Finite Group Databasebeta

← C31×#24664 #21481423

Subgroups — C31×#24664 #21481423

Order 7936.

814 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#462C211yesmaximal, characteristic, complemented
2C2×C31×#433C211yesmaximal, characteristic
3C31×#2621C211yesmaximal, characteristic
4C31×#2323C211yesmaximal, characteristic
5C31×#2036C211yesmaximal, characteristic
6C31×#2035C211yesmaximal, characteristic
7C31×#2001C211yesmaximal, characteristic
8C31×#2001C211yesmaximal, characteristic
9C31×#1981C211yesmaximal, characteristic, complemented
10C31×#1971C211yesmaximal, characteristic, complemented
11C31×#1969C211yesmaximal, characteristic, complemented
12C31×#1949C211yesmaximal, characteristic, complemented
13C31×#1935C211yesmaximal, characteristic, complemented
14C31×#1933C211yesmaximal, characteristic, complemented
15C31×#1805C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C31×#117C2211yescharacteristic
24C31×#462—24no—
25C31×#433—24no—
26C2×C31×#107C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic
41C2×C4×C8×C31C2211yescharacteristic
42C31×#398—21no—
43C31×#398—21no—
44C31×#397—21no—
45C31×#397—21no—
46C31×#391C2211yescharacteristic
47C31×#391C2211yescharacteristic
48C31×#391C2211yescharacteristic
49C31×#389—21no—
50C31×#389C2211yescharacteristic
51C31×#388—21no—
52C31×#388—21no—
53C31×#387—21no—
54C31×#382C2211yescharacteristic
55C31×#380C2211yescharacteristic
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C2×Q16×C31—22no—
66C2×Q16×C31—22no—
67C2×Q16×C31—22no—
68C2×Q16×C31—22no—
69C2×Q16×C31—41no—
70C2×Q16×C31—41no—
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C31×C4⋊Q8—22no—
76C31×C4⋊Q8—22no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—22no—
79C31×C22⋊Q8—41no—
80C31×C22⋊Q8—41no—
81C31×C22⋊Q8—41no—
82C31×C22⋊Q8—41no—
83C4×Q8×C31—22no—
84C4×Q8×C31—22no—
85C31×#117—22no—
86C31×#117—22no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31D411yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31D411yescharacteristic
106C2×C22⋊C4×C31D411yescharacteristic
107C2×C42×C31—21no—
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C2×C42×C31C2311yescharacteristic
111C31×#107—41no—
112C31×#106—41no—
113C31×C4⋊C8—22no—
114C31×C4⋊C8D414yes—
115C31×#103—22no—
116C31×#103—22no—
117C31×#103—22no—
118C31×#103—22no—
119C31×#103—41no—
120C31×#103—41no—
121C31×#103—41no—
122C31×#103—41no—
123C31×C22⋊C8—22no—
124C31×C22⋊C8—22no—
125C31×#97—22no—
126C4×C8×C31—22no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C24×C31C2×D411yescharacteristic
139C2×Q8×C31—21no—
140C2×Q8×C31—21no—
141C2×Q8×C31—21no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31#4112yes—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2411yescharacteristic
177Q16×C31—44no—
178Q16×C31—44no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31C2×D412yes—
190C2×C8×C31C2×D412yes—
191C4⋊C4×C31—24no—
192C4⋊C4×C31—22no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—81no—
209C4⋊C4×C31#4112yes—
210C22⋊C4×C31—24no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—81no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—42no—
219C42×C31—81no—
220C42×C31C2×D412yes—
221C42×C31#4112yes—
222#24664C3111yesmaximal, characteristic, direct product factor, Sylow
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31C22×D411yescharacteristic
231Q8×C31—22no—
232Q8×C31—22no—
233Q8×C31—41no—
234Q8×C31—41no—
235Q8×C31—41no—
236Q8×C31—41no—
237Q8×C31—41no—
238Q8×C31—41no—
239Q8×C31—41no—
240Q8×C31—41no—
241Q8×C31—41no—
242Q8×C31—41no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—22no—
251C2×C4×C31—22no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
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—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31#12112yes—
285C2×C4×C31#12112yes—
286C2×C4×C31C22×D411yescharacteristic
287C2×C4×C31C2×#4111yescharacteristic
288C2×C4×C31C2×#4111yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31H(5,𝔽2)11yescharacteristic
291C2×C4×C31H(5,𝔽2)11yescharacteristic
292C8×C31—22no—
293C8×C31—22no—
294C8×C31—41no—
295C8×C31—41no—
296C2×#462C2×C3111yescharacteristic, complemented
297C2×#433C2×C3111yescharacteristic
298#2621C2×C3111yescharacteristic
299#2323C2×C3111yescharacteristic
300#2036C2×C3111yescharacteristic
301#2035C2×C3111yescharacteristic
302#2001C2×C3111yescharacteristic
303#2001C2×C3111yescharacteristic
304#1981C2×C3111yescharacteristic, complemented
305#1971C2×C3111yescharacteristic, complemented
306#1969C2×C3111yescharacteristic, complemented
307#1949C2×C3111yescharacteristic, complemented
308#1935C2×C3111yescharacteristic, complemented
309#1933C2×C3111yescharacteristic, complemented
310#1805C2×C3111yescharacteristic, complemented
311C22×C31—41no—
312C22×C31—41no—
313C22×C31—41no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31C2×#12111yescharacteristic
319C22×C31#52511yescharacteristic
320C22×C31#53511yescharacteristic
321C22×C31#57711yescharacteristic
322C22×C31#57811yescharacteristic
323C22×C31#57811yescharacteristic
324C22×C31#57811yescharacteristic
325C4×C31—22no—
326C4×C31—22no—
327C4×C31—42no—
328C4×C31—41no—
329C4×C31—42no—
330C4×C31—41no—
331C4×C31—41no—
332C4×C31—81no—
333C4×C31—81no—
334C4×C31—81no—
335C4×C31—81no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31#54611yescharacteristic
339C4×C31#55011yescharacteristic
340C4×C31#55311yescharacteristic
341C4×C31#55511yescharacteristic
342C22×Q16C22×C3111yescharacteristic
343C22×Q16C22×C3111yescharacteristic
344C2×C4⋊Q8C22×C3111yescharacteristic
345C2×C22⋊Q8C22×C3111yescharacteristic
346C2×C22⋊Q8C22×C3111yescharacteristic
347C2×C22⋊Q8C22×C3111yescharacteristic
348C2×C4×Q8C22×C3111yescharacteristic
349C2×#117C22×C3111yescharacteristic
350#462—24no—
351#433—24no—
352C2×#107C22×C3111yescharacteristic
353C2×#106C22×C3111yescharacteristic
354C2×C4⋊C8C22×C3111yescharacteristic
355C2×C4⋊C8C22×C3111yescharacteristic
356C2×#103C22×C3111yescharacteristic
357C2×#103C22×C3111yescharacteristic
358C2×#103C22×C3111yescharacteristic
359C2×#103C22×C3111yescharacteristic
360C2×#103C22×C3111yescharacteristic
361C2×#103C22×C3111yescharacteristic
362C2×#103C22×C3111yescharacteristic
363C2×#103C22×C3111yescharacteristic
364C2×C22⋊C8C22×C3111yescharacteristic
365C2×C22⋊C8C22×C3111yescharacteristic
366C2×#97C22×C3111yescharacteristic
367C2×C4×C8C22×C3111yescharacteristic
368#398—21no—
369#398—21no—
370#397—21no—
371#397—21no—
372#391C22×C3111yescharacteristic
373#391C22×C3111yescharacteristic
374#391C22×C3111yescharacteristic
375#389—21no—
376#389C22×C3111yescharacteristic
377#388—21no—
378#388—21no—
379#387—21no—
380#382C22×C3111yescharacteristic
381#380C22×C3111yescharacteristic
382C4×C4⋊C4C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387C2×C31—81no—
388C2×C31#241411yescharacteristic
389C2×C31#305911yescharacteristic
390C2×C31#306311yescharacteristic
391C2×C31#312011yescharacteristic
392C2×C31#312711yescharacteristic
393C2×C31#322311yescharacteristic
394C2×C31#322511yescharacteristic
395C22×Q8C23×C3111yescharacteristic
396C22×Q8C23×C3111yescharacteristic
397C22×Q8C23×C3111yescharacteristic
398C23×C4C23×C3111yescharacteristic
399C2×Q16—22no—
400C2×Q16—22no—
401C2×Q16—22no—
402C2×Q16—22no—
403C2×Q16—41no—
404C2×Q16—41no—
405C22×C8C23×C3111yescharacteristic
406C22×C8C23×C3111yescharacteristic
407C22×C8C23×C3111yescharacteristic
408C22×C8C23×C3111yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—41no—
414C22⋊Q8—41no—
415C22⋊Q8—41no—
416C22⋊Q8—41no—
417C4×Q8—22no—
418C4×Q8—22no—
419#117—22no—
420#117—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4D4×C3111yescharacteristic
429C2×C4⋊C4D4×C3111yescharacteristic
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C4⋊C4C23×C3111yescharacteristic
432C2×C4⋊C4C23×C3111yescharacteristic
433C2×C4⋊C4C23×C3111yescharacteristic
434C2×C4⋊C4C23×C3111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C3111yescharacteristic
440C2×C22⋊C4D4×C3111yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C3111yescharacteristic
444C2×C42C23×C3111yescharacteristic
445#107—41no—
446#106—41no—
447C4⋊C8—22no—
448C4⋊C8D4×C3114yes—
449#103—22no—
450#103—22no—
451#103—22no—
452#103—22no—
453#103—41no—
454#103—41no—
455#103—41no—
456#103—41no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459#97—22no—
460C4×C8—22no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C31#2466411yescharacteristic, direct product factor, Sylow
473C24C2×D4×C3111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8#41×C3112yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4C2×D4×C3111yescharacteristic
507C22×C4C2×D4×C3111yescharacteristic
508C22×C4C2×D4×C3111yescharacteristic
509C22×C4C2×D4×C3111yescharacteristic
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C24×C3111yescharacteristic
512Q16—44no—
513Q16—44no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C2×D4×C3112yes—
525C2×C8C2×D4×C3112yes—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—81no—
544C4⋊C4#41×C3112yes—
545C22⋊C4—24no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—81no—
555C42C2×D4×C3112yes—
556C42#41×C3112yes—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23C22×D4×C3111yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
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—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4C31×#12112yes—
619C2×C4C31×#12112yes—
620C2×C4C22×D4×C3111yescharacteristic
621C2×C4C2×#41×C3111yescharacteristic
622C2×C4C2×#41×C3111yescharacteristic
623C2×C4C2×#41×C3111yescharacteristic
624C2×C4C31×H(5,𝔽2)11yescharacteristic
625C2×C4C31×H(5,𝔽2)11yescharacteristic
626C8—22no—
627C8—22no—
628C8—41no—
629C8—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22C2×C31×#12111yescharacteristic
638C22C31×#52511yescharacteristic
639C22C31×#53511yescharacteristic
640C22C31×#57711yescharacteristic
641C22C31×#57811yescharacteristic
642C22C31×#57811yescharacteristic
643C22C31×#57811yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—41no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4C31×#54611yescharacteristic
658C4C31×#55011yescharacteristic
659C4C31×#55311yescharacteristic
660C4C31×#55511yescharacteristic
661C2—81no—
662C2C31×#241411yescharacteristic
663C2C31×#305911yescharacteristic
664C2C31×#306311yescharacteristic
665C2C31×#312011yescharacteristic
666C2C31×#312711yescharacteristic
667C2C31×#322311yescharacteristic
668C2C31×#322511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#462C2semidirect
9. C31×#1981C2semidirect
10. C31×#1971C2semidirect
11. C31×#1969C2semidirect
12. C31×#1949C2semidirect
13. C31×#1935C2semidirect
14. C31×#1933C2semidirect
15. C31×#1805C2semidirect
222. #24664C31direct (N × H)
296. C2×#462C2×C31semidirect
304. #1981C2×C31semidirect
305. #1971C2×C31semidirect
306. #1969C2×C31semidirect
307. #1949C2×C31semidirect
308. #1935C2×C31semidirect
309. #1933C2×C31semidirect
310. #1805C2×C31semidirect
472. C31#24664direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4622
C2×C31×#4332
C31×#26212
C31×#23232
C31×#20362
C31×#20352
C31×#20012
C31×#19812
C31×#19712
C31×#19692
C31×#19492
C31×#19352
C31×#19332
C31×#18052
#2466431