Finite Group Databasebeta

← C31×#13087 #21469846

Subgroups — C31×#13087 #21469846

Order 7936.

820 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#410C211yesmaximal, characteristic, complemented
2C31×#2404C211yesmaximal, characteristic
3C2×C31×AΣL(1,𝔽16)C212yesmaximal, complemented
4C31×#1785C211yesmaximal, characteristic, complemented
5C31×#1390C212yesmaximal, complemented
6C22×#41×C31C2211yescharacteristic
7C2×C31×#120C411yescharacteristic, complemented
8C2×C31×#120C2211yescharacteristic
9C2×C31×#117—21no—
10C22×C22⋊C4×C31C411yescharacteristic, complemented
11C2×C31×#101—21no—
12C2×C31×#100C2212yes—
13C31×#410—24no—
14C2×C31×#99—21no—
15C2×C31×#99C2212yes—
16C31×#407—21no—
17C31×#393—21no—
18C31×#392—21no—
19C31×#386—21no—
20C31×#386—21no—
21C31×#386C411yescharacteristic, complemented
22C31×#386C2211yescharacteristic
23C31×#381C411yescharacteristic, complemented
24C31×AΣL(1,𝔽16)—24no—
25C25×C31C2×C411yescharacteristic
26C2×#41×C31—22no—
27C2×#41×C31—22no—
28C2×#41×C31—41no—
29C2×#41×C31—41no—
30C2×#41×C31—42no—
31C22×Q8×C31D411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31—21no—
34C22×D4×C31C2×C411yescharacteristic
35C22×D4×C31D411yescharacteristic
36C22×D4×C31C2311yescharacteristic
37C23×C4×C31C2×C411yescharacteristic
38C23×C4×C31C2×C411yescharacteristic
39C23×C4×C31D411yescharacteristic
40C23×C4×C31D411yescharacteristic
41C2×M16×C31—22no—
42C31×#120—22no—
43C31×#120—22no—
44C31×#120—42no—
45C31×#117—24no—
46C31×#117—42no—
47C2×C4⋊C4×C31—41no—
48C2×C22⋊C4×C31—22no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—41no—
56C2×C22⋊C4×C31—41no—
57C2×C22⋊C4×C31C2×C411yescharacteristic
58C2×C22⋊C4×C31C2×C411yescharacteristic
59C2×C42×C31—41no—
60C31×#101—42no—
61C31×#100—22no—
62C31×#100—22no—
63C31×#99—24no—
64C31×#99—22no—
65C31×#99D414yescomplemented
66C31×C22⋊C8—41no—
67C31×C22⋊C8—41no—
68C31×#95—21no—
69C31×#95—21no—
70C31×#95—21no—
71C31×#95—21no—
72C24×C31—21no—
73C24×C31—22no—
74C24×C31—41no—
75C24×C31—42no—
76C24×C31—41no—
77C24×C31—81no—
78C24×C31C22⋊C411yescharacteristic
79C24×C31C22×C411yescharacteristic
80C24×C31C2×D411yescharacteristic
81#41×C31—44no—
82#41×C31—44no—
83#41×C31—44no—
84#41×C31—44no—
85C2×Q8×C31—22no—
86C2×Q8×C31—22no—
87C2×Q8×C31—41no—
88C2×D4×C31—22no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31—22no—
92C2×D4×C31—41no—
93C2×D4×C31—41no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31—41no—
97C2×D4×C31—42no—
98C2×D4×C31—42no—
99C2×D4×C31—42no—
100C2×D4×C31—41no—
101C2×D4×C31—41no—
102C2×D4×C31—81no—
103C2×D4×C31—81no—
104C2×D4×C31C2×D412yes—
105C2×D4×C31#4112yes—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—21no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—22no—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—21no—
120C22×C4×C31—41no—
121C22×C4×C31—41no—
122C22×C4×C31—42no—
123C22×C4×C31—41no—
124C22×C4×C31—81no—
125C22×C4×C31C22⋊C411yescharacteristic
126C22×C4×C31C22⋊C411yescharacteristic
127C22×C4×C31C22⋊C411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129M16×C31—42no—
130M16×C31—42no—
131C2×C8×C31—42no—
132C4⋊C4×C31—44no—
133C22⋊C4×C31—22no—
134C22⋊C4×C31—24no—
135C22⋊C4×C31—42no—
136C22⋊C4×C31—42no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—41no—
139C22⋊C4×C31—42no—
140C22⋊C4×C31—42no—
141C22⋊C4×C31—41no—
142C22⋊C4×C31—81no—
143C22⋊C4×C31—81no—
144C42×C31—44no—
145#13087C3111yesmaximal, characteristic, direct product factor, Sylow
146C23×C31—21no—
147C23×C31—21no—
148C23×C31—21no—
149C23×C31—21no—
150C23×C31—22no—
151C23×C31—21no—
152C23×C31—21no—
153C23×C31—21no—
154C23×C31—41no—
155C23×C31—41no—
156C23×C31—41no—
157C23×C31—41no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31—41no—
161C23×C31—41no—
162C23×C31—41no—
163C23×C31—42no—
164C23×C31—42no—
165C23×C31—41no—
166C23×C31—41no—
167C23×C31—41no—
168C23×C31—82no—
169C23×C31—84no—
170C23×C31—84no—
171C23×C31—82no—
172C23×C31C2×C22⋊C411yescharacteristic
173C23×C31C4×D412yes—
174C23×C31#12011yescharacteristic
175C23×C31#12311yescharacteristic
176Q8×C31—44no—
177D4×C31—42no—
178D4×C31—42no—
179D4×C31—44no—
180D4×C31—42no—
181D4×C31—42no—
182D4×C31—82no—
183D4×C31—82no—
184D4×C31—84no—
185C2×C4×C31—22no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—21no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—21no—
196C2×C4×C31—21no—
197C2×C4×C31—21no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—44no—
203C2×C4×C31—41no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—82no—
213C2×C4×C31—82no—
214C2×C4×C31—82no—
215C2×C4×C31#9912yes—
216C2×C4×C31#9911yescharacteristic
217C2×C4×C31#9911yescharacteristic
218C2×C4×C31#12112yes—
219C8×C31—82no—
220C2×#410C2×C3111yescharacteristic, complemented
221#2404C2×C3111yescharacteristic
222C2×AΣL(1,𝔽16)C2×C3112yescomplemented
223#1785C2×C3111yescharacteristic, complemented
224#1390C2×C3112yescomplemented
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—22no—
230C22×C31—41no—
231C22×C31—41no—
232C22×C31—42no—
233C22×C31—42no—
234C22×C31—42no—
235C22×C31—42no—
236C22×C31—42no—
237C22×C31—41no—
238C22×C31—41no—
239C22×C31—41no—
240C22×C31—41no—
241C22×C31—41no—
242C22×C31—42no—
243C22×C31—41no—
244C22×C31—41no—
245C22×C31—81no—
246C22×C31—81no—
247C22×C31—81no—
248C22×C31—81no—
249C22×C31—84no—
250C22×C31—84no—
251C22×C31—81no—
252C22×C31—81no—
253C22×C31#38611yescharacteristic
254C22×C31C2×#9911yescharacteristic
255C22×C31C2×#9911yescharacteristic
256C4×C31—22no—
257C4×C31—21no—
258C4×C31—21no—
259C4×C31—22no—
260C4×C31—41no—
261C4×C31—81no—
262C4×C31—81no—
263C4×C31—84no—
264C4×C31—81no—
265C22×#41C22×C3111yescharacteristic
266C2×#120C4×C3111yescharacteristic, complemented
267C2×#120C22×C3111yescharacteristic
268C2×#117—21no—
269C22×C22⋊C4C4×C3111yescharacteristic, complemented
270C2×#101—21no—
271C2×#100C22×C3112yes—
272#410—24no—
273C2×#99—21no—
274C2×#99C22×C3112yes—
275#407—21no—
276#393—21no—
277#392—21no—
278#386—21no—
279#386—21no—
280#386C4×C3111yescharacteristic, complemented
281#386C22×C3111yescharacteristic
282#381C4×C3111yescharacteristic, complemented
283AΣL(1,𝔽16)—24no—
284C2×C31—21no—
285C2×C31—21no—
286C2×C31—41no—
287C2×C31—42no—
288C2×C31—41no—
289C2×C31—81no—
290C2×C31—82no—
291C2×C31#189811yescharacteristic
292C2×C31#212011yescharacteristic
293C2×C31#212211yescharacteristic
294C25C2×C4×C3111yescharacteristic
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—41no—
298C2×#41—41no—
299C2×#41—42no—
300C22×Q8D4×C3111yescharacteristic
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C2×C4×C3111yescharacteristic
304C22×D4D4×C3111yescharacteristic
305C22×D4C23×C3111yescharacteristic
306C23×C4C2×C4×C3111yescharacteristic
307C23×C4C2×C4×C3111yescharacteristic
308C23×C4D4×C3111yescharacteristic
309C23×C4D4×C3111yescharacteristic
310C2×M16—22no—
311#120—22no—
312#120—22no—
313#120—42no—
314#117—24no—
315#117—42no—
316C2×C4⋊C4—41no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4C2×C4×C3111yescharacteristic
327C2×C22⋊C4C2×C4×C3111yescharacteristic
328C2×C42—41no—
329#101—42no—
330#100—22no—
331#100—22no—
332#99—24no—
333#99—22no—
334#99D4×C3114yescomplemented
335C22⋊C8—41no—
336C22⋊C8—41no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341C31#1308711yescharacteristic, direct product factor, Sylow
342C24—21no—
343C24—22no—
344C24—41no—
345C24—42no—
346C24—41no—
347C24—81no—
348C24C22⋊C4×C3111yescharacteristic
349C24C22×C4×C3111yescharacteristic
350C24C2×D4×C3111yescharacteristic
351#41—44no—
352#41—44no—
353#41—44no—
354#41—44no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—81no—
373C2×D4—81no—
374C2×D4C2×D4×C3112yes—
375C2×D4#41×C3112yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—42no—
393C22×C4—41no—
394C22×C4—81no—
395C22×C4C22⋊C4×C3111yescharacteristic
396C22×C4C22⋊C4×C3111yescharacteristic
397C22×C4C22⋊C4×C3111yescharacteristic
398C22×C4C2×D4×C3111yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—44no—
403C22⋊C4—22no—
404C22⋊C4—24no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—41no—
412C22⋊C4—81no—
413C22⋊C4—81no—
414C42—44no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—22no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—82no—
438C23—84no—
439C23—84no—
440C23—82no—
441C23C2×C22⋊C4×C3111yescharacteristic
442C23C4×D4×C3112yes—
443C23C31×#12011yescharacteristic
444C23C31×#12311yescharacteristic
445Q8—44no—
446D4—42no—
447D4—42no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—82no—
452D4—82no—
453D4—84no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4C31×#9911yescharacteristic
485C2×C4C31×#9911yescharacteristic
486C2×C4C31×#9912yes—
487C2×C4C31×#12112yes—
488C8—82no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—22no—
494C22—41no—
495C22—41no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—84no—
514C22—84no—
515C22—81no—
516C22—81no—
517C22C31×#38611yescharacteristic
518C22C2×C31×#9911yescharacteristic
519C22C2×C31×#9911yescharacteristic
520C4—22no—
521C4—21no—
522C4—21no—
523C4—22no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—84no—
528C4—81no—
529C2—21no—
530C2—21no—
531C2—41no—
532C2—42no—
533C2—41no—
534C2—81no—
535C2—82no—
536C2C31×#189811yescharacteristic
537C2C31×#212011yescharacteristic
538C2C31×#212211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC31×#2404C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#410C2semidirect
3. C2×C31×AΣL(1,𝔽16)C2semidirect
4. C31×#1785C2semidirect
5. C31×#1390C2semidirect
7. C2×C31×#120C4semidirect
10. C22×C22⋊C4×C31C4semidirect
21. C31×#386C4semidirect
23. C31×#381C4semidirect
65. C31×#99D4semidirect
145. #13087C31direct (N × H)
220. C2×#410C2×C31semidirect
222. C2×AΣL(1,𝔽16)C2×C31semidirect
223. #1785C2×C31semidirect
224. #1390C2×C31semidirect
266. C2×#120C4×C31semidirect
269. C22×C22⋊C4C4×C31semidirect
280. #386C4×C31semidirect
282. #381C4×C31semidirect
334. #99D4×C31semidirect
341. C31#13087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4102
C31×#24042
C2×C31×AΣL(1,𝔽16)2
C31×#17852
C31×#13902
#1308731