Finite Group Databasebeta

← C31×#24750 #21481509

Subgroups — C31×#24750 #21481509

Order 7936.

1216 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#466C212yesmaximal, complemented
2C2×C31×#459C211yesmaximal, characteristic, complemented
3C22×C31×C4⋊C8C211yesmaximal, characteristic, complemented
4C31×#2856C211yesmaximal, characteristic, complemented
5C4×C31×#121C211yesmaximal, characteristic, complemented
6C31×#2067C212yesmaximal, complemented
7C31×#2054C212yesmaximal, complemented
8C31×#1982C211yesmaximal, characteristic, complemented
9C31×#1947C211yesmaximal, characteristic, complemented
10C31×#1893C212yesmaximal, complemented
11C31×#1802C211yesmaximal, characteristic, complemented
12C22×D8×C31C2212yes—
13C23×C8×C31C2212yes—
14C2×C31×#127C2211yescharacteristic
15C2×C31×#121—21no—
16C2×C31×#121—21no—
17C2×C31×#121C2212yes—
18C2×C31×#121C2211yescharacteristic
19C2×C4×D4×C31—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C31×#466—28no—
23C31×#459—24no—
24C2×C31×#107C2212yes—
25C2×C31×C4⋊C8—24no—
26C2×C31×C4⋊C8C2212yes—
27C2×C31×C4⋊C8C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#102C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×#102C2212yes—
32C2×C31×#102C2212yes—
33C31×#390—21no—
34C31×#390—21no—
35C31×#390C2211yescharacteristic
36C31×#390C2212yes—
37C31×#389C2211yescharacteristic
38C31×#388—21no—
39C31×#386—21no—
40C31×#384C2211yescharacteristic
41C31×#380C2211yescharacteristic
42C4×C4⋊C4×C31C2211yescharacteristic
43C4×C22⋊C4×C31—21no—
44C31×#340C2212yes—
45C31×#340C2212yes—
46C22×D4×C31—21no—
47C22×D4×C31—22no—
48C22×D4×C31—21no—
49C22×D4×C31—21no—
50C22×D4×C31C2312yes—
51C22×D4×C31C2311yescharacteristic
52C23×C4×C31—21no—
53C23×C4×C31D411yescharacteristic
54C23×C4×C31D411yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C2×D8×C31—24no—
57C2×D8×C31—24no—
58C2×D8×C31—42no—
59C22×C8×C31—24no—
60C22×C8×C31—24no—
61C22×C8×C31—42no—
62C22×C8×C31C2312yes—
63C22×C8×C31C2312yes—
64C31×#127—22no—
65C31×#127—22no—
66C31×#121—22no—
67C31×#121—24no—
68C31×#121—24no—
69C31×#121—44no—
70C31×#121—44no—
71C31×#121D414yescomplemented
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C4×D4×C31—44no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31C2312yes—
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C22⋊C4×C31—21no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—21no—
90C2×C42×C31—22no—
91C2×C42×C31—22no—
92C2×C42×C31—21no—
93C2×C42×C31D411yescharacteristic
94C2×C42×C31D411yescharacteristic
95C2×C42×C31C2311yescharacteristic
96C2×C42×C31C2311yescharacteristic
97C31×#107—24no—
98C31×C4⋊C8—24no—
99C31×C4⋊C8—22no—
100C31×C4⋊C8D414yescomplemented
101C31×#102—24no—
102C31×#102—24no—
103C31×#102—24no—
104C31×#102—42no—
105C31×#95—21no—
106C31×#95—21no—
107C31×#95—21no—
108C24×C31—21no—
109C24×C31—22no—
110C24×C31C2×D411yescharacteristic
111C2×D4×C31—24no—
112C2×D4×C31—21no—
113C2×D4×C31—22no—
114C2×D4×C31—22no—
115C2×D4×C31—21no—
116C2×D4×C31—21no—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—21no—
120C2×D4×C31—22no—
121C2×D4×C31—21no—
122C2×D4×C31—22no—
123C2×D4×C31—42no—
124C2×D4×C31—42no—
125C2×D4×C31—42no—
126C2×D4×C31—42no—
127C2×D4×C31—44no—
128C2×D4×C31—44no—
129C2×D4×C31—44no—
130C2×D4×C31—42no—
131C2×D4×C31—42no—
132C2×D4×C31—42no—
133C2×D4×C31—42no—
134C2×D4×C31C2×D412yes—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—21no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—41no—
148C22×C4×C31—42no—
149C22×C4×C31—42no—
150C22×C4×C31—42no—
151C22×C4×C31D814yescomplemented
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×D411yescharacteristic
157C22×C4×C31C2×D411yescharacteristic
158C22×C4×C31#4112yes—
159C22×C4×C31C2411yescharacteristic
160D8×C31—48no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31—22no—
164C2×C8×C31—22no—
165C2×C8×C31—22no—
166C2×C8×C31—48no—
167C2×C8×C31C2×D414yes—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—21no—
175C4⋊C4×C31—42no—
176C4⋊C4×C31—42no—
177C4⋊C4×C31—42no—
178C4⋊C4×C31C2×D412yes—
179C22⋊C4×C31—24no—
180C22⋊C4×C31—42no—
181C22⋊C4×C31—44no—
182C22⋊C4×C31—42no—
183C22⋊C4×C31—42no—
184C22⋊C4×C31—44no—
185C22⋊C4×C31—42no—
186C22⋊C4×C31—44no—
187C42×C31—22no—
188C42×C31—22no—
189C42×C31—21no—
190C42×C31—21no—
191C42×C31—42no—
192C42×C31C2×D412yes—
193C42×C31#4112yes—
194#24750C3111yesmaximal, characteristic, direct product factor, Sylow
195C23×C31—21no—
196C23×C31—21no—
197C23×C31—21no—
198C23×C31—21no—
199C23×C31—22no—
200C23×C31—41no—
201C23×C31—41no—
202C23×C31—41no—
203C23×C31—41no—
204C23×C31—41no—
205C23×C31—41no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—42no—
210C23×C31—42no—
211C23×C31—42no—
212C23×C31—42no—
213C23×C31#12112yes—
214C23×C31C2×D812yes—
215C23×C31AGL(1,ℤ/8)12yes—
216C23×C31C22×D411yescharacteristic
217D4×C31—22no—
218D4×C31—22no—
219D4×C31—48no—
220D4×C31—42no—
221D4×C31—42no—
222D4×C31—41no—
223D4×C31—42no—
224D4×C31—41no—
225D4×C31—42no—
226D4×C31—84no—
227D4×C31—88no—
228D4×C31—84no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—28no—
240C2×C4×C31—21no—
241C2×C4×C31—22no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—44no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—42no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—42no—
253C2×C4×C31—41no—
254C2×C4×C31—42no—
255C2×C4×C31—41no—
256C2×C4×C31—84no—
257C2×C4×C31#12112yes—
258C2×C4×C31#12112yes—
259C2×C4×C31#12112yes—
260C2×C4×C31C2×D812yes—
261C2×C4×C31C2×D812yes—
262C2×C4×C31#13512yes—
263C2×C4×C31C22×D411yescharacteristic
264C2×C4×C31C22×D411yescharacteristic
265C2×C4×C31C2×#4111yescharacteristic
266C2×C4×C31C2×#4111yescharacteristic
267C2×C4×C31H(5,𝔽2)11yescharacteristic
268C2×C4×C312−1+411yescharacteristic
269C8×C31—24no—
270C8×C31—42no—
271C2×#466C2×C3112yescomplemented
272C2×#459C2×C3111yescharacteristic, complemented
273C22×C4⋊C8C2×C3111yescharacteristic, complemented
274#2856C2×C3111yescharacteristic, complemented
275C4×#121C2×C3111yescharacteristic, complemented
276#2067C2×C3112yescomplemented
277#2054C2×C3112yescomplemented
278#1982C2×C3111yescharacteristic, complemented
279#1947C2×C3111yescharacteristic, complemented
280#1893C2×C3112yescomplemented
281#1802C2×C3111yescharacteristic, complemented
282C22×C31—22no—
283C22×C31—22no—
284C22×C31—22no—
285C22×C31—22no—
286C22×C31—22no—
287C22×C31—22no—
288C22×C31—42no—
289C22×C31—42no—
290C22×C31—42no—
291C22×C31—81no—
292C22×C31—81no—
293C22×C31—81no—
294C22×C31—81no—
295C22×C31—82no—
296C22×C31—82no—
297C22×C31—82no—
298C22×C31—82no—
299C22×C31—82no—
300C22×C31—82no—
301C22×C31—82no—
302C22×C31#45914yescomplemented
303C22×C31C2×#12111yescharacteristic
304C22×C31C2×#12111yescharacteristic
305C22×C31#53711yescharacteristic
306C22×C31C22×D811yescharacteristic
307C22×C31C2×#13511yescharacteristic
308C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C31#57511yescharacteristic
310C4×C31—22no—
311C4×C31—22no—
312C4×C31—22no—
313C4×C31—42no—
314C4×C31—41no—
315C4×C31—81no—
316C4×C31—82no—
317C4×C31—81no—
318C4×C31#46614yescomplemented
319C4×C31D4211yescharacteristic
320C4×C31#54711yescharacteristic
321C4×C31#54811yescharacteristic
322C4×C31#55311yescharacteristic
323C22×D8C22×C3112yes—
324C23×C8C22×C3112yes—
325C2×#127C22×C3111yescharacteristic
326C2×#121—21no—
327C2×#121—21no—
328C2×#121C22×C3112yes—
329C2×#121C22×C3111yescharacteristic
330C2×C4×D4—21no—
331C2×C4×D4C22×C3111yescharacteristic
332C22×C42C22×C3111yescharacteristic
333#466—28no—
334#459—24no—
335C2×#107C22×C3112yes—
336C2×C4⋊C8—24no—
337C2×C4⋊C8C22×C3112yes—
338C2×C4⋊C8C22×C3111yescharacteristic
339C2×C4⋊C8C22×C3111yescharacteristic
340C2×#102C22×C3112yes—
341C2×#102C22×C3112yes—
342C2×#102C22×C3112yes—
343C2×#102C22×C3112yes—
344#390—21no—
345#390—21no—
346#390C22×C3111yescharacteristic
347#390C22×C3112yes—
348#389C22×C3111yescharacteristic
349#388—21no—
350#386—21no—
351#384C22×C3111yescharacteristic
352#380C22×C3111yescharacteristic
353C4×C4⋊C4C22×C3111yescharacteristic
354C4×C22⋊C4—21no—
355#340C22×C3112yes—
356#340C22×C3112yes—
357C2×C31—24no—
358C2×C31—82no—
359C2×C31—162no—
360C2×C31#241611yescharacteristic
361C2×C31C2×#45911yescharacteristic
362C2×C31#303511yescharacteristic
363C2×C31C2×#46611yescharacteristic
364C2×C31#305511yescharacteristic
365C2×C31#324511yescharacteristic
366C2×C31#324711yescharacteristic
367C22×D4—21no—
368C22×D4—22no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4C23×C3112yes—
372C22×D4C23×C3111yescharacteristic
373C23×C4—21no—
374C23×C4D4×C3111yescharacteristic
375C23×C4D4×C3111yescharacteristic
376C23×C4C23×C3111yescharacteristic
377C2×D8—24no—
378C2×D8—24no—
379C2×D8—42no—
380C22×C8—24no—
381C22×C8—24no—
382C22×C8—42no—
383C22×C8C23×C3112yes—
384C22×C8C23×C3112yes—
385#127—22no—
386#127—22no—
387#121—22no—
388#121—24no—
389#121—24no—
390#121—44no—
391#121—44no—
392#121D4×C3114yescomplemented
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—44no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4C23×C3111yescharacteristic
400C2×C4⋊C4C23×C3112yes—
401C2×C4⋊C4C23×C3111yescharacteristic
402C2×C4⋊C4C23×C3111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—21no—
414C2×C42D4×C3111yescharacteristic
415C2×C42D4×C3111yescharacteristic
416C2×C42C23×C3111yescharacteristic
417C2×C42C23×C3111yescharacteristic
418#107—24no—
419C4⋊C8—24no—
420C4⋊C8—22no—
421C4⋊C8D4×C3114yescomplemented
422#102—24no—
423#102—24no—
424#102—24no—
425#102—42no—
426#95—21no—
427#95—21no—
428#95—21no—
429C31#2475011yescharacteristic, direct product factor, Sylow
430C24—21no—
431C24—22no—
432C24C2×D4×C3111yescharacteristic
433C2×D4—24no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4C2×D4×C3112yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4D8×C3114yescomplemented
474C22×C4C2×D4×C3111yescharacteristic
475C22×C4C2×D4×C3111yescharacteristic
476C22×C4C2×D4×C3111yescharacteristic
477C22×C4C2×D4×C3112yes—
478C22×C4C2×D4×C3111yescharacteristic
479C22×C4C2×D4×C3111yescharacteristic
480C22×C4#41×C3112yes—
481C22×C4C24×C3111yescharacteristic
482D8—48no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—48no—
489C2×C8C2×D4×C3114yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4C2×D4×C3112yes—
501C22⋊C4—24no—
502C22⋊C4—42no—
503C22⋊C4—44no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—44no—
507C22⋊C4—42no—
508C22⋊C4—44no—
509C42—22no—
510C42—22no—
511C42—21no—
512C42—21no—
513C42—42no—
514C42C2×D4×C3112yes—
515C42#41×C3112yes—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23C31×#12112yes—
535C23C2×D8×C3112yes—
536C23C31×AGL(1,ℤ/8)12yes—
537C23C22×D4×C3111yescharacteristic
538D4—22no—
539D4—22no—
540D4—48no—
541D4—42no—
542D4—42no—
543D4—41no—
544D4—42no—
545D4—41no—
546D4—42no—
547D4—84no—
548D4—88no—
549D4—84no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—44no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4C31×#12112yes—
579C2×C4C31×#12112yes—
580C2×C4C31×#12112yes—
581C2×C4C2×D8×C3112yes—
582C2×C4C2×D8×C3112yes—
583C2×C4C31×#13512yes—
584C2×C4C22×D4×C3111yescharacteristic
585C2×C4C22×D4×C3111yescharacteristic
586C2×C4C2×#41×C3111yescharacteristic
587C2×C4C2×#41×C3111yescharacteristic
588C2×C4C31×H(5,𝔽2)11yescharacteristic
589C2×C4C31×2−1+411yescharacteristic
590C8—24no—
591C8—42no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—82no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22C31×#45914yescomplemented
613C22C2×C31×#12111yescharacteristic
614C22C2×C31×#12111yescharacteristic
615C22C31×#53711yescharacteristic
616C22C22×D8×C3111yescharacteristic
617C22C2×C31×#13511yescharacteristic
618C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
619C22C31×#57511yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—42no—
624C4—41no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4C31×#46614yescomplemented
629C4D42×C3111yescharacteristic
630C4C31×#54711yescharacteristic
631C4C31×#54811yescharacteristic
632C4C31×#55311yescharacteristic
633C2—24no—
634C2—82no—
635C2—162no—
636C2C31×#241611yescharacteristic
637C2C2×C31×#45911yescharacteristic
638C2C31×#303511yescharacteristic
639C2C2×C31×#46611yescharacteristic
640C2C31×#305511yescharacteristic
641C2C31×#324511yescharacteristic
642C2C31×#324711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
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×#466C2semidirect
2. C2×C31×#459C2semidirect
3. C22×C31×C4⋊C8C2semidirect
4. C31×#2856C2semidirect
5. C4×C31×#121C2semidirect
6. C31×#2067C2semidirect
7. C31×#2054C2semidirect
8. C31×#1982C2semidirect
9. C31×#1947C2semidirect
10. C31×#1893C2semidirect
11. C31×#1802C2semidirect
71. C31×#121D4semidirect
100. C31×C4⋊C8D4semidirect
151. C22×C4×C31D8semidirect
194. #24750C31direct (N × H)
271. C2×#466C2×C31semidirect
272. C2×#459C2×C31semidirect
273. C22×C4⋊C8C2×C31semidirect
274. #2856C2×C31semidirect
275. C4×#121C2×C31semidirect
276. #2067C2×C31semidirect
277. #2054C2×C31semidirect
278. #1982C2×C31semidirect
279. #1947C2×C31semidirect
280. #1893C2×C31semidirect
281. #1802C2×C31semidirect
302. C22×C31#459semidirect
318. C4×C31#466semidirect
392. #121D4×C31semidirect
421. C4⋊C8D4×C31semidirect
429. C31#24750direct (N × H)
473. C22×C4D8×C31semidirect
612. C22C31×#459semidirect
628. C4C31×#466semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4662
C2×C31×#4592
C22×C31×C4⋊C82
C31×#28562
C4×C31×#1212
C31×#20672
C31×#20542
C31×#19822
C31×#19472
C31×#18932
C31×#18022
#2475031