Finite Group Databasebeta

← C31×#23759 #21480518

Subgroups — C31×#23759 #21480518

Order 7936.

752 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×C22⋊Q8C211yesmaximal, characteristic
2C31×#2283C211yesmaximal, characteristic
3C31×#2101C211yesmaximal, characteristic, complemented
4C31×#2097C211yesmaximal, characteristic, complemented
5C31×#2085C211yesmaximal, characteristic, complemented
6C31×#2077C211yesmaximal, characteristic
7C31×#2075C211yesmaximal, characteristic
8C31×#2074C211yesmaximal, characteristic, complemented
9C31×#2036C211yesmaximal, characteristic
10C31×#2035C211yesmaximal, characteristic
11C4×C31×#107C211yesmaximal, characteristic, complemented
12C4×C31×#106C211yesmaximal, characteristic, complemented
13C4×C31×#103C211yesmaximal, characteristic, complemented
14C4×C31×#103C211yesmaximal, characteristic, complemented
15C4×C31×C22⋊C8C211yesmaximal, characteristic
16C2×C31×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C2×C31×#107C2211yescharacteristic
20C2×C31×#107C2211yescharacteristic
21C2×C31×#106C2211yescharacteristic
22C2×C31×#106C2211yescharacteristic
23C2×C31×#103C2211yescharacteristic
24C2×C31×#103C2211yescharacteristic
25C2×C31×#103C2211yescharacteristic
26C2×C31×#103C2211yescharacteristic
27C2×C31×C22⋊C8C2211yescharacteristic
28C2×C31×C22⋊C8C2211yescharacteristic
29C2×C4×C8×C31C2211yescharacteristic
30C2×C4×C8×C31C2211yescharacteristic
31C31×#391C2211yescharacteristic
32C31×#389C2211yescharacteristic
33C31×#387—21no—
34C31×#385—21no—
35C31×#383—21no—
36C31×#382C2211yescharacteristic
37C31×#382C2211yescharacteristic
38C31×#381—21no—
39C31×#380C2211yescharacteristic
40C31×#380C2211yescharacteristic
41C31×#380C2211yescharacteristic
42C4×C4⋊C4×C31—21no—
43C4×C4⋊C4×C31C2211yescharacteristic
44C4×C4⋊C4×C31C2211yescharacteristic
45C4×C4⋊C4×C31C2211yescharacteristic
46C4×C22⋊C4×C31—21no—
47C4×C22⋊C4×C31—21no—
48C31×#376—21no—
49C31×#340C2211yescharacteristic
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C22×Q8×C31C2311yescharacteristic
60C23×C4×C31D411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C22×C8×C31C2311yescharacteristic
64C22×C8×C31C2311yescharacteristic
65C22×C8×C31C2311yescharacteristic
66C22×C8×C31C2311yescharacteristic
67C31×C22⋊Q8—22no—
68C31×C22⋊Q8—22no—
69C4×Q8×C31—22no—
70C4×Q8×C31—22no—
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31C2311yescharacteristic
75C2×C4⋊C4×C31C2311yescharacteristic
76C2×C4⋊C4×C31C2311yescharacteristic
77C2×C4⋊C4×C31C2311yescharacteristic
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C22⋊C4×C31—21no—
82C2×C22⋊C4×C31—21no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—21no—
85C2×C42×C31—22no—
86C2×C42×C31—22no—
87C2×C42×C31—21no—
88C2×C42×C31—21no—
89C2×C42×C31—21no—
90C2×C42×C31—21no—
91C2×C42×C31D411yescharacteristic
92C2×C42×C31D411yescharacteristic
93C2×C42×C31C2311yescharacteristic
94C2×C42×C31C2311yescharacteristic
95C31×#107—22no—
96C31×#107—22no—
97C31×#106—22no—
98C31×#106—22no—
99C31×#103—22no—
100C31×#103—22no—
101C31×#103—22no—
102C31×#103—22no—
103C31×C22⋊C8—22no—
104C31×C22⋊C8—22no—
105C4×C8×C31—22no—
106C4×C8×C31—22no—
107C31×#95—21no—
108C31×#95—21no—
109C31×#95—21no—
110C31×#95—21no—
111C31×#95—21no—
112C31×#95—21no—
113C31×#95—21no—
114C31×#95—21no—
115C31×#95—21no—
116C31×#95—21no—
117C31×#95—21no—
118C31×#95—21no—
119C31×#95—21no—
120C24×C31C2×D411yescharacteristic
121C2×Q8×C31—21no—
122C2×Q8×C31—21no—
123C2×Q8×C31—21no—
124C2×Q8×C31—21no—
125C2×Q8×C31—21no—
126C2×Q8×C31#4112yes—
127C22×C4×C31—22no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—41no—
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2411yescharacteristic
153C2×C8×C31—21no—
154C2×C8×C31—21no—
155C2×C8×C31—21no—
156C2×C8×C31—21no—
157C2×C8×C31—21no—
158C2×C8×C31—21no—
159C2×C8×C31—21no—
160C2×C8×C31—21no—
161C2×C8×C31—21no—
162C2×C8×C31—21no—
163C2×C8×C31#4112yes—
164C2×C8×C31#4112yes—
165C4⋊C4×C31—24no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—21no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—21no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—21no—
175C4⋊C4×C31—21no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—42no—
180C4⋊C4×C31—42no—
181C4⋊C4×C31#4112yes—
182C22⋊C4×C31—24no—
183C22⋊C4×C31—42no—
184C22⋊C4×C31—42no—
185C22⋊C4×C31—42no—
186C42×C31—22no—
187C42×C31—22no—
188C42×C31—21no—
189C42×C31—21no—
190C42×C31—42no—
191C42×C31—42no—
192C42×C31—42no—
193C42×C31—42no—
194C42×C31#4112yes—
195C42×C31#4112yes—
196#23759C3111yesmaximal, characteristic, direct product factor, Sylow
197C23×C31—21no—
198C23×C31—21no—
199C23×C31—21no—
200C23×C31—21no—
201C23×C31—21no—
202C23×C31—21no—
203C23×C31#13512yes—
204C23×C31C22×D411yescharacteristic
205Q8×C31—22no—
206Q8×C31—22no—
207Q8×C31—41no—
208Q8×C31—41no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—21no—
220C2×C4×C31—21no—
221C2×C4×C31—21no—
222C2×C4×C31—44no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—41no—
231C2×C4×C31—44no—
232C2×C4×C31—41no—
233C2×C4×C31—41no—
234C2×C4×C31—41no—
235C2×C4×C31—41no—
236C2×C4×C31—41no—
237C2×C4×C31—41no—
238C2×C4×C31—41no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—41no—
242C2×C4×C31—41no—
243C2×C4×C31—41no—
244C2×C4×C31—41no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—41no—
250C2×C4×C31#12312yes—
251C2×C4×C31#12312yes—
252C2×C4×C31#13512yes—
253C2×C4×C31#13712yes—
254C2×C4×C31C2×#4111yescharacteristic
255C2×C4×C31C2×#4111yescharacteristic
256C2×C4×C31C2×#4111yescharacteristic
257C2×C4×C31C2×#4111yescharacteristic
258C2×C4×C31C2×#4111yescharacteristic
259C2×C4×C31C2×#4111yescharacteristic
260C8×C31—22no—
261C8×C31—22no—
262C8×C31—41no—
263C8×C31—41no—
264C4×C22⋊Q8C2×C3111yescharacteristic
265#2283C2×C3111yescharacteristic
266#2101C2×C3111yescharacteristic, complemented
267#2097C2×C3111yescharacteristic, complemented
268#2085C2×C3111yescharacteristic, complemented
269#2077C2×C3111yescharacteristic
270#2075C2×C3111yescharacteristic
271#2074C2×C3111yescharacteristic, complemented
272#2036C2×C3111yescharacteristic
273#2035C2×C3111yescharacteristic
274C4×#107C2×C3111yescharacteristic, complemented
275C4×#106C2×C3111yescharacteristic, complemented
276C4×#103C2×C3111yescharacteristic, complemented
277C4×#103C2×C3111yescharacteristic, complemented
278C4×C22⋊C8C2×C3111yescharacteristic
279C22×C31—22no—
280C22×C31—22no—
281C22×C31—22no—
282C22×C31—41no—
283C22×C31—41no—
284C22×C31—41no—
285C22×C31—41no—
286C22×C31C2×#12311yescharacteristic
287C22×C31#52511yescharacteristic
288C22×C31#53211yescharacteristic
289C22×C31C2×#13511yescharacteristic
290C22×C31C2×#13511yescharacteristic
291C22×C31C2×#13711yescharacteristic
292C22×C31#57511yescharacteristic
293C4×C31—22no—
294C4×C31—41no—
295C4×C31—41no—
296C4×C31—42no—
297C4×C31—41no—
298C4×C31—42no—
299C4×C31—81no—
300C4×C31—81no—
301C4×C31—81no—
302C4×C31—81no—
303C4×C31—81no—
304C4×C31—81no—
305C4×C31#48514yes—
306C4×C31#52911yescharacteristic
307C4×C31#52911yescharacteristic
308C4×C31#52911yescharacteristic
309C4×C31#52911yescharacteristic
310C2×C22⋊Q8C22×C3111yescharacteristic
311C2×C4×Q8C22×C3111yescharacteristic
312C22×C42C22×C3111yescharacteristic
313C2×#107C22×C3111yescharacteristic
314C2×#107C22×C3111yescharacteristic
315C2×#106C22×C3111yescharacteristic
316C2×#106C22×C3111yescharacteristic
317C2×#103C22×C3111yescharacteristic
318C2×#103C22×C3111yescharacteristic
319C2×#103C22×C3111yescharacteristic
320C2×#103C22×C3111yescharacteristic
321C2×C22⋊C8C22×C3111yescharacteristic
322C2×C22⋊C8C22×C3111yescharacteristic
323C2×C4×C8C22×C3111yescharacteristic
324C2×C4×C8C22×C3111yescharacteristic
325#391C22×C3111yescharacteristic
326#389C22×C3111yescharacteristic
327#387—21no—
328#385—21no—
329#383—21no—
330#382C22×C3111yescharacteristic
331#382C22×C3111yescharacteristic
332#381—21no—
333#380C22×C3111yescharacteristic
334#380C22×C3111yescharacteristic
335#380C22×C3111yescharacteristic
336C4×C4⋊C4—21no—
337C4×C4⋊C4C22×C3111yescharacteristic
338C4×C4⋊C4C22×C3111yescharacteristic
339C4×C4⋊C4C22×C3111yescharacteristic
340C4×C22⋊C4—21no—
341C4×C22⋊C4—21no—
342#376—21no—
343#340C22×C3111yescharacteristic
344#340C22×C3111yescharacteristic
345#340C22×C3111yescharacteristic
346#340C22×C3111yescharacteristic
347#340C22×C3111yescharacteristic
348#340C22×C3111yescharacteristic
349#340C22×C3111yescharacteristic
350#340C22×C3111yescharacteristic
351#336C22×C3111yescharacteristic
352#336C22×C3111yescharacteristic
353C2×C31—42no—
354C2×C31#239511yescharacteristic
355C2×C31C2×#48511yescharacteristic
356C2×C31#309111yescharacteristic
357C2×C31#310211yescharacteristic
358C2×C31#310811yescharacteristic
359C2×C31#316811yescharacteristic
360C2×C31#317211yescharacteristic
361C22×Q8C23×C3111yescharacteristic
362C23×C4D4×C3111yescharacteristic
363C23×C4D4×C3111yescharacteristic
364C23×C4C23×C3111yescharacteristic
365C22×C8C23×C3111yescharacteristic
366C22×C8C23×C3111yescharacteristic
367C22×C8C23×C3111yescharacteristic
368C22×C8C23×C3111yescharacteristic
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C23×C3111yescharacteristic
377C2×C4⋊C4C23×C3111yescharacteristic
378C2×C4⋊C4C23×C3111yescharacteristic
379C2×C4⋊C4C23×C3111yescharacteristic
380C2×C4⋊C4C23×C3111yescharacteristic
381C2×C4⋊C4C23×C3111yescharacteristic
382C2×C4⋊C4C23×C3111yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42D4×C3111yescharacteristic
394C2×C42D4×C3111yescharacteristic
395C2×C42C23×C3111yescharacteristic
396C2×C42C23×C3111yescharacteristic
397#107—22no—
398#107—22no—
399#106—22no—
400#106—22no—
401#103—22no—
402#103—22no—
403#103—22no—
404#103—22no—
405C22⋊C8—22no—
406C22⋊C8—22no—
407C4×C8—22no—
408C4×C8—22no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422C31#2375911yescharacteristic, direct product factor, Sylow
423C24C2×D4×C3111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8#41×C3112yes—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4C2×D4×C3111yescharacteristic
451C22×C4C2×D4×C3111yescharacteristic
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3111yescharacteristic
454C22×C4C2×D4×C3111yescharacteristic
455C22×C4C24×C3111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8#41×C3112yes—
467C2×C8#41×C3112yes—
468C4⋊C4—24no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4#41×C3112yes—
485C22⋊C4—24no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C42—22no—
490C42—22no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—42no—
495C42—42no—
496C42—42no—
497C42#41×C3112yes—
498C42#41×C3112yes—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23C31×#13512yes—
506C23C22×D4×C3111yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—44no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—44no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4C31×#12312yes—
553C2×C4C31×#12312yes—
554C2×C4C31×#13512yes—
555C2×C4C31×#13712yes—
556C2×C4C2×#41×C3111yescharacteristic
557C2×C4C2×#41×C3111yescharacteristic
558C2×C4C2×#41×C3111yescharacteristic
559C2×C4C2×#41×C3111yescharacteristic
560C2×C4C2×#41×C3111yescharacteristic
561C2×C4C2×#41×C3111yescharacteristic
562C8—22no—
563C8—22no—
564C8—41no—
565C8—41no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22C2×C31×#12311yescharacteristic
574C22C31×#52511yescharacteristic
575C22C31×#53211yescharacteristic
576C22C2×C31×#13511yescharacteristic
577C22C2×C31×#13511yescharacteristic
578C22C2×C31×#13711yescharacteristic
579C22C31×#57511yescharacteristic
580C4—22no—
581C4—41no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4C31×#48514yes—
593C4C31×#52911yescharacteristic
594C4C31×#52911yescharacteristic
595C4C31×#52911yescharacteristic
596C4C31×#52911yescharacteristic
597C2—42no—
598C2C31×#239511yescharacteristic
599C2C2×C31×#48511yescharacteristic
600C2C31×#309111yescharacteristic
601C2C31×#310211yescharacteristic
602C2C31×#310811yescharacteristic
603C2C31×#316811yescharacteristic
604C2C31×#317211yescharacteristic
subgroupG/H
centerC22×C4×C31C2×D4
commutator, Frattini, cosocleC22×C4C24×C31
socleC23×C31C22×D4
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#2101C2semidirect
4. C31×#2097C2semidirect
5. C31×#2085C2semidirect
8. C31×#2074C2semidirect
11. C4×C31×#107C2semidirect
12. C4×C31×#106C2semidirect
13. C4×C31×#103C2semidirect
14. C4×C31×#103C2semidirect
196. #23759C31direct (N × H)
266. #2101C2×C31semidirect
267. #2097C2×C31semidirect
268. #2085C2×C31semidirect
271. #2074C2×C31semidirect
274. C4×#107C2×C31semidirect
275. C4×#106C2×C31semidirect
276. C4×#103C2×C31semidirect
277. C4×#103C2×C31semidirect
422. C31#23759direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×C22⋊Q82
C31×#22832
C31×#21012
C31×#20972
C31×#20852
C31×#20772
C31×#20752
C31×#20742
C31×#20362
C31×#20352
C4×C31×#1072
C4×C31×#1062
C4×C31×#1032
C4×C31×C22⋊C82
#2375931