Finite Group Databasebeta

← C31×#23402 #21480161

Subgroups — C31×#23402 #21480161

Order 7936.

2198 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic, complemented
2C2×C31×#535C211yesmaximal, characteristic, complemented
3C2×C31×#535C211yesmaximal, characteristic, complemented
4C2×C31×#421C211yesmaximal, characteristic, complemented
5C31×#2896C211yesmaximal, characteristic, complemented
6C22×C31×#100C211yesmaximal, characteristic, complemented
7C31×#2004C214yesmaximal, complemented
8C31×#2002C214yesmaximal, complemented
9C31×#1733C211yesmaximal, characteristic, complemented
10C22×#41×C31C2211yescharacteristic
11C22×#41×C31C2211yescharacteristic
12C23×D4×C31C2211yescharacteristic
13C31×#575—24no—
14C31×#575—24no—
15C2×C31×#137—21no—
16C2×C31×#137C2212yescomplemented
17C2×C31×AGL(1,ℤ/8)—21no—
18C2×C31×AGL(1,ℤ/8)C2212yescomplemented
19C2×C31×#135—22no—
20C22×M16×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C31×#535—22no—
23C31×#535—24no—
24C31×#535—22no—
25C31×#535—22no—
26C31×#535—24no—
27C31×#535C2214yes—
28C2×C31×#127—21no—
29C2×C31×#127C2212yescomplemented
30C2×C31×#124—21no—
31C2×C31×#124C2212yescomplemented
32C2×C31×#121—22no—
33C2×C31×#121—22no—
34C2×C31×#120—22no—
35C2×C31×#120—22no—
36C2×C31×#117C2211yescharacteristic
37C2×C31×#117C2211yescharacteristic
38C31×#421—24no—
39C2×C31×#104C2214yescomplemented
40C31×#419C2212yescomplemented
41C31×#418C2212yescomplemented
42C31×#417—22no—
43C31×#416—22no—
44C2×C31×#100—24no—
45C2×C31×#100C2214yescomplemented
46C31×#339C2214yescomplemented
47C25×C31D412yes—
48C2×#41×C31—21no—
49C2×#41×C31—22no—
50C2×#41×C31—21no—
51C2×#41×C31—21no—
52C2×#41×C31—21no—
53C2×#41×C31—22no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—22no—
57C2×#41×C31—22no—
58C2×#41×C31—22no—
59C2×#41×C31—22no—
60C2×#41×C31—22no—
61C2×#41×C31D412yescomplemented
62C2×#41×C31D414yescomplemented
63C2×#41×C31C2312yes—
64C22×Q8×C31D411yescharacteristic, complemented
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—24no—
69C22×D4×C31—24no—
70C22×D4×C31—22no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31—22no—
75C22×D4×C31—21no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31D412yes—
79C22×D4×C31D411yescharacteristic, complemented
80C22×D4×C31C2312yes—
81C22×D4×C31C2311yescharacteristic
82C23×C4×C31—21no—
83C23×C4×C31—21no—
84C23×C4×C31C2311yescharacteristic
85C31×#137—28no—
86C31×#137—24no—
87C31×#137—24no—
88C31×AGL(1,ℤ/8)—28no—
89C31×AGL(1,ℤ/8)—24no—
90C31×AGL(1,ℤ/8)—24no—
91C31×#135—216no—
92C2×Q16×C31—22no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×D8×C31—22no—
96C2×M16×C31—21no—
97C2×M16×C31—22no—
98C2×M16×C31—21no—
99C2×M16×C31—22no—
100C2×M16×C31—22no—
101C2×M16×C31D414yescomplemented
102C2×M16×C31C2312yes—
103C2×M16×C31C2312yes—
104C22×C8×C31—21no—
105C22×C8×C31—21no—
106C31×#127—24no—
107C31×#127—24no—
108C31×#127—24no—
109C31×#127—24no—
110C31×#124—24no—
111C31×#124—24no—
112C31×#124—24no—
113C31×#124—24no—
114C31×#121—216no—
115C31×#121—28no—
116C31×#121—28no—
117C31×#120—216no—
118C31×#120—28no—
119C31×#120—28no—
120C31×#117—21no—
121C31×#117—21no—
122C31×#117—22no—
123C31×#117D412yescomplemented
124C31×#117D414yescomplemented
125C31×#117C2312yes—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31D412yescomplemented
128C2×C22⋊C4×C31—24no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—24no—
132C2×C42×C31—21no—
133C2×C42×C31C2312yes—
134C31×#104—28no—
135C31×#103—24no—
136C31×#102—24no—
137C31×#100—28no—
138C24×C31—22no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—24no—
142C24×C31—22no—
143C24×C31—24no—
144C24×C31—84no—
145C24×C31C2×D414yes—
146C24×C31C2×D411yescharacteristic
147#41×C31—24no—
148#41×C31—24no—
149#41×C31—24no—
150#41×C31—24no—
151#41×C31—24no—
152#41×C31—24no—
153#41×C31—22no—
154#41×C31—22no—
155#41×C31—22no—
156#41×C31—22no—
157#41×C31—42no—
158#41×C31—42no—
159#41×C31—42no—
160#41×C31—42no—
161#41×C31—42no—
162#41×C31—42no—
163#41×C31—42no—
164#41×C31—42no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—22no—
168C2×Q8×C31—22no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31C2×D412yes—
174C2×Q8×C31C2×D412yescomplemented
175C2×D4×C31—24no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—216no—
179C2×D4×C31—216no—
180C2×D4×C31—22no—
181C2×D4×C31—24no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—21no—
185C2×D4×C31—22no—
186C2×D4×C31—24no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—22no—
198C2×D4×C31—41no—
199C2×D4×C31—41no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—88no—
212C2×D4×C31—88no—
213C2×D4×C31C2×D412yes—
214C2×D4×C31C2×D412yescomplemented
215C22×C4×C31—22no—
216C22×C4×C31—21no—
217C22×C4×C31—22no—
218C22×C4×C31—21no—
219C22×C4×C31—24no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—41no—
223C22×C4×C31—41no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—42no—
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D412yes—
235C22×C4×C31#4112yes—
236C22×C4×C31C2411yescharacteristic
237Q16×C31—28no—
238SD16×C31—28no—
239SD16×C31—28no—
240D8×C31—28no—
241M16×C31—24no—
242M16×C31—22no—
243M16×C31—22no—
244M16×C31—22no—
245M16×C31—42no—
246M16×C31C2×D414yescomplemented
247C2×C8×C31—24no—
248C2×C8×C31—22no—
249C2×C8×C31—22no—
250C2×C8×C31—42no—
251C4⋊C4×C31—24no—
252C4⋊C4×C31—22no—
253C4⋊C4×C31C2×D414yes—
254C22⋊C4×C31—216no—
255C22⋊C4×C31—216no—
256C22⋊C4×C31—24no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—22no—
259C42×C31—22no—
260C42×C31—22no—
261C42×C31—22no—
262C42×C31C2×D414yescomplemented
263#23402C3111yesmaximal, characteristic, direct product factor, Sylow
264C23×C31—24no—
265C23×C31—22no—
266C23×C31—24no—
267C23×C31—22no—
268C23×C31—24no—
269C23×C31—42no—
270C23×C31—48no—
271C23×C31—44no—
272C23×C31—44no—
273C23×C31—48no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—42no—
277C23×C31—44no—
278C23×C31—44no—
279C23×C31—84no—
280C23×C31—88no—
281C23×C31—88no—
282C23×C31#12011yescharacteristic
283C23×C31#12011yescharacteristic
284C23×C31#12012yes—
285C23×C31#12112yes—
286C23×C31C22×D411yescharacteristic
287Q8×C31—22no—
288Q8×C31—22no—
289Q8×C31—22no—
290Q8×C31—22no—
291Q8×C31—41no—
292Q8×C31—41no—
293Q8×C31—42no—
294D4×C31—22no—
295D4×C31—22no—
296D4×C31—22no—
297D4×C31—22no—
298D4×C31—42no—
299D4×C31—42no—
300D4×C31—44no—
301D4×C31—44no—
302D4×C31—44no—
303D4×C31—42no—
304D4×C31—42no—
305D4×C31—42no—
306D4×C31—41no—
307D4×C31—42no—
308D4×C31—41no—
309D4×C31—44no—
310D4×C31—44no—
311D4×C31—42no—
312D4×C31—816no—
313D4×C31—816no—
314C2×C4×C31—24no—
315C2×C4×C31—22no—
316C2×C4×C31—24no—
317C2×C4×C31—22no—
318C2×C4×C31—44no—
319C2×C4×C31—44no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—44no—
326C2×C4×C31—44no—
327C2×C4×C31—44no—
328C2×C4×C31#12012yes—
329C2×C4×C31#12012yes—
330C2×C4×C31#12012yes—
331C2×C4×C31#12011yescharacteristic
332C2×C4×C31#12011yescharacteristic
333C2×C4×C31#12112yes—
334C2×C4×C31#12112yes—
335C2×C4×C31#12112yes—
336C2×C4×C31#12112yes—
337C2×C4×C31#12112yes—
338C2×C4×C31#12712yes—
339C2×C4×C31#12712yes—
340C2×C4×C31C22×D411yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C22×D411yescharacteristic
344C2×C4×C31C22×D411yescharacteristic
345C2×C4×C31C2×#4111yescharacteristic
346C8×C31—24no—
347C8×C31—42no—
348C2×#575C2×C3111yescharacteristic, complemented
349C2×#535C2×C3111yescharacteristic, complemented
350C2×#535C2×C3111yescharacteristic, complemented
351C2×#421C2×C3111yescharacteristic, complemented
352#2896C2×C3111yescharacteristic, complemented
353C22×#100C2×C3111yescharacteristic, complemented
354#2004C2×C3114yescomplemented
355#2002C2×C3114yescomplemented
356#1733C2×C3111yescharacteristic, complemented
357C22×C31—22no—
358C22×C31—22no—
359C22×C31—22no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—44no—
363C22×C31—48no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—44no—
367C22×C31—44no—
368C22×C31—48no—
369C22×C31—84no—
370C22×C31—82no—
371C22×C31—84no—
372C22×C31—88no—
373C22×C31—88no—
374C22×C31—82no—
375C22×C31#39212yes—
376C22×C31#39212yes—
377C22×C31C2×#12011yescharacteristic
378C22×C31C2×#12011yescharacteristic
379C22×C31C2×#12111yescharacteristic
380C4×C31—44no—
381C4×C31—42no—
382C4×C31—42no—
383C4×C31—44no—
384C4×C31#39212yes—
385C4×C31#39212yes—
386C4×C31C2×#12011yescharacteristic
387C4×C31C2×#12111yescharacteristic
388C4×C31C2×#12111yescharacteristic
389C4×C31C2×#12711yescharacteristic
390C22×#41C22×C3111yescharacteristic
391C22×#41C22×C3111yescharacteristic
392C23×D4C22×C3111yescharacteristic
393#575—24no—
394#575—24no—
395C2×#137—21no—
396C2×#137C22×C3112yescomplemented
397C2×AGL(1,ℤ/8)—21no—
398C2×AGL(1,ℤ/8)C22×C3112yescomplemented
399C2×#135—22no—
400C22×M16C22×C3111yescharacteristic
401C22×M16C22×C3111yescharacteristic
402#535—22no—
403#535—24no—
404#535—22no—
405#535—22no—
406#535—24no—
407#535C22×C3114yes—
408C2×#127—21no—
409C2×#127C22×C3112yescomplemented
410C2×#124—21no—
411C2×#124C22×C3112yescomplemented
412C2×#121—22no—
413C2×#121—22no—
414C2×#120—22no—
415C2×#120—22no—
416C2×#117C22×C3111yescharacteristic
417C2×#117C22×C3111yescharacteristic
418#421—24no—
419C2×#104C22×C3114yescomplemented
420#419C22×C3112yescomplemented
421#418C22×C3112yescomplemented
422#417—22no—
423#416—22no—
424C2×#100—24no—
425C2×#100C22×C3114yescomplemented
426#339C22×C3114yescomplemented
427C2×C31—21no—
428C2×C31—21no—
429C2×C31—22no—
430C2×C31—22no—
431C2×C31—84no—
432C2×C31—82no—
433C2×C31—82no—
434C2×C31C2×#39211yescharacteristic
435C2×C31#301912yes—
436C25D4×C3112yes—
437C2×#41—21no—
438C2×#41—22no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41D4×C3112yescomplemented
451C2×#41D4×C3114yescomplemented
452C2×#41C23×C3112yes—
453C22×Q8D4×C3111yescharacteristic, complemented
454C22×Q8C23×C3111yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4D4×C3112yes—
468C22×D4D4×C3111yescharacteristic, complemented
469C22×D4C23×C3112yes—
470C22×D4C23×C3111yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4C23×C3111yescharacteristic
474#137—28no—
475#137—24no—
476#137—24no—
477AGL(1,ℤ/8)—28no—
478AGL(1,ℤ/8)—24no—
479AGL(1,ℤ/8)—24no—
480#135—216no—
481C2×Q16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×D8—22no—
485C2×M16—21no—
486C2×M16—22no—
487C2×M16—21no—
488C2×M16—22no—
489C2×M16—22no—
490C2×M16D4×C3114yescomplemented
491C2×M16C23×C3112yes—
492C2×M16C23×C3112yes—
493C22×C8—21no—
494C22×C8—21no—
495#127—24no—
496#127—24no—
497#127—24no—
498#127—24no—
499#124—24no—
500#124—24no—
501#124—24no—
502#124—24no—
503#121—216no—
504#121—28no—
505#121—28no—
506#120—28no—
507#120—216no—
508#120—28no—
509#117—21no—
510#117—21no—
511#117—22no—
512#117D4×C3112yescomplemented
513#117D4×C3114yescomplemented
514#117C23×C3112yes—
515C2×C4⋊C4—21no—
516C2×C4⋊C4D4×C3112yescomplemented
517C2×C22⋊C4—24no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—24no—
521C2×C42—21no—
522C2×C42C23×C3112yes—
523#104—28no—
524#103—24no—
525#102—24no—
526#100—28no—
527C31#2340211yescharacteristic, direct product factor, Sylow
528C24—22no—
529C24—21no—
530C24—21no—
531C24—22no—
532C24—24no—
533C24—24no—
534C24—84no—
535C24C2×D4×C3114yes—
536C24C2×D4×C3111yescharacteristic
537#41—24no—
538#41—24no—
539#41—24no—
540#41—24no—
541#41—24no—
542#41—24no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—42no—
548#41—42no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8C2×D4×C3112yes—
564C2×Q8C2×D4×C3112yescomplemented
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—216no—
569C2×D4—216no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—24no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—88no—
602C2×D4—88no—
603C2×D4C2×D4×C3112yes—
604C2×D4C2×D4×C3112yescomplemented
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C2×D4×C3112yes—
621C22×C4C2×D4×C3112yes—
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3112yes—
625C22×C4#41×C3112yes—
626C22×C4C24×C3111yescharacteristic
627Q16—28no—
628SD16—28no—
629SD16—28no—
630D8—28no—
631M16—24no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—42no—
636M16C2×D4×C3114yescomplemented
637C2×C8—24no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—42no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4C2×D4×C3114yes—
644C22⋊C4—216no—
645C22⋊C4—216no—
646C22⋊C4—22no—
647C22⋊C4—24no—
648C22⋊C4—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42C2×D4×C3114yescomplemented
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—42no—
659C23—48no—
660C23—44no—
661C23—44no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—44no—
667C23—44no—
668C23—84no—
669C23—88no—
670C23—88no—
671C23C31×#12011yescharacteristic
672C23C31×#12011yescharacteristic
673C23C31×#12012yes—
674C23C31×#12112yes—
675C23C22×D4×C3111yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—42no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—42no—
697D4—41no—
698D4—44no—
699D4—44no—
700D4—42no—
701D4—816no—
702D4—816no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4C31×#12012yes—
718C2×C4C31×#12012yes—
719C2×C4C31×#12011yescharacteristic
720C2×C4C31×#12011yescharacteristic
721C2×C4C31×#12012yes—
722C2×C4C31×#12112yes—
723C2×C4C31×#12112yes—
724C2×C4C31×#12112yes—
725C2×C4C31×#12112yes—
726C2×C4C31×#12112yes—
727C2×C4C31×#12712yes—
728C2×C4C31×#12712yes—
729C2×C4C22×D4×C3111yescharacteristic
730C2×C4C22×D4×C3111yescharacteristic
731C2×C4C22×D4×C3111yescharacteristic
732C2×C4C22×D4×C3111yescharacteristic
733C2×C4C22×D4×C3111yescharacteristic
734C2×C4C2×#41×C3111yescharacteristic
735C8—24no—
736C8—42no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—48no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—44no—
748C22—48no—
749C22—84no—
750C22—88no—
751C22—82no—
752C22—84no—
753C22—88no—
754C22—82no—
755C22C31×#39212yes—
756C22C31×#39212yes—
757C22C2×C31×#12011yescharacteristic
758C22C2×C31×#12011yescharacteristic
759C22C2×C31×#12111yescharacteristic
760C4—44no—
761C4—42no—
762C4—42no—
763C4—44no—
764C4C31×#39212yes—
765C4C31×#39212yes—
766C4C2×C31×#12011yescharacteristic
767C4C2×C31×#12111yescharacteristic
768C4C2×C31×#12111yescharacteristic
769C4C2×C31×#12711yescharacteristic
770C2—21no—
771C2—21no—
772C2—22no—
773C2—22no—
774C2—84no—
775C2—82no—
776C2—82no—
777C2C2×C31×#39211yescharacteristic
778C2C31×#301912yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
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. C2×C31×#575C2semidirect
2. C2×C31×#535C2semidirect
3. C2×C31×#535C2semidirect
4. C2×C31×#421C2semidirect
5. C31×#2896C2semidirect
6. C22×C31×#100C2semidirect
7. C31×#2004C2semidirect
8. C31×#2002C2semidirect
9. C31×#1733C2semidirect
16. C2×C31×#137C22semidirect
18. C2×C31×AGL(1,ℤ/8)C22semidirect
29. C2×C31×#127C22semidirect
31. C2×C31×#124C22semidirect
39. C2×C31×#104C22semidirect
40. C31×#419C22semidirect
41. C31×#418C22semidirect
45. C2×C31×#100C22semidirect
46. C31×#339C22semidirect
61. C2×#41×C31D4semidirect
62. C2×#41×C31D4semidirect
64. C22×Q8×C31D4semidirect
79. C22×D4×C31D4semidirect
101. C2×M16×C31D4semidirect
123. C31×#117D4semidirect
124. C31×#117D4semidirect
127. C2×C4⋊C4×C31D4semidirect
174. C2×Q8×C31C2×D4semidirect
214. C2×D4×C31C2×D4semidirect
246. M16×C31C2×D4semidirect
262. C42×C31C2×D4semidirect
263. #23402C31direct (N × H)
348. C2×#575C2×C31semidirect
349. C2×#535C2×C31semidirect
350. C2×#535C2×C31semidirect
351. C2×#421C2×C31semidirect
352. #2896C2×C31semidirect
353. C22×#100C2×C31semidirect
354. #2004C2×C31semidirect
355. #2002C2×C31semidirect
356. #1733C2×C31semidirect
396. C2×#137C22×C31semidirect
398. C2×AGL(1,ℤ/8)C22×C31semidirect
409. C2×#127C22×C31semidirect
411. C2×#124C22×C31semidirect
419. C2×#104C22×C31semidirect
420. #419C22×C31semidirect
421. #418C22×C31semidirect
425. C2×#100C22×C31semidirect
426. #339C22×C31semidirect
450. C2×#41D4×C31semidirect
451. C2×#41D4×C31semidirect
453. C22×Q8D4×C31semidirect
468. C22×D4D4×C31semidirect
490. C2×M16D4×C31semidirect
512. #117D4×C31semidirect
513. #117D4×C31semidirect
516. C2×C4⋊C4D4×C31semidirect
527. C31#23402direct (N × H)
564. C2×Q8C2×D4×C31semidirect
604. C2×D4C2×D4×C31semidirect
636. M16C2×D4×C31semidirect
652. C42C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C2×C31×#5352
C2×C31×#4212
C31×#28962
C22×C31×#1002
C31×#20042
C31×#20022
C31×#17332
#2340231