Finite Group Databasebeta

← C31×#9239 #21465998

Subgroups — C31×#9239 #21465998

Order 7936.

686 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#452C211yesmaximal, characteristic
2C31×#2880C211yesmaximal, characteristic
3C31×#1789C211yesmaximal, characteristic
4C31×#1508C211yesmaximal, characteristic, complemented
5C31×#1472C211yesmaximal, characteristic, complemented
6C31×#1293C211yesmaximal, characteristic, complemented
7C31×#1282C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×Q16×C31C411yescharacteristic, complemented
10C22×SD16×C31C411yescharacteristic, complemented
11C2×C31×#131—21no—
12C2×C31×C22⋊Q8C2211yescharacteristic
13C31×#452—21no—
14C31×#452—21no—
15C31×#452—21no—
16C31×#452—21no—
17C2×C31×#104—21no—
18C2×C31×#104—21no—
19C2×C31×#103C411yescharacteristic, complemented
20C2×C31×#102C411yescharacteristic, complemented
21C31×#408—21no—
22C31×#408—22no—
23C31×#407—21no—
24C31×#407C2211yescharacteristic
25C31×#407C2211yescharacteristic
26C2×C31×C22⋊C8—21no—
27C2×C31×C22⋊C8C2211yescharacteristic
28C2×C31×C22⋊C8C2211yescharacteristic
29C4×C22⋊C4×C31C2211yescharacteristic
30C31×#328—22no—
31C31×#324—21no—
32C31×#324—21no—
33C2×#41×C31—21no—
34C2×#41×C31—21no—
35C2×#41×C31—42no—
36C2×#41×C31—42no—
37C2×#41×C31D411yescharacteristic
38C2×#41×C31D411yescharacteristic
39C2×#41×C31D411yescharacteristic
40C2×#41×C31D411yescharacteristic
41C22×Q8×C31C2×C411yescharacteristic
42C22×Q8×C31C2×C411yescharacteristic
43C22×D4×C31—21no—
44C22×D4×C31C2×C411yescharacteristic
45C23×C4×C31—21no—
46C23×C4×C31C2311yescharacteristic
47C2×Q16×C31—21no—
48C2×Q16×C31—21no—
49C2×Q16×C31—42no—
50C2×SD16×C31—21no—
51C2×SD16×C31—21no—
52C2×SD16×C31—42no—
53C31×#131—42no—
54C31×#131—42no—
55C2×M16×C31—22no—
56C2×M16×C31—21no—
57C2×M16×C31—21no—
58C22×C8×C31—22no—
59C22×C8×C31—21no—
60C22×C8×C31C2×C411yescharacteristic
61C22×C8×C31C2×C411yescharacteristic
62C31×C22⋊Q8—21no—
63C31×C22⋊Q8—21no—
64C31×C22⋊Q8—21no—
65C31×C22⋊Q8—21no—
66C2×C4⋊C4×C31—21no—
67C2×C4⋊C4×C31C2×C411yescharacteristic
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—21no—
70C2×C42×C31—21no—
71C31×#104—42no—
72C31×#104—42no—
73C31×#103—21no—
74C31×#103—21no—
75C31×#102—21no—
76C31×#102—21no—
77C31×C22⋊C8—22no—
78C31×C22⋊C8—22no—
79C31×C22⋊C8—21no—
80C31×C22⋊C8—21no—
81C31×C22⋊C8—21no—
82C31×C22⋊C8—21no—
83C31×C22⋊C8—21no—
84C31×C22⋊C8—21no—
85C31×C22⋊C8D411yescharacteristic
86C31×C22⋊C8D411yescharacteristic
87C31×C22⋊C8D412yes—
88C31×#95—21no—
89C24×C31—21no—
90C24×C31#4111yescharacteristic
91#41×C31—22no—
92#41×C31—22no—
93#41×C31—22no—
94#41×C31—22no—
95#41×C31—41no—
96#41×C31—41no—
97#41×C31—41no—
98#41×C31—41no—
99#41×C31—44no—
100#41×C31—44no—
101C2×Q8×C31—21no—
102C2×Q8×C31—22no—
103C2×Q8×C31—21no—
104C2×Q8×C31—21no—
105C2×Q8×C31—41no—
106C2×Q8×C31—41no—
107C2×Q8×C31—41no—
108C2×Q8×C31C22⋊C411yescharacteristic
109C2×Q8×C31C22⋊C411yescharacteristic
110C2×D4×C31—21no—
111C2×D4×C31—22no—
112C2×D4×C31—21no—
113C2×D4×C31—21no—
114C2×D4×C31—21no—
115C2×D4×C31—21no—
116C2×D4×C31—41no—
117C2×D4×C31—44no—
118C2×D4×C31C22⋊C411yescharacteristic
119C2×D4×C31C22⋊C411yescharacteristic
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—41no—
128C22×C4×C31—41no—
129C22×C4×C31—44no—
130C22×C4×C31—41no—
131C22×C4×C31C22×C411yescharacteristic
132C22×C4×C31C2×D411yescharacteristic
133C22×C4×C31C2×D411yescharacteristic
134C22×C4×C31C2×D411yescharacteristic
135C22×C4×C31C2×D411yescharacteristic
136C22×C4×C31#4111yescharacteristic
137Q16×C31—42no—
138Q16×C31—42no—
139SD16×C31—42no—
140SD16×C31—42no—
141M16×C31—44no—
142M16×C31—41no—
143M16×C31—41no—
144M16×C31—41no—
145M16×C31—41no—
146C2×C8×C31—21no—
147C2×C8×C31—21no—
148C2×C8×C31—21no—
149C2×C8×C31—22no—
150C2×C8×C31—21no—
151C2×C8×C31—44no—
152C2×C8×C31—41no—
153C2×C8×C31—41no—
154C2×C8×C31—41no—
155C2×C8×C31—41no—
156C2×C8×C31—41no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—41no—
160C4⋊C4×C31—41no—
161C22⋊C4×C31—22no—
162C22⋊C4×C31—41no—
163C22⋊C4×C31—41no—
164C22⋊C4×C31—41no—
165C42×C31—41no—
166C42×C31—41no—
167#9239C3111yesmaximal, characteristic, direct product factor, Sylow
168C23×C31—21no—
169C23×C31—21no—
170C23×C31—21no—
171C23×C31—21no—
172C23×C31—41no—
173C23×C31—41no—
174C23×C31—42no—
175C23×C31—41no—
176C23×C31—41no—
177C23×C31—81no—
178C23×C31C4×D411yescharacteristic
179C23×C31#12111yescharacteristic
180C23×C31#12311yescharacteristic
181Q8×C31—21no—
182Q8×C31—21no—
183Q8×C31—21no—
184Q8×C31—42no—
185Q8×C31—41no—
186Q8×C31—41no—
187Q8×C31—81no—
188Q8×C31#9912yes—
189D4×C31—24no—
190D4×C31—21no—
191D4×C31—21no—
192D4×C31—21no—
193D4×C31—42no—
194D4×C31—42no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31#9912yes—
198C2×C4×C31—24no—
199C2×C4×C31—21no—
200C2×C4×C31—21no—
201C2×C4×C31—21no—
202C2×C4×C31—21no—
203C2×C4×C31—21no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—21no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—41no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—81no—
220C2×C4×C31—81no—
221C2×C4×C31—81no—
222C2×C4×C31C2×C22⋊C411yescharacteristic
223C2×C4×C31C4×D411yescharacteristic
224C2×C4×C31#12011yescharacteristic
225C2×C4×C31#12111yescharacteristic
226C8×C31—41no—
227C8×C31—42no—
228C8×C31—41no—
229C8×C31—41no—
230C8×C31—41no—
231C8×C31—81no—
232C2×#452C2×C3111yescharacteristic
233#2880C2×C3111yescharacteristic
234#1789C2×C3111yescharacteristic
235#1508C2×C3111yescharacteristic, complemented
236#1472C2×C3111yescharacteristic, complemented
237#1293C2×C3111yescharacteristic, complemented
238#1282C2×C3111yescharacteristic, complemented
239C22×C31—21no—
240C22×C31—21no—
241C22×C31—21no—
242C22×C31—21no—
243C22×C31—21no—
244C22×C31—21no—
245C22×C31—22no—
246C22×C31—21no—
247C22×C31—21no—
248C22×C31—41no—
249C22×C31—41no—
250C22×C31—41no—
251C22×C31—41no—
252C22×C31—41no—
253C22×C31—81no—
254C22×C31—81no—
255C22×C31—82no—
256C22×C31—82no—
257C22×C31#38611yescharacteristic
258C22×C31#44311yescharacteristic
259C22×C31#44411yescharacteristic
260C4×C31—21no—
261C4×C31—21no—
262C4×C31—22no—
263C4×C31—21no—
264C4×C31—41no—
265C4×C31—82no—
266C4×C31—81no—
267C4×C31—81no—
268C4×C31C2×#9911yescharacteristic
269C4×C31C2×#9911yescharacteristic
270C22×#41C22×C3111yescharacteristic
271C22×Q16C4×C3111yescharacteristic, complemented
272C22×SD16C4×C3111yescharacteristic, complemented
273C2×#131—21no—
274C2×C22⋊Q8C22×C3111yescharacteristic
275#452—21no—
276#452—21no—
277#452—21no—
278#452—21no—
279C2×#104—21no—
280C2×#104—21no—
281C2×#103C4×C3111yescharacteristic, complemented
282C2×#102C4×C3111yescharacteristic, complemented
283#408—21no—
284#408—22no—
285#407—21no—
286#407C22×C3111yescharacteristic
287#407C22×C3111yescharacteristic
288C2×C22⋊C8—21no—
289C2×C22⋊C8C22×C3111yescharacteristic
290C2×C22⋊C8C22×C3111yescharacteristic
291C4×C22⋊C4C22×C3111yescharacteristic
292#328—22no—
293#324—21no—
294#324—21no—
295C2×C31—21no—
296C2×C31—21no—
297C2×C31—41no—
298C2×C31—41no—
299C2×C31—42no—
300C2×C31—81no—
301C2×C31#187611yescharacteristic
302C2×C31#189811yescharacteristic
303C2×C31#190211yescharacteristic
304C2×#41—21no—
305C2×#41—21no—
306C2×#41—42no—
307C2×#41—42no—
308C2×#41D4×C3111yescharacteristic
309C2×#41D4×C3111yescharacteristic
310C2×#41D4×C3111yescharacteristic
311C2×#41D4×C3111yescharacteristic
312C22×Q8C2×C4×C3111yescharacteristic
313C22×Q8C2×C4×C3111yescharacteristic
314C22×D4—21no—
315C22×D4C2×C4×C3111yescharacteristic
316C23×C4—21no—
317C23×C4C23×C3111yescharacteristic
318C2×Q16—21no—
319C2×Q16—21no—
320C2×Q16—42no—
321C2×SD16—21no—
322C2×SD16—21no—
323C2×SD16—42no—
324#131—42no—
325#131—42no—
326C2×M16—22no—
327C2×M16—21no—
328C2×M16—21no—
329C22×C8—22no—
330C22×C8—21no—
331C22×C8C2×C4×C3111yescharacteristic
332C22×C8C2×C4×C3111yescharacteristic
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C2×C4×C3111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C42—21no—
342#104—42no—
343#104—42no—
344#103—21no—
345#103—21no—
346#102—21no—
347#102—21no—
348C22⋊C8—22no—
349C22⋊C8—22no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8D4×C3111yescharacteristic
357C22⋊C8D4×C3111yescharacteristic
358C22⋊C8D4×C3112yes—
359#95—21no—
360C31#923911yescharacteristic, direct product factor, Sylow
361C24—21no—
362C24#41×C3111yescharacteristic
363#41—22no—
364#41—22no—
365#41—22no—
366#41—22no—
367#41—41no—
368#41—41no—
369#41—41no—
370#41—41no—
371#41—44no—
372#41—44no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8C22⋊C4×C3111yescharacteristic
381C2×Q8C22⋊C4×C3111yescharacteristic
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4C22⋊C4×C3111yescharacteristic
391C2×D4C22⋊C4×C3111yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—44no—
402C22×C4—41no—
403C22×C4C22×C4×C3111yescharacteristic
404C22×C4C2×D4×C3111yescharacteristic
405C22×C4C2×D4×C3111yescharacteristic
406C22×C4C2×D4×C3111yescharacteristic
407C22×C4C2×D4×C3111yescharacteristic
408C22×C4#41×C3111yescharacteristic
409Q16—42no—
410Q16—42no—
411SD16—42no—
412SD16—42no—
413M16—44no—
414M16—41no—
415M16—41no—
416M16—41no—
417M16—41no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—21no—
423C2×C8—44no—
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—41no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C22⋊C4—22no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C42—41no—
438C42—41no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—41no—
444C23—41no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—81no—
449C23C4×D4×C3111yescharacteristic
450C23C31×#12111yescharacteristic
451C23C31×#12311yescharacteristic
452Q8—21no—
453Q8—21no—
454Q8—21no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—81no—
459Q8C31×#9912yes—
460D4—24no—
461D4—21no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4C31×#9912yes—
469C2×C4—24no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4C2×C22⋊C4×C3111yescharacteristic
494C2×C4C4×D4×C3111yescharacteristic
495C2×C4C31×#12011yescharacteristic
496C2×C4C31×#12111yescharacteristic
497C8—41no—
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—81no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—21no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—81no—
518C22—81no—
519C22—82no—
520C22—82no—
521C22C31×#38611yescharacteristic
522C22C31×#44311yescharacteristic
523C22C31×#44411yescharacteristic
524C4—21no—
525C4—21no—
526C4—22no—
527C4—21no—
528C4—41no—
529C4—82no—
530C4—81no—
531C4—81no—
532C4C2×C31×#9911yescharacteristic
533C4C2×C31×#9911yescharacteristic
534C2—21no—
535C2—21no—
536C2—41no—
537C2—41no—
538C2—42no—
539C2—81no—
540C2C31×#187611yescharacteristic
541C2C31×#189811yescharacteristic
542C2C31×#190211yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×#41×C31C22
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
4. C31×#1508C2semidirect
5. C31×#1472C2semidirect
6. C31×#1293C2semidirect
7. C31×#1282C2semidirect
9. C22×Q16×C31C4semidirect
10. C22×SD16×C31C4semidirect
19. C2×C31×#103C4semidirect
20. C2×C31×#102C4semidirect
167. #9239C31direct (N × H)
235. #1508C2×C31semidirect
236. #1472C2×C31semidirect
237. #1293C2×C31semidirect
238. #1282C2×C31semidirect
271. C22×Q16C4×C31semidirect
272. C22×SD16C4×C31semidirect
281. C2×#103C4×C31semidirect
282. C2×#102C4×C31semidirect
360. C31#9239direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4522
C31×#28802
C31×#17892
C31×#15082
C31×#14722
C31×#12932
C31×#12822
#923931