Finite Group Databasebeta

← C31×#19016 #21475775

Subgroups — C31×#19016 #21475775

Order 7936.

1008 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3559C211yesmaximal, characteristic, complemented
2C31×#3217C211yesmaximal, characteristic, complemented
3C31×#3151C211yesmaximal, characteristic, complemented
4C2×C31×#490C211yesmaximal, characteristic, complemented
5C31×#1657C214yesmaximal, complemented
6C31×#1656C214yesmaximal, complemented
7C31×#1530C211yesmaximal, characteristic, complemented
8C31×#1528C211yesmaximal, characteristic, complemented
9C31×#1524C211yesmaximal, characteristic, complemented
10C2×C31×AGL(1,ℤ/8)—22no—
11C31×#563C2212yescomplemented
12C31×#562C2212yescomplemented
13C31×#554—21no—
14C31×#553—21no—
15C31×#553—21no—
16C31×#547—22no—
17C31×#547—21no—
18C31×#544—21no—
19C31×#540—21no—
20C31×#539—22no—
21C31×#539—21no—
22C31×#537—21no—
23C31×#532C2211yescharacteristic
24C2×C31×#127C2211yescharacteristic
25C31×#529C2211yescharacteristic
26C2×C31×#125C2211yescharacteristic
27C31×#496C2214yes—
28C31×#496C2212yes—
29C31×#493—21no—
30C31×#492—21no—
31C31×#490—22no—
32C31×#490C2214yes—
33C31×#490C2212yes—
34C31×#460—21no—
35C31×#459—21no—
36C31×#450—21no—
37C31×#447—21no—
38C31×#432C2211yescharacteristic
39C2×C31×#102—21no—
40C2×C31×#102—21no—
41C4×M16×C31C2211yescharacteristic
42C2×C31×#97C2211yescharacteristic
43C31×#330C2214yescomplemented
44C31×#330C2212yescomplemented
45C31×#329C2212yescomplemented
46C31×#329C2214yescomplemented
47C2×#41×C31—22no—
48C2×#41×C31D412yes—
49C22×D4×C31—21no—
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C31×AGL(1,ℤ/8)—48no—
53C2×SD16×C31—24no—
54C2×SD16×C31—22no—
55C2×D8×C31—24no—
56C2×D8×C31—22no—
57C2×M16×C31—21no—
58C22×C8×C31—21no—
59C31×C4⋊Q8—21no—
60C31×C4⋊Q8—22no—
61C31×C4⋊Q8D411yescharacteristic
62C31×#127—21no—
63C31×#127—21no—
64C31×#127—21no—
65C31×#127D411yescharacteristic
66C31×#127C2312yes—
67C31×#126—22no—
68C31×#126—22no—
69C31×#126—21no—
70C31×#125—22no—
71C31×#125—21no—
72C31×#125—21no—
73C31×#125—21no—
74C31×#125D412yes—
75C31×#125C2312yes—
76C31×#125C2311yescharacteristic
77C31×#124C2311yescharacteristic
78C31×#124C2312yes—
79C31×#123—22no—
80C31×#123—22no—
81C31×#123—22no—
82C31×#123—22no—
83C31×#123—21no—
84C31×#123—22no—
85C31×#123—22no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8D411yescharacteristic
93C31×#121—22no—
94C31×#121—22no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—21no—
100C31×#121—21no—
101C31×#121D411yescharacteristic
102C4×Q8×C31D411yescharacteristic
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—21no—
106C4×D4×C31—21no—
107C4×D4×C31—21no—
108C4×D4×C31—21no—
109C4×D4×C31—21no—
110C4×D4×C31D411yescharacteristic
111C31×#117—21no—
112C31×#117—21no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31D411yescharacteristic
118C2×C4⋊C4×C31D411yescharacteristic
119C2×C42×C31C2311yescharacteristic
120C31×C4⋊C8—21no—
121C31×#102—24no—
122C31×#102—24no—
123C31×#102—22no—
124C31×#102—22no—
125C31×C22⋊C8—21no—
126C31×#97—21no—
127C31×#97C2312yes—
128C31×#97C2312yes—
129C31×#97C2312yes—
130C4×C8×C31—21no—
131C24×C31—41no—
132#41×C31—44no—
133#41×C31—84no—
134C2×Q8×C31—22no—
135C2×Q8×C31C2×D411yescharacteristic
136C2×Q8×C31C2×D412yes—
137C2×D4×C31—22no—
138C2×D4×C31—21no—
139C2×D4×C31—22no—
140C2×D4×C31—22no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—22no—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—44no—
147C2×D4×C31—44no—
148C2×D4×C31—41no—
149C2×D4×C31—41no—
150C2×D4×C31—41no—
151C2×D4×C31—82no—
152C2×D4×C31C2×D411yescharacteristic
153C2×D4×C31C2×D412yes—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—22no—
161C22×C4×C31C2×D411yescharacteristic
162C22×C4×C31C2×D411yescharacteristic
163C22×C4×C31C2×D411yescharacteristic
164SD16×C31—48no—
165SD16×C31—82no—
166D8×C31—48no—
167D8×C31—82no—
168M16×C31—24no—
169C2×C8×C31—22no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31—42no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—22no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—22no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31C2×D412yes—
190C4⋊C4×C31C2×D412yes—
191C4⋊C4×C31C2×D411yescharacteristic
192C4⋊C4×C31C2×D411yescharacteristic
193C22⋊C4×C31—22no—
194C22⋊C4×C31—22no—
195C22⋊C4×C31—22no—
196C22⋊C4×C31—22no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—21no—
199C22⋊C4×C31—21no—
200C22⋊C4×C31—21no—
201C22⋊C4×C31—21no—
202C22⋊C4×C31—22no—
203C22⋊C4×C31—22no—
204C22⋊C4×C31—21no—
205C42×C31—22no—
206C42×C31—21no—
207C42×C31C2×D411yescharacteristic
208C42×C31C2×D411yescharacteristic
209C42×C31C2×D411yescharacteristic
210C42×C31C2411yescharacteristic
211#19016C3111yesmaximal, characteristic, direct product factor, Sylow
212C23×C31—22no—
213C23×C31—21no—
214C23×C31—42no—
215C23×C31—82no—
216C23×C31—82no—
217C23×C31—82no—
218C23×C31#12011yescharacteristic
219Q8×C31—42no—
220Q8×C31—41no—
221Q8×C31—82no—
222D4×C31—42no—
223D4×C31—41no—
224D4×C31—44no—
225D4×C31—42no—
226D4×C31—42no—
227D4×C31—44no—
228D4×C31—44no—
229D4×C31—42no—
230D4×C31—42no—
231D4×C31—81no—
232D4×C31—82no—
233D4×C31—82no—
234D4×C31—82no—
235D4×C31—82no—
236D4×C31—82no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—21no—
240C2×C4×C31—21no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—21no—
244C2×C4×C31—22no—
245C2×C4×C31—41no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—82no—
249C2×C4×C31—81no—
250C2×C4×C31—82no—
251C2×C4×C31—82no—
252C2×C4×C31—82no—
253C2×C4×C31#12011yescharacteristic
254C2×C4×C31#12011yescharacteristic
255C2×C4×C31#12011yescharacteristic
256C2×C4×C31C22×D411yescharacteristic
257C2×C4×C31C22×D411yescharacteristic
258C2×C4×C31C22×D411yescharacteristic
259C8×C31—24no—
260C8×C31—42no—
261C8×C31—42no—
262#3559C2×C3111yescharacteristic, complemented
263#3217C2×C3111yescharacteristic, complemented
264#3151C2×C3111yescharacteristic, complemented
265C2×#490C2×C3111yescharacteristic, complemented
266#1657C2×C3114yescomplemented
267#1656C2×C3114yescomplemented
268#1530C2×C3111yescharacteristic, complemented
269#1528C2×C3111yescharacteristic, complemented
270#1524C2×C3111yescharacteristic, complemented
271C22×C31—21no—
272C22×C31—21no—
273C22×C31—42no—
274C22×C31—41no—
275C22×C31—41no—
276C22×C31—42no—
277C22×C31—42no—
278C22×C31—41no—
279C22×C31—82no—
280C22×C31—82no—
281C22×C31—82no—
282C22×C31—164no—
283C22×C31#45312yes—
284C22×C31C2×#12011yescharacteristic
285C4×C31—21no—
286C4×C31—21no—
287C4×C31—21no—
288C4×C31—21no—
289C4×C31—21no—
290C4×C31—42no—
291C4×C31—42no—
292C4×C31—41no—
293C4×C31—41no—
294C4×C31—42no—
295C4×C31—41no—
296C4×C31#45412yes—
297C2×AGL(1,ℤ/8)—22no—
298#563C22×C3112yescomplemented
299#562C22×C3112yescomplemented
300#554—21no—
301#553—21no—
302#553—21no—
303#547—22no—
304#547—21no—
305#544—21no—
306#540—21no—
307#539—22no—
308#539—21no—
309#537—21no—
310#532C22×C3111yescharacteristic
311C2×#127C22×C3111yescharacteristic
312#529C22×C3111yescharacteristic
313C2×#125C22×C3111yescharacteristic
314#496C22×C3114yes—
315#496C22×C3112yes—
316#493—21no—
317#492—21no—
318#490—22no—
319#490C22×C3114yes—
320#490C22×C3112yes—
321#460—21no—
322#459—21no—
323#450—21no—
324#447—21no—
325#432C22×C3111yescharacteristic
326C2×#102—21no—
327C2×#102—21no—
328C4×M16C22×C3111yescharacteristic
329C2×#97C22×C3111yescharacteristic
330#330C22×C3114yescomplemented
331#330C22×C3112yescomplemented
332#329C22×C3112yescomplemented
333#329C22×C3114yescomplemented
334C2×C31—22no—
335C2×C31—82no—
336C2×C31—81no—
337C2×C31—162no—
338C2×C31C2×#45311yescharacteristic
339C2×C31C2×#45411yescharacteristic
340C2×C31#302111yescharacteristic
341C2×#41—22no—
342C2×#41D4×C3112yes—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346AGL(1,ℤ/8)—48no—
347C2×SD16—24no—
348C2×SD16—22no—
349C2×D8—24no—
350C2×D8—22no—
351C2×M16—21no—
352C22×C8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—22no—
355C4⋊Q8D4×C3111yescharacteristic
356#127—21no—
357#127—21no—
358#127—21no—
359#127D4×C3111yescharacteristic
360#127C23×C3112yes—
361#126—22no—
362#126—22no—
363#126—21no—
364#125—22no—
365#125—21no—
366#125—21no—
367#125—21no—
368#125D4×C3112yes—
369#125C23×C3112yes—
370#125C23×C3111yescharacteristic
371#124C23×C3111yescharacteristic
372#124C23×C3112yes—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—22no—
377#123—21no—
378#123—22no—
379#123—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8D4×C3111yescharacteristic
387#121—22no—
388#121—22no—
389#121—21no—
390#121—21no—
391#121—22no—
392#121—22no—
393#121—21no—
394#121—21no—
395#121D4×C3111yescharacteristic
396C4×Q8D4×C3111yescharacteristic
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4D4×C3111yescharacteristic
405#117—21no—
406#117—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4D4×C3111yescharacteristic
412C2×C4⋊C4D4×C3111yescharacteristic
413C2×C42C23×C3111yescharacteristic
414C4⋊C8—21no—
415#102—24no—
416#102—24no—
417#102—22no—
418#102—22no—
419C22⋊C8—21no—
420#97—21no—
421#97C23×C3112yes—
422#97C23×C3112yes—
423#97C23×C3112yes—
424C4×C8—21no—
425C31#1901611yescharacteristic, direct product factor, Sylow
426C24—41no—
427#41—44no—
428#41—84no—
429C2×Q8—22no—
430C2×Q8C2×D4×C3111yescharacteristic
431C2×Q8C2×D4×C3112yes—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—82no—
447C2×D4C2×D4×C3111yescharacteristic
448C2×D4C2×D4×C3112yes—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4C2×D4×C3111yescharacteristic
457C22×C4C2×D4×C3111yescharacteristic
458C22×C4C2×D4×C3111yescharacteristic
459SD16—48no—
460SD16—82no—
461D8—48no—
462D8—82no—
463M16—24no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—42no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4C2×D4×C3112yes—
485C4⋊C4C2×D4×C3112yes—
486C4⋊C4C2×D4×C3111yescharacteristic
487C4⋊C4C2×D4×C3111yescharacteristic
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C42—22no—
501C42—21no—
502C42C2×D4×C3111yescharacteristic
503C42C2×D4×C3111yescharacteristic
504C42C2×D4×C3111yescharacteristic
505C42C24×C3111yescharacteristic
506C23—22no—
507C23—21no—
508C23—42no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23C31×#12011yescharacteristic
513Q8—42no—
514Q8—41no—
515Q8—82no—
516D4—42no—
517D4—41no—
518D4—44no—
519D4—42no—
520D4—42no—
521D4—44no—
522D4—44no—
523D4—42no—
524D4—42no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—82no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—82no—
543C2×C4—81no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4C31×#12011yescharacteristic
548C2×C4C31×#12011yescharacteristic
549C2×C4C31×#12011yescharacteristic
550C2×C4C22×D4×C3111yescharacteristic
551C2×C4C22×D4×C3111yescharacteristic
552C2×C4C22×D4×C3111yescharacteristic
553C8—24no—
554C8—42no—
555C8—42no—
556C22—21no—
557C22—21no—
558C22—42no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—164no—
568C22C31×#45312yes—
569C22C2×C31×#12011yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4C31×#45412yes—
582C2—22no—
583C2—82no—
584C2—81no—
585C2—162no—
586C2C2×C31×#45311yescharacteristic
587C2C2×C31×#45411yescharacteristic
588C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
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
1. C31×#3559C2semidirect
2. C31×#3217C2semidirect
3. C31×#3151C2semidirect
4. C2×C31×#490C2semidirect
5. C31×#1657C2semidirect
6. C31×#1656C2semidirect
7. C31×#1530C2semidirect
8. C31×#1528C2semidirect
9. C31×#1524C2semidirect
11. C31×#563C22semidirect
12. C31×#562C22semidirect
43. C31×#330C22semidirect
44. C31×#330C22semidirect
45. C31×#329C22semidirect
46. C31×#329C22semidirect
211. #19016C31direct (N × H)
262. #3559C2×C31semidirect
263. #3217C2×C31semidirect
264. #3151C2×C31semidirect
265. C2×#490C2×C31semidirect
266. #1657C2×C31semidirect
267. #1656C2×C31semidirect
268. #1530C2×C31semidirect
269. #1528C2×C31semidirect
270. #1524C2×C31semidirect
298. #563C22×C31semidirect
299. #562C22×C31semidirect
330. #330C22×C31semidirect
331. #330C22×C31semidirect
332. #329C22×C31semidirect
333. #329C22×C31semidirect
425. C31#19016direct (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×#32172
C31×#31512
C2×C31×#4902
C31×#16572
C31×#16562
C31×#15302
C31×#15282
C31×#15242
#1901631