Finite Group Databasebeta

← C31×#8465 #21465224

Subgroups — C31×#8465 #21465224

Order 7936.

1088 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3488C211yesmaximal, characteristic
2C31×#1964C211yesmaximal, characteristic, complemented
3C31×#1789C211yesmaximal, characteristic, complemented
4C31×#1788C211yesmaximal, characteristic, complemented
5C31×#1513C211yesmaximal, characteristic, complemented
6C31×#1501C211yesmaximal, characteristic, complemented
7C31×#1471C211yesmaximal, characteristic, complemented
8C2×C31×H(5,𝔽2)C411yescharacteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C31×#550—21no—
11C31×#548—21no—
12C31×#546—21no—
13C31×#546—22no—
14D42×C31—22no—
15D42×C31—21no—
16C31×#537—21no—
17C31×#537C411yescharacteristic, complemented
18C31×#535—21no—
19C31×#535C411yescharacteristic, complemented
20C31×#525—21no—
21C31×#525C2211yescharacteristic
22C2×C31×#121—21no—
23C2×C31×#121C2211yescharacteristic
24C31×#520C411yescharacteristic, complemented
25C2×C31×#104—21no—
26C2×C31×#104—21no—
27C2×C31×#103—21no—
28C2×C31×#102—21no—
29C2×C31×#99—22no—
30C31×#407C2211yescharacteristic, complemented
31C2×C31×C22⋊C8C2211yescharacteristic, complemented
32C31×#380C2211yescharacteristic, complemented
33C4×C22⋊C4×C31C2211yescharacteristic, complemented
34C31×#328—21no—
35C31×#328—21no—
36C31×#327—21no—
37C31×#327—21no—
38C31×#323—22no—
39C31×H(5,𝔽2)—42no—
40C31×H(5,𝔽2)—42no—
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—42no—
46C2×#41×C31—42no—
47C2×#41×C31C2×C411yescharacteristic
48C2×#41×C31C2×C411yescharacteristic
49C2×#41×C31C2×C411yescharacteristic
50C2×#41×C31D411yescharacteristic
51C2×#41×C31D411yescharacteristic
52C22×Q8×C31D411yescharacteristic
53C22×D4×C31—22no—
54C22×D4×C31—21no—
55C22×D4×C31—22no—
56C22×D4×C31—21no—
57C22×D4×C31—21no—
58C22×D4×C31C2×C411yescharacteristic
59C22×D4×C31D412yes—
60C22×D4×C31D411yescharacteristic
61C23×C4×C31—21no—
62C23×C4×C31C2311yescharacteristic
63C2×M16×C31—21no—
64C22×C8×C31—21no—
65C31×#127—22no—
66C31×#127—21no—
67C31×#124—22no—
68C31×#124—21no—
69C31×#123—22no—
70C31×#123—21no—
71C31×C22⋊Q8—22no—
72C31×C22⋊Q8—21no—
73C31×C22⋊Q8—21no—
74C31×C22⋊Q8D411yescharacteristic
75C31×C22⋊Q8D411yescharacteristic
76C31×#121—22no—
77C31×#121—22no—
78C31×#121—22no—
79C31×#121—22no—
80C31×#121—22no—
81C31×#121—21no—
82C31×#121—21no—
83C31×#121—22no—
84C31×#121—21no—
85C31×#121—21no—
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121D411yescharacteristic
91C31×#121D411yescharacteristic
92C31×#120—22no—
93C31×#120—22no—
94C31×#120—22no—
95C31×#120—22no—
96C31×#120—21no—
97C4×Q8×C31—21no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—21no—
101C4×D4×C31—22no—
102C4×D4×C31—21no—
103C4×D4×C31—21no—
104C31×#117—21no—
105C31×#117C2×C411yescharacteristic
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31C2×C411yescharacteristic
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31D412yes—
113C2×C42×C31—21no—
114C31×#104—42no—
115C31×#104—42no—
116C31×#103—42no—
117C31×#102—42no—
118C31×#99—44no—
119C31×C22⋊C8—21no—
120C31×C22⋊C8—21no—
121C31×C22⋊C8—21no—
122C31×C22⋊C8—21no—
123C31×#95—21no—
124C31×#95—21no—
125C24×C31—22no—
126C24×C31—21no—
127C24×C31C22⋊C412yes—
128C24×C31C2×D411yescharacteristic
129#41×C31—22no—
130#41×C31—22no—
131#41×C31—22no—
132#41×C31—22no—
133#41×C31—41no—
134#41×C31—41no—
135#41×C31—41no—
136#41×C31—41no—
137#41×C31—44no—
138#41×C31—44no—
139#41×C31—41no—
140#41×C31—41no—
141#41×C31—44no—
142#41×C31—42no—
143#41×C31—42no—
144C2×Q8×C31—21no—
145C2×Q8×C31—22no—
146C2×Q8×C31—41no—
147C2×Q8×C31C22⋊C411yescharacteristic
148C2×Q8×C31C22⋊C411yescharacteristic
149C2×Q8×C31C22⋊C411yescharacteristic
150C2×D4×C31—21no—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—22no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—22no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—41no—
169C2×D4×C31—44no—
170C2×D4×C31—41no—
171C2×D4×C31—41no—
172C2×D4×C31—44no—
173C2×D4×C31—48no—
174C2×D4×C31—42no—
175C2×D4×C31—42no—
176C2×D4×C31—42no—
177C2×D4×C31—42no—
178C2×D4×C31—82no—
179C2×D4×C31—82no—
180C2×D4×C31C22⋊C411yescharacteristic
181C2×D4×C31C22⋊C411yescharacteristic
182C2×D4×C31C22⋊C411yescharacteristic
183C22×C4×C31—21no—
184C22×C4×C31—22no—
185C22×C4×C31—21no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—41no—
192C22×C4×C31—41no—
193C22×C4×C31—44no—
194C22×C4×C31—41no—
195C22×C4×C31—41no—
196C22×C4×C31C22⋊C412yes—
197C22×C4×C31C22×C411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203M16×C31—41no—
204M16×C31—41no—
205C2×C8×C31—41no—
206C2×C8×C31—41no—
207C2×C8×C31—41no—
208C2×C8×C31—41no—
209C4⋊C4×C31—22no—
210C4⋊C4×C31—22no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—41no—
216C4⋊C4×C31—41no—
217C4⋊C4×C31C22⋊C411yescharacteristic
218C4⋊C4×C31C22⋊C411yescharacteristic
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—21no—
225C22⋊C4×C31—21no—
226C22⋊C4×C31—21no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—21no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—41no—
233C22⋊C4×C31—42no—
234C42×C31—22no—
235C42×C31—21no—
236C42×C31—41no—
237C42×C31—41no—
238#8465C3111yesmaximal, characteristic, direct product factor, Sylow
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—22no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—42no—
248C23×C31—44no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—81no—
255C23×C31—82no—
256C23×C31—82no—
257C23×C31C2×C22⋊C411yescharacteristic
258C23×C31#12011yescharacteristic
259C23×C31#12011yescharacteristic
260Q8×C31—21no—
261Q8×C31—21no—
262Q8×C31—21no—
263Q8×C31—42no—
264Q8×C31—41no—
265Q8×C31#9912yescomplemented
266D4×C31—24no—
267D4×C31—21no—
268D4×C31—21no—
269D4×C31—21no—
270D4×C31—42no—
271D4×C31—42no—
272D4×C31—41no—
273D4×C31—42no—
274D4×C31—44no—
275D4×C31—42no—
276D4×C31—42no—
277D4×C31—44no—
278D4×C31—42no—
279D4×C31—42no—
280D4×C31—41no—
281D4×C31—42no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—81no—
286D4×C31—82no—
287D4×C31—82no—
288D4×C31—82no—
289D4×C31—82no—
290D4×C31#9912yescomplemented
291C2×C4×C31—24no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—44no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—82no—
317C2×C4×C31—81no—
318C2×C4×C31—81no—
319C2×C4×C31—81no—
320C2×C4×C31—81no—
321C2×C4×C31—81no—
322C2×C4×C31C2×C22⋊C411yescharacteristic
323C2×C4×C31C2×C22⋊C411yescharacteristic
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31#12011yescharacteristic
326C8×C31—81no—
327C8×C31—81no—
328#3488C2×C3111yescharacteristic
329#1964C2×C3111yescharacteristic, complemented
330#1789C2×C3111yescharacteristic, complemented
331#1788C2×C3111yescharacteristic, complemented
332#1513C2×C3111yescharacteristic, complemented
333#1501C2×C3111yescharacteristic, complemented
334#1471C2×C3111yescharacteristic, complemented
335C22×C31—21no—
336C22×C31—21no—
337C22×C31—21no—
338C22×C31—21no—
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—22no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—42no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—42no—
354C22×C31—41no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—82no—
358C22×C31—82no—
359C22×C31—162no—
360C22×C31—164no—
361C22×C31#37911yescharacteristic
362C22×C31#45311yescharacteristic
363C22×C31#45511yescharacteristic
364C4×C31—21no—
365C4×C31—21no—
366C4×C31—21no—
367C4×C31—22no—
368C4×C31—42no—
369C4×C31—41no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—41no—
373C4×C31—82no—
374C4×C31—161no—
375C4×C31C2×#9911yescharacteristic
376C4×C31C2×#9911yescharacteristic
377C2×H(5,𝔽2)C4×C3111yescharacteristic, complemented
378C22×#41C22×C3111yescharacteristic
379#550—21no—
380#548—21no—
381#546—21no—
382#546—22no—
383D42—22no—
384D42—21no—
385#537—21no—
386#537C4×C3111yescharacteristic, complemented
387#535—21no—
388#535C4×C3111yescharacteristic, complemented
389#525—21no—
390#525C22×C3111yescharacteristic
391C2×#121—21no—
392C2×#121C22×C3111yescharacteristic
393#520C4×C3111yescharacteristic, complemented
394C2×#104—21no—
395C2×#104—21no—
396C2×#103—21no—
397C2×#102—21no—
398C2×#99—22no—
399#407C22×C3111yescharacteristic, complemented
400C2×C22⋊C8C22×C3111yescharacteristic, complemented
401#380C22×C3111yescharacteristic, complemented
402C4×C22⋊C4C22×C3111yescharacteristic, complemented
403#328—21no—
404#328—21no—
405#327—21no—
406#327—21no—
407#323—22no—
408C2×C31—21no—
409C2×C31—21no—
410C2×C31—41no—
411C2×C31—41no—
412C2×C31—42no—
413C2×C31—81no—
414C2×C31—82no—
415C2×C31—81no—
416C2×C31#178111yescharacteristic
417C2×C31#179211yescharacteristic
418C2×C31#179411yescharacteristic
419H(5,𝔽2)—42no—
420H(5,𝔽2)—42no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—42no—
426C2×#41—42no—
427C2×#41C2×C4×C3111yescharacteristic
428C2×#41C2×C4×C3111yescharacteristic
429C2×#41C2×C4×C3111yescharacteristic
430C2×#41D4×C3111yescharacteristic
431C2×#41D4×C3111yescharacteristic
432C22×Q8D4×C3111yescharacteristic
433C22×D4—22no—
434C22×D4—21no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C2×C4×C3111yescharacteristic
439C22×D4D4×C3112yes—
440C22×D4D4×C3111yescharacteristic
441C23×C4—21no—
442C23×C4C23×C3111yescharacteristic
443C2×M16—21no—
444C22×C8—21no—
445#127—22no—
446#127—21no—
447#124—22no—
448#124—21no—
449#123—22no—
450#123—21no—
451C22⋊Q8—22no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8D4×C3111yescharacteristic
455C22⋊Q8D4×C3111yescharacteristic
456#121—22no—
457#121—22no—
458#121—22no—
459#121—22no—
460#121—22no—
461#121—21no—
462#121—21no—
463#121—22no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121D4×C3111yescharacteristic
471#121D4×C3111yescharacteristic
472#120—22no—
473#120—22no—
474#120—22no—
475#120—22no—
476#120—21no—
477C4×Q8—21no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—21no—
481C4×D4—22no—
482C4×D4—21no—
483C4×D4—21no—
484#117—21no—
485#117C2×C4×C3111yescharacteristic
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4C2×C4×C3111yescharacteristic
489C2×C22⋊C4—22no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C3112yes—
493C2×C42—21no—
494#104—42no—
495#104—42no—
496#103—42no—
497#102—42no—
498#99—44no—
499C22⋊C8—21no—
500C22⋊C8—21no—
501C22⋊C8—21no—
502C22⋊C8—21no—
503#95—21no—
504#95—21no—
505C31#846511yescharacteristic, direct product factor, Sylow
506C24—22no—
507C24—21no—
508C24C22⋊C4×C3112yes—
509C24C2×D4×C3111yescharacteristic
510#41—22no—
511#41—22no—
512#41—22no—
513#41—22no—
514#41—41no—
515#41—41no—
516#41—41no—
517#41—41no—
518#41—44no—
519#41—44no—
520#41—41no—
521#41—41no—
522#41—44no—
523#41—42no—
524#41—42no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—41no—
528C2×Q8C22⋊C4×C3111yescharacteristic
529C2×Q8C22⋊C4×C3111yescharacteristic
530C2×Q8C22⋊C4×C3111yescharacteristic
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—41no—
550C2×D4—44no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—44no—
554C2×D4—48no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4C22⋊C4×C3111yescharacteristic
562C2×D4C22⋊C4×C3111yescharacteristic
563C2×D4C22⋊C4×C3111yescharacteristic
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—44no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4C22⋊C4×C3112yes—
578C22×C4C22×C4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584M16—41no—
585M16—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4C22⋊C4×C3111yescharacteristic
599C4⋊C4C22⋊C4×C3111yescharacteristic
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—41no—
614C22⋊C4—42no—
615C42—22no—
616C42—21no—
617C42—41no—
618C42—41no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—21no—
624C23—21no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—44no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—81no—
635C23—82no—
636C23—82no—
637C23C2×C22⋊C4×C3111yescharacteristic
638C23C31×#12011yescharacteristic
639C23C31×#12011yescharacteristic
640Q8—21no—
641Q8—21no—
642Q8—21no—
643Q8—42no—
644Q8—41no—
645Q8C31×#9912yescomplemented
646D4—24no—
647D4—21no—
648D4—21no—
649D4—21no—
650D4—42no—
651D4—42no—
652D4—41no—
653D4—42no—
654D4—44no—
655D4—42no—
656D4—42no—
657D4—44no—
658D4—42no—
659D4—42no—
660D4—41no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—82no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4C31×#9912yescomplemented
671C2×C4—24no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—82no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4C2×C22⋊C4×C3111yescharacteristic
703C2×C4C2×C22⋊C4×C3111yescharacteristic
704C2×C4C31×#12011yescharacteristic
705C2×C4C31×#12011yescharacteristic
706C8—81no—
707C8—81no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—82no—
732C22—162no—
733C22—164no—
734C22C31×#37911yescharacteristic
735C22C31×#45311yescharacteristic
736C22C31×#45511yescharacteristic
737C4—21no—
738C4—21no—
739C4—21no—
740C4—22no—
741C4—41no—
742C4—41no—
743C4—42no—
744C4—41no—
745C4—41no—
746C4—82no—
747C4—161no—
748C4C2×C31×#9911yescharacteristic
749C4C2×C31×#9911yescharacteristic
750C2—21no—
751C2—21no—
752C2—41no—
753C2—41no—
754C2—42no—
755C2—81no—
756C2—81no—
757C2—82no—
758C2C31×#178111yescharacteristic
759C2C31×#179211yescharacteristic
760C2C31×#179411yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3488C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1964C2semidirect
3. C31×#1789C2semidirect
4. C31×#1788C2semidirect
5. C31×#1513C2semidirect
6. C31×#1501C2semidirect
7. C31×#1471C2semidirect
8. C2×C31×H(5,𝔽2)C4semidirect
17. C31×#537C4semidirect
19. C31×#535C4semidirect
24. C31×#520C4semidirect
30. C31×#407C22semidirect
31. C2×C31×C22⋊C8C22semidirect
32. C31×#380C22semidirect
33. C4×C22⋊C4×C31C22semidirect
238. #8465C31direct (N × H)
265. Q8×C31#99semidirect
290. D4×C31#99semidirect
329. #1964C2×C31semidirect
330. #1789C2×C31semidirect
331. #1788C2×C31semidirect
332. #1513C2×C31semidirect
333. #1501C2×C31semidirect
334. #1471C2×C31semidirect
377. C2×H(5,𝔽2)C4×C31semidirect
386. #537C4×C31semidirect
388. #535C4×C31semidirect
393. #520C4×C31semidirect
399. #407C22×C31semidirect
400. C2×C22⋊C8C22×C31semidirect
401. #380C22×C31semidirect
402. C4×C22⋊C4C22×C31semidirect
505. C31#8465direct (N × H)
645. Q8C31×#99semidirect
670. D4C31×#99semidirect

Maximal subgroups

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

subgroupindex
C31×#34882
C31×#19642
C31×#17892
C31×#17882
C31×#15132
C31×#15012
C31×#14712
#846531