Finite Group Databasebeta

← C31×#9523 #21466282

Subgroups — C31×#9523 #21466282

Order 7936.

742 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3006C211yesmaximal, characteristic
2C31×#2333C211yesmaximal, characteristic, complemented
3C31×#1789C211yesmaximal, characteristic, complemented
4C31×#1782C211yesmaximal, characteristic, complemented
5C31×#1510C211yesmaximal, characteristic, complemented
6C31×#1306C211yesmaximal, characteristic, complemented
7C31×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C2×C31×AGL(1,ℤ/8)—21no—
10C2×C31×#121C2211yescharacteristic
11C31×#449—22no—
12C31×#448C412yescomplemented
13C31×#447C412yescomplemented
14C2×C31×#104—21no—
15C2×C31×#104—21no—
16C31×#417—21no—
17C2×C31×#99—21no—
18C2×C31×#99—21no—
19C31×#407C2211yescharacteristic
20C31×#407C2211yescharacteristic
21C31×#390—21no—
22C31×#388—21no—
23C31×#387—21no—
24C31×#386—21no—
25C31×#386—21no—
26C31×#381C2211yescharacteristic
27C31×#381C2211yescharacteristic
28C4×C22⋊C4×C31—21no—
29C4×C22⋊C4×C31C2211yescharacteristic
30C31×#327—22no—
31C2×#41×C31—21no—
32C2×#41×C31—21no—
33C2×#41×C31—21no—
34C2×#41×C31—21no—
35C2×#41×C31—42no—
36C2×#41×C31—42no—
37C22×Q8×C31C2×C411yescharacteristic, complemented
38C22×D4×C31—21no—
39C22×D4×C31—21no—
40C22×D4×C31C2×C411yescharacteristic, complemented
41C22×D4×C31D411yescharacteristic
42C23×C4×C31—21no—
43C23×C4×C31—21no—
44C23×C4×C31C2311yescharacteristic
45C31×AGL(1,ℤ/8)—42no—
46C31×AGL(1,ℤ/8)—42no—
47C2×SD16×C31—22no—
48C2×D8×C31—22no—
49C2×M16×C31—21no—
50C2×M16×C31—21no—
51C31×#121—21no—
52C31×#121—21no—
53C31×#121C2×C412yes—
54C31×#121D412yes—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31D411yescharacteristic
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31D411yescharacteristic
64C2×C22⋊C4×C31D411yescharacteristic
65C2×C42×C31—21no—
66C2×C42×C31D411yescharacteristic
67C2×C42×C31D411yescharacteristic
68C31×#104—42no—
69C31×#104—42no—
70C31×#103—22no—
71C31×#102—22no—
72C31×#99—42no—
73C31×#99—42no—
74C31×C22⋊C8—21no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8—21no—
77C31×C22⋊C8C2×C412yescomplemented
78C31×#95—21no—
79C31×#95—21no—
80C31×#95—21no—
81C31×#95—21no—
82C31×#95—21no—
83C31×#95—21no—
84C31×#95—21no—
85C24×C31—21no—
86C24×C31—21no—
87C24×C31C2×D411yescharacteristic
88#41×C31—22no—
89#41×C31—22no—
90#41×C31—22no—
91#41×C31—22no—
92#41×C31—41no—
93#41×C31—41no—
94#41×C31—41no—
95#41×C31—41no—
96#41×C31—42no—
97#41×C31—42no—
98#41×C31—42no—
99#41×C31—42no—
100C2×Q8×C31—21no—
101C2×Q8×C31—21no—
102C2×Q8×C31—42no—
103C2×D4×C31—22no—
104C2×D4×C31—22no—
105C2×D4×C31—22no—
106C2×D4×C31—22no—
107C2×D4×C31—21no—
108C2×D4×C31—21no—
109C2×D4×C31—21no—
110C2×D4×C31—41no—
111C2×D4×C31—41no—
112C2×D4×C31—42no—
113C2×D4×C31—41no—
114C2×D4×C31—41no—
115C2×D4×C31—41no—
116C2×D4×C31—41no—
117C2×D4×C31—81no—
118C2×D4×C31—81no—
119C2×D4×C31C22⋊C412yes—
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—41no—
127C22×C4×C31—41no—
128C22×C4×C31—42no—
129C22×C4×C31—42no—
130C22×C4×C31—42no—
131C22×C4×C31—41no—
132C22×C4×C31—41no—
133C22×C4×C31—41no—
134C22×C4×C31—81no—
135C22×C4×C31—81no—
136C22×C4×C31C22×C411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D411yescharacteristic
139C22×C4×C31C2×D411yescharacteristic
140C22×C4×C31#4111yescharacteristic
141C22×C4×C31#4111yescharacteristic
142SD16×C31—44no—
143D8×C31—44no—
144M16×C31—41no—
145M16×C31—41no—
146M16×C31—41no—
147M16×C31—41no—
148C2×C8×C31—22no—
149C2×C8×C31—41no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—81no—
152C4⋊C4×C31C22⋊C412yes—
153C22⋊C4×C31—22no—
154C22⋊C4×C31—22no—
155C22⋊C4×C31—42no—
156C22⋊C4×C31—42no—
157C22⋊C4×C31—41no—
158C22⋊C4×C31—41no—
159C22⋊C4×C31—41no—
160C22⋊C4×C31—41no—
161C22⋊C4×C31—81no—
162C22⋊C4×C31—81no—
163C42×C31—41no—
164C42×C31—41no—
165C42×C31—81no—
166#9523C3111yesmaximal, characteristic, direct product factor, Sylow
167C23×C31—21no—
168C23×C31—21no—
169C23×C31—22no—
170C23×C31—22no—
171C23×C31—41no—
172C23×C31—41no—
173C23×C31—41no—
174C23×C31—41no—
175C23×C31—41no—
176C23×C31—41no—
177C23×C31—41no—
178C23×C31—41no—
179C23×C31—41no—
180C23×C31—41no—
181C23×C31—81no—
182C23×C31—81no—
183C23×C31C4×D411yescharacteristic
184C23×C31#12011yescharacteristic
185C23×C31#12111yescharacteristic
186Q8×C31—22no—
187Q8×C31—22no—
188Q8×C31—41no—
189Q8×C31—41no—
190D4×C31—22no—
191D4×C31—22no—
192D4×C31—42no—
193D4×C31—41no—
194D4×C31—41no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31—42no—
198D4×C31—42no—
199D4×C31—81no—
200D4×C31—82no—
201D4×C31—82no—
202C2×C4×C31—21no—
203C2×C4×C31—21no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31—84no—
233C2×C4×C31—81no—
234C2×C4×C31—81no—
235C2×C4×C31—81no—
236C2×C4×C31C2×C22⋊C411yescharacteristic
237C2×C4×C31C4×D411yescharacteristic
238C2×C4×C31#12111yescharacteristic
239C2×C4×C31#12311yescharacteristic
240C8×C31—42no—
241C8×C31—81no—
242#3006C2×C3111yescharacteristic
243#2333C2×C3111yescharacteristic, complemented
244#1789C2×C3111yescharacteristic, complemented
245#1782C2×C3111yescharacteristic, complemented
246#1510C2×C3111yescharacteristic, complemented
247#1306C2×C3111yescharacteristic, complemented
248#1284C2×C3111yescharacteristic, complemented
249C22×C31—21no—
250C22×C31—21no—
251C22×C31—21no—
252C22×C31—21no—
253C22×C31—21no—
254C22×C31—21no—
255C22×C31—21no—
256C22×C31—21no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—81no—
262C22×C31—81no—
263C22×C31—81no—
264C22×C31—81no—
265C22×C31—81no—
266C22×C31—81no—
267C22×C31—82no—
268C22×C31—82no—
269C22×C31—81no—
270C22×C31—81no—
271C22×C31#38611yescharacteristic
272C22×C31B(4,𝔽2)11yescharacteristic
273C22×C31B(4,𝔽2)11yescharacteristic
274C4×C31—21no—
275C4×C31—21no—
276C4×C31—21no—
277C4×C31—21no—
278C4×C31—42no—
279C4×C31—42no—
280C4×C31—42no—
281C4×C31—81no—
282C4×C31—81no—
283C4×C31—81no—
284C4×C31—161no—
285C22×#41C22×C3111yescharacteristic
286C2×AGL(1,ℤ/8)—21no—
287C2×#121C22×C3111yescharacteristic
288#449—22no—
289#448C4×C3112yescomplemented
290#447C4×C3112yescomplemented
291C2×#104—21no—
292C2×#104—21no—
293#417—21no—
294C2×#99—21no—
295C2×#99—21no—
296#407C22×C3111yescharacteristic
297#407C22×C3111yescharacteristic
298#390—21no—
299#388—21no—
300#387—21no—
301#386—21no—
302#386—21no—
303#381C22×C3111yescharacteristic
304#381C22×C3111yescharacteristic
305C4×C22⋊C4—21no—
306C4×C22⋊C4C22×C3111yescharacteristic
307#327—22no—
308C2×C31—21no—
309C2×C31—21no—
310C2×C31—41no—
311C2×C31—41no—
312C2×C31—82no—
313C2×C31—82no—
314C2×C31#188911yescharacteristic
315C2×C31#190411yescharacteristic
316C2×C31#190611yescharacteristic
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—42no—
322C2×#41—42no—
323C22×Q8C2×C4×C3111yescharacteristic, complemented
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×C4×C3111yescharacteristic, complemented
327C22×D4D4×C3111yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4C23×C3111yescharacteristic
331AGL(1,ℤ/8)—42no—
332AGL(1,ℤ/8)—42no—
333C2×SD16—22no—
334C2×D8—22no—
335C2×M16—21no—
336C2×M16—21no—
337#121—21no—
338#121—21no—
339#121C2×C4×C3112yes—
340#121D4×C3112yes—
341C2×C4⋊C4—21no—
342C2×C4⋊C4D4×C3111yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4D4×C3111yescharacteristic
350C2×C22⋊C4D4×C3111yescharacteristic
351C2×C42—21no—
352C2×C42D4×C3111yescharacteristic
353C2×C42D4×C3111yescharacteristic
354#104—42no—
355#104—42no—
356#103—22no—
357#102—22no—
358#99—42no—
359#99—42no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8C2×C4×C3112yescomplemented
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371C31#952311yescharacteristic, direct product factor, Sylow
372C24—21no—
373C24—21no—
374C24C2×D4×C3111yescharacteristic
375#41—22no—
376#41—22no—
377#41—22no—
378#41—22no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—41no—
383#41—42no—
384#41—42no—
385#41—42no—
386#41—42no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—42no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—42no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—81no—
405C2×D4—81no—
406C2×D4C22⋊C4×C3112yes—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4C22×C4×C3111yescharacteristic
424C22×C4C2×D4×C3111yescharacteristic
425C22×C4C2×D4×C3111yescharacteristic
426C22×C4C2×D4×C3111yescharacteristic
427C22×C4#41×C3111yescharacteristic
428C22×C4#41×C3111yescharacteristic
429SD16—44no—
430D8—44no—
431M16—41no—
432M16—41no—
433M16—41no—
434M16—41no—
435C2×C8—22no—
436C2×C8—41no—
437C4⋊C4—21no—
438C4⋊C4—81no—
439C4⋊C4C22⋊C4×C3112yes—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—81no—
449C22⋊C4—81no—
450C42—41no—
451C42—41no—
452C42—81no—
453C23—21no—
454C23—21no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—81no—
468C23—81no—
469C23C4×D4×C3111yescharacteristic
470C23C31×#12011yescharacteristic
471C23C31×#12111yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—41no—
475Q8—41no—
476D4—22no—
477D4—22no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—81no—
486D4—82no—
487D4—82no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—84no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4C2×C22⋊C4×C3111yescharacteristic
523C2×C4C4×D4×C3111yescharacteristic
524C2×C4C31×#12111yescharacteristic
525C2×C4C31×#12311yescharacteristic
526C8—42no—
527C8—81no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—81no—
549C22—81no—
550C22C31×#38611yescharacteristic
551C22C31×B(4,𝔽2)11yescharacteristic
552C22C31×B(4,𝔽2)11yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—161no—
564C2—21no—
565C2—21no—
566C2—41no—
567C2—41no—
568C2—82no—
569C2—82no—
570C2C31×#188911yescharacteristic
571C2C31×#190411yescharacteristic
572C2C31×#190611yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3006C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2333C2semidirect
3. C31×#1789C2semidirect
4. C31×#1782C2semidirect
5. C31×#1510C2semidirect
6. C31×#1306C2semidirect
7. C31×#1284C2semidirect
12. C31×#448C4semidirect
13. C31×#447C4semidirect
37. C22×Q8×C31C2×C4semidirect
40. C22×D4×C31C2×C4semidirect
77. C31×C22⋊C8C2×C4semidirect
166. #9523C31direct (N × H)
243. #2333C2×C31semidirect
244. #1789C2×C31semidirect
245. #1782C2×C31semidirect
246. #1510C2×C31semidirect
247. #1306C2×C31semidirect
248. #1284C2×C31semidirect
289. #448C4×C31semidirect
290. #447C4×C31semidirect
323. C22×Q8C2×C4×C31semidirect
326. C22×D4C2×C4×C31semidirect
363. C22⋊C8C2×C4×C31semidirect
371. C31#9523direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30062
C31×#23332
C31×#17892
C31×#17822
C31×#15102
C31×#13062
C31×#12842
#952331