Finite Group Databasebeta

← C31×#18787 #21475546

Subgroups — C31×#18787 #21475546

Order 7936.

1206 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#41×C31C211yesmaximal, characteristic
2C31×#3206C211yesmaximal, characteristic, complemented
3C31×#3079C211yesmaximal, characteristic, complemented
4C2×C31×#476C211yesmaximal, characteristic, complemented
5C31×#1637C212yesmaximal, complemented
6C31×#1635C212yesmaximal, complemented
7C31×#1631C212yesmaximal, complemented
8C31×#1629C212yesmaximal, complemented
9C31×#1547C211yesmaximal, characteristic, complemented
10C31×#1486C211yesmaximal, characteristic, complemented
11C31×#1477C211yesmaximal, characteristic, complemented
12C22×#41×C31—21no—
13C31×#550C2211yescharacteristic
14D4×Q8×C31C2211yescharacteristic
15C31×#548—21no—
16C31×#547—21no—
17C31×#547C2211yescharacteristic
18C31×#546—22no—
19C31×#546—21no—
20D42×C31—21no—
21D42×C31C2211yescharacteristic
22C31×#532—21no—
23C31×#532C2211yescharacteristic
24C2×C31×C4⋊Q8C2211yescharacteristic, complemented
25C31×#525—22no—
26C31×#525—21no—
27C4×#41×C31C2211yescharacteristic
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C31×#492C2212yescomplemented
31C31×#487C2212yescomplemented
32C31×#477C2212yescomplemented
33C31×#476—21no—
34C31×#476—21no—
35C31×#476C2212yes—
36C31×#476C2212yescomplemented
37C31×#476C2212yescomplemented
38C31×#475—21no—
39C31×#474—21no—
40C31×#461—22no—
41C31×#448—22no—
42C31×#431C2211yescharacteristic, complemented
43C31×#428—21no—
44C2×C31×#106—21no—
45C31×#423C2211yescharacteristic, complemented
46C2×C31×C4⋊C8C2211yescharacteristic, complemented
47C31×#417—21no—
48C2×C31×#102—21no—
49C31×#332C2212yescomplemented
50C31×#331C2212yescomplemented
51C31×Q8⋊C8C2212yescomplemented
52C31×D4⋊C8C2212yes—
53C31×D4⋊C8C2212yescomplemented
54C31×D4⋊C8C2212yescomplemented
55C2×#41×C31—22no—
56C2×#41×C31—22no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—21no—
60C2×#41×C31—44no—
61C2×#41×C31—44no—
62C2×#41×C31D411yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31—21no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31D411yescharacteristic
69C23×C4×C31—22no—
70C23×C4×C31—21no—
71C2×SD16×C31—24no—
72C2×M16×C31—21no—
73C22×C8×C31—21no—
74C31×C4⋊Q8—21no—
75C31×C4⋊Q8—21no—
76C31×C4⋊Q8—21no—
77C31×C4⋊Q8—21no—
78C31×C4⋊Q8C2312yes—
79C31×C4⋊Q8C2311yescharacteristic
80C31×#127—21no—
81C31×#127C2311yescharacteristic
82C31×#124—22no—
83C31×#124—21no—
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—21no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—21no—
99C31×#121D412yes—
100C31×#120—22no—
101C31×#120—22no—
102C31×#120—22no—
103C4×Q8×C31D411yescharacteristic
104C4×Q8×C31C2311yescharacteristic
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—21no—
109C4×D4×C31—21no—
110C4×D4×C31—21no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31D412yes—
116C4×D4×C31D411yescharacteristic
117C4×D4×C31D411yescharacteristic
118C4×D4×C31D411yescharacteristic
119C4×D4×C31C2311yescharacteristic
120C4×D4×C31C2311yescharacteristic
121C4×D4×C31C2311yescharacteristic
122C31×#117—21no—
123C31×#117D411yescharacteristic
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31D411yescharacteristic
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—21no—
130C2×C42×C31—21no—
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×#106—22no—
134C31×#106—22no—
135C31×#106—22no—
136C31×C4⋊C8—21no—
137C31×C4⋊C8—21no—
138C31×C4⋊C8—21no—
139C31×C4⋊C8C2312yes—
140C31×C4⋊C8C2312yes—
141C31×#103—22no—
142C31×#103—24no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×C22⋊C8—21no—
147C4×C8×C31C2312yes—
148C24×C31—22no—
149C24×C31—21no—
150#41×C31—22no—
151#41×C31—48no—
152#41×C31—48no—
153#41×C31—42no—
154#41×C31—42no—
155#41×C31—42no—
156#41×C31—42no—
157#41×C31—42no—
158#41×C31—42no—
159#41×C31SD1614yescomplemented
160C2×Q8×C31—22no—
161C2×Q8×C31—21no—
162C2×Q8×C31—22no—
163C2×Q8×C31—42no—
164C2×Q8×C31—42no—
165C2×Q8×C31—41no—
166C2×Q8×C31—82no—
167C2×Q8×C31C2×D411yescharacteristic
168C2×D4×C31—21no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—22no—
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—41no—
180C2×D4×C31—42no—
181C2×D4×C31—48no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31C2×D411yescharacteristic
186C2×D4×C31C2×D411yescharacteristic
187C2×D4×C31C2×D411yescharacteristic
188C2×D4×C31C2×D412yes—
189C22×C4×C31—21no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—22no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—48no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—41no—
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208SD16×C31—84no—
209M16×C31—42no—
210C2×C8×C31—22no—
211C2×C8×C31—22no—
212C2×C8×C31—22no—
213C2×C8×C31—42no—
214C4⋊C4×C31—22no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—41no—
223C4⋊C4×C31—41no—
224C4⋊C4×C31C2×D412yes—
225C4⋊C4×C31C2×D411yescharacteristic
226C4⋊C4×C31C2×D411yescharacteristic
227C4⋊C4×C31C2×D411yescharacteristic
228C4⋊C4×C31C2×D411yescharacteristic
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—21no—
234C22⋊C4×C31—21no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—21no—
237C22⋊C4×C31—21no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—21no—
242C42×C31—21no—
243C42×C31—21no—
244C42×C31—21no—
245C42×C31C2×D411yescharacteristic
246C42×C31C2×D411yescharacteristic
247C42×C31C2×D411yescharacteristic
248C42×C31C2411yescharacteristic
249#18787C3111yesmaximal, characteristic, direct product factor, Sylow
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—22no—
254C23×C31—42no—
255C23×C31—44no—
256C23×C31—44no—
257C23×C31—42no—
258C23×C31—81no—
259C23×C31—82no—
260C23×C31#12011yescharacteristic
261Q8×C31—21no—
262Q8×C31—44no—
263Q8×C31—44no—
264Q8×C31—41no—
265Q8×C31—41no—
266Q8×C31—82no—
267Q8×C31C2×SD1612yes—
268D4×C31—24no—
269D4×C31—21no—
270D4×C31—21no—
271D4×C31—21no—
272D4×C31—21no—
273D4×C31—42no—
274D4×C31—42no—
275D4×C31—44no—
276D4×C31—44no—
277D4×C31—44no—
278D4×C31—44no—
279D4×C31—44no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—82no—
285D4×C31C2×SD1612yes—
286D4×C31#13712yes—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—24no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—22no—
295C2×C4×C31—21no—
296C2×C4×C31—41no—
297C2×C4×C31—44no—
298C2×C4×C31—44no—
299C2×C4×C31—44no—
300C2×C4×C31—42no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—42no—
308C2×C4×C31—44no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—81no—
312C2×C4×C31—82no—
313C2×C4×C31#12011yescharacteristic
314C2×C4×C31#12011yescharacteristic
315C2×C4×C31#12011yescharacteristic
316C2×C4×C31C2×SD1612yes—
317C2×C4×C31AGL(1,ℤ/8)12yes—
318C2×C4×C31C22×D411yescharacteristic
319C2×C4×C31C22×D411yescharacteristic
320C2×C4×C31C22×D411yescharacteristic
321C8×C31—42no—
322C8×C31—42no—
323C8×C31—42no—
324D4×#41C2×C3111yescharacteristic
325#3206C2×C3111yescharacteristic, complemented
326#3079C2×C3111yescharacteristic, complemented
327C2×#476C2×C3111yescharacteristic, complemented
328#1637C2×C3112yescomplemented
329#1635C2×C3112yescomplemented
330#1631C2×C3112yescomplemented
331#1629C2×C3112yescomplemented
332#1547C2×C3111yescharacteristic, complemented
333#1486C2×C3111yescharacteristic, complemented
334#1477C2×C3111yescharacteristic, complemented
335C22×C31—21no—
336C22×C31—21no—
337C22×C31—22no—
338C22×C31—22no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—41no—
342C22×C31—41no—
343C22×C31—42no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—41no—
349C22×C31—84no—
350C22×C31—88no—
351C22×C31#45012yes—
352C22×C31C2×#12011yescharacteristic
353C4×C31—22no—
354C4×C31—21no—
355C4×C31—21no—
356C4×C31—21no—
357C4×C31—41no—
358C4×C31—42no—
359C4×C31—41no—
360C4×C31—41no—
361C4×C31—41no—
362C4×C31—82no—
363C4×C31#45012yes—
364C4×C31C22×SD1611yescharacteristic
365C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
366C4×C31C2×#13711yescharacteristic
367C4×C31#57511yescharacteristic
368C22×#41—21no—
369#550C22×C3111yescharacteristic
370D4×Q8C22×C3111yescharacteristic
371#548—21no—
372#547—21no—
373#547C22×C3111yescharacteristic
374#546—22no—
375#546—21no—
376D42—21no—
377D42C22×C3111yescharacteristic
378#532—21no—
379#532C22×C3111yescharacteristic
380C2×C4⋊Q8C22×C3111yescharacteristic, complemented
381#525—22no—
382#525—21no—
383C4×#41C22×C3111yescharacteristic
384C2×C4×D4—21no—
385C2×C4×D4C22×C3111yescharacteristic
386#492C22×C3112yescomplemented
387#487C22×C3112yescomplemented
388#477C22×C3112yescomplemented
389#476—21no—
390#476—21no—
391#476C22×C3112yes—
392#476C22×C3112yescomplemented
393#476C22×C3112yescomplemented
394#475—21no—
395#474—21no—
396#461—22no—
397#448—22no—
398#431C22×C3111yescharacteristic, complemented
399#428—21no—
400C2×#106—21no—
401#423C22×C3111yescharacteristic, complemented
402C2×C4⋊C8C22×C3111yescharacteristic, complemented
403#417—21no—
404C2×#102—21no—
405#332C22×C3112yescomplemented
406#331C22×C3112yescomplemented
407Q8⋊C8C22×C3112yescomplemented
408D4⋊C8C22×C3112yes—
409D4⋊C8C22×C3112yescomplemented
410D4⋊C8C22×C3112yescomplemented
411C2×C31—22no—
412C2×C31—42no—
413C2×C31—42no—
414C2×C31—81no—
415C2×C31—82no—
416C2×C31C2×#45011yescharacteristic
417C2×C31#300711yescharacteristic
418C2×C31#302111yescharacteristic
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—44no—
425C2×#41—44no—
426C2×#41D4×C3111yescharacteristic
427C22×Q8—21no—
428C22×Q8—21no—
429C22×D4—22no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4D4×C3111yescharacteristic
433C23×C4—22no—
434C23×C4—21no—
435C2×SD16—24no—
436C2×M16—21no—
437C22×C8—21no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8—21no—
441C4⋊Q8—21no—
442C4⋊Q8C23×C3112yes—
443C4⋊Q8C23×C3111yescharacteristic
444#127—21no—
445#127C23×C3111yescharacteristic
446#124—22no—
447#124—21no—
448#123—22no—
449#123—22no—
450#123—22no—
451C22⋊Q8—22no—
452C22⋊Q8—21no—
453C22⋊Q8—22no—
454C22⋊Q8—21no—
455#121—22no—
456#121—22no—
457#121—22no—
458#121—21no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121D4×C3112yes—
464#120—22no—
465#120—22no—
466#120—22no—
467C4×Q8D4×C3111yescharacteristic
468C4×Q8C23×C3111yescharacteristic
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4D4×C3111yescharacteristic
480C4×D4D4×C3111yescharacteristic
481C4×D4D4×C3111yescharacteristic
482C4×D4D4×C3112yes—
483C4×D4C23×C3111yescharacteristic
484C4×D4C23×C3111yescharacteristic
485C4×D4C23×C3111yescharacteristic
486#117—21no—
487#117D4×C3111yescharacteristic
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4D4×C3111yescharacteristic
492C2×C22⋊C4—22no—
493C2×C22⋊C4—21no—
494C2×C42—21no—
495C2×C42C23×C3111yescharacteristic
496#107—22no—
497#106—22no—
498#106—22no—
499#106—22no—
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503C4⋊C8C23×C3112yes—
504C4⋊C8C23×C3112yes—
505#103—22no—
506#103—24no—
507#102—22no—
508#102—22no—
509#102—22no—
510C22⋊C8—21no—
511C4×C8C23×C3112yes—
512C31#1878711yescharacteristic, direct product factor, Sylow
513C24—22no—
514C24—21no—
515#41—22no—
516#41—48no—
517#41—48no—
518#41—42no—
519#41—42no—
520#41—42no—
521#41—42no—
522#41—42no—
523#41—42no—
524#41SD16×C3114yescomplemented
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—41no—
531C2×Q8—82no—
532C2×Q8C2×D4×C3111yescharacteristic
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4—48no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4C2×D4×C3111yescharacteristic
551C2×D4C2×D4×C3111yescharacteristic
552C2×D4C2×D4×C3111yescharacteristic
553C2×D4C2×D4×C3112yes—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—48no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—41no—
570C22×C4C2×D4×C3111yescharacteristic
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4C2×D4×C3111yescharacteristic
573SD16—84no—
574M16—42no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—42no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4C2×D4×C3112yes—
590C4⋊C4C2×D4×C3111yescharacteristic
591C4⋊C4C2×D4×C3111yescharacteristic
592C4⋊C4C2×D4×C3111yescharacteristic
593C4⋊C4C2×D4×C3111yescharacteristic
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42C2×D4×C3111yescharacteristic
611C42C2×D4×C3111yescharacteristic
612C42C2×D4×C3111yescharacteristic
613C42C24×C3111yescharacteristic
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—42no—
619C23—44no—
620C23—44no—
621C23—42no—
622C23—81no—
623C23—82no—
624C23C31×#12011yescharacteristic
625Q8—21no—
626Q8—44no—
627Q8—44no—
628Q8—41no—
629Q8—41no—
630Q8—82no—
631Q8C2×SD16×C3112yes—
632D4—24no—
633D4—21no—
634D4—21no—
635D4—21no—
636D4—21no—
637D4—42no—
638D4—42no—
639D4—44no—
640D4—44no—
641D4—44no—
642D4—44no—
643D4—44no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—82no—
649D4C2×SD16×C3112yes—
650D4C31×#13712yes—
651C2×C4—21no—
652C2×C4—24no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—44no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—81no—
676C2×C4—82no—
677C2×C4C31×#12011yescharacteristic
678C2×C4C31×#12011yescharacteristic
679C2×C4C31×#12011yescharacteristic
680C2×C4C2×SD16×C3112yes—
681C2×C4C31×AGL(1,ℤ/8)12yes—
682C2×C4C22×D4×C3111yescharacteristic
683C2×C4C22×D4×C3111yescharacteristic
684C2×C4C22×D4×C3111yescharacteristic
685C8—42no—
686C8—42no—
687C8—42no—
688C22—21no—
689C22—21no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—41no—
702C22—84no—
703C22—88no—
704C22C31×#45012yes—
705C22C2×C31×#12011yescharacteristic
706C4—22no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—41no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—82no—
716C4C31×#45012yes—
717C4C22×SD16×C3111yescharacteristic
718C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
719C4C2×C31×#13711yescharacteristic
720C4C31×#57511yescharacteristic
721C2—22no—
722C2—42no—
723C2—42no—
724C2—81no—
725C2—82no—
726C2C2×C31×#45011yescharacteristic
727C2C31×#300711yescharacteristic
728C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalD4×#41×C31C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3206C2semidirect
3. C31×#3079C2semidirect
4. C2×C31×#476C2semidirect
5. C31×#1637C2semidirect
6. C31×#1635C2semidirect
7. C31×#1631C2semidirect
8. C31×#1629C2semidirect
9. C31×#1547C2semidirect
10. C31×#1486C2semidirect
11. C31×#1477C2semidirect
24. C2×C31×C4⋊Q8C22semidirect
30. C31×#492C22semidirect
31. C31×#487C22semidirect
32. C31×#477C22semidirect
36. C31×#476C22semidirect
37. C31×#476C22semidirect
42. C31×#431C22semidirect
45. C31×#423C22semidirect
46. C2×C31×C4⋊C8C22semidirect
49. C31×#332C22semidirect
50. C31×#331C22semidirect
51. C31×Q8⋊C8C22semidirect
53. C31×D4⋊C8C22semidirect
54. C31×D4⋊C8C22semidirect
159. #41×C31SD16semidirect
249. #18787C31direct (N × H)
325. #3206C2×C31semidirect
326. #3079C2×C31semidirect
327. C2×#476C2×C31semidirect
328. #1637C2×C31semidirect
329. #1635C2×C31semidirect
330. #1631C2×C31semidirect
331. #1629C2×C31semidirect
332. #1547C2×C31semidirect
333. #1486C2×C31semidirect
334. #1477C2×C31semidirect
380. C2×C4⋊Q8C22×C31semidirect
386. #492C22×C31semidirect
387. #487C22×C31semidirect
388. #477C22×C31semidirect
392. #476C22×C31semidirect
393. #476C22×C31semidirect
398. #431C22×C31semidirect
401. #423C22×C31semidirect
402. C2×C4⋊C8C22×C31semidirect
405. #332C22×C31semidirect
406. #331C22×C31semidirect
407. Q8⋊C8C22×C31semidirect
409. D4⋊C8C22×C31semidirect
410. D4⋊C8C22×C31semidirect
512. C31#18787direct (N × H)
524. #41SD16×C31semidirect

Maximal subgroups

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

subgroupindex
D4×#41×C312
C31×#32062
C31×#30792
C2×C31×#4762
C31×#16372
C31×#16352
C31×#16312
C31×#16292
C31×#15472
C31×#14862
C31×#14772
#1878731