Finite Group Databasebeta

← C31×#15175 #21471934

Subgroups — C31×#15175 #21471934

Order 7936.

1418 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C211yesmaximal, characteristic, complemented
2C2×C31×#399C211yesmaximal, characteristic
3C2×C31×#388C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#1442C212yesmaximal, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal
8C31×#1439C211yesmaximal, characteristic
9C31×#1437C212yesmaximal
10C31×#1436C212yesmaximal, complemented
11C31×#1434C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C42×C31C2211yescharacteristic
22C22×C42×C31C2212yes—
23C31×#400—24no—
24C31×#399—24no—
25C31×#388—24no—
26C4×C4⋊C4×C31—24no—
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C25×C31C2311yescharacteristic
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2312yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—42no—
60C2×C4⋊C4×C31D414yes—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—42no—
75C2×C42×C31—24no—
76C2×C42×C31—24no—
77C2×C42×C31—42no—
78C2×C42×C31—42no—
79C2×C42×C31D414yes—
80C31×#95—22no—
81C31×#95—24no—
82C31×#95—22no—
83C31×#95—24no—
84C31×#95—24no—
85C31×#95—22no—
86C31×#95—22no—
87C31×#95—24no—
88C31×#95—24no—
89C31×#95—24no—
90C31×#95—24no—
91C31×#95—42no—
92C24×C31—21no—
93C24×C31—21no—
94C24×C31—21no—
95C24×C31—22no—
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—21no—
99C24×C31—22no—
100C24×C31—21no—
101C24×C31—21no—
102C24×C31#4112yes—
103C24×C31C2411yescharacteristic
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—21no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—21no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31C2×D412yes—
155C22×C4×C31C2×D414yes—
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2×D412yes—
159C22×C4×C31#4112yes—
160C22×C4×C31#4114yes—
161C22×C4×C31#4114yes—
162C22×C4×C31#4112yes—
163C22×C4×C31#4114yes—
164C4⋊C4×C31—28no—
165C4⋊C4×C31—28no—
166C4⋊C4×C31—48no—
167C4⋊C4×C31—44no—
168C22⋊C4×C31—28no—
169C22⋊C4×C31—48no—
170C22⋊C4×C31—48no—
171C22⋊C4×C31—44no—
172C22⋊C4×C31—44no—
173C42×C31—28no—
174C42×C31—48no—
175#15175C3111yesmaximal, characteristic, direct product factor, Sylow
176C23×C31—22no—
177C23×C31—24no—
178C23×C31—22no—
179C23×C31—24no—
180C23×C31—22no—
181C23×C31—41no—
182C23×C31—41no—
183C23×C31—41no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—41no—
188C23×C31—41no—
189C23×C31—41no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—41no—
194C23×C31—42no—
195C23×C31—41no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31C22×D411yescharacteristic
200C23×C31C22×D411yescharacteristic
201C23×C31C2×#4111yescharacteristic
202C23×C31C2×#4112yes—
203C23×C31C2×#4111yescharacteristic
204C23×C31C2×#4111yescharacteristic
205C23×C31C2×#4112yes—
206C23×C31C2×#4112yes—
207C23×C31H(5,𝔽2)12yes—
208C23×C312−1+411yescharacteristic
209C23×C312−1+411yescharacteristic
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—24no—
213C2×C4×C31—24no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—24no—
217C2×C4×C31—24no—
218C2×C4×C31—24no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—22no—
225C2×C4×C31—24no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—22no—
229C2×C4×C31—24no—
230C2×C4×C31—22no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—41no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241C2×C4×C31—41no—
242C2×C4×C31—42no—
243C2×C4×C31—41no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—41no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—41no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—42no—
262C2×C4×C31—42no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31#12114yes—
269C2×C4×C31#12314yes—
270C2×#400C2×C3111yescharacteristic, complemented
271C2×#399C2×C3111yescharacteristic
272C2×#388C2×C3111yescharacteristic
273C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
274#1442C2×C3112yescomplemented
275#1441C2×C3111yescharacteristic, complemented
276#1440C2×C3112yes—
277#1439C2×C3111yescharacteristic
278#1437C2×C3112yes—
279#1436C2×C3112yescomplemented
280#1434C2×C3111yescharacteristic, complemented
281C22×C31—44no—
282C22×C31—44no—
283C22×C31—42no—
284C22×C31—42no—
285C22×C31—42no—
286C22×C31—82no—
287C22×C31—81no—
288C22×C31—81no—
289C22×C31—81no—
290C22×C31—81no—
291C22×C31—82no—
292C22×C31C2×#12111yescharacteristic
293C22×C31C2×#12311yescharacteristic
294C22×C31#52511yescharacteristic
295C22×C31#52511yescharacteristic
296C22×C31#52912yes—
297C22×C31#52912yes—
298C22×C31#52912yes—
299C22×C31#53212yes—
300C22×C31#53211yescharacteristic
301C22×C31#53511yescharacteristic
302C22×C31#53611yescharacteristic
303C22×C31#53912yes—
304C22×C31#53912yes—
305C22×C31#54612yes—
306C22×C31#54811yescharacteristic
307C22×C31#54811yescharacteristic
308C22×C31#55112yes—
309C22×C31#55211yescharacteristic
310C22×C31#55212yes—
311C22×C31#55211yescharacteristic
312C22×C31#55312yes—
313C22×C31#55612yes—
314C22×C31#55912yes—
315C4×C31—24no—
316C4×C31—24no—
317C4×C31—44no—
318C4×C31—42no—
319C4×C31—42no—
320C4×C31—44no—
321C4×C31—44no—
322C4×C31—82no—
323C4×C31—81no—
324C4×C31—81no—
325C22×C4⋊C4C22×C3111yescharacteristic
326C22×C4⋊C4C22×C3111yescharacteristic
327C22×C4⋊C4C22×C3112yes—
328C22×C4⋊C4C22×C3111yescharacteristic
329C22×C22⋊C4C22×C3111yescharacteristic
330C22×C22⋊C4C22×C3111yescharacteristic
331C22×C22⋊C4C22×C3111yescharacteristic
332C22×C22⋊C4C22×C3112yes—
333C22×C22⋊C4C22×C3112yes—
334C22×C42C22×C3111yescharacteristic
335C22×C42C22×C3112yes—
336#400—24no—
337#399—24no—
338#388—24no—
339C4×C4⋊C4—24no—
340C2×#95C22×C3111yescharacteristic
341C2×#95C22×C3111yescharacteristic
342C2×#95C22×C3112yes—
343C2×#95C22×C3112yes—
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3111yescharacteristic
347C2×#95C22×C3112yes—
348C2×#95C22×C3112yes—
349C2×#95C22×C3112yes—
350C2×#95C22×C3111yescharacteristic
351C2×#95C22×C3112yes—
352C2×C31—82no—
353C2×C31#239511yescharacteristic
354C2×C31#253611yescharacteristic
355C2×C31#254411yescharacteristic
356C2×C31#255812yes—
357C2×C31#256012yes—
358C2×C31#257512yes—
359C2×C31#259612yes—
360C2×C31#259811yescharacteristic
361C2×C31#260411yescharacteristic
362C2×C31#262311yescharacteristic
363C2×C31#285411yescharacteristic
364C25C23×C3111yescharacteristic
365C23×C4C23×C3111yescharacteristic
366C23×C4C23×C3111yescharacteristic
367C23×C4C23×C3112yes—
368C23×C4C23×C3112yes—
369C23×C4C23×C3111yescharacteristic
370C23×C4C23×C3111yescharacteristic
371C23×C4C23×C3112yes—
372C23×C4C23×C3112yes—
373C23×C4C23×C3111yescharacteristic
374C23×C4C23×C3111yescharacteristic
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4D4×C3114yes—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42D4×C3114yes—
405#95—24no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—24no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—42no—
417C31#1517511yescharacteristic, direct product factor, Sylow
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24#41×C3112yes—
429C24C24×C3111yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4C2×D4×C3112yes—
481C22×C4C2×D4×C3114yes—
482C22×C4C2×D4×C3112yes—
483C22×C4C2×D4×C3112yes—
484C22×C4C2×D4×C3112yes—
485C22×C4#41×C3112yes—
486C22×C4#41×C3114yes—
487C22×C4#41×C3114yes—
488C22×C4#41×C3112yes—
489C22×C4#41×C3114yes—
490C4⋊C4—28no—
491C4⋊C4—28no—
492C4⋊C4—48no—
493C4⋊C4—44no—
494C22⋊C4—28no—
495C22⋊C4—48no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4—44no—
499C42—28no—
500C42—48no—
501C23—22no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—42no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C22×D4×C3111yescharacteristic
525C23C22×D4×C3111yescharacteristic
526C23C2×#41×C3111yescharacteristic
527C23C2×#41×C3112yes—
528C23C2×#41×C3111yescharacteristic
529C23C2×#41×C3111yescharacteristic
530C23C2×#41×C3112yes—
531C23C2×#41×C3112yes—
532C23C31×H(5,𝔽2)12yes—
533C23C31×2−1+411yescharacteristic
534C23C31×2−1+411yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4C31×#12114yes—
594C2×C4C31×#12314yes—
595C22—44no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—44no—
600C22—82no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—82no—
606C22C2×C31×#12111yescharacteristic
607C22C2×C31×#12311yescharacteristic
608C22C31×#52511yescharacteristic
609C22C31×#52511yescharacteristic
610C22C31×#52912yes—
611C22C31×#52912yes—
612C22C31×#52912yes—
613C22C31×#53212yes—
614C22C31×#53211yescharacteristic
615C22C31×#53511yescharacteristic
616C22C31×#53611yescharacteristic
617C22C31×#53912yes—
618C22C31×#53912yes—
619C22C31×#54612yes—
620C22C31×#54811yescharacteristic
621C22C31×#54811yescharacteristic
622C22C31×#55112yes—
623C22C31×#55211yescharacteristic
624C22C31×#55212yes—
625C22C31×#55211yescharacteristic
626C22C31×#55312yes—
627C22C31×#55612yes—
628C22C31×#55912yes—
629C4—24no—
630C4—24no—
631C4—44no—
632C4—42no—
633C4—42no—
634C4—44no—
635C4—44no—
636C4—81no—
637C4—81no—
638C4—82no—
639C2—82no—
640C2C31×#239511yescharacteristic
641C2C31×#253611yescharacteristic
642C2C31×#254411yescharacteristic
643C2C31×#255812yes—
644C2C31×#256012yes—
645C2C31×#257512yes—
646C2C31×#259612yes—
647C2C31×#259811yescharacteristic
648C2C31×#260411yescharacteristic
649C2C31×#262311yescharacteristic
650C2C31×#285411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#400C2semidirect
4. C2×C4×C4⋊C4×C31C2semidirect
5. C31×#1442C2semidirect
6. C31×#1441C2semidirect
10. C31×#1436C2semidirect
11. C31×#1434C2semidirect
175. #15175C31direct (N × H)
270. C2×#400C2×C31semidirect
273. C2×C4×C4⋊C4C2×C31semidirect
274. #1442C2×C31semidirect
275. #1441C2×C31semidirect
279. #1436C2×C31semidirect
280. #1434C2×C31semidirect
417. C31#15175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4002
C2×C31×#3992
C2×C31×#3882
C2×C4×C4⋊C4×C312
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14372
C31×#14362
C31×#14342
#1517531