Finite Group Databasebeta

← C31×#24841 #21481600

Subgroups — C31×#24841 #21481600

Order 7936.

912 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#478C211yesmaximal, characteristic, complemented
2C2×C31×#423C211yesmaximal, characteristic, complemented
3C31×#2851C211yesmaximal, characteristic, complemented
4C4×C31×#121C211yesmaximal, characteristic
5C31×#2088C211yesmaximal, characteristic, complemented
6C31×#2086C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic, complemented
9C31×#1989C211yesmaximal, characteristic, complemented
10C31×#1949C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic
12C31×#1895C211yesmaximal, characteristic
13C31×#1809C211yesmaximal, characteristic, complemented
14C31×#1809C211yesmaximal, characteristic, complemented
15C31×#1804C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C2×C31×#125C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C31×#478—24no—
24C2×C31×#107C2211yescharacteristic
25C2×C31×#107C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C31×#423—24no—
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C31×#390C2211yescharacteristic
38C31×#389C2211yescharacteristic
39C31×#389C2211yescharacteristic
40C31×#389C2211yescharacteristic
41C31×#388—21no—
42C31×#387—21no—
43C31×#387—21no—
44C31×#386—21no—
45C31×#385—21no—
46C31×#385—21no—
47C31×#382C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C22⋊C4×C31—21no—
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31D411yescharacteristic
65C23×C4×C31D411yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C2×M16×C31—22no—
68C2×M16×C31—22no—
69C2×M16×C31—22no—
70C2×M16×C31—22no—
71C2×M16×C31—41no—
72C2×M16×C31—41no—
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×#125—22no—
78C31×#125—22no—
79C31×#121—22no—
80C31×#121Q814yes—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C4×D4×C31—44no—
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×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
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×C42×C31—22no—
104C2×C42×C31—22no—
105C2×C42×C31—21no—
106C2×C42×C31D411yescharacteristic
107C2×C42×C31D411yescharacteristic
108C2×C42×C31C2311yescharacteristic
109C2×C42×C31C2311yescharacteristic
110C31×#107—22no—
111C31×#107—41no—
112C31×#106—22no—
113C31×#106—41no—
114C31×C4⋊C8—22no—
115C31×C4⋊C8—22no—
116C31×C4⋊C8—22no—
117C31×C4⋊C8D414yescomplemented
118C31×#102—22no—
119C31×#102—22no—
120C31×#102—41no—
121C31×#102—41no—
122C31×#95—21no—
123C31×#95—21no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C24×C31—21no—
132C24×C31C2×D411yescharacteristic
133C2×D4×C31—24no—
134C2×D4×C31—21no—
135C2×D4×C31—21no—
136C2×D4×C31—21no—
137C2×D4×C31—21no—
138C2×D4×C31—21no—
139C2×D4×C31—42no—
140C2×D4×C31—42no—
141C2×D4×C31C2×Q812yes—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—41no—
157C22×C4×C31—41no—
158C22×C4×C31—41no—
159C22×C4×C31—42no—
160C22×C4×C31—42no—
161C22×C4×C31—42no—
162C22×C4×C31C2×D411yescharacteristic
163C22×C4×C31C2×D411yescharacteristic
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×Q812yes—
168C22×C4×C31#4112yes—
169C22×C4×C31C2411yescharacteristic
170M16×C31—44no—
171M16×C31—44no—
172C2×C8×C31—21no—
173C2×C8×C31—21no—
174C2×C8×C31—21no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31C2×D412yes—
183C2×C8×C31C2×D412yes—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—42no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31C2×Q812yes—
203C22⋊C4×C31—24no—
204C22⋊C4×C31—42no—
205C22⋊C4×C31—42no—
206C22⋊C4×C31—42no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C42×C31—22no—
211C42×C31—22no—
212C42×C31—21no—
213C42×C31—21no—
214C42×C31—42no—
215C42×C31C2×D412yes—
216C42×C31#4112yes—
217#24841C3111yesmaximal, characteristic, direct product factor, Sylow
218C23×C31—21no—
219C23×C31—21no—
220C23×C31—21no—
221C23×C31—21no—
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—22no—
225C23×C31—41no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31C22⋊Q812yes—
232C23×C31C22×D411yescharacteristic
233D4×C31—22no—
234D4×C31—22no—
235D4×C31—48no—
236D4×C31—41no—
237D4×C31—41no—
238C2×C4×C31—21no—
239C2×C4×C31—21no—
240C2×C4×C31—21no—
241C2×C4×C31—21no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—22no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—21no—
251C2×C4×C31—22no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—44no—
255C2×C4×C31—44no—
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—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—84no—
277C2×C4×C31#12112yes—
278C2×C4×C31#12112yes—
279C2×C4×C31C22⋊Q812yes—
280C2×C4×C31AGL(1,ℤ/8)12yes—
281C2×C4×C31C22×D411yescharacteristic
282C2×C4×C31C22×Q811yescharacteristic
283C2×C4×C31C2×#4111yescharacteristic
284C2×C4×C31C2×#4111yescharacteristic
285C2×C4×C31H(5,𝔽2)11yescharacteristic
286C2×C4×C312−1+411yescharacteristic
287C8×C31—22no—
288C8×C31—22no—
289C8×C31—41no—
290C8×C31—41no—
291C2×#478C2×C3111yescharacteristic, complemented
292C2×#423C2×C3111yescharacteristic, complemented
293#2851C2×C3111yescharacteristic, complemented
294C4×#121C2×C3111yescharacteristic
295#2088C2×C3111yescharacteristic, complemented
296#2086C2×C3111yescharacteristic, complemented
297#2067C2×C3111yescharacteristic, complemented
298#2065C2×C3111yescharacteristic, complemented
299#1989C2×C3111yescharacteristic, complemented
300#1949C2×C3111yescharacteristic, complemented
301#1895C2×C3111yescharacteristic
302#1895C2×C3111yescharacteristic
303#1809C2×C3111yescharacteristic, complemented
304#1809C2×C3111yescharacteristic, complemented
305#1804C2×C3111yescharacteristic, complemented
306C22×C31—22no—
307C22×C31—22no—
308C22×C31—22no—
309C22×C31—41no—
310C22×C31—41no—
311C22×C31—41no—
312C22×C31—41no—
313C22×C31—42no—
314C22×C31—42no—
315C22×C31—42no—
316C22×C31—81no—
317C22×C31—81no—
318C22×C31—81no—
319C22×C31—81no—
320C22×C31C2×#12111yescharacteristic
321C22×C31C2×C22⋊Q811yescharacteristic
322C22×C31#53711yescharacteristic
323C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C31#57511yescharacteristic
325C22×C31#57511yescharacteristic
326C22×C31#57511yescharacteristic
327C4×C31—22no—
328C4×C31—22no—
329C4×C31—22no—
330C4×C31—22no—
331C4×C31—42no—
332C4×C31—41no—
333C4×C31—81no—
334C4×C31—81no—
335C4×C31—81no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31#54611yescharacteristic
340C4×C31D4×Q811yescharacteristic
341C4×C31#55211yescharacteristic
342C4×C31#55411yescharacteristic
343C22×M16C22×C3111yescharacteristic
344C22×M16C22×C3111yescharacteristic
345C2×#125C22×C3111yescharacteristic
346C2×#121C22×C3111yescharacteristic
347C2×C4×D4—21no—
348C2×C4×D4C22×C3111yescharacteristic
349C22×C42C22×C3111yescharacteristic
350#478—24no—
351C2×#107C22×C3111yescharacteristic
352C2×#107C22×C3111yescharacteristic
353C2×#106C22×C3111yescharacteristic
354C2×#106C22×C3111yescharacteristic
355#423—24no—
356C2×C4⋊C8C22×C3111yescharacteristic
357C2×C4⋊C8C22×C3111yescharacteristic
358C2×C4⋊C8C22×C3111yescharacteristic
359C2×C4⋊C8C22×C3111yescharacteristic
360C2×#102C22×C3111yescharacteristic
361C2×#102C22×C3111yescharacteristic
362C2×#102C22×C3111yescharacteristic
363C2×#102C22×C3111yescharacteristic
364#390C22×C3111yescharacteristic
365#389C22×C3111yescharacteristic
366#389C22×C3111yescharacteristic
367#389C22×C3111yescharacteristic
368#388—21no—
369#387—21no—
370#387—21no—
371#386—21no—
372#385—21no—
373#385—21no—
374#382C22×C3111yescharacteristic
375#380C22×C3111yescharacteristic
376#380C22×C3111yescharacteristic
377#380C22×C3111yescharacteristic
378C4×C4⋊C4C22×C3111yescharacteristic
379C4×C22⋊C4—21no—
380#340C22×C3111yescharacteristic
381#340C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388C2×C31—42no—
389C2×C31—82no—
390C2×C31#241711yescharacteristic
391C2×C31#305411yescharacteristic
392C2×C31#305511yescharacteristic
393C2×C31#307711yescharacteristic
394C2×C31#308011yescharacteristic
395C2×C31#325111yescharacteristic
396C2×C31#325611yescharacteristic
397C22×D4—21no—
398C22×D4C23×C3111yescharacteristic
399C23×C4—21no—
400C23×C4D4×C3111yescharacteristic
401C23×C4D4×C3111yescharacteristic
402C23×C4C23×C3111yescharacteristic
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—22no—
407C2×M16—41no—
408C2×M16—41no—
409C22×C8C23×C3111yescharacteristic
410C22×C8C23×C3111yescharacteristic
411C22×C8C23×C3111yescharacteristic
412C22×C8C23×C3111yescharacteristic
413#125—22no—
414#125—22no—
415#121—22no—
416#121Q8×C3114yes—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—44no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4C23×C3111yescharacteristic
426C2×C4⋊C4C23×C3111yescharacteristic
427C2×C4⋊C4C23×C3111yescharacteristic
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C4⋊C4C23×C3111yescharacteristic
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C4⋊C4C23×C3111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—21no—
442C2×C42D4×C3111yescharacteristic
443C2×C42D4×C3111yescharacteristic
444C2×C42C23×C3111yescharacteristic
445C2×C42C23×C3111yescharacteristic
446#107—22no—
447#107—41no—
448#106—22no—
449#106—41no—
450C4⋊C8—22no—
451C4⋊C8—22no—
452C4⋊C8—22no—
453C4⋊C8D4×C3114yescomplemented
454#102—22no—
455#102—22no—
456#102—41no—
457#102—41no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467C31#2484111yescharacteristic, direct product factor, Sylow
468C24—21no—
469C24C2×D4×C3111yescharacteristic
470C2×D4—24no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4C2×Q8×C3112yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4C2×D4×C3111yescharacteristic
500C22×C4C2×D4×C3111yescharacteristic
501C22×C4C2×D4×C3111yescharacteristic
502C22×C4C2×D4×C3111yescharacteristic
503C22×C4C2×D4×C3111yescharacteristic
504C22×C4C2×Q8×C3112yes—
505C22×C4#41×C3112yes—
506C22×C4C24×C3111yescharacteristic
507M16—44no—
508M16—44no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8C2×D4×C3112yes—
520C2×C8C2×D4×C3112yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4C2×Q8×C3112yes—
540C22⋊C4—24no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C42—22no—
548C42—22no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42C2×D4×C3112yes—
553C42#41×C3112yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23C31×C22⋊Q812yes—
568C23C22×D4×C3111yescharacteristic
569D4—22no—
570D4—22no—
571D4—48no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—44no—
591C2×C4—44no—
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—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4C31×#12112yes—
614C2×C4C31×#12112yes—
615C2×C4C31×C22⋊Q812yes—
616C2×C4C31×AGL(1,ℤ/8)12yes—
617C2×C4C22×D4×C3111yescharacteristic
618C2×C4C22×Q8×C3111yescharacteristic
619C2×C4C2×#41×C3111yescharacteristic
620C2×C4C2×#41×C3111yescharacteristic
621C2×C4C31×H(5,𝔽2)11yescharacteristic
622C2×C4C31×2−1+411yescharacteristic
623C8—22no—
624C8—22no—
625C8—41no—
626C8—41no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22C2×C31×#12111yescharacteristic
642C22C2×C31×C22⋊Q811yescharacteristic
643C22C31×#53711yescharacteristic
644C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
645C22C31×#57511yescharacteristic
646C22C31×#57511yescharacteristic
647C22C31×#57511yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—22no—
652C4—42no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4C31×#54611yescharacteristic
661C4D4×Q8×C3111yescharacteristic
662C4C31×#55211yescharacteristic
663C4C31×#55411yescharacteristic
664C2—42no—
665C2—82no—
666C2C31×#241711yescharacteristic
667C2C31×#305411yescharacteristic
668C2C31×#305511yescharacteristic
669C2C31×#307711yescharacteristic
670C2C31×#308011yescharacteristic
671C2C31×#325111yescharacteristic
672C2C31×#325611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#478C2semidirect
2. C2×C31×#423C2semidirect
3. C31×#2851C2semidirect
5. C31×#2088C2semidirect
6. C31×#2086C2semidirect
7. C31×#2067C2semidirect
8. C31×#2065C2semidirect
9. C31×#1989C2semidirect
10. C31×#1949C2semidirect
13. C31×#1809C2semidirect
14. C31×#1809C2semidirect
15. C31×#1804C2semidirect
117. C31×C4⋊C8D4semidirect
217. #24841C31direct (N × H)
291. C2×#478C2×C31semidirect
292. C2×#423C2×C31semidirect
293. #2851C2×C31semidirect
295. #2088C2×C31semidirect
296. #2086C2×C31semidirect
297. #2067C2×C31semidirect
298. #2065C2×C31semidirect
299. #1989C2×C31semidirect
300. #1949C2×C31semidirect
303. #1809C2×C31semidirect
304. #1809C2×C31semidirect
305. #1804C2×C31semidirect
453. C4⋊C8D4×C31semidirect
467. C31#24841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4782
C2×C31×#4232
C31×#28512
C4×C31×#1212
C31×#20882
C31×#20862
C31×#20672
C31×#20652
C31×#19892
C31×#19492
C31×#18952
C31×#18092
C31×#18042
#2484131