Finite Group Databasebeta

← C31×#24185 #21480944

Subgroups — C31×#24185 #21480944

Order 7936.

1150 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#556C211yesmaximal, characteristic, complemented
2C2×C31×#461C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic
4C31×#2538C211yesmaximal, characteristic, complemented
5C31×#2042C212yesmaximal, complemented
6C31×#2012C212yesmaximal
7C31×#1984C211yesmaximal, characteristic, complemented
8C31×#1956C211yesmaximal, characteristic, complemented
9C31×#1880C212yesmaximal, complemented
10C31×#1863C212yesmaximal, complemented
11C31×#1802C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2212yes—
13C22×D8×C31C2211yescharacteristic
14C31×#556—24no—
15C31×#556—24no—
16C2×C31×C4⋊Q8C2211yescharacteristic
17C2×C31×#126—22no—
18C2×C31×#124C2212yes—
19C2×C31×C22⋊Q8—21no—
20C2×C31×C22⋊Q8—21no—
21C2×C4×Q8×C31C2212yes—
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C31×#117—21no—
26C31×#461—24no—
27C4×D8×C31—24no—
28C2×C31×#107C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#103C2212yes—
31C2×C31×#103C2212yes—
32C2×C31×#103C2212yes—
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2212yes—
36C2×C4×C8×C31C2211yescharacteristic
37C31×#396—22no—
38C31×#390C2212yes—
39C31×#389C2212yes—
40C31×#384C2211yescharacteristic
41C31×#380—21no—
42C31×#340C2212yes—
43C31×#336C2212yes—
44C31×#336C2212yes—
45C22×Q8×C31D411yescharacteristic
46C22×Q8×C31C2312yes—
47C22×D4×C31C2311yescharacteristic
48C22×D4×C31C2311yescharacteristic
49C23×C4×C31—21no—
50C23×C4×C31—21no—
51C2×SD16×C31—24no—
52C2×SD16×C31—24no—
53C2×SD16×C31—42no—
54C2×D8×C31—22no—
55C2×D8×C31—22no—
56C2×D8×C31—22no—
57C22×C8×C31C2311yescharacteristic
58C22×C8×C31C2312yes—
59C22×C8×C31C2311yescharacteristic
60C31×C4⋊Q8—22no—
61C31×C4⋊Q8D414yes—
62C31×#126—216no—
63C31×#124—24no—
64C31×#124—24no—
65C31×C22⋊Q8—28no—
66C31×C22⋊Q8—44no—
67C4×Q8×C31—24no—
68C4×Q8×C31—24no—
69C4×Q8×C31—22no—
70C4×Q8×C31—22no—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C4×D4×C31D414yes—
75C31×#117—28no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31D412yes—
83C2×C4⋊C4×C31D411yescharacteristic
84C2×C4⋊C4×C31C2311yescharacteristic
85C2×C4⋊C4×C31C2312yes—
86C2×C4⋊C4×C31C2311yescharacteristic
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C42×C31—22no—
94C2×C42×C31C2312yes—
95C2×C42×C31C2311yescharacteristic
96C31×#107—22no—
97C31×C4⋊C8—22no—
98C31×#103—24no—
99C31×#103—24no—
100C31×#103—42no—
101C31×#102—22no—
102C31×#102—22no—
103C31×#102—42no—
104C4×C8×C31—22no—
105C31×#95—22no—
106C24×C31—21no—
107C24×C31—21no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—22no—
112C2×Q8×C31—22no—
113C2×Q8×C31—22no—
114C2×Q8×C31—22no—
115C2×Q8×C31—22no—
116C2×Q8×C31C2×D414yes—
117C2×D4×C31—21no—
118C2×D4×C31—21no—
119C2×D4×C31—21no—
120C2×D4×C31—21no—
121C2×D4×C31—21no—
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—21no—
127C2×D4×C31C2×D412yes—
128C2×D4×C31#4112yes—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—24no—
132C22×C4×C31—21no—
133C22×C4×C31—22no—
134C22×C4×C31—42no—
135C22×C4×C31—42no—
136C22×C4×C31—42no—
137C22×C4×C31—42no—
138C22×C4×C31—42no—
139C22×C4×C31C2×D412yes—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2411yescharacteristic
144SD16×C31—48no—
145D8×C31—28no—
146C2×C8×C31—21no—
147C2×C8×C31—21no—
148C2×C8×C31—21no—
149C2×C8×C31—22no—
150C2×C8×C31—22no—
151C2×C8×C31—22no—
152C2×C8×C31—21no—
153C2×C8×C31—21no—
154C2×C8×C31#4112yes—
155C4⋊C4×C31—28no—
156C4⋊C4×C31—24no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—24no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—44no—
166C4⋊C4×C31—42no—
167C4⋊C4×C31—81no—
168C4⋊C4×C31C2×D412yes—
169C22⋊C4×C31—28no—
170C22⋊C4×C31—28no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—44no—
173C22⋊C4×C31—42no—
174C22⋊C4×C31—82no—
175C42×C31—28no—
176C42×C31—22no—
177C42×C31—22no—
178C42×C31C2×D412yes—
179C42×C31C2×D412yes—
180#24185C3111yesmaximal, characteristic, direct product factor, Sylow
181C23×C31—22no—
182C23×C31—22no—
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—41no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31C22×D411yescharacteristic
196Q8×C31—24no—
197Q8×C31—24no—
198Q8×C31—42no—
199Q8×C31—42no—
200Q8×C31—44no—
201D4×C31—22no—
202D4×C31—22no—
203D4×C31—22no—
204D4×C31—22no—
205D4×C31—41no—
206D4×C31—41no—
207D4×C31—41no—
208D4×C31—41no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—24no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—48no—
224C2×C4×C31—41no—
225C2×C4×C31—42no—
226C2×C4×C31—41no—
227C2×C4×C31—42no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—84no—
231C2×C4×C31#12012yes—
232C2×C4×C31#12012yes—
233C2×C4×C31#13512yes—
234C2×C4×C31AGL(1,ℤ/8)12yes—
235C2×C4×C31C22×D411yescharacteristic
236C2×C4×C31C22×D411yescharacteristic
237C2×C4×C31C2×#4111yescharacteristic
238C2×C4×C31C2×#4111yescharacteristic
239C2×C4×C31H(5,𝔽2)11yescharacteristic
240C2×C4×C312−1+411yescharacteristic
241C8×C31—22no—
242C8×C31—41no—
243C8×C31—42no—
244C2×#556C2×C3111yescharacteristic, complemented
245C2×#461C2×C3111yescharacteristic, complemented
246C2×C4×D8C2×C3111yescharacteristic
247#2538C2×C3111yescharacteristic, complemented
248#2042C2×C3112yescomplemented
249#2012C2×C3112yes—
250#1984C2×C3111yescharacteristic, complemented
251#1956C2×C3111yescharacteristic, complemented
252#1880C2×C3112yescomplemented
253#1863C2×C3112yescomplemented
254#1802C2×C3111yescharacteristic, complemented
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—81no—
262C22×C31—81no—
263C22×C31—81no—
264C22×C31—81no—
265C22×C31—81no—
266C22×C31—81no—
267C22×C31—81no—
268C22×C31—81no—
269C22×C31C2×#12011yescharacteristic
270C22×C31#54811yescharacteristic
271C22×C31#55011yescharacteristic
272C22×C31C2×#13511yescharacteristic
273C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C31#57711yescharacteristic
275C22×C31#57811yescharacteristic
276C4×C31—22no—
277C4×C31—44no—
278C4×C31—42no—
279C4×C31—42no—
280C4×C31—42no—
281C4×C31—82no—
282C4×C31—81no—
283C4×C31#44914yes—
284C4×C31#52511yescharacteristic
285C4×C31#53711yescharacteristic
286C4×C31#54611yescharacteristic
287C4×C31#54711yescharacteristic
288C22×SD16C22×C3112yes—
289C22×D8C22×C3111yescharacteristic
290#556—24no—
291#556—24no—
292C2×C4⋊Q8C22×C3111yescharacteristic
293C2×#126—22no—
294C2×#124C22×C3112yes—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8—21no—
297C2×C4×Q8C22×C3112yes—
298C2×C4×Q8C22×C3111yescharacteristic
299C2×C4×D4C22×C3111yescharacteristic
300C2×C4×D4C22×C3111yescharacteristic
301C2×#117—21no—
302#461—24no—
303C4×D8—24no—
304C2×#107C22×C3111yescharacteristic
305C2×C4⋊C8C22×C3111yescharacteristic
306C2×#103C22×C3112yes—
307C2×#103C22×C3112yes—
308C2×#103C22×C3112yes—
309C2×#102C22×C3111yescharacteristic
310C2×#102C22×C3111yescharacteristic
311C2×#102C22×C3112yes—
312C2×C4×C8C22×C3111yescharacteristic
313#396—22no—
314#390C22×C3112yes—
315#389C22×C3112yes—
316#384C22×C3111yescharacteristic
317#380—21no—
318#340C22×C3112yes—
319#336C22×C3112yes—
320#336C22×C3112yes—
321C2×C31—82no—
322C2×C31—82no—
323C2×C31#240711yescharacteristic
324C2×C31C2×#44911yescharacteristic
325C2×C31#301311yescharacteristic
326C2×C31#336011yescharacteristic
327C2×C31#336711yescharacteristic
328C2×C31#339311yescharacteristic
329C2×C31#339711yescharacteristic
330C22×Q8D4×C3111yescharacteristic
331C22×Q8C23×C3112yes—
332C22×D4C23×C3111yescharacteristic
333C22×D4C23×C3111yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C2×SD16—24no—
337C2×SD16—24no—
338C2×SD16—42no—
339C2×D8—22no—
340C2×D8—22no—
341C2×D8—22no—
342C22×C8C23×C3112yes—
343C22×C8C23×C3111yescharacteristic
344C22×C8C23×C3111yescharacteristic
345C4⋊Q8—22no—
346C4⋊Q8D4×C3114yes—
347#126—216no—
348#124—24no—
349#124—24no—
350C22⋊Q8—28no—
351C22⋊Q8—44no—
352C4×Q8—24no—
353C4×Q8—24no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4D4×C3114yes—
360#117—28no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C3111yescharacteristic
368C2×C4⋊C4D4×C3112yes—
369C2×C4⋊C4C23×C3111yescharacteristic
370C2×C4⋊C4C23×C3112yes—
371C2×C4⋊C4C23×C3111yescharacteristic
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C42—22no—
379C2×C42C23×C3112yes—
380C2×C42C23×C3111yescharacteristic
381#107—22no—
382C4⋊C8—22no—
383#103—24no—
384#103—24no—
385#103—42no—
386#102—22no—
387#102—22no—
388#102—42no—
389C4×C8—22no—
390#95—22no—
391C31#2418511yescharacteristic, direct product factor, Sylow
392C24—21no—
393C24—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8C2×D4×C3114yes—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C2×D4×C3112yes—
414C2×D4#41×C3112yes—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4C2×D4×C3112yes—
426C22×C4C2×D4×C3112yes—
427C22×C4C2×D4×C3111yescharacteristic
428C22×C4C2×D4×C3111yescharacteristic
429C22×C4C24×C3111yescharacteristic
430SD16—48no—
431D8—28no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8#41×C3112yes—
441C4⋊C4—28no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—44no—
452C4⋊C4—42no—
453C4⋊C4—81no—
454C4⋊C4C2×D4×C3112yes—
455C22⋊C4—28no—
456C22⋊C4—28no—
457C22⋊C4—24no—
458C22⋊C4—44no—
459C22⋊C4—42no—
460C22⋊C4—82no—
461C42—28no—
462C42—22no—
463C42—22no—
464C42C2×D4×C3112yes—
465C42C2×D4×C3112yes—
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23C22×D4×C3111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—44no—
484Q8—42no—
485Q8—42no—
486D4—22no—
487D4—22no—
488D4—22no—
489D4—22no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—48no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4C31×#12012yes—
517C2×C4C31×#12012yes—
518C2×C4C31×#13512yes—
519C2×C4C31×AGL(1,ℤ/8)12yes—
520C2×C4C22×D4×C3111yescharacteristic
521C2×C4C22×D4×C3111yescharacteristic
522C2×C4C2×#41×C3111yescharacteristic
523C2×C4C2×#41×C3111yescharacteristic
524C2×C4C31×H(5,𝔽2)11yescharacteristic
525C2×C4C31×2−1+411yescharacteristic
526C8—22no—
527C8—41no—
528C8—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C2×C31×#12011yescharacteristic
544C22C31×#54811yescharacteristic
545C22C31×#55011yescharacteristic
546C22C2×C31×#13511yescharacteristic
547C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
548C22C31×#57711yescharacteristic
549C22C31×#57811yescharacteristic
550C4—22no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—82no—
556C4—81no—
557C4C31×#44914yes—
558C4C31×#52511yescharacteristic
559C4C31×#53711yescharacteristic
560C4C31×#54611yescharacteristic
561C4C31×#54711yescharacteristic
562C2—82no—
563C2—82no—
564C2C31×#240711yescharacteristic
565C2C2×C31×#44911yescharacteristic
566C2C31×#301311yescharacteristic
567C2C31×#336011yescharacteristic
568C2C31×#336711yescharacteristic
569C2C31×#339311yescharacteristic
570C2C31×#339711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#556C2semidirect
2. C2×C31×#461C2semidirect
4. C31×#2538C2semidirect
5. C31×#2042C2semidirect
7. C31×#1984C2semidirect
8. C31×#1956C2semidirect
9. C31×#1880C2semidirect
10. C31×#1863C2semidirect
11. C31×#1802C2semidirect
180. #24185C31direct (N × H)
244. C2×#556C2×C31semidirect
245. C2×#461C2×C31semidirect
247. #2538C2×C31semidirect
248. #2042C2×C31semidirect
250. #1984C2×C31semidirect
251. #1956C2×C31semidirect
252. #1880C2×C31semidirect
253. #1863C2×C31semidirect
254. #1802C2×C31semidirect
391. C31#24185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5562
C2×C31×#4612
C2×C4×D8×C312
C31×#25382
C31×#20422
C31×#20122
C31×#19842
C31×#19562
C31×#18802
C31×#18632
C31×#18022
#2418531