Finite Group Databasebeta

← C31×#24911 #21481670

Subgroups — C31×#24911 #21481670

Order 7936.

1064 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#449C211yesmaximal, characteristic
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C31×#2422C211yesmaximal, characteristic, complemented
4C31×#2339C211yesmaximal, characteristic, complemented
5C31×#2096C211yesmaximal, characteristic, complemented
6C31×#2077C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#1935C211yesmaximal, characteristic, complemented
10C31×#1924C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1877C211yesmaximal, characteristic, complemented
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×#123—21no—
20C2×C31×#121C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#449—24no—
25C31×#442—24no—
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×#97C2211yescharacteristic
40C31×#397—21no—
41C31×#394—21no—
42C31×#391C2211yescharacteristic
43C31×#391C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#386—21no—
47C31×#386—21no—
48C31×#385—21no—
49C31×#384C2211yescharacteristic
50C31×#381—21no—
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C4×C22⋊C4×C31C2211yescharacteristic
54C2×C31×#95—21no—
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C2×#41×C31—22no—
62C2×#41×C31—22no—
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—41no—
66C2×#41×C31—41no—
67C22×Q8×C31C2311yescharacteristic
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31C2311yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31C2311yescharacteristic
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—41no—
80C2×D8×C31—22no—
81C2×D8×C31—22no—
82C2×D8×C31D414yes—
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C31×#123—44no—
88C31×#121—22no—
89C31×#121—41no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—41no—
94C4×D4×C31—41no—
95C4×D4×C31—41no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31D411yescharacteristic
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×#106—22no—
117C31×#106—41no—
118C31×C4⋊C8—41no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—41no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—41no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—41no—
129C31×#97—22no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95D411yescharacteristic
138C31×#95D411yescharacteristic
139C24×C31—21no—
140C24×C31—21no—
141C24×C31C2×D411yescharacteristic
142#41×C31—44no—
143#41×C31—44no—
144#41×C31—44no—
145#41×C31—44no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31#4112yes—
152C2×D4×C31—24no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—42no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31—81no—
166C2×D4×C31C2×D412yes—
167C2×D4×C31C2×D412yes—
168C2×D4×C31#4112yes—
169C2×D4×C31#4112yes—
170C22×C4×C31—24no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—42no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—42no—
187C22×C4×C31—42no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—81no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2411yescharacteristic
200SD16×C31—44no—
201D8×C31—28no—
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—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31C2×D412yes—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
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—42no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—81no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—41no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—81no—
237C42×C31—21no—
238C42×C31—21no—
239C42×C31—21no—
240C42×C31—21no—
241#24911C3111yesmaximal, characteristic, direct product factor, Sylow
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—21no—
246C23×C31—22no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
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×C31—41no—
262C23×C31—41no—
263C23×C31C22×D411yescharacteristic
264Q8×C31—22no—
265Q8×C31—22no—
266Q8×C31—41no—
267Q8×C31—41no—
268D4×C31—22no—
269D4×C31—22no—
270D4×C31—22no—
271D4×C31—22no—
272D4×C31—22no—
273D4×C31—48no—
274D4×C31—41no—
275D4×C31—41no—
276D4×C31—84no—
277D4×C31#12314yescomplemented
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—22no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
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—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—48no—
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—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—84no—
316C2×C4×C31—84no—
317C2×C4×C31—84no—
318C2×C4×C31AGL(1,ℤ/8)12yes—
319C2×C4×C31C22×D411yescharacteristic
320C2×C4×C31C2×#4111yescharacteristic
321C2×C4×C31C2×#4111yescharacteristic
322C2×C4×C31C2×#4111yescharacteristic
323C2×C4×C31H(5,𝔽2)11yescharacteristic
324C2×C4×C31H(5,𝔽2)11yescharacteristic
325C8×C31—22no—
326C8×C31—41no—
327C8×C31—41no—
328C8×C31—41no—
329C2×#449C2×C3111yescharacteristic
330C2×#442C2×C3111yescharacteristic, complemented
331#2422C2×C3111yescharacteristic, complemented
332#2339C2×C3111yescharacteristic, complemented
333#2096C2×C3111yescharacteristic, complemented
334#2077C2×C3111yescharacteristic, complemented
335#2055C2×C3111yescharacteristic, complemented
336#2034C2×C3111yescharacteristic, complemented
337#1935C2×C3111yescharacteristic, complemented
338#1924C2×C3111yescharacteristic, complemented
339#1879C2×C3111yescharacteristic, complemented
340#1877C2×C3111yescharacteristic, complemented
341#1864C2×C3111yescharacteristic, complemented
342#1802C2×C3111yescharacteristic, complemented
343#1788C2×C3111yescharacteristic, complemented
344C22×C31—24no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—42no—
355C22×C31—41no—
356C22×C31—42no—
357C22×C31—42no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31#52511yescharacteristic
366C22×C31D4211yescharacteristic
367C22×C31#54611yescharacteristic
368C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C31#57511yescharacteristic
370C22×C31#57711yescharacteristic
371C22×C31#57711yescharacteristic
372C4×C31—22no—
373C4×C31—41no—
374C4×C31—42no—
375C4×C31—41no—
376C4×C31—41no—
377C4×C31—41no—
378C4×C31—81no—
379C4×C31—81no—
380C4×C31—81no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31C2×#12311yescharacteristic
384C4×C31#53811yescharacteristic
385C4×C31#54611yescharacteristic
386C4×C31#55111yescharacteristic
387C22×#41C22×C3111yescharacteristic
388C22×SD16C22×C3111yescharacteristic
389C22×D8C22×C3111yescharacteristic
390C2×#123—21no—
391C2×#121C22×C3111yescharacteristic
392C2×C4×D4C22×C3111yescharacteristic
393C2×C4×D4C22×C3111yescharacteristic
394C2×C4×D4C22×C3111yescharacteristic
395#449—24no—
396#442—24no—
397C2×#106C22×C3111yescharacteristic
398C2×#106C22×C3111yescharacteristic
399C2×C4⋊C8C22×C3111yescharacteristic
400C2×#103C22×C3111yescharacteristic
401C2×#103C22×C3111yescharacteristic
402C2×#103C22×C3111yescharacteristic
403C2×#102C22×C3111yescharacteristic
404C2×#102C22×C3111yescharacteristic
405C2×#102C22×C3111yescharacteristic
406C2×#102C22×C3111yescharacteristic
407C2×#102C22×C3111yescharacteristic
408C2×C22⋊C8C22×C3111yescharacteristic
409C2×C22⋊C8C22×C3111yescharacteristic
410C2×#97C22×C3111yescharacteristic
411#397—21no—
412#394—21no—
413#391C22×C3111yescharacteristic
414#391C22×C3111yescharacteristic
415#390C22×C3111yescharacteristic
416#389C22×C3111yescharacteristic
417#386—21no—
418#386—21no—
419#385—21no—
420#384C22×C3111yescharacteristic
421#381—21no—
422#380C22×C3111yescharacteristic
423#380C22×C3111yescharacteristic
424C4×C22⋊C4C22×C3111yescharacteristic
425C2×#95—21no—
426#340C22×C3111yescharacteristic
427#340C22×C3111yescharacteristic
428#340C22×C3111yescharacteristic
429#340C22×C3111yescharacteristic
430#336C22×C3111yescharacteristic
431#336C22×C3111yescharacteristic
432C2×C31—44no—
433C2×C31—81no—
434C2×C31—82no—
435C2×C31#241811yescharacteristic
436C2×C31#311511yescharacteristic
437C2×C31#312511yescharacteristic
438C2×C31#326711yescharacteristic
439C2×C31#327211yescharacteristic
440C2×C31#330611yescharacteristic
441C2×C31#330711yescharacteristic
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—41no—
447C2×#41—41no—
448C22×Q8C23×C3111yescharacteristic
449C22×D4—21no—
450C22×D4—21no—
451C22×D4C23×C3111yescharacteristic
452C22×D4C23×C3111yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4C23×C3111yescharacteristic
458C2×SD16—22no—
459C2×SD16—22no—
460C2×SD16—41no—
461C2×D8—22no—
462C2×D8—22no—
463C2×D8D4×C3114yes—
464C22×C8C23×C3111yescharacteristic
465C22×C8C23×C3111yescharacteristic
466C22×C8C23×C3111yescharacteristic
467C22×C8C23×C3111yescharacteristic
468#123—44no—
469#121—22no—
470#121—41no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
476C4×D4—41no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4C23×C3111yescharacteristic
481C2×C4⋊C4C23×C3111yescharacteristic
482C2×C4⋊C4C23×C3111yescharacteristic
483C2×C4⋊C4C23×C3111yescharacteristic
484C2×C4⋊C4C23×C3111yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4D4×C3111yescharacteristic
494C2×C22⋊C4D4×C3111yescharacteristic
495C2×C42C23×C3111yescharacteristic
496C2×C42C23×C3111yescharacteristic
497#106—22no—
498#106—41no—
499C4⋊C8—41no—
500#103—22no—
501#103—22no—
502#103—41no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—41no—
508C22⋊C8—22no—
509C22⋊C8—41no—
510#97—22no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95D4×C3111yescharacteristic
519#95D4×C3111yescharacteristic
520C31#2491111yescharacteristic, direct product factor, Sylow
521C24—21no—
522C24—21no—
523C24C2×D4×C3111yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8#41×C3112yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4C2×D4×C3112yes—
549C2×D4C2×D4×C3112yes—
550C2×D4#41×C3112yes—
551C2×D4#41×C3112yes—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C24×C3111yescharacteristic
582SD16—44no—
583D8—28no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8C2×D4×C3112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—81no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—21no—
627C23—22no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23C22×D4×C3111yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—48no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4C31×#12314yescomplemented
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—48no—
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—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4C31×AGL(1,ℤ/8)12yes—
700C2×C4C22×D4×C3111yescharacteristic
701C2×C4C2×#41×C3111yescharacteristic
702C2×C4C2×#41×C3111yescharacteristic
703C2×C4C2×#41×C3111yescharacteristic
704C2×C4C31×H(5,𝔽2)11yescharacteristic
705C2×C4C31×H(5,𝔽2)11yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—42no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C31×#52511yescharacteristic
732C22D42×C3111yescharacteristic
733C22C31×#54611yescharacteristic
734C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
735C22C31×#57511yescharacteristic
736C22C31×#57711yescharacteristic
737C22C31×#57711yescharacteristic
738C4—22no—
739C4—41no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C2×C31×#12311yescharacteristic
750C4C31×#53811yescharacteristic
751C4C31×#54611yescharacteristic
752C4C31×#55111yescharacteristic
753C2—44no—
754C2—81no—
755C2—82no—
756C2C31×#241811yescharacteristic
757C2C31×#311511yescharacteristic
758C2C31×#312511yescharacteristic
759C2C31×#326711yescharacteristic
760C2C31×#327211yescharacteristic
761C2C31×#330611yescharacteristic
762C2C31×#330711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#442C2semidirect
3. C31×#2422C2semidirect
4. C31×#2339C2semidirect
5. C31×#2096C2semidirect
6. C31×#2077C2semidirect
7. C31×#2055C2semidirect
8. C31×#2034C2semidirect
9. C31×#1935C2semidirect
10. C31×#1924C2semidirect
11. C31×#1879C2semidirect
12. C31×#1877C2semidirect
13. C31×#1864C2semidirect
14. C31×#1802C2semidirect
15. C31×#1788C2semidirect
241. #24911C31direct (N × H)
277. D4×C31#123semidirect
330. C2×#442C2×C31semidirect
331. #2422C2×C31semidirect
332. #2339C2×C31semidirect
333. #2096C2×C31semidirect
334. #2077C2×C31semidirect
335. #2055C2×C31semidirect
336. #2034C2×C31semidirect
337. #1935C2×C31semidirect
338. #1924C2×C31semidirect
339. #1879C2×C31semidirect
340. #1877C2×C31semidirect
341. #1864C2×C31semidirect
342. #1802C2×C31semidirect
343. #1788C2×C31semidirect
520. C31#24911direct (N × H)
658. D4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4492
C2×C31×#4422
C31×#24222
C31×#23392
C31×#20962
C31×#20772
C31×#20552
C31×#20342
C31×#19352
C31×#19242
C31×#18792
C31×#18772
C31×#18642
C31×#18022
C31×#17882
#2491131