Finite Group Databasebeta

← C31×#13101 #21469860

Subgroups — C31×#13101 #21469860

Order 7936.

630 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3011C211yesmaximal, characteristic
2C31×#2884C211yesmaximal, characteristic
3C31×#2129C211yesmaximal, characteristic, complemented
4C31×#2123C211yesmaximal, characteristic, complemented
5C31×#1796C211yesmaximal, characteristic
6C31×#1395C211yesmaximal, characteristic, complemented
7C31×#1391C211yesmaximal, characteristic, complemented
8C2×C31×2−1+4C2211yescharacteristic
9C2×C31×#137C411yescharacteristic, complemented
10C22×Q16×C31C411yescharacteristic, complemented
11C31×#536C2211yescharacteristic
12C31×#519—21no—
13C31×#452—21no—
14C31×#452—21no—
15C31×#451—21no—
16C31×#451—21no—
17C31×#421—21no—
18C31×#419—21no—
19C31×#419C411yescharacteristic, complemented
20C31×#416C411yescharacteristic, complemented
21C31×#413C2211yescharacteristic
22C31×#410—21no—
23C31×#410—22no—
24C31×#410—22no—
25C31×#410C2211yescharacteristic
26C31×#410C2211yescharacteristic
27C31×#410C2211yescharacteristic
28C31×#408C2211yescharacteristic
29C31×#354—22no—
30C31×#352—22no—
31C31×2−1+4—42no—
32C31×2−1+4—42no—
33C2×#41×C31—21no—
34C2×#41×C31—21no—
35C2×#41×C31—21no—
36C2×#41×C31C2×C411yescharacteristic
37C2×#41×C31D411yescharacteristic
38C2×#41×C31D411yescharacteristic
39C2×#41×C31C2311yescharacteristic
40C22×Q8×C31—21no—
41C22×Q8×C31C2×C411yescharacteristic
42C22×Q8×C31C2×C411yescharacteristic
43C22×Q8×C31D411yescharacteristic
44C22×Q8×C31D411yescharacteristic
45C31×#137—42no—
46C2×Q16×C31—21no—
47C2×Q16×C31—21no—
48C2×Q16×C31—21no—
49C2×Q16×C31—42no—
50C2×SD16×C31—21no—
51C2×M16×C31—21no—
52C2×M16×C31C2×C411yescharacteristic
53C22×C8×C31C2×C411yescharacteristic
54C31×C4⋊Q8—21no—
55C31×#124—21no—
56C31×#123—21no—
57C31×#123—21no—
58C31×C22⋊Q8—21no—
59C31×C22⋊Q8—21no—
60C4×Q8×C31—42no—
61C4×Q8×C31—42no—
62C31×#117—24no—
63C31×#117—21no—
64C31×#117—21no—
65C31×#117—21no—
66C31×#117C2×C411yescharacteristic
67C31×#104—42no—
68C31×#103—21no—
69C31×#103—21no—
70C31×#103—21no—
71C31×#103—42no—
72C31×#102—21no—
73C31×#101—21no—
74C31×#100—21no—
75C31×#99—24no—
76C31×#99—21no—
77C31×#99—21no—
78C31×#99—21no—
79C31×#99—21no—
80C31×#99D412yes—
81C31×#99D412yes—
82C31×C22⋊C8—21no—
83C31×C22⋊C8—21no—
84#41×C31—22no—
85#41×C31—22no—
86#41×C31—41no—
87#41×C31—41no—
88#41×C31—41no—
89#41×C31—41no—
90#41×C31—41no—
91#41×C31—41no—
92#41×C31—44no—
93#41×C31—44no—
94#41×C31—44no—
95C2×Q8×C31—22no—
96C2×Q8×C31—22no—
97C2×Q8×C31—21no—
98C2×Q8×C31—21no—
99C2×Q8×C31—21no—
100C2×Q8×C31—22no—
101C2×Q8×C31—22no—
102C2×Q8×C31—21no—
103C2×Q8×C31—21no—
104C2×Q8×C31—41no—
105C2×Q8×C31—41no—
106C2×Q8×C31—41no—
107C2×Q8×C31—41no—
108C2×Q8×C31—44no—
109C2×Q8×C31C22⋊C411yescharacteristic
110C2×Q8×C31C22⋊C411yescharacteristic
111C2×Q8×C31C22⋊C411yescharacteristic
112C2×Q8×C31#4111yescharacteristic
113C2×D4×C31—21no—
114C2×D4×C31—21no—
115C2×D4×C31—21no—
116C2×D4×C31C22⋊C411yescharacteristic
117C2×D4×C31C2×D411yescharacteristic
118C2×D4×C31C2×D411yescharacteristic
119C2×D4×C31#4111yescharacteristic
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—21no—
127C22×C4×C31C22×C411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×D411yescharacteristic
130Q16×C31—42no—
131Q16×C31—42no—
132Q16×C31—42no—
133SD16×C31—42no—
134M16×C31—41no—
135M16×C31—41no—
136M16×C31—41no—
137C2×C8×C31—21no—
138C2×C8×C31—21no—
139C2×C8×C31—41no—
140C2×C8×C31—41no—
141C4⋊C4×C31—21no—
142C4⋊C4×C31—44no—
143C4⋊C4×C31—41no—
144C4⋊C4×C31—41no—
145C4⋊C4×C31—41no—
146C4⋊C4×C31—41no—
147C4⋊C4×C31—41no—
148C22⋊C4×C31—21no—
149C22⋊C4×C31—22no—
150C22⋊C4×C31—22no—
151C22⋊C4×C31—41no—
152C22⋊C4×C31—41no—
153C22⋊C4×C31—41no—
154C42×C31—21no—
155C42×C31—44no—
156C42×C31—41no—
157C42×C31—41no—
158C42×C31—41no—
159#13101C3111yesmaximal, characteristic, direct product factor, Sylow
160C23×C31—21no—
161C23×C31C4×D411yescharacteristic
162C23×C31#12011yescharacteristic
163C23×C31#12111yescharacteristic
164Q8×C31—24no—
165Q8×C31—21no—
166Q8×C31—21no—
167Q8×C31—21no—
168Q8×C31—21no—
169Q8×C31—41no—
170Q8×C31—42no—
171Q8×C31—42no—
172Q8×C31—41no—
173Q8×C31—41no—
174Q8×C31—81no—
175Q8×C31#9912yes—
176Q8×C31#9912yes—
177D4×C31—21no—
178D4×C31—21no—
179D4×C31—41no—
180D4×C31—41no—
181D4×C31—41no—
182D4×C31—42no—
183D4×C31—42no—
184D4×C31—42no—
185C2×C4×C31—24no—
186C2×C4×C31—21no—
187C2×C4×C31—21no—
188C2×C4×C31—21no—
189C2×C4×C31—21no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—42no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—81no—
205C2×C4×C31—81no—
206C2×C4×C31C2×C22⋊C411yescharacteristic
207C2×C4×C31C4×D411yescharacteristic
208C2×C4×C31#12111yescharacteristic
209C2×C4×C31#12311yescharacteristic
210C8×C31—41no—
211C8×C31—41no—
212C8×C31—81no—
213#3011C2×C3111yescharacteristic
214#2884C2×C3111yescharacteristic
215#2129C2×C3111yescharacteristic, complemented
216#2123C2×C3111yescharacteristic, complemented
217#1796C2×C3111yescharacteristic
218#1395C2×C3111yescharacteristic, complemented
219#1391C2×C3111yescharacteristic, complemented
220C22×C31—21no—
221C22×C31—21no—
222C22×C31—21no—
223C22×C31—41no—
224C22×C31—41no—
225C22×C31—41no—
226C22×C31—41no—
227C22×C31—81no—
228C22×C31#38611yescharacteristic
229C4×C31—21no—
230C4×C31—22no—
231C4×C31—22no—
232C4×C31—21no—
233C4×C31—21no—
234C4×C31—41no—
235C4×C31—81no—
236C4×C31—82no—
237C4×C31—82no—
238C4×C31—81no—
239C4×C31—161no—
240C4×C31C2×#9911yescharacteristic
241C4×C31C2×#9911yescharacteristic
242C2×2−1+4C22×C3111yescharacteristic
243C2×#137C4×C3111yescharacteristic, complemented
244C22×Q16C4×C3111yescharacteristic, complemented
245#536C22×C3111yescharacteristic
246#519—21no—
247#452—21no—
248#452—21no—
249#451—21no—
250#451—21no—
251#421—21no—
252#419—21no—
253#419C4×C3111yescharacteristic, complemented
254#416C4×C3111yescharacteristic, complemented
255#413C22×C3111yescharacteristic
256#410—21no—
257#410—22no—
258#410—22no—
259#410C22×C3111yescharacteristic
260#410C22×C3111yescharacteristic
261#410C22×C3111yescharacteristic
262#408C22×C3111yescharacteristic
263#354—22no—
264#352—22no—
265C2×C31—21no—
266C2×C31—41no—
267C2×C31—41no—
268C2×C31—41no—
269C2×C31—81no—
270C2×C31#189811yescharacteristic
2712−1+4—42no—
2722−1+4—42no—
273C2×#41—21no—
274C2×#41—21no—
275C2×#41—21no—
276C2×#41C2×C4×C3111yescharacteristic
277C2×#41D4×C3111yescharacteristic
278C2×#41D4×C3111yescharacteristic
279C2×#41C23×C3111yescharacteristic
280C22×Q8—21no—
281C22×Q8C2×C4×C3111yescharacteristic
282C22×Q8C2×C4×C3111yescharacteristic
283C22×Q8D4×C3111yescharacteristic
284C22×Q8D4×C3111yescharacteristic
285#137—42no—
286C2×Q16—21no—
287C2×Q16—21no—
288C2×Q16—21no—
289C2×Q16—42no—
290C2×SD16—21no—
291C2×M16—21no—
292C2×M16C2×C4×C3111yescharacteristic
293C22×C8C2×C4×C3111yescharacteristic
294C4⋊Q8—21no—
295#124—21no—
296#123—21no—
297#123—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C4×Q8—42no—
301C4×Q8—42no—
302#117—24no—
303#117—21no—
304#117—21no—
305#117—21no—
306#117C2×C4×C3111yescharacteristic
307#104—42no—
308#103—21no—
309#103—21no—
310#103—21no—
311#103—42no—
312#102—21no—
313#101—21no—
314#100—21no—
315#99—24no—
316#99—21no—
317#99—21no—
318#99—21no—
319#99—21no—
320#99D4×C3112yes—
321#99D4×C3112yes—
322C22⋊C8—21no—
323C22⋊C8—21no—
324C31#1310111yescharacteristic, direct product factor, Sylow
325#41—22no—
326#41—22no—
327#41—41no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—41no—
332#41—41no—
333#41—44no—
334#41—44no—
335#41—44no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—44no—
350C2×Q8C22⋊C4×C3111yescharacteristic
351C2×Q8C22⋊C4×C3111yescharacteristic
352C2×Q8C22⋊C4×C3111yescharacteristic
353C2×Q8#41×C3111yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4C22⋊C4×C3111yescharacteristic
358C2×D4C2×D4×C3111yescharacteristic
359C2×D4C2×D4×C3111yescharacteristic
360C2×D4#41×C3111yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4C22×C4×C3111yescharacteristic
369C22×C4C2×D4×C3111yescharacteristic
370C22×C4C2×D4×C3111yescharacteristic
371Q16—42no—
372Q16—42no—
373Q16—42no—
374SD16—42no—
375M16—41no—
376M16—41no—
377M16—41no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—41no—
381C2×C8—41no—
382C4⋊C4—21no—
383C4⋊C4—44no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C22⋊C4—21no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—21no—
396C42—44no—
397C42—41no—
398C42—41no—
399C42—41no—
400C23—21no—
401C23C4×D4×C3111yescharacteristic
402C23C31×#12011yescharacteristic
403C23C31×#12111yescharacteristic
404Q8—24no—
405Q8—21no—
406Q8—21no—
407Q8—21no—
408Q8—21no—
409Q8—41no—
410Q8—42no—
411Q8—42no—
412Q8—41no—
413Q8—41no—
414Q8—81no—
415Q8C31×#9912yes—
416Q8C31×#9912yes—
417D4—21no—
418D4—21no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—42no—
423D4—42no—
424D4—42no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4C2×C22⋊C4×C3111yescharacteristic
447C2×C4C4×D4×C3111yescharacteristic
448C2×C4C31×#12111yescharacteristic
449C2×C4C31×#12311yescharacteristic
450C8—41no—
451C8—41no—
452C8—81no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—81no—
461C22C31×#38611yescharacteristic
462C4—21no—
463C4—22no—
464C4—22no—
465C4—21no—
466C4—21no—
467C4—41no—
468C4—81no—
469C4—82no—
470C4—82no—
471C4—81no—
472C4—161no—
473C4C2×C31×#9911yescharacteristic
474C4C2×C31×#9911yescharacteristic
475C2—21no—
476C2—41no—
477C2—41no—
478C2—41no—
479C2—81no—
480C2C31×#189811yescharacteristic
subgroupG/H
center, socleC2×C31#1898
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×#41C23×C31
prime radicalC2×C31×2−1+4C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×C31×2−1+4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#2129C2semidirect
4. C31×#2123C2semidirect
6. C31×#1395C2semidirect
7. C31×#1391C2semidirect
9. C2×C31×#137C4semidirect
10. C22×Q16×C31C4semidirect
19. C31×#419C4semidirect
20. C31×#416C4semidirect
159. #13101C31direct (N × H)
215. #2129C2×C31semidirect
216. #2123C2×C31semidirect
218. #1395C2×C31semidirect
219. #1391C2×C31semidirect
243. C2×#137C4×C31semidirect
244. C22×Q16C4×C31semidirect
253. #419C4×C31semidirect
254. #416C4×C31semidirect
324. C31#13101direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30112
C31×#28842
C31×#21292
C31×#21232
C31×#17962
C31×#13952
C31×#13912
#1310131