Finite Group Databasebeta

← C31×#33013 #21489772

Subgroups — C31×#33013 #21489772

Order 7936.

1334 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#520C211yesmaximal, characteristic, complemented
2C2×C31×#481C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic
4C31×#2624C211yesmaximal, characteristic, complemented
5C31×#1880C212yesmaximal, complemented
6C31×#1879C212yesmaximal, complemented
7C31×#1865C212yesmaximal, complemented
8C31×#1864C212yesmaximal, complemented
9C31×#1823C211yesmaximal, characteristic, complemented
10C31×#1818C211yesmaximal, characteristic, complemented
11C31×#1788C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×SD16×C31C2211yescharacteristic
14C22×D8×C31C2211yescharacteristic
15C2×C31×#121C2211yescharacteristic
16C31×#520—24no—
17C31×#520—24no—
18C2×C4×Q8×C31C2212yes—
19C2×C4×D4×C31—22no—
20C2×C4×D4×C31C2212yes—
21C2×C31×#117—21no—
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31—21no—
24C22×C4⋊C4×C31C2211yescharacteristic
25C31×#481—24no—
26C31×#449—24no—
27C2×C31×#106C2212yes—
28C2×C31×#103C2211yescharacteristic
29C2×C31×#103C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2212yes—
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×C22⋊C8C2211yescharacteristic
35C31×#399—21no—
36C31×#397—21no—
37C31×#394—22no—
38C31×#390C2212yes—
39C31×#389C2212yes—
40C31×#380C2211yescharacteristic
41C31×#340C2212yes—
42C31×#340C2212yes—
43C31×#336C2212yes—
44C31×#336C2212yes—
45C2×#41×C31—24no—
46C2×#41×C31—24no—
47C2×#41×C31—22no—
48C2×#41×C31D414yes—
49C22×Q8×C31C2311yescharacteristic
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31C2311yescharacteristic
53C22×D4×C31C2311yescharacteristic
54C23×C4×C31—21no—
55C23×C4×C31—21no—
56C23×C4×C31—22no—
57C23×C4×C31C2311yescharacteristic
58C2×SD16×C31—22no—
59C2×SD16×C31—24no—
60C2×D8×C31—22no—
61C2×D8×C31—24no—
62C22×C8×C31C2312yes—
63C22×C8×C31C2311yescharacteristic
64C22×C8×C31C2311yescharacteristic
65C31×#121—22no—
66C31×#121—22no—
67C4×Q8×C31—24no—
68C4×Q8×C31—24no—
69C4×D4×C31—216no—
70C4×D4×C31—24no—
71C4×D4×C31—24no—
72C31×#117—28no—
73C31×#117—22no—
74C31×#117—22no—
75C2×C4⋊C4×C31—28no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31D411yescharacteristic
81C2×C4⋊C4×C31D411yescharacteristic
82C2×C4⋊C4×C31D414yes—
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C4⋊C4×C31C2312yes—
85C2×C4⋊C4×C31C2312yes—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31D412yes—
92C2×C42×C31—22no—
93C2×C42×C31C2312yes—
94C31×#106—24no—
95C31×#103—22no—
96C31×#103—24no—
97C31×#102—22no—
98C31×#102—24no—
99C31×#102—24no—
100C31×C22⋊C8—22no—
101C31×C22⋊C8—22no—
102C31×#95—21no—
103C31×#95—22no—
104C24×C31—21no—
105C24×C31—21no—
106C24×C31C2×D411yescharacteristic
107#41×C31—216no—
108#41×C31—28no—
109#41×C31—28no—
110C2×Q8×C31—21no—
111C2×Q8×C31—22no—
112C2×Q8×C31C2×D412yes—
113C2×Q8×C31#4114yes—
114C2×D4×C31—28no—
115C2×D4×C31—24no—
116C2×D4×C31—21no—
117C2×D4×C31—21no—
118C2×D4×C31—21no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—42no—
123C2×D4×C31—82no—
124C2×D4×C31C2×D412yes—
125C2×D4×C31#4114yes—
126C22×C4×C31—28no—
127C22×C4×C31—21no—
128C22×C4×C31—24no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—28no—
133C22×C4×C31—24no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—82no—
137C22×C4×C31—82no—
138C22×C4×C31—81no—
139C22×C4×C31—81no—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2411yescharacteristic
146SD16×C31—44no—
147D8×C31—44no—
148C2×C8×C31—22no—
149C2×C8×C31—21no—
150C2×C8×C31—21no—
151C2×C8×C31—22no—
152C2×C8×C31—22no—
153C2×C8×C31—22no—
154C2×C8×C31—22no—
155C4⋊C4×C31—28no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—82no—
165C4⋊C4×C31C2×D414yes—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—24no—
168C22⋊C4×C31—42no—
169C22⋊C4×C31—82no—
170C22⋊C4×C31—82no—
171C22⋊C4×C31—81no—
172C42×C31—28no—
173C42×C31—22no—
174C42×C31—22no—
175#33013C3111yesmaximal, characteristic, direct product factor, Sylow
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—24no—
179C23×C31—21no—
180C23×C31—21no—
181C23×C31—22no—
182C23×C31—41no—
183C23×C31—41no—
184C23×C31—42no—
185C23×C31—41no—
186C23×C31—42no—
187C23×C31—41no—
188C23×C31—42no—
189C23×C31—41no—
190C23×C31#12012yes—
191C23×C31C22×D411yescharacteristic
192Q8×C31—22no—
193Q8×C31—24no—
194Q8×C31#12314yes—
195D4×C31—216no—
196D4×C31—22no—
197D4×C31—24no—
198D4×C31—41no—
199D4×C31—41no—
200D4×C31—42no—
201D4×C31—84no—
202D4×C31#12314yes—
203C2×C4×C31—216no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—24no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—24no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—24no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—41no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—84no—
225C2×C4×C31—88no—
226C2×C4×C31#12012yes—
227C2×C4×C31C22×D411yescharacteristic
228C2×C4×C31C22×D411yescharacteristic
229C2×C4×C31C2×#4112yes—
230C2×C4×C31C2×#4112yes—
231C8×C31—41no—
232C8×C31—41no—
233C8×C31—42no—
234C2×#520C2×C3111yescharacteristic, complemented
235C2×#481C2×C3111yescharacteristic, complemented
236C2×#449C2×C3111yescharacteristic
237#2624C2×C3111yescharacteristic, complemented
238#1880C2×C3112yescomplemented
239#1879C2×C3112yescomplemented
240#1865C2×C3112yescomplemented
241#1864C2×C3112yescomplemented
242#1823C2×C3111yescharacteristic, complemented
243#1818C2×C3111yescharacteristic, complemented
244#1788C2×C3111yescharacteristic, complemented
245C22×C31—22no—
246C22×C31—24no—
247C22×C31—22no—
248C22×C31—22no—
249C22×C31—42no—
250C22×C31—44no—
251C22×C31—42no—
252C22×C31—44no—
253C22×C31—42no—
254C22×C31—42no—
255C22×C31—81no—
256C22×C31—82no—
257C22×C31—82no—
258C22×C31—81no—
259C22×C31—81no—
260C22×C31C2×#12011yescharacteristic
261C22×C31#52512yes—
262C22×C31#57611yescharacteristic
263C22×C31#57712yes—
264C22×C31#57711yescharacteristic
265C4×C31—22no—
266C4×C31—24no—
267C4×C31—42no—
268C4×C31—42no—
269C4×C31—44no—
270C4×C31—82no—
271C4×C31—81no—
272C4×C31C2×#12311yescharacteristic
273C4×C31C2×#12311yescharacteristic
274C4×C31#52512yes—
275C22×#41C22×C3111yescharacteristic
276C22×SD16C22×C3111yescharacteristic
277C22×D8C22×C3111yescharacteristic
278C2×#121C22×C3111yescharacteristic
279#520—24no—
280#520—24no—
281C2×C4×Q8C22×C3112yes—
282C2×C4×D4—22no—
283C2×C4×D4C22×C3112yes—
284C2×#117—21no—
285C2×#117C22×C3111yescharacteristic
286C22×C4⋊C4—21no—
287C22×C4⋊C4C22×C3111yescharacteristic
288#481—24no—
289#449—24no—
290C2×#106C22×C3112yes—
291C2×#103C22×C3111yescharacteristic
292C2×#103C22×C3112yes—
293C2×#102C22×C3112yes—
294C2×#102C22×C3111yescharacteristic
295C2×#102C22×C3112yes—
296C2×C22⋊C8C22×C3111yescharacteristic
297C2×C22⋊C8C22×C3111yescharacteristic
298#399—21no—
299#397—21no—
300#394—22no—
301#390C22×C3112yes—
302#389C22×C3112yes—
303#380C22×C3111yescharacteristic
304#340C22×C3112yes—
305#340C22×C3112yes—
306#336C22×C3112yes—
307#336C22×C3112yes—
308C2×C31—42no—
309C2×C31—44no—
310C2×C31—161no—
311C2×C31#284911yescharacteristic
312C2×C31#301011yescharacteristic
313C2×C31#301211yescharacteristic
314C2×C31#311912yes—
315C2×C31#312512yes—
316C2×#41—24no—
317C2×#41—24no—
318C2×#41—22no—
319C2×#41D4×C3114yes—
320C22×Q8C23×C3111yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C23×C3111yescharacteristic
324C22×D4C23×C3111yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—22no—
328C23×C4C23×C3111yescharacteristic
329C2×SD16—22no—
330C2×SD16—24no—
331C2×D8—22no—
332C2×D8—24no—
333C22×C8C23×C3111yescharacteristic
334C22×C8C23×C3111yescharacteristic
335C22×C8C23×C3112yes—
336#121—22no—
337#121—22no—
338C4×Q8—24no—
339C4×Q8—24no—
340C4×D4—216no—
341C4×D4—24no—
342C4×D4—24no—
343#117—28no—
344#117—22no—
345#117—22no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4D4×C3111yescharacteristic
352C2×C4⋊C4D4×C3111yescharacteristic
353C2×C4⋊C4D4×C3114yes—
354C2×C4⋊C4C23×C3111yescharacteristic
355C2×C4⋊C4C23×C3112yes—
356C2×C4⋊C4C23×C3112yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4D4×C3112yes—
363C2×C42—22no—
364C2×C42C23×C3112yes—
365#106—24no—
366#103—22no—
367#103—24no—
368#102—22no—
369#102—24no—
370#102—24no—
371C22⋊C8—22no—
372C22⋊C8—22no—
373#95—21no—
374#95—22no—
375C31#3301311yescharacteristic, direct product factor, Sylow
376C24—21no—
377C24—21no—
378C24C2×D4×C3111yescharacteristic
379#41—216no—
380#41—28no—
381#41—28no—
382C2×Q8—21no—
383C2×Q8—22no—
384C2×Q8C2×D4×C3112yes—
385C2×Q8#41×C3114yes—
386C2×D4—28no—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—42no—
395C2×D4—82no—
396C2×D4C2×D4×C3112yes—
397C2×D4#41×C3114yes—
398C22×C4—28no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—28no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4—81no—
411C22×C4—81no—
412C22×C4C2×D4×C3112yes—
413C22×C4C2×D4×C3112yes—
414C22×C4C2×D4×C3111yescharacteristic
415C22×C4C2×D4×C3112yes—
416C22×C4C2×D4×C3112yes—
417C22×C4C24×C3111yescharacteristic
418SD16—44no—
419D8—44no—
420C2×C8—22no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C4⋊C4—28no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—82no—
437C4⋊C4C2×D4×C3114yes—
438C22⋊C4—28no—
439C22⋊C4—24no—
440C22⋊C4—42no—
441C22⋊C4—82no—
442C22⋊C4—82no—
443C22⋊C4—81no—
444C42—28no—
445C42—22no—
446C42—22no—
447C23—22no—
448C23—22no—
449C23—24no—
450C23—21no—
451C23—21no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—41no—
457C23—42no—
458C23—41no—
459C23—42no—
460C23—41no—
461C23C31×#12012yes—
462C23C22×D4×C3111yescharacteristic
463Q8—22no—
464Q8—24no—
465Q8C31×#12314yes—
466D4—216no—
467D4—22no—
468D4—24no—
469D4—41no—
470D4—41no—
471D4—42no—
472D4—84no—
473D4C31×#12314yes—
474C2×C4—216no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—84no—
496C2×C4—88no—
497C2×C4C31×#12012yes—
498C2×C4C22×D4×C3111yescharacteristic
499C2×C4C22×D4×C3111yescharacteristic
500C2×C4C2×#41×C3112yes—
501C2×C4C2×#41×C3112yes—
502C8—41no—
503C8—41no—
504C8—42no—
505C22—22no—
506C22—24no—
507C22—22no—
508C22—22no—
509C22—42no—
510C22—44no—
511C22—42no—
512C22—44no—
513C22—42no—
514C22—42no—
515C22—81no—
516C22—82no—
517C22—82no—
518C22—81no—
519C22—81no—
520C22C2×C31×#12011yescharacteristic
521C22C31×#52512yes—
522C22C31×#57611yescharacteristic
523C22C31×#57712yes—
524C22C31×#57711yescharacteristic
525C4—22no—
526C4—24no—
527C4—42no—
528C4—42no—
529C4—44no—
530C4—82no—
531C4—81no—
532C4C2×C31×#12311yescharacteristic
533C4C2×C31×#12311yescharacteristic
534C4C31×#52512yes—
535C2—42no—
536C2—44no—
537C2—161no—
538C2C31×#284911yescharacteristic
539C2C31×#301011yescharacteristic
540C2C31×#301211yescharacteristic
541C2C31×#311912yes—
542C2C31×#312512yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#449C2
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×#520C2semidirect
2. C2×C31×#481C2semidirect
4. C31×#2624C2semidirect
5. C31×#1880C2semidirect
6. C31×#1879C2semidirect
7. C31×#1865C2semidirect
8. C31×#1864C2semidirect
9. C31×#1823C2semidirect
10. C31×#1818C2semidirect
11. C31×#1788C2semidirect
175. #33013C31direct (N × H)
234. C2×#520C2×C31semidirect
235. C2×#481C2×C31semidirect
237. #2624C2×C31semidirect
238. #1880C2×C31semidirect
239. #1879C2×C31semidirect
240. #1865C2×C31semidirect
241. #1864C2×C31semidirect
242. #1823C2×C31semidirect
243. #1818C2×C31semidirect
244. #1788C2×C31semidirect
375. C31#33013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5202
C2×C31×#4812
C2×C31×#4492
C31×#26242
C31×#18802
C31×#18792
C31×#18652
C31×#18642
C31×#18232
C31×#18182
C31×#17882
#3301331