Finite Group Databasebeta

← C31×#23715 #21480474

Subgroups — C31×#23715 #21480474

Order 7936.

876 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#440C211yesmaximal, characteristic, complemented
2C2×C31×#433C211yesmaximal, characteristic, complemented
3C31×#2324C211yesmaximal, characteristic
4C31×#2323C211yesmaximal, characteristic, complemented
5C31×#2086C211yesmaximal, characteristic, complemented
6C31×#2076C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic, complemented
9C31×#2055C211yesmaximal, characteristic, complemented
10C31×#2035C211yesmaximal, characteristic, complemented
11C31×#2033C211yesmaximal, characteristic
12C31×#2000C211yesmaximal, characteristic
13C31×#1776C211yesmaximal, characteristic, complemented
14C4×C31×#103C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C31×#121C2211yescharacteristic
19C2×C4×Q8×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C31×#440—24no—
23C31×#433—24no—
24C2×C31×#107C2211yescharacteristic
25C2×C31×#107C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×C4⋊C8C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×#97C2211yescharacteristic
38C2×C4×C8×C31C2211yescharacteristic
39C31×#391C2211yescharacteristic
40C31×#390—21no—
41C31×#390C2211yescharacteristic
42C31×#389—21no—
43C31×#389C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#388—21no—
46C31×#388—21no—
47C31×#388—21no—
48C31×#387—21no—
49C31×#386—21no—
50C31×#385—21no—
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C4⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31C2311yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31C2311yescharacteristic
66C2×SD16×C31—22no—
67C2×SD16×C31—22no—
68C2×SD16×C31—22no—
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C31×C22⋊Q8—22no—
74C31×C22⋊Q8—22no—
75C31×#121—22no—
76C31×#121—22no—
77C4×Q8×C31—22no—
78C4×Q8×C31—22no—
79C4×D4×C31—22no—
80C4×D4×C31—22no—
81C31×#117—22no—
82C31×#117—22no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31D411yescharacteristic
88C2×C4⋊C4×C31D411yescharacteristic
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×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C42×C31—21no—
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31C2311yescharacteristic
108C2×C42×C31C2311yescharacteristic
109C31×#107—22no—
110C31×#107—22no—
111C31×#106—22no—
112C31×C4⋊C8—22no—
113C31×C4⋊C8—22no—
114C31×#103—22no—
115C31×#103—22no—
116C31×#103—22no—
117C31×#102—22no—
118C31×#102—22no—
119C31×#102—22no—
120C31×C22⋊C8—22no—
121C31×C22⋊C8—22no—
122C31×#97D414yescomplemented
123C4×C8×C31—22no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C24×C31—21no—
133C24×C31C2×D411yescharacteristic
134C2×Q8×C31—21no—
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31#4112yes—
140C2×D4×C31—24no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—81no—
147C2×D4×C31—81no—
148C2×D4×C31#4112yes—
149C22×C4×C31—21no—
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—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—42no—
163C22×C4×C31—81no—
164C22×C4×C31—81no—
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2411yescharacteristic
171SD16×C31—28no—
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—24no—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—22no—
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—81no—
199C4⋊C4×C31—81no—
200C4⋊C4×C31#4112yes—
201C4⋊C4×C31#4112yes—
202C22⋊C4×C31—24no—
203C22⋊C4×C31—24no—
204C22⋊C4×C31—22no—
205C22⋊C4×C31—22no—
206C22⋊C4×C31—42no—
207C22⋊C4×C31—81no—
208C22⋊C4×C31—81no—
209C22⋊C4×C31—81no—
210C22⋊C4×C31—81no—
211C42×C31—21no—
212C42×C31—21no—
213C42×C31—42no—
214C42×C31—81no—
215C42×C31—81no—
216C42×C31C2×D412yes—
217C42×C31#4112yes—
218#23715C3111yesmaximal, characteristic, direct product factor, Sylow
219C23×C31—21no—
220C23×C31—21no—
221C23×C31—22no—
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31C22×D411yescharacteristic
234Q8×C31—22no—
235Q8×C31—22no—
236Q8×C31—41no—
237Q8×C31—41no—
238D4×C31—22no—
239D4×C31—22no—
240D4×C31—41no—
241D4×C31—41no—
242D4×C31—84no—
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—21no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—22no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
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—84no—
282C2×C4×C31#12112yes—
283C2×C4×C31#12112yes—
284C2×C4×C31C22×D411yescharacteristic
285C2×C4×C31C2×#4111yescharacteristic
286C2×C4×C31C2×#4111yescharacteristic
287C2×C4×C31C2×#4111yescharacteristic
288C2×C4×C31C2×#4111yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C8×C31—22no—
291C8×C31—22no—
292C8×C31—41no—
293C8×C31—41no—
294C2×#440C2×C3111yescharacteristic, complemented
295C2×#433C2×C3111yescharacteristic, complemented
296#2324C2×C3111yescharacteristic
297#2323C2×C3111yescharacteristic, complemented
298#2086C2×C3111yescharacteristic, complemented
299#2076C2×C3111yescharacteristic, complemented
300#2068C2×C3111yescharacteristic, complemented
301#2065C2×C3111yescharacteristic, complemented
302#2055C2×C3111yescharacteristic, complemented
303#2035C2×C3111yescharacteristic, complemented
304#2033C2×C3111yescharacteristic
305#2000C2×C3111yescharacteristic
306#1776C2×C3111yescharacteristic, complemented
307C4×#103C2×C3111yescharacteristic, complemented
308C4×#102C2×C3111yescharacteristic, complemented
309C22×C31—41no—
310C22×C31—42no—
311C22×C31—41no—
312C22×C31—42no—
313C22×C31—41no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—42no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—81no—
320C22×C31—81no—
321C22×C31—81no—
322C22×C31—81no—
323C22×C31C2×#12111yescharacteristic
324C22×C31#52511yescharacteristic
325C22×C31#52511yescharacteristic
326C22×C31#57611yescharacteristic
327C22×C31#57711yescharacteristic
328C22×C31#57711yescharacteristic
329C22×C31#57811yescharacteristic
330C4×C31—22no—
331C4×C31—22no—
332C4×C31—42no—
333C4×C31—42no—
334C4×C31—41no—
335C4×C31—42no—
336C4×C31—41no—
337C4×C31—41no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31—81no—
341C4×C31—81no—
342C4×C31#52511yescharacteristic
343C4×C31#52911yescharacteristic
344C4×C31#52911yescharacteristic
345C4×C31#53211yescharacteristic
346C22×SD16C22×C3111yescharacteristic
347C2×C22⋊Q8C22×C3111yescharacteristic
348C2×#121C22×C3111yescharacteristic
349C2×C4×Q8C22×C3111yescharacteristic
350C2×C4×D4C22×C3111yescharacteristic
351C2×#117C22×C3111yescharacteristic
352#440—24no—
353#433—24no—
354C2×#107C22×C3111yescharacteristic
355C2×#107C22×C3111yescharacteristic
356C2×#106C22×C3111yescharacteristic
357C2×C4⋊C8C22×C3111yescharacteristic
358C2×C4⋊C8C22×C3111yescharacteristic
359C2×#103C22×C3111yescharacteristic
360C2×#103C22×C3111yescharacteristic
361C2×#103C22×C3111yescharacteristic
362C2×#102C22×C3111yescharacteristic
363C2×#102C22×C3111yescharacteristic
364C2×#102C22×C3111yescharacteristic
365C2×C22⋊C8C22×C3111yescharacteristic
366C2×C22⋊C8C22×C3111yescharacteristic
367C2×#97C22×C3111yescharacteristic
368C2×C4×C8C22×C3111yescharacteristic
369#391C22×C3111yescharacteristic
370#390—21no—
371#390C22×C3111yescharacteristic
372#389—21no—
373#389C22×C3111yescharacteristic
374#389C22×C3111yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#387—21no—
379#386—21no—
380#385—21no—
381#380C22×C3111yescharacteristic
382#380C22×C3111yescharacteristic
383C4×C4⋊C4C22×C3111yescharacteristic
384C4×C4⋊C4C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#340C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#340C22×C3111yescharacteristic
391C2×C31—81no—
392C2×C31—82no—
393C2×C31#239211yescharacteristic
394C2×C31#306211yescharacteristic
395C2×C31#306311yescharacteristic
396C2×C31#311811yescharacteristic
397C2×C31#312011yescharacteristic
398C2×C31#312411yescharacteristic
399C2×C31#312611yescharacteristic
400C22×Q8C23×C3111yescharacteristic
401C22×D4—21no—
402C22×D4C23×C3111yescharacteristic
403C23×C4—21no—
404C23×C4C23×C3111yescharacteristic
405C2×SD16—22no—
406C2×SD16—22no—
407C2×SD16—22no—
408C22×C8C23×C3111yescharacteristic
409C22×C8C23×C3111yescharacteristic
410C22×C8C23×C3111yescharacteristic
411C22×C8C23×C3111yescharacteristic
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414#121—22no—
415#121—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4D4×C3111yescharacteristic
427C2×C4⋊C4D4×C3111yescharacteristic
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C4⋊C4C23×C3111yescharacteristic
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C4⋊C4C23×C3111yescharacteristic
432C2×C4⋊C4C23×C3111yescharacteristic
433C2×C4⋊C4C23×C3111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4D4×C3111yescharacteristic
442C2×C22⋊C4D4×C3111yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42C23×C3111yescharacteristic
447C2×C42C23×C3111yescharacteristic
448#107—22no—
449#107—22no—
450#106—22no—
451C4⋊C8—22no—
452C4⋊C8—22no—
453#103—22no—
454#103—22no—
455#103—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461#97D4×C3114yescomplemented
462C4×C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471C31#2371511yescharacteristic, direct product factor, Sylow
472C24—21no—
473C24C2×D4×C3111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8#41×C3112yes—
480C2×D4—24no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4#41×C3112yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
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—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C2×D4×C3111yescharacteristic
507C22×C4C2×D4×C3111yescharacteristic
508C22×C4C2×D4×C3111yescharacteristic
509C22×C4C2×D4×C3111yescharacteristic
510C22×C4C24×C3111yescharacteristic
511SD16—28no—
512C2×C8—21no—
513C2×C8—21no—
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×C8C2×D4×C3112yes—
523C2×C8C2×D4×C3112yes—
524C4⋊C4—24no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
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—42no—
538C4⋊C4—81no—
539C4⋊C4—81no—
540C4⋊C4#41×C3112yes—
541C4⋊C4#41×C3112yes—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—81no—
555C42—81no—
556C42C2×D4×C3112yes—
557C42#41×C3112yes—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×D4×C3111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—84no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
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×C4—41no—
619C2×C4—41no—
620C2×C4—84no—
621C2×C4C31×#12112yes—
622C2×C4C31×#12112yes—
623C2×C4C22×D4×C3111yescharacteristic
624C2×C4C2×#41×C3111yescharacteristic
625C2×C4C2×#41×C3111yescharacteristic
626C2×C4C2×#41×C3111yescharacteristic
627C2×C4C2×#41×C3111yescharacteristic
628C2×C4C2×#41×C3111yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—42no—
641C22—41no—
642C22—41no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22C2×C31×#12111yescharacteristic
648C22C31×#52511yescharacteristic
649C22C31×#52511yescharacteristic
650C22C31×#57611yescharacteristic
651C22C31×#57711yescharacteristic
652C22C31×#57711yescharacteristic
653C22C31×#57811yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4C31×#52511yescharacteristic
667C4C31×#52911yescharacteristic
668C4C31×#52911yescharacteristic
669C4C31×#53211yescharacteristic
670C2—81no—
671C2—82no—
672C2C31×#239211yescharacteristic
673C2C31×#306211yescharacteristic
674C2C31×#306311yescharacteristic
675C2C31×#311811yescharacteristic
676C2C31×#312011yescharacteristic
677C2C31×#312411yescharacteristic
678C2C31×#312611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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×#440C2semidirect
2. C2×C31×#433C2semidirect
4. C31×#2323C2semidirect
5. C31×#2086C2semidirect
6. C31×#2076C2semidirect
7. C31×#2068C2semidirect
8. C31×#2065C2semidirect
9. C31×#2055C2semidirect
10. C31×#2035C2semidirect
13. C31×#1776C2semidirect
14. C4×C31×#103C2semidirect
15. C4×C31×#102C2semidirect
122. C31×#97D4semidirect
218. #23715C31direct (N × H)
294. C2×#440C2×C31semidirect
295. C2×#433C2×C31semidirect
297. #2323C2×C31semidirect
298. #2086C2×C31semidirect
299. #2076C2×C31semidirect
300. #2068C2×C31semidirect
301. #2065C2×C31semidirect
302. #2055C2×C31semidirect
303. #2035C2×C31semidirect
306. #1776C2×C31semidirect
307. C4×#103C2×C31semidirect
308. C4×#102C2×C31semidirect
461. #97D4×C31semidirect
471. C31#23715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4402
C2×C31×#4332
C31×#23242
C31×#23232
C31×#20862
C31×#20762
C31×#20682
C31×#20652
C31×#20552
C31×#20352
C31×#20332
C31×#20002
C31×#17762
C4×C31×#1032
C4×C31×#1022
#2371531