Finite Group Databasebeta

← C31×#25643 #21482402

Subgroups — C31×#25643 #21482402

Order 7936.

1108 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#556C211yesmaximal, characteristic
2C2×C31×#497C211yesmaximal, characteristic
3C2×C31×#462C211yesmaximal, characteristic, complemented
4C31×#2568C211yesmaximal, characteristic, complemented
5C31×#2016C212yesmaximal, complemented
6C31×#2015C212yesmaximal
7C31×#1985C211yesmaximal, characteristic, complemented
8C31×#1983C211yesmaximal, characteristic
9C31×#1878C212yesmaximal, complemented
10C31×#1877C212yesmaximal
11C31×#1763C211yesmaximal, characteristic, complemented
12C22×Q16×C31C2212yes—
13C22×Q16×C31C2212yes—
14C22×SD16×C31C2212yes—
15C31×#556—24no—
16C31×#556—24no—
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#126—21no—
20C2×C31×#126—21no—
21C2×C31×#124C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×C22⋊Q8—21no—
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117—21no—
29C31×#497—24no—
30C31×#462—24no—
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2212yes—
33C2×C31×#103C2212yes—
34C2×C31×#103C2212yes—
35C2×C31×#102C2212yes—
36C2×C31×#97C2211yescharacteristic
37C31×#400—21no—
38C31×#400—21no—
39C31×#391—21no—
40C31×#391C2212yes—
41C31×#391C2212yes—
42C31×#382—21no—
43C4×C4⋊C4×C31C2211yescharacteristic
44C31×#340C2212yes—
45C31×#336C2212yes—
46C31×#336C2212yes—
47C22×Q8×C31D411yescharacteristic
48C22×Q8×C31C2312yes—
49C22×Q8×C31C2311yescharacteristic
50C22×Q8×C31C2311yescharacteristic
51C22×D4×C31C2311yescharacteristic
52C23×C4×C31—21no—
53C2×Q16×C31—24no—
54C2×Q16×C31—24no—
55C2×Q16×C31—24no—
56C2×Q16×C31—42no—
57C2×Q16×C31—42no—
58C2×Q16×C31—42no—
59C2×SD16×C31—24no—
60C2×SD16×C31—24no—
61C2×SD16×C31—42no—
62C22×C8×C31C2312yes—
63C22×C8×C31C2312yes—
64C31×C4⋊Q8—22no—
65C31×C4⋊Q8—22no—
66C31×C4⋊Q8—22no—
67C31×C4⋊Q8—22no—
68C31×#126—28no—
69C31×#126—28no—
70C31×#124—22no—
71C31×#124—22no—
72C31×#124—22no—
73C31×#124D414yes—
74C31×C22⋊Q8—28no—
75C4×Q8×C31—22no—
76C4×Q8×C31—22no—
77C4×Q8×C31—22no—
78C4×Q8×C31—22no—
79C4×Q8×C31—22no—
80C4×Q8×C31D414yes—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C31×#117—28no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31D411yescharacteristic
91C2×C4⋊C4×C31D411yescharacteristic
92C2×C4⋊C4×C31D411yescharacteristic
93C2×C4⋊C4×C31C2312yes—
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C22⋊C4×C31—21no—
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C42×C31—21no—
101C2×C42×C31—21no—
102C2×C42×C31—21no—
103C2×C42×C31C2311yescharacteristic
104C2×C42×C31C2311yescharacteristic
105C2×C42×C31C2311yescharacteristic
106C31×C4⋊C8—22no—
107C31×#103—24no—
108C31×#103—24no—
109C31×#103—42no—
110C31×#102—42no—
111C31×#97—22no—
112C31×#95—21no—
113C31×#95—22no—
114C31×#95—22no—
115C31×#95—22no—
116C31×#95—22no—
117C24×C31—21no—
118C2×Q8×C31—22no—
119C2×Q8×C31—22no—
120C2×Q8×C31—21no—
121C2×Q8×C31—21no—
122C2×Q8×C31—22no—
123C2×Q8×C31—22no—
124C2×Q8×C31—22no—
125C2×Q8×C31—22no—
126C2×Q8×C31—22no—
127C2×Q8×C31—22no—
128C2×Q8×C31—22no—
129C2×Q8×C31—22no—
130C2×Q8×C31—22no—
131C2×Q8×C31—22no—
132C2×Q8×C31—41no—
133C2×Q8×C31C2×D412yes—
134C2×Q8×C31C2×D412yes—
135C2×D4×C31—21no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31C2×D412yes—
139C22×C4×C31—24no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—42no—
146C22×C4×C31—42no—
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2411yescharacteristic
154Q16×C31—48no—
155Q16×C31—48no—
156SD16×C31—48no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31#4114yes—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—24no—
165C4⋊C4×C31—24no—
166C4⋊C4×C31—24no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—21no—
171C4⋊C4×C31—22no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—42no—
174C4⋊C4×C31—42no—
175C4⋊C4×C31C2×D412yes—
176C22⋊C4×C31—24no—
177C22⋊C4×C31—24no—
178C22⋊C4×C31—24no—
179C22⋊C4×C31—24no—
180C22⋊C4×C31—24no—
181C42×C31—24no—
182C42×C31—24no—
183C42×C31—21no—
184C42×C31—21no—
185C42×C31—21no—
186C42×C31—21no—
187C42×C31—42no—
188C42×C31C2×D412yes—
189C42×C31C2×D412yes—
190#25643C3111yesmaximal, characteristic, direct product factor, Sylow
191C23×C31—22no—
192C23×C31—42no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—42no—
196C23×C31C22×D411yescharacteristic
197Q8×C31—22no—
198Q8×C31—22no—
199Q8×C31—24no—
200Q8×C31—44no—
201Q8×C31—41no—
202Q8×C31—41no—
203Q8×C31—42no—
204Q8×C31—42no—
205Q8×C31—42no—
206Q8×C31—42no—
207Q8×C31—42no—
208D4×C31—24no—
209D4×C31—41no—
210D4×C31—41no—
211C2×C4×C31—21no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—21no—
215C2×C4×C31—22no—
216C2×C4×C31—21no—
217C2×C4×C31—22no—
218C2×C4×C31—21no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—21no—
222C2×C4×C31—21no—
223C2×C4×C31—21no—
224C2×C4×C31—22no—
225C2×C4×C31—22no—
226C2×C4×C31—48no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—41no—
230C2×C4×C31—41no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31#12012yes—
238C2×C4×C31#12012yes—
239C2×C4×C31#13712yes—
240C2×C4×C31C22×D411yescharacteristic
241C2×C4×C31C22×D411yescharacteristic
242C2×C4×C31C2×#4112yes—
243C2×C4×C31H(5,𝔽2)12yes—
244C8×C31—24no—
245C8×C31—42no—
246C2×#556C2×C3111yescharacteristic
247C2×#497C2×C3111yescharacteristic
248C2×#462C2×C3111yescharacteristic, complemented
249#2568C2×C3111yescharacteristic, complemented
250#2016C2×C3112yescomplemented
251#2015C2×C3112yes—
252#1985C2×C3111yescharacteristic, complemented
253#1983C2×C3111yescharacteristic
254#1878C2×C3112yescomplemented
255#1877C2×C3112yes—
256#1763C2×C3111yescharacteristic, complemented
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—82no—
261C22×C31—82no—
262C22×C31C2×#12011yescharacteristic
263C22×C31#55012yes—
264C22×C31C2×#13711yescharacteristic
265C22×C31#57511yescharacteristic
266C22×C31#57812yes—
267C4×C31—22no—
268C4×C31—22no—
269C4×C31—22no—
270C4×C31—42no—
271C4×C31—42no—
272C4×C31—41no—
273C4×C31—42no—
274C4×C31—41no—
275C4×C31—41no—
276C4×C31—82no—
277C4×C31—82no—
278C4×C31#53211yescharacteristic
279C4×C31#53511yescharacteristic
280C4×C31#54612yes—
281C22×Q16C22×C3112yes—
282C22×Q16C22×C3112yes—
283C22×SD16C22×C3112yes—
284#556—24no—
285#556—24no—
286C2×C4⋊Q8C22×C3111yescharacteristic
287C2×C4⋊Q8C22×C3111yescharacteristic
288C2×#126—21no—
289C2×#126—21no—
290C2×#124C22×C3111yescharacteristic
291C2×#124C22×C3111yescharacteristic
292C2×C22⋊Q8—21no—
293C2×C4×Q8C22×C3111yescharacteristic
294C2×C4×Q8C22×C3111yescharacteristic
295C2×C4×Q8C22×C3111yescharacteristic
296C2×C4×D4C22×C3111yescharacteristic
297C2×#117—21no—
298#497—24no—
299#462—24no—
300C2×C4⋊C8C22×C3111yescharacteristic
301C2×#103C22×C3112yes—
302C2×#103C22×C3112yes—
303C2×#103C22×C3112yes—
304C2×#102C22×C3112yes—
305C2×#97C22×C3111yescharacteristic
306#400—21no—
307#400—21no—
308#391—21no—
309#391C22×C3112yes—
310#391C22×C3112yes—
311#382—21no—
312C4×C4⋊C4C22×C3111yescharacteristic
313#340C22×C3112yes—
314#336C22×C3112yes—
315#336C22×C3112yes—
316C2×C31—82no—
317C2×C31#243111yescharacteristic
318C2×C31#300711yescharacteristic
319C2×C31#301111yescharacteristic
320C2×C31#339812yes—
321C2×C31#340212yes—
322C22×Q8D4×C3111yescharacteristic
323C22×Q8C23×C3112yes—
324C22×Q8C23×C3111yescharacteristic
325C22×Q8C23×C3111yescharacteristic
326C22×D4C23×C3111yescharacteristic
327C23×C4—21no—
328C2×Q16—24no—
329C2×Q16—24no—
330C2×Q16—24no—
331C2×Q16—42no—
332C2×Q16—42no—
333C2×Q16—42no—
334C2×SD16—24no—
335C2×SD16—24no—
336C2×SD16—42no—
337C22×C8C23×C3112yes—
338C22×C8C23×C3112yes—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343#126—28no—
344#126—28no—
345#124—22no—
346#124—22no—
347#124—22no—
348#124D4×C3114yes—
349C22⋊Q8—28no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8D4×C3114yes—
356C4×D4—22no—
357C4×D4—22no—
358#117—28no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C3111yescharacteristic
366C2×C4⋊C4D4×C3111yescharacteristic
367C2×C4⋊C4D4×C3111yescharacteristic
368C2×C4⋊C4C23×C3112yes—
369C2×C4⋊C4C23×C3111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42C23×C3111yescharacteristic
379C2×C42C23×C3111yescharacteristic
380C2×C42C23×C3111yescharacteristic
381C4⋊C8—22no—
382#103—24no—
383#103—24no—
384#103—42no—
385#102—42no—
386#97—22no—
387#95—21no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392C31#2564311yescharacteristic, direct product factor, Sylow
393C24—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—41no—
409C2×Q8C2×D4×C3112yes—
410C2×Q8C2×D4×C3112yes—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4C2×D4×C3112yes—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4C2×D4×C3111yescharacteristic
424C22×C4C2×D4×C3111yescharacteristic
425C22×C4C2×D4×C3111yescharacteristic
426C22×C4C2×D4×C3111yescharacteristic
427C22×C4C2×D4×C3111yescharacteristic
428C22×C4C2×D4×C3111yescharacteristic
429C22×C4C24×C3111yescharacteristic
430Q16—48no—
431Q16—48no—
432SD16—48no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8#41×C3114yes—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4C2×D4×C3112yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C42—24no—
458C42—24no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—42no—
464C42C2×D4×C3112yes—
465C42C2×D4×C3112yes—
466C23—22no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—42no—
471C23C22×D4×C3111yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—24no—
475Q8—44no—
476Q8—41no—
477Q8—41no—
478Q8—42no—
479Q8—42no—
480Q8—42no—
481Q8—42no—
482Q8—42no—
483D4—24no—
484D4—41no—
485D4—41no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4C31×#12012yes—
513C2×C4C31×#12012yes—
514C2×C4C31×#13712yes—
515C2×C4C22×D4×C3111yescharacteristic
516C2×C4C22×D4×C3111yescharacteristic
517C2×C4C2×#41×C3112yes—
518C2×C4C31×H(5,𝔽2)12yes—
519C8—24no—
520C8—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—82no—
525C22—82no—
526C22C2×C31×#12011yescharacteristic
527C22C31×#55012yes—
528C22C2×C31×#13711yescharacteristic
529C22C31×#57511yescharacteristic
530C22C31×#57812yes—
531C4—22no—
532C4—22no—
533C4—22no—
534C4—42no—
535C4—42no—
536C4—41no—
537C4—42no—
538C4—41no—
539C4—41no—
540C4—82no—
541C4—82no—
542C4C31×#53211yescharacteristic
543C4C31×#53511yescharacteristic
544C4C31×#54612yes—
545C2—82no—
546C2C31×#243111yescharacteristic
547C2C31×#300711yescharacteristic
548C2C31×#301111yescharacteristic
549C2C31×#339812yes—
550C2C31×#340212yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#462C2semidirect
4. C31×#2568C2semidirect
5. C31×#2016C2semidirect
7. C31×#1985C2semidirect
9. C31×#1878C2semidirect
11. C31×#1763C2semidirect
190. #25643C31direct (N × H)
248. C2×#462C2×C31semidirect
249. #2568C2×C31semidirect
250. #2016C2×C31semidirect
252. #1985C2×C31semidirect
254. #1878C2×C31semidirect
256. #1763C2×C31semidirect
392. C31#25643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5562
C2×C31×#4972
C2×C31×#4622
C31×#25682
C31×#20162
C31×#20152
C31×#19852
C31×#19832
C31×#18782
C31×#18772
C31×#17632
#2564331