Finite Group Databasebeta

← C31×#24377 #21481136

Subgroups — C31×#24377 #21481136

Order 7936.

1450 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
1C22×C31×#137C211yesmaximal, characteristic, complemented
2C2×C31×#463C212yesmaximal, complemented
3C2×C31×#449C211yesmaximal, characteristic
4C31×#2436C211yesmaximal, characteristic, complemented
5C31×#2339C211yesmaximal, characteristic, complemented
6C31×#2056C212yesmaximal, complemented
7C31×#2015C212yesmaximal, complemented
8C31×#1895C211yesmaximal, characteristic, complemented
9C31×#1877C212yesmaximal, complemented
10C31×#1851C211yesmaximal, characteristic, complemented
11C31×#1787C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C23×Q8×C31C2211yescharacteristic
14C2×C31×#137—24no—
15C2×C31×#137—28no—
16C22×Q16×C31C2212yes—
17C22×SD16×C31C2212yes—
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×#124C2212yes—
22C2×C31×#121C2211yescharacteristic
23C2×C4×D4×C31C2212yes—
24C31×#463—28no—
25C31×#449—24no—
26C2×C31×C4⋊C8C2212yes—
27C2×C31×#103C2211yescharacteristic
28C2×C31×#103C2212yes—
29C2×C31×#103C2212yes—
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2212yes—
32C2×C31×C22⋊C8C2211yescharacteristic
33C31×#393—21no—
34C31×#393—21no—
35C31×#391C2212yes—
36C31×#391C2212yes—
37C31×#386—22no—
38C31×#386—22no—
39C31×#381—21no—
40C31×#380C2211yescharacteristic
41C4×C22⋊C4×C31C2211yescharacteristic
42C2×C31×#95—21no—
43C31×#340C2212yes—
44C31×#336C2212yes—
45C2×#41×C31—22no—
46C2×#41×C31—24no—
47C2×#41×C31—42no—
48C2×#41×C31D414yes—
49C22×Q8×C31—21no—
50C22×Q8×C31—24no—
51C22×Q8×C31—22no—
52C22×Q8×C31—22no—
53C22×Q8×C31—42no—
54C22×Q8×C31C2312yes—
55C22×Q8×C31C2311yescharacteristic
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31C2311yescharacteristic
59C22×D4×C31C2311yescharacteristic
60C23×C4×C31—21no—
61C23×C4×C31—21no—
62C23×C4×C31—22no—
63C23×C4×C31C2311yescharacteristic
64C31×#137—232no—
65C2×Q16×C31—24no—
66C2×Q16×C31—24no—
67C2×Q16×C31—24no—
68C2×SD16×C31—24no—
69C2×SD16×C31—24no—
70C2×SD16×C31—22no—
71C2×SD16×C31—42no—
72C2×SD16×C31D418yescomplemented
73C2×D8×C31—22no—
74C2×D8×C31—24no—
75C2×M16×C31—22no—
76C2×M16×C31—24no—
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2312yes—
80C31×#124—24no—
81C31×#124—42no—
82C31×#121—22no—
83C31×#121—22no—
84C4×D4×C31—24no—
85C4×D4×C31—42no—
86C2×C4⋊C4×C31C2312yes—
87C2×C4⋊C4×C31C2311yescharacteristic
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—21no—
93C2×C22⋊C4×C31D412yes—
94C2×C42×C31C2312yes—
95C31×C4⋊C8—24no—
96C31×#103—22no—
97C31×#103—24no—
98C31×#103—42no—
99C31×#102—22no—
100C31×#102—24no—
101C31×C22⋊C8—22no—
102C31×#95—21no—
103C31×#95—22no—
104C31×#95—22no—
105C31×#95—22no—
106C31×#95—22no—
107C31×#95D411yescharacteristic
108C31×#95D411yescharacteristic
109C24×C31—21no—
110C24×C31—21no—
111C24×C31C2×D411yescharacteristic
112#41×C31—28no—
113#41×C31—44no—
114#41×C31—48no—
115C2×Q8×C31—21no—
116C2×Q8×C31—22no—
117C2×Q8×C31—28no—
118C2×Q8×C31—22no—
119C2×Q8×C31—22no—
120C2×Q8×C31—22no—
121C2×Q8×C31—22no—
122C2×Q8×C31—22no—
123C2×Q8×C31—22no—
124C2×Q8×C31—44no—
125C2×Q8×C31—48no—
126C2×Q8×C31—44no—
127C2×Q8×C31—42no—
128C2×Q8×C31C2×D414yes—
129C2×Q8×C31C2×D412yes—
130C2×D4×C31—24no—
131C2×D4×C31—22no—
132C2×D4×C31—21no—
133C2×D4×C31—21no—
134C2×D4×C31—21no—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—44no—
138C2×D4×C31—44no—
139C2×D4×C31—42no—
140C2×D4×C31C2×D412yes—
141C2×D4×C31C2×D414yes—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—22no—
146C22×C4×C31—24no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—44no—
150C22×C4×C31—44no—
151C22×C4×C31—44no—
152C22×C4×C31—44no—
153C22×C4×C31—42no—
154C22×C4×C31—82no—
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D411yescharacteristic
158C22×C4×C31C2×D412yes—
159C22×C4×C31#4112yes—
160C22×C4×C31C2411yescharacteristic
161Q16×C31—216no—
162SD16×C31—216no—
163SD16×C31—44no—
164D8×C31—44no—
165M16×C31—28no—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31—21no—
169C2×C8×C31—21no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31C2×D414yes—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—21no—
175C4⋊C4×C31—21no—
176C4⋊C4×C31—22no—
177C22⋊C4×C31—42no—
178C22⋊C4×C31—44no—
179C22⋊C4×C31—44no—
180C22⋊C4×C31—44no—
181C22⋊C4×C31—42no—
182C22⋊C4×C31—81no—
183C42×C31—22no—
184C42×C31—22no—
185#24377C3111yesmaximal, characteristic, direct product factor, Sylow
186C23×C31—22no—
187C23×C31—24no—
188C23×C31—22no—
189C23×C31—22no—
190C23×C31—21no—
191C23×C31—21no—
192C23×C31—42no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—41no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31#12112yes—
201C23×C31C22×D411yescharacteristic
202Q8×C31—24no—
203Q8×C31—22no—
204Q8×C31—22no—
205Q8×C31—24no—
206Q8×C31—48no—
207Q8×C31—42no—
208Q8×C31—42no—
209Q8×C31—42no—
210D4×C31—22no—
211D4×C31—24no—
212D4×C31—48no—
213D4×C31—41no—
214D4×C31—41no—
215D4×C31—42no—
216D4×C31—84no—
217D4×C31#12014yes—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—24no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—24no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—48no—
231C2×C4×C31—48no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—41no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—88no—
241C2×C4×C31#12112yes—
242C2×C4×C31C22×D411yescharacteristic
243C2×C4×C31C22×D412yes—
244C2×C4×C31C2×#4111yescharacteristic
245C2×C4×C31H(5,𝔽2)12yes—
246C8×C31—24no—
247C8×C31—41no—
248C8×C31—41no—
249C22×#137C2×C3111yescharacteristic, complemented
250C2×#463C2×C3112yescomplemented
251C2×#449C2×C3111yescharacteristic
252#2436C2×C3111yescharacteristic, complemented
253#2339C2×C3111yescharacteristic, complemented
254#2056C2×C3112yescomplemented
255#2015C2×C3112yescomplemented
256#1895C2×C3111yescharacteristic, complemented
257#1877C2×C3112yescomplemented
258#1851C2×C3111yescharacteristic, complemented
259#1787C2×C3111yescharacteristic, complemented
260C22×C31—22no—
261C22×C31—24no—
262C22×C31—22no—
263C22×C31—22no—
264C22×C31—42no—
265C22×C31—44no—
266C22×C31—44no—
267C22×C31—42no—
268C22×C31—42no—
269C22×C31—42no—
270C22×C31—81no—
271C22×C31—82no—
272C22×C31—82no—
273C22×C31—81no—
274C22×C31—81no—
275C22×C31C2×#12111yescharacteristic
276C22×C31D4212yes—
277C22×C31#57512yes—
278C22×C31#57711yescharacteristic
279C22×C31#57811yescharacteristic
280C4×C31—22no—
281C4×C31—42no—
282C4×C31—44no—
283C4×C31—42no—
284C4×C31—42no—
285C4×C31—82no—
286C4×C31—81no—
287C4×C31C2×#12011yescharacteristic
288C4×C31#53411yescharacteristic
289C4×C31#54612yes—
290C22×#41C22×C3111yescharacteristic
291C23×Q8C22×C3111yescharacteristic
292C2×#137—24no—
293C2×#137—28no—
294C22×Q16C22×C3112yes—
295C22×SD16C22×C3112yes—
296C22×SD16C22×C3111yescharacteristic
297C22×D8C22×C3111yescharacteristic
298C22×M16C22×C3111yescharacteristic
299C2×#124C22×C3112yes—
300C2×#121C22×C3111yescharacteristic
301C2×C4×D4C22×C3112yes—
302#463—28no—
303#449—24no—
304C2×C4⋊C8C22×C3112yes—
305C2×#103C22×C3111yescharacteristic
306C2×#103C22×C3112yes—
307C2×#103C22×C3112yes—
308C2×#102C22×C3111yescharacteristic
309C2×#102C22×C3112yes—
310C2×C22⋊C8C22×C3111yescharacteristic
311#393—21no—
312#393—21no—
313#391C22×C3112yes—
314#391C22×C3112yes—
315#386—22no—
316#386—22no—
317#381—21no—
318#380C22×C3111yescharacteristic
319C4×C22⋊C4C22×C3111yescharacteristic
320C2×#95—21no—
321#340C22×C3112yes—
322#336C22×C3112yes—
323C2×C31—42no—
324C2×C31—44no—
325C2×C31—161no—
326C2×C31#241011yescharacteristic
327C2×C31#304011yescharacteristic
328C2×C31#304611yescharacteristic
329C2×C31#326912yes—
330C2×C31#327512yes—
331C2×#41—22no—
332C2×#41—24no—
333C2×#41—42no—
334C2×#41D4×C3114yes—
335C22×Q8—21no—
336C22×Q8—24no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—42no—
340C22×Q8C23×C3112yes—
341C22×Q8C23×C3111yescharacteristic
342C22×D4—21no—
343C22×D4—21no—
344C22×D4C23×C3111yescharacteristic
345C22×D4C23×C3111yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—22no—
349C23×C4C23×C3111yescharacteristic
350#137—232no—
351C2×Q16—24no—
352C2×Q16—24no—
353C2×Q16—24no—
354C2×SD16—24no—
355C2×SD16—24no—
356C2×SD16—22no—
357C2×SD16—42no—
358C2×SD16D4×C3118yescomplemented
359C2×D8—22no—
360C2×D8—24no—
361C2×M16—22no—
362C2×M16—24no—
363C22×C8C23×C3111yescharacteristic
364C22×C8C23×C3111yescharacteristic
365C22×C8C23×C3112yes—
366#124—24no—
367#124—42no—
368#121—22no—
369#121—22no—
370C4×D4—24no—
371C4×D4—42no—
372C2×C4⋊C4C23×C3112yes—
373C2×C4⋊C4C23×C3111yescharacteristic
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4D4×C3112yes—
380C2×C42C23×C3112yes—
381C4⋊C8—24no—
382#103—22no—
383#103—24no—
384#103—42no—
385#102—22no—
386#102—24no—
387C22⋊C8—22no—
388#95—21no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95D4×C3111yescharacteristic
394#95D4×C3111yescharacteristic
395C31#2437711yescharacteristic, direct product factor, Sylow
396C24—21no—
397C24—21no—
398C24C2×D4×C3111yescharacteristic
399#41—28no—
400#41—44no—
401#41—48no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—28no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—44no—
412C2×Q8—48no—
413C2×Q8—44no—
414C2×Q8—42no—
415C2×Q8C2×D4×C3114yes—
416C2×Q8C2×D4×C3112yes—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—42no—
427C2×D4C2×D4×C3112yes—
428C2×D4C2×D4×C3114yes—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4—42no—
441C22×C4—82no—
442C22×C4C2×D4×C3112yes—
443C22×C4C2×D4×C3112yes—
444C22×C4C2×D4×C3111yescharacteristic
445C22×C4C2×D4×C3112yes—
446C22×C4#41×C3112yes—
447C22×C4C24×C3111yescharacteristic
448Q16—216no—
449SD16—216no—
450SD16—44no—
451D8—44no—
452M16—28no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8C2×D4×C3114yes—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C22⋊C4—42no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—42no—
469C22⋊C4—81no—
470C42—22no—
471C42—22no—
472C23—22no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—41no—
485C23—41no—
486C23C31×#12112yes—
487C23C22×D4×C3111yescharacteristic
488Q8—24no—
489Q8—22no—
490Q8—22no—
491Q8—24no—
492Q8—48no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496D4—22no—
497D4—24no—
498D4—48no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—84no—
503D4C31×#12014yes—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—48no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—88no—
527C2×C4C31×#12112yes—
528C2×C4C22×D4×C3111yescharacteristic
529C2×C4C22×D4×C3112yes—
530C2×C4C2×#41×C3111yescharacteristic
531C2×C4C31×H(5,𝔽2)12yes—
532C8—24no—
533C8—41no—
534C8—41no—
535C22—22no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—42no—
540C22—44no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—81no—
549C22—81no—
550C22C2×C31×#12111yescharacteristic
551C22D42×C3112yes—
552C22C31×#57512yes—
553C22C31×#57711yescharacteristic
554C22C31×#57811yescharacteristic
555C4—22no—
556C4—42no—
557C4—44no—
558C4—42no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4C2×C31×#12011yescharacteristic
563C4C31×#53411yescharacteristic
564C4C31×#54612yes—
565C2—42no—
566C2—44no—
567C2—161no—
568C2C31×#241011yescharacteristic
569C2C31×#304011yescharacteristic
570C2C31×#304611yescharacteristic
571C2C31×#326912yes—
572C2C31×#327512yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#137C2semidirect
2. C2×C31×#463C2semidirect
4. C31×#2436C2semidirect
5. C31×#2339C2semidirect
6. C31×#2056C2semidirect
7. C31×#2015C2semidirect
8. C31×#1895C2semidirect
9. C31×#1877C2semidirect
10. C31×#1851C2semidirect
11. C31×#1787C2semidirect
72. C2×SD16×C31D4semidirect
185. #24377C31direct (N × H)
249. C22×#137C2×C31semidirect
250. C2×#463C2×C31semidirect
252. #2436C2×C31semidirect
253. #2339C2×C31semidirect
254. #2056C2×C31semidirect
255. #2015C2×C31semidirect
256. #1895C2×C31semidirect
257. #1877C2×C31semidirect
258. #1851C2×C31semidirect
259. #1787C2×C31semidirect
358. C2×SD16D4×C31semidirect
395. C31#24377direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C2×C31×#4632
C2×C31×#4492
C31×#24362
C31×#23392
C31×#20562
C31×#20152
C31×#18952
C31×#18772
C31×#18512
C31×#17872
#2437731