Finite Group Databasebeta

← C31×#18382 #21475141

Subgroups — C31×#18382 #21475141

Order 7936.

1056 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic, complemented
2C31×#3187C212yesmaximal, complemented
3C31×#2543C211yesmaximal, characteristic
4C31×#1611C212yesmaximal, complemented
5C31×#1608C212yesmaximal, complemented
6C31×#1599C212yesmaximal, complemented
7C31×#1596C212yesmaximal, complemented
8C2×C31×#328C212yesmaximal, complemented
9C31×#1459C211yesmaximal, characteristic, complemented
10C31×#554—24no—
11C31×#554—22no—
12D4×Q8×C31—22no—
13C31×#544C2212yes—
14C31×#543—21no—
15C31×#543C2212yes—
16C31×#533—21no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8C2212yes—
19C2×C31×#121—21no—
20C2×C31×#121C2211yescharacteristic
21C31×#518—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C31×#483C2214yes—
24C31×#481—22no—
25C31×#465—24no—
26C31×#450C2214yes—
27C31×#448—22no—
28C2×C31×C22⋊C8C2212yes—
29C31×#398C2211yescharacteristic
30C31×#397C2211yescharacteristic
31C31×#394C2211yescharacteristic
32C31×#392C2211yescharacteristic
33C31×#388—21no—
34C31×#386—21no—
35C31×#386—21no—
36C2×C31×#95C2211yescharacteristic
37C31×#328C2214yes—
38C31×#328C2214yes—
39C31×#324C2212yes—
40C31×#323C2212yes—
41C22×Q8×C31—21no—
42C22×Q8×C31D412yescomplemented
43C22×D4×C31—21no—
44C22×D4×C31—21no—
45C22×D4×C31D411yescharacteristic
46C22×D4×C31C2311yescharacteristic
47C23×C4×C31—21no—
48C23×C4×C31D411yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C2×SD16×C31—24no—
51C22×C8×C31—22no—
52C31×C4⋊Q8—21no—
53C31×C4⋊Q8—21no—
54C31×C4⋊Q8—24no—
55C31×#125—22no—
56C31×#125—24no—
57C31×C22⋊Q8—22no—
58C31×C22⋊Q8—22no—
59C31×C22⋊Q8—24no—
60C31×C22⋊Q8—24no—
61C31×C22⋊Q8—24no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—22no—
64C31×C22⋊Q8—22no—
65C31×C22⋊Q8—22no—
66C31×C22⋊Q8—24no—
67C31×C22⋊Q8D414yescomplemented
68C31×C22⋊Q8C2314yes—
69C31×#121—22no—
70C31×#121—22no—
71C31×#121—44no—
72C4×Q8×C31—22no—
73C4×Q8×C31—22no—
74C4×D4×C31—24no—
75C4×D4×C31—24no—
76C4×D4×C31—22no—
77C4×D4×C31—22no—
78C31×#117—22no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31D412yescomplemented
84C2×C4⋊C4×C31C2311yescharacteristic
85C2×C4⋊C4×C31C2311yescharacteristic
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—21no—
93C2×C22⋊C4×C31D411yescharacteristic
94C2×C22⋊C4×C31C2311yescharacteristic
95C2×C42×C31D411yescharacteristic
96C31×#106—24no—
97C31×#103—24no—
98C31×#102—24no—
99C31×C22⋊C8—22no—
100C31×C22⋊C8C2314yes—
101C31×#95—21no—
102C31×#95—21no—
103C31×#95—21no—
104C31×#95C2311yescharacteristic
105C31×#95C2311yescharacteristic
106C24×C31—21no—
107C24×C31C2×D411yescharacteristic
108C24×C31C2×D411yescharacteristic
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—22no—
112C2×Q8×C31—82no—
113C2×Q8×C31—82no—
114C2×Q8×C31C2×D414yes—
115C2×D4×C31—22no—
116C2×D4×C31—22no—
117C2×D4×C31—22no—
118C2×D4×C31—42no—
119C2×D4×C31—42no—
120C2×D4×C31—42no—
121C2×D4×C31—42no—
122C2×D4×C31—42no—
123C2×D4×C31—81no—
124C2×D4×C31—81no—
125C2×D4×C31SD1614yescomplemented
126C22×C4×C31—21no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—42no—
136C22×C4×C31—42no—
137C22×C4×C31—81no—
138C22×C4×C31—81no—
139C22×C4×C31—81no—
140C22×C4×C31C2×D411yescharacteristic
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2411yescharacteristic
147SD16×C31—84no—
148C2×C8×C31—24no—
149C2×C8×C31—82no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—24no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—24no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—24no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—24no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—42no—
162C4⋊C4×C31C2×D414yes—
163C22⋊C4×C31—24no—
164C22⋊C4×C31—24no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—24no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—42no—
169C22⋊C4×C31—42no—
170C22⋊C4×C31—41no—
171C22⋊C4×C31—41no—
172C22⋊C4×C31—42no—
173C22⋊C4×C31—81no—
174C42×C31—24no—
175C42×C31—21no—
176C42×C31—21no—
177#18382C3111yesmaximal, characteristic, direct product factor, Sylow
178C23×C31—21no—
179C23×C31—21no—
180C23×C31—41no—
181C23×C31—41no—
182C23×C31—41no—
183C23×C31—41no—
184C23×C31—41no—
185C23×C31—41no—
186C23×C31—41no—
187C23×C31—41no—
188C23×C31—41no—
189C23×C31—41no—
190C23×C31—41no—
191C23×C31#12012yes—
192C23×C31C2×SD1612yes—
193C23×C31C2×SD1612yes—
194C23×C31#13712yes—
195C23×C31C22×D411yescharacteristic
196Q8×C31—44no—
197Q8×C31—44no—
198Q8×C31—82no—
199Q8×C31—82no—
200D4×C31—28no—
201D4×C31—44no—
202D4×C31—84no—
203D4×C31—84no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—22no—
207C2×C4×C31—21no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—21no—
211C2×C4×C31—42no—
212C2×C4×C31—41no—
213C2×C4×C31—42no—
214C2×C4×C31—41no—
215C2×C4×C31—42no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—81no—
227C2×C4×C31—82no—
228C2×C4×C31—82no—
229C2×C4×C31—82no—
230C2×C4×C31—82no—
231C2×C4×C31—84no—
232C2×C4×C31#12011yescharacteristic
233C2×C4×C31#12011yescharacteristic
234C2×C4×C31C2×SD1612yes—
235C2×C4×C31C22×D412yes—
236C8×C31—44no—
237#3501C2×C3111yescharacteristic, complemented
238#3187C2×C3112yescomplemented
239#2543C2×C3111yescharacteristic
240#1611C2×C3112yescomplemented
241#1608C2×C3112yescomplemented
242#1599C2×C3112yescomplemented
243#1596C2×C3112yescomplemented
244C2×#328C2×C3112yescomplemented
245#1459C2×C3111yescharacteristic, complemented
246C22×C31—21no—
247C22×C31—22no—
248C22×C31—21no—
249C22×C31—22no—
250C22×C31—22no—
251C22×C31—42no—
252C22×C31—42no—
253C22×C31—42no—
254C22×C31—41no—
255C22×C31—41no—
256C22×C31—81no—
257C22×C31—81no—
258C22×C31—81no—
259C22×C31—81no—
260C22×C31—81no—
261C22×C31—81no—
262C22×C31—81no—
263C22×C31—81no—
264C22×C31#44814yes—
265C22×C31C2×#12011yescharacteristic
266C22×C31C22×SD1611yescharacteristic
267C22×C31C2×#13711yescharacteristic
268C4×C31—22no—
269C4×C31—22no—
270C4×C31—21no—
271C4×C31—21no—
272C4×C31—42no—
273C4×C31—41no—
274C4×C31—44no—
275C4×C31—41no—
276C4×C31—44no—
277C4×C31—81no—
278C4×C31—81no—
279#554—24no—
280#554—22no—
281D4×Q8—22no—
282#544C22×C3112yes—
283#543—21no—
284#543C22×C3112yes—
285#533—21no—
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8C22×C3112yes—
288C2×#121—21no—
289C2×#121C22×C3111yescharacteristic
290#518—21no—
291C2×C4×D4C22×C3111yescharacteristic
292#483C22×C3114yes—
293#481—22no—
294#465—24no—
295#450C22×C3114yes—
296#448—22no—
297C2×C22⋊C8C22×C3112yes—
298#398C22×C3111yescharacteristic
299#397C22×C3111yescharacteristic
300#394C22×C3111yescharacteristic
301#392C22×C3111yescharacteristic
302#388—21no—
303#386—21no—
304#386—21no—
305C2×#95C22×C3111yescharacteristic
306#328C22×C3114yes—
307#328C22×C3114yes—
308#324C22×C3112yes—
309#323C22×C3112yes—
310C2×C31—21no—
311C2×C31—21no—
312C2×C31—24no—
313C2×C31—42no—
314C2×C31—161no—
315C2×C31C2×#44811yescharacteristic
316C2×C31#301811yescharacteristic
317C2×C31#302611yescharacteristic
318C22×Q8—21no—
319C22×Q8D4×C3112yescomplemented
320C22×D4—21no—
321C22×D4—21no—
322C22×D4D4×C3111yescharacteristic
323C22×D4C23×C3111yescharacteristic
324C23×C4—21no—
325C23×C4D4×C3111yescharacteristic
326C23×C4C23×C3111yescharacteristic
327C2×SD16—24no—
328C22×C8—22no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8—24no—
332#125—22no—
333#125—24no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—24no—
344C22⋊Q8D4×C3114yescomplemented
345C22⋊Q8C23×C3114yes—
346#121—22no—
347#121—22no—
348#121—44no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—22no—
354C4×D4—22no—
355#117—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4D4×C3112yescomplemented
361C2×C4⋊C4C23×C3111yescharacteristic
362C2×C4⋊C4C23×C3111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4D4×C3111yescharacteristic
371C2×C22⋊C4C23×C3111yescharacteristic
372C2×C42D4×C3111yescharacteristic
373#106—24no—
374#103—24no—
375#102—24no—
376C22⋊C8—22no—
377C22⋊C8C23×C3114yes—
378#95—21no—
379#95—21no—
380#95—21no—
381#95C23×C3111yescharacteristic
382#95C23×C3111yescharacteristic
383C31#1838211yescharacteristic, direct product factor, Sylow
384C24—21no—
385C24C2×D4×C3111yescharacteristic
386C24C2×D4×C3111yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—82no—
391C2×Q8—82no—
392C2×Q8C2×D4×C3114yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—81no—
402C2×D4—81no—
403C2×D4SD16×C3114yescomplemented
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4—81no—
418C22×C4C2×D4×C3111yescharacteristic
419C22×C4C2×D4×C3111yescharacteristic
420C22×C4C2×D4×C3111yescharacteristic
421C22×C4C2×D4×C3111yescharacteristic
422C22×C4C2×D4×C3112yes—
423C22×C4C2×D4×C3112yes—
424C22×C4C24×C3111yescharacteristic
425SD16—84no—
426C2×C8—24no—
427C2×C8—82no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4C2×D4×C3114yes—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—42no—
447C22⋊C4—42no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—42no—
451C22⋊C4—81no—
452C42—24no—
453C42—21no—
454C42—21no—
455C23—21no—
456C23—21no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23C31×#12012yes—
469C23C2×SD16×C3112yes—
470C23C2×SD16×C3112yes—
471C23C31×#13712yes—
472C23C22×D4×C3111yescharacteristic
473Q8—44no—
474Q8—44no—
475Q8—82no—
476Q8—82no—
477D4—28no—
478D4—44no—
479D4—84no—
480D4—84no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—21no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—81no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4—84no—
509C2×C4C31×#12011yescharacteristic
510C2×C4C31×#12011yescharacteristic
511C2×C4C2×SD16×C3112yes—
512C2×C4C22×D4×C3112yes—
513C8—44no—
514C22—21no—
515C22—22no—
516C22—21no—
517C22—22no—
518C22—22no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22C31×#44814yes—
533C22C2×C31×#12011yescharacteristic
534C22C22×SD16×C3111yescharacteristic
535C22C2×C31×#13711yescharacteristic
536C4—22no—
537C4—22no—
538C4—21no—
539C4—21no—
540C4—42no—
541C4—41no—
542C4—44no—
543C4—41no—
544C4—44no—
545C4—81no—
546C4—81no—
547C2—21no—
548C2—21no—
549C2—24no—
550C2—42no—
551C2—161no—
552C2C2×C31×#44811yescharacteristic
553C2C31×#301811yescharacteristic
554C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2543C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3501C2semidirect
2. C31×#3187C2semidirect
4. C31×#1611C2semidirect
5. C31×#1608C2semidirect
6. C31×#1599C2semidirect
7. C31×#1596C2semidirect
8. C2×C31×#328C2semidirect
9. C31×#1459C2semidirect
42. C22×Q8×C31D4semidirect
67. C31×C22⋊Q8D4semidirect
83. C2×C4⋊C4×C31D4semidirect
125. C2×D4×C31SD16semidirect
177. #18382C31direct (N × H)
237. #3501C2×C31semidirect
238. #3187C2×C31semidirect
240. #1611C2×C31semidirect
241. #1608C2×C31semidirect
242. #1599C2×C31semidirect
243. #1596C2×C31semidirect
244. C2×#328C2×C31semidirect
245. #1459C2×C31semidirect
319. C22×Q8D4×C31semidirect
344. C22⋊Q8D4×C31semidirect
360. C2×C4⋊C4D4×C31semidirect
383. C31#18382direct (N × H)
403. C2×D4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#31872
C31×#25432
C31×#16112
C31×#16082
C31×#15992
C31×#15962
C2×C31×#3282
C31×#14592
#1838231