Finite Group Databasebeta

← C31×#23935 #21480694

Subgroups — C31×#23935 #21480694

Order 7936.

1276 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#533C211yesmaximal, characteristic, complemented
2C2×C31×#452C212yesmaximal
3C31×#2297C211yesmaximal, characteristic
4C31×#2024C211yesmaximal, characteristic, complemented
5C31×#2023C211yesmaximal, characteristic, complemented
6C31×#2016C211yesmaximal, characteristic, complemented
7C31×#2013C211yesmaximal, characteristic, complemented
8C31×#1880C212yesmaximal, complemented
9C31×#1878C212yesmaximal, complemented
10C31×#1873C212yesmaximal, complemented
11C31×#1817C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×Q16×C31C2212yes—
14C22×SD16×C31C2212yes—
15C31×#533—28no—
16C2×C31×C4⋊Q8C2211yescharacteristic
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×#125—21no—
19C2×C31×C22⋊Q8—21no—
20C2×C31×C22⋊Q8C2212yes—
21C2×C4×Q8×C31—21no—
22C2×C4×Q8×C31C2212yes—
23C2×C31×#117—21no—
24C2×C31×#117C2211yescharacteristic
25C22×C42×C31C2211yescharacteristic
26C31×#452—28no—
27C2×C31×#103C2212yes—
28C2×C31×#103C2212yes—
29C2×C31×#103C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×C22⋊C8C2212yes—
32C31×#391C2211yescharacteristic
33C31×#391C2211yescharacteristic
34C31×#390C2211yescharacteristic
35C31×#390C2211yescharacteristic
36C31×#386—21no—
37C31×#386—21no—
38C4×C22⋊C4×C31—21no—
39C4×C22⋊C4×C31—21no—
40C31×#340C2212yes—
41C31×#340C2212yes—
42C31×#336C2212yes—
43C31×#336C2211yescharacteristic
44C31×#336C2211yescharacteristic
45C2×#41×C31—22no—
46C2×#41×C31—22no—
47C2×#41×C31—24no—
48C2×#41×C31—42no—
49C22×Q8×C31—21no—
50C22×Q8×C31C2312yes—
51C22×Q8×C31C2311yescharacteristic
52C22×D4×C31—21no—
53C22×D4×C31C2311yescharacteristic
54C23×C4×C31—21no—
55C23×C4×C31D411yescharacteristic
56C23×C4×C31D411yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C2×Q16×C31—24no—
59C2×Q16×C31—24no—
60C2×Q16×C31—42no—
61C2×SD16×C31—24no—
62C2×SD16×C31—24no—
63C2×SD16×C31—42no—
64C22×C8×C31C2312yes—
65C22×C8×C31C2312yes—
66C31×C4⋊Q8—24no—
67C31×C4⋊Q8—24no—
68C31×#125—28no—
69C31×C22⋊Q8—28no—
70C31×C22⋊Q8—24no—
71C31×C22⋊Q8D418yes—
72C4×Q8×C31—28no—
73C4×Q8×C31—24no—
74C4×Q8×C31—24no—
75C31×#117—28no—
76C31×#117—42no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C4⋊C4×C31C2312yes—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—21no—
91C2×C42×C31—24no—
92C2×C42×C31—22no—
93C2×C42×C31—21no—
94C2×C42×C31D411yescharacteristic
95C2×C42×C31D411yescharacteristic
96C2×C42×C31C2311yescharacteristic
97C2×C42×C31C2311yescharacteristic
98C31×#103—24no—
99C31×#103—42no—
100C31×#103—42no—
101C31×#102—24no—
102C31×C22⋊C8—24no—
103C31×#95—21no—
104C31×#95—21no—
105C31×#95—21no—
106C31×#95—21no—
107C24×C31—21no—
108C24×C31C2×D411yescharacteristic
109#41×C31—48no—
110#41×C31—48no—
111C2×Q8×C31—24no—
112C2×Q8×C31—22no—
113C2×Q8×C31—21no—
114C2×Q8×C31—22no—
115C2×Q8×C31—22no—
116C2×Q8×C31—22no—
117C2×Q8×C31—22no—
118C2×Q8×C31—22no—
119C2×Q8×C31—22no—
120C2×Q8×C31—42no—
121C2×Q8×C31—42no—
122C2×Q8×C31C2×D414yes—
123C2×Q8×C31#4112yes—
124C2×D4×C31—24no—
125C2×D4×C31—22no—
126C2×D4×C31—21no—
127C2×D4×C31—22no—
128C2×D4×C31—42no—
129C2×D4×C31—42no—
130C2×D4×C31#4112yes—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—24no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—41no—
146C22×C4×C31—42no—
147C22×C4×C31—42no—
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D414yes—
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2411yescharacteristic
155Q16×C31—48no—
156SD16×C31—48no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—24no—
165C4⋊C4×C31—28no—
166C4⋊C4×C31—24no—
167C4⋊C4×C31—28no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31C2×D414yes—
172C22⋊C4×C31—28no—
173C22⋊C4×C31—42no—
174C22⋊C4×C31—42no—
175C22⋊C4×C31—42no—
176C22⋊C4×C31—42no—
177C22⋊C4×C31—42no—
178C42×C31—28no—
179C42×C31—22no—
180C42×C31—22no—
181C42×C31—22no—
182C42×C31—22no—
183C42×C31—42no—
184#23935C3111yesmaximal, characteristic, direct product factor, Sylow
185C23×C31—21no—
186C23×C31—21no—
187C23×C31—21no—
188C23×C31—21no—
189C23×C31—21no—
190C23×C31—21no—
191C23×C31—22no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—41no—
196C23×C31—41no—
197C23×C31—41no—
198C23×C31#12012yes—
199C23×C31C22×D411yescharacteristic
200Q8×C31—24no—
201Q8×C31—24no—
202Q8×C31—24no—
203Q8×C31—48no—
204Q8×C31—42no—
205Q8×C31—42no—
206Q8×C31—42no—
207D4×C31—24no—
208D4×C31—48no—
209D4×C31—42no—
210C2×C4×C31—28no—
211C2×C4×C31—21no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—21no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—21no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—22no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—44no—
228C2×C4×C31—48no—
229C2×C4×C31—41no—
230C2×C4×C31—42no—
231C2×C4×C31—41no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
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#12012yes—
242C2×C4×C31#13512yes—
243C2×C4×C31#13712yes—
244C2×C4×C31#13712yes—
245C2×C4×C31C22×D412yes—
246C2×C4×C31C2×#4111yescharacteristic
247C2×C4×C31C2×#4111yescharacteristic
248C2×C4×C31H(5,𝔽2)12yes—
249C8×C31—42no—
250C8×C31—42no—
251C2×#533C2×C3111yescharacteristic, complemented
252C2×#452C2×C3112yes—
253#2297C2×C3111yescharacteristic
254#2024C2×C3111yescharacteristic, complemented
255#2023C2×C3111yescharacteristic, complemented
256#2016C2×C3111yescharacteristic, complemented
257#2013C2×C3111yescharacteristic, complemented
258#1880C2×C3112yescomplemented
259#1878C2×C3112yescomplemented
260#1873C2×C3112yescomplemented
261#1817C2×C3111yescharacteristic, complemented
262C22×C31—22no—
263C22×C31—22no—
264C22×C31—22no—
265C22×C31—41no—
266C22×C31—41no—
267C22×C31—41no—
268C22×C31—41no—
269C22×C31—42no—
270C22×C31—42no—
271C22×C31—42no—
272C22×C31—81no—
273C22×C31—81no—
274C22×C31—81no—
275C22×C31—81no—
276C22×C31C2×#12011yescharacteristic
277C22×C31#52511yescharacteristic
278C22×C31#53511yescharacteristic
279C22×C31C2×#13511yescharacteristic
280C22×C31C2×#13711yescharacteristic
281C22×C31C2×#13711yescharacteristic
282C22×C31#57511yescharacteristic
283C4×C31—22no—
284C4×C31—22no—
285C4×C31—22no—
286C4×C31—22no—
287C4×C31—42no—
288C4×C31—44no—
289C4×C31—41no—
290C4×C31—44no—
291C4×C31—81no—
292C4×C31—81no—
293C4×C31#54612yes—
294C4×C31#54612yes—
295C22×#41C22×C3111yescharacteristic
296C22×Q16C22×C3112yes—
297C22×SD16C22×C3112yes—
298#533—28no—
299C2×C4⋊Q8C22×C3111yescharacteristic
300C2×C4⋊Q8C22×C3111yescharacteristic
301C2×#125—21no—
302C2×C22⋊Q8—21no—
303C2×C22⋊Q8C22×C3112yes—
304C2×C4×Q8—21no—
305C2×C4×Q8C22×C3112yes—
306C2×#117—21no—
307C2×#117C22×C3111yescharacteristic
308C22×C42C22×C3111yescharacteristic
309#452—28no—
310C2×#103C22×C3112yes—
311C2×#103C22×C3112yes—
312C2×#103C22×C3112yes—
313C2×#102C22×C3112yes—
314C2×C22⋊C8C22×C3112yes—
315#391C22×C3111yescharacteristic
316#391C22×C3111yescharacteristic
317#390C22×C3111yescharacteristic
318#390C22×C3111yescharacteristic
319#386—21no—
320#386—21no—
321C4×C22⋊C4—21no—
322C4×C22⋊C4—21no—
323#340C22×C3112yes—
324#340C22×C3112yes—
325#336C22×C3112yes—
326#336C22×C3111yescharacteristic
327#336C22×C3111yescharacteristic
328C2×C31—42no—
329C2×C31—82no—
330C2×C31#240411yescharacteristic
331C2×C31#300211yescharacteristic
332C2×C31#300411yescharacteristic
333C2×C31#310711yescharacteristic
334C2×C31#311611yescharacteristic
335C2×C31#321011yescharacteristic
336C2×C31#321611yescharacteristic
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—24no—
340C2×#41—42no—
341C22×Q8—21no—
342C22×Q8C23×C3112yes—
343C22×Q8C23×C3111yescharacteristic
344C22×D4—21no—
345C22×D4C23×C3111yescharacteristic
346C23×C4—21no—
347C23×C4D4×C3111yescharacteristic
348C23×C4D4×C3111yescharacteristic
349C23×C4C23×C3111yescharacteristic
350C2×Q16—24no—
351C2×Q16—24no—
352C2×Q16—42no—
353C2×SD16—24no—
354C2×SD16—24no—
355C2×SD16—42no—
356C22×C8C23×C3112yes—
357C22×C8C23×C3112yes—
358C4⋊Q8—24no—
359C4⋊Q8—24no—
360#125—28no—
361C22⋊Q8—28no—
362C22⋊Q8—24no—
363C22⋊Q8D4×C3118yes—
364C4×Q8—28no—
365C4×Q8—24no—
366C4×Q8—24no—
367#117—28no—
368#117—42no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4C23×C3111yescharacteristic
375C2×C4⋊C4C23×C3111yescharacteristic
376C2×C4⋊C4C23×C3112yes—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—21no—
386C2×C42D4×C3111yescharacteristic
387C2×C42D4×C3111yescharacteristic
388C2×C42C23×C3111yescharacteristic
389C2×C42C23×C3111yescharacteristic
390#103—24no—
391#103—42no—
392#103—42no—
393#102—24no—
394C22⋊C8—24no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399C31#2393511yescharacteristic, direct product factor, Sylow
400C24—21no—
401C24C2×D4×C3111yescharacteristic
402#41—48no—
403#41—48no—
404C2×Q8—24no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×Q8C2×D4×C3114yes—
416C2×Q8#41×C3112yes—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4#41×C3112yes—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4C2×D4×C3111yescharacteristic
442C22×C4C2×D4×C3111yescharacteristic
443C22×C4C2×D4×C3114yes—
444C22×C4C2×D4×C3111yescharacteristic
445C22×C4C2×D4×C3111yescharacteristic
446C22×C4C2×D4×C3111yescharacteristic
447C22×C4C24×C3111yescharacteristic
448Q16—48no—
449SD16—48no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—28no—
459C4⋊C4—24no—
460C4⋊C4—28no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4C2×D4×C3114yes—
465C22⋊C4—28no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C42—28no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—22no—
476C42—42no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C31×#12012yes—
491C23C22×D4×C3111yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—24no—
495Q8—48no—
496Q8—42no—
497Q8—42no—
498Q8—42no—
499D4—24no—
500D4—48no—
501D4—42no—
502C2×C4—28no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4C31×#12012yes—
534C2×C4C31×#13512yes—
535C2×C4C31×#13712yes—
536C2×C4C31×#13712yes—
537C2×C4C22×D4×C3112yes—
538C2×C4C2×#41×C3111yescharacteristic
539C2×C4C2×#41×C3111yescharacteristic
540C2×C4C31×H(5,𝔽2)12yes—
541C8—42no—
542C8—42no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C31×#12011yescharacteristic
558C22C31×#52511yescharacteristic
559C22C31×#53511yescharacteristic
560C22C2×C31×#13511yescharacteristic
561C22C2×C31×#13711yescharacteristic
562C22C2×C31×#13711yescharacteristic
563C22C31×#57511yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—42no—
569C4—44no—
570C4—41no—
571C4—44no—
572C4—81no—
573C4—81no—
574C4C31×#54612yes—
575C4C31×#54612yes—
576C2—42no—
577C2—82no—
578C2C31×#240411yescharacteristic
579C2C31×#300211yescharacteristic
580C2C31×#300411yescharacteristic
581C2C31×#310711yescharacteristic
582C2C31×#311611yescharacteristic
583C2C31×#321011yescharacteristic
584C2C31×#321611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#533C2semidirect
4. C31×#2024C2semidirect
5. C31×#2023C2semidirect
6. C31×#2016C2semidirect
7. C31×#2013C2semidirect
8. C31×#1880C2semidirect
9. C31×#1878C2semidirect
10. C31×#1873C2semidirect
11. C31×#1817C2semidirect
184. #23935C31direct (N × H)
251. C2×#533C2×C31semidirect
254. #2024C2×C31semidirect
255. #2023C2×C31semidirect
256. #2016C2×C31semidirect
257. #2013C2×C31semidirect
258. #1880C2×C31semidirect
259. #1878C2×C31semidirect
260. #1873C2×C31semidirect
261. #1817C2×C31semidirect
399. C31#23935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5332
C2×C31×#4522
C31×#22972
C31×#20242
C31×#20232
C31×#20162
C31×#20132
C31×#18802
C31×#18782
C31×#18732
C31×#18172
#2393531