Finite Group Databasebeta

← C31×#24327 #21481086

Subgroups — C31×#24327 #21481086

Order 7936.

1146 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic, complemented
2C2×C31×#476C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic
4C31×#2538C211yesmaximal, characteristic, complemented
5C31×#2059C212yesmaximal, complemented
6C31×#2025C212yesmaximal, complemented
7C31×#1990C211yesmaximal, characteristic, complemented
8C31×#1984C211yesmaximal, characteristic, complemented
9C31×#1879C212yesmaximal
10C31×#1864C212yesmaximal, complemented
11C31×#1802C211yesmaximal, characteristic, complemented
12C22×D8×C31C2211yescharacteristic
13C31×#554—24no—
14C31×#554—24no—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C31×#125C2212yes—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8—21no—
19C2×C31×C22⋊Q8—22no—
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31C2212yes—
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C22×C4⋊C4×C31—21no—
25C31×#476—24no—
26C4×D8×C31—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2212yes—
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#102C2212yes—
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2212yes—
33C2×C31×#102C2211yescharacteristic
34C2×C4×C8×C31C2211yescharacteristic
35C31×#396—22no—
36C31×#390C2212yes—
37C31×#389C2212yes—
38C31×#384C2211yescharacteristic
39C31×#380—21no—
40C31×#340C2212yes—
41C31×#340C2212yes—
42C31×#340C2212yes—
43C31×#336C2212yes—
44C31×#336C2212yes—
45C22×Q8×C31—21no—
46C22×Q8×C31D411yescharacteristic
47C22×D4×C31C2311yescharacteristic
48C22×D4×C31C2311yescharacteristic
49C23×C4×C31—21no—
50C23×C4×C31—22no—
51C23×C4×C31—21no—
52C2×D8×C31—22no—
53C2×D8×C31—22no—
54C2×D8×C31Q814yescomplemented
55C22×C8×C31C2311yescharacteristic
56C22×C8×C31C2312yes—
57C22×C8×C31C2311yescharacteristic
58C31×C4⋊Q8—22no—
59C31×C4⋊Q8D414yes—
60C31×#125—24no—
61C31×#125—24no—
62C31×C22⋊Q8—28no—
63C31×C22⋊Q8—216no—
64C31×C22⋊Q8—44no—
65C4×Q8×C31—22no—
66C4×Q8×C31—22no—
67C4×D4×C31—24no—
68C4×D4×C31—24no—
69C4×D4×C31—22no—
70C4×D4×C31—22no—
71C4×D4×C31—22no—
72C4×D4×C31D414yes—
73C2×C4⋊C4×C31—28no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31D412yes—
81C2×C4⋊C4×C31D411yescharacteristic
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2312yes—
84C2×C4⋊C4×C31C2312yes—
85C2×C4⋊C4×C31C2311yescharacteristic
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C42×C31C2312yes—
92C2×C42×C31C2311yescharacteristic
93C31×#107—22no—
94C31×#106—24no—
95C31×C4⋊C8—22no—
96C31×#102—22no—
97C31×#102—24no—
98C31×#102—22no—
99C31×#102—24no—
100C4×C8×C31—22no—
101C31×#95—22no—
102C24×C31—21no—
103C24×C31—21no—
104C2×Q8×C31—22no—
105C2×Q8×C31—24no—
106C2×Q8×C31—22no—
107C2×Q8×C31—22no—
108C2×Q8×C31—81no—
109C2×Q8×C31—81no—
110C2×D4×C31—21no—
111C2×D4×C31—21no—
112C2×D4×C31—21no—
113C2×D4×C31—21no—
114C2×D4×C31—21no—
115C2×D4×C31—21no—
116C2×D4×C31—21no—
117C2×D4×C31—21no—
118C2×D4×C31C2×D412yes—
119C2×D4×C31C2×Q812yes—
120C2×D4×C31C2×Q812yes—
121C2×D4×C31#4112yes—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—28no—
125C22×C4×C31—24no—
126C22×C4×C31—21no—
127C22×C4×C31—22no—
128C22×C4×C31—42no—
129C22×C4×C31—42no—
130C22×C4×C31—42no—
131C22×C4×C31—42no—
132C22×C4×C31—42no—
133C22×C4×C31—82no—
134C22×C4×C31—82no—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2×D412yes—
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D411yescharacteristic
139C22×C4×C31C2411yescharacteristic
140D8×C31—28no—
141C2×C8×C31—21no—
142C2×C8×C31—21no—
143C2×C8×C31—21no—
144C2×C8×C31—22no—
145C2×C8×C31—22no—
146C2×C8×C31—21no—
147C2×C8×C31—21no—
148C2×C8×C31—22no—
149C2×C8×C31C2×Q812yes—
150C4⋊C4×C31—28no—
151C4⋊C4×C31—28no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—24no—
154C4⋊C4×C31—24no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—44no—
162C4⋊C4×C31—42no—
163C4⋊C4×C31—81no—
164C4⋊C4×C31C2×D414yes—
165C4⋊C4×C31C2×D412yes—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—24no—
168C22⋊C4×C31—44no—
169C22⋊C4×C31—42no—
170C22⋊C4×C31—82no—
171C42×C31—22no—
172C42×C31—22no—
173C42×C31C2×D412yes—
174C42×C31C2×D412yes—
175#24327C3111yesmaximal, characteristic, direct product factor, Sylow
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—22no—
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×C31C22×D411yescharacteristic
191Q8×C31—44no—
192Q8×C31—84no—
193D4×C31—22no—
194D4×C31—22no—
195D4×C31—22no—
196D4×C31—22no—
197D4×C31—22no—
198D4×C31—41no—
199D4×C31—41no—
200D4×C31C22⋊Q814yescomplemented
201C2×C4×C31—21no—
202C2×C4×C31—21no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—24no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—48no—
216C2×C4×C31—41no—
217C2×C4×C31—42no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—41no—
221C2×C4×C31—42no—
222C2×C4×C31—88no—
223C2×C4×C31—84no—
224C2×C4×C31#12012yes—
225C2×C4×C31#12012yes—
226C2×C4×C31#13512yes—
227C2×C4×C31AGL(1,ℤ/8)12yes—
228C2×C4×C31C22×D411yescharacteristic
229C2×C4×C31C22×D411yescharacteristic
230C2×C4×C31C22×Q811yescharacteristic
231C2×C4×C31C2×#4111yescharacteristic
232C2×C4×C312−1+411yescharacteristic
233C2×C4×C312−1+411yescharacteristic
234C8×C31—22no—
235C8×C31—41no—
236C8×C31—42no—
237C2×#554C2×C3111yescharacteristic, complemented
238C2×#476C2×C3111yescharacteristic, complemented
239C2×C4×D8C2×C3111yescharacteristic
240#2538C2×C3111yescharacteristic, complemented
241#2059C2×C3112yescomplemented
242#2025C2×C3112yescomplemented
243#1990C2×C3111yescharacteristic, complemented
244#1984C2×C3111yescharacteristic, complemented
245#1879C2×C3112yes—
246#1864C2×C3112yescomplemented
247#1802C2×C3111yescharacteristic, complemented
248C22×C31—24no—
249C22×C31—42no—
250C22×C31—42no—
251C22×C31—42no—
252C22×C31—42no—
253C22×C31—42no—
254C22×C31—42no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—81no—
259C22×C31—81no—
260C22×C31—81no—
261C22×C31—81no—
262C22×C31C2×#12011yescharacteristic
263C22×C31#54811yescharacteristic
264C22×C31D4×Q811yescharacteristic
265C22×C31C2×#13511yescharacteristic
266C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C31#57611yescharacteristic
268C22×C31#57711yescharacteristic
269C4×C31—22no—
270C4×C31—42no—
271C4×C31—42no—
272C4×C31—42no—
273C4×C31—44no—
274C4×C31—82no—
275C4×C31—81no—
276C4×C31#44914yes—
277C4×C31C2×C22⋊Q811yescharacteristic
278C4×C31#53611yescharacteristic
279C4×C31#54811yescharacteristic
280C4×C31D4×Q811yescharacteristic
281C22×D8C22×C3111yescharacteristic
282#554—24no—
283#554—24no—
284C2×C4⋊Q8C22×C3111yescharacteristic
285C2×#125C22×C3112yes—
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8—21no—
288C2×C22⋊Q8—22no—
289C2×C4×Q8C22×C3111yescharacteristic
290C2×C4×D4C22×C3112yes—
291C2×C4×D4C22×C3111yescharacteristic
292C2×C4×D4C22×C3111yescharacteristic
293C22×C4⋊C4—21no—
294#476—24no—
295C4×D8—24no—
296C2×#107C22×C3111yescharacteristic
297C2×#106C22×C3112yes—
298C2×C4⋊C8C22×C3111yescharacteristic
299C2×#102C22×C3112yes—
300C2×#102C22×C3111yescharacteristic
301C2×#102C22×C3112yes—
302C2×#102C22×C3111yescharacteristic
303C2×C4×C8C22×C3111yescharacteristic
304#396—22no—
305#390C22×C3112yes—
306#389C22×C3112yes—
307#384C22×C3111yescharacteristic
308#380—21no—
309#340C22×C3112yes—
310#340C22×C3112yes—
311#340C22×C3112yes—
312#336C22×C3112yes—
313#336C22×C3112yes—
314C2×C31—44no—
315C2×C31—82no—
316C2×C31#240911yescharacteristic
317C2×C31C2×#44911yescharacteristic
318C2×C31#301211yescharacteristic
319C2×C31#336011yescharacteristic
320C2×C31#336611yescharacteristic
321C2×C31#338011yescharacteristic
322C2×C31#338411yescharacteristic
323C22×Q8—21no—
324C22×Q8D4×C3111yescharacteristic
325C22×D4C23×C3111yescharacteristic
326C22×D4C23×C3111yescharacteristic
327C23×C4—21no—
328C23×C4—22no—
329C23×C4—21no—
330C2×D8—22no—
331C2×D8—22no—
332C2×D8Q8×C3114yescomplemented
333C22×C8C23×C3111yescharacteristic
334C22×C8C23×C3112yes—
335C22×C8C23×C3111yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8D4×C3114yes—
338#125—24no—
339#125—24no—
340C22⋊Q8—28no—
341C22⋊Q8—216no—
342C22⋊Q8—44no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4D4×C3114yes—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4D4×C3111yescharacteristic
359C2×C4⋊C4D4×C3112yes—
360C2×C4⋊C4C23×C3111yescharacteristic
361C2×C4⋊C4C23×C3112yes—
362C2×C4⋊C4C23×C3111yescharacteristic
363C2×C4⋊C4C23×C3112yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C42C23×C3112yes—
370C2×C42C23×C3111yescharacteristic
371#107—22no—
372#106—24no—
373C4⋊C8—22no—
374#102—22no—
375#102—24no—
376#102—22no—
377#102—24no—
378C4×C8—22no—
379#95—22no—
380C31#2432711yescharacteristic, direct product factor, Sylow
381C24—21no—
382C24—21no—
383C2×Q8—22no—
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—81no—
388C2×Q8—81no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4C2×D4×C3112yes—
398C2×D4C2×Q8×C3112yes—
399C2×D4C2×Q8×C3112yes—
400C2×D4#41×C3112yes—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—28no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—82no—
413C22×C4—82no—
414C22×C4C2×D4×C3112yes—
415C22×C4C2×D4×C3112yes—
416C22×C4C2×D4×C3111yescharacteristic
417C22×C4C2×D4×C3111yescharacteristic
418C22×C4C24×C3111yescharacteristic
419D8—28no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8C2×Q8×C3112yes—
429C4⋊C4—28no—
430C4⋊C4—28no—
431C4⋊C4—22no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—44no—
441C4⋊C4—42no—
442C4⋊C4—81no—
443C4⋊C4C2×D4×C3114yes—
444C4⋊C4C2×D4×C3112yes—
445C22⋊C4—28no—
446C22⋊C4—24no—
447C22⋊C4—44no—
448C22⋊C4—42no—
449C22⋊C4—82no—
450C42—22no—
451C42—22no—
452C42C2×D4×C3112yes—
453C42C2×D4×C3112yes—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23C22×D4×C3111yescharacteristic
469Q8—44no—
470Q8—84no—
471D4—22no—
472D4—22no—
473D4—22no—
474D4—22no—
475D4—22no—
476D4—41no—
477D4—41no—
478D4C31×C22⋊Q814yescomplemented
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—48no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—88no—
501C2×C4—84no—
502C2×C4C31×#12012yes—
503C2×C4C31×#12012yes—
504C2×C4C31×#13512yes—
505C2×C4C31×AGL(1,ℤ/8)12yes—
506C2×C4C22×D4×C3111yescharacteristic
507C2×C4C22×D4×C3111yescharacteristic
508C2×C4C22×Q8×C3111yescharacteristic
509C2×C4C2×#41×C3111yescharacteristic
510C2×C4C31×2−1+411yescharacteristic
511C2×C4C31×2−1+411yescharacteristic
512C8—22no—
513C8—41no—
514C8—42no—
515C22—24no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22C2×C31×#12011yescharacteristic
530C22C31×#54811yescharacteristic
531C22D4×Q8×C3111yescharacteristic
532C22C2×C31×#13511yescharacteristic
533C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
534C22C31×#57611yescharacteristic
535C22C31×#57711yescharacteristic
536C4—22no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—44no—
541C4—82no—
542C4—81no—
543C4C31×#44914yes—
544C4C2×C31×C22⋊Q811yescharacteristic
545C4C31×#53611yescharacteristic
546C4C31×#54811yescharacteristic
547C4D4×Q8×C3111yescharacteristic
548C2—44no—
549C2—82no—
550C2C31×#240911yescharacteristic
551C2C2×C31×#44911yescharacteristic
552C2C31×#301211yescharacteristic
553C2C31×#336011yescharacteristic
554C2C31×#336611yescharacteristic
555C2C31×#338011yescharacteristic
556C2C31×#338411yescharacteristic
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×#554C2semidirect
2. C2×C31×#476C2semidirect
4. C31×#2538C2semidirect
5. C31×#2059C2semidirect
6. C31×#2025C2semidirect
7. C31×#1990C2semidirect
8. C31×#1984C2semidirect
10. C31×#1864C2semidirect
11. C31×#1802C2semidirect
54. C2×D8×C31Q8semidirect
175. #24327C31direct (N × H)
200. D4×C31C22⋊Q8semidirect
237. C2×#554C2×C31semidirect
238. C2×#476C2×C31semidirect
240. #2538C2×C31semidirect
241. #2059C2×C31semidirect
242. #2025C2×C31semidirect
243. #1990C2×C31semidirect
244. #1984C2×C31semidirect
246. #1864C2×C31semidirect
247. #1802C2×C31semidirect
332. C2×D8Q8×C31semidirect
380. C31#24327direct (N × H)
478. D4C31×C22⋊Q8semidirect

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×#4762
C2×C4×D8×C312
C31×#25382
C31×#20592
C31×#20252
C31×#19902
C31×#19842
C31×#18792
C31×#18642
C31×#18022
#2432731