Finite Group Databasebeta

← C31×#23957 #21480716

Subgroups — C31×#23957 #21480716

Order 7936.

1318 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3495C211yesmaximal, characteristic, complemented
2C31×#3003C211yesmaximal, characteristic
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C31×#2435C211yesmaximal, characteristic, complemented
5C31×#2027C212yesmaximal, complemented
6C31×#2003C212yesmaximal, complemented
7C31×#1901C211yesmaximal, characteristic, complemented
8C31×#1888C212yesmaximal, complemented
9C31×#1883C212yesmaximal, complemented
10C31×#1871C211yesmaximal, characteristic, complemented
11C31×#1826C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C2×C31×AGL(1,ℤ/8)C2212yes—
14C22×M16×C31C2211yescharacteristic
15C31×#556—21no—
16C31×#554—21no—
17C31×#552—21no—
18C31×#552—22no—
19C31×#552—21no—
20C31×#551—22no—
21C31×#544C2211yescharacteristic, complemented
22C31×#542—21no—
23C31×#541—21no—
24C31×#536C2211yescharacteristic, complemented
25C31×#533—21no—
26C31×#529—21no—
27C2×C31×#124C2212yes—
28C31×#525C2211yescharacteristic
29C2×C31×C22⋊Q8C2211yescharacteristic
30C31×#520C2211yescharacteristic, complemented
31C31×#519C2211yescharacteristic, complemented
32C2×C31×#117C2211yescharacteristic
33C31×#450—21no—
34C31×#450—21no—
35C31×#447—21no—
36C31×#447—21no—
37C2×C31×#104C2212yescomplemented
38C31×#418—21no—
39C31×#418—21no—
40C31×#418C2212yes—
41C31×#418C2212yes—
42C31×#418C2212yes—
43C2×C31×#102—21no—
44C2×C31×#102—21no—
45C2×C31×#101C2212yescomplemented
46C31×#407C2211yescharacteristic
47C31×#394—22no—
48C31×#390C2212yes—
49C31×#379—22no—
50C4×C22⋊C4×C31C2211yescharacteristic
51C31×#343C2212yescomplemented
52C31×#339C2212yescomplemented
53C31×#339C2212yescomplemented
54C31×#339C2212yescomplemented
55C25×C31—21no—
56C2×#41×C31C2311yescharacteristic
57C22×Q8×C31C2311yescharacteristic
58C22×D4×C31—24no—
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—42no—
65C22×D4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C31×AGL(1,ℤ/8)—24no—
68C31×AGL(1,ℤ/8)—42no—
69C2×SD16×C31—22no—
70C2×D8×C31—22no—
71C2×M16×C31—21no—
72C2×M16×C31—42no—
73C2×M16×C31C2312yes—
74C2×M16×C31C2312yes—
75C22×C8×C31—21no—
76C31×C4⋊Q8—21no—
77C31×C4⋊Q8—21no—
78C31×C4⋊Q8—21no—
79C31×#126—22no—
80C31×#126—22no—
81C31×#126—22no—
82C31×#126—22no—
83C31×#125—22no—
84C31×#125—22no—
85C31×#125—22no—
86C31×#125—21no—
87C31×#125—21no—
88C31×#124—22no—
89C31×#124—21no—
90C31×#124—24no—
91C31×#124—42no—
92C31×#123—22no—
93C31×#123—22no—
94C31×#123—21no—
95C31×#123—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8—21no—
100C31×C22⋊Q8—21no—
101C31×C22⋊Q8—21no—
102C31×C22⋊Q8—22no—
103C31×C22⋊Q8—21no—
104C31×C22⋊Q8—21no—
105C31×C22⋊Q8D411yescharacteristic
106C31×C22⋊Q8D411yescharacteristic
107C31×#121D411yescharacteristic
108C31×#121D411yescharacteristic
109C31×#120—21no—
110C4×Q8×C31—22no—
111C4×Q8×C31—21no—
112C4×Q8×C31—21no—
113C4×Q8×C31—21no—
114C4×Q8×C31—21no—
115C4×Q8×C31—21no—
116C4×D4×C31—22no—
117C4×D4×C31—21no—
118C4×D4×C31—22no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C31×#117—22no—
122C31×#117—22no—
123C31×#117—21no—
124C31×#117—21no—
125C31×#117—22no—
126C31×#117—21no—
127C31×#117D411yescharacteristic
128C31×#117D411yescharacteristic
129C31×#117C2311yescharacteristic
130C31×#117C2311yescharacteristic
131C31×#117C2311yescharacteristic
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31D412yes—
134C2×C4⋊C4×C31D411yescharacteristic
135C2×C4⋊C4×C31D411yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—24no—
140C2×C22⋊C4×C31—24no—
141C2×C22⋊C4×C31D412yes—
142C2×C42×C31—21no—
143C2×C42×C31C2312yes—
144C31×#104—42no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—22no—
149C31×#102—22no—
150C31×#102—22no—
151C31×#101—42no—
152C31×C22⋊C8—21no—
153C31×C22⋊C8—21no—
154C31×#95—21no—
155C24×C31—22no—
156C24×C31—44no—
157C24×C31—44no—
158C24×C31—41no—
159C24×C31—41no—
160C24×C31—82no—
161C24×C31C2×D411yescharacteristic
162#41×C31—22no—
163#41×C31—22no—
164C2×Q8×C31—22no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—22no—
168C2×Q8×C31—22no—
169C2×Q8×C31C2×D411yescharacteristic
170C2×D4×C31—24no—
171C2×D4×C31—24no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—44no—
181C2×D4×C31—44no—
182C2×D4×C31—44no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—41no—
186C2×D4×C31—41no—
187C2×D4×C31C2×D411yescharacteristic
188C2×D4×C31#4114yes—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—21no—
192C22×C4×C31—22no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—22no—
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D412yes—
203C22×C4×C31C2411yescharacteristic
204SD16×C31—44no—
205D8×C31—44no—
206M16×C31—22no—
207M16×C31—22no—
208M16×C31—22no—
209M16×C31—22no—
210M16×C31—42no—
211C2×C8×C31—22no—
212C2×C8×C31—22no—
213C2×C8×C31—42no—
214C4⋊C4×C31—22no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—22no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31—22no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31C2×D411yescharacteristic
231C4⋊C4×C31C2×D411yescharacteristic
232C4⋊C4×C31C2×D411yescharacteristic
233C4⋊C4×C31C2×D411yescharacteristic
234C4⋊C4×C31C2×D411yescharacteristic
235C4⋊C4×C31C2×D411yescharacteristic
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—48no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—84no—
253C42×C31—22no—
254C42×C31—22no—
255C42×C31—22no—
256C42×C31—21no—
257C42×C31—21no—
258C42×C31—21no—
259C42×C31—21no—
260C42×C31—21no—
261C42×C31—22no—
262C42×C31—22no—
263#23957C3111yesmaximal, characteristic, direct product factor, Sylow
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—21no—
267C23×C31—24no—
268C23×C31—41no—
269C23×C31—44no—
270C23×C31—44no—
271C23×C31—44no—
272C23×C31—44no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—82no—
276C23×C31—82no—
277C23×C31—82no—
278C23×C31—816no—
279C23×C31—82no—
280C23×C31#12011yescharacteristic
281C23×C31#12011yescharacteristic
282C23×C31C22×D411yescharacteristic
283Q8×C31—22no—
284Q8×C31—41no—
285Q8×C31—41no—
286Q8×C31—42no—
287Q8×C31—82no—
288D4×C31—24no—
289D4×C31—22no—
290D4×C31—24no—
291D4×C31—44no—
292D4×C31—44no—
293D4×C31—42no—
294D4×C31—42no—
295D4×C31—42no—
296D4×C31—42no—
297D4×C31—81no—
298C2×C4×C31—22no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—22no—
314C2×C4×C31—24no—
315C2×C4×C31—42no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—81no—
323C2×C4×C31—82no—
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31#12011yescharacteristic
326C2×C4×C31C22×D411yescharacteristic
327C2×C4×C31C22×D411yescharacteristic
328C2×C4×C31C2×#4112yes—
329C2×C4×C31H(5,𝔽2)12yes—
330C8×C31—42no—
331C8×C31—42no—
332#3495C2×C3111yescharacteristic, complemented
333#3003C2×C3111yescharacteristic
334C2×#418C2×C3111yescharacteristic, complemented
335#2435C2×C3111yescharacteristic, complemented
336#2027C2×C3112yescomplemented
337#2003C2×C3112yescomplemented
338#1901C2×C3111yescharacteristic, complemented
339#1888C2×C3112yescomplemented
340#1883C2×C3112yescomplemented
341#1871C2×C3111yescharacteristic, complemented
342#1826C2×C3111yescharacteristic, complemented
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—21no—
349C22×C31—21no—
350C22×C31—44no—
351C22×C31—48no—
352C22×C31—41no—
353C22×C31—44no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—84no—
357C22×C31—88no—
358C22×C31—88no—
359C22×C31—82no—
360C22×C31—82no—
361C22×C31#45412yes—
362C22×C31C2×#12011yescharacteristic
363C22×C31#54612yes—
364C4×C31—21no—
365C4×C31—21no—
366C4×C31—42no—
367C4×C31—41no—
368C4×C31—41no—
369C4×C31—41no—
370C4×C31—41no—
371C4×C31—42no—
372C4×C31—41no—
373C4×C31—41no—
374C4×C31—41no—
375C4×C31—82no—
376C4×C31#52511yescharacteristic
377C4×C31#53511yescharacteristic
378C4×C31#54612yes—
379C23×D4C22×C3111yescharacteristic
380C2×AGL(1,ℤ/8)C22×C3112yes—
381C22×M16C22×C3111yescharacteristic
382#556—21no—
383#554—21no—
384#552—21no—
385#552—22no—
386#552—21no—
387#551—22no—
388#544C22×C3111yescharacteristic, complemented
389#542—21no—
390#541—21no—
391#536C22×C3111yescharacteristic, complemented
392#533—21no—
393#529—21no—
394C2×#124C22×C3112yes—
395#525C22×C3111yescharacteristic
396C2×C22⋊Q8C22×C3111yescharacteristic
397#520C22×C3111yescharacteristic, complemented
398#519C22×C3111yescharacteristic, complemented
399C2×#117C22×C3111yescharacteristic
400#450—21no—
401#450—21no—
402#447—21no—
403#447—21no—
404C2×#104C22×C3112yescomplemented
405#418—21no—
406#418—21no—
407#418C22×C3112yes—
408#418C22×C3112yes—
409#418C22×C3112yes—
410C2×#102—21no—
411C2×#102—21no—
412C2×#101C22×C3112yescomplemented
413#407C22×C3111yescharacteristic
414#394—22no—
415#390C22×C3112yes—
416#379—22no—
417C4×C22⋊C4C22×C3111yescharacteristic
418#343C22×C3112yescomplemented
419#339C22×C3112yescomplemented
420#339C22×C3112yescomplemented
421#339C22×C3112yescomplemented
422C2×C31—22no—
423C2×C31—22no—
424C2×C31—41no—
425C2×C31—81no—
426C2×C31—84no—
427C2×C31#240411yescharacteristic
428C2×C31C2×#45411yescharacteristic
429C2×C31#302111yescharacteristic
430C25—21no—
431C2×#41C23×C3111yescharacteristic
432C22×Q8C23×C3111yescharacteristic
433C22×D4—24no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—42no—
440C22×D4C23×C3112yes—
441C23×C4C23×C3111yescharacteristic
442AGL(1,ℤ/8)—24no—
443AGL(1,ℤ/8)—42no—
444C2×SD16—22no—
445C2×D8—22no—
446C2×M16—21no—
447C2×M16—42no—
448C2×M16C23×C3112yes—
449C2×M16C23×C3112yes—
450C22×C8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454#126—22no—
455#126—22no—
456#126—22no—
457#126—22no—
458#125—22no—
459#125—22no—
460#125—22no—
461#125—21no—
462#125—21no—
463#124—22no—
464#124—21no—
465#124—24no—
466#124—42no—
467#123—22no—
468#123—22no—
469#123—21no—
470#123—22no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—22no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8D4×C3111yescharacteristic
481C22⋊Q8D4×C3111yescharacteristic
482#121D4×C3111yescharacteristic
483#121D4×C3111yescharacteristic
484#120—21no—
485C4×Q8—22no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496#117—22no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117—22no—
501#117—21no—
502#117D4×C3111yescharacteristic
503#117D4×C3111yescharacteristic
504#117C23×C3111yescharacteristic
505#117C23×C3111yescharacteristic
506#117C23×C3111yescharacteristic
507C2×C4⋊C4—21no—
508C2×C4⋊C4D4×C3112yes—
509C2×C4⋊C4D4×C3111yescharacteristic
510C2×C4⋊C4D4×C3111yescharacteristic
511C2×C4⋊C4C23×C3111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4D4×C3112yes—
517C2×C42—21no—
518C2×C42C23×C3112yes—
519#104—42no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#101—42no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529#95—21no—
530C31#2395711yescharacteristic, direct product factor, Sylow
531C24—22no—
532C24—44no—
533C24—44no—
534C24—41no—
535C24—41no—
536C24—82no—
537C24C2×D4×C3111yescharacteristic
538#41—22no—
539#41—22no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8C2×D4×C3111yescharacteristic
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4C2×D4×C3111yescharacteristic
564C2×D4#41×C3114yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4C2×D4×C3112yes—
573C22×C4C2×D4×C3111yescharacteristic
574C22×C4C2×D4×C3111yescharacteristic
575C22×C4C2×D4×C3111yescharacteristic
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3112yes—
579C22×C4C24×C3111yescharacteristic
580SD16—44no—
581D8—44no—
582M16—22no—
583M16—22no—
584M16—22no—
585M16—22no—
586M16—42no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—42no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4C2×D4×C3111yescharacteristic
607C4⋊C4C2×D4×C3111yescharacteristic
608C4⋊C4C2×D4×C3111yescharacteristic
609C4⋊C4C2×D4×C3111yescharacteristic
610C4⋊C4C2×D4×C3111yescharacteristic
611C4⋊C4C2×D4×C3111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—48no—
627C22⋊C4—42no—
628C22⋊C4—84no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—22no—
638C42—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—24no—
643C23—41no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23—82no—
651C23—82no—
652C23—82no—
653C23—816no—
654C23—82no—
655C23C31×#12011yescharacteristic
656C23C31×#12011yescharacteristic
657C23C22×D4×C3111yescharacteristic
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—42no—
662Q8—82no—
663D4—24no—
664D4—22no—
665D4—24no—
666D4—44no—
667D4—44no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—81no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4C31×#12011yescharacteristic
700C2×C4C31×#12011yescharacteristic
701C2×C4C22×D4×C3111yescharacteristic
702C2×C4C22×D4×C3111yescharacteristic
703C2×C4C2×#41×C3112yes—
704C2×C4C31×H(5,𝔽2)12yes—
705C8—42no—
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—44no—
715C22—48no—
716C22—41no—
717C22—44no—
718C22—41no—
719C22—41no—
720C22—84no—
721C22—88no—
722C22—88no—
723C22—82no—
724C22—82no—
725C22C31×#45412yes—
726C22C2×C31×#12011yescharacteristic
727C22C31×#54612yes—
728C4—21no—
729C4—21no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—82no—
740C4C31×#52511yescharacteristic
741C4C31×#53511yescharacteristic
742C4C31×#54612yes—
743C2—22no—
744C2—22no—
745C2—41no—
746C2—84no—
747C2—81no—
748C2C31×#240411yescharacteristic
749C2C2×C31×#45411yescharacteristic
750C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3003C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3495C2semidirect
3. C2×C31×#418C2semidirect
4. C31×#2435C2semidirect
5. C31×#2027C2semidirect
6. C31×#2003C2semidirect
7. C31×#1901C2semidirect
8. C31×#1888C2semidirect
9. C31×#1883C2semidirect
10. C31×#1871C2semidirect
11. C31×#1826C2semidirect
21. C31×#544C22semidirect
24. C31×#536C22semidirect
30. C31×#520C22semidirect
31. C31×#519C22semidirect
37. C2×C31×#104C22semidirect
45. C2×C31×#101C22semidirect
51. C31×#343C22semidirect
52. C31×#339C22semidirect
53. C31×#339C22semidirect
54. C31×#339C22semidirect
263. #23957C31direct (N × H)
332. #3495C2×C31semidirect
334. C2×#418C2×C31semidirect
335. #2435C2×C31semidirect
336. #2027C2×C31semidirect
337. #2003C2×C31semidirect
338. #1901C2×C31semidirect
339. #1888C2×C31semidirect
340. #1883C2×C31semidirect
341. #1871C2×C31semidirect
342. #1826C2×C31semidirect
388. #544C22×C31semidirect
391. #536C22×C31semidirect
397. #520C22×C31semidirect
398. #519C22×C31semidirect
404. C2×#104C22×C31semidirect
412. C2×#101C22×C31semidirect
418. #343C22×C31semidirect
419. #339C22×C31semidirect
420. #339C22×C31semidirect
421. #339C22×C31semidirect
530. C31#23957direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34952
C31×#30032
C2×C31×#4182
C31×#24352
C31×#20272
C31×#20032
C31×#19012
C31×#18882
C31×#18832
C31×#18712
C31×#18262
#2395731