Finite Group Databasebeta

← C31×#25893 #21482652

Subgroups — C31×#25893 #21482652

Order 7936.

1344 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#550C211yesmaximal, characteristic
2C2×C31×#490C211yesmaximal, characteristic, complemented
3C2×C31×#479C211yesmaximal, characteristic, complemented
4C31×#2562C211yesmaximal, characteristic, complemented
5C31×#2034C212yesmaximal, complemented
6C31×#2033C212yesmaximal, complemented
7C31×#1982C211yesmaximal, characteristic, complemented
8C31×#1955C211yesmaximal, characteristic, complemented
9C31×#1788C212yesmaximal, complemented
10C31×#1788C212yesmaximal, complemented
11C31×#1763C211yesmaximal, characteristic, complemented
12C22×#41×C31C2212yes—
13C31×#550—24no—
14C31×#550—24no—
15C2×C31×#127—21no—
16C2×C31×#127C2211yescharacteristic
17C2×C31×#125C2211yescharacteristic
18C2×C31×#121—22no—
19C2×C31×#121C2212yes—
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C31×#490—24no—
24C31×#479—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×C4⋊C8C2211yescharacteristic
28C2×C31×#103C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2212yes—
31C2×C31×#102C2212yes—
32C2×C31×#102C2212yes—
33C2×C31×#102C2212yes—
34C2×C31×#102C2212yes—
35C2×C31×C22⋊C8C2212yes—
36C2×C31×C22⋊C8C2212yes—
37C2×C31×#97C2211yescharacteristic
38C31×#400—21no—
39C31×#394—21no—
40C31×#388—22no—
41C31×#380C2212yes—
42C31×#380C2212yes—
43C4×C4⋊C4×C31C2211yescharacteristic
44C31×#340C2212yes—
45C2×#41×C31—24no—
46C2×#41×C31—24no—
47C2×#41×C31—24no—
48C2×#41×C31—24no—
49C2×#41×C31—42no—
50C2×#41×C31—42no—
51C22×Q8×C31C2311yescharacteristic
52C22×D4×C31—22no—
53C22×D4×C31—22no—
54C22×D4×C31—21no—
55C22×D4×C31—21no—
56C22×D4×C31D411yescharacteristic
57C22×D4×C31C2312yes—
58C23×C4×C31—22no—
59C23×C4×C31C2312yes—
60C22×C8×C31C2312yes—
61C22×C8×C31C2311yescharacteristic
62C22×C8×C31C2311yescharacteristic
63C31×#127—28no—
64C31×#127—22no—
65C31×#127D414yes—
66C31×#125—22no—
67C31×#125—22no—
68C31×#121—216no—
69C31×#121—24no—
70C31×#121—24no—
71C4×Q8×C31—22no—
72C4×Q8×C31D414yes—
73C4×D4×C31—28no—
74C4×D4×C31—22no—
75C4×D4×C31—22no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31D411yescharacteristic
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2312yes—
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31D412yes—
88C2×C42×C31—21no—
89C2×C42×C31—21no—
90C2×C42×C31C2311yescharacteristic
91C31×#107—22no—
92C31×#106—22no—
93C31×C4⋊C8—22no—
94C31×#103—22no—
95C31×#103—22no—
96C31×#103—24no—
97C31×#102—24no—
98C31×#102—24no—
99C31×#102—42no—
100C31×#102—42no—
101C31×C22⋊C8—42no—
102C31×C22⋊C8—42no—
103C31×#97—22no—
104C31×#95—21no—
105C31×#95—22no—
106C31×#95—22no—
107C24×C31—22no—
108C24×C31C2×D412yes—
109#41×C31—48no—
110#41×C31—48no—
111#41×C31—48no—
112#41×C31—48no—
113C2×Q8×C31—21no—
114C2×Q8×C31—22no—
115C2×Q8×C31C2×D412yes—
116C2×Q8×C31#4114yes—
117C2×D4×C31—28no—
118C2×D4×C31—28no—
119C2×D4×C31—22no—
120C2×D4×C31—24no—
121C2×D4×C31—24no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—22no—
125C2×D4×C31—22no—
126C2×D4×C31—22no—
127C2×D4×C31—42no—
128C2×D4×C31—44no—
129C2×D4×C31—44no—
130C2×D4×C31—44no—
131C2×D4×C31—81no—
132C2×D4×C31—81no—
133C2×D4×C31—82no—
134C2×D4×C31—82no—
135C2×D4×C31C2×D414yes—
136C22×C4×C31—21no—
137C22×C4×C31—28no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—44no—
149C22×C4×C31—44no—
150C22×C4×C31C2×D412yes—
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2411yescharacteristic
154C2×C8×C31—22no—
155C2×C8×C31—21no—
156C2×C8×C31—21no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C4⋊C4×C31—24no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—42no—
171C4⋊C4×C31—42no—
172C4⋊C4×C31C2×D412yes—
173C22⋊C4×C31—28no—
174C22⋊C4×C31—24no—
175C22⋊C4×C31—44no—
176C22⋊C4×C31—82no—
177C42×C31—24no—
178C42×C31—81no—
179C42×C31C2×D412yes—
180C42×C31C2×D412yes—
181#25893C3111yesmaximal, characteristic, direct product factor, Sylow
182C23×C31—22no—
183C23×C31—24no—
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—22no—
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—22no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31C22×D411yescharacteristic
197Q8×C31—22no—
198Q8×C31—24no—
199Q8×C31#12414yes—
200D4×C31—24no—
201D4×C31—24no—
202D4×C31—44no—
203D4×C31—48no—
204D4×C31—416no—
205D4×C31—42no—
206D4×C31—42no—
207D4×C31—84no—
208D4×C31—88no—
209C2×C4×C31—22no—
210C2×C4×C31—24no—
211C2×C4×C31—22no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—416no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31#12012yes—
234C2×C4×C31#12012yes—
235C2×C4×C31C22×D411yescharacteristic
236C2×C4×C31C22×D411yescharacteristic
237C2×C4×C31C2×#4112yes—
238C2×C4×C31H(5,𝔽2)12yes—
239C8×C31—41no—
240C8×C31—41no—
241C8×C31—42no—
242C2×#550C2×C3111yescharacteristic
243C2×#490C2×C3111yescharacteristic, complemented
244C2×#479C2×C3111yescharacteristic, complemented
245#2562C2×C3111yescharacteristic, complemented
246#2034C2×C3112yescomplemented
247#2033C2×C3112yescomplemented
248#1982C2×C3111yescharacteristic, complemented
249#1955C2×C3111yescharacteristic, complemented
250#1788C2×C3112yescomplemented
251#1788C2×C3112yescomplemented
252#1763C2×C3111yescharacteristic, complemented
253C22×C31—44no—
254C22×C31—42no—
255C22×C31—42no—
256C22×C31—44no—
257C22×C31—42no—
258C22×C31—44no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—42no—
262C22×C31—42no—
263C22×C31—82no—
264C22×C31—82no—
265C22×C31—82no—
266C22×C31—82no—
267C22×C31C2×#12011yescharacteristic
268C22×C31#54612yes—
269C22×C31#57512yes—
270C22×C31#57611yescharacteristic
271C22×C31#57711yescharacteristic
272C4×C31—24no—
273C4×C31—22no—
274C4×C31—22no—
275C4×C31—42no—
276C4×C31—42no—
277C4×C31—81no—
278C4×C31—81no—
279C4×C31—82no—
280C4×C31C2×#12411yescharacteristic
281C4×C31#53511yescharacteristic
282C4×C31#54612yes—
283C22×#41C22×C3112yes—
284#550—24no—
285#550—24no—
286C2×#127—21no—
287C2×#127C22×C3111yescharacteristic
288C2×#125C22×C3111yescharacteristic
289C2×#121—22no—
290C2×#121C22×C3112yes—
291C2×C4×Q8C22×C3111yescharacteristic
292C2×C4×D4—21no—
293C2×C4×D4C22×C3111yescharacteristic
294#490—24no—
295#479—24no—
296C2×#107C22×C3111yescharacteristic
297C2×#106C22×C3111yescharacteristic
298C2×C4⋊C8C22×C3111yescharacteristic
299C2×#103C22×C3111yescharacteristic
300C2×#103C22×C3111yescharacteristic
301C2×#103C22×C3112yes—
302C2×#102C22×C3112yes—
303C2×#102C22×C3112yes—
304C2×#102C22×C3112yes—
305C2×#102C22×C3112yes—
306C2×C22⋊C8C22×C3112yes—
307C2×C22⋊C8C22×C3112yes—
308C2×#97C22×C3111yescharacteristic
309#400—21no—
310#394—21no—
311#388—22no—
312#380C22×C3112yes—
313#380C22×C3112yes—
314C4×C4⋊C4C22×C3111yescharacteristic
315#340C22×C3112yes—
316C2×C31—82no—
317C2×C31—84no—
318C2×C31#243511yescharacteristic
319C2×C31#300511yescharacteristic
320C2×C31#301211yescharacteristic
321C2×C31#330912yes—
322C2×C31#331712yes—
323C2×#41—24no—
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—24no—
327C2×#41—42no—
328C2×#41—42no—
329C22×Q8C23×C3111yescharacteristic
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4D4×C3111yescharacteristic
335C22×D4C23×C3112yes—
336C23×C4—22no—
337C23×C4C23×C3112yes—
338C22×C8C23×C3112yes—
339C22×C8C23×C3111yescharacteristic
340C22×C8C23×C3111yescharacteristic
341#127—28no—
342#127—22no—
343#127D4×C3114yes—
344#125—22no—
345#125—22no—
346#121—216no—
347#121—24no—
348#121—24no—
349C4×Q8—22no—
350C4×Q8D4×C3114yes—
351C4×D4—28no—
352C4×D4—22no—
353C4×D4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C3111yescharacteristic
358C2×C4⋊C4C23×C3111yescharacteristic
359C2×C4⋊C4C23×C3111yescharacteristic
360C2×C4⋊C4C23×C3112yes—
361C2×C4⋊C4C23×C3111yescharacteristic
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4D4×C3112yes—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42C23×C3111yescharacteristic
369#107—22no—
370#106—22no—
371C4⋊C8—22no—
372#103—22no—
373#103—22no—
374#103—24no—
375#102—24no—
376#102—24no—
377#102—42no—
378#102—42no—
379C22⋊C8—42no—
380C22⋊C8—42no—
381#97—22no—
382#95—21no—
383#95—22no—
384#95—22no—
385C31#2589311yescharacteristic, direct product factor, Sylow
386C24—22no—
387C24C2×D4×C3112yes—
388#41—48no—
389#41—48no—
390#41—48no—
391#41—48no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8C2×D4×C3112yes—
395C2×Q8#41×C3114yes—
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—42no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—82no—
413C2×D4—82no—
414C2×D4C2×D4×C3114yes—
415C22×C4—21no—
416C22×C4—28no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4C2×D4×C3112yes—
430C22×C4C2×D4×C3111yescharacteristic
431C22×C4C2×D4×C3111yescharacteristic
432C22×C4C24×C3111yescharacteristic
433C2×C8—22no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4C2×D4×C3112yes—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—82no—
456C42—24no—
457C42—81no—
458C42C2×D4×C3112yes—
459C42C2×D4×C3112yes—
460C23—22no—
461C23—24no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23C22×D4×C3111yescharacteristic
475Q8—22no—
476Q8—24no—
477Q8C31×#12414yes—
478D4—24no—
479D4—24no—
480D4—44no—
481D4—48no—
482D4—416no—
483D4—42no—
484D4—42no—
485D4—84no—
486D4—88no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—416no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4C31×#12012yes—
512C2×C4C31×#12012yes—
513C2×C4C22×D4×C3111yescharacteristic
514C2×C4C22×D4×C3111yescharacteristic
515C2×C4C2×#41×C3112yes—
516C2×C4C31×H(5,𝔽2)12yes—
517C8—41no—
518C8—41no—
519C8—42no—
520C22—44no—
521C22—42no—
522C22—42no—
523C22—44no—
524C22—42no—
525C22—44no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22C2×C31×#12011yescharacteristic
535C22C31×#54612yes—
536C22C31×#57512yes—
537C22C31×#57611yescharacteristic
538C22C31×#57711yescharacteristic
539C4—24no—
540C4—22no—
541C4—22no—
542C4—42no—
543C4—42no—
544C4—81no—
545C4—81no—
546C4—82no—
547C4C2×C31×#12411yescharacteristic
548C4C31×#53511yescharacteristic
549C4C31×#54612yes—
550C2—82no—
551C2—84no—
552C2C31×#243511yescharacteristic
553C2C31×#300511yescharacteristic
554C2C31×#301211yescharacteristic
555C2C31×#330912yes—
556C2C31×#331712yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#550C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#490C2semidirect
3. C2×C31×#479C2semidirect
4. C31×#2562C2semidirect
5. C31×#2034C2semidirect
6. C31×#2033C2semidirect
7. C31×#1982C2semidirect
8. C31×#1955C2semidirect
9. C31×#1788C2semidirect
10. C31×#1788C2semidirect
11. C31×#1763C2semidirect
181. #25893C31direct (N × H)
243. C2×#490C2×C31semidirect
244. C2×#479C2×C31semidirect
245. #2562C2×C31semidirect
246. #2034C2×C31semidirect
247. #2033C2×C31semidirect
248. #1982C2×C31semidirect
249. #1955C2×C31semidirect
250. #1788C2×C31semidirect
251. #1788C2×C31semidirect
252. #1763C2×C31semidirect
385. C31#25893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5502
C2×C31×#4902
C2×C31×#4792
C31×#25622
C31×#20342
C31×#20332
C31×#19822
C31×#19552
C31×#17882
C31×#17632
#2589331