Finite Group Databasebeta

← C31×#13100 #21469859

Subgroups — C31×#13100 #21469859

Order 7936.

672 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3009C211yesmaximal, characteristic
2C31×#2883C211yesmaximal, characteristic
3C31×#2129C211yesmaximal, characteristic, complemented
4C31×#2123C211yesmaximal, characteristic, complemented
5C31×#1795C211yesmaximal, characteristic
6C31×#1395C211yesmaximal, characteristic, complemented
7C31×#1391C211yesmaximal, characteristic, complemented
8C2×C31×H(5,𝔽2)C2211yescharacteristic
9C2×C31×#137C411yescharacteristic, complemented
10C22×SD16×C31C411yescharacteristic, complemented
11C31×#536C2211yescharacteristic
12C31×#518—21no—
13C31×#452—21no—
14C31×#452—21no—
15C31×#450—21no—
16C31×#450—21no—
17C31×#421—21no—
18C31×#418—21no—
19C31×#418C411yescharacteristic, complemented
20C31×#416C411yescharacteristic, complemented
21C31×#413C2211yescharacteristic
22C31×#410—21no—
23C31×#410C2211yescharacteristic
24C31×#410C2211yescharacteristic
25C31×#410C2211yescharacteristic
26C2×C31×#99—22no—
27C2×C31×#99—22no—
28C31×#408C2211yescharacteristic
29C31×#354—22no—
30C31×#352—22no—
31C31×H(5,𝔽2)—42no—
32C31×H(5,𝔽2)—42no—
33C2×#41×C31—21no—
34C2×#41×C31C2×C411yescharacteristic
35C2×#41×C31D411yescharacteristic
36C2×#41×C31D411yescharacteristic
37C2×#41×C31C2311yescharacteristic
38C22×Q8×C31C2×C411yescharacteristic, complemented
39C22×D4×C31—21no—
40C22×D4×C31—21no—
41C22×D4×C31—21no—
42C22×D4×C31C2×C411yescharacteristic
43C22×D4×C31D411yescharacteristic
44C22×D4×C31D411yescharacteristic
45C31×#137—42no—
46C2×Q16×C31—21no—
47C2×SD16×C31—21no—
48C2×SD16×C31—21no—
49C2×SD16×C31—21no—
50C2×SD16×C31—42no—
51C2×M16×C31—21no—
52C2×M16×C31C2×C411yescharacteristic, complemented
53C22×C8×C31C2×C411yescharacteristic, complemented
54C31×C4⋊Q8—21no—
55C31×#124—21no—
56C31×#123—21no—
57C31×#123—21no—
58C31×C22⋊Q8—21no—
59C31×C22⋊Q8—21no—
60C4×D4×C31—42no—
61C4×D4×C31—42no—
62C31×#117—21no—
63C31×#117—21no—
64C31×#117—21no—
65C31×#117C2×C411yescharacteristic, complemented
66C2×C22⋊C4×C31—24no—
67C31×#104—42no—
68C31×#103—21no—
69C31×#102—21no—
70C31×#102—21no—
71C31×#102—21no—
72C31×#102—42no—
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—
84C24×C31—21no—
85C24×C31—21no—
86C24×C31—21no—
87#41×C31—22no—
88#41×C31—22no—
89#41×C31—41no—
90#41×C31—41no—
91#41×C31—41no—
92#41×C31—41no—
93#41×C31—41no—
94#41×C31—41no—
95#41×C31—44no—
96C2×Q8×C31—21no—
97C2×Q8×C31—21no—
98C2×Q8×C31—41no—
99C2×Q8×C31—41no—
100C2×Q8×C31C22⋊C411yescharacteristic
101C2×Q8×C31#4111yescharacteristic
102C2×D4×C31—22no—
103C2×D4×C31—22no—
104C2×D4×C31—22no—
105C2×D4×C31—22no—
106C2×D4×C31—21no—
107C2×D4×C31—21no—
108C2×D4×C31—21no—
109C2×D4×C31—21no—
110C2×D4×C31—21no—
111C2×D4×C31—21no—
112C2×D4×C31—41no—
113C2×D4×C31—41no—
114C2×D4×C31—44no—
115C2×D4×C31—44no—
116C2×D4×C31—44no—
117C2×D4×C31C22⋊C411yescharacteristic
118C2×D4×C31C22⋊C411yescharacteristic
119C2×D4×C31C22⋊C411yescharacteristic
120C2×D4×C31C2×D411yescharacteristic
121C2×D4×C31C2×D411yescharacteristic
122C2×D4×C31#4111yescharacteristic
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—44no—
128C22×C4×C31C22×C411yescharacteristic
129C22×C4×C31C2×D411yescharacteristic
130C22×C4×C31C2×D411yescharacteristic
131Q16×C31—42no—
132SD16×C31—42no—
133SD16×C31—42no—
134SD16×C31—42no—
135M16×C31—41no—
136M16×C31—41no—
137M16×C31—41no—
138C2×C8×C31—21no—
139C2×C8×C31—21no—
140C2×C8×C31—41no—
141C2×C8×C31—41no—
142C4⋊C4×C31—21no—
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—44no—
152C22⋊C4×C31—41no—
153C22⋊C4×C31—41no—
154C22⋊C4×C31—41no—
155C42×C31—21no—
156C42×C31—41no—
157C42×C31—41no—
158C42×C31—41no—
159#13100C3111yesmaximal, characteristic, direct product factor, Sylow
160C23×C31—24no—
161C23×C31—21no—
162C23×C31—21no—
163C23×C31—21no—
164C23×C31—42no—
165C23×C31—42no—
166C23×C31—161no—
167C23×C31—161no—
168C23×C31—161no—
169C23×C31C4×D411yescharacteristic
170C23×C31#12011yescharacteristic
171C23×C31#12111yescharacteristic
172Q8×C31—21no—
173Q8×C31—21no—
174Q8×C31—41no—
175Q8×C31—41no—
176Q8×C31—41no—
177Q8×C31—81no—
178D4×C31—24no—
179D4×C31—21no—
180D4×C31—21no—
181D4×C31—21no—
182D4×C31—21no—
183D4×C31—41no—
184D4×C31—41no—
185D4×C31—41no—
186D4×C31—42no—
187D4×C31—42no—
188D4×C31—42no—
189D4×C31—42no—
190D4×C31—42no—
191D4×C31#9912yes—
192D4×C31#9912yes—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—21no—
197C2×C4×C31—21no—
198C2×C4×C31—21no—
199C2×C4×C31—21no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—81no—
208C2×C4×C31—81no—
209C2×C4×C31—164no—
210C2×C4×C31C2×C22⋊C411yescharacteristic
211C2×C4×C31C4×D411yescharacteristic
212C2×C4×C31#12111yescharacteristic
213C2×C4×C31#12311yescharacteristic
214C8×C31—41no—
215C8×C31—41no—
216C8×C31—81no—
217#3009C2×C3111yescharacteristic
218#2883C2×C3111yescharacteristic
219#2129C2×C3111yescharacteristic, complemented
220#2123C2×C3111yescharacteristic, complemented
221#1795C2×C3111yescharacteristic
222#1395C2×C3111yescharacteristic, complemented
223#1391C2×C3111yescharacteristic, complemented
224C22×C31—21no—
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—22no—
228C22×C31—22no—
229C22×C31—41no—
230C22×C31—41no—
231C22×C31—41no—
232C22×C31—41no—
233C22×C31—81no—
234C22×C31—81no—
235C22×C31—81no—
236C22×C31—84no—
237C22×C31—162no—
238C22×C31—162no—
239C22×C31#38611yescharacteristic
240C4×C31—21no—
241C4×C31—21no—
242C4×C31—21no—
243C4×C31—41no—
244C4×C31—81no—
245C4×C31—82no—
246C4×C31—82no—
247C4×C31—81no—
248C4×C31—161no—
249C4×C31C2×#9911yescharacteristic
250C4×C31C2×#9911yescharacteristic
251C2×H(5,𝔽2)C22×C3111yescharacteristic
252C2×#137C4×C3111yescharacteristic, complemented
253C22×SD16C4×C3111yescharacteristic, complemented
254#536C22×C3111yescharacteristic
255#518—21no—
256#452—21no—
257#452—21no—
258#450—21no—
259#450—21no—
260#421—21no—
261#418—21no—
262#418C4×C3111yescharacteristic, complemented
263#416C4×C3111yescharacteristic, complemented
264#413C22×C3111yescharacteristic
265#410—21no—
266#410C22×C3111yescharacteristic
267#410C22×C3111yescharacteristic
268#410C22×C3111yescharacteristic
269C2×#99—22no—
270C2×#99—22no—
271#408C22×C3111yescharacteristic
272#354—22no—
273#352—22no—
274C2×C31—21no—
275C2×C31—41no—
276C2×C31—41no—
277C2×C31—41no—
278C2×C31—42no—
279C2×C31—42no—
280C2×C31—81no—
281C2×C31#189811yescharacteristic
282H(5,𝔽2)—42no—
283H(5,𝔽2)—42no—
284C2×#41—21no—
285C2×#41C2×C4×C3111yescharacteristic
286C2×#41D4×C3111yescharacteristic
287C2×#41D4×C3111yescharacteristic
288C2×#41C23×C3111yescharacteristic
289C22×Q8C2×C4×C3111yescharacteristic, complemented
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2×C4×C3111yescharacteristic
294C22×D4D4×C3111yescharacteristic
295C22×D4D4×C3111yescharacteristic
296#137—42no—
297C2×Q16—21no—
298C2×SD16—21no—
299C2×SD16—21no—
300C2×SD16—21no—
301C2×SD16—42no—
302C2×M16—21no—
303C2×M16C2×C4×C3111yescharacteristic, complemented
304C22×C8C2×C4×C3111yescharacteristic, complemented
305C4⋊Q8—21no—
306#124—21no—
307#123—21no—
308#123—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C4×D4—42no—
312C4×D4—42no—
313#117—21no—
314#117—21no—
315#117—21no—
316#117C2×C4×C3111yescharacteristic, complemented
317C2×C22⋊C4—24no—
318#104—42no—
319#103—21no—
320#102—21no—
321#102—21no—
322#102—21no—
323#102—42no—
324#101—21no—
325#100—21no—
326#99—24no—
327#99—21no—
328#99—21no—
329#99—21no—
330#99—21no—
331#99D4×C3112yes—
332#99D4×C3112yes—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C31#1310011yescharacteristic, direct product factor, Sylow
336C24—21no—
337C24—21no—
338C24—21no—
339#41—22no—
340#41—22no—
341#41—41no—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—41no—
346#41—41no—
347#41—44no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8C22⋊C4×C3111yescharacteristic
353C2×Q8#41×C3111yescharacteristic
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—44no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4C22⋊C4×C3111yescharacteristic
370C2×D4C22⋊C4×C3111yescharacteristic
371C2×D4C22⋊C4×C3111yescharacteristic
372C2×D4C2×D4×C3111yescharacteristic
373C2×D4C2×D4×C3111yescharacteristic
374C2×D4#41×C3111yescharacteristic
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—44no—
380C22×C4C22×C4×C3111yescharacteristic
381C22×C4C2×D4×C3111yescharacteristic
382C22×C4C2×D4×C3111yescharacteristic
383Q16—42no—
384SD16—42no—
385SD16—42no—
386SD16—42no—
387M16—41no—
388M16—41no—
389M16—41no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—41no—
393C2×C8—41no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C22⋊C4—21no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—44no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C42—21no—
408C42—41no—
409C42—41no—
410C42—41no—
411C23—24no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—42no—
416C23—42no—
417C23—161no—
418C23—161no—
419C23—161no—
420C23C4×D4×C3111yescharacteristic
421C23C31×#12011yescharacteristic
422C23C31×#12111yescharacteristic
423Q8—21no—
424Q8—21no—
425Q8—41no—
426Q8—41no—
427Q8—41no—
428Q8—81no—
429D4—24no—
430D4—21no—
431D4—21no—
432D4—21no—
433D4—21no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4C31×#9912yes—
443D4C31×#9912yes—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—164no—
461C2×C4C2×C22⋊C4×C3111yescharacteristic
462C2×C4C4×D4×C3111yescharacteristic
463C2×C4C31×#12111yescharacteristic
464C2×C4C31×#12311yescharacteristic
465C8—41no—
466C8—41no—
467C8—81no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—22no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—84no—
481C22—162no—
482C22—162no—
483C22C31×#38611yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—41no—
488C4—81no—
489C4—82no—
490C4—82no—
491C4—81no—
492C4—161no—
493C4C2×C31×#9911yescharacteristic
494C4C2×C31×#9911yescharacteristic
495C2—21no—
496C2—41no—
497C2—41no—
498C2—41no—
499C2—42no—
500C2—42no—
501C2—81no—
502C2C31×#189811yescharacteristic
subgroupG/H
center, socleC2×C31#1898
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×#41C23×C31
prime radicalC2×C31×H(5,𝔽2)C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×C31×H(5,𝔽2) ◁ 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×SD16×C31C4semidirect
19. C31×#418C4semidirect
20. C31×#416C4semidirect
38. C22×Q8×C31C2×C4semidirect
52. C2×M16×C31C2×C4semidirect
53. C22×C8×C31C2×C4semidirect
65. C31×#117C2×C4semidirect
159. #13100C31direct (N × H)
219. #2129C2×C31semidirect
220. #2123C2×C31semidirect
222. #1395C2×C31semidirect
223. #1391C2×C31semidirect
252. C2×#137C4×C31semidirect
253. C22×SD16C4×C31semidirect
262. #418C4×C31semidirect
263. #416C4×C31semidirect
289. C22×Q8C2×C4×C31semidirect
303. C2×M16C2×C4×C31semidirect
304. C22×C8C2×C4×C31semidirect
316. #117C2×C4×C31semidirect
335. C31#13100direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30092
C31×#28832
C31×#21292
C31×#21232
C31×#17952
C31×#13952
C31×#13912
#1310031