Finite Group Databasebeta

← C31×#8414 #21465173

Subgroups — C31×#8414 #21465173

Order 7936.

758 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3517C211yesmaximal, characteristic
2C31×#1759C211yesmaximal, characteristic, complemented
3C31×#1529C211yesmaximal, characteristic, complemented
4C31×#1505C211yesmaximal, characteristic, complemented
5C31×#1500C211yesmaximal, characteristic, complemented
6C31×#1488C211yesmaximal, characteristic, complemented
7C31×#1484C211yesmaximal, characteristic, complemented
8C31×#557C411yescharacteristic, complemented
9C31×#553—22no—
10C31×#553—21no—
11C31×#550—21no—
12C31×#550—21no—
13C31×#550C411yescharacteristic, complemented
14C31×#550C411yescharacteristic, complemented
15C31×#547—21no—
16C31×#547C411yescharacteristic, complemented
17C31×#540—22no—
18C31×#540—21no—
19C31×#532—21no—
20C31×#532C2211yescharacteristic
21C31×#529—21no—
22C31×#529C2211yescharacteristic
23C31×#520—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×#327—21no—
35C31×#327—22no—
36C31×Q8⋊C8—21no—
37C31×D4⋊C8—22no—
38C31×D4⋊C8—21no—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31D411yescharacteristic
44C2×M16×C31—21no—
45C31×C4⋊Q8—21no—
46C31×C4⋊Q8C2×C411yescharacteristic
47C31×#127—22no—
48C31×#127—21no—
49C31×#127—21no—
50C31×#127C2×C411yescharacteristic
51C31×#126—22no—
52C31×#126—21no—
53C31×#125—22no—
54C31×#125—21no—
55C31×#125D411yescharacteristic
56C31×#124—21no—
57C31×#124D411yescharacteristic
58C31×#123—22no—
59C31×#123—22no—
60C31×#123—22no—
61C31×#123—21no—
62C31×#123—22no—
63C31×C22⋊Q8—21no—
64C31×C22⋊Q8D411yescharacteristic
65C31×#121—22no—
66C31×#121—22no—
67C31×#121—22no—
68C31×#121—22no—
69C31×#121—22no—
70C31×#121—21no—
71C31×#121—22no—
72C31×#121—22no—
73C31×#121—21no—
74C31×#121—21no—
75C31×#121—21no—
76C31×#121D411yescharacteristic
77C31×#121D412yes—
78C4×Q8×C31—21no—
79C4×Q8×C31—21no—
80C4×Q8×C31C2×C411yescharacteristic
81C4×Q8×C31C2×C411yescharacteristic
82C4×Q8×C31D411yescharacteristic
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—21no—
88C4×D4×C31—21no—
89C4×D4×C31—21no—
90C4×D4×C31—21no—
91C4×D4×C31—21no—
92C4×D4×C31—21no—
93C4×D4×C31C2×C411yescharacteristic
94C4×D4×C31C2×C411yescharacteristic
95C4×D4×C31D411yescharacteristic
96C4×D4×C31D412yes—
97C31×#117—22no—
98C31×#117—21no—
99C31×#117—21no—
100C31×#117D411yescharacteristic
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—21no—
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—
119#41×C31—42no—
120#41×C31—42no—
121#41×C31—82no—
122#41×C31—82no—
123#41×C31—82no—
124C2×Q8×C31—21no—
125C2×Q8×C31C22⋊C411yescharacteristic
126C2×Q8×C31C22⋊C411yescharacteristic
127C2×D4×C31—22no—
128C2×D4×C31—21no—
129C2×D4×C31—22no—
130C2×D4×C31—22no—
131C2×D4×C31—22no—
132C2×D4×C31—22no—
133C2×D4×C31—21no—
134C2×D4×C31—22no—
135C2×D4×C31—21no—
136C2×D4×C31—21no—
137C2×D4×C31C22⋊C411yescharacteristic
138C2×D4×C31C22⋊C411yescharacteristic
139C2×D4×C31C22⋊C412yes—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—41no—
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152M16×C31—22no—
153M16×C31—41no—
154C2×C8×C31—41no—
155C2×C8×C31—41no—
156C2×C8×C31—41no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31C22⋊C411yescharacteristic
169C4⋊C4×C31C22⋊C411yescharacteristic
170C4⋊C4×C31C22⋊C411yescharacteristic
171C4⋊C4×C31C22⋊C412yes—
172C4⋊C4×C31C22⋊C411yescharacteristic
173C22⋊C4×C31—22no—
174C22⋊C4×C31—22no—
175C22⋊C4×C31—22no—
176C22⋊C4×C31—21no—
177C22⋊C4×C31—21no—
178C22⋊C4×C31—21no—
179C22⋊C4×C31—21no—
180C22⋊C4×C31—21no—
181C22⋊C4×C31—21no—
182C22⋊C4×C31—22no—
183C22⋊C4×C31—21no—
184C22⋊C4×C31—21no—
185C22⋊C4×C31—22no—
186C42×C31—22no—
187C42×C31—21no—
188C42×C31—21no—
189C42×C31—21no—
190C42×C31—21no—
191C42×C31—22no—
192C42×C31—41no—
193C42×C31C22×C411yescharacteristic
194C42×C31C2×D411yescharacteristic
195C42×C31C2×D411yescharacteristic
196C42×C31C2×D411yescharacteristic
197#8414C3111yesmaximal, characteristic, direct product factor, Sylow
198C23×C31—21no—
199C23×C31—22no—
200C23×C31—21no—
201C23×C31#12011yescharacteristic
202Q8×C31—21no—
203Q8×C31—41no—
204Q8×C31—42no—
205Q8×C31#10412yes—
206D4×C31—21no—
207D4×C31—21no—
208D4×C31—42no—
209D4×C31—42no—
210D4×C31—41no—
211D4×C31—44no—
212D4×C31—42no—
213D4×C31—41no—
214D4×C31—41no—
215D4×C31—81no—
216D4×C31—82no—
217D4×C31—82no—
218D4×C31—82no—
219D4×C31—82no—
220D4×C31—82no—
221C2×C4×C31—21no—
222C2×C4×C31—21no—
223C2×C4×C31—21no—
224C2×C4×C31—21no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—21no—
228C2×C4×C31—22no—
229C2×C4×C31—21no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31—42no—
233C2×C4×C31—44no—
234C2×C4×C31—42no—
235C2×C4×C31—41no—
236C2×C4×C31—41no—
237C2×C4×C31—42no—
238C2×C4×C31—81no—
239C2×C4×C31—82no—
240C2×C4×C31—82no—
241C2×C4×C31—82no—
242C2×C4×C31—81no—
243C2×C4×C31—81no—
244C2×C4×C31C2×C22⋊C411yescharacteristic
245C2×C4×C31C2×C22⋊C411yescharacteristic
246C2×C4×C31C2×C22⋊C411yescharacteristic
247C2×C4×C31#12011yescharacteristic
248C2×C4×C31#12011yescharacteristic
249C2×C4×C31#12011yescharacteristic
250C8×C31—42no—
251C8×C31—81no—
252C8×C31—81no—
253#3517C2×C3111yescharacteristic
254#1759C2×C3111yescharacteristic, complemented
255#1529C2×C3111yescharacteristic, complemented
256#1505C2×C3111yescharacteristic, complemented
257#1500C2×C3111yescharacteristic, complemented
258#1488C2×C3111yescharacteristic, complemented
259#1484C2×C3111yescharacteristic, complemented
260C22×C31—21no—
261C22×C31—21no—
262C22×C31—21no—
263C22×C31—41no—
264C22×C31—42no—
265C22×C31—41no—
266C22×C31—41no—
267C22×C31—42no—
268C22×C31—41no—
269C22×C31—41no—
270C22×C31—42no—
271C22×C31—41no—
272C22×C31#37911yescharacteristic
273C4×C31—21no—
274C4×C31—21no—
275C4×C31—21no—
276C4×C31—21no—
277C4×C31—21no—
278C4×C31—22no—
279C4×C31—41no—
280C4×C31—41no—
281C4×C31—41no—
282C4×C31—41no—
283C4×C31—42no—
284C4×C31—41no—
285C4×C31—82no—
286C4×C31C2×#10411yescharacteristic
287C4×C31#42111yescharacteristic
288#557C4×C3111yescharacteristic, complemented
289#553—22no—
290#553—21no—
291#550—21no—
292#550—21no—
293#550C4×C3111yescharacteristic, complemented
294#550C4×C3111yescharacteristic, complemented
295#547—21no—
296#547C4×C3111yescharacteristic, complemented
297#540—22no—
298#540—21no—
299#532—21no—
300#532C22×C3111yescharacteristic
301#529—21no—
302#529C22×C3111yescharacteristic
303#520—21no—
304C4×#41C22×C3111yescharacteristic
305#432C22×C3111yescharacteristic
306#431C22×C3111yescharacteristic
307C2×#104—21no—
308C4×M16C22×C3111yescharacteristic
309#376C22×C3111yescharacteristic
310#339—21no—
311#330—21no—
312#329—21no—
313#328—21no—
314#327—21no—
315#327—22no—
316Q8⋊C8—21no—
317D4⋊C8—22no—
318D4⋊C8—21no—
319C2×C31—41no—
320C2×C31—81no—
321C2×C31—82no—
322C2×C31—81no—
323C2×C31#178911yescharacteristic
324C2×C31#179411yescharacteristic
325C2×C31#179511yescharacteristic
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41D4×C3111yescharacteristic
331C2×M16—21no—
332C4⋊Q8—21no—
333C4⋊Q8C2×C4×C3111yescharacteristic
334#127—22no—
335#127—21no—
336#127—21no—
337#127C2×C4×C3111yescharacteristic
338#126—22no—
339#126—21no—
340#125—22no—
341#125—21no—
342#125D4×C3111yescharacteristic
343#124—21no—
344#124D4×C3111yescharacteristic
345#123—22no—
346#123—22no—
347#123—22no—
348#123—21no—
349#123—22no—
350C22⋊Q8—21no—
351C22⋊Q8D4×C3111yescharacteristic
352#121—22no—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—21no—
358#121—22no—
359#121—22no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121D4×C3111yescharacteristic
364#121D4×C3112yes—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C2×C4×C3111yescharacteristic
368C4×Q8C2×C4×C3111yescharacteristic
369C4×Q8D4×C3111yescharacteristic
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×C4×C3111yescharacteristic
381C4×D4C2×C4×C3111yescharacteristic
382C4×D4D4×C3111yescharacteristic
383C4×D4D4×C3112yes—
384#117—22no—
385#117—21no—
386#117—21no—
387#117D4×C3111yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C3111yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395#104—24no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398#97—21no—
399#97—21no—
400C4×C8—21no—
401C4×C8—21no—
402#95—21no—
403#95—21no—
404C31#841411yescharacteristic, direct product factor, Sylow
405#41—22no—
406#41—41no—
407#41—42no—
408#41—42no—
409#41—82no—
410#41—82no—
411#41—82no—
412C2×Q8—21no—
413C2×Q8C22⋊C4×C3111yescharacteristic
414C2×Q8C22⋊C4×C3111yescharacteristic
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C22⋊C4×C3111yescharacteristic
426C2×D4C22⋊C4×C3111yescharacteristic
427C2×D4C22⋊C4×C3112yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4C2×D4×C3111yescharacteristic
438C22×C4C2×D4×C3111yescharacteristic
439C22×C4C2×D4×C3111yescharacteristic
440M16—22no—
441M16—41no—
442C2×C8—41no—
443C2×C8—41no—
444C2×C8—41no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4C22⋊C4×C3111yescharacteristic
457C4⋊C4C22⋊C4×C3111yescharacteristic
458C4⋊C4C22⋊C4×C3111yescharacteristic
459C4⋊C4C22⋊C4×C3112yes—
460C4⋊C4C22⋊C4×C3111yescharacteristic
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—22no—
480C42—41no—
481C42C22×C4×C3111yescharacteristic
482C42C2×D4×C3111yescharacteristic
483C42C2×D4×C3111yescharacteristic
484C42C2×D4×C3111yescharacteristic
485C23—21no—
486C23—22no—
487C23—21no—
488C23C31×#12011yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—42no—
492Q8C31×#10412yes—
493D4—21no—
494D4—21no—
495D4—42no—
496D4—42no—
497D4—41no—
498D4—44no—
499D4—42no—
500D4—41no—
501D4—41no—
502D4—81no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—82no—
507D4—82no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4C2×C22⋊C4×C3111yescharacteristic
532C2×C4C2×C22⋊C4×C3111yescharacteristic
533C2×C4C2×C22⋊C4×C3111yescharacteristic
534C2×C4C31×#12011yescharacteristic
535C2×C4C31×#12011yescharacteristic
536C2×C4C31×#12011yescharacteristic
537C8—42no—
538C8—81no—
539C8—81no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—41no—
552C22C31×#37911yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—22no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—42no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—82no—
566C4C2×C31×#10411yescharacteristic
567C4C31×#42111yescharacteristic
568C2—41no—
569C2—81no—
570C2—82no—
571C2—81no—
572C2C31×#178911yescharacteristic
573C2C31×#179411yescharacteristic
574C2C31×#179511yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3517C2
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×#1505C2semidirect
5. C31×#1500C2semidirect
6. C31×#1488C2semidirect
7. C31×#1484C2semidirect
8. C31×#557C4semidirect
13. C31×#550C4semidirect
14. C31×#550C4semidirect
16. C31×#547C4semidirect
197. #8414C31direct (N × H)
254. #1759C2×C31semidirect
255. #1529C2×C31semidirect
256. #1505C2×C31semidirect
257. #1500C2×C31semidirect
258. #1488C2×C31semidirect
259. #1484C2×C31semidirect
288. #557C4×C31semidirect
293. #550C4×C31semidirect
294. #550C4×C31semidirect
296. #547C4×C31semidirect
404. C31#8414direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35172
C31×#17592
C31×#15292
C31×#15052
C31×#15002
C31×#14882
C31×#14842
#841431