Finite Group Databasebeta

← C31×#24879 #21481638

Subgroups — C31×#24879 #21481638

Order 7936.

1064 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#483C211yesmaximal, characteristic, complemented
2C2×C31×#417C211yesmaximal, characteristic, complemented
3C31×#2407C211yesmaximal, characteristic
4D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2072C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1928C211yesmaximal, characteristic, complemented
10C31×#1926C211yesmaximal, characteristic, complemented
11C31×#1874C211yesmaximal, characteristic, complemented
12C31×#1870C211yesmaximal, characteristic, complemented
13C31×#1853C211yesmaximal, characteristic, complemented
14C31×#1809C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#483—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C31×#417—24no—
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×C22⋊C8C2211yescharacteristic
41C31×#394—21no—
42C31×#392—21no—
43C31×#391C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389—21no—
46C31×#386—21no—
47C31×#385—21no—
48C31×#385—21no—
49C31×#385—21no—
50C31×#384C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C4×C4⋊C4×C31C2211yescharacteristic
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×C31D411yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C2×M16×C31—22no—
78C2×M16×C31—22no—
79C2×M16×C31—41no—
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8—41no—
86C31×#121—22no—
87C31×#121—41no—
88C4×D4×C31—22no—
89C4×D4×C31—22no—
90C4×D4×C31—44no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—41no—
99C2×C4⋊C4×C31—41no—
100C2×C4⋊C4×C31D411yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C22⋊C4×C31D411yescharacteristic
116C2×C42×C31—21no—
117C2×C42×C31C2311yescharacteristic
118C31×#107—41no—
119C31×#106—22no—
120C31×#106—22no—
121C31×#106—41no—
122C31×#103—22no—
123C31×#103—22no—
124C31×#103—41no—
125C31×#103D414yescomplemented
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—22no—
129C31×#102—41no—
130C31×C22⋊C8—22no—
131C31×C22⋊C8—22no—
132C31×C22⋊C8—41no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C24×C31—21no—
140C24×C31C2×D411yescharacteristic
141C24×C31C2×D411yescharacteristic
142#41×C31—28no—
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×C31C2×D412yes—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—42no—
161C2×D4×C31—42no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31—81no—
166C2×D4×C31#4112yes—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
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—21no—
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×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31#4112yes—
198C22×C4×C31#4112yes—
199C22×C4×C31C2411yescharacteristic
200M16×C31—44no—
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—21no—
211C2×C8×C31—21no—
212C2×C8×C31C2×D412yes—
213C4⋊C4×C31—22no—
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—21no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31—81no—
230C4⋊C4×C31C2×D412yes—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—81no—
239C22⋊C4×C31—81no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—42no—
243#24879C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—22no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31#12312yes—
264C23×C31AGL(1,ℤ/8)12yes—
265C23×C31C22×D411yescharacteristic
266Q8×C31—22no—
267Q8×C31—22no—
268Q8×C31—41no—
269Q8×C31—41no—
270D4×C31—28no—
271D4×C31—22no—
272D4×C31—22no—
273D4×C31—48no—
274D4×C31—41no—
275D4×C31—41no—
276D4×C31—84no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
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—41no—
316C2×C4×C31—41no—
317C2×C4×C31—84no—
318C2×C4×C31—84no—
319C2×C4×C31#12312yes—
320C2×C4×C31#13712yes—
321C2×C4×C31C22×D411yescharacteristic
322C2×C4×C31C2×#4111yescharacteristic
323C2×C4×C31C2×#4111yescharacteristic
324C2×C4×C31C2×#4111yescharacteristic
325C2×C4×C31H(5,𝔽2)11yescharacteristic
326C2×C4×C31H(5,𝔽2)11yescharacteristic
327C8×C31—22no—
328C8×C31—41no—
329C8×C31—41no—
330C8×C31—41no—
331C2×#483C2×C3111yescharacteristic, complemented
332C2×#417C2×C3111yescharacteristic, complemented
333#2407C2×C3111yescharacteristic
334D4×C4⋊C4C2×C3111yescharacteristic, complemented
335#2094C2×C3111yescharacteristic, complemented
336#2072C2×C3111yescharacteristic, complemented
337#2035C2×C3111yescharacteristic, complemented
338#2033C2×C3111yescharacteristic, complemented
339#1928C2×C3111yescharacteristic, complemented
340#1926C2×C3111yescharacteristic, complemented
341#1874C2×C3111yescharacteristic, complemented
342#1870C2×C3111yescharacteristic, complemented
343#1853C2×C3111yescharacteristic, complemented
344#1809C2×C3111yescharacteristic, complemented
345#1788C2×C3111yescharacteristic, complemented
346C22×C31—22no—
347C22×C31—22no—
348C22×C31—22no—
349C22×C31—22no—
350C22×C31—22no—
351C22×C31—22no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31C2×#12311yescharacteristic
368C22×C31D4211yescharacteristic
369C22×C31#54611yescharacteristic
370C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C31C2×#13711yescharacteristic
372C22×C31#57711yescharacteristic
373C22×C31#57711yescharacteristic
374C4×C31—22no—
375C4×C31—22no—
376C4×C31—41no—
377C4×C31—41no—
378C4×C31—42no—
379C4×C31—42no—
380C4×C31—81no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31#52511yescharacteristic
386C4×C31#53811yescharacteristic
387C4×C31#54611yescharacteristic
388C4×C31#55111yescharacteristic
389C22×#41C22×C3111yescharacteristic
390C22×M16C22×C3111yescharacteristic
391C2×C22⋊Q8C22×C3111yescharacteristic
392C2×#121C22×C3111yescharacteristic
393C2×C4×D4—21no—
394C2×C4×D4C22×C3111yescharacteristic
395C22×C4⋊C4C22×C3111yescharacteristic
396C22×C4⋊C4C22×C3111yescharacteristic
397#483—24no—
398C2×#107C22×C3111yescharacteristic
399C2×#106C22×C3111yescharacteristic
400C2×#106C22×C3111yescharacteristic
401C2×#106C22×C3111yescharacteristic
402#417—24no—
403C2×#103C22×C3111yescharacteristic
404C2×#103C22×C3111yescharacteristic
405C2×#103C22×C3111yescharacteristic
406C2×#103C22×C3111yescharacteristic
407C2×#102C22×C3111yescharacteristic
408C2×#102C22×C3111yescharacteristic
409C2×#102C22×C3111yescharacteristic
410C2×#102C22×C3111yescharacteristic
411C2×C22⋊C8C22×C3111yescharacteristic
412C2×C22⋊C8C22×C3111yescharacteristic
413C2×C22⋊C8C22×C3111yescharacteristic
414#394—21no—
415#392—21no—
416#391C22×C3111yescharacteristic
417#390C22×C3111yescharacteristic
418#389—21no—
419#386—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#384C22×C3111yescharacteristic
424#380C22×C3111yescharacteristic
425#380C22×C3111yescharacteristic
426#380C22×C3111yescharacteristic
427C4×C4⋊C4C22×C3111yescharacteristic
428#340C22×C3111yescharacteristic
429#340C22×C3111yescharacteristic
430#340C22×C3111yescharacteristic
431#340C22×C3111yescharacteristic
432#336C22×C3111yescharacteristic
433#336C22×C3111yescharacteristic
434C2×C31—42no—
435C2×C31—42no—
436C2×C31—82no—
437C2×C31#241811yescharacteristic
438C2×C31#309211yescharacteristic
439C2×C31#309911yescharacteristic
440C2×C31#326511yescharacteristic
441C2×C31#327811yescharacteristic
442C2×C31#330611yescharacteristic
443C2×C31#333111yescharacteristic
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—41no—
449C2×#41—41no—
450C22×Q8C23×C3111yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4D4×C3111yescharacteristic
454C22×D4C23×C3111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4C23×C3111yescharacteristic
459C23×C4C23×C3111yescharacteristic
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—41no—
463C22×C8C23×C3111yescharacteristic
464C22×C8C23×C3111yescharacteristic
465C22×C8C23×C3111yescharacteristic
466C22×C8C23×C3111yescharacteristic
467C22⋊Q8—22no—
468C22⋊Q8—41no—
469#121—22no—
470#121—41no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—44no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4D4×C3111yescharacteristic
484C2×C4⋊C4C23×C3111yescharacteristic
485C2×C4⋊C4C23×C3111yescharacteristic
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
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⋊C4D4×C3111yescharacteristic
498C2×C22⋊C4D4×C3111yescharacteristic
499C2×C42—21no—
500C2×C42C23×C3111yescharacteristic
501#107—41no—
502#106—22no—
503#106—22no—
504#106—41no—
505#103—22no—
506#103—22no—
507#103—41no—
508#103D4×C3114yescomplemented
509#102—22no—
510#102—22no—
511#102—22no—
512#102—41no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—41no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522C31#2487911yescharacteristic, direct product factor, Sylow
523C24—21no—
524C24C2×D4×C3111yescharacteristic
525C24C2×D4×C3111yescharacteristic
526#41—28no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C2×D4×C3112yes—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—81no—
550C2×D4#41×C3112yes—
551C22×C4—21no—
552C22×C4—21no—
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—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4#41×C3112yes—
582C22×C4#41×C3112yes—
583C22×C4C24×C3111yescharacteristic
584M16—44no—
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×C8—21no—
596C2×C8C2×D4×C3112yes—
597C4⋊C4—22no—
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—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—81no—
614C4⋊C4C2×D4×C3112yes—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C42—21no—
625C42—21no—
626C42—42no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23C31×#12312yes—
647C23C31×AGL(1,ℤ/8)12yes—
648C23C22×D4×C3111yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—41no—
652Q8—41no—
653D4—28no—
654D4—22no—
655D4—22no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—84no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—48no—
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—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4C31×#12312yes—
703C2×C4C31×#13712yes—
704C2×C4C22×D4×C3111yescharacteristic
705C2×C4C2×#41×C3111yescharacteristic
706C2×C4C2×#41×C3111yescharacteristic
707C2×C4C2×#41×C3111yescharacteristic
708C2×C4C31×H(5,𝔽2)11yescharacteristic
709C2×C4C31×H(5,𝔽2)11yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22C2×C31×#12311yescharacteristic
736C22D42×C3111yescharacteristic
737C22C31×#54611yescharacteristic
738C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
739C22C2×C31×#13711yescharacteristic
740C22C31×#57711yescharacteristic
741C22C31×#57711yescharacteristic
742C4—22no—
743C4—22no—
744C4—41no—
745C4—41no—
746C4—42no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4C31×#52511yescharacteristic
754C4C31×#53811yescharacteristic
755C4C31×#54611yescharacteristic
756C4C31×#55111yescharacteristic
757C2—42no—
758C2—42no—
759C2—82no—
760C2C31×#241811yescharacteristic
761C2C31×#309211yescharacteristic
762C2C31×#309911yescharacteristic
763C2C31×#326511yescharacteristic
764C2C31×#327811yescharacteristic
765C2C31×#330611yescharacteristic
766C2C31×#333111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2407C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#483C2semidirect
2. C2×C31×#417C2semidirect
4. D4×C4⋊C4×C31C2semidirect
5. C31×#2094C2semidirect
6. C31×#2072C2semidirect
7. C31×#2035C2semidirect
8. C31×#2033C2semidirect
9. C31×#1928C2semidirect
10. C31×#1926C2semidirect
11. C31×#1874C2semidirect
12. C31×#1870C2semidirect
13. C31×#1853C2semidirect
14. C31×#1809C2semidirect
15. C31×#1788C2semidirect
125. C31×#103D4semidirect
243. #24879C31direct (N × H)
331. C2×#483C2×C31semidirect
332. C2×#417C2×C31semidirect
334. D4×C4⋊C4C2×C31semidirect
335. #2094C2×C31semidirect
336. #2072C2×C31semidirect
337. #2035C2×C31semidirect
338. #2033C2×C31semidirect
339. #1928C2×C31semidirect
340. #1926C2×C31semidirect
341. #1874C2×C31semidirect
342. #1870C2×C31semidirect
343. #1853C2×C31semidirect
344. #1809C2×C31semidirect
345. #1788C2×C31semidirect
508. #103D4×C31semidirect
522. C31#24879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4832
C2×C31×#4172
C31×#24072
D4×C4⋊C4×C312
C31×#20942
C31×#20722
C31×#20352
C31×#20332
C31×#19282
C31×#19262
C31×#18742
C31×#18702
C31×#18532
C31×#18092
C31×#17882
#2487931