Finite Group Databasebeta

← C31×#24118 #21480877

Subgroups — C31×#24118 #21480877

Order 7936.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 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×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2537C211yesmaximal, characteristic
5C31×#2035C212yesmaximal, complemented
6C31×#2000C212yesmaximal, complemented
7C31×#1990C211yesmaximal, characteristic, complemented
8C31×#1954C211yesmaximal, characteristic, complemented
9C31×#1874C212yesmaximal, complemented
10C31×#1853C212yesmaximal, complemented
11C31×#1803C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2211yescharacteristic
13C31×#554—24no—
14C31×#554—24no—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C31×#125—21no—
17C2×C31×C22⋊Q8—22no—
18C2×C31×C22⋊Q8C2212yes—
19C2×C31×#121—21no—
20C2×C31×#121C2212yes—
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×D4×C31—21no—
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2212yes—
26C31×#476—24no—
27C4×SD16×C31—24no—
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2212yes—
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2212yes—
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2212yes—
35C2×C31×C22⋊C8C2212yes—
36C2×C31×C22⋊C8C2212yes—
37C2×C4×C8×C31C2211yescharacteristic
38C31×#394—22no—
39C31×#384C2211yescharacteristic
40C31×#380—21no—
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—22no—
51C23×C4×C31—21no—
52C23×C4×C31C2312yes—
53C2×SD16×C31—22no—
54C2×SD16×C31—22no—
55C2×SD16×C31—22no—
56C22×C8×C31C2311yescharacteristic
57C22×C8×C31C2312yes—
58C22×C8×C31C2311yescharacteristic
59C31×C4⋊Q8—22no—
60C31×C4⋊Q8D414yescomplemented
61C31×#125—28no—
62C31×C22⋊Q8—216no—
63C31×C22⋊Q8—24no—
64C31×C22⋊Q8—24no—
65C31×#121—24no—
66C31×#121—42no—
67C31×#121—44no—
68C4×Q8×C31—22no—
69C4×Q8×C31D414yescomplemented
70C4×D4×C31—28no—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C4×D4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31D411yescharacteristic
84C2×C4⋊C4×C31C2311yescharacteristic
85C2×C4⋊C4×C31C2312yes—
86C2×C4⋊C4×C31C2311yescharacteristic
87C2×C4⋊C4×C31C2312yes—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31D412yes—
93C2×C42×C31—21no—
94C2×C42×C31C2311yescharacteristic
95C31×#106—22no—
96C31×#106—24no—
97C31×C4⋊C8—22no—
98C31×#103—22no—
99C31×#103—42no—
100C31×#102—22no—
101C31×#102—24no—
102C31×C22⋊C8—24no—
103C31×C22⋊C8—42no—
104C4×C8×C31—22no—
105C31×#95—22no—
106C24×C31—21no—
107C24×C31C2×D412yes—
108C2×Q8×C31—24no—
109C2×Q8×C31—21no—
110C2×Q8×C31—21no—
111C2×Q8×C31—21no—
112C2×Q8×C31—21no—
113C2×Q8×C31—21no—
114C2×Q8×C31—81no—
115C2×Q8×C31—81no—
116C2×Q8×C31C2×D412yes—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—21no—
120C2×D4×C31—21no—
121C2×D4×C31—21no—
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—44no—
125C2×D4×C31—44no—
126C2×D4×C31—82no—
127C2×D4×C31SD1614yescomplemented
128C2×D4×C31#4112yes—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—28no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—22no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31—42no—
144C22×C4×C31—82no—
145C22×C4×C31—82no—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2411yescharacteristic
150SD16×C31—28no—
151C2×C8×C31—21no—
152C2×C8×C31—21no—
153C2×C8×C31—21no—
154C2×C8×C31—22no—
155C2×C8×C31—22no—
156C2×C8×C31—21no—
157C2×C8×C31—22no—
158C2×C8×C31—21no—
159C2×C8×C31#4112yes—
160C4⋊C4×C31—28no—
161C4⋊C4×C31—28no—
162C4⋊C4×C31—24no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—42no—
172C4⋊C4×C31—81no—
173C4⋊C4×C31C2×D412yes—
174C4⋊C4×C31C2×D414yes—
175C22⋊C4×C31—28no—
176C22⋊C4×C31—24no—
177C22⋊C4×C31—44no—
178C22⋊C4×C31—44no—
179C22⋊C4×C31—42no—
180C42×C31—24no—
181C42×C31C2×D412yes—
182C42×C31C2×D412yes—
183#24118C3111yesmaximal, characteristic, direct product factor, Sylow
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—22no—
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—22no—
190C23×C31—22no—
191C23×C31—41no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—41no—
196C23×C31—41no—
197C23×C31C2×SD1614yes—
198C23×C31C22×D411yescharacteristic
199Q8×C31—22no—
200Q8×C31—22no—
201Q8×C31—41no—
202Q8×C31—41no—
203Q8×C31—84no—
204D4×C31—22no—
205D4×C31—22no—
206D4×C31—28no—
207D4×C31—41no—
208D4×C31—41no—
209D4×C31—88no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—24no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—42no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—41no—
231C2×C4×C31—42no—
232C2×C4×C31—41no—
233C2×C4×C31—42no—
234C2×C4×C31—88no—
235C2×C4×C31—84no—
236C2×C4×C31#12012yes—
237C2×C4×C31#12012yes—
238C2×C4×C31C2×SD1612yes—
239C2×C4×C31#13712yes—
240C2×C4×C31C22×D411yescharacteristic
241C2×C4×C31C22×D411yescharacteristic
242C2×C4×C31C2×#4111yescharacteristic
243C2×C4×C31C2×#4111yescharacteristic
244C2×C4×C31H(5,𝔽2)11yescharacteristic
245C2×C4×C312−1+411yescharacteristic
246C8×C31—22no—
247C8×C31—41no—
248C8×C31—42no—
249C2×#554C2×C3111yescharacteristic, complemented
250C2×#476C2×C3111yescharacteristic, complemented
251C2×C4×SD16C2×C3111yescharacteristic, complemented
252#2537C2×C3111yescharacteristic
253#2035C2×C3112yescomplemented
254#2000C2×C3112yescomplemented
255#1990C2×C3111yescharacteristic, complemented
256#1954C2×C3111yescharacteristic, complemented
257#1874C2×C3112yescomplemented
258#1853C2×C3112yescomplemented
259#1803C2×C3111yescharacteristic, complemented
260C22×C31—24no—
261C22×C31—24no—
262C22×C31—24no—
263C22×C31—42no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31—42no—
267C22×C31—42no—
268C22×C31—42no—
269C22×C31—42no—
270C22×C31—81no—
271C22×C31—81no—
272C22×C31—81no—
273C22×C31—81no—
274C22×C31C2×#12011yescharacteristic
275C22×C31#54611yescharacteristic
276C22×C31#54711yescharacteristic
277C22×C31C22×SD1611yescharacteristic
278C22×C31C2×#13711yescharacteristic
279C22×C31#57611yescharacteristic
280C22×C31#57711yescharacteristic
281C4×C31—22no—
282C4×C31—42no—
283C4×C31—42no—
284C4×C31—42no—
285C4×C31—44no—
286C4×C31—81no—
287C4×C31—82no—
288C4×C31#44814yes—
289C4×C31#52511yescharacteristic
290C4×C31#53711yescharacteristic
291C4×C31#54811yescharacteristic
292C4×C31#55011yescharacteristic
293C22×SD16C22×C3111yescharacteristic
294#554—24no—
295#554—24no—
296C2×C4⋊Q8C22×C3111yescharacteristic
297C2×#125—21no—
298C2×C22⋊Q8—22no—
299C2×C22⋊Q8C22×C3112yes—
300C2×#121—21no—
301C2×#121C22×C3112yes—
302C2×C4×Q8C22×C3111yescharacteristic
303C2×C4×D4—21no—
304C2×C4×D4C22×C3111yescharacteristic
305C2×C4×D4C22×C3111yescharacteristic
306C22×C4⋊C4C22×C3112yes—
307#476—24no—
308C4×SD16—24no—
309C2×#106C22×C3111yescharacteristic
310C2×#106C22×C3112yes—
311C2×C4⋊C8C22×C3111yescharacteristic
312C2×#103C22×C3111yescharacteristic
313C2×#103C22×C3112yes—
314C2×#102C22×C3111yescharacteristic
315C2×#102C22×C3112yes—
316C2×C22⋊C8C22×C3112yes—
317C2×C22⋊C8C22×C3112yes—
318C2×C4×C8C22×C3111yescharacteristic
319#394—22no—
320#384C22×C3111yescharacteristic
321#380—21no—
322#380C22×C3112yes—
323#340C22×C3112yes—
324#340C22×C3112yes—
325#340C22×C3112yes—
326C2×C31—44no—
327C2×C31—82no—
328C2×C31#240711yescharacteristic
329C2×C31C2×#44811yescharacteristic
330C2×C31#301211yescharacteristic
331C2×C31#329511yescharacteristic
332C2×C31#333111yescharacteristic
333C2×C31#333511yescharacteristic
334C2×C31#335711yescharacteristic
335C22×Q8—21no—
336C22×Q8C23×C3111yescharacteristic
337C22×D4—22no—
338C22×D4D4×C3111yescharacteristic
339C22×D4C23×C3111yescharacteristic
340C23×C4—22no—
341C23×C4—21no—
342C23×C4C23×C3112yes—
343C2×SD16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C22×C8C23×C3111yescharacteristic
347C22×C8C23×C3112yes—
348C22×C8C23×C3111yescharacteristic
349C4⋊Q8—22no—
350C4⋊Q8D4×C3114yescomplemented
351#125—28no—
352C22⋊Q8—216no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355#121—24no—
356#121—42no—
357#121—44no—
358C4×Q8—22no—
359C4×Q8D4×C3114yescomplemented
360C4×D4—28no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C3111yescharacteristic
374C2×C4⋊C4C23×C3111yescharacteristic
375C2×C4⋊C4C23×C3112yes—
376C2×C4⋊C4C23×C3111yescharacteristic
377C2×C4⋊C4C23×C3112yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4D4×C3112yes—
383C2×C42—21no—
384C2×C42C23×C3111yescharacteristic
385#106—22no—
386#106—24no—
387C4⋊C8—22no—
388#103—22no—
389#103—42no—
390#102—22no—
391#102—24no—
392C22⋊C8—24no—
393C22⋊C8—42no—
394C4×C8—22no—
395#95—22no—
396C31#2411811yescharacteristic, direct product factor, Sylow
397C24—21no—
398C24C2×D4×C3112yes—
399C2×Q8—24no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—81no—
406C2×Q8—81no—
407C2×Q8C2×D4×C3112yes—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—82no—
418C2×D4SD16×C3114yescomplemented
419C2×D4#41×C3112yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—28no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—82no—
436C22×C4—82no—
437C22×C4C2×D4×C3112yes—
438C22×C4C2×D4×C3111yescharacteristic
439C22×C4C2×D4×C3111yescharacteristic
440C22×C4C24×C3111yescharacteristic
441SD16—28no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—21no—
450C2×C8#41×C3112yes—
451C4⋊C4—28no—
452C4⋊C4—28no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4C2×D4×C3112yes—
465C4⋊C4C2×D4×C3114yes—
466C22⋊C4—28no—
467C22⋊C4—24no—
468C22⋊C4—44no—
469C22⋊C4—44no—
470C22⋊C4—42no—
471C42—24no—
472C42C2×D4×C3112yes—
473C42C2×D4×C3112yes—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23C2×SD16×C3114yes—
488C23C22×D4×C3111yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—84no—
494D4—28no—
495D4—22no—
496D4—22no—
497D4—41no—
498D4—41no—
499D4—88no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—88no—
525C2×C4—84no—
526C2×C4C31×#12012yes—
527C2×C4C31×#12012yes—
528C2×C4C2×SD16×C3112yes—
529C2×C4C31×#13712yes—
530C2×C4C22×D4×C3111yescharacteristic
531C2×C4C22×D4×C3111yescharacteristic
532C2×C4C2×#41×C3111yescharacteristic
533C2×C4C2×#41×C3111yescharacteristic
534C2×C4C31×H(5,𝔽2)11yescharacteristic
535C2×C4C31×2−1+411yescharacteristic
536C8—22no—
537C8—41no—
538C8—42no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×C31×#12011yescharacteristic
554C22C31×#54611yescharacteristic
555C22C31×#54711yescharacteristic
556C22C22×SD16×C3111yescharacteristic
557C22C2×C31×#13711yescharacteristic
558C22C31×#57611yescharacteristic
559C22C31×#57711yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4—81no—
566C4—82no—
567C4C31×#44814yes—
568C4C31×#52511yescharacteristic
569C4C31×#53711yescharacteristic
570C4C31×#54811yescharacteristic
571C4C31×#55011yescharacteristic
572C2—44no—
573C2—82no—
574C2C31×#240711yescharacteristic
575C2C2×C31×#44811yescharacteristic
576C2C31×#301211yescharacteristic
577C2C31×#329511yescharacteristic
578C2C31×#333111yescharacteristic
579C2C31×#333511yescharacteristic
580C2C31×#335711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2537C2
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
1. C2×C31×#554C2semidirect
2. C2×C31×#476C2semidirect
3. C2×C4×SD16×C31C2semidirect
5. C31×#2035C2semidirect
6. C31×#2000C2semidirect
7. C31×#1990C2semidirect
8. C31×#1954C2semidirect
9. C31×#1874C2semidirect
10. C31×#1853C2semidirect
11. C31×#1803C2semidirect
60. C31×C4⋊Q8D4semidirect
69. C4×Q8×C31D4semidirect
127. C2×D4×C31SD16semidirect
183. #24118C31direct (N × H)
249. C2×#554C2×C31semidirect
250. C2×#476C2×C31semidirect
251. C2×C4×SD16C2×C31semidirect
253. #2035C2×C31semidirect
254. #2000C2×C31semidirect
255. #1990C2×C31semidirect
256. #1954C2×C31semidirect
257. #1874C2×C31semidirect
258. #1853C2×C31semidirect
259. #1803C2×C31semidirect
350. C4⋊Q8D4×C31semidirect
359. C4×Q8D4×C31semidirect
396. C31#24118direct (N × H)
418. C2×D4SD16×C31semidirect

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×SD16×C312
C31×#25372
C31×#20352
C31×#20002
C31×#19902
C31×#19542
C31×#18742
C31×#18532
C31×#18032
#2411831