Finite Group Databasebeta

← C31×#26425 #21483184

Subgroups — C31×#26425 #21483184

Order 7936.

840 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2440C211yesmaximal, characteristic, complemented
2C31×#2363C211yesmaximal, characteristic
3C31×#2100C211yesmaximal, characteristic, complemented
4C31×#2087C211yesmaximal, characteristic, complemented
5C31×#2067C211yesmaximal, characteristic, complemented
6C31×#2023C211yesmaximal, characteristic, complemented
7C31×#1988C211yesmaximal, characteristic, complemented
8C31×#1919C211yesmaximal, characteristic, complemented
9C31×#1895C211yesmaximal, characteristic
10C31×#1874C211yesmaximal, characteristic
11C31×#1864C211yesmaximal, characteristic, complemented
12C31×#1854C211yesmaximal, characteristic, complemented
13C31×#1851C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1736C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×C22⋊Q8—21no—
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C2×C31×#107C2211yescharacteristic
24C2×C31×#106C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C2×C31×C4⋊C8C2211yescharacteristic
27C2×C31×#102C2211yescharacteristic
28C2×C31×#102C2211yescharacteristic
29C2×C31×#102C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C31×#398—21no—
33C31×#395—21no—
34C31×#390—21no—
35C31×#390C2211yescharacteristic
36C31×#389C2211yescharacteristic
37C31×#389C2211yescharacteristic
38C31×#389C2211yescharacteristic
39C31×#388—21no—
40C31×#386—21no—
41C31×#385—21no—
42C31×#384C2211yescharacteristic
43C31×#380C2211yescharacteristic
44C4×C4⋊C4×C31C2211yescharacteristic
45C4×C22⋊C4×C31—21no—
46C4×C22⋊C4×C31C2211yescharacteristic
47C31×#340C2211yescharacteristic
48C31×#340C2211yescharacteristic
49C31×#340C2211yescharacteristic
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C22×Q8×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31C2311yescharacteristic
62C23×C4×C31—21no—
63C23×C4×C31—21no—
64C23×C4×C31C2311yescharacteristic
65C2×M16×C31—22no—
66C2×M16×C31—41no—
67C2×M16×C31—41no—
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C31×C4⋊Q8—22no—
73C31×C4⋊Q8—41no—
74C31×C22⋊Q8—44no—
75C31×#121—22no—
76C31×#121Q814yescomplemented
77C4×D4×C31—22no—
78C4×D4×C31—41no—
79C31×#117—22no—
80C31×#117—41no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—41no—
90C2×C4⋊C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C22⋊C4×C31D411yescharacteristic
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31C2311yescharacteristic
108C2×C42×C31C2311yescharacteristic
109C31×#107—41no—
110C31×#106—22no—
111C31×C4⋊C8—41no—
112C31×C4⋊C8—41no—
113C31×#102—22no—
114C31×#102—41no—
115C31×#102—41no—
116C31×#102—41no—
117C31×C22⋊C8—22no—
118C31×#95—21no—
119C31×#95—21no—
120C31×#95—21no—
121C31×#95—21no—
122C31×#95—21no—
123C31×#95D411yescharacteristic
124C31×#95D411yescharacteristic
125C24×C31—21no—
126C24×C31C2×D411yescharacteristic
127C2×Q8×C31—42no—
128C2×Q8×C31—42no—
129C2×Q8×C31—81no—
130C2×D4×C31—24no—
131C2×D4×C31—21no—
132C2×D4×C31—21no—
133C2×D4×C31—21no—
134C2×D4×C31—21no—
135C2×D4×C31—21no—
136C2×D4×C31—81no—
137C2×D4×C31—81no—
138C2×D4×C31C2×Q812yes—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—42no—
151C22×C4×C31—42no—
152C22×C4×C31—42no—
153C22×C4×C31—42no—
154C22×C4×C31—81no—
155C22×C4×C31—81no—
156C22×C4×C31C2×D411yescharacteristic
157C22×C4×C31C2×D411yescharacteristic
158C22×C4×C31C2×D411yescharacteristic
159C22×C4×C31C2×D411yescharacteristic
160C22×C4×C31C2×D411yescharacteristic
161C22×C4×C31C2×Q812yes—
162C22×C4×C31#4112yes—
163C22×C4×C31C2411yescharacteristic
164M16×C31—44no—
165C2×C8×C31—21no—
166C2×C8×C31—21no—
167C2×C8×C31—21no—
168C2×C8×C31—21no—
169C2×C8×C31—21no—
170C2×C8×C31—21no—
171C2×C8×C31—21no—
172C2×C8×C31—21no—
173C2×C8×C31—21no—
174C2×C8×C31—21no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—21no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—42no—
189C4⋊C4×C31—42no—
190C4⋊C4×C31—42no—
191C4⋊C4×C31—42no—
192C4⋊C4×C31—42no—
193C4⋊C4×C31—81no—
194C4⋊C4×C31—81no—
195C4⋊C4×C31C2×Q812yes—
196C4⋊C4×C31#4112yes—
197C4⋊C4×C31#4112yes—
198C22⋊C4×C31—24no—
199C22⋊C4×C31—22no—
200C22⋊C4×C31—22no—
201C22⋊C4×C31—42no—
202C22⋊C4×C31—42no—
203C22⋊C4×C31—42no—
204C22⋊C4×C31—42no—
205C22⋊C4×C31—81no—
206C42×C31—21no—
207C42×C31—21no—
208C42×C31—21no—
209C42×C31—21no—
210C42×C31—42no—
211C42×C31—81no—
212#26425C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—21no—
214C23×C31—21no—
215C23×C31—21no—
216C23×C31—21no—
217C23×C31—21no—
218C23×C31—21no—
219C23×C31—22no—
220C23×C31—41no—
221C23×C31—41no—
222C23×C31—41no—
223C23×C31—41no—
224C23×C31—41no—
225C23×C31—41no—
226C23×C31C22⋊Q812yes—
227C23×C31C22×D411yescharacteristic
228Q8×C31—84no—
229D4×C31—22no—
230D4×C31—22no—
231D4×C31—41no—
232D4×C31—41no—
233D4×C31—84no—
234C2×C4×C31—21no—
235C2×C4×C31—21no—
236C2×C4×C31—21no—
237C2×C4×C31—21no—
238C2×C4×C31—21no—
239C2×C4×C31—21no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—22no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—41no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—41no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—84no—
272C2×C4×C31—84no—
273C2×C4×C31C22⋊Q812yes—
274C2×C4×C31AGL(1,ℤ/8)12yes—
275C2×C4×C31#13712yes—
276C2×C4×C31C22×Q811yescharacteristic
277C2×C4×C31C2×#4111yescharacteristic
278C2×C4×C31C2×#4111yescharacteristic
279C2×C4×C31C2×#4111yescharacteristic
280C2×C4×C31H(5,𝔽2)11yescharacteristic
281C2×C4×C31H(5,𝔽2)11yescharacteristic
282C8×C31—41no—
283C8×C31—41no—
284C8×C31—41no—
285C8×C31—41no—
286#2440C2×C3111yescharacteristic, complemented
287#2363C2×C3111yescharacteristic
288#2100C2×C3111yescharacteristic, complemented
289#2087C2×C3111yescharacteristic, complemented
290#2067C2×C3111yescharacteristic, complemented
291#2023C2×C3111yescharacteristic, complemented
292#1988C2×C3111yescharacteristic, complemented
293#1919C2×C3111yescharacteristic, complemented
294#1895C2×C3111yescharacteristic
295#1874C2×C3111yescharacteristic
296#1864C2×C3111yescharacteristic, complemented
297#1854C2×C3111yescharacteristic, complemented
298#1851C2×C3111yescharacteristic, complemented
299#1802C2×C3111yescharacteristic, complemented
300#1736C2×C3111yescharacteristic, complemented
301C22×C31—22no—
302C22×C31—22no—
303C22×C31—22no—
304C22×C31—41no—
305C22×C31—41no—
306C22×C31—41no—
307C22×C31—41no—
308C22×C31—42no—
309C22×C31—42no—
310C22×C31—42no—
311C22×C31—81no—
312C22×C31—81no—
313C22×C31—81no—
314C22×C31—81no—
315C22×C31C2×C22⋊Q811yescharacteristic
316C22×C31#54611yescharacteristic
317C22×C31#54611yescharacteristic
318C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C31C2×#13711yescharacteristic
320C22×C31#57611yescharacteristic
321C22×C31#57711yescharacteristic
322C4×C31—22no—
323C4×C31—22no—
324C4×C31—22no—
325C4×C31—41no—
326C4×C31—41no—
327C4×C31—42no—
328C4×C31—42no—
329C4×C31—42no—
330C4×C31—81no—
331C4×C31—81no—
332C4×C31—81no—
333C4×C31—81no—
334C4×C31#52911yescharacteristic
335C4×C31#53811yescharacteristic
336C4×C31#55411yescharacteristic
337C4×C31#55411yescharacteristic
338C22×M16C22×C3111yescharacteristic
339C2×C4⋊Q8C22×C3111yescharacteristic
340C2×C22⋊Q8—21no—
341C2×#121C22×C3111yescharacteristic
342C2×C4×D4C22×C3111yescharacteristic
343C2×#117C22×C3111yescharacteristic
344C22×C4⋊C4C22×C3111yescharacteristic
345C2×#107C22×C3111yescharacteristic
346C2×#106C22×C3111yescharacteristic
347C2×C4⋊C8C22×C3111yescharacteristic
348C2×C4⋊C8C22×C3111yescharacteristic
349C2×#102C22×C3111yescharacteristic
350C2×#102C22×C3111yescharacteristic
351C2×#102C22×C3111yescharacteristic
352C2×#102C22×C3111yescharacteristic
353C2×C22⋊C8C22×C3111yescharacteristic
354#398—21no—
355#395—21no—
356#390—21no—
357#390C22×C3111yescharacteristic
358#389C22×C3111yescharacteristic
359#389C22×C3111yescharacteristic
360#389C22×C3111yescharacteristic
361#388—21no—
362#386—21no—
363#385—21no—
364#384C22×C3111yescharacteristic
365#380C22×C3111yescharacteristic
366C4×C4⋊C4C22×C3111yescharacteristic
367C4×C22⋊C4—21no—
368C4×C22⋊C4C22×C3111yescharacteristic
369#340C22×C3111yescharacteristic
370#340C22×C3111yescharacteristic
371#340C22×C3111yescharacteristic
372#340C22×C3111yescharacteristic
373#340C22×C3111yescharacteristic
374#340C22×C3111yescharacteristic
375#340C22×C3111yescharacteristic
376#340C22×C3111yescharacteristic
377#340C22×C3111yescharacteristic
378#340C22×C3111yescharacteristic
379#336C22×C3111yescharacteristic
380#336C22×C3111yescharacteristic
381C2×C31—42no—
382C2×C31—82no—
383C2×C31#245011yescharacteristic
384C2×C31#307911yescharacteristic
385C2×C31#308111yescharacteristic
386C2×C31#331411yescharacteristic
387C2×C31#331811yescharacteristic
388C2×C31#332911yescharacteristic
389C2×C31#333211yescharacteristic
390C22×Q8—21no—
391C22×D4—21no—
392C22×D4C23×C3111yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4C23×C3111yescharacteristic
396C2×M16—22no—
397C2×M16—41no—
398C2×M16—41no—
399C22×C8C23×C3111yescharacteristic
400C22×C8C23×C3111yescharacteristic
401C22×C8C23×C3111yescharacteristic
402C22×C8C23×C3111yescharacteristic
403C4⋊Q8—22no—
404C4⋊Q8—41no—
405C22⋊Q8—44no—
406#121—22no—
407#121Q8×C3114yescomplemented
408C4×D4—22no—
409C4×D4—41no—
410#117—22no—
411#117—41no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4C23×C3111yescharacteristic
422C2×C4⋊C4C23×C3111yescharacteristic
423C2×C4⋊C4C23×C3111yescharacteristic
424C2×C4⋊C4C23×C3111yescharacteristic
425C2×C4⋊C4C23×C3111yescharacteristic
426C2×C4⋊C4C23×C3111yescharacteristic
427C2×C4⋊C4C23×C3111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4D4×C3111yescharacteristic
435C2×C22⋊C4D4×C3111yescharacteristic
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C3111yescharacteristic
439C2×C42C23×C3111yescharacteristic
440#107—41no—
441#106—22no—
442C4⋊C8—41no—
443C4⋊C8—41no—
444#102—22no—
445#102—41no—
446#102—41no—
447#102—41no—
448C22⋊C8—22no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95D4×C3111yescharacteristic
455#95D4×C3111yescharacteristic
456C31#2642511yescharacteristic, direct product factor, Sylow
457C24—21no—
458C24C2×D4×C3111yescharacteristic
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—81no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4C2×Q8×C3112yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4C2×D4×C3111yescharacteristic
489C22×C4C2×D4×C3111yescharacteristic
490C22×C4C2×D4×C3111yescharacteristic
491C22×C4C2×D4×C3111yescharacteristic
492C22×C4C2×D4×C3111yescharacteristic
493C22×C4C2×Q8×C3112yes—
494C22×C4#41×C3112yes—
495C22×C4C24×C3111yescharacteristic
496M16—44no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—81no—
526C4⋊C4—81no—
527C4⋊C4C2×Q8×C3112yes—
528C4⋊C4#41×C3112yes—
529C4⋊C4#41×C3112yes—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—81no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—81no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C31×C22⋊Q812yes—
558C23C22×D4×C3111yescharacteristic
559Q8—84no—
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—84no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—84no—
604C2×C4C31×C22⋊Q812yes—
605C2×C4C31×AGL(1,ℤ/8)12yes—
606C2×C4C31×#13712yes—
607C2×C4C22×Q8×C3111yescharacteristic
608C2×C4C2×#41×C3111yescharacteristic
609C2×C4C2×#41×C3111yescharacteristic
610C2×C4C2×#41×C3111yescharacteristic
611C2×C4C31×H(5,𝔽2)11yescharacteristic
612C2×C4C31×H(5,𝔽2)11yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×C31×C22⋊Q811yescharacteristic
632C22C31×#54611yescharacteristic
633C22C31×#54611yescharacteristic
634C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
635C22C2×C31×#13711yescharacteristic
636C22C31×#57611yescharacteristic
637C22C31×#57711yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—41no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4C31×#52911yescharacteristic
651C4C31×#53811yescharacteristic
652C4C31×#55411yescharacteristic
653C4C31×#55411yescharacteristic
654C2—42no—
655C2—82no—
656C2C31×#245011yescharacteristic
657C2C31×#307911yescharacteristic
658C2C31×#308111yescharacteristic
659C2C31×#331411yescharacteristic
660C2C31×#331811yescharacteristic
661C2C31×#332911yescharacteristic
662C2C31×#333211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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
1. C31×#2440C2semidirect
3. C31×#2100C2semidirect
4. C31×#2087C2semidirect
5. C31×#2067C2semidirect
6. C31×#2023C2semidirect
7. C31×#1988C2semidirect
8. C31×#1919C2semidirect
11. C31×#1864C2semidirect
12. C31×#1854C2semidirect
13. C31×#1851C2semidirect
14. C31×#1802C2semidirect
15. C31×#1736C2semidirect
76. C31×#121Q8semidirect
212. #26425C31direct (N × H)
286. #2440C2×C31semidirect
288. #2100C2×C31semidirect
289. #2087C2×C31semidirect
290. #2067C2×C31semidirect
291. #2023C2×C31semidirect
292. #1988C2×C31semidirect
293. #1919C2×C31semidirect
296. #1864C2×C31semidirect
297. #1854C2×C31semidirect
298. #1851C2×C31semidirect
299. #1802C2×C31semidirect
300. #1736C2×C31semidirect
407. #121Q8×C31semidirect
456. C31#26425direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24402
C31×#23632
C31×#21002
C31×#20872
C31×#20672
C31×#20232
C31×#19882
C31×#19192
C31×#18952
C31×#18742
C31×#18642
C31×#18542
C31×#18512
C31×#18022
C31×#17362
#2642531