Finite Group Databasebeta

← C31×#23954 #21480713

Subgroups — C31×#23954 #21480713

Order 7936.

1482 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3494C211yesmaximal, characteristic, complemented
2C31×#3003C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C31×#2433C211yesmaximal, characteristic, complemented
5C31×#2027C212yesmaximal, complemented
6C31×#2002C212yesmaximal, complemented
7C31×#1900C211yesmaximal, characteristic, complemented
8C31×#1887C212yesmaximal, 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×#555—21no—
16C31×#553—21no—
17C31×#553—21no—
18C31×#551—22no—
19C31×#547—21no—
20C31×#546—22no—
21C31×#544C2211yescharacteristic, complemented
22C31×#542—21no—
23C31×#540—21no—
24C31×#535C2211yescharacteristic, complemented
25C31×#532—21no—
26C2×C31×#127C2212yes—
27C31×#529—21no—
28C31×#525C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#120—22no—
31C31×#520C2211yescharacteristic, complemented
32C31×#518C2211yescharacteristic, complemented
33C2×C31×#117C2211yescharacteristic
34C31×#450—21no—
35C31×#450—21no—
36C31×#447—21no—
37C31×#447—21no—
38C2×C31×#104C2212yescomplemented
39C31×#418—21no—
40C31×#418—21no—
41C31×#418C2212yes—
42C31×#418C2212yes—
43C31×#418C2212yes—
44C2×C31×#102—21no—
45C2×C31×#102—21no—
46C2×C31×#100C2212yescomplemented
47C31×#407C2211yescharacteristic
48C31×#392—22no—
49C31×#390C2212yes—
50C4×C22⋊C4×C31C2211yescharacteristic
51C31×#343C2212yescomplemented
52C31×#339C2212yescomplemented
53C31×#339C2212yescomplemented
54C31×#339C2212yescomplemented
55C25×C31—21no—
56C2×#41×C31—22no—
57C2×#41×C31C2311yescharacteristic
58C22×D4×C31—24no—
59C22×D4×C31—24no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—42no—
66C22×D4×C31D412yes—
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2312yes—
69C23×C4×C31C2311yescharacteristic
70C31×AGL(1,ℤ/8)—24no—
71C31×AGL(1,ℤ/8)—42no—
72C2×SD16×C31—22no—
73C2×D8×C31—22no—
74C2×M16×C31—21no—
75C2×M16×C31—42no—
76C2×M16×C31C2312yes—
77C2×M16×C31C2312yes—
78C22×C8×C31—21no—
79C31×C4⋊Q8—21no—
80C31×C4⋊Q8—21no—
81C31×#127—21no—
82C31×#127—24no—
83C31×#127—42no—
84C31×#126—22no—
85C31×#126—22no—
86C31×#125—21no—
87C31×#125—21no—
88C31×#124—22no—
89C31×#124—22no—
90C31×#124—21no—
91C31×#123—22no—
92C31×#123—22no—
93C31×#123—22no—
94C31×#123—22no—
95C31×#123—21no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8D411yescharacteristic, complemented
99C31×C22⋊Q8D411yescharacteristic, complemented
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121—21no—
109C31×#121D411yescharacteristic, complemented
110C31×#121D411yescharacteristic, complemented
111C31×#120—21no—
112C31×#120—22no—
113C31×#120—48no—
114C4×Q8×C31—21no—
115C4×D4×C31—22no—
116C4×D4×C31—22no—
117C4×D4×C31—21no—
118C4×D4×C31—22no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31—21no—
123C4×D4×C31—21no—
124C4×D4×C31—21no—
125C31×#117—22no—
126C31×#117—21no—
127C31×#117—21no—
128C31×#117—21no—
129C31×#117D411yescharacteristic, complemented
130C31×#117D411yescharacteristic, complemented
131C31×#117C2311yescharacteristic
132C31×#117C2311yescharacteristic
133C31×#117C2311yescharacteristic
134C2×C4⋊C4×C31—21no—
135C2×C4⋊C4×C31D411yescharacteristic, complemented
136C2×C4⋊C4×C31D411yescharacteristic, complemented
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—22no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—24no—
142C2×C22⋊C4×C31D412yes—
143C2×C42×C31—21no—
144C2×C42×C31C2312yes—
145C31×#104—42no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—22no—
149C31×#102—22no—
150C31×#102—22no—
151C31×#102—22no—
152C31×#100—42no—
153C31×C22⋊C8—21no—
154C31×C22⋊C8—21no—
155C31×#95—21no—
156C24×C31—22no—
157C24×C31—44no—
158C24×C31—44no—
159C24×C31—41no—
160C24×C31—41no—
161C24×C31—82no—
162C24×C31C2×D411yescharacteristic
163C24×C31C2×D412yes—
164#41×C31—22no—
165#41×C31—22no—
166#41×C31—84no—
167C2×Q8×C31—22no—
168C2×Q8×C31C2×D411yescharacteristic
169C2×D4×C31—24no—
170C2×D4×C31—24no—
171C2×D4×C31—21no—
172C2×D4×C31—22no—
173C2×D4×C31—21no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—21no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—44no—
188C2×D4×C31—44no—
189C2×D4×C31—44no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—48no—
193C2×D4×C31—44no—
194C2×D4×C31—48no—
195C2×D4×C31—41no—
196C2×D4×C31—41no—
197C2×D4×C31—84no—
198C2×D4×C31C2×D411yescharacteristic
199C2×D4×C31#4114yescomplemented
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—21no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D412yes—
215C22×C4×C31C2411yescharacteristic
216SD16×C31—44no—
217D8×C31—44no—
218M16×C31—22no—
219M16×C31—22no—
220M16×C31—22no—
221M16×C31—22no—
222M16×C31—42no—
223C2×C8×C31—22no—
224C2×C8×C31—22no—
225C2×C8×C31—42no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—22no—
229C4⋊C4×C31—22no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31C2×D411yescharacteristic
237C4⋊C4×C31C2×D411yescharacteristic
238C4⋊C4×C31C2×D411yescharacteristic
239C4⋊C4×C31C2×D411yescharacteristic
240C4⋊C4×C31C2×D411yescharacteristic
241C4⋊C4×C31C2×D411yescharacteristic
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—24no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—21no—
253C22⋊C4×C31—21no—
254C22⋊C4×C31—21no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—21no—
258C22⋊C4×C31—21no—
259C22⋊C4×C31—48no—
260C42×C31—22no—
261C42×C31—21no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—21no—
266C42×C31—22no—
267C42×C31—22no—
268#23954C3111yesmaximal, characteristic, direct product factor, Sylow
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—21no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—41no—
276C23×C31—44no—
277C23×C31—44no—
278C23×C31—44no—
279C23×C31—44no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—82no—
285C23×C31—82no—
286C23×C31—82no—
287C23×C31—816no—
288C23×C31—82no—
289C23×C31#12011yescharacteristic
290C23×C31#12011yescharacteristic
291C23×C31C22×D411yescharacteristic
292Q8×C31—22no—
293Q8×C31—82no—
294D4×C31—24no—
295D4×C31—22no—
296D4×C31—24no—
297D4×C31—44no—
298D4×C31—44no—
299D4×C31—42no—
300D4×C31—44no—
301D4×C31—42no—
302D4×C31—41no—
303D4×C31—41no—
304D4×C31—42no—
305D4×C31—42no—
306D4×C31—42no—
307D4×C31—81no—
308D4×C31—82no—
309D4×C31—82no—
310D4×C31—82no—
311D4×C31—816no—
312C2×C4×C31—22no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—24no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—22no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—42no—
334C2×C4×C31—81no—
335C2×C4×C31—82no—
336C2×C4×C31—82no—
337C2×C4×C31—82no—
338C2×C4×C31#12011yescharacteristic
339C2×C4×C31#12011yescharacteristic
340C2×C4×C31C22×D411yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C2×#4112yes—
343C2×C4×C31H(5,𝔽2)12yes—
344C8×C31—42no—
345C8×C31—42no—
346#3494C2×C3111yescharacteristic, complemented
347#3003C2×C3111yescharacteristic, complemented
348C2×#418C2×C3111yescharacteristic, complemented
349#2433C2×C3111yescharacteristic, complemented
350#2027C2×C3112yescomplemented
351#2002C2×C3112yescomplemented
352#1900C2×C3111yescharacteristic, complemented
353#1887C2×C3112yescomplemented
354#1883C2×C3112yescomplemented
355#1871C2×C3111yescharacteristic, complemented
356#1826C2×C3111yescharacteristic, complemented
357C22×C31—21no—
358C22×C31—21no—
359C22×C31—21no—
360C22×C31—21no—
361C22×C31—21no—
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—44no—
365C22×C31—48no—
366C22×C31—41no—
367C22×C31—44no—
368C22×C31—42no—
369C22×C31—41no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—41no—
373C22×C31—84no—
374C22×C31—84no—
375C22×C31—88no—
376C22×C31—88no—
377C22×C31—82no—
378C22×C31—82no—
379C22×C31#45312yes—
380C22×C31C2×#12011yescharacteristic
381C22×C31#54612yes—
382C4×C31—21no—
383C4×C31—21no—
384C4×C31—44no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—41no—
388C4×C31—42no—
389C4×C31—41no—
390C4×C31—41no—
391C4×C31—41no—
392C4×C31—41no—
393C4×C31#52511yescharacteristic
394C4×C31#53511yescharacteristic
395C4×C31#54612yes—
396C23×D4C22×C3111yescharacteristic
397C2×AGL(1,ℤ/8)C22×C3112yes—
398C22×M16C22×C3111yescharacteristic
399#555—21no—
400#553—21no—
401#553—21no—
402#551—22no—
403#547—21no—
404#546—22no—
405#544C22×C3111yescharacteristic, complemented
406#542—21no—
407#540—21no—
408#535C22×C3111yescharacteristic, complemented
409#532—21no—
410C2×#127C22×C3112yes—
411#529—21no—
412#525C22×C3111yescharacteristic
413C2×#121C22×C3111yescharacteristic
414C2×#120—22no—
415#520C22×C3111yescharacteristic, complemented
416#518C22×C3111yescharacteristic, complemented
417C2×#117C22×C3111yescharacteristic
418#450—21no—
419#450—21no—
420#447—21no—
421#447—21no—
422C2×#104C22×C3112yescomplemented
423#418—21no—
424#418—21no—
425#418C22×C3112yes—
426#418C22×C3112yes—
427#418C22×C3112yes—
428C2×#102—21no—
429C2×#102—21no—
430C2×#100C22×C3112yescomplemented
431#407C22×C3111yescharacteristic
432#392—22no—
433#390C22×C3112yes—
434C4×C22⋊C4C22×C3111yescharacteristic
435#343C22×C3112yescomplemented
436#339C22×C3112yescomplemented
437#339C22×C3112yescomplemented
438#339C22×C3112yescomplemented
439C2×C31—22no—
440C2×C31—22no—
441C2×C31—41no—
442C2×C31—81no—
443C2×C31—82no—
444C2×C31—84no—
445C2×C31#240411yescharacteristic
446C2×C31C2×#45311yescharacteristic
447C2×C31#302111yescharacteristic
448C25—21no—
449C2×#41—22no—
450C2×#41C23×C3111yescharacteristic
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—42no—
459C22×D4D4×C3112yes—
460C22×D4C23×C3111yescharacteristic
461C22×D4C23×C3112yes—
462C23×C4C23×C3111yescharacteristic
463AGL(1,ℤ/8)—24no—
464AGL(1,ℤ/8)—42no—
465C2×SD16—22no—
466C2×D8—22no—
467C2×M16—21no—
468C2×M16—42no—
469C2×M16C23×C3112yes—
470C2×M16C23×C3112yes—
471C22×C8—21no—
472C4⋊Q8—21no—
473C4⋊Q8—21no—
474#127—21no—
475#127—24no—
476#127—42no—
477#126—22no—
478#126—22no—
479#125—21no—
480#125—21no—
481#124—22no—
482#124—22no—
483#124—21no—
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—21no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8D4×C3111yescharacteristic, complemented
492C22⋊Q8D4×C3111yescharacteristic, complemented
493#121—22no—
494#121—22no—
495#121—22no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121D4×C3111yescharacteristic, complemented
503#121D4×C3111yescharacteristic, complemented
504#120—21no—
505#120—22no—
506#120—48no—
507C4×Q8—21no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—22no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518#117—22no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117D4×C3111yescharacteristic, complemented
523#117D4×C3111yescharacteristic, complemented
524#117C23×C3111yescharacteristic
525#117C23×C3111yescharacteristic
526#117C23×C3111yescharacteristic
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C3111yescharacteristic, complemented
529C2×C4⋊C4D4×C3111yescharacteristic, complemented
530C2×C4⋊C4C23×C3111yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4D4×C3112yes—
536C2×C42—21no—
537C2×C42C23×C3112yes—
538#104—42no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#100—42no—
546C22⋊C8—21no—
547C22⋊C8—21no—
548#95—21no—
549C31#2395411yescharacteristic, direct product factor, Sylow
550C24—22no—
551C24—44no—
552C24—44no—
553C24—41no—
554C24—41no—
555C24—82no—
556C24C2×D4×C3111yescharacteristic
557C24C2×D4×C3112yes—
558#41—22no—
559#41—22no—
560#41—84no—
561C2×Q8—22no—
562C2×Q8C2×D4×C3111yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—48no—
587C2×D4—44no—
588C2×D4—48no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—84no—
592C2×D4C2×D4×C3111yescharacteristic
593C2×D4#41×C3114yescomplemented
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3111yescharacteristic
608C22×C4C2×D4×C3112yes—
609C22×C4C24×C3111yescharacteristic
610SD16—44no—
611D8—44no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—42no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—42no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4C2×D4×C3111yescharacteristic
631C4⋊C4C2×D4×C3111yescharacteristic
632C4⋊C4C2×D4×C3111yescharacteristic
633C4⋊C4C2×D4×C3111yescharacteristic
634C4⋊C4C2×D4×C3111yescharacteristic
635C4⋊C4C2×D4×C3111yescharacteristic
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—24no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—48no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—21no—
666C23—24no—
667C23—24no—
668C23—41no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23—816no—
681C23—82no—
682C23C31×#12011yescharacteristic
683C23C31×#12011yescharacteristic
684C23C22×D4×C3111yescharacteristic
685Q8—22no—
686Q8—82no—
687D4—24no—
688D4—22no—
689D4—24no—
690D4—44no—
691D4—44no—
692D4—44no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—81no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—816no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4C31×#12011yescharacteristic
732C2×C4C31×#12011yescharacteristic
733C2×C4C22×D4×C3111yescharacteristic
734C2×C4C22×D4×C3111yescharacteristic
735C2×C4C2×#41×C3112yes—
736C2×C4C31×H(5,𝔽2)12yes—
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—44no—
747C22—48no—
748C22—41no—
749C22—44no—
750C22—42no—
751C22—41no—
752C22—42no—
753C22—42no—
754C22—41no—
755C22—84no—
756C22—84no—
757C22—88no—
758C22—88no—
759C22—82no—
760C22—82no—
761C22C31×#45312yes—
762C22C2×C31×#12011yescharacteristic
763C22C31×#54612yes—
764C4—21no—
765C4—21no—
766C4—44no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4C31×#52511yescharacteristic
776C4C31×#53511yescharacteristic
777C4C31×#54612yes—
778C2—22no—
779C2—22no—
780C2—41no—
781C2—84no—
782C2—82no—
783C2—81no—
784C2C31×#240411yescharacteristic
785C2C2×C31×#45311yescharacteristic
786C2C31×#302111yescharacteristic
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. C31×#3494C2semidirect
2. C31×#3003C2semidirect
3. C2×C31×#418C2semidirect
4. C31×#2433C2semidirect
5. C31×#2027C2semidirect
6. C31×#2002C2semidirect
7. C31×#1900C2semidirect
8. C31×#1887C2semidirect
9. C31×#1883C2semidirect
10. C31×#1871C2semidirect
11. C31×#1826C2semidirect
21. C31×#544C22semidirect
24. C31×#535C22semidirect
31. C31×#520C22semidirect
32. C31×#518C22semidirect
38. C2×C31×#104C22semidirect
46. C2×C31×#100C22semidirect
51. C31×#343C22semidirect
52. C31×#339C22semidirect
53. C31×#339C22semidirect
54. C31×#339C22semidirect
98. C31×C22⋊Q8D4semidirect
99. C31×C22⋊Q8D4semidirect
109. C31×#121D4semidirect
110. C31×#121D4semidirect
129. C31×#117D4semidirect
130. C31×#117D4semidirect
135. C2×C4⋊C4×C31D4semidirect
136. C2×C4⋊C4×C31D4semidirect
199. C2×D4×C31#41semidirect
268. #23954C31direct (N × H)
346. #3494C2×C31semidirect
347. #3003C2×C31semidirect
348. C2×#418C2×C31semidirect
349. #2433C2×C31semidirect
350. #2027C2×C31semidirect
351. #2002C2×C31semidirect
352. #1900C2×C31semidirect
353. #1887C2×C31semidirect
354. #1883C2×C31semidirect
355. #1871C2×C31semidirect
356. #1826C2×C31semidirect
405. #544C22×C31semidirect
408. #535C22×C31semidirect
415. #520C22×C31semidirect
416. #518C22×C31semidirect
422. C2×#104C22×C31semidirect
430. C2×#100C22×C31semidirect
435. #343C22×C31semidirect
436. #339C22×C31semidirect
437. #339C22×C31semidirect
438. #339C22×C31semidirect
491. C22⋊Q8D4×C31semidirect
492. C22⋊Q8D4×C31semidirect
502. #121D4×C31semidirect
503. #121D4×C31semidirect
522. #117D4×C31semidirect
523. #117D4×C31semidirect
528. C2×C4⋊C4D4×C31semidirect
529. C2×C4⋊C4D4×C31semidirect
549. C31#23954direct (N × H)
593. C2×D4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34942
C31×#30032
C2×C31×#4182
C31×#24332
C31×#20272
C31×#20022
C31×#19002
C31×#18872
C31×#18832
C31×#18712
C31×#18262
#2395431