Finite Group Databasebeta

← C31×#23400 #21480159

Subgroups — C31×#23400 #21480159

Order 7936.

2146 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C31×#3449C211yesmaximal, characteristic, complemented
3C2×C31×#535C211yesmaximal, characteristic, complemented
4C2×C31×#421C211yesmaximal, characteristic, complemented
5C2×C31×#418C211yesmaximal, characteristic, complemented
6C2×C31×#413C211yesmaximal, characteristic, complemented
7C31×#2003C214yesmaximal, complemented
8C31×#2002C214yesmaximal, complemented
9C31×#1733C211yesmaximal, characteristic, complemented
10C22×#41×C31C2211yescharacteristic
11C22×#41×C31C2211yescharacteristic
12C23×D4×C31C2211yescharacteristic
13C2×C31×AGL(1,ℤ/8)—22no—
14C2×C31×AGL(1,ℤ/8)—24no—
15C2×C31×AGL(1,ℤ/8)—24no—
16C2×C31×AGL(1,ℤ/8)C2214yes—
17C22×SD16×C31—21no—
18C22×D8×C31—21no—
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C31×#537—22no—
22C31×#536—21no—
23C31×#536C2212yescomplemented
24C31×#535—24no—
25C31×#535—21no—
26C31×#535—24no—
27C31×#535C2212yescomplemented
28C31×#534—22no—
29C31×#532—22no—
30C2×C31×#127C2212yescomplemented
31C2×C31×#124C2212yescomplemented
32C31×#525—22no—
33C31×#525—22no—
34C2×C31×#121—22no—
35C2×C31×#120—22no—
36C2×C31×#117C2211yescharacteristic
37C2×C31×#117C2211yescharacteristic
38C31×#421—24no—
39C2×C31×#104C2214yescomplemented
40C31×#418—22no—
41C31×#418C2214yescomplemented
42C2×C31×#102—22no—
43C31×#413—24no—
44C2×C31×#101C2212yescomplemented
45C2×C31×#100C2212yescomplemented
46C31×#339C2214yescomplemented
47C25×C31—21no—
48C2×#41×C31—22no—
49C2×#41×C31—21no—
50C2×#41×C31—21no—
51C2×#41×C31—21no—
52C2×#41×C31—22no—
53C2×#41×C31—22no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—22no—
58C2×#41×C31—22no—
59C2×#41×C31—22no—
60C2×#41×C31—22no—
61C2×#41×C31—22no—
62C2×#41×C31D412yescomplemented
63C2×#41×C31C2312yes—
64C22×Q8×C31D411yescharacteristic, complemented
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31—21no—
67C22×D4×C31—24no—
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—22no—
73C22×D4×C31—21no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31D412yes—
77C22×D4×C31D411yescharacteristic, complemented
78C22×D4×C31D414yescomplemented
79C22×D4×C31C2311yescharacteristic
80C22×D4×C31C2312yes—
81C23×C4×C31—21no—
82C23×C4×C31D412yes—
83C23×C4×C31C2311yescharacteristic
84C31×AGL(1,ℤ/8)—216no—
85C31×AGL(1,ℤ/8)—28no—
86C31×AGL(1,ℤ/8)—28no—
87C2×SD16×C31—28no—
88C2×SD16×C31—24no—
89C2×D8×C31—28no—
90C2×D8×C31—24no—
91C2×M16×C31—22no—
92C2×M16×C31—21no—
93C2×M16×C31—21no—
94C2×M16×C31—22no—
95C2×M16×C31—22no—
96C2×M16×C31D414yescomplemented
97C2×M16×C31C2312yes—
98C2×M16×C31C2312yes—
99C22×C8×C31—21no—
100C22×C8×C31—21no—
101C31×C4⋊Q8—22no—
102C31×#127—24no—
103C31×#127—22no—
104C31×#127—24no—
105C31×#124—22no—
106C31×#124—24no—
107C31×#124—22no—
108C31×#124—24no—
109C31×#123—24no—
110C31×#123—24no—
111C31×C22⋊Q8—24no—
112C31×C22⋊Q8—24no—
113C31×#121—216no—
114C31×#121—24no—
115C31×#121—28no—
116C31×#121—24no—
117C31×#120—216no—
118C31×#120—24no—
119C31×#120—24no—
120C4×D4×C31—28no—
121C31×#117—21no—
122C31×#117—22no—
123C31×#117—21no—
124C31×#117D412yescomplemented
125C31×#117D414yescomplemented
126C31×#117C2312yes—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31D412yescomplemented
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×#102—28no—
136C31×#101—24no—
137C31×#100—24no—
138C24×C31—22no—
139C24×C31—21no—
140C24×C31—24no—
141C24×C31—41no—
142C24×C31—41no—
143C24×C31—42no—
144C24×C31—84no—
145C24×C31C2×D412yes—
146C24×C31C2×D411yescharacteristic
147#41×C31—24no—
148#41×C31—24no—
149#41×C31—22no—
150#41×C31—22no—
151#41×C31—22no—
152#41×C31—22no—
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×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—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—22no—
173C2×Q8×C31—22no—
174C2×Q8×C31C2×D412yes—
175C2×D4×C31—24no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—24no—
180C2×D4×C31—22no—
181C2×D4×C31—28no—
182C2×D4×C31—216no—
183C2×D4×C31—22no—
184C2×D4×C31—24no—
185C2×D4×C31—24no—
186C2×D4×C31—24no—
187C2×D4×C31—21no—
188C2×D4×C31—24no—
189C2×D4×C31—24no—
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—22no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—22no—
201C2×D4×C31—21no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—41no—
205C2×D4×C31—41no—
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×C31C2×D412yes—
213C2×D4×C31C2×D414yes—
214C22×C4×C31—21no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—24no—
220C22×C4×C31—22no—
221C22×C4×C31—24no—
222C22×C4×C31—22no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31C2×D412yes—
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D412yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D412yes—
234C22×C4×C31#4112yes—
235C22×C4×C31C2411yescharacteristic
236SD16×C31—216no—
237D8×C31—216no—
238M16×C31—24no—
239M16×C31—22no—
240M16×C31—22no—
241M16×C31—22no—
242M16×C31—42no—
243M16×C31C2×D414yes—
244C2×C8×C31—24no—
245C2×C8×C31—22no—
246C2×C8×C31—22no—
247C2×C8×C31—42no—
248C4⋊C4×C31—28no—
249C4⋊C4×C31—24no—
250C4⋊C4×C31—22no—
251C4⋊C4×C31C2×D414yes—
252C22⋊C4×C31—216no—
253C22⋊C4×C31—28no—
254C22⋊C4×C31—28no—
255C22⋊C4×C31—24no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C42×C31—22no—
259C42×C31—22no—
260C42×C31—22no—
261C42×C31C2×D414yes—
262#23400C3111yesmaximal, characteristic, direct product factor, Sylow
263C23×C31—24no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—42no—
269C23×C31—44no—
270C23×C31—48no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—44no—
275C23×C31—44no—
276C23×C31—82no—
277C23×C31—84no—
278C23×C31—84no—
279C23×C31—88no—
280C23×C31—88no—
281C23×C31#12011yescharacteristic
282C23×C31#12011yescharacteristic
283C23×C31#12012yes—
284C23×C31#12112yes—
285C23×C31C22×D411yescharacteristic
286Q8×C31—22no—
287Q8×C31—22no—
288Q8×C31—41no—
289Q8×C31—41no—
290Q8×C31—41no—
291Q8×C31—41no—
292Q8×C31—42no—
293D4×C31—22no—
294D4×C31—24no—
295D4×C31—24no—
296D4×C31—22no—
297D4×C31—42no—
298D4×C31—42no—
299D4×C31—44no—
300D4×C31—44no—
301D4×C31—44no—
302D4×C31—41no—
303D4×C31—42no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—42no—
307D4×C31—41no—
308D4×C31—44no—
309D4×C31—44no—
310D4×C31—42no—
311D4×C31—88no—
312D4×C31—816no—
313C2×C4×C31—24no—
314C2×C4×C31—22no—
315C2×C4×C31—24no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—44no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—44no—
324C2×C4×C31—44no—
325C2×C4×C31—44no—
326C2×C4×C31—82no—
327C2×C4×C31#12012yes—
328C2×C4×C31#12012yes—
329C2×C4×C31#12012yes—
330C2×C4×C31#12011yescharacteristic
331C2×C4×C31#12011yescharacteristic
332C2×C4×C31#12112yes—
333C2×C4×C31#12112yes—
334C2×C4×C31#12112yes—
335C2×C4×C31#12112yes—
336C2×C4×C31#12112yes—
337C2×C4×C31#12712yes—
338C2×C4×C31#12712yes—
339C2×C4×C31C22×D411yescharacteristic
340C2×C4×C31C22×D411yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C22×D411yescharacteristic
344C2×C4×C31C2×#4111yescharacteristic
345C8×C31—24no—
346C8×C31—42no—
347C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
348#3449C2×C3111yescharacteristic, complemented
349C2×#535C2×C3111yescharacteristic, complemented
350C2×#421C2×C3111yescharacteristic, complemented
351C2×#418C2×C3111yescharacteristic, complemented
352C2×#413C2×C3111yescharacteristic, complemented
353#2003C2×C3114yescomplemented
354#2002C2×C3114yescomplemented
355#1733C2×C3111yescharacteristic, complemented
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—22no—
359C22×C31—42no—
360C22×C31—42no—
361C22×C31—44no—
362C22×C31—48no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—44no—
366C22×C31—44no—
367C22×C31—44no—
368C22×C31—82no—
369C22×C31—84no—
370C22×C31—84no—
371C22×C31—88no—
372C22×C31—88no—
373C22×C31—84no—
374C22×C31#39212yes—
375C22×C31#39212yes—
376C22×C31C2×#12011yescharacteristic
377C22×C31C2×#12011yescharacteristic
378C22×C31C2×#12111yescharacteristic
379C4×C31—44no—
380C4×C31—42no—
381C4×C31—42no—
382C4×C31—44no—
383C4×C31#39212yes—
384C4×C31#39212yes—
385C4×C31C2×#12011yescharacteristic
386C4×C31C2×#12111yescharacteristic
387C4×C31C2×#12111yescharacteristic
388C4×C31C2×#12711yescharacteristic
389C22×#41C22×C3111yescharacteristic
390C22×#41C22×C3111yescharacteristic
391C23×D4C22×C3111yescharacteristic
392C2×AGL(1,ℤ/8)—22no—
393C2×AGL(1,ℤ/8)—24no—
394C2×AGL(1,ℤ/8)—24no—
395C2×AGL(1,ℤ/8)C22×C3114yes—
396C22×SD16—21no—
397C22×D8—21no—
398C22×M16C22×C3111yescharacteristic
399C22×M16C22×C3111yescharacteristic
400#537—22no—
401#536—21no—
402#536C22×C3112yescomplemented
403#535—24no—
404#535—21no—
405#535—24no—
406#535C22×C3112yescomplemented
407#534—22no—
408#532—22no—
409C2×#127C22×C3112yescomplemented
410C2×#124C22×C3112yescomplemented
411#525—22no—
412#525—22no—
413C2×#121—22no—
414C2×#120—22no—
415C2×#117C22×C3111yescharacteristic
416C2×#117C22×C3111yescharacteristic
417#421—24no—
418C2×#104C22×C3114yescomplemented
419#418—22no—
420#418C22×C3114yescomplemented
421C2×#102—22no—
422#413—24no—
423C2×#101C22×C3112yescomplemented
424C2×#100C22×C3112yescomplemented
425#339C22×C3114yescomplemented
426C2×C31—21no—
427C2×C31—21no—
428C2×C31—22no—
429C2×C31—22no—
430C2×C31—82no—
431C2×C31—82no—
432C2×C31—84no—
433C2×C31C2×#39211yescharacteristic
434C2×C31#302112yes—
435C25—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41D4×C3112yescomplemented
451C2×#41C23×C3112yes—
452C22×Q8D4×C3111yescharacteristic, complemented
453C22×Q8C23×C3111yescharacteristic
454C22×D4—21no—
455C22×D4—24no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—22no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4D4×C3112yes—
465C22×D4D4×C3111yescharacteristic, complemented
466C22×D4D4×C3114yescomplemented
467C22×D4C23×C3111yescharacteristic
468C22×D4C23×C3112yes—
469C23×C4—21no—
470C23×C4D4×C3112yes—
471C23×C4C23×C3111yescharacteristic
472AGL(1,ℤ/8)—216no—
473AGL(1,ℤ/8)—28no—
474AGL(1,ℤ/8)—28no—
475C2×SD16—28no—
476C2×SD16—24no—
477C2×D8—28no—
478C2×D8—24no—
479C2×M16—22no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—22no—
483C2×M16—22no—
484C2×M16D4×C3114yescomplemented
485C2×M16C23×C3112yes—
486C2×M16C23×C3112yes—
487C22×C8—21no—
488C22×C8—21no—
489C4⋊Q8—22no—
490#127—24no—
491#127—22no—
492#127—24no—
493#124—22no—
494#124—24no—
495#124—22no—
496#124—24no—
497#123—24no—
498#123—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501#121—216no—
502#121—24no—
503#121—28no—
504#121—24no—
505#120—216no—
506#120—24no—
507#120—24no—
508C4×D4—28no—
509#117—21no—
510#117—22no—
511#117—21no—
512#117D4×C3112yescomplemented
513#117D4×C3114yescomplemented
514#117C23×C3112yes—
515C2×C4⋊C4—21no—
516C2×C4⋊C4D4×C3112yescomplemented
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—24no—
520C2×C42—21no—
521C2×C42C23×C3112yes—
522#104—28no—
523#102—28no—
524#101—24no—
525#100—24no—
526C31#2340011yescharacteristic, direct product factor, Sylow
527C24—22no—
528C24—21no—
529C24—24no—
530C24—41no—
531C24—41no—
532C24—42no—
533C24—84no—
534C24C2×D4×C3112yes—
535C24C2×D4×C3111yescharacteristic
536#41—24no—
537#41—24no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—42no—
543#41—42no—
544#41—42no—
545#41—42no—
546#41—42no—
547#41—42no—
548#41—42no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8C2×D4×C3112yes—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—24no—
569C2×D4—22no—
570C2×D4—28no—
571C2×D4—216no—
572C2×D4—22no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—88no—
601C2×D4C2×D4×C3112yes—
602C2×D4C2×D4×C3114yes—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4C2×D4×C3112yes—
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3112yes—
619C22×C4C2×D4×C3112yes—
620C22×C4C2×D4×C3111yescharacteristic
621C22×C4C2×D4×C3111yescharacteristic
622C22×C4C2×D4×C3112yes—
623C22×C4#41×C3112yes—
624C22×C4C24×C3111yescharacteristic
625SD16—216no—
626D8—216no—
627M16—24no—
628M16—22no—
629M16—22no—
630M16—22no—
631M16—42no—
632M16C2×D4×C3114yes—
633C2×C8—24no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—42no—
637C4⋊C4—28no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4C2×D4×C3114yes—
641C22⋊C4—216no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—24no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42C2×D4×C3114yes—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—44no—
658C23—48no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—82no—
665C23—84no—
666C23—84no—
667C23—88no—
668C23—88no—
669C23C31×#12011yescharacteristic
670C23C31×#12011yescharacteristic
671C23C31×#12012yes—
672C23C31×#12112yes—
673C23C22×D4×C3111yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—42no—
681D4—22no—
682D4—24no—
683D4—24no—
684D4—22no—
685D4—42no—
686D4—42no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4—42no—
695D4—41no—
696D4—44no—
697D4—44no—
698D4—42no—
699D4—88no—
700D4—816no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—82no—
715C2×C4C31×#12012yes—
716C2×C4C31×#12012yes—
717C2×C4C31×#12011yescharacteristic
718C2×C4C31×#12012yes—
719C2×C4C31×#12011yescharacteristic
720C2×C4C31×#12112yes—
721C2×C4C31×#12112yes—
722C2×C4C31×#12112yes—
723C2×C4C31×#12112yes—
724C2×C4C31×#12112yes—
725C2×C4C31×#12712yes—
726C2×C4C31×#12712yes—
727C2×C4C22×D4×C3111yescharacteristic
728C2×C4C22×D4×C3111yescharacteristic
729C2×C4C22×D4×C3111yescharacteristic
730C2×C4C22×D4×C3111yescharacteristic
731C2×C4C22×D4×C3111yescharacteristic
732C2×C4C2×#41×C3111yescharacteristic
733C8—24no—
734C8—42no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—48no—
742C22—42no—
743C22—42no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—82no—
748C22—84no—
749C22—88no—
750C22—88no—
751C22—84no—
752C22—84no—
753C22C31×#39212yes—
754C22C31×#39212yes—
755C22C2×C31×#12011yescharacteristic
756C22C2×C31×#12011yescharacteristic
757C22C2×C31×#12111yescharacteristic
758C4—44no—
759C4—42no—
760C4—42no—
761C4—44no—
762C4C31×#39212yes—
763C4C31×#39212yes—
764C4C2×C31×#12011yescharacteristic
765C4C2×C31×#12111yescharacteristic
766C4C2×C31×#12111yescharacteristic
767C4C2×C31×#12711yescharacteristic
768C2—21no—
769C2—21no—
770C2—22no—
771C2—22no—
772C2—82no—
773C2—84no—
774C2—82no—
775C2C2×C31×#39211yescharacteristic
776C2C31×#302112yes—
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. C22×C31×AGL(1,ℤ/8)C2semidirect
2. C31×#3449C2semidirect
3. C2×C31×#535C2semidirect
4. C2×C31×#421C2semidirect
5. C2×C31×#418C2semidirect
6. C2×C31×#413C2semidirect
7. C31×#2003C2semidirect
8. C31×#2002C2semidirect
9. C31×#1733C2semidirect
23. C31×#536C22semidirect
27. C31×#535C22semidirect
30. C2×C31×#127C22semidirect
31. C2×C31×#124C22semidirect
39. C2×C31×#104C22semidirect
41. C31×#418C22semidirect
44. C2×C31×#101C22semidirect
45. C2×C31×#100C22semidirect
46. C31×#339C22semidirect
62. C2×#41×C31D4semidirect
64. C22×Q8×C31D4semidirect
77. C22×D4×C31D4semidirect
78. C22×D4×C31D4semidirect
96. C2×M16×C31D4semidirect
124. C31×#117D4semidirect
125. C31×#117D4semidirect
128. C2×C4⋊C4×C31D4semidirect
262. #23400C31direct (N × H)
347. C22×AGL(1,ℤ/8)C2×C31semidirect
348. #3449C2×C31semidirect
349. C2×#535C2×C31semidirect
350. C2×#421C2×C31semidirect
351. C2×#418C2×C31semidirect
352. C2×#413C2×C31semidirect
353. #2003C2×C31semidirect
354. #2002C2×C31semidirect
355. #1733C2×C31semidirect
402. #536C22×C31semidirect
406. #535C22×C31semidirect
409. C2×#127C22×C31semidirect
410. C2×#124C22×C31semidirect
418. C2×#104C22×C31semidirect
420. #418C22×C31semidirect
423. C2×#101C22×C31semidirect
424. C2×#100C22×C31semidirect
425. #339C22×C31semidirect
450. C2×#41D4×C31semidirect
452. C22×Q8D4×C31semidirect
465. C22×D4D4×C31semidirect
466. C22×D4D4×C31semidirect
484. C2×M16D4×C31semidirect
512. #117D4×C31semidirect
513. #117D4×C31semidirect
516. C2×C4⋊C4D4×C31semidirect
526. C31#23400direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C31×#34492
C2×C31×#5352
C2×C31×#4212
C2×C31×#4182
C2×C31×#4132
C31×#20032
C31×#20022
C31×#17332
#2340031