Finite Group Databasebeta

← C31×#25644 #21482403

Subgroups — C31×#25644 #21482403

Order 7936.

1212 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#556C211yesmaximal, characteristic, complemented
2C2×C31×#496C211yesmaximal, characteristic
3C2×C31×#460C211yesmaximal, characteristic, complemented
4C31×#2548C211yesmaximal, characteristic, complemented
5C31×#2013C212yesmaximal, complemented
6C31×#2012C212yesmaximal, complemented
7C31×#1985C211yesmaximal, characteristic, complemented
8C31×#1983C211yesmaximal, characteristic, complemented
9C31×#1880C212yesmaximal, complemented
10C31×#1879C212yesmaximal, complemented
11C31×#1763C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2212yes—
13C22×SD16×C31C2212yes—
14C22×D8×C31C2212yes—
15C31×#556—24no—
16C31×#556—24no—
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×#127C2211yescharacteristic
19C2×C31×#126—21no—
20C2×C31×#126—21no—
21C2×C31×#124—21no—
22C2×C31×#124C2211yescharacteristic
23C2×C31×#124C2211yescharacteristic
24C2×C31×C22⋊Q8—21no—
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117—21no—
30C31×#496—24no—
31C31×#460—24no—
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×#103C2212yes—
34C2×C31×#103C2212yes—
35C2×C31×#102C2212yes—
36C2×C31×#102C2212yes—
37C2×C31×#97C2211yescharacteristic
38C31×#394—21no—
39C31×#394—21no—
40C31×#390—21no—
41C31×#390C2212yes—
42C31×#390C2212yes—
43C4×C4⋊C4×C31C2211yescharacteristic
44C31×#340C2212yes—
45C31×#336C2212yes—
46C31×#336C2212yes—
47C22×Q8×C31D411yescharacteristic
48C22×Q8×C31C2311yescharacteristic
49C22×Q8×C31C2311yescharacteristic
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31C2312yes—
53C22×D4×C31C2311yescharacteristic
54C23×C4×C31—21no—
55C2×SD16×C31—24no—
56C2×SD16×C31—24no—
57C2×SD16×C31—24no—
58C2×SD16×C31—42no—
59C2×SD16×C31—42no—
60C2×SD16×C31—42no—
61C2×D8×C31—24no—
62C2×D8×C31—24no—
63C2×D8×C31—42no—
64C22×C8×C31C2312yes—
65C22×C8×C31C2312yes—
66C31×C4⋊Q8—22no—
67C31×C4⋊Q8—22no—
68C31×#127—22no—
69C31×#127—22no—
70C31×#126—28no—
71C31×#126—28no—
72C31×#124—22no—
73C31×#124—22no—
74C31×#124—22no—
75C31×#124—44no—
76C31×#124D414yes—
77C31×C22⋊Q8—28no—
78C4×Q8×C31—22no—
79C4×Q8×C31—22no—
80C4×Q8×C31—22no—
81C4×Q8×C31—22no—
82C4×Q8×C31—22no—
83C4×Q8×C31D414yes—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C31×#117—28no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31D411yescharacteristic
92C2×C4⋊C4×C31D411yescharacteristic
93C2×C4⋊C4×C31D411yescharacteristic
94C2×C4⋊C4×C31C2312yes—
95C2×C4⋊C4×C31C2311yescharacteristic
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—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31—21no—
108C2×C42×C31C2311yescharacteristic
109C2×C42×C31C2311yescharacteristic
110C2×C42×C31C2311yescharacteristic
111C31×C4⋊C8—22no—
112C31×#103—24no—
113C31×#103—42no—
114C31×#102—24no—
115C31×#102—42no—
116C31×#97—22no—
117C31×#95—21no—
118C24×C31—21no—
119C24×C31—22no—
120C2×Q8×C31—22no—
121C2×Q8×C31—22no—
122C2×Q8×C31—21no—
123C2×Q8×C31—21no—
124C2×Q8×C31—22no—
125C2×Q8×C31—22no—
126C2×Q8×C31—22no—
127C2×Q8×C31—22no—
128C2×Q8×C31—41no—
129C2×Q8×C31C2×D412yes—
130C2×Q8×C31C2×D412yes—
131C2×D4×C31—21no—
132C2×D4×C31—22no—
133C2×D4×C31—22no—
134C2×D4×C31—22no—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—22no—
139C2×D4×C31—22no—
140C2×D4×C31—42no—
141C2×D4×C31—42no—
142C2×D4×C31—42no—
143C2×D4×C31—42no—
144C2×D4×C31—82no—
145C2×D4×C31C2×D412yes—
146C22×C4×C31—24no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—22no—
151C22×C4×C31—42no—
152C22×C4×C31—42no—
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2×D411yescharacteristic
157C22×C4×C31C2×D411yescharacteristic
158C22×C4×C31C2×D411yescharacteristic
159C22×C4×C31C2411yescharacteristic
160SD16×C31—48no—
161SD16×C31—48no—
162D8×C31—48no—
163C2×C8×C31—22no—
164C2×C8×C31—22no—
165C2×C8×C31—22no—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31#4114yes—
169C4⋊C4×C31—24no—
170C4⋊C4×C31—24no—
171C4⋊C4×C31—24no—
172C4⋊C4×C31—24no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31C2×D412yes—
180C22⋊C4×C31—24no—
181C22⋊C4×C31—24no—
182C22⋊C4×C31—24no—
183C22⋊C4×C31—24no—
184C22⋊C4×C31—24no—
185C22⋊C4×C31—44no—
186C22⋊C4×C31—44no—
187C22⋊C4×C31—82no—
188C22⋊C4×C31—82no—
189C42×C31—24no—
190C42×C31—24no—
191C42×C31—21no—
192C42×C31—21no—
193C42×C31—21no—
194C42×C31—21no—
195C42×C31—42no—
196C42×C31C2×D412yes—
197C42×C31C2×D412yes—
198#25644C3111yesmaximal, characteristic, direct product factor, Sylow
199C23×C31—22no—
200C23×C31—42no—
201C23×C31—41no—
202C23×C31—41no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—42no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—42no—
210C23×C31—42no—
211C23×C31C22×D411yescharacteristic
212Q8×C31—22no—
213Q8×C31—22no—
214Q8×C31—24no—
215Q8×C31—44no—
216Q8×C31—41no—
217Q8×C31—41no—
218Q8×C31—42no—
219D4×C31—24no—
220D4×C31—41no—
221D4×C31—42no—
222D4×C31—41no—
223D4×C31—42no—
224D4×C31—42no—
225D4×C31—42no—
226D4×C31—84no—
227D4×C31—84no—
228C2×C4×C31—21no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—22no—
233C2×C4×C31—21no—
234C2×C4×C31—22no—
235C2×C4×C31—21no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—21no—
239C2×C4×C31—21no—
240C2×C4×C31—21no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—48no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31#12012yes—
252C2×C4×C31#12012yes—
253C2×C4×C31AGL(1,ℤ/8)12yes—
254C2×C4×C31C22×D411yescharacteristic
255C2×C4×C31C22×D411yescharacteristic
256C2×C4×C31C2×#4112yes—
257C2×C4×C31H(5,𝔽2)12yes—
258C8×C31—24no—
259C8×C31—42no—
260C2×#556C2×C3111yescharacteristic, complemented
261C2×#496C2×C3111yescharacteristic
262C2×#460C2×C3111yescharacteristic, complemented
263#2548C2×C3111yescharacteristic, complemented
264#2013C2×C3112yescomplemented
265#2012C2×C3112yescomplemented
266#1985C2×C3111yescharacteristic, complemented
267#1983C2×C3111yescharacteristic, complemented
268#1880C2×C3112yescomplemented
269#1879C2×C3112yescomplemented
270#1763C2×C3111yescharacteristic, complemented
271C22×C31—42no—
272C22×C31—42no—
273C22×C31—42no—
274C22×C31—82no—
275C22×C31—82no—
276C22×C31—82no—
277C22×C31—82no—
278C22×C31—82no—
279C22×C31—82no—
280C22×C31—82no—
281C22×C31—82no—
282C22×C31—82no—
283C22×C31C2×#12011yescharacteristic
284C22×C31#55012yes—
285C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C31#57511yescharacteristic
287C22×C31#57712yes—
288C4×C31—22no—
289C4×C31—22no—
290C4×C31—22no—
291C4×C31—42no—
292C4×C31—42no—
293C4×C31—41no—
294C4×C31—42no—
295C4×C31—41no—
296C4×C31—41no—
297C4×C31—82no—
298C4×C31#53211yescharacteristic
299C4×C31#53511yescharacteristic
300C4×C31#54612yes—
301C22×SD16C22×C3112yes—
302C22×SD16C22×C3112yes—
303C22×D8C22×C3112yes—
304#556—24no—
305#556—24no—
306C2×C4⋊Q8C22×C3111yescharacteristic
307C2×#127C22×C3111yescharacteristic
308C2×#126—21no—
309C2×#126—21no—
310C2×#124—21no—
311C2×#124C22×C3111yescharacteristic
312C2×#124C22×C3111yescharacteristic
313C2×C22⋊Q8—21no—
314C2×C4×Q8C22×C3111yescharacteristic
315C2×C4×Q8C22×C3111yescharacteristic
316C2×C4×Q8C22×C3111yescharacteristic
317C2×C4×D4C22×C3111yescharacteristic
318C2×#117—21no—
319#496—24no—
320#460—24no—
321C2×C4⋊C8C22×C3111yescharacteristic
322C2×#103C22×C3112yes—
323C2×#103C22×C3112yes—
324C2×#102C22×C3112yes—
325C2×#102C22×C3112yes—
326C2×#97C22×C3111yescharacteristic
327#394—21no—
328#394—21no—
329#390—21no—
330#390C22×C3112yes—
331#390C22×C3112yes—
332C4×C4⋊C4C22×C3111yescharacteristic
333#340C22×C3112yes—
334#336C22×C3112yes—
335#336C22×C3112yes—
336C2×C31—82no—
337C2×C31—162no—
338C2×C31#243111yescharacteristic
339C2×C31#300611yescharacteristic
340C2×C31#301011yescharacteristic
341C2×C31#339712yes—
342C2×C31#340112yes—
343C22×Q8D4×C3111yescharacteristic
344C22×Q8C23×C3111yescharacteristic
345C22×Q8C23×C3111yescharacteristic
346C22×D4—21no—
347C22×D4—21no—
348C22×D4C23×C3112yes—
349C22×D4C23×C3111yescharacteristic
350C23×C4—21no—
351C2×SD16—24no—
352C2×SD16—24no—
353C2×SD16—24no—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×SD16—42no—
357C2×D8—24no—
358C2×D8—24no—
359C2×D8—42no—
360C22×C8C23×C3112yes—
361C22×C8C23×C3112yes—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364#127—22no—
365#127—22no—
366#126—28no—
367#126—28no—
368#124—22no—
369#124—22no—
370#124—22no—
371#124—44no—
372#124D4×C3114yes—
373C22⋊Q8—28no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8D4×C3114yes—
380C4×D4—22no—
381C4×D4—22no—
382#117—28no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4D4×C3111yescharacteristic
388C2×C4⋊C4D4×C3111yescharacteristic
389C2×C4⋊C4D4×C3111yescharacteristic
390C2×C4⋊C4C23×C3112yes—
391C2×C4⋊C4C23×C3111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C23×C3111yescharacteristic
405C2×C42C23×C3111yescharacteristic
406C2×C42C23×C3111yescharacteristic
407C4⋊C8—22no—
408#103—24no—
409#103—42no—
410#102—24no—
411#102—42no—
412#97—22no—
413#95—21no—
414C31#2564411yescharacteristic, direct product factor, Sylow
415C24—21no—
416C24—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—41no—
426C2×Q8C2×D4×C3112yes—
427C2×Q8C2×D4×C3112yes—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—82no—
442C2×D4C2×D4×C3112yes—
443C22×C4—24no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4C2×D4×C3111yescharacteristic
451C22×C4C2×D4×C3111yescharacteristic
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3111yescharacteristic
454C22×C4C2×D4×C3111yescharacteristic
455C22×C4C2×D4×C3111yescharacteristic
456C22×C4C24×C3111yescharacteristic
457SD16—48no—
458SD16—48no—
459D8—48no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8#41×C3114yes—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4C2×D4×C3112yes—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—44no—
483C22⋊C4—44no—
484C22⋊C4—82no—
485C22⋊C4—82no—
486C42—24no—
487C42—24no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—42no—
493C42C2×D4×C3112yes—
494C42C2×D4×C3112yes—
495C23—22no—
496C23—42no—
497C23—41no—
498C23—41no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23C22×D4×C3111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—24no—
511Q8—44no—
512Q8—41no—
513Q8—41no—
514Q8—42no—
515D4—24no—
516D4—41no—
517D4—42no—
518D4—41no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—84no—
523D4—84no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—48no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4C31×#12012yes—
548C2×C4C31×#12012yes—
549C2×C4C31×AGL(1,ℤ/8)12yes—
550C2×C4C22×D4×C3111yescharacteristic
551C2×C4C22×D4×C3111yescharacteristic
552C2×C4C2×#41×C3112yes—
553C2×C4C31×H(5,𝔽2)12yes—
554C8—24no—
555C8—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—82no—
560C22—82no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22C2×C31×#12011yescharacteristic
569C22C31×#55012yes—
570C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
571C22C31×#57511yescharacteristic
572C22C31×#57712yes—
573C4—22no—
574C4—22no—
575C4—22no—
576C4—42no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—82no—
583C4C31×#53211yescharacteristic
584C4C31×#53511yescharacteristic
585C4C31×#54612yes—
586C2—82no—
587C2—162no—
588C2C31×#243111yescharacteristic
589C2C31×#300611yescharacteristic
590C2C31×#301011yescharacteristic
591C2C31×#339712yes—
592C2C31×#340112yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#496C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#556C2semidirect
3. C2×C31×#460C2semidirect
4. C31×#2548C2semidirect
5. C31×#2013C2semidirect
6. C31×#2012C2semidirect
7. C31×#1985C2semidirect
8. C31×#1983C2semidirect
9. C31×#1880C2semidirect
10. C31×#1879C2semidirect
11. C31×#1763C2semidirect
198. #25644C31direct (N × H)
260. C2×#556C2×C31semidirect
262. C2×#460C2×C31semidirect
263. #2548C2×C31semidirect
264. #2013C2×C31semidirect
265. #2012C2×C31semidirect
266. #1985C2×C31semidirect
267. #1983C2×C31semidirect
268. #1880C2×C31semidirect
269. #1879C2×C31semidirect
270. #1763C2×C31semidirect
414. C31#25644direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5562
C2×C31×#4962
C2×C31×#4602
C31×#25482
C31×#20132
C31×#20122
C31×#19852
C31×#19832
C31×#18802
C31×#18792
C31×#17632
#2564431