
229C22⋊C4×C31—24no—
230C22⋊C4×C31—24no—
231C22⋊C4×C31—24no—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31—81no—
238C42×C31—24no—
239C42×C31—24no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—21no—
243C42×C31—21no—
244C42×C31C2×D412yes—
245C42×C31C2×D412yes—
246#24193C3111yesmaximal, characteristic, direct product factor, Sylow
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31C22×D411yescharacteristic
262Q8×C31—22no—
263Q8×C31—22no—
264Q8×C31—22no—
265Q8×C31—22no—
266Q8×C31—44no—
267Q8×C31—41no—
268Q8×C31—41no—
269Q8×C31—41no—
270Q8×C31—41no—
271D4×C31—22no—
272D4×C31—22no—
273D4×C31—22no—
274D4×C31—22no—
275D4×C31—41no—
276D4×C31—41no—
277D4×C31—41no—
278D4×C31—41no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—22no—
287C2×C4×C31—21no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—48no—
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—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—84no—
314C2×C4×C31#12012yes—
315C2×C4×C31#12012yes—
316C2×C4×C31#13512yes—
317C2×C4×C31C22×D411yescharacteristic
318C2×C4×C31C22×D411yescharacteristic
319C2×C4×C31C2×#4111yescharacteristic
320C2×C4×C31C2×#4111yescharacteristic
321C2×C4×C31H(5,𝔽2)11yescharacteristic
322C2×C4×C312−1+411yescharacteristic
323C8×C31—22no—
324C8×C31—41no—
325C8×C31—41no—
326C8×C31—41no—
327C2×#556C2×C3111yescharacteristic, complemented
328C2×#463C2×C3111yescharacteristic
329C2×C4×SD16C2×C3111yescharacteristic, complemented
330#2580C2×C3111yescharacteristic, complemented
331#2043C2×C3111yescharacteristic, complemented
332#2042C2×C3111yescharacteristic, complemented
333#2013C2×C3111yescharacteristic, complemented
334#2012C2×C3111yescharacteristic
335#1984C2×C3111yescharacteristic, complemented
336#1958C2×C3111yescharacteristic, complemented
337#1880C2×C3111yescharacteristic, complemented
338#1879C2×C3111yescharacteristic
339#1865C2×C3111yescharacteristic, complemented
340#1864C2×C3111yescharacteristic, complemented
341#1805C2×C3111yescharacteristic, complemented
342C22×C31—42no—
343C22×C31—42no—
344C22×C31—42no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—81no—
349C22×C31—81no—
350C22×C31—81no—
351C22×C31—81no—
352C22×C31—81no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31C2×#12011yescharacteristic
357C22×C31#54811yescharacteristic
358C22×C31#55011yescharacteristic
359C22×C31C2×#13511yescharacteristic
360C22×C31#57511yescharacteristic
361C22×C31#57711yescharacteristic
362C22×C31#57711yescharacteristic
363C4×C31—22no—
364C4×C31—22no—
365C4×C31—22no—
366C4×C31—42no—
367C4×C31—42no—
368C4×C31—41no—
369C4×C31—42no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—81no—
373C4×C31—81no—
374C4×C31—81no—
375C4×C31#52511yescharacteristic
376C4×C31#53711yescharacteristic
377C4×C31#54611yescharacteristic
378C4×C31#54711yescharacteristic
379C22×SD16C22×C3111yescharacteristic
380C22×SD16C22×C3111yescharacteristic
381C22×D8C22×C3111yescharacteristic
382#556—24no—
383#556—24no—
384C2×C4⋊Q8C22×C3111yescharacteristic
385C2×#126—21no—
386C2×#126—21no—
387C2×#124C22×C3111yescharacteristic
388C2×#124C22×C3111yescharacteristic
389C2×C22⋊Q8—21no—
390C2×C4×Q8C22×C3111yescharacteristic
391C2×C4×Q8C22×C3111yescharacteristic
392C2×C4×Q8C22×C3111yescharacteristic
393C2×C4×D4C22×C3111yescharacteristic
394C2×C4×D4C22×C3111yescharacteristic
395C2×#117—21no—
396#463—24no—
397C4×SD16—24no—
398C2×#106C22×C3111yescharacteristic
399C2×C4⋊C8C22×C3111yescharacteristic
400C2×#103C22×C3111yescharacteristic
401C2×#103C22×C3111yescharacteristic
402C2×#103C22×C3111yescharacteristic
403C2×#103C22×C3111yescharacteristic
404C2×#103C22×C3111yescharacteristic
405C2×#103C22×C3111yescharacteristic
406C2×#102C22×C3111yescharacteristic
407C2×#102C22×C3111yescharacteristic
408C2×#102C22×C3111yescharacteristic
409C2×#102C22×C3111yescharacteristic
410C2×C4×C8C22×C3111yescharacteristic
411#399—21no—
412#393—21no—
413#390C22×C3111yescharacteristic
414#390C22×C3111yescharacteristic
415#389C22×C3111yescharacteristic
416#389C22×C3111yescharacteristic
417#385—21no—
418#385—21no—
419#382C22×C3111yescharacteristic
420#340C22×C3111yescharacteristic
421#340C22×C3111yescharacteristic
422#336C22×C3111yescharacteristic
423#336C22×C3111yescharacteristic
424#336C22×C3111yescharacteristic
425#336C22×C3111yescharacteristic
426C2×C31—82no—
427C2×C31—82no—
428C2×C31#240711yescharacteristic
429C2×C31#300211yescharacteristic
430C2×C31#301011yescharacteristic
431C2×C31#336011yescharacteristic
432C2×C31#337611yescharacteristic
433C2×C31#339411yescharacteristic
434C2×C31#340111yescharacteristic
435C22×Q8D4×C3111yescharacteristic
436C22×Q8C23×C3111yescharacteristic
437C22×Q8C23×C3111yescharacteristic
438C22×D4C23×C3111yescharacteristic
439C22×D4C23×C3111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—41no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8—41no—
451C22×C8C23×C3111yescharacteristic
452C22×C8C23×C3111yescharacteristic
453C22×C8C23×C3111yescharacteristic
454C22×C8C23×C3111yescharacteristic
455C4⋊Q8—22no—
456C4⋊Q8—22no—
457#126—28no—
458#126—28no—
459#124—22no—
460#124—22no—
461#124—22no—
462#124D4×C3114yes—
463C22⋊Q8—28no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8D4×C3114yes—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474#117—28no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4D4×C3111yescharacteristic
482C2×C4⋊C4D4×C3111yescharacteristic
483C2×C4⋊C4D4×C3111yescharacteristic
484C2×C4⋊C4C23×C3111yescharacteristic
485C2×C4⋊C4C23×C3111yescharacteristic
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42C23×C3111yescharacteristic
501C2×C42C23×C3111yescharacteristic
502C2×C42C23×C3111yescharacteristic
503#106—22no—
504C4⋊C8—22no—
505#103—22no—
506#103—22no—
507#103—22no—
508#103—41no—
509#103—41no—
510#103—41no—
511#102—22no—
512#102—22no—
513#102—22no—
514#102—41no—
515C4×C8—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C31#2419311yescharacteristic, direct product factor, Sylow
521C24—21no—
522C24—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—41no—
536C2×Q8C2×D4×C3112yes—
537C2×Q8C2×D4×C3112yes—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4C2×D4×C3112yes—
549C2×D4#41×C3112yes—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—81no—
561C22×C4—81no—
562C22×C4C2×D4×C3111yescharacteristic
563C22×C4C2×D4×C3111yescharacteristic
564C22×C4C2×D4×C3111yescharacteristic
565C22×C4C2×D4×C3111yescharacteristic
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C24×C3111yescharacteristic
569SD16—28no—
570SD16—44no—
571D8—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8#41×C3112yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—81no—
599C4⋊C4—81no—
600C4⋊C4C2×D4×C3112yes—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C42—24no—
612C42—24no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42C2×D4×C3112yes—
618C42C2×D4×C3112yes—
619C23—22no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C22×D4×C3111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—44no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4C31×#12012yes—
687C2×C4C31×#12012yes—
688C2×C4C31×#13512yes—
689C2×C4C22×D4×C3111yescharacteristic
690C2×C4C22×D4×C3111yescharacteristic
691C2×C4C2×#41×C3111yescharacteristic
692C2×C4C2×#41×C3111yescharacteristic
693C2×C4C31×H(5,𝔽2)11yescharacteristic
694C2×C4C31×2−1+411yescharacteristic
695C8—22no—
696C8—41no—
697C8—41no—
698C8—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×C31×#12011yescharacteristic
714C22C31×#54811yescharacteristic
715C22C31×#55011yescharacteristic
716C22C2×C31×#13511yescharacteristic
717C22C31×#57511yescharacteristic
718C22C31×#57711yescharacteristic
719C22C31×#57711yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—42no—
724C4—42no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4C31×#52511yescharacteristic
733C4C31×#53711yescharacteristic
734C4C31×#54611yescharacteristic
735C4C31×#54711yescharacteristic
736C2—82no—
737C2—82no—
738C2C31×#240711yescharacteristic
739C2C31×#300211yescharacteristic
740C2C31×#301011yescharacteristic
741C2C31×#336011yescharacteristic
742C2C31×#337611yescharacteristic
743C2C31×#339411yescharacteristic
744C2C31×#340111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#556C2semidirect
3. C2×C4×SD16×C31C2semidirect
4. C31×#2580C2semidirect
5. C31×#2043C2semidirect
6. C31×#2042C2semidirect
7. C31×#2013C2semidirect
9. C31×#1984C2semidirect
10. C31×#1958C2semidirect
11. C31×#1880C2semidirect
13. C31×#1865C2semidirect
14. C31×#1864C2semidirect
15. C31×#1805C2semidirect
246. #24193C31direct (N × H)
327. C2×#556C2×C31semidirect
329. C2×C4×SD16C2×C31semidirect
330. #2580C2×C31semidirect
331. #2043C2×C31semidirect
332. #2042C2×C31semidirect
333. #2013C2×C31semidirect
335. #1984C2×C31semidirect
336. #1958C2×C31semidirect
337. #1880C2×C31semidirect
339. #1865C2×C31semidirect
340. #1864C2×C31semidirect
341. #1805C2×C31semidirect
520. C31#24193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5562
C2×C31×#4632
C2×C4×SD16×C312
C31×#25802
C31×#20432
C31×#20422
C31×#20132
C31×#20122
C31×#19842
C31×#19582
C31×#18802
C31×#18792
C31×#18652
C31×#18642
C31×#18052
#2419331