Finite Group Databasebeta

← C31×#24121 #21480880

Subgroups — C31×#24121 #21480880

Order 7936.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#555C211yesmaximal, characteristic
2C2×C31×#477C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2538C211yesmaximal, characteristic, complemented
5C31×#2033C212yesmaximal, complemented
6C31×#2000C212yesmaximal, complemented
7C31×#1990C211yesmaximal, characteristic, complemented
8C31×#1954C211yesmaximal, characteristic, complemented
9C31×#1873C212yesmaximal, complemented
10C31×#1854C212yesmaximal, complemented
11C31×#1802C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2211yescharacteristic
13C31×#555—24no—
14C31×#555—24no—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C31×#124—22no—
17C2×C31×C22⋊Q8C2212yes—
18C2×C31×#121—21no—
19C2×C31×#121C2212yes—
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C31×#117—21no—
24C2×C31×#117C2212yes—
25C31×#477—24no—
26C4×SD16×C31—24no—
27C2×C31×#107C2212yes—
28C2×C31×#106C2211yescharacteristic
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×C4×C8×C31C2211yescharacteristic
37C31×#396—22no—
38C31×#390—21no—
39C31×#389—21no—
40C31×#384C2211yescharacteristic
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—21no—
51C23×C4×C31C2312yes—
52C2×SD16×C31—22no—
53C2×SD16×C31—22no—
54C2×SD16×C31—22no—
55C22×C8×C31C2311yescharacteristic
56C22×C8×C31C2312yes—
57C22×C8×C31C2311yescharacteristic
58C31×C4⋊Q8—22no—
59C31×C4⋊Q8D414yes—
60C31×#124—216no—
61C31×C22⋊Q8—24no—
62C31×C22⋊Q8—42no—
63C31×#121—28no—
64C31×#121—24no—
65C31×#121—24no—
66C4×Q8×C31—22no—
67C4×Q8×C31—22no—
68C4×D4×C31—22no—
69C4×D4×C31—22no—
70C4×D4×C31—22no—
71C4×D4×C31D414yes—
72C31×#117—28no—
73C31×#117—24no—
74C31×#117—24no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
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—22no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31D412yes—
91C2×C42×C31—22no—
92C2×C42×C31—21no—
93C2×C42×C31C2311yescharacteristic
94C31×#107—24no—
95C31×#106—22no—
96C31×C4⋊C8—22no—
97C31×#103—22no—
98C31×#103—24no—
99C31×#102—22no—
100C31×#102—42no—
101C31×C22⋊C8—24no—
102C31×C22⋊C8—42no—
103C4×C8×C31—22no—
104C31×#95—22no—
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—81no—
114C2×Q8×C31—81no—
115C2×Q8×C31#4112yes—
116C2×D4×C31—28no—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—22no—
120C2×D4×C31—21no—
121C2×D4×C31—21no—
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—82no—
126C2×D4×C31—82no—
127C2×D4×C31C2×D412yes—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—24no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
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—24no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—44no—
165C4⋊C4×C31—42no—
166C4⋊C4×C31—42no—
167C4⋊C4×C31—81no—
168C4⋊C4×C31C2×D412yes—
169C4⋊C4×C31C2×D414yes—
170C22⋊C4×C31—28no—
171C22⋊C4×C31—28no—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—24no—
174C22⋊C4×C31—44no—
175C22⋊C4×C31—82no—
176C42×C31—28no—
177C42×C31—42no—
178C42×C31C2×D412yes—
179C42×C31C2×D412yes—
180#24121C3111yesmaximal, characteristic, direct product factor, Sylow
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—22no—
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—41no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31C22×D411yescharacteristic
196Q8×C31—22no—
197Q8×C31—22no—
198Q8×C31—41no—
199Q8×C31—41no—
200Q8×C31—84no—
201D4×C31—22no—
202D4×C31—22no—
203D4×C31—41no—
204D4×C31—41no—
205D4×C31—44no—
206D4×C31—88no—
207C2×C4×C31—21no—
208C2×C4×C31—21no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—24no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—48no—
226C2×C4×C31—41no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—41no—
230C2×C4×C31—42no—
231C2×C4×C31—41no—
232C2×C4×C31#12012yes—
233C2×C4×C31#12012yes—
234C2×C4×C31#13512yes—
235C2×C4×C31#13712yes—
236C2×C4×C31C22×D411yescharacteristic
237C2×C4×C31C22×D411yescharacteristic
238C2×C4×C31C2×#4111yescharacteristic
239C2×C4×C31C2×#4111yescharacteristic
240C2×C4×C31H(5,𝔽2)11yescharacteristic
241C2×C4×C312−1+411yescharacteristic
242C8×C31—22no—
243C8×C31—41no—
244C8×C31—42no—
245C2×#555C2×C3111yescharacteristic
246C2×#477C2×C3111yescharacteristic, complemented
247C2×C4×SD16C2×C3111yescharacteristic, complemented
248#2538C2×C3111yescharacteristic, complemented
249#2033C2×C3112yescomplemented
250#2000C2×C3112yescomplemented
251#1990C2×C3111yescharacteristic, complemented
252#1954C2×C3111yescharacteristic, complemented
253#1873C2×C3112yescomplemented
254#1854C2×C3112yescomplemented
255#1802C2×C3111yescharacteristic, complemented
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—42no—
262C22×C31—42no—
263C22×C31—42no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31—81no—
267C22×C31—81no—
268C22×C31—81no—
269C22×C31—81no—
270C22×C31C2×#12011yescharacteristic
271C22×C31#54611yescharacteristic
272C22×C31#54711yescharacteristic
273C22×C31C2×#13511yescharacteristic
274C22×C31C2×#13711yescharacteristic
275C22×C31#57611yescharacteristic
276C22×C31#57711yescharacteristic
277C4×C31—22no—
278C4×C31—42no—
279C4×C31—42no—
280C4×C31—42no—
281C4×C31—44no—
282C4×C31—81no—
283C4×C31—82no—
284C4×C31#45214yes—
285C4×C31#52511yescharacteristic
286C4×C31#53711yescharacteristic
287C4×C31#54811yescharacteristic
288C4×C31#55011yescharacteristic
289C22×SD16C22×C3111yescharacteristic
290#555—24no—
291#555—24no—
292C2×C4⋊Q8C22×C3111yescharacteristic
293C2×#124—22no—
294C2×C22⋊Q8C22×C3112yes—
295C2×#121—21no—
296C2×#121C22×C3112yes—
297C2×C4×Q8C22×C3111yescharacteristic
298C2×C4×D4C22×C3111yescharacteristic
299C2×C4×D4C22×C3111yescharacteristic
300C2×#117—21no—
301C2×#117C22×C3112yes—
302#477—24no—
303C4×SD16—24no—
304C2×#107C22×C3112yes—
305C2×#106C22×C3111yescharacteristic
306C2×C4⋊C8C22×C3111yescharacteristic
307C2×#103C22×C3112yes—
308C2×#103C22×C3111yescharacteristic
309C2×#102C22×C3111yescharacteristic
310C2×#102C22×C3112yes—
311C2×C22⋊C8C22×C3112yes—
312C2×C22⋊C8C22×C3112yes—
313C2×C4×C8C22×C3111yescharacteristic
314#396—22no—
315#390—21no—
316#389—21no—
317#384C22×C3111yescharacteristic
318#380C22×C3112yes—
319#340C22×C3112yes—
320#340C22×C3112yes—
321#340C22×C3112yes—
322C2×C31—82no—
323C2×C31—82no—
324C2×C31#240711yescharacteristic
325C2×C31C2×#45211yescharacteristic
326C2×C31#301211yescharacteristic
327C2×C31#330511yescharacteristic
328C2×C31#332911yescharacteristic
329C2×C31#334011yescharacteristic
330C2×C31#335711yescharacteristic
331C22×Q8—21no—
332C22×Q8C23×C3111yescharacteristic
333C22×D4—22no—
334C22×D4D4×C3111yescharacteristic
335C22×D4C23×C3111yescharacteristic
336C23×C4—21no—
337C23×C4C23×C3112yes—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C22×C8C23×C3111yescharacteristic
342C22×C8C23×C3112yes—
343C22×C8C23×C3111yescharacteristic
344C4⋊Q8—22no—
345C4⋊Q8D4×C3114yes—
346#124—216no—
347C22⋊Q8—24no—
348C22⋊Q8—42no—
349#121—28no—
350#121—24no—
351#121—24no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4D4×C3114yes—
358#117—28no—
359#117—24no—
360#117—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4D4×C3111yescharacteristic
367C2×C4⋊C4C23×C3111yescharacteristic
368C2×C4⋊C4C23×C3112yes—
369C2×C4⋊C4C23×C3111yescharacteristic
370C2×C4⋊C4C23×C3112yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4D4×C3112yes—
377C2×C42—22no—
378C2×C42—21no—
379C2×C42C23×C3111yescharacteristic
380#107—24no—
381#106—22no—
382C4⋊C8—22no—
383#103—22no—
384#103—24no—
385#102—22no—
386#102—42no—
387C22⋊C8—24no—
388C22⋊C8—42no—
389C4×C8—22no—
390#95—22no—
391C31#2412111yescharacteristic, direct product factor, Sylow
392C24—21no—
393C24C2×D4×C3112yes—
394C2×Q8—24no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—81no—
401C2×Q8—81no—
402C2×Q8#41×C3112yes—
403C2×D4—28no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—82no—
413C2×D4—82no—
414C2×D4C2×D4×C3112yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4C2×D4×C3112yes—
430C22×C4C2×D4×C3111yescharacteristic
431C22×C4C2×D4×C3111yescharacteristic
432C22×C4C24×C3111yescharacteristic
433SD16—28no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—21no—
440C2×C8—22no—
441C2×C8—21no—
442C2×C8#41×C3112yes—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—44no—
452C4⋊C4—42no—
453C4⋊C4—42no—
454C4⋊C4—81no—
455C4⋊C4C2×D4×C3112yes—
456C4⋊C4C2×D4×C3114yes—
457C22⋊C4—28no—
458C22⋊C4—28no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—44no—
462C22⋊C4—82no—
463C42—28no—
464C42—42no—
465C42C2×D4×C3112yes—
466C42C2×D4×C3112yes—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×D4×C3111yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—84no—
487D4—22no—
488D4—22no—
489D4—44no—
490D4—41no—
491D4—41no—
492D4—88no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—48no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4C31×#12012yes—
519C2×C4C31×#12012yes—
520C2×C4C31×#13512yes—
521C2×C4C31×#13712yes—
522C2×C4C22×D4×C3111yescharacteristic
523C2×C4C22×D4×C3111yescharacteristic
524C2×C4C2×#41×C3111yescharacteristic
525C2×C4C2×#41×C3111yescharacteristic
526C2×C4C31×H(5,𝔽2)11yescharacteristic
527C2×C4C31×2−1+411yescharacteristic
528C8—22no—
529C8—41no—
530C8—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22C2×C31×#12011yescharacteristic
546C22C31×#54611yescharacteristic
547C22C31×#54711yescharacteristic
548C22C2×C31×#13511yescharacteristic
549C22C2×C31×#13711yescharacteristic
550C22C31×#57611yescharacteristic
551C22C31×#57711yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—44no—
557C4—81no—
558C4—82no—
559C4C31×#45214yes—
560C4C31×#52511yescharacteristic
561C4C31×#53711yescharacteristic
562C4C31×#54811yescharacteristic
563C4C31×#55011yescharacteristic
564C2—82no—
565C2—82no—
566C2C31×#240711yescharacteristic
567C2C2×C31×#45211yescharacteristic
568C2C31×#301211yescharacteristic
569C2C31×#330511yescharacteristic
570C2C31×#332911yescharacteristic
571C2C31×#334011yescharacteristic
572C2C31×#335711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#555C2
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
2. C2×C31×#477C2semidirect
3. C2×C4×SD16×C31C2semidirect
4. C31×#2538C2semidirect
5. C31×#2033C2semidirect
6. C31×#2000C2semidirect
7. C31×#1990C2semidirect
8. C31×#1954C2semidirect
9. C31×#1873C2semidirect
10. C31×#1854C2semidirect
11. C31×#1802C2semidirect
180. #24121C31direct (N × H)
246. C2×#477C2×C31semidirect
247. C2×C4×SD16C2×C31semidirect
248. #2538C2×C31semidirect
249. #2033C2×C31semidirect
250. #2000C2×C31semidirect
251. #1990C2×C31semidirect
252. #1954C2×C31semidirect
253. #1873C2×C31semidirect
254. #1854C2×C31semidirect
255. #1802C2×C31semidirect
391. C31#24121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5552
C2×C31×#4772
C2×C4×SD16×C312
C31×#25382
C31×#20332
C31×#20002
C31×#19902
C31×#19542
C31×#18732
C31×#18542
C31×#18022
#2412131