Finite Group Databasebeta

← C31×#10229 #21466988

Subgroups — C31×#10229 #21466988

Order 7936.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#460C211yesmaximal, characteristic, complemented
2C2×C31×#459C211yesmaximal, characteristic
3C31×#2538C211yesmaximal, characteristic, complemented
4C31×#1957C211yesmaximal, characteristic, complemented
5C2×C31×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C31×D4⋊C8C211yesmaximal, characteristic, complemented
7C31×#1296C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C22×D8×C31—21no—
10C2×C31×#127C2211yescharacteristic
11C2×C31×C22⋊Q8—21no—
12C2×C4×Q8×C31C2211yescharacteristic
13C2×C4×D4×C31C2211yescharacteristic
14C31×#460—22no—
15C31×#460—22no—
16C31×#459—22no—
17C31×#459—22no—
18C2×C31×C4⋊C8C2211yescharacteristic
19C2×C31×C4⋊C8C2211yescharacteristic
20C2×C31×#102—21no—
21C2×C31×#102—21no—
22C2×C31×#102—22no—
23C2×C4×C8×C31C2211yescharacteristic
24C31×#396—22no—
25C31×#390—21no—
26C31×#389—21no—
27C31×#384C2211yescharacteristic
28C31×#380—21no—
29C31×Q8⋊C8—22no—
30C31×D4⋊C8—22no—
31C22×Q8×C31D411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31—21no—
34C22×D4×C31—21no—
35C22×D4×C31D411yescharacteristic
36C23×C4×C31—21no—
37C2×SD16×C31—24no—
38C2×SD16×C31—42no—
39C2×SD16×C31—42no—
40C2×D8×C31—24no—
41C2×D8×C31—42no—
42C2×D8×C31—42no—
43C22×C8×C31—21no—
44C22×C8×C31—21no—
45C22×C8×C31—21no—
46C31×#127—21no—
47C31×#127—21no—
48C31×#127—21no—
49C31×#127D412yes—
50C31×C22⋊Q8—42no—
51C31×C22⋊Q8—42no—
52C4×Q8×C31—21no—
53C4×Q8×C31—21no—
54C4×Q8×C31—21no—
55C4×Q8×C31—21no—
56C4×D4×C31—21no—
57C4×D4×C31—21no—
58C4×D4×C31—21no—
59C4×D4×C31—21no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31D411yescharacteristic
65C2×C4⋊C4×C31D411yescharacteristic
66C2×C4⋊C4×C31D412yes—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—22no—
70C2×C42×C31—21no—
71C2×C42×C31C2311yescharacteristic
72C31×C4⋊C8—21no—
73C31×C4⋊C8—21no—
74C31×C4⋊C8D412yes—
75C31×C4⋊C8D412yes—
76C31×#102—24no—
77C31×#102—24no—
78C31×#102—44no—
79C4×C8×C31—21no—
80C4×C8×C31—21no—
81C31×#95—22no—
82C24×C31—21no—
83C24×C31—41no—
84C2×Q8×C31—21no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31—21no—
88C2×Q8×C31—21no—
89C2×Q8×C31D812yescomplemented
90C2×D4×C31—21no—
91C2×D4×C31—22no—
92C2×D4×C31—22no—
93C2×D4×C31—21no—
94C2×D4×C31—22no—
95C2×D4×C31—21no—
96C2×D4×C31—21no—
97C2×D4×C31—21no—
98C2×D4×C31—42no—
99C2×D4×C31—42no—
100C2×D4×C31—41no—
101C2×D4×C31—41no—
102C2×D4×C31—41no—
103C2×D4×C31—41no—
104C2×D4×C31—41no—
105C2×D4×C31—41no—
106C2×D4×C31—41no—
107C2×D4×C31—41no—
108C2×D4×C31—41no—
109C2×D4×C31—41no—
110C2×D4×C31—41no—
111C2×D4×C31SD1612yescomplemented
112C22×C4×C31—21no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—22no—
116C22×C4×C31—41no—
117C22×C4×C31—41no—
118C22×C4×C31—41no—
119C22×C4×C31—41no—
120C22×C4×C31—41no—
121C22×C4×C31—41no—
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×D411yescharacteristic
124C22×C4×C31C2×D411yescharacteristic
125SD16×C31—48no—
126D8×C31—48no—
127C2×C8×C31—22no—
128C2×C8×C31—22no—
129C2×C8×C31—22no—
130C2×C8×C31—41no—
131C2×C8×C31—41no—
132C2×C8×C31—41no—
133C2×C8×C31—41no—
134C2×C8×C31—41no—
135C2×C8×C31—41no—
136C4⋊C4×C31—21no—
137C4⋊C4×C31—21no—
138C4⋊C4×C31—21no—
139C4⋊C4×C31—21no—
140C4⋊C4×C31—44no—
141C4⋊C4×C31—42no—
142C4⋊C4×C31—41no—
143C4⋊C4×C31—41no—
144C4⋊C4×C31—41no—
145C4⋊C4×C31—41no—
146C4⋊C4×C31—41no—
147C4⋊C4×C31—41no—
148C22⋊C4×C31—44no—
149C22⋊C4×C31—41no—
150C22⋊C4×C31—41no—
151C22⋊C4×C31—82no—
152C42×C31—41no—
153C42×C31—41no—
154C42×C31C2×D411yescharacteristic
155C42×C31C2×D411yescharacteristic
156C42×C31C2×D411yescharacteristic
157C42×C31#4111yescharacteristic
158#10229C3111yesmaximal, characteristic, direct product factor, Sylow
159C23×C31—22no—
160C23×C31—41no—
161C23×C31—41no—
162C23×C31—41no—
163C23×C31—41no—
164C23×C31—41no—
165C23×C31—41no—
166C23×C31—42no—
167C23×C31—81no—
168C23×C31—81no—
169C23×C31—81no—
170C23×C31—81no—
171C23×C31—81no—
172C23×C31—81no—
173C23×C31#12011yescharacteristic
174Q8×C31—22no—
175Q8×C31—22no—
176Q8×C31—41no—
177Q8×C31—41no—
178D4×C31—22no—
179D4×C31—22no—
180D4×C31—44no—
181D4×C31—42no—
182D4×C31—42no—
183D4×C31—42no—
184D4×C31—41no—
185D4×C31—42no—
186D4×C31—41no—
187D4×C31—82no—
188D4×C31—81no—
189D4×C31—81no—
190D4×C31—81no—
191D4×C31—81no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—22no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—42no—
200C2×C4×C31—41no—
201C2×C4×C31—42no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—42no—
205C2×C4×C31—41no—
206C2×C4×C31—81no—
207C2×C4×C31—81no—
208C2×C4×C31—81no—
209C2×C4×C31—81no—
210C2×C4×C31#12011yescharacteristic
211C2×C4×C31#12011yescharacteristic
212C2×C4×C31#12111yescharacteristic
213C2×C4×C31#12111yescharacteristic
214C2×C4×C31#12111yescharacteristic
215C2×C4×C31#12711yescharacteristic
216C2×C4×C31C2×D811yescharacteristic
217C2×C4×C31C2×SD1611yescharacteristic
218C2×C4×C31#13511yescharacteristic
219C2×C4×C31#13511yescharacteristic
220C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
221C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
222C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
223C2×C4×C31#13711yescharacteristic
224C8×C31—42no—
225C8×C31—42no—
226C8×C31—42no—
227C2×#460C2×C3111yescharacteristic, complemented
228C2×#459C2×C3111yescharacteristic
229#2538C2×C3111yescharacteristic, complemented
230#1957C2×C3111yescharacteristic, complemented
231C2×Q8⋊C8C2×C3111yescharacteristic, complemented
232C2×D4⋊C8C2×C3111yescharacteristic, complemented
233#1296C2×C3111yescharacteristic, complemented
234C22×C31—42no—
235C22×C31—42no—
236C22×C31—42no—
237C22×C31—81no—
238C22×C31—81no—
239C22×C31—81no—
240C22×C31—81no—
241C22×C31—82no—
242C22×C31—82no—
243C22×C31—82no—
244C22×C31—161no—
245C22×C31—161no—
246C22×C31—161no—
247C22×C31—161no—
248C22×C31#39211yescharacteristic
249C22×C31#44711yescharacteristic
250C22×C31#44811yescharacteristic
251C22×C31#44911yescharacteristic
252C22×C31#44911yescharacteristic
253C22×C31#45311yescharacteristic
254C22×C31#45411yescharacteristic
255C4×C31—21no—
256C4×C31—21no—
257C4×C31—42no—
258C4×C31—82no—
259C4×C31—81no—
260C4×C31—81no—
261C4×C31#44711yescharacteristic
262C4×C31#44911yescharacteristic
263C4×C31#45011yescharacteristic
264C4×C31#45211yescharacteristic
265C4×C31#46511yescharacteristic
266C4×C31#46611yescharacteristic
267C4×C31#46811yescharacteristic
268C4×C31#46911yescharacteristic
269C22×SD16—21no—
270C22×D8—21no—
271C2×#127C22×C3111yescharacteristic
272C2×C22⋊Q8—21no—
273C2×C4×Q8C22×C3111yescharacteristic
274C2×C4×D4C22×C3111yescharacteristic
275#460—22no—
276#460—22no—
277#459—22no—
278#459—22no—
279C2×C4⋊C8C22×C3111yescharacteristic
280C2×C4⋊C8C22×C3111yescharacteristic
281C2×#102—21no—
282C2×#102—21no—
283C2×#102—22no—
284C2×C4×C8C22×C3111yescharacteristic
285#396—22no—
286#390—21no—
287#389—21no—
288#384C22×C3111yescharacteristic
289#380—21no—
290Q8⋊C8—22no—
291D4⋊C8—22no—
292C2×C31—82no—
293C2×C31—162no—
294C2×C31#162111yescharacteristic
295C2×C31#162211yescharacteristic
296C2×C31#162711yescharacteristic
297C2×C31#162811yescharacteristic
298C2×C31#199911yescharacteristic
299C2×C31#200011yescharacteristic
300C2×C31#200611yescharacteristic
301C22×Q8D4×C3111yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4D4×C3111yescharacteristic
306C23×C4—21no—
307C2×SD16—24no—
308C2×SD16—42no—
309C2×SD16—42no—
310C2×D8—24no—
311C2×D8—42no—
312C2×D8—42no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316#127—21no—
317#127—21no—
318#127—21no—
319#127D4×C3112yes—
320C22⋊Q8—42no—
321C22⋊Q8—42no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4D4×C3111yescharacteristic
335C2×C4⋊C4D4×C3111yescharacteristic
336C2×C4⋊C4D4×C3112yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—22no—
340C2×C42—21no—
341C2×C42C23×C3111yescharacteristic
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8D4×C3112yes—
345C4⋊C8D4×C3112yes—
346#102—24no—
347#102—24no—
348#102—44no—
349C4×C8—21no—
350C4×C8—21no—
351#95—22no—
352C31#1022911yescharacteristic, direct product factor, Sylow
353C24—21no—
354C24—41no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8D8×C3112yescomplemented
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4SD16×C3112yescomplemented
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4C2×D4×C3111yescharacteristic
394C22×C4C2×D4×C3111yescharacteristic
395C22×C4C2×D4×C3111yescharacteristic
396SD16—48no—
397D8—48no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—42no—
412C4⋊C4—44no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C22⋊C4—44no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—82no—
423C42—41no—
424C42—41no—
425C42C2×D4×C3111yescharacteristic
426C42C2×D4×C3111yescharacteristic
427C42C2×D4×C3111yescharacteristic
428C42#41×C3111yescharacteristic
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—81no—
438C23—81no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23C31×#12011yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—22no—
449D4—22no—
450D4—44no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—41no—
455D4—42no—
456D4—41no—
457D4—82no—
458D4—81no—
459D4—81no—
460D4—81no—
461D4—81no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4C31×#12011yescharacteristic
481C2×C4C31×#12011yescharacteristic
482C2×C4C31×#12111yescharacteristic
483C2×C4C31×#12111yescharacteristic
484C2×C4C31×#12111yescharacteristic
485C2×C4C31×#12711yescharacteristic
486C2×C4C2×D8×C3111yescharacteristic
487C2×C4C2×SD16×C3111yescharacteristic
488C2×C4C31×#13511yescharacteristic
489C2×C4C31×#13511yescharacteristic
490C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
491C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
492C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
493C2×C4C31×#13711yescharacteristic
494C8—42no—
495C8—42no—
496C8—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22—161no—
508C22—161no—
509C22—161no—
510C22—161no—
511C22C31×#39211yescharacteristic
512C22C31×#44711yescharacteristic
513C22C31×#44811yescharacteristic
514C22C31×#44911yescharacteristic
515C22C31×#44911yescharacteristic
516C22C31×#45311yescharacteristic
517C22C31×#45411yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—82no—
522C4—81no—
523C4—81no—
524C4C31×#44711yescharacteristic
525C4C31×#44911yescharacteristic
526C4C31×#45011yescharacteristic
527C4C31×#45211yescharacteristic
528C4C31×#46511yescharacteristic
529C4C31×#46611yescharacteristic
530C4C31×#46811yescharacteristic
531C4C31×#46911yescharacteristic
532C2—82no—
533C2—162no—
534C2C31×#162111yescharacteristic
535C2C31×#162211yescharacteristic
536C2C31×#162711yescharacteristic
537C2C31×#162811yescharacteristic
538C2C31×#199911yescharacteristic
539C2C31×#200011yescharacteristic
540C2C31×#200611yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#460C2semidirect
3. C31×#2538C2semidirect
4. C31×#1957C2semidirect
5. C2×C31×Q8⋊C8C2semidirect
6. C2×C31×D4⋊C8C2semidirect
7. C31×#1296C2semidirect
89. C2×Q8×C31D8semidirect
111. C2×D4×C31SD16semidirect
158. #10229C31direct (N × H)
227. C2×#460C2×C31semidirect
229. #2538C2×C31semidirect
230. #1957C2×C31semidirect
231. C2×Q8⋊C8C2×C31semidirect
232. C2×D4⋊C8C2×C31semidirect
233. #1296C2×C31semidirect
352. C31#10229direct (N × H)
360. C2×Q8D8×C31semidirect
382. C2×D4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4602
C2×C31×#4592
C31×#25382
C31×#19572
C2×C31×Q8⋊C82
C2×C31×D4⋊C82
C31×#12962
#1022931