Finite Group Databasebeta

← C31×#32987 #21489746

Subgroups — C31×#32987 #21489746

Order 7936.

1358 conjugacy classes of subgroups.

The subgroup lattice has 556 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×#482C211yesmaximal, characteristic, complemented
4C31×#2615C211yesmaximal, characteristic
5C31×#1875C212yesmaximal, complemented
6C31×#1874C212yesmaximal, complemented
7C31×#1854C212yesmaximal, complemented
8C31×#1853C212yesmaximal, complemented
9C31×#1825C211yesmaximal, characteristic, complemented
10C31×#1823C211yesmaximal, 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×#481—24no—
26C2×C31×#107C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2212yes—
29C2×C31×#102C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2212yes—
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×C31C2312yes—
83C2×C4⋊C4×C31C2311yescharacteristic
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—22no—
93C31×#106—24no—
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—81no—
140C22×C4×C31—82no—
141C22×C4×C31—81no—
142C22×C4×C31—82no—
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31#4114yes—
148C22×C4×C31#4114yes—
149C22×C4×C31C2411yescharacteristic
150C2×C8×C31—22no—
151C2×C8×C31—21no—
152C2×C8×C31—21no—
153C2×C8×C31—22no—
154C2×C8×C31—22no—
155C2×C8×C31—22no—
156C2×C8×C31—22no—
157C4⋊C4×C31—28no—
158C4⋊C4×C31—24no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31C2×D412yes—
167C4⋊C4×C31C2×D414yes—
168C4⋊C4×C31C2×D412yes—
169C22⋊C4×C31—28no—
170C22⋊C4×C31—24no—
171C22⋊C4×C31—42no—
172C22⋊C4×C31—44no—
173C22⋊C4×C31—81no—
174C22⋊C4×C31—82no—
175C42×C31—28no—
176C42×C31—24no—
177#32987C3111yesmaximal, characteristic, direct product factor, Sylow
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—22no—
181C23×C31—21no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—22no—
185C23×C31—21no—
186C23×C31—22no—
187C23×C31—22no—
188C23×C31—41no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—42no—
192C23×C31—41no—
193C23×C31#12012yes—
194C23×C31#12314yes—
195C23×C31C22×D411yescharacteristic
196Q8×C31—28no—
197D4×C31—28no—
198D4×C31—216no—
199D4×C31—42no—
200D4×C31—41no—
201D4×C31—41no—
202D4×C31—88no—
203D4×C31—84no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—24no—
214C2×C4×C31—22no—
215C2×C4×C31—24no—
216C2×C4×C31—22no—
217C2×C4×C31—42no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—84no—
228C2×C4×C31—88no—
229C2×C4×C31#12012yes—
230C2×C4×C31#12314yes—
231C2×C4×C31C22×D411yescharacteristic
232C2×C4×C31C22×D411yescharacteristic
233C2×C4×C31C2×#4112yes—
234C2×C4×C31C2×#4112yes—
235C8×C31—42no—
236C8×C31—41no—
237C8×C31—41no—
238C2×#520C2×C3111yescharacteristic, complemented
239C2×#481C2×C3111yescharacteristic, complemented
240C2×#482C2×C3111yescharacteristic, complemented
241#2615C2×C3111yescharacteristic
242#1875C2×C3112yescomplemented
243#1874C2×C3112yescomplemented
244#1854C2×C3112yescomplemented
245#1853C2×C3112yescomplemented
246#1825C2×C3111yescharacteristic, complemented
247#1823C2×C3111yescharacteristic, complemented
248#1780C2×C3111yescharacteristic, complemented
249C22×C31—24no—
250C22×C31—24no—
251C22×C31—22no—
252C22×C31—24no—
253C22×C31—22no—
254C22×C31—22no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—82no—
262C22×C31—82no—
263C22×C31—81no—
264C22×C31—81no—
265C22×C31—81no—
266C22×C31C2×#12011yescharacteristic
267C22×C31C2×#12312yes—
268C22×C31#57611yescharacteristic
269C22×C31#57712yes—
270C22×C31#57711yescharacteristic
271C4×C31—22no—
272C4×C31—24no—
273C4×C31—42no—
274C4×C31—44no—
275C4×C31—42no—
276C4×C31—82no—
277C4×C31—81no—
278C4×C31#52511yescharacteristic
279C4×C31#52512yes—
280C4×C31#52511yescharacteristic
281C22×#41C22×C3111yescharacteristic
282C2×#121C22×C3111yescharacteristic
283C2×#121C22×C3112yes—
284#520—24no—
285#520—24no—
286C2×C4×Q8—21no—
287C2×C4×D4—22no—
288C2×C4×D4—21no—
289C2×#117C22×C3112yes—
290C2×#117C22×C3111yescharacteristic
291C22×C4⋊C4C22×C3112yes—
292C22×C4⋊C4C22×C3111yescharacteristic
293#482—24no—
294#481—24no—
295C2×#107C22×C3111yescharacteristic
296C2×#106C22×C3111yescharacteristic
297C2×#106C22×C3112yes—
298C2×#102C22×C3111yescharacteristic
299C2×#102C22×C3111yescharacteristic
300C2×#102C22×C3112yes—
301C2×C22⋊C8C22×C3111yescharacteristic
302C2×C22⋊C8C22×C3111yescharacteristic
303C2×C22⋊C8C22×C3112yes—
304C2×C22⋊C8C22×C3112yes—
305#393—21no—
306#392—21no—
307#392—22no—
308#380C22×C3111yescharacteristic
309#380C22×C3112yes—
310#340C22×C3112yes—
311#340C22×C3112yes—
312#340C22×C3112yes—
313#340C22×C3112yes—
314C2×C31—44no—
315C2×C31—42no—
316C2×C31—161no—
317C2×C31#284911yescharacteristic
318C2×C31#301011yescharacteristic
319C2×C31#301211yescharacteristic
320C2×C31#309612yes—
321C2×C31#309912yes—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—24no—
325C2×#41—24no—
326C22×Q8D4×C3111yescharacteristic
327C22×D4—21no—
328C22×D4—22no—
329C22×D4D4×C3111yescharacteristic
330C22×D4D4×C3112yes—
331C22×D4C23×C3111yescharacteristic
332C23×C4—22no—
333C23×C4—21no—
334C23×C4C23×C3111yescharacteristic
335C23×C4C23×C3112yes—
336C22×C8C23×C3111yescharacteristic
337C22×C8C23×C3112yes—
338C22×C8C23×C3111yescharacteristic
339#121—22no—
340#121—22no—
341#121—24no—
342#121—24no—
343C4×Q8—28no—
344C4×D4—216no—
345C4×D4—28no—
346#117—22no—
347#117—24no—
348#117—24no—
349#117D4×C3114yescomplemented
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4D4×C3114yescomplemented
356C2×C4⋊C4C23×C3112yes—
357C2×C4⋊C4C23×C3111yescharacteristic
358C2×C4⋊C4C23×C3111yescharacteristic
359C2×C4⋊C4C23×C3112yes—
360C2×C4⋊C4C23×C3111yescharacteristic
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C42—22no—
368C2×C42—21no—
369#107—22no—
370#106—24no—
371#106—22no—
372#102—24no—
373#102—22no—
374#102—22no—
375C22⋊C8—22no—
376C22⋊C8—22no—
377C22⋊C8—24no—
378C22⋊C8—24no—
379#95—21no—
380#95—22no—
381C31#3298711yescharacteristic, direct product factor, Sylow
382C24—21no—
383C24C2×D4×C3111yescharacteristic
384C24C2×D4×C3112yes—
385#41—28no—
386#41—28no—
387#41—216no—
388C2×Q8—22no—
389C2×Q8—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—22no—
394C2×D4—24no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—42no—
400C2×D4—44no—
401C2×D4—82no—
402C2×D4—82no—
403C2×D4—82no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—28no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—81no—
418C22×C4—82no—
419C22×C4—81no—
420C22×C4—82no—
421C22×C4C2×D4×C3111yescharacteristic
422C22×C4C2×D4×C3112yes—
423C22×C4C2×D4×C3112yes—
424C22×C4C2×D4×C3112yes—
425C22×C4#41×C3114yes—
426C22×C4#41×C3114yes—
427C22×C4C24×C3111yescharacteristic
428C2×C8—22no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C4⋊C4—28no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4C2×D4×C3112yes—
445C4⋊C4C2×D4×C3114yes—
446C4⋊C4C2×D4×C3112yes—
447C22⋊C4—28no—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—44no—
451C22⋊C4—81no—
452C22⋊C4—82no—
453C42—28no—
454C42—24no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—21no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—22no—
464C23—22no—
465C23—41no—
466C23—42no—
467C23—41no—
468C23—42no—
469C23—41no—
470C23C31×#12012yes—
471C23C31×#12314yes—
472C23C22×D4×C3111yescharacteristic
473Q8—28no—
474D4—28no—
475D4—216no—
476D4—42no—
477D4—41no—
478D4—41no—
479D4—88no—
480D4—84no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—84no—
505C2×C4—88no—
506C2×C4C31×#12012yes—
507C2×C4C31×#12314yes—
508C2×C4C22×D4×C3111yescharacteristic
509C2×C4C22×D4×C3111yescharacteristic
510C2×C4C2×#41×C3112yes—
511C2×C4C2×#41×C3112yes—
512C8—42no—
513C8—41no—
514C8—41no—
515C22—24no—
516C22—24no—
517C22—22no—
518C22—24no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—82no—
528C22—82no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22C2×C31×#12011yescharacteristic
533C22C2×C31×#12312yes—
534C22C31×#57611yescharacteristic
535C22C31×#57712yes—
536C22C31×#57711yescharacteristic
537C4—22no—
538C4—24no—
539C4—42no—
540C4—44no—
541C4—42no—
542C4—82no—
543C4—81no—
544C4C31×#52511yescharacteristic
545C4C31×#52512yes—
546C4C31×#52511yescharacteristic
547C2—44no—
548C2—42no—
549C2—161no—
550C2C31×#284911yescharacteristic
551C2C31×#301011yescharacteristic
552C2C31×#301211yescharacteristic
553C2C31×#309612yes—
554C2C31×#309912yes—
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×#481C2semidirect
3. C2×C31×#482C2semidirect
5. C31×#1875C2semidirect
6. C31×#1874C2semidirect
7. C31×#1854C2semidirect
8. C31×#1853C2semidirect
9. C31×#1825C2semidirect
10. C31×#1823C2semidirect
11. C31×#1780C2semidirect
72. C31×#117D4semidirect
78. C2×C4⋊C4×C31D4semidirect
177. #32987C31direct (N × H)
238. C2×#520C2×C31semidirect
239. C2×#481C2×C31semidirect
240. C2×#482C2×C31semidirect
242. #1875C2×C31semidirect
243. #1874C2×C31semidirect
244. #1854C2×C31semidirect
245. #1853C2×C31semidirect
246. #1825C2×C31semidirect
247. #1823C2×C31semidirect
248. #1780C2×C31semidirect
349. #117D4×C31semidirect
355. C2×C4⋊C4D4×C31semidirect
381. C31#32987direct (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×#4822
C31×#26152
C31×#18752
C31×#18742
C31×#18542
C31×#18532
C31×#18252
C31×#18232
C31×#17802
#3298731