Finite Group Databasebeta

← C31×#18430 #21475189

Subgroups — C31×#18430 #21475189

Order 7936.

996 conjugacy classes of subgroups.

The subgroup lattice has 594 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×#3205C211yesmaximal, characteristic, complemented
4C31×#2641C211yesmaximal, characteristic, complemented
5C31×#1598C214yesmaximal, complemented
6C31×#1597C214yesmaximal, complemented
7C31×#1505C211yesmaximal, characteristic, complemented
8C31×#1500C211yesmaximal, characteristic, complemented
9C31×#1470C211yesmaximal, characteristic, complemented
10C31×#563—21no—
11C31×#562—21no—
12C31×#554—21no—
13C31×#553—21no—
14C31×#553—21no—
15C31×#547—22no—
16C31×#547—21no—
17C31×#544—21no—
18C31×#540—21no—
19C31×#539—22no—
20C31×#539C2212yes—
21C31×#537C2212yes—
22C31×#532C2211yescharacteristic
23C2×C31×#127C2211yescharacteristic
24C31×#529C2211yescharacteristic
25C2×C31×#125C2211yescharacteristic
26C31×#496—21no—
27C31×#493—21no—
28C31×#490—21no—
29C31×#486—21no—
30C31×#460—21no—
31C31×#459—22no—
32C31×#459—21no—
33C31×#450C2212yes—
34C31×#447C2214yes—
35C31×#447C2212yes—
36C31×#432C2211yescharacteristic
37C31×#431C2211yescharacteristic
38C31×#394—22no—
39C31×#394C2214yes—
40C31×#390—21no—
41C31×#390—21no—
42C31×#376C2211yescharacteristic
43C31×#328C2212yes—
44C31×#327C2214yes—
45C31×#327C2212yes—
46C31×#324C2214yes—
47C2×#41×C31—21no—
48C2×#41×C31—22no—
49C22×D4×C31—21no—
50C22×D4×C31—21no—
51C22×D4×C31C2312yes—
52C2×SD16×C31—22no—
53C2×D8×C31—24no—
54C2×D8×C31—22no—
55C31×C4⋊Q8—21no—
56C31×C4⋊Q8—22no—
57C31×C4⋊Q8D411yescharacteristic
58C31×#127—21no—
59C31×#127—21no—
60C31×#127—21no—
61C31×#127—21no—
62C31×#127D411yescharacteristic
63C31×#126—22no—
64C31×#126—22no—
65C31×#126—21no—
66C31×#125—21no—
67C31×#125—22no—
68C31×#125—21no—
69C31×#125—21no—
70C31×#125—21no—
71C31×#125—21no—
72C31×#125D411yescharacteristic
73C31×#124—21no—
74C31×#124D411yescharacteristic
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×#123—22no—
79C31×#123—22no—
80C31×#123—21no—
81C31×#123—22no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8C2311yescharacteristic
89C31×#121—21no—
90C31×#121—22no—
91C31×#121—21no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—21no—
95C31×#121—22no—
96C31×#121C2311yescharacteristic
97C31×#121C2312yes—
98C4×Q8×C31D411yescharacteristic
99C4×D4×C31—22no—
100C4×D4×C31—21no—
101C4×D4×C31—21no—
102C4×D4×C31—21no—
103C4×D4×C31—22no—
104C4×D4×C31—21no—
105C4×D4×C31D411yescharacteristic
106C4×D4×C31D412yes—
107C31×#117—21no—
108C31×#117—21no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31D412yes—
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C4⋊C4×C31C2312yes—
115C2×C22⋊C4×C31—24no—
116C2×C22⋊C4×C31—24no—
117C2×C42×C31—21no—
118C2×C42×C31C2311yescharacteristic
119C31×C4⋊C8—21no—
120C31×C4⋊C8—21no—
121C31×#102—24no—
122C31×#102—22no—
123C31×#102—22no—
124C31×C22⋊C8C2312yes—
125C31×C22⋊C8C2312yes—
126C31×#97—21no—
127C4×C8×C31—21no—
128C31×#95—21no—
129C31×#95C2312yes—
130C24×C31—22no—
131#41×C31—82no—
132#41×C31—84no—
133C2×Q8×C31—22no—
134C2×Q8×C31—21no—
135C2×Q8×C31C2×D411yescharacteristic
136C2×D4×C31—21no—
137C2×D4×C31—22no—
138C2×D4×C31—22no—
139C2×D4×C31—22no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—22no—
143C2×D4×C31—22no—
144C2×D4×C31—44no—
145C2×D4×C31—41no—
146C2×D4×C31—41no—
147C2×D4×C31—41no—
148C2×D4×C31—41no—
149C2×D4×C31—82no—
150C2×D4×C31—82no—
151C2×D4×C31C2×D411yescharacteristic
152C2×D4×C31C2×D412yes—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31C2×D412yes—
160C22×C4×C31C2×D411yescharacteristic
161C22×C4×C31C2×D411yescharacteristic
162C22×C4×C31C2×D412yes—
163C22×C4×C31C2411yescharacteristic
164SD16×C31—82no—
165D8×C31—84no—
166D8×C31—82no—
167C2×C8×C31—22no—
168C2×C8×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—22no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—21no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—21no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31C2×D412yes—
187C4⋊C4×C31C2×D411yescharacteristic
188C4⋊C4×C31C2×D411yescharacteristic
189C22⋊C4×C31—22no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—22no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—22no—
194C22⋊C4×C31—21no—
195C22⋊C4×C31—21no—
196C22⋊C4×C31—21no—
197C22⋊C4×C31—21no—
198C22⋊C4×C31—22no—
199C22⋊C4×C31—21no—
200C22⋊C4×C31—22no—
201C22⋊C4×C31—84no—
202C22⋊C4×C31—84no—
203C42×C31—22no—
204C42×C31—21no—
205C42×C31—42no—
206C42×C31C2×D411yescharacteristic
207C42×C31C2×D411yescharacteristic
208C42×C31C2×D411yescharacteristic
209C42×C31C2×D411yescharacteristic
210#18430C3111yesmaximal, characteristic, direct product factor, Sylow
211C23×C31—21no—
212C23×C31—22no—
213C23×C31—44no—
214C23×C31—44no—
215C23×C31—42no—
216C23×C31—44no—
217C23×C31C22×D411yescharacteristic
218Q8×C31—41no—
219Q8×C31—81no—
220Q8×C31—82no—
221D4×C31—42no—
222D4×C31—41no—
223D4×C31—44no—
224D4×C31—42no—
225D4×C31—42no—
226D4×C31—44no—
227D4×C31—42no—
228D4×C31—42no—
229D4×C31—81no—
230D4×C31—82no—
231D4×C31—82no—
232D4×C31—82no—
233D4×C31—82no—
234D4×C31—82no—
235D4×C31—82no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—21no—
239C2×C4×C31—21no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—21no—
243C2×C4×C31—22no—
244C2×C4×C31—24no—
245C2×C4×C31—41no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—82no—
252C2×C4×C31—82no—
253C2×C4×C31—82no—
254C2×C4×C31—82no—
255C2×C4×C31#12011yescharacteristic
256C2×C4×C31#12011yescharacteristic
257C2×C4×C31#12011yescharacteristic
258C2×C4×C31#12011yescharacteristic
259C2×C4×C31C22×D411yescharacteristic
260C2×C4×C31C22×D411yescharacteristic
261C8×C31—42no—
262C8×C31—42no—
263#3559C2×C3111yescharacteristic, complemented
264#3217C2×C3111yescharacteristic, complemented
265#3205C2×C3111yescharacteristic, complemented
266#2641C2×C3111yescharacteristic, complemented
267#1598C2×C3114yescomplemented
268#1597C2×C3114yescomplemented
269#1505C2×C3111yescharacteristic, complemented
270#1500C2×C3111yescharacteristic, complemented
271#1470C2×C3111yescharacteristic, complemented
272C22×C31—21no—
273C22×C31—21no—
274C22×C31—42no—
275C22×C31—41no—
276C22×C31—41no—
277C22×C31—42no—
278C22×C31—42no—
279C22×C31—41no—
280C22×C31—88no—
281C22×C31—82no—
282C22×C31—82no—
283C22×C31—82no—
284C22×C31C2×#12011yescharacteristic
285C22×C31#57612yes—
286C4×C31—21no—
287C4×C31—21no—
288C4×C31—21no—
289C4×C31—21no—
290C4×C31—21no—
291C4×C31—42no—
292C4×C31—42no—
293C4×C31—41no—
294C4×C31—41no—
295C4×C31—42no—
296C4×C31—41no—
297C4×C31—82no—
298C4×C31#45412yes—
299#563—21no—
300#562—21no—
301#554—21no—
302#553—21no—
303#553—21no—
304#547—22no—
305#547—21no—
306#544—21no—
307#540—21no—
308#539—22no—
309#539C22×C3112yes—
310#537C22×C3112yes—
311#532C22×C3111yescharacteristic
312C2×#127C22×C3111yescharacteristic
313#529C22×C3111yescharacteristic
314C2×#125C22×C3111yescharacteristic
315#496—21no—
316#493—21no—
317#490—21no—
318#486—21no—
319#460—21no—
320#459—22no—
321#459—21no—
322#450C22×C3112yes—
323#447C22×C3114yes—
324#447C22×C3112yes—
325#432C22×C3111yescharacteristic
326#431C22×C3111yescharacteristic
327#394—22no—
328#394C22×C3114yes—
329#390—21no—
330#390—21no—
331#376C22×C3111yescharacteristic
332#328C22×C3112yes—
333#327C22×C3114yes—
334#327C22×C3112yes—
335#324C22×C3114yes—
336C2×C31—22no—
337C2×C31—81no—
338C2×C31—82no—
339C2×C31—162no—
340C2×C31#300811yescharacteristic
341C2×C31C2×#45411yescharacteristic
342C2×C31#302711yescharacteristic
343C2×#41—21no—
344C2×#41—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4C23×C3112yes—
348C2×SD16—22no—
349C2×D8—24no—
350C2×D8—22no—
351C4⋊Q8—21no—
352C4⋊Q8—22no—
353C4⋊Q8D4×C3111yescharacteristic
354#127—21no—
355#127—21no—
356#127—21no—
357#127—21no—
358#127D4×C3111yescharacteristic
359#126—22no—
360#126—22no—
361#126—21no—
362#125—21no—
363#125—22no—
364#125—21no—
365#125—21no—
366#125—21no—
367#125—21no—
368#125D4×C3111yescharacteristic
369#124—21no—
370#124D4×C3111yescharacteristic
371#123—22no—
372#123—22no—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—21no—
377#123—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8C23×C3111yescharacteristic
385#121—21no—
386#121—22no—
387#121—21no—
388#121—22no—
389#121—22no—
390#121—21no—
391#121—22no—
392#121C23×C3111yescharacteristic
393#121C23×C3112yes—
394C4×Q8D4×C3111yescharacteristic
395C4×D4—22no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4D4×C3111yescharacteristic
402C4×D4D4×C3112yes—
403#117—21no—
404#117—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4D4×C3111yescharacteristic
408C2×C4⋊C4D4×C3112yes—
409C2×C4⋊C4D4×C3111yescharacteristic
410C2×C4⋊C4C23×C3112yes—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C42—21no—
414C2×C42C23×C3111yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—21no—
417#102—24no—
418#102—22no—
419#102—22no—
420C22⋊C8C23×C3112yes—
421C22⋊C8C23×C3112yes—
422#97—21no—
423C4×C8—21no—
424#95—21no—
425#95C23×C3112yes—
426C31#1843011yescharacteristic, direct product factor, Sylow
427C24—22no—
428#41—82no—
429#41—84no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8C2×D4×C3111yescharacteristic
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—44no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—82no—
447C2×D4—82no—
448C2×D4C2×D4×C3111yescharacteristic
449C2×D4C2×D4×C3112yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4C2×D4×C3112yes—
457C22×C4C2×D4×C3111yescharacteristic
458C22×C4C2×D4×C3111yescharacteristic
459C22×C4C2×D4×C3112yes—
460C22×C4C24×C3111yescharacteristic
461SD16—82no—
462D8—84no—
463D8—82no—
464C2×C8—22no—
465C2×C8—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4C2×D4×C3112yes—
484C4⋊C4C2×D4×C3111yescharacteristic
485C4⋊C4C2×D4×C3111yescharacteristic
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—84no—
499C22⋊C4—84no—
500C42—22no—
501C42—21no—
502C42—42no—
503C42C2×D4×C3111yescharacteristic
504C42C2×D4×C3111yescharacteristic
505C42C2×D4×C3111yescharacteristic
506C42C2×D4×C3111yescharacteristic
507C23—21no—
508C23—22no—
509C23—44no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23C22×D4×C3111yescharacteristic
514Q8—41no—
515Q8—81no—
516Q8—82no—
517D4—42no—
518D4—41no—
519D4—44no—
520D4—42no—
521D4—42no—
522D4—44no—
523D4—42no—
524D4—42no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—82no—
531D4—82no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4C31×#12011yescharacteristic
552C2×C4C31×#12011yescharacteristic
553C2×C4C31×#12011yescharacteristic
554C2×C4C31×#12011yescharacteristic
555C2×C4C22×D4×C3111yescharacteristic
556C2×C4C22×D4×C3111yescharacteristic
557C8—42no—
558C8—42no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—88no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22C2×C31×#12011yescharacteristic
572C22C31×#57612yes—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—82no—
585C4C31×#45412yes—
586C2—22no—
587C2—81no—
588C2—82no—
589C2—162no—
590C2C31×#300811yescharacteristic
591C2C2×C31×#45411yescharacteristic
592C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ 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×#3205C2semidirect
4. C31×#2641C2semidirect
5. C31×#1598C2semidirect
6. C31×#1597C2semidirect
7. C31×#1505C2semidirect
8. C31×#1500C2semidirect
9. C31×#1470C2semidirect
210. #18430C31direct (N × H)
263. #3559C2×C31semidirect
264. #3217C2×C31semidirect
265. #3205C2×C31semidirect
266. #2641C2×C31semidirect
267. #1598C2×C31semidirect
268. #1597C2×C31semidirect
269. #1505C2×C31semidirect
270. #1500C2×C31semidirect
271. #1470C2×C31semidirect
426. C31#18430direct (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×#32052
C31×#26412
C31×#15982
C31×#15972
C31×#15052
C31×#15002
C31×#14702
#1843031