Finite Group Databasebeta

← C31×#19089 #21475848

Subgroups — C31×#19089 #21475848

Order 7936.

850 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3559C211yesmaximal, characteristic
2C31×#3240C211yesmaximal, characteristic, complemented
3C31×#3236C211yesmaximal, characteristic, complemented
4C31×#3216C211yesmaximal, characteristic, complemented
5C31×#1664C212yesmaximal, complemented
6C31×#1662C212yesmaximal, complemented
7C31×#1661C212yesmaximal, complemented
8C31×#1660C212yesmaximal, complemented
9C31×#1536C211yesmaximal, characteristic, complemented
10C31×#1535C211yesmaximal, characteristic, complemented
11C31×#1534C211yesmaximal, characteristic, complemented
12C31×#563C2212yes—
13C31×#562C2212yes—
14C31×#554—21no—
15C31×#553—21no—
16C31×#553—21no—
17C31×#547—22no—
18C31×#547—21no—
19C31×#544—21no—
20C31×#540—21no—
21C31×#539—22no—
22C31×#539—21no—
23C31×#537—21no—
24C31×#533C2211yescharacteristic
25C31×#532C2211yescharacteristic
26C31×#529C2211yescharacteristic
27C2×C31×#125C2211yescharacteristic
28C31×#501C2211yescharacteristic
29C31×#501C2212yes—
30C31×#501C2211yescharacteristic
31C31×#497C2212yes—
32C31×#491C2212yes—
33C31×#489C2211yescharacteristic
34C31×#489C2211yescharacteristic
35C31×#489C2212yes—
36C31×#485—21no—
37C31×#484—21no—
38C31×#483—21no—
39C31×#482—21no—
40C31×#479—22no—
41C31×#479—21no—
42C31×#478—21no—
43C31×#462—21no—
44C31×#460—21no—
45C31×#452—22no—
46C31×#432C2211yescharacteristic
47C31×#432C2211yescharacteristic
48C31×#432C2211yescharacteristic
49C31×#330C2212yes—
50C31×#330C2212yes—
51C31×#330C2212yes—
52C31×#329C2212yes—
53C31×#329C2212yes—
54C31×#329C2212yes—
55C2×#41×C31—22no—
56C2×#41×C31D412yes—
57C2×Q16×C31—22no—
58C2×SD16×C31—22no—
59C31×C4⋊Q8—21no—
60C31×C4⋊Q8—22no—
61C31×C4⋊Q8D411yescharacteristic
62C31×C4⋊Q8C2311yescharacteristic
63C31×C4⋊Q8C2311yescharacteristic
64C31×#127D411yescharacteristic
65C31×#126—22no—
66C31×#126—22no—
67C31×#126—21no—
68C31×#125—22no—
69C31×#125—21no—
70C31×#125—21no—
71C31×#125—21no—
72C31×#125—21no—
73C31×#125D412yes—
74C31×#125C2312yes—
75C31×#125C2311yescharacteristic
76C31×#124C2311yescharacteristic
77C31×#124C2312yes—
78C31×#123—22no—
79C31×#123—22no—
80C31×#123—22no—
81C31×#123—22no—
82C31×#123—21no—
83C31×#123—22no—
84C31×#123—22no—
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—21no—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8D411yescharacteristic
94C31×#121—22no—
95C31×#121—22no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—21no—
101C31×#121—21no—
102C31×#121D411yescharacteristic
103C4×Q8×C31—21no—
104C4×Q8×C31—21no—
105C4×Q8×C31D411yescharacteristic
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—21no—
109C4×D4×C31—21no—
110C4×D4×C31—21no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31D411yescharacteristic
114C31×#117—21no—
115C31×#117—21no—
116C31×#117—21no—
117C2×C4⋊C4×C31—22no—
118C2×C4⋊C4×C31—21no—
119C2×C4⋊C4×C31—21no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31D411yescharacteristic
122C2×C4⋊C4×C31D411yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#107—21no—
125C31×#107—21no—
126C31×#107—22no—
127C31×#106—21no—
128C31×#106—21no—
129C31×#106—22no—
130C31×C4⋊C8—21no—
131C31×C4⋊C8—21no—
132C31×C4⋊C8—21no—
133C31×#103—22no—
134C31×#103—21no—
135C31×#103—21no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#102—22no—
139C31×#102—21no—
140C31×#102—21no—
141C31×C22⋊C8—21no—
142C31×C22⋊C8—21no—
143C31×C22⋊C8—21no—
144C31×#97C2312yes—
145C31×#97C2311yescharacteristic
146C31×#97C2311yescharacteristic
147C31×#97C2312yes—
148#41×C31—84no—
149#41×C31—82no—
150C2×Q8×C31—22no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31C2×D411yescharacteristic
154C2×Q8×C31C2×D412yes—
155C2×D4×C31—22no—
156C2×D4×C31—21no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31C2×D411yescharacteristic
162C2×D4×C31C2×D412yes—
163C22×C4×C31—21no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—22no—
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173Q16×C31—82no—
174SD16×C31—82no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—22no—
178C2×C8×C31—22no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—22no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—22no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—41no—
200C4⋊C4×C31—41no—
201C4⋊C4×C31C2×D412yes—
202C4⋊C4×C31C2×D412yes—
203C4⋊C4×C31C2×D411yescharacteristic
204C4⋊C4×C31C2×D411yescharacteristic
205C22⋊C4×C31—22no—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—22no—
208C22⋊C4×C31—22no—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—21no—
211C22⋊C4×C31—21no—
212C22⋊C4×C31—21no—
213C22⋊C4×C31—21no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—21no—
217C22⋊C4×C31—41no—
218C42×C31—22no—
219C42×C31—21no—
220C42×C31—41no—
221C42×C31C2×D411yescharacteristic
222C42×C31C2×D411yescharacteristic
223C42×C31C2×D411yescharacteristic
224C42×C31C2411yescharacteristic
225#19089C3111yesmaximal, characteristic, direct product factor, Sylow
226C23×C31—22no—
227C23×C31—21no—
228C23×C31#12011yescharacteristic
229Q8×C31—42no—
230Q8×C31—41no—
231Q8×C31—41no—
232Q8×C31—41no—
233Q8×C31—42no—
234Q8×C31—82no—
235D4×C31—42no—
236D4×C31—41no—
237D4×C31—42no—
238D4×C31—44no—
239D4×C31—42no—
240D4×C31—81no—
241D4×C31—82no—
242D4×C31—82no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—22no—
246C2×C4×C31—22no—
247C2×C4×C31—21no—
248C2×C4×C31—22no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—82no—
257C2×C4×C31—81no—
258C2×C4×C31—82no—
259C2×C4×C31—82no—
260C2×C4×C31—82no—
261C2×C4×C31#12011yescharacteristic
262C2×C4×C31#12011yescharacteristic
263C2×C4×C31#12011yescharacteristic
264C2×C4×C31C22×D411yescharacteristic
265C2×C4×C31C22×D411yescharacteristic
266C2×C4×C31C22×D411yescharacteristic
267C8×C31—42no—
268C8×C31—41no—
269C8×C31—41no—
270C8×C31—42no—
271#3559C2×C3111yescharacteristic
272#3240C2×C3111yescharacteristic, complemented
273#3236C2×C3111yescharacteristic, complemented
274#3216C2×C3111yescharacteristic, complemented
275#1664C2×C3112yescomplemented
276#1662C2×C3112yescomplemented
277#1661C2×C3112yescomplemented
278#1660C2×C3112yescomplemented
279#1536C2×C3111yescharacteristic, complemented
280#1535C2×C3111yescharacteristic, complemented
281#1534C2×C3111yescharacteristic, complemented
282C22×C31—21no—
283C22×C31—21no—
284C22×C31—21no—
285C22×C31—42no—
286C22×C31—41no—
287C22×C31—41no—
288C22×C31—42no—
289C22×C31—42no—
290C22×C31—41no—
291C22×C31C2×#12011yescharacteristic
292C4×C31—21no—
293C4×C31—21no—
294C4×C31—21no—
295C4×C31—21no—
296C4×C31—21no—
297C4×C31—21no—
298C4×C31—42no—
299C4×C31—42no—
300C4×C31—41no—
301C4×C31—41no—
302C4×C31—42no—
303C4×C31—41no—
304C4×C31—81no—
305C4×C31—81no—
306#563C22×C3112yes—
307#562C22×C3112yes—
308#554—21no—
309#553—21no—
310#553—21no—
311#547—22no—
312#547—21no—
313#544—21no—
314#540—21no—
315#539—22no—
316#539—21no—
317#537—21no—
318#533C22×C3111yescharacteristic
319#532C22×C3111yescharacteristic
320#529C22×C3111yescharacteristic
321C2×#125C22×C3111yescharacteristic
322#501C22×C3111yescharacteristic
323#501C22×C3112yes—
324#501C22×C3111yescharacteristic
325#497C22×C3112yes—
326#491C22×C3112yes—
327#489C22×C3111yescharacteristic
328#489C22×C3111yescharacteristic
329#489C22×C3112yes—
330#485—21no—
331#484—21no—
332#483—21no—
333#482—21no—
334#479—22no—
335#479—21no—
336#478—21no—
337#462—21no—
338#460—21no—
339#452—22no—
340#432C22×C3111yescharacteristic
341#432C22×C3111yescharacteristic
342#432C22×C3111yescharacteristic
343#330C22×C3112yes—
344#330C22×C3112yes—
345#330C22×C3112yes—
346#329C22×C3112yes—
347#329C22×C3112yes—
348#329C22×C3112yes—
349C2×C31—41no—
350C2×C31—82no—
351C2×C31—81no—
352C2×C31#301911yescharacteristic
353C2×C31#302011yescharacteristic
354C2×C31#302211yescharacteristic
355C2×#41—22no—
356C2×#41D4×C3112yes—
357C2×Q16—22no—
358C2×SD16—22no—
359C4⋊Q8—21no—
360C4⋊Q8—22no—
361C4⋊Q8D4×C3111yescharacteristic
362C4⋊Q8C23×C3111yescharacteristic
363C4⋊Q8C23×C3111yescharacteristic
364#127D4×C3111yescharacteristic
365#126—22no—
366#126—22no—
367#126—21no—
368#125—22no—
369#125—21no—
370#125—21no—
371#125—21no—
372#125—21no—
373#125D4×C3112yes—
374#125C23×C3112yes—
375#125C23×C3111yescharacteristic
376#124C23×C3111yescharacteristic
377#124C23×C3112yes—
378#123—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382#123—21no—
383#123—22no—
384#123—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8D4×C3111yescharacteristic
394#121—22no—
395#121—22no—
396#121—21no—
397#121—21no—
398#121—22no—
399#121—22no—
400#121—21no—
401#121—21no—
402#121D4×C3111yescharacteristic
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8D4×C3111yescharacteristic
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4D4×C3111yescharacteristic
414#117—21no—
415#117—21no—
416#117—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4D4×C3111yescharacteristic
422C2×C4⋊C4D4×C3111yescharacteristic
423C2×C42C23×C3111yescharacteristic
424#107—21no—
425#107—21no—
426#107—22no—
427#106—21no—
428#106—21no—
429#106—22no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433#103—22no—
434#103—21no—
435#103—21no—
436#103—22no—
437#103—22no—
438#102—22no—
439#102—21no—
440#102—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97C23×C3112yes—
445#97C23×C3111yescharacteristic
446#97C23×C3111yescharacteristic
447#97C23×C3112yes—
448C31#1908911yescharacteristic, direct product factor, Sylow
449#41—84no—
450#41—82no—
451C2×Q8—22no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C3111yescharacteristic
455C2×Q8C2×D4×C3112yes—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4C2×D4×C3111yescharacteristic
463C2×D4C2×D4×C3112yes—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4C2×D4×C3111yescharacteristic
472C22×C4C2×D4×C3111yescharacteristic
473C22×C4C2×D4×C3111yescharacteristic
474Q16—82no—
475SD16—82no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C3112yes—
503C4⋊C4C2×D4×C3112yes—
504C4⋊C4C2×D4×C3111yescharacteristic
505C4⋊C4C2×D4×C3111yescharacteristic
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C42—22no—
520C42—21no—
521C42—41no—
522C42C2×D4×C3111yescharacteristic
523C42C2×D4×C3111yescharacteristic
524C42C2×D4×C3111yescharacteristic
525C42C24×C3111yescharacteristic
526C23—22no—
527C23—21no—
528C23C31×#12011yescharacteristic
529Q8—42no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—42no—
534Q8—82no—
535D4—42no—
536D4—41no—
537D4—42no—
538D4—44no—
539D4—42no—
540D4—81no—
541D4—82no—
542D4—82no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—81no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4C31×#12011yescharacteristic
562C2×C4C31×#12011yescharacteristic
563C2×C4C31×#12011yescharacteristic
564C2×C4C22×D4×C3111yescharacteristic
565C2×C4C22×D4×C3111yescharacteristic
566C2×C4C22×D4×C3111yescharacteristic
567C8—42no—
568C8—41no—
569C8—41no—
570C8—42no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22C2×C31×#12011yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—42no—
588C4—42no—
589C4—41no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C2—41no—
596C2—82no—
597C2—81no—
598C2C31×#301911yescharacteristic
599C2C31×#302011yescharacteristic
600C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3559C2
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×#3240C2semidirect
3. C31×#3236C2semidirect
4. C31×#3216C2semidirect
5. C31×#1664C2semidirect
6. C31×#1662C2semidirect
7. C31×#1661C2semidirect
8. C31×#1660C2semidirect
9. C31×#1536C2semidirect
10. C31×#1535C2semidirect
11. C31×#1534C2semidirect
225. #19089C31direct (N × H)
272. #3240C2×C31semidirect
273. #3236C2×C31semidirect
274. #3216C2×C31semidirect
275. #1664C2×C31semidirect
276. #1662C2×C31semidirect
277. #1661C2×C31semidirect
278. #1660C2×C31semidirect
279. #1536C2×C31semidirect
280. #1535C2×C31semidirect
281. #1534C2×C31semidirect
448. C31#19089direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35592
C31×#32402
C31×#32362
C31×#32162
C31×#16642
C31×#16622
C31×#16612
C31×#16602
C31×#15362
C31×#15352
C31×#15342
#1908931