Finite Group Databasebeta

← C31×#8413 #21465172

Subgroups — C31×#8413 #21465172

Order 7936.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3518C211yesmaximal, characteristic
2C31×#1759C211yesmaximal, characteristic, complemented
3C31×#1529C211yesmaximal, characteristic, complemented
4C31×#1506C211yesmaximal, characteristic, complemented
5C31×#1500C211yesmaximal, characteristic, complemented
6C31×#1488C211yesmaximal, characteristic, complemented
7C31×#1485C211yesmaximal, characteristic, complemented
8Q82×C31C411yescharacteristic, complemented
9C31×#556—21no—
10C31×#556—22no—
11C31×#556—21no—
12C31×#556C411yescharacteristic, complemented
13C31×#555—21no—
14C31×#555C411yescharacteristic, complemented
15D4×Q8×C31C411yescharacteristic, complemented
16C31×#548—21no—
17C31×#542—22no—
18C31×#542—21no—
19C31×#533—21no—
20C31×#533C2211yescharacteristic
21C31×#529—21no—
22C31×#529C2211yescharacteristic
23C31×#519—21no—
24C4×#41×C31C2211yescharacteristic
25C31×#432C2211yescharacteristic
26C31×#431C2211yescharacteristic
27C2×C31×#104—21no—
28C4×M16×C31C2211yescharacteristic
29C31×#376C2211yescharacteristic
30C31×#339—21no—
31C31×#330—21no—
32C31×#329—21no—
33C31×#328—21no—
34C31×#328—22no—
35C31×#327—21no—
36C31×Q8⋊C8—22no—
37C31×Q8⋊C8—21no—
38C31×D4⋊C8—21no—
39C2×#41×C31D411yescharacteristic
40C22×Q8×C31—21no—
41C2×M16×C31—21no—
42C31×C4⋊Q8—22no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C31×C4⋊Q8—21no—
46C31×C4⋊Q8C2×C411yescharacteristic
47C31×C4⋊Q8C2×C411yescharacteristic
48C31×#126—22no—
49C31×#126—22no—
50C31×#126—22no—
51C31×#126—22no—
52C31×#126—21no—
53C31×#125—21no—
54C31×#125D411yescharacteristic
55C31×#124—22no—
56C31×#124—22no—
57C31×#124—22no—
58C31×#124—22no—
59C31×#124—21no—
60C31×#124D411yescharacteristic
61C31×#123—22no—
62C31×#123—21no—
63C31×C22⋊Q8—22no—
64C31×C22⋊Q8—22no—
65C31×C22⋊Q8—21no—
66C31×C22⋊Q8—21no—
67C31×C22⋊Q8—21no—
68C31×C22⋊Q8—22no—
69C31×C22⋊Q8D411yescharacteristic
70C31×C22⋊Q8D412yes—
71C31×#121—22no—
72C31×#121—21no—
73C31×#121—21no—
74C31×#121D411yescharacteristic
75C4×Q8×C31—22no—
76C4×Q8×C31—22no—
77C4×Q8×C31—22no—
78C4×Q8×C31—21no—
79C4×Q8×C31—21no—
80C4×Q8×C31—21no—
81C4×Q8×C31—21no—
82C4×Q8×C31C2×C411yescharacteristic
83C4×Q8×C31C2×C411yescharacteristic
84C4×Q8×C31D411yescharacteristic
85C4×Q8×C31D412yes—
86C4×D4×C31—22no—
87C4×D4×C31—21no—
88C4×D4×C31—21no—
89C4×D4×C31—21no—
90C4×D4×C31—21no—
91C4×D4×C31C2×C411yescharacteristic
92C4×D4×C31C2×C411yescharacteristic
93C4×D4×C31D411yescharacteristic
94C31×#117—22no—
95C31×#117—22no—
96C31×#117—21no—
97C31×#117—21no—
98C31×#117—21no—
99C31×#117—21no—
100C31×#117—21no—
101C31×#117—21no—
102C31×#117D411yescharacteristic
103C2×C42×C31—21no—
104C2×C42×C31—21no—
105C2×C42×C31C2311yescharacteristic
106C31×C4⋊C8—21no—
107C31×C4⋊C8—21no—
108C31×#104—24no—
109C31×C22⋊C8—21no—
110C31×C22⋊C8—21no—
111C31×#97—21no—
112C31×#97—21no—
113C4×C8×C31—21no—
114C4×C8×C31—21no—
115C31×#95—21no—
116C31×#95—21no—
117#41×C31—22no—
118#41×C31—41no—
119C2×Q8×C31—22no—
120C2×Q8×C31—22no—
121C2×Q8×C31—21no—
122C2×Q8×C31—42no—
123C2×Q8×C31—42no—
124C2×Q8×C31C22⋊C411yescharacteristic
125C2×Q8×C31C22⋊C411yescharacteristic
126C2×Q8×C31C22⋊C412yes—
127C2×D4×C31—21no—
128C2×D4×C31—22no—
129C2×D4×C31—21no—
130C2×D4×C31C22⋊C411yescharacteristic
131C2×D4×C31C22⋊C411yescharacteristic
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—41no—
138C22×C4×C31C2×D411yescharacteristic
139C22×C4×C31C2×D411yescharacteristic
140C22×C4×C31C2×D411yescharacteristic
141M16×C31—22no—
142M16×C31—41no—
143C2×C8×C31—41no—
144C2×C8×C31—41no—
145C2×C8×C31—41no—
146C4⋊C4×C31—22no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—22no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—21no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31C22⋊C411yescharacteristic
162C4⋊C4×C31C22⋊C411yescharacteristic
163C4⋊C4×C31C22⋊C411yescharacteristic
164C4⋊C4×C31C22⋊C411yescharacteristic
165C4⋊C4×C31C22⋊C412yes—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—22no—
169C22⋊C4×C31—22no—
170C22⋊C4×C31—22no—
171C22⋊C4×C31—22no—
172C22⋊C4×C31—21no—
173C22⋊C4×C31—21no—
174C22⋊C4×C31—21no—
175C22⋊C4×C31—21no—
176C22⋊C4×C31—21no—
177C22⋊C4×C31—21no—
178C22⋊C4×C31—21no—
179C22⋊C4×C31—21no—
180C42×C31—22no—
181C42×C31—22no—
182C42×C31—22no—
183C42×C31—21no—
184C42×C31—21no—
185C42×C31—21no—
186C42×C31—21no—
187C42×C31—22no—
188C42×C31—22no—
189C42×C31—41no—
190C42×C31C22×C411yescharacteristic
191C42×C31C2×D411yescharacteristic
192C42×C31C2×D411yescharacteristic
193C42×C31C2×D411yescharacteristic
194#8413C3111yesmaximal, characteristic, direct product factor, Sylow
195C23×C31—21no—
196C23×C31—21no—
197C23×C31#12011yescharacteristic
198Q8×C31—21no—
199Q8×C31—42no—
200Q8×C31—41no—
201Q8×C31—44no—
202Q8×C31—41no—
203Q8×C31—41no—
204Q8×C31—82no—
205Q8×C31#10412yes—
206D4×C31—21no—
207D4×C31—21no—
208D4×C31—42no—
209D4×C31—41no—
210D4×C31—81no—
211D4×C31—82no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—21no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—22no—
218C2×C4×C31—21no—
219C2×C4×C31—21no—
220C2×C4×C31—21no—
221C2×C4×C31—22no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—44no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—81no—
231C2×C4×C31—81no—
232C2×C4×C31—81no—
233C2×C4×C31C2×C22⋊C411yescharacteristic
234C2×C4×C31C2×C22⋊C411yescharacteristic
235C2×C4×C31C2×C22⋊C411yescharacteristic
236C2×C4×C31#12011yescharacteristic
237C2×C4×C31#12011yescharacteristic
238C2×C4×C31#12011yescharacteristic
239C8×C31—42no—
240C8×C31—81no—
241C8×C31—81no—
242#3518C2×C3111yescharacteristic
243#1759C2×C3111yescharacteristic, complemented
244#1529C2×C3111yescharacteristic, complemented
245#1506C2×C3111yescharacteristic, complemented
246#1500C2×C3111yescharacteristic, complemented
247#1488C2×C3111yescharacteristic, complemented
248#1485C2×C3111yescharacteristic, complemented
249C22×C31—21no—
250C22×C31—21no—
251C22×C31—21no—
252C22×C31—41no—
253C22×C31—41no—
254C22×C31—41no—
255C22×C31—41no—
256C22×C31—41no—
257C22×C31—41no—
258C22×C31#37911yescharacteristic
259C4×C31—21no—
260C4×C31—21no—
261C4×C31—21no—
262C4×C31—21no—
263C4×C31—21no—
264C4×C31—22no—
265C4×C31—41no—
266C4×C31—42no—
267C4×C31—41no—
268C4×C31—41no—
269C4×C31—41no—
270C4×C31—42no—
271C4×C31—41no—
272C4×C31—82no—
273C4×C31C2×#10411yescharacteristic
274C4×C31#42111yescharacteristic
275Q82C4×C3111yescharacteristic, complemented
276#556—21no—
277#556—22no—
278#556—21no—
279#556C4×C3111yescharacteristic, complemented
280#555—21no—
281#555C4×C3111yescharacteristic, complemented
282D4×Q8C4×C3111yescharacteristic, complemented
283#548—21no—
284#542—22no—
285#542—21no—
286#533—21no—
287#533C22×C3111yescharacteristic
288#529—21no—
289#529C22×C3111yescharacteristic
290#519—21no—
291C4×#41C22×C3111yescharacteristic
292#432C22×C3111yescharacteristic
293#431C22×C3111yescharacteristic
294C2×#104—21no—
295C4×M16C22×C3111yescharacteristic
296#376C22×C3111yescharacteristic
297#339—21no—
298#330—21no—
299#329—21no—
300#328—21no—
301#328—22no—
302#327—21no—
303Q8⋊C8—22no—
304Q8⋊C8—21no—
305D4⋊C8—21no—
306C2×C31—41no—
307C2×C31—81no—
308C2×C31—81no—
309C2×C31#178911yescharacteristic
310C2×C31#179411yescharacteristic
311C2×C31#179611yescharacteristic
312C2×#41D4×C3111yescharacteristic
313C22×Q8—21no—
314C2×M16—21no—
315C4⋊Q8—22no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8C2×C4×C3111yescharacteristic
320C4⋊Q8C2×C4×C3111yescharacteristic
321#126—22no—
322#126—22no—
323#126—22no—
324#126—22no—
325#126—21no—
326#125—21no—
327#125D4×C3111yescharacteristic
328#124—22no—
329#124—22no—
330#124—22no—
331#124—22no—
332#124—21no—
333#124D4×C3111yescharacteristic
334#123—22no—
335#123—21no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—22no—
342C22⋊Q8D4×C3111yescharacteristic
343C22⋊Q8D4×C3112yes—
344#121—22no—
345#121—21no—
346#121—21no—
347#121D4×C3111yescharacteristic
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C2×C4×C3111yescharacteristic
356C4×Q8C2×C4×C3111yescharacteristic
357C4×Q8D4×C3111yescharacteristic
358C4×Q8D4×C3112yes—
359C4×D4—22no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4C2×C4×C3111yescharacteristic
365C4×D4C2×C4×C3111yescharacteristic
366C4×D4D4×C3111yescharacteristic
367#117—22no—
368#117—22no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117D4×C3111yescharacteristic
376C2×C42—21no—
377C2×C42—21no—
378C2×C42C23×C3111yescharacteristic
379C4⋊C8—21no—
380C4⋊C8—21no—
381#104—24no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384#97—21no—
385#97—21no—
386C4×C8—21no—
387C4×C8—21no—
388#95—21no—
389#95—21no—
390C31#841311yescharacteristic, direct product factor, Sylow
391#41—22no—
392#41—41no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—21no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8C22⋊C4×C3111yescharacteristic
399C2×Q8C22⋊C4×C3111yescharacteristic
400C2×Q8C22⋊C4×C3112yes—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4C22⋊C4×C3111yescharacteristic
405C2×D4C22⋊C4×C3111yescharacteristic
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4C2×D4×C3111yescharacteristic
413C22×C4C2×D4×C3111yescharacteristic
414C22×C4C2×D4×C3111yescharacteristic
415M16—22no—
416M16—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—41no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4C22⋊C4×C3111yescharacteristic
436C4⋊C4C22⋊C4×C3111yescharacteristic
437C4⋊C4C22⋊C4×C3111yescharacteristic
438C4⋊C4C22⋊C4×C3111yescharacteristic
439C4⋊C4C22⋊C4×C3112yes—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—22no—
462C42—22no—
463C42—41no—
464C42C22×C4×C3111yescharacteristic
465C42C2×D4×C3111yescharacteristic
466C42C2×D4×C3111yescharacteristic
467C42C2×D4×C3111yescharacteristic
468C23—21no—
469C23—21no—
470C23C31×#12011yescharacteristic
471Q8—21no—
472Q8—41no—
473Q8—42no—
474Q8—44no—
475Q8—41no—
476Q8—41no—
477Q8—82no—
478Q8C31×#10412yes—
479D4—21no—
480D4—21no—
481D4—42no—
482D4—41no—
483D4—81no—
484D4—82no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4C2×C22⋊C4×C3111yescharacteristic
507C2×C4C2×C22⋊C4×C3111yescharacteristic
508C2×C4C2×C22⋊C4×C3111yescharacteristic
509C2×C4C31×#12011yescharacteristic
510C2×C4C31×#12011yescharacteristic
511C2×C4C31×#12011yescharacteristic
512C8—42no—
513C8—81no—
514C8—81no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22C31×#37911yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—22no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—42no—
534C4—41no—
535C4—41no—
536C4—42no—
537C4—41no—
538C4—82no—
539C4C2×C31×#10411yescharacteristic
540C4C31×#42111yescharacteristic
541C2—41no—
542C2—81no—
543C2—81no—
544C2C31×#178911yescharacteristic
545C2C31×#179411yescharacteristic
546C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3518C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1759C2semidirect
3. C31×#1529C2semidirect
4. C31×#1506C2semidirect
5. C31×#1500C2semidirect
6. C31×#1488C2semidirect
7. C31×#1485C2semidirect
8. Q82×C31C4semidirect
12. C31×#556C4semidirect
14. C31×#555C4semidirect
15. D4×Q8×C31C4semidirect
194. #8413C31direct (N × H)
243. #1759C2×C31semidirect
244. #1529C2×C31semidirect
245. #1506C2×C31semidirect
246. #1500C2×C31semidirect
247. #1488C2×C31semidirect
248. #1485C2×C31semidirect
275. Q82C4×C31semidirect
279. #556C4×C31semidirect
281. #555C4×C31semidirect
282. D4×Q8C4×C31semidirect
390. C31#8413direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35182
C31×#17592
C31×#15292
C31×#15062
C31×#15002
C31×#14882
C31×#14852
#841331