Finite Group Databasebeta

← C31×#32986 #21489745

Subgroups — C31×#32986 #21489745

Order 7936.

1358 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#520C211yesmaximal, characteristic, complemented
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#480C211yesmaximal, characteristic, complemented
4C31×#2615C211yesmaximal, characteristic
5C31×#1875C212yesmaximal, complemented
6C31×#1874C212yesmaximal, complemented
7C31×#1854C212yesmaximal, complemented
8C31×#1852C212yesmaximal, complemented
9C31×#1825C211yesmaximal, characteristic, complemented
10C31×#1824C211yesmaximal, characteristic, complemented
11C31×#1780C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C2×C31×#121C2211yescharacteristic
14C2×C31×#121C2212yes—
15C31×#520—24no—
16C31×#520—24no—
17C2×C4×Q8×C31—21no—
18C2×C4×D4×C31—22no—
19C2×C4×D4×C31—21no—
20C2×C31×#117C2212yes—
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2212yes—
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#482—24no—
25C31×#480—24no—
26C2×C31×#107C2212yes—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#102C2212yes—
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×C22⋊C8C2212yes—
35C2×C31×C22⋊C8C2212yes—
36C31×#393—21no—
37C31×#392—21no—
38C31×#392—22no—
39C31×#380C2211yescharacteristic
40C31×#380C2212yes—
41C31×#340C2212yes—
42C31×#340C2212yes—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C2×#41×C31—22no—
46C2×#41×C31—22no—
47C2×#41×C31—24no—
48C2×#41×C31—24no—
49C22×Q8×C31D411yescharacteristic
50C22×D4×C31—21no—
51C22×D4×C31—22no—
52C22×D4×C31D411yescharacteristic
53C22×D4×C31D412yes—
54C22×D4×C31C2311yescharacteristic
55C23×C4×C31—22no—
56C23×C4×C31—21no—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2312yes—
59C22×C8×C31C2311yescharacteristic
60C22×C8×C31C2312yes—
61C22×C8×C31C2311yescharacteristic
62C31×#121—22no—
63C31×#121—22no—
64C31×#121—24no—
65C31×#121—24no—
66C4×Q8×C31—28no—
67C4×D4×C31—216no—
68C4×D4×C31—28no—
69C31×#117—22no—
70C31×#117—24no—
71C31×#117—24no—
72C31×#117D414yescomplemented
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—24no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31D414yescomplemented
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31C2312yes—
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2312yes—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—22no—
90C2×C42×C31—22no—
91C2×C42×C31—21no—
92C31×#107—24no—
93C31×#107—22no—
94C31×#106—22no—
95C31×#102—24no—
96C31×#102—22no—
97C31×#102—22no—
98C31×C22⋊C8—22no—
99C31×C22⋊C8—22no—
100C31×C22⋊C8—24no—
101C31×C22⋊C8—24no—
102C31×#95—21no—
103C31×#95—22no—
104C24×C31—21no—
105C24×C31C2×D411yescharacteristic
106C24×C31C2×D412yes—
107#41×C31—28no—
108#41×C31—28no—
109#41×C31—216no—
110C2×Q8×C31—22no—
111C2×Q8×C31—24no—
112C2×D4×C31—24no—
113C2×D4×C31—24no—
114C2×D4×C31—24no—
115C2×D4×C31—22no—
116C2×D4×C31—24no—
117C2×D4×C31—21no—
118C2×D4×C31—21no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—42no—
122C2×D4×C31—44no—
123C2×D4×C31—82no—
124C2×D4×C31—82no—
125C2×D4×C31—82no—
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—21no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—28no—
136C22×C4×C31—24no—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—82no—
140C22×C4×C31—82no—
141C22×C4×C31—82no—
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31#4114yes—
147C22×C4×C31#4114yes—
148C22×C4×C31C2411yescharacteristic
149C2×C8×C31—21no—
150C2×C8×C31—22no—
151C2×C8×C31—21no—
152C2×C8×C31—22no—
153C2×C8×C31—22no—
154C2×C8×C31—22no—
155C2×C8×C31—22no—
156C4⋊C4×C31—28no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31C2×D412yes—
166C4⋊C4×C31C2×D412yes—
167C4⋊C4×C31C2×D414yes—
168C22⋊C4×C31—28no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—42no—
171C22⋊C4×C31—44no—
172C22⋊C4×C31—82no—
173C22⋊C4×C31—81no—
174C42×C31—28no—
175C42×C31—24no—
176#32986C3111yesmaximal, characteristic, direct product factor, Sylow
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—21no—
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—21no—
187C23×C31—41no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31#12012yes—
193C23×C31#12314yes—
194C23×C31C22×D411yescharacteristic
195Q8×C31—28no—
196D4×C31—28no—
197D4×C31—216no—
198D4×C31—42no—
199D4×C31—41no—
200D4×C31—41no—
201D4×C31—88no—
202D4×C31—84no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—22no—
214C2×C4×C31—24no—
215C2×C4×C31—22no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—84no—
227C2×C4×C31—88no—
228C2×C4×C31#12012yes—
229C2×C4×C31#12314yes—
230C2×C4×C31C22×D411yescharacteristic
231C2×C4×C31C22×D411yescharacteristic
232C2×C4×C31C2×#4112yes—
233C2×C4×C31C2×#4112yes—
234C8×C31—41no—
235C8×C31—42no—
236C8×C31—41no—
237C2×#520C2×C3111yescharacteristic, complemented
238C2×#482C2×C3111yescharacteristic, complemented
239C2×#480C2×C3111yescharacteristic, complemented
240#2615C2×C3111yescharacteristic
241#1875C2×C3112yescomplemented
242#1874C2×C3112yescomplemented
243#1854C2×C3112yescomplemented
244#1852C2×C3112yescomplemented
245#1825C2×C3111yescharacteristic, complemented
246#1824C2×C3111yescharacteristic, complemented
247#1780C2×C3111yescharacteristic, complemented
248C22×C31—24no—
249C22×C31—24no—
250C22×C31—22no—
251C22×C31—24no—
252C22×C31—22no—
253C22×C31—22no—
254C22×C31—42no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—82no—
261C22×C31—82no—
262C22×C31—81no—
263C22×C31—81no—
264C22×C31—81no—
265C22×C31C2×#12011yescharacteristic
266C22×C31C2×#12312yes—
267C22×C31#57612yes—
268C22×C31#57711yescharacteristic
269C22×C31#57811yescharacteristic
270C4×C31—22no—
271C4×C31—24no—
272C4×C31—44no—
273C4×C31—42no—
274C4×C31—42no—
275C4×C31—82no—
276C4×C31—81no—
277C4×C31#52511yescharacteristic
278C4×C31#52511yescharacteristic
279C4×C31#52512yes—
280C22×#41C22×C3111yescharacteristic
281C2×#121C22×C3111yescharacteristic
282C2×#121C22×C3112yes—
283#520—24no—
284#520—24no—
285C2×C4×Q8—21no—
286C2×C4×D4—22no—
287C2×C4×D4—21no—
288C2×#117C22×C3112yes—
289C2×#117C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3112yes—
291C22×C4⋊C4C22×C3111yescharacteristic
292#482—24no—
293#480—24no—
294C2×#107C22×C3112yes—
295C2×#107C22×C3111yescharacteristic
296C2×#106C22×C3111yescharacteristic
297C2×#102C22×C3112yes—
298C2×#102C22×C3111yescharacteristic
299C2×#102C22×C3111yescharacteristic
300C2×C22⋊C8C22×C3111yescharacteristic
301C2×C22⋊C8C22×C3111yescharacteristic
302C2×C22⋊C8C22×C3112yes—
303C2×C22⋊C8C22×C3112yes—
304#393—21no—
305#392—21no—
306#392—22no—
307#380C22×C3111yescharacteristic
308#380C22×C3112yes—
309#340C22×C3112yes—
310#340C22×C3112yes—
311#340C22×C3112yes—
312#340C22×C3112yes—
313C2×C31—44no—
314C2×C31—42no—
315C2×C31—161no—
316C2×C31#284911yescharacteristic
317C2×C31#300811yescharacteristic
318C2×C31#301311yescharacteristic
319C2×C31#309612yes—
320C2×C31#309812yes—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—24no—
324C2×#41—24no—
325C22×Q8D4×C3111yescharacteristic
326C22×D4—21no—
327C22×D4—22no—
328C22×D4D4×C3111yescharacteristic
329C22×D4D4×C3112yes—
330C22×D4C23×C3111yescharacteristic
331C23×C4—22no—
332C23×C4—21no—
333C23×C4C23×C3111yescharacteristic
334C23×C4C23×C3112yes—
335C22×C8C23×C3111yescharacteristic
336C22×C8C23×C3111yescharacteristic
337C22×C8C23×C3112yes—
338#121—22no—
339#121—22no—
340#121—24no—
341#121—24no—
342C4×Q8—28no—
343C4×D4—216no—
344C4×D4—28no—
345#117—22no—
346#117—24no—
347#117—24no—
348#117D4×C3114yescomplemented
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4D4×C3114yescomplemented
355C2×C4⋊C4C23×C3112yes—
356C2×C4⋊C4C23×C3111yescharacteristic
357C2×C4⋊C4C23×C3111yescharacteristic
358C2×C4⋊C4C23×C3112yes—
359C2×C4⋊C4C23×C3111yescharacteristic
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C42—22no—
367C2×C42—21no—
368#107—24no—
369#107—22no—
370#106—22no—
371#102—24no—
372#102—22no—
373#102—22no—
374C22⋊C8—22no—
375C22⋊C8—22no—
376C22⋊C8—24no—
377C22⋊C8—24no—
378#95—21no—
379#95—22no—
380C31#3298611yescharacteristic, direct product factor, Sylow
381C24—21no—
382C24C2×D4×C3111yescharacteristic
383C24C2×D4×C3112yes—
384#41—28no—
385#41—28no—
386#41—216no—
387C2×Q8—22no—
388C2×Q8—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—22no—
393C2×D4—24no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—42no—
399C2×D4—44no—
400C2×D4—82no—
401C2×D4—82no—
402C2×D4—82no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—28no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—82no—
417C22×C4—82no—
418C22×C4—82no—
419C22×C4C2×D4×C3111yescharacteristic
420C22×C4C2×D4×C3112yes—
421C22×C4C2×D4×C3112yes—
422C22×C4C2×D4×C3112yes—
423C22×C4#41×C3114yes—
424C22×C4#41×C3114yes—
425C22×C4C24×C3111yescharacteristic
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C4⋊C4—28no—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4C2×D4×C3112yes—
443C4⋊C4C2×D4×C3112yes—
444C4⋊C4C2×D4×C3114yes—
445C22⋊C4—28no—
446C22⋊C4—24no—
447C22⋊C4—42no—
448C22⋊C4—44no—
449C22⋊C4—82no—
450C22⋊C4—81no—
451C42—28no—
452C42—24no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23C31×#12012yes—
469C23C31×#12314yes—
470C23C22×D4×C3111yescharacteristic
471Q8—28no—
472D4—28no—
473D4—216no—
474D4—42no—
475D4—41no—
476D4—41no—
477D4—88no—
478D4—84no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—84no—
503C2×C4—88no—
504C2×C4C31×#12012yes—
505C2×C4C31×#12314yes—
506C2×C4C22×D4×C3111yescharacteristic
507C2×C4C22×D4×C3111yescharacteristic
508C2×C4C2×#41×C3112yes—
509C2×C4C2×#41×C3112yes—
510C8—41no—
511C8—42no—
512C8—41no—
513C22—24no—
514C22—24no—
515C22—22no—
516C22—24no—
517C22—22no—
518C22—22no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—82no—
526C22—82no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22C2×C31×#12011yescharacteristic
531C22C2×C31×#12312yes—
532C22C31×#57612yes—
533C22C31×#57711yescharacteristic
534C22C31×#57811yescharacteristic
535C4—22no—
536C4—24no—
537C4—44no—
538C4—42no—
539C4—42no—
540C4—82no—
541C4—81no—
542C4C31×#52511yescharacteristic
543C4C31×#52511yescharacteristic
544C4C31×#52512yes—
545C2—44no—
546C2—42no—
547C2—161no—
548C2C31×#284911yescharacteristic
549C2C31×#300811yescharacteristic
550C2C31×#301311yescharacteristic
551C2C31×#309612yes—
552C2C31×#309812yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#520C2semidirect
2. C2×C31×#482C2semidirect
3. C2×C31×#480C2semidirect
5. C31×#1875C2semidirect
6. C31×#1874C2semidirect
7. C31×#1854C2semidirect
8. C31×#1852C2semidirect
9. C31×#1825C2semidirect
10. C31×#1824C2semidirect
11. C31×#1780C2semidirect
72. C31×#117D4semidirect
78. C2×C4⋊C4×C31D4semidirect
176. #32986C31direct (N × H)
237. C2×#520C2×C31semidirect
238. C2×#482C2×C31semidirect
239. C2×#480C2×C31semidirect
241. #1875C2×C31semidirect
242. #1874C2×C31semidirect
243. #1854C2×C31semidirect
244. #1852C2×C31semidirect
245. #1825C2×C31semidirect
246. #1824C2×C31semidirect
247. #1780C2×C31semidirect
348. #117D4×C31semidirect
354. C2×C4⋊C4D4×C31semidirect
380. C31#32986direct (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×#4822
C2×C31×#4802
C31×#26152
C31×#18752
C31×#18742
C31×#18542
C31×#18522
C31×#18252
C31×#18242
C31×#17802
#3298631