Finite Group Databasebeta

← C31×#24130 #21480889

Subgroups — C31×#24130 #21480889

Order 7936.

1184 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic, complemented
2C2×C31×#474C211yesmaximal, characteristic, complemented
3C2×C31×#440C211yesmaximal, characteristic, complemented
4C31×#2535C211yesmaximal, characteristic
5C31×#2036C212yesmaximal, complemented
6C31×#2000C212yesmaximal, complemented
7C31×#1993C211yesmaximal, characteristic, complemented
8C31×#1955C211yesmaximal, characteristic, complemented
9C31×#1874C212yesmaximal, complemented
10C31×#1852C212yesmaximal, complemented
11C31×#1805C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2211yescharacteristic
13C31×#554—24no—
14C31×#554—24no—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C31×#125—21no—
17C2×C31×C22⋊Q8—22no—
18C2×C31×C22⋊Q8C2212yes—
19C2×C31×#121C2212yes—
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2212yes—
25C31×#474—24no—
26C31×#440—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2212yes—
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2212yes—
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2212yes—
34C2×C31×C22⋊C8C2212yes—
35C2×C31×C22⋊C8C2212yes—
36C2×C31×#97C2211yescharacteristic
37C31×#397—21no—
38C31×#392—21no—
39C31×#386—22no—
40C31×#382C2211yescharacteristic
41C31×#380C2212yes—
42C31×#340C2212yes—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C22×Q8×C31—21no—
46C22×Q8×C31C2311yescharacteristic
47C22×D4×C31—22no—
48C22×D4×C31D411yescharacteristic
49C22×D4×C31C2311yescharacteristic
50C23×C4×C31—22no—
51C23×C4×C31—21no—
52C23×C4×C31C2312yes—
53C2×SD16×C31—22no—
54C2×SD16×C31—22no—
55C2×SD16×C31—22no—
56C22×C8×C31C2311yescharacteristic
57C22×C8×C31C2312yes—
58C22×C8×C31C2311yescharacteristic
59C31×C4⋊Q8—22no—
60C31×C4⋊Q8D414yescomplemented
61C31×#125—28no—
62C31×C22⋊Q8—216no—
63C31×C22⋊Q8—24no—
64C31×C22⋊Q8—24no—
65C31×#121—24no—
66C31×#121—42no—
67C4×Q8×C31—22no—
68C4×Q8×C31D414yescomplemented
69C4×D4×C31—28no—
70C4×D4×C31—22no—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31D411yescharacteristic
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2312yes—
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C4⋊C4×C31C2312yes—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31D412yes—
90C2×C42×C31—21no—
91C2×C42×C31C2311yescharacteristic
92C31×#107—22no—
93C31×#107—24no—
94C31×C4⋊C8—22no—
95C31×#103—22no—
96C31×#103—42no—
97C31×#102—22no—
98C31×#102—24no—
99C31×C22⋊C8—24no—
100C31×C22⋊C8—42no—
101C31×#97—22no—
102C31×#95—22no—
103C31×#95—21no—
104C31×#95—21no—
105C24×C31—21no—
106C24×C31C2×D412yes—
107C2×Q8×C31—24no—
108C2×Q8×C31—21no—
109C2×Q8×C31—21no—
110C2×Q8×C31—21no—
111C2×Q8×C31—21no—
112C2×Q8×C31—21no—
113C2×Q8×C31—82no—
114C2×Q8×C31C2×D412yes—
115C2×D4×C31—24no—
116C2×D4×C31—22no—
117C2×D4×C31—21no—
118C2×D4×C31—21no—
119C2×D4×C31—21no—
120C2×D4×C31—21no—
121C2×D4×C31—21no—
122C2×D4×C31—44no—
123C2×D4×C31—44no—
124C2×D4×C31—82no—
125C2×D4×C31#4112yes—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—22no—
129C22×C4×C31—28no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—21no—
138C22×C4×C31—42no—
139C22×C4×C31—82no—
140C22×C4×C31—82no—
141C22×C4×C31—82no—
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2411yescharacteristic
146SD16×C31—28no—
147C2×C8×C31—21no—
148C2×C8×C31—21no—
149C2×C8×C31—21no—
150C2×C8×C31—22no—
151C2×C8×C31—22no—
152C2×C8×C31—21no—
153C2×C8×C31—22no—
154C2×C8×C31—21no—
155C2×C8×C31#4112yes—
156C4⋊C4×C31—28no—
157C4⋊C4×C31—28no—
158C4⋊C4×C31—24no—
159C4⋊C4×C31—24no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31C2×D412yes—
168C4⋊C4×C31C2×D414yes—
169C22⋊C4×C31—28no—
170C22⋊C4×C31—24no—
171C22⋊C4×C31—44no—
172C22⋊C4×C31—42no—
173C22⋊C4×C31—82no—
174C42×C31—24no—
175C42×C31C2×D412yes—
176C42×C31C2×D412yes—
177#24130C3111yesmaximal, characteristic, direct product factor, Sylow
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—22no—
185C23×C31—41no—
186C23×C31—41no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31#13714yes—
190C23×C31C22×D411yescharacteristic
191Q8×C31—22no—
192Q8×C31—22no—
193Q8×C31—41no—
194Q8×C31—41no—
195Q8×C31—84no—
196D4×C31—28no—
197D4×C31—22no—
198D4×C31—22no—
199D4×C31—41no—
200D4×C31—41no—
201D4×C31—88no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—24no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—41no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—84no—
225C2×C4×C31—88no—
226C2×C4×C31#12012yes—
227C2×C4×C31#12012yes—
228C2×C4×C31C22×D411yescharacteristic
229C2×C4×C31C22×D411yescharacteristic
230C2×C4×C31C2×#4111yescharacteristic
231C2×C4×C31C2×#4111yescharacteristic
232C2×C4×C31H(5,𝔽2)11yescharacteristic
233C2×C4×C312−1+411yescharacteristic
234C8×C31—22no—
235C8×C31—41no—
236C8×C31—42no—
237C2×#554C2×C3111yescharacteristic, complemented
238C2×#474C2×C3111yescharacteristic, complemented
239C2×#440C2×C3111yescharacteristic, complemented
240#2535C2×C3111yescharacteristic
241#2036C2×C3112yescomplemented
242#2000C2×C3112yescomplemented
243#1993C2×C3111yescharacteristic, complemented
244#1955C2×C3111yescharacteristic, complemented
245#1874C2×C3112yescomplemented
246#1852C2×C3112yescomplemented
247#1805C2×C3111yescharacteristic, complemented
248C22×C31—24no—
249C22×C31—24no—
250C22×C31—24no—
251C22×C31—42no—
252C22×C31—42no—
253C22×C31—42no—
254C22×C31—42no—
255C22×C31—42no—
256C22×C31—44no—
257C22×C31—82no—
258C22×C31—81no—
259C22×C31—81no—
260C22×C31C2×#12011yescharacteristic
261C22×C31#54611yescharacteristic
262C22×C31#54711yescharacteristic
263C22×C31C2×#13712yes—
264C22×C31#57612yes—
265C4×C31—22no—
266C4×C31—22no—
267C4×C31—42no—
268C4×C31—42no—
269C4×C31—42no—
270C4×C31—44no—
271C4×C31—81no—
272C4×C31—82no—
273C4×C31#52511yescharacteristic
274C4×C31#53711yescharacteristic
275C4×C31#54811yescharacteristic
276C4×C31#55011yescharacteristic
277C22×SD16C22×C3111yescharacteristic
278#554—24no—
279#554—24no—
280C2×C4⋊Q8C22×C3111yescharacteristic
281C2×#125—21no—
282C2×C22⋊Q8—22no—
283C2×C22⋊Q8C22×C3112yes—
284C2×#121C22×C3112yes—
285C2×C4×Q8C22×C3111yescharacteristic
286C2×C4×D4—21no—
287C2×C4×D4C22×C3111yescharacteristic
288C2×C4×D4C22×C3111yescharacteristic
289C22×C4⋊C4C22×C3112yes—
290#474—24no—
291#440—24no—
292C2×#107C22×C3111yescharacteristic
293C2×#107C22×C3112yes—
294C2×C4⋊C8C22×C3111yescharacteristic
295C2×#103C22×C3111yescharacteristic
296C2×#103C22×C3112yes—
297C2×#102C22×C3111yescharacteristic
298C2×#102C22×C3112yes—
299C2×C22⋊C8C22×C3112yes—
300C2×C22⋊C8C22×C3112yes—
301C2×#97C22×C3111yescharacteristic
302#397—21no—
303#392—21no—
304#386—22no—
305#382C22×C3111yescharacteristic
306#380C22×C3112yes—
307#340C22×C3112yes—
308#340C22×C3112yes—
309#340C22×C3112yes—
310C2×C31—44no—
311C2×C31—82no—
312C2×C31#240711yescharacteristic
313C2×C31#300411yescharacteristic
314C2×C31#300811yescharacteristic
315C2×C31#331412yes—
316C2×C31#334612yes—
317C22×Q8—21no—
318C22×Q8C23×C3111yescharacteristic
319C22×D4—22no—
320C22×D4D4×C3111yescharacteristic
321C22×D4C23×C3111yescharacteristic
322C23×C4—22no—
323C23×C4—21no—
324C23×C4C23×C3112yes—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—22no—
328C22×C8C23×C3111yescharacteristic
329C22×C8C23×C3112yes—
330C22×C8C23×C3111yescharacteristic
331C4⋊Q8—22no—
332C4⋊Q8D4×C3114yescomplemented
333#125—28no—
334C22⋊Q8—216no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337#121—24no—
338#121—42no—
339C4×Q8—22no—
340C4×Q8D4×C3114yescomplemented
341C4×D4—28no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4D4×C3111yescharacteristic
353C2×C4⋊C4C23×C3111yescharacteristic
354C2×C4⋊C4C23×C3112yes—
355C2×C4⋊C4C23×C3111yescharacteristic
356C2×C4⋊C4C23×C3112yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4D4×C3112yes—
362C2×C42—21no—
363C2×C42C23×C3111yescharacteristic
364#107—22no—
365#107—24no—
366C4⋊C8—22no—
367#103—22no—
368#103—42no—
369#102—22no—
370#102—24no—
371C22⋊C8—24no—
372C22⋊C8—42no—
373#97—22no—
374#95—22no—
375#95—21no—
376#95—21no—
377C31#2413011yescharacteristic, direct product factor, Sylow
378C24—21no—
379C24C2×D4×C3112yes—
380C2×Q8—24no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—82no—
387C2×Q8C2×D4×C3112yes—
388C2×D4—24no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—44no—
396C2×D4—44no—
397C2×D4—82no—
398C2×D4#41×C3112yes—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—28no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—82no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4C2×D4×C3112yes—
416C22×C4C2×D4×C3111yescharacteristic
417C22×C4C2×D4×C3111yescharacteristic
418C22×C4C24×C3111yescharacteristic
419SD16—28no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8—21no—
428C2×C8#41×C3112yes—
429C4⋊C4—28no—
430C4⋊C4—28no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4C2×D4×C3112yes—
441C4⋊C4C2×D4×C3114yes—
442C22⋊C4—28no—
443C22⋊C4—24no—
444C22⋊C4—44no—
445C22⋊C4—42no—
446C22⋊C4—82no—
447C42—24no—
448C42C2×D4×C3112yes—
449C42C2×D4×C3112yes—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—42no—
460C23—42no—
461C23C31×#13714yes—
462C23C22×D4×C3111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467Q8—84no—
468D4—28no—
469D4—22no—
470D4—22no—
471D4—41no—
472D4—41no—
473D4—88no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—84no—
497C2×C4—88no—
498C2×C4C31×#12012yes—
499C2×C4C31×#12012yes—
500C2×C4C22×D4×C3111yescharacteristic
501C2×C4C22×D4×C3111yescharacteristic
502C2×C4C2×#41×C3111yescharacteristic
503C2×C4C2×#41×C3111yescharacteristic
504C2×C4C31×H(5,𝔽2)11yescharacteristic
505C2×C4C31×2−1+411yescharacteristic
506C8—22no—
507C8—41no—
508C8—42no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—82no—
519C22—81no—
520C22—81no—
521C22C2×C31×#12011yescharacteristic
522C22C31×#54611yescharacteristic
523C22C31×#54711yescharacteristic
524C22C2×C31×#13712yes—
525C22C31×#57612yes—
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—44no—
532C4—81no—
533C4—82no—
534C4C31×#52511yescharacteristic
535C4C31×#53711yescharacteristic
536C4C31×#54811yescharacteristic
537C4C31×#55011yescharacteristic
538C2—44no—
539C2—82no—
540C2C31×#240711yescharacteristic
541C2C31×#300411yescharacteristic
542C2C31×#300811yescharacteristic
543C2C31×#331412yes—
544C2C31×#334612yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#554C2semidirect
2. C2×C31×#474C2semidirect
3. C2×C31×#440C2semidirect
5. C31×#2036C2semidirect
6. C31×#2000C2semidirect
7. C31×#1993C2semidirect
8. C31×#1955C2semidirect
9. C31×#1874C2semidirect
10. C31×#1852C2semidirect
11. C31×#1805C2semidirect
60. C31×C4⋊Q8D4semidirect
68. C4×Q8×C31D4semidirect
177. #24130C31direct (N × H)
237. C2×#554C2×C31semidirect
238. C2×#474C2×C31semidirect
239. C2×#440C2×C31semidirect
241. #2036C2×C31semidirect
242. #2000C2×C31semidirect
243. #1993C2×C31semidirect
244. #1955C2×C31semidirect
245. #1874C2×C31semidirect
246. #1852C2×C31semidirect
247. #1805C2×C31semidirect
332. C4⋊Q8D4×C31semidirect
340. C4×Q8D4×C31semidirect
377. C31#24130direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5542
C2×C31×#4742
C2×C31×#4402
C31×#25352
C31×#20362
C31×#20002
C31×#19932
C31×#19552
C31×#18742
C31×#18522
C31×#18052
#2413031