Finite Group Databasebeta

← C31×#13788 #21470547

Subgroups — C31×#13788 #21470547

Order 7936.

1710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#388C212yesmaximal
2C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
3C31×#1437C212yesmaximal
4C31×#1436C212yesmaximal, complemented
5C31×C4⋊#95C211yesmaximal, characteristic, complemented
6C31×#1434C211yesmaximal, characteristic, complemented
7C31×#1434C212yesmaximal, complemented
8C31×C22⋊#95C211yesmaximal, characteristic
9C31×C22⋊#95C211yesmaximal, characteristic
10C4×C31×#95C211yesmaximal, characteristic, complemented
11C4×C31×#95C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2212yes—
19C22×C42×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2212yes—
22C31×#388C4116yescomplemented
23C4×C22⋊C4×C31C418yescomplemented
24C2×C31×#95C2211yescharacteristic
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C25×C31C2311yescharacteristic
38C23×C4×C31—22no—
39C23×C4×C31—22no—
40C23×C4×C31—42no—
41C23×C4×C31—42no—
42C23×C4×C31C2×C414yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2311yescharacteristic
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C2×C4⋊C4×C31—42no—
54C2×C4⋊C4×C31—42no—
55C2×C4⋊C4×C31C2×C418yescomplemented
56C2×C22⋊C4×C31—24no—
57C2×C22⋊C4×C31—42no—
58C2×C22⋊C4×C31—42no—
59C2×C22⋊C4×C31—42no—
60C2×C22⋊C4×C31—42no—
61C2×C22⋊C4×C31C2×C414yes—
62C2×C22⋊C4×C31C2×C418yes—
63C2×C22⋊C4×C31C2×C418yes—
64C2×C22⋊C4×C31C2×C414yes—
65C2×C22⋊C4×C31C2×C418yes—
66C2×C42×C31—24no—
67C2×C42×C31—42no—
68C2×C42×C31—42no—
69C2×C42×C31—42no—
70C2×C42×C31—42no—
71C2×C42×C31—42no—
72C2×C42×C31—42no—
73C2×C42×C31C2×C414yes—
74C2×C42×C31C2×C414yes—
75C2×C42×C31C2×C418yescomplemented
76C31×#95—22no—
77C31×#95—22no—
78C31×#95—22no—
79C31×#95—22no—
80C31×#95—24no—
81C31×#95—42no—
82C31×#95—42no—
83C31×#95—42no—
84C31×#95—42no—
85C31×#95C2×C414yes—
86C31×#95C2×C414yes—
87C31×#95C2×C418yescomplemented
88C31×#95C2×C418yescomplemented
89C24×C31—22no—
90C24×C31—21no—
91C24×C31—21no—
92C24×C31—21no—
93C24×C31—21no—
94C24×C31—22no—
95C24×C31—22no—
96C24×C31—21no—
97C24×C31—21no—
98C24×C31C22×C414yes—
99C24×C31C22×C412yes—
100C24×C31C2411yescharacteristic
101C22×C4×C31—22no—
102C22×C4×C31—21no—
103C22×C4×C31—22no—
104C22×C4×C31—21no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—22no—
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—22no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—21no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—22no—
144C22×C4×C31—28no—
145C22×C4×C31—44no—
146C22×C4×C31—44no—
147C22×C4×C31—48no—
148C22×C4×C31—48no—
149C22×C4×C31C22×C412yes—
150C22×C4×C31C22×C412yes—
151C22×C4×C31C22×C414yes—
152C22×C4×C31C22×C414yes—
153C22×C4×C31C22×C414yes—
154C22×C4×C31C22×C414yes—
155C22×C4×C31C22×C412yes—
156C22×C4×C31C22×C412yes—
157C22×C4×C31C22×C414yes—
158C22×C4×C31C22×C414yes—
159C22×C4×C31C22×C412yes—
160C22×C4×C31C22×C412yes—
161C22×C4×C31#4112yes—
162C22×C4×C31#4112yes—
163C22×C4×C31#4114yes—
164C4⋊C4×C31—48no—
165C22⋊C4×C31—28no—
166C22⋊C4×C31—48no—
167C22⋊C4×C31—48no—
168C22⋊C4×C31C42116yescomplemented
169C42×C31—44no—
170C42×C31—44no—
171C42×C31—48no—
172C42×C31—48no—
173#13788C3111yesmaximal, characteristic, direct product factor, Sylow
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—24no—
177C23×C31—24no—
178C23×C31—24no—
179C23×C31—24no—
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—42no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—42no—
196C23×C31C2×C4214yes—
197C23×C31C23×C411yescharacteristic
198C23×C31C23×C412yes—
199C23×C31C2×#4111yescharacteristic
200C23×C31C2×#4111yescharacteristic
201C23×C31C2×#4112yes—
202C23×C31H(5,𝔽2)12yes—
203C23×C31H(5,𝔽2)12yes—
204C23×C31H(5,𝔽2)11yescharacteristic
205C23×C31H(5,𝔽2)11yescharacteristic
206C23×C312−1+411yescharacteristic
207C23×C312−1+411yescharacteristic
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—24no—
214C2×C4×C31—24no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—24no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—22no—
225C2×C4×C31—22no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—24no—
229C2×C4×C31—24no—
230C2×C4×C31—24no—
231C2×C4×C31—22no—
232C2×C4×C31—24no—
233C2×C4×C31—24no—
234C2×C4×C31—24no—
235C2×C4×C31—24no—
236C2×C4×C31—24no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—24no—
241C2×C4×C31—24no—
242C2×C4×C31—416no—
243C2×C4×C31—42no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31—42no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31—42no—
263C2×C4×C31C2×C4214yes—
264C2×C4×C31C2×C4214yes—
265C2×C4×C31#11714yes—
266C2×C4×C31#11714yes—
267C2×#388C2×C3112yes—
268C2×C4×C22⋊C4C2×C3111yescharacteristic
269#1437C2×C3112yes—
270#1436C2×C3112yescomplemented
271C4⋊#95C2×C3111yescharacteristic, complemented
272#1434C2×C3111yescharacteristic, complemented
273#1434C2×C3112yescomplemented
274C22⋊#95C2×C3111yescharacteristic
275C22⋊#95C2×C3111yescharacteristic
276C4×#95C2×C3111yescharacteristic, complemented
277C4×#95C2×C3111yescharacteristic, complemented
278C22×C31—24no—
279C22×C31—24no—
280C22×C31—24no—
281C22×C31—42no—
282C22×C31—42no—
283C22×C31—42no—
284C22×C31—42no—
285C22×C31—44no—
286C22×C31—44no—
287C22×C31—44no—
288C22×C31—44no—
289C22×C31C22×C4211yescharacteristic
290C22×C31C2×#11711yescharacteristic
291C22×C31C2×#11711yescharacteristic
292C22×C31C4×#4112yes—
293C22×C31C4×#4112yes—
294C22×C31#51811yescharacteristic
295C22×C31#51811yescharacteristic
296C22×C31#51812yes—
297C22×C31#51812yes—
298C22×C31#52011yescharacteristic
299C22×C31#52011yescharacteristic
300C22×C31#52012yes—
301C22×C31#52012yes—
302C22×C31#53812yes—
303C22×C31#53812yes—
304C22×C31#53812yes—
305C22×C31#53912yes—
306C22×C31#54011yescharacteristic
307C22×C31#54012yes—
308C22×C31#54111yescharacteristic
309C22×C31#54211yescharacteristic
310C22×C31#54211yescharacteristic
311C22×C31#54212yes—
312C4×C31—24no—
313C4×C31—24no—
314C4×C31—24no—
315C4×C31—24no—
316C4×C31—42no—
317C4×C31—42no—
318C4×C31—44no—
319C4×C31—44no—
320C4×C31—44no—
321C4×C31—44no—
322C24×C4C22×C3111yescharacteristic
323C22×C4⋊C4C22×C3112yes—
324C22×C22⋊C4C22×C3111yescharacteristic
325C22×C22⋊C4C22×C3112yes—
326C22×C22⋊C4C22×C3112yes—
327C22×C22⋊C4C22×C3111yescharacteristic
328C22×C42C22×C3112yes—
329C22×C42C22×C3111yescharacteristic
330C22×C42C22×C3111yescharacteristic
331C22×C42C22×C3112yes—
332#388C4×C31116yescomplemented
333C4×C22⋊C4C4×C3118yescomplemented
334C2×#95C22×C3111yescharacteristic
335C2×#95C22×C3111yescharacteristic
336C2×#95C22×C3111yescharacteristic
337C2×#95C22×C3111yescharacteristic
338C2×#95C22×C3112yes—
339C2×#95C22×C3112yes—
340C2×#95C22×C3112yes—
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3111yescharacteristic
344C2×#95C22×C3111yescharacteristic
345C2×#95C22×C3112yes—
346C2×#95C22×C3112yes—
347C2×C31—44no—
348C2×C31C4×#11711yescharacteristic
349C2×C31#227511yescharacteristic
350C2×C31#227511yescharacteristic
351C2×C31#231211yescharacteristic
352C2×C31#231411yescharacteristic
353C2×C31#231811yescharacteristic
354C2×C31#231911yescharacteristic
355C2×C31#233312yes—
356C2×C31#233412yes—
357C2×C31#233512yes—
358C2×C31#233712yes—
359C25C23×C3111yescharacteristic
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4C2×C4×C3114yes—
365C23×C4C23×C3112yes—
366C23×C4C23×C3112yes—
367C23×C4C23×C3112yes—
368C23×C4C23×C3112yes—
369C23×C4C23×C3111yescharacteristic
370C23×C4C23×C3111yescharacteristic
371C23×C4C23×C3111yescharacteristic
372C23×C4C23×C3111yescharacteristic
373C23×C4C23×C3111yescharacteristic
374C23×C4C23×C3111yescharacteristic
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4C2×C4×C3118yescomplemented
378C2×C22⋊C4—24no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4C2×C4×C3114yes—
384C2×C22⋊C4C2×C4×C3118yes—
385C2×C22⋊C4C2×C4×C3118yes—
386C2×C22⋊C4C2×C4×C3114yes—
387C2×C22⋊C4C2×C4×C3118yes—
388C2×C42—24no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42C2×C4×C3114yes—
396C2×C42C2×C4×C3114yes—
397C2×C42C2×C4×C3118yescomplemented
398#95—22no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—24no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95C2×C4×C3114yes—
408#95C2×C4×C3114yes—
409#95C2×C4×C3118yescomplemented
410#95C2×C4×C3118yescomplemented
411C31#1378811yescharacteristic, direct product factor, Sylow
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24C22×C4×C3114yes—
422C24C22×C4×C3112yes—
423C24C24×C3111yescharacteristic
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—28no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—48no—
471C22×C4—48no—
472C22×C4C22×C4×C3112yes—
473C22×C4C22×C4×C3112yes—
474C22×C4C22×C4×C3114yes—
475C22×C4C22×C4×C3114yes—
476C22×C4C22×C4×C3114yes—
477C22×C4C22×C4×C3114yes—
478C22×C4C22×C4×C3112yes—
479C22×C4C22×C4×C3112yes—
480C22×C4C22×C4×C3114yes—
481C22×C4C22×C4×C3114yes—
482C22×C4C22×C4×C3112yes—
483C22×C4C22×C4×C3112yes—
484C22×C4#41×C3112yes—
485C22×C4#41×C3112yes—
486C22×C4#41×C3114yes—
487C4⋊C4—48no—
488C22⋊C4—28no—
489C22⋊C4—48no—
490C22⋊C4—48no—
491C22⋊C4C42×C31116yescomplemented
492C42—44no—
493C42—44no—
494C42—48no—
495C42—48no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23C2×C42×C3114yes—
519C23C23×C4×C3111yescharacteristic
520C23C23×C4×C3112yes—
521C23C2×#41×C3111yescharacteristic
522C23C2×#41×C3111yescharacteristic
523C23C2×#41×C3112yes—
524C23C31×H(5,𝔽2)12yes—
525C23C31×H(5,𝔽2)12yes—
526C23C31×H(5,𝔽2)11yescharacteristic
527C23C31×H(5,𝔽2)11yescharacteristic
528C23C31×2−1+411yescharacteristic
529C23C31×2−1+411yescharacteristic
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—416no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4C2×C42×C3114yes—
586C2×C4C2×C42×C3114yes—
587C2×C4C31×#11714yes—
588C2×C4C31×#11714yes—
589C22—24no—
590C22—24no—
591C22—24no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22C22×C42×C3111yescharacteristic
601C22C2×C31×#11711yescharacteristic
602C22C2×C31×#11711yescharacteristic
603C22C4×#41×C3112yes—
604C22C4×#41×C3112yes—
605C22C31×#51811yescharacteristic
606C22C31×#51811yescharacteristic
607C22C31×#51812yes—
608C22C31×#51812yes—
609C22C31×#52011yescharacteristic
610C22C31×#52011yescharacteristic
611C22C31×#52012yes—
612C22C31×#52012yes—
613C22C31×#53812yes—
614C22C31×#53812yes—
615C22C31×#53812yes—
616C22C31×#53912yes—
617C22C31×#54011yescharacteristic
618C22C31×#54012yes—
619C22C31×#54111yescharacteristic
620C22C31×#54211yescharacteristic
621C22C31×#54211yescharacteristic
622C22C31×#54212yes—
623C4—24no—
624C4—24no—
625C4—24no—
626C4—24no—
627C4—42no—
628C4—42no—
629C4—44no—
630C4—44no—
631C4—44no—
632C4—44no—
633C2—44no—
634C2C4×C31×#11711yescharacteristic
635C2C31×#227511yescharacteristic
636C2C31×#227511yescharacteristic
637C2C31×#231211yescharacteristic
638C2C31×#231411yescharacteristic
639C2C31×#231811yescharacteristic
640C2C31×#231911yescharacteristic
641C2C31×#233312yes—
642C2C31×#233412yes—
643C2C31×#233512yes—
644C2C31×#233712yes—
subgroupG/H
center, socleC24×C31C24
commutatorC22C22×C42×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1436C2semidirect
5. C31×C4⋊#95C2semidirect
6. C31×#1434C2semidirect
7. C31×#1434C2semidirect
10. C4×C31×#95C2semidirect
11. C4×C31×#95C2semidirect
22. C31×#388C4semidirect
23. C4×C22⋊C4×C31C4semidirect
55. C2×C4⋊C4×C31C2×C4semidirect
75. C2×C42×C31C2×C4semidirect
87. C31×#95C2×C4semidirect
88. C31×#95C2×C4semidirect
168. C22⋊C4×C31C42semidirect
173. #13788C31direct (N × H)
270. #1436C2×C31semidirect
271. C4⋊#95C2×C31semidirect
272. #1434C2×C31semidirect
273. #1434C2×C31semidirect
276. C4×#95C2×C31semidirect
277. C4×#95C2×C31semidirect
332. #388C4×C31semidirect
333. C4×C22⋊C4C4×C31semidirect
377. C2×C4⋊C4C2×C4×C31semidirect
397. C2×C42C2×C4×C31semidirect
409. #95C2×C4×C31semidirect
410. #95C2×C4×C31semidirect
411. C31#13788direct (N × H)
491. C22⋊C4C42×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3882
C2×C4×C22⋊C4×C312
C31×#14372
C31×#14362
C31×C4⋊#952
C31×#14342
C31×C22⋊#952
C4×C31×#952
#1378831