Finite Group Databasebeta

← C31×#8411 #21465170

Subgroups — C31×#8411 #21465170

Order 7936.

714 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3455C211yesmaximal, characteristic
2C31×#1798C211yesmaximal, characteristic, complemented
3C31×#1542C211yesmaximal, characteristic, complemented
4C31×#1540C211yesmaximal, characteristic, complemented
5C31×#1481C211yesmaximal, characteristic, complemented
6C31×#1480C211yesmaximal, characteristic, complemented
7C31×#1458C211yesmaximal, characteristic, complemented
8C31×#542—21no—
9C31×#542—21no—
10C31×#541—21no—
11C31×#540—21no—
12C31×#539—21no—
13C31×#539C412yes—
14C31×#538—21no—
15C31×#538C412yes—
16C31×#533C2211yescharacteristic
17C31×#532C2211yescharacteristic
18C31×#529—22no—
19C31×#529—22no—
20C31×#525—21no—
21C4×#41×C31—21no—
22C2×C31×#117C2211yescharacteristic
23C31×#431C2211yescharacteristic
24C31×#431C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C2×C31×C4⋊C8C2211yescharacteristic
27C2×C31×C22⋊C8—21no—
28C31×#336—21no—
29C31×#333—21no—
30C31×#332—21no—
31C31×#332—21no—
32C31×#331—21no—
33C31×Q8⋊C8—22no—
34C31×D4⋊C8—22no—
35C31×#324—21no—
36C31×#323—21no—
37C2×#41×C31—21no—
38C23×C4×C31D411yescharacteristic
39C22×C8×C31—21no—
40C22×C8×C31—21no—
41C31×C4⋊Q8D411yescharacteristic
42C31×C4⋊Q8D411yescharacteristic
43C31×C4⋊Q8D411yescharacteristic
44C31×#127D411yescharacteristic
45C31×#126—22no—
46C31×#126—22no—
47C31×#126—22no—
48C31×#126—22no—
49C31×#125—22no—
50C31×#125—22no—
51C31×#125—21no—
52C31×#124—22no—
53C31×#124—22no—
54C31×#124—21no—
55C31×#123—22no—
56C31×#123—22no—
57C31×#123—22no—
58C31×#123—22no—
59C31×#123—22no—
60C31×C22⋊Q8—21no—
61C31×C22⋊Q8—21no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—22no—
64C31×C22⋊Q8—21no—
65C31×C22⋊Q8C2×C412yes—
66C31×#121—21no—
67C31×#121—21no—
68C31×#121—22no—
69C31×#121—22no—
70C31×#121—21no—
71C31×#121C2×C412yes—
72C31×#120—22no—
73C4×Q8×C31—21no—
74C4×Q8×C31—21no—
75C4×Q8×C31—21no—
76C4×Q8×C31D412yes—
77C4×D4×C31—21no—
78C4×D4×C31—21no—
79C4×D4×C31—22no—
80C4×D4×C31—22no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C4×D4×C31—21no—
84C4×D4×C31D412yes—
85C31×#117—22no—
86C31×#117—21no—
87C31×#117—21no—
88C31×#117—21no—
89C31×#117—21no—
90C31×#117—21no—
91C2×C4⋊C4×C31C2×C411yescharacteristic
92C2×C4⋊C4×C31D411yescharacteristic
93C2×C22⋊C4×C31C2×C411yescharacteristic
94C2×C22⋊C4×C31D411yescharacteristic
95C2×C42×C31—22no—
96C2×C42×C31D411yescharacteristic
97C2×C42×C31C2311yescharacteristic
98C31×C4⋊C8—21no—
99C31×C4⋊C8—21no—
100C31×C4⋊C8—21no—
101C31×C4⋊C8—21no—
102C31×C4⋊C8—21no—
103C31×C4⋊C8—21no—
104C31×C22⋊C8—21no—
105C31×C22⋊C8—21no—
106C31×C22⋊C8—42no—
107C4×C8×C31—21no—
108C4×C8×C31—21no—
109C24×C31C22⋊C411yescharacteristic
110#41×C31—41no—
111#41×C31—41no—
112#41×C31—41no—
113#41×C31—41no—
114C2×Q8×C31—21no—
115C2×Q8×C31—21no—
116C2×Q8×C31C22⋊C412yes—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—22no—
120C2×D4×C31—21no—
121C2×D4×C31—21no—
122C2×D4×C31C22⋊C412yes—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—21no—
126C22×C4×C31—22no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31C22⋊C411yescharacteristic
133C22×C4×C31C22⋊C411yescharacteristic
134C22×C4×C31C22⋊C411yescharacteristic
135C22×C4×C31C22×C411yescharacteristic
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C2×C8×C31—41no—
139C2×C8×C31—41no—
140C2×C8×C31—41no—
141C2×C8×C31—41no—
142C2×C8×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—22no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—21no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31C22⋊C412yes—
161C4⋊C4×C31C22⋊C412yes—
162C22⋊C4×C31—22no—
163C22⋊C4×C31—22no—
164C22⋊C4×C31—22no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—22no—
169C22⋊C4×C31—21no—
170C22⋊C4×C31—21no—
171C22⋊C4×C31—22no—
172C22⋊C4×C31—21no—
173C22⋊C4×C31—21no—
174C22⋊C4×C31—22no—
175C42×C31—22no—
176C42×C31—22no—
177C42×C31—21no—
178C42×C31—21no—
179C42×C31—22no—
180C42×C31C2×D411yescharacteristic
181C42×C31C2×D411yescharacteristic
182C42×C31C2×D411yescharacteristic
183C42×C31C2×D411yescharacteristic
184#8411C3111yesmaximal, characteristic, direct product factor, Sylow
185C23×C31—21no—
186C23×C31—22no—
187C23×C31—21no—
188C23×C31—21no—
189C23×C31—41no—
190C23×C31—41no—
191C23×C31C2×C22⋊C411yescharacteristic
192Q8×C31—42no—
193Q8×C31—41no—
194Q8×C31—41no—
195Q8×C31—81no—
196D4×C31—42no—
197D4×C31—42no—
198D4×C31—42no—
199D4×C31—41no—
200D4×C31—41no—
201D4×C31—81no—
202D4×C31—82no—
203D4×C31—82no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—41no—
213C2×C4×C31—41no—
214C2×C4×C31—41no—
215C2×C4×C31—41no—
216C2×C4×C31—42no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—82no—
223C2×C4×C31—82no—
224C2×C4×C31C2×C22⋊C411yescharacteristic
225C2×C4×C31C2×C22⋊C411yescharacteristic
226C2×C4×C31#12011yescharacteristic
227C2×C4×C31#12011yescharacteristic
228C2×C4×C31#12011yescharacteristic
229C2×C4×C31#12011yescharacteristic
230C2×C4×C31#13511yescharacteristic
231C2×C4×C31#13511yescharacteristic
232C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
233C2×C4×C31#13711yescharacteristic
234C8×C31—81no—
235C8×C31—81no—
236C8×C31—81no—
237C8×C31—81no—
238#3455C2×C3111yescharacteristic
239#1798C2×C3111yescharacteristic, complemented
240#1542C2×C3111yescharacteristic, complemented
241#1540C2×C3111yescharacteristic, complemented
242#1481C2×C3111yescharacteristic, complemented
243#1480C2×C3111yescharacteristic, complemented
244#1458C2×C3111yescharacteristic, complemented
245C22×C31—21no—
246C22×C31—21no—
247C22×C31—42no—
248C22×C31—42no—
249C22×C31—41no—
250C22×C31—41no—
251C22×C31—42no—
252C22×C31—42no—
253C22×C31—41no—
254C22×C31—81no—
255C22×C31#37911yescharacteristic
256C22×C31#41611yescharacteristic
257C22×C31#41711yescharacteristic
258C4×C31—21no—
259C4×C31—21no—
260C4×C31—21no—
261C4×C31—21no—
262C4×C31—41no—
263C4×C31—42no—
264C4×C31—41no—
265C4×C31—42no—
266C4×C31—41no—
267C4×C31—42no—
268C4×C31#44911yescharacteristic
269C4×C31#44911yescharacteristic
270C4×C31#45211yescharacteristic
271C4×C31#45211yescharacteristic
272#542—21no—
273#542—21no—
274#541—21no—
275#540—21no—
276#539—21no—
277#539C4×C3112yes—
278#538—21no—
279#538C4×C3112yes—
280#533C22×C3111yescharacteristic
281#532C22×C3111yescharacteristic
282#529—22no—
283#529—22no—
284#525—21no—
285C4×#41—21no—
286C2×#117C22×C3111yescharacteristic
287#431C22×C3111yescharacteristic
288#431C22×C3111yescharacteristic
289C2×C4⋊C8C22×C3111yescharacteristic
290C2×C4⋊C8C22×C3111yescharacteristic
291C2×C22⋊C8—21no—
292#336—21no—
293#333—21no—
294#332—21no—
295#332—21no—
296#331—21no—
297Q8⋊C8—22no—
298D4⋊C8—22no—
299#324—21no—
300#323—21no—
301C2×C31—21no—
302C2×C31—21no—
303C2×C31—82no—
304C2×C31—81no—
305C2×C31#178811yescharacteristic
306C2×C31#179111yescharacteristic
307C2×C31#179411yescharacteristic
308C2×#41—21no—
309C23×C4D4×C3111yescharacteristic
310C22×C8—21no—
311C22×C8—21no—
312C4⋊Q8D4×C3111yescharacteristic
313C4⋊Q8D4×C3111yescharacteristic
314C4⋊Q8D4×C3111yescharacteristic
315#127D4×C3111yescharacteristic
316#126—22no—
317#126—22no—
318#126—22no—
319#126—22no—
320#125—22no—
321#125—22no—
322#125—21no—
323#124—22no—
324#124—22no—
325#124—21no—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—21no—
336C22⋊Q8C2×C4×C3112yes—
337#121—21no—
338#121—21no—
339#121—22no—
340#121—22no—
341#121—21no—
342#121C2×C4×C3112yes—
343#120—22no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8D4×C3112yes—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—21no—
355C4×D4D4×C3112yes—
356#117—22no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362C2×C4⋊C4C2×C4×C3111yescharacteristic
363C2×C4⋊C4D4×C3111yescharacteristic
364C2×C22⋊C4C2×C4×C3111yescharacteristic
365C2×C22⋊C4D4×C3111yescharacteristic
366C2×C42—22no—
367C2×C42D4×C3111yescharacteristic
368C2×C42C23×C3111yescharacteristic
369C4⋊C8—21no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8—42no—
378C4×C8—21no—
379C4×C8—21no—
380C31#841111yescharacteristic, direct product factor, Sylow
381C24C22⋊C4×C3111yescharacteristic
382#41—41no—
383#41—41no—
384#41—41no—
385#41—41no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8C22⋊C4×C3112yes—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C22⋊C4×C3112yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4C22⋊C4×C3111yescharacteristic
405C22×C4C22⋊C4×C3111yescharacteristic
406C22×C4C22⋊C4×C3111yescharacteristic
407C22×C4C22×C4×C3111yescharacteristic
408C22×C4C2×D4×C3111yescharacteristic
409C22×C4C2×D4×C3111yescharacteristic
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4C22⋊C4×C3112yes—
433C4⋊C4C22⋊C4×C3112yes—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—22no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—22no—
451C42—21no—
452C42C2×D4×C3111yescharacteristic
453C42C2×D4×C3111yescharacteristic
454C42C2×D4×C3111yescharacteristic
455C42C2×D4×C3111yescharacteristic
456C23—21no—
457C23—21no—
458C23—22no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23C2×C22⋊C4×C3111yescharacteristic
463Q8—42no—
464Q8—41no—
465Q8—41no—
466Q8—81no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—41no—
471D4—41no—
472D4—81no—
473D4—82no—
474D4—82no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4C2×C22⋊C4×C3111yescharacteristic
496C2×C4C2×C22⋊C4×C3111yescharacteristic
497C2×C4C31×#12011yescharacteristic
498C2×C4C31×#12011yescharacteristic
499C2×C4C31×#12011yescharacteristic
500C2×C4C31×#12011yescharacteristic
501C2×C4C31×#13511yescharacteristic
502C2×C4C31×#13511yescharacteristic
503C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
504C2×C4C31×#13711yescharacteristic
505C8—81no—
506C8—81no—
507C8—81no—
508C8—81no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—41no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22—42no—
517C22—41no—
518C22—81no—
519C22C31×#37911yescharacteristic
520C22C31×#41611yescharacteristic
521C22C31×#41711yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—41no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—41no—
531C4—42no—
532C4C31×#44911yescharacteristic
533C4C31×#44911yescharacteristic
534C4C31×#45211yescharacteristic
535C4C31×#45211yescharacteristic
536C2—21no—
537C2—21no—
538C2—81no—
539C2—82no—
540C2C31×#178811yescharacteristic
541C2C31×#179111yescharacteristic
542C2C31×#179411yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#379
prime radicalC31×#3455C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1798C2semidirect
3. C31×#1542C2semidirect
4. C31×#1540C2semidirect
5. C31×#1481C2semidirect
6. C31×#1480C2semidirect
7. C31×#1458C2semidirect
184. #8411C31direct (N × H)
239. #1798C2×C31semidirect
240. #1542C2×C31semidirect
241. #1540C2×C31semidirect
242. #1481C2×C31semidirect
243. #1480C2×C31semidirect
244. #1458C2×C31semidirect
380. C31#8411direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34552
C31×#17982
C31×#15422
C31×#15402
C31×#14812
C31×#14802
C31×#14582
#841131