Finite Group Databasebeta

← C31×#18224 #21474983

Subgroups — C31×#18224 #21474983

Order 7936.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3534C211yesmaximal, characteristic, complemented
2C31×#3003C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic, complemented
4C31×#2613C211yesmaximal, characteristic, complemented
5C31×#1600C212yesmaximal, complemented
6C31×#1598C212yesmaximal, complemented
7C31×#1597C212yesmaximal, complemented
8C31×#1595C212yesmaximal, complemented
9C31×#1516C211yesmaximal, characteristic, complemented
10C31×#1510C211yesmaximal, characteristic, complemented
11C31×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic, complemented
13C2×C31×AGL(1,ℤ/8)—21no—
14C22×D8×C31—21no—
15C31×#562—21no—
16C31×#560—21no—
17C31×#553—21no—
18C31×#551—21no—
19C31×#546—21no—
20C31×#546—21no—
21C31×#546—21no—
22D42×C31—21no—
23C31×#540—21no—
24C31×#539—21no—
25C31×#539C2211yescharacteristic, complemented
26C31×#538—21no—
27C31×#538C2211yescharacteristic, complemented
28C31×#537C2211yescharacteristic, complemented
29C31×#534—21no—
30C31×#534C2211yescharacteristic, complemented
31C31×#525C2211yescharacteristic
32C2×C31×#123C2211yescharacteristic
33C2×C31×#121C2211yescharacteristic
34C2×C31×#120—21no—
35C31×#450—21no—
36C31×#450C2212yescomplemented
37C31×#447—21no—
38C31×#447—21no—
39C31×#447—21no—
40C31×#447C2212yes—
41C31×#447C2212yescomplemented
42C31×#447C2212yescomplemented
43C31×#418—21no—
44C2×C31×#102—21no—
45C31×#407C2211yescharacteristic, complemented
46C2×C31×C22⋊C8C2211yescharacteristic, complemented
47C31×#394—21no—
48C31×#394C2212yescomplemented
49C31×#392—21no—
50C31×#392C2212yescomplemented
51C31×#381C2211yescharacteristic, complemented
52C31×#379—21no—
53C31×#328C2212yescomplemented
54C31×#327C2212yescomplemented
55C31×#327C2212yescomplemented
56C31×#327C2212yescomplemented
57C31×#324C2212yescomplemented
58C31×#323C2212yescomplemented
59C25×C31—21no—
60C2×#41×C31—21no—
61C2×#41×C31D411yescharacteristic, complemented
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—44no—
72C22×D4×C31D411yescharacteristic
73C22×D4×C31D411yescharacteristic, complemented
74C22×D4×C31C2312yes—
75C23×C4×C31C2311yescharacteristic
76C31×AGL(1,ℤ/8)—44no—
77C2×SD16×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C2×D8×C31—44no—
82C2×M16×C31—21no—
83C22×C8×C31—21no—
84C31×#127—21no—
85C31×#126—21no—
86C31×#126—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#125—21no—
90C31×#125—21no—
91C31×#124—21no—
92C31×#124—21no—
93C31×#124—21no—
94C31×#123—21no—
95C31×#123—21no—
96C31×#123—21no—
97C31×#123—21no—
98C31×#123—21no—
99C31×#123—21no—
100C31×#123—21no—
101C31×#123—21no—
102C31×#123—21no—
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8D411yescharacteristic, complemented
114C31×C22⋊Q8C2311yescharacteristic
115C31×#121—21no—
116C31×#121—21no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121—21no—
130C31×#121D411yescharacteristic, complemented
131C31×#121D411yescharacteristic, complemented
132C31×#121D411yescharacteristic, complemented
133C31×#121C2311yescharacteristic
134C31×#121C2311yescharacteristic
135C31×#121C2311yescharacteristic
136C31×#120—21no—
137C31×#120—21no—
138C31×#120—21no—
139C31×#120—21no—
140C31×#120—21no—
141C31×#120—21no—
142C31×#120—21no—
143C31×#120—21no—
144C31×#120—44no—
145C4×D4×C31—21no—
146C4×D4×C31—21no—
147C4×D4×C31—21no—
148C4×D4×C31—21no—
149C4×D4×C31—21no—
150C4×D4×C31—21no—
151C4×D4×C31—21no—
152C4×D4×C31—21no—
153C31×#117—21no—
154C31×#117D411yescharacteristic, complemented
155C2×C4⋊C4×C31D411yescharacteristic
156C2×C4⋊C4×C31D411yescharacteristic, complemented
157C2×C4⋊C4×C31C2311yescharacteristic
158C2×C22⋊C4×C31—21no—
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—21no—
161C2×C22⋊C4×C31—21no—
162C2×C22⋊C4×C31—22no—
163C2×C22⋊C4×C31—22no—
164C2×C22⋊C4×C31—22no—
165C2×C22⋊C4×C31D411yescharacteristic
166C2×C22⋊C4×C31D411yescharacteristic
167C2×C22⋊C4×C31C2311yescharacteristic
168C31×#102—22no—
169C31×#102—22no—
170C31×#102—22no—
171C31×#102—22no—
172C31×C22⋊C8—21no—
173C31×C22⋊C8—21no—
174C31×C22⋊C8C2312yes—
175C31×C22⋊C8C2312yes—
176C31×#95—21no—
177C31×#95C2312yes—
178C24×C31—24no—
179C24×C31—21no—
180C24×C31—22no—
181C24×C31—21no—
182C24×C31—42no—
183C24×C31—41no—
184C24×C31—41no—
185C24×C31—82no—
186C24×C31—82no—
187C24×C31C2×D411yescharacteristic
188C24×C31C2×D411yescharacteristic
189#41×C31—42no—
190#41×C31—82no—
191C2×Q8×C31—21no—
192C2×Q8×C31C2×D411yescharacteristic
193C2×D4×C31—24no—
194C2×D4×C31—24no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—22no—
213C2×D4×C31—22no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—42no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—44no—
221C2×D4×C31—42no—
222C2×D4×C31—44no—
223C2×D4×C31—41no—
224C2×D4×C31—41no—
225C2×D4×C31—82no—
226C2×D4×C31—82no—
227C2×D4×C31—82no—
228C2×D4×C31—82no—
229C2×D4×C31—82no—
230C2×D4×C31C2×D411yescharacteristic
231C2×D4×C31C2×D411yescharacteristic
232C2×D4×C31C2×D411yescharacteristic
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—22no—
241C22×C4×C31—42no—
242C22×C4×C31C2×D411yescharacteristic
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2411yescharacteristic
251SD16×C31—44no—
252D8×C31—44no—
253D8×C31—44no—
254D8×C31—44no—
255M16×C31—42no—
256C2×C8×C31—22no—
257C2×C8×C31—22no—
258C2×C8×C31—42no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31C2×D411yescharacteristic
273C4⋊C4×C31C2×D411yescharacteristic
274C4⋊C4×C31C2×D411yescharacteristic
275C4⋊C4×C31C2×D411yescharacteristic
276C22⋊C4×C31—21no—
277C22⋊C4×C31—21no—
278C22⋊C4×C31—21no—
279C22⋊C4×C31—21no—
280C22⋊C4×C31—21no—
281C22⋊C4×C31—21no—
282C22⋊C4×C31—21no—
283C22⋊C4×C31—21no—
284C22⋊C4×C31—21no—
285C22⋊C4×C31—21no—
286C22⋊C4×C31—21no—
287C22⋊C4×C31—21no—
288C22⋊C4×C31—21no—
289C22⋊C4×C31—21no—
290C22⋊C4×C31—21no—
291C22⋊C4×C31—21no—
292C22⋊C4×C31—21no—
293C22⋊C4×C31—21no—
294C22⋊C4×C31—21no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—21no—
298C22⋊C4×C31—21no—
299C22⋊C4×C31—21no—
300C22⋊C4×C31—21no—
301C22⋊C4×C31—44no—
302C22⋊C4×C31—42no—
303C22⋊C4×C31—82no—
304C22⋊C4×C31—82no—
305C42×C31—21no—
306C42×C31—21no—
307C42×C31—21no—
308#18224C3111yesmaximal, characteristic, direct product factor, Sylow
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—24no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—21no—
315C23×C31—21no—
316C23×C31—22no—
317C23×C31—41no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—44no—
321C23×C31—42no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—42no—
325C23×C31—42no—
326C23×C31—42no—
327C23×C31—44no—
328C23×C31—42no—
329C23×C31—81no—
330C23×C31—81no—
331C23×C31—82no—
332C23×C31—82no—
333C23×C31—82no—
334C23×C31—82no—
335C23×C31—88no—
336C23×C31—81no—
337C23×C31—81no—
338C23×C31—81no—
339C23×C31—88no—
340C23×C31#12011yescharacteristic
341C23×C31#12011yescharacteristic
342C23×C31C22×D411yescharacteristic
343Q8×C31—41no—
344Q8×C31—81no—
345D4×C31—24no—
346D4×C31—24no—
347D4×C31—41no—
348D4×C31—41no—
349D4×C31—41no—
350D4×C31—42no—
351D4×C31—42no—
352D4×C31—44no—
353D4×C31—44no—
354D4×C31—42no—
355D4×C31—42no—
356D4×C31—42no—
357D4×C31—42no—
358D4×C31—42no—
359D4×C31—81no—
360D4×C31—81no—
361D4×C31—81no—
362D4×C31—81no—
363D4×C31—81no—
364D4×C31—81no—
365D4×C31—81no—
366D4×C31—81no—
367D4×C31—81no—
368D4×C31—81no—
369D4×C31—81no—
370D4×C31—81no—
371D4×C31—88no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—21no—
375C2×C4×C31—21no—
376C2×C4×C31—21no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—22no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—42no—
390C2×C4×C31—42no—
391C2×C4×C31—42no—
392C2×C4×C31—81no—
393C2×C4×C31—81no—
394C2×C4×C31—81no—
395C2×C4×C31—81no—
396C2×C4×C31—81no—
397C2×C4×C31—81no—
398C2×C4×C31—81no—
399C2×C4×C31#12011yescharacteristic
400C2×C4×C31#12011yescharacteristic
401C2×C4×C31C22×D411yescharacteristic
402C2×C4×C31C22×D411yescharacteristic
403C8×C31—42no—
404C8×C31—42no—
405#3534C2×C3111yescharacteristic, complemented
406#3003C2×C3111yescharacteristic, complemented
407C2×#447C2×C3111yescharacteristic, complemented
408#2613C2×C3111yescharacteristic, complemented
409#1600C2×C3112yescomplemented
410#1598C2×C3112yescomplemented
411#1597C2×C3112yescomplemented
412#1595C2×C3112yescomplemented
413#1516C2×C3111yescharacteristic, complemented
414#1510C2×C3111yescharacteristic, complemented
415#1468C2×C3111yescharacteristic, complemented
416C22×C31—21no—
417C22×C31—21no—
418C22×C31—21no—
419C22×C31—21no—
420C22×C31—21no—
421C22×C31—21no—
422C22×C31—21no—
423C22×C31—44no—
424C22×C31—44no—
425C22×C31—44no—
426C22×C31—41no—
427C22×C31—41no—
428C22×C31—41no—
429C22×C31—41no—
430C22×C31—41no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—41no—
435C22×C31—41no—
436C22×C31—44no—
437C22×C31—41no—
438C22×C31—41no—
439C22×C31—82no—
440C22×C31—82no—
441C22×C31—82no—
442C22×C31—88no—
443C22×C31—88no—
444C22×C31—82no—
445C22×C31—82no—
446C22×C31—162no—
447C22×C31—162no—
448C22×C31B(4,𝔽2)12yes—
449C22×C31C2×#12011yescharacteristic
450C22×C31#57612yes—
451C4×C31—21no—
452C4×C31—21no—
453C4×C31—21no—
454C4×C31—21no—
455C4×C31—41no—
456C4×C31—41no—
457C4×C31—41no—
458C4×C31—41no—
459C4×C31—41no—
460C4×C31—41no—
461C4×C31—41no—
462C4×C31—41no—
463C4×C31—82no—
464C23×D4C22×C3111yescharacteristic, complemented
465C2×AGL(1,ℤ/8)—21no—
466C22×D8—21no—
467#562—21no—
468#560—21no—
469#553—21no—
470#551—21no—
471#546—21no—
472#546—21no—
473#546—21no—
474D42—21no—
475#540—21no—
476#539—21no—
477#539C22×C3111yescharacteristic, complemented
478#538—21no—
479#538C22×C3111yescharacteristic, complemented
480#537C22×C3111yescharacteristic, complemented
481#534—21no—
482#534C22×C3111yescharacteristic, complemented
483#525C22×C3111yescharacteristic
484C2×#123C22×C3111yescharacteristic
485C2×#121C22×C3111yescharacteristic
486C2×#120—21no—
487#450—21no—
488#450C22×C3112yescomplemented
489#447—21no—
490#447—21no—
491#447—21no—
492#447C22×C3112yes—
493#447C22×C3112yescomplemented
494#447C22×C3112yescomplemented
495#418—21no—
496C2×#102—21no—
497#407C22×C3111yescharacteristic, complemented
498C2×C22⋊C8C22×C3111yescharacteristic, complemented
499#394—21no—
500#394C22×C3112yescomplemented
501#392—21no—
502#392C22×C3112yescomplemented
503#381C22×C3111yescharacteristic, complemented
504#379—21no—
505#328C22×C3112yescomplemented
506#327C22×C3112yescomplemented
507#327C22×C3112yescomplemented
508#327C22×C3112yescomplemented
509#324C22×C3112yescomplemented
510#323C22×C3112yescomplemented
511C2×C31—22no—
512C2×C31—22no—
513C2×C31—41no—
514C2×C31—84no—
515C2×C31—81no—
516C2×C31—81no—
517C2×C31—81no—
518C2×C31—81no—
519C2×C31#300811yescharacteristic
520C2×C31#302111yescharacteristic
521C2×C31C2×B(4,𝔽2)11yescharacteristic
522C25—21no—
523C2×#41—21no—
524C2×#41D4×C3111yescharacteristic, complemented
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—44no—
535C22×D4D4×C3111yescharacteristic
536C22×D4D4×C3111yescharacteristic, complemented
537C22×D4C23×C3112yes—
538C23×C4C23×C3111yescharacteristic
539AGL(1,ℤ/8)—44no—
540C2×SD16—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—44no—
545C2×M16—21no—
546C22×C8—21no—
547#127—21no—
548#126—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#125—21no—
553#125—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8D4×C3111yescharacteristic, complemented
577C22⋊Q8C23×C3111yescharacteristic
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121D4×C3111yescharacteristic, complemented
594#121D4×C3111yescharacteristic, complemented
595#121D4×C3111yescharacteristic, complemented
596#121C23×C3111yescharacteristic
597#121C23×C3111yescharacteristic
598#121C23×C3111yescharacteristic
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—44no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616#117—21no—
617#117D4×C3111yescharacteristic, complemented
618C2×C4⋊C4D4×C3111yescharacteristic
619C2×C4⋊C4D4×C3111yescharacteristic, complemented
620C2×C4⋊C4C23×C3111yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4D4×C3111yescharacteristic
629C2×C22⋊C4D4×C3111yescharacteristic
630C2×C22⋊C4C23×C3111yescharacteristic
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8C23×C3112yes—
638C22⋊C8C23×C3112yes—
639#95—21no—
640#95C23×C3112yes—
641C31#1822411yescharacteristic, direct product factor, Sylow
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C3111yescharacteristic
652C24C2×D4×C3111yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C3111yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C3111yescharacteristic
695C2×D4C2×D4×C3111yescharacteristic
696C2×D4C2×D4×C3111yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C3111yescharacteristic
707C22×C4C2×D4×C3111yescharacteristic
708C22×C4C2×D4×C3111yescharacteristic
709C22×C4C2×D4×C3111yescharacteristic
710C22×C4C2×D4×C3111yescharacteristic
711C22×C4C2×D4×C3111yescharacteristic
712C22×C4C2×D4×C3111yescharacteristic
713C22×C4C2×D4×C3111yescharacteristic
714C22×C4C24×C3111yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C3111yescharacteristic
737C4⋊C4C2×D4×C3111yescharacteristic
738C4⋊C4C2×D4×C3111yescharacteristic
739C4⋊C4C2×D4×C3111yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23C31×#12011yescharacteristic
804C23C31×#12011yescharacteristic
805C23C22×D4×C3111yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4C31×#12011yescharacteristic
863C2×C4C31×#12011yescharacteristic
864C2×C4C22×D4×C3111yescharacteristic
865C2×C4C22×D4×C3111yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22C31×B(4,𝔽2)12yes—
901C22C2×C31×#12011yescharacteristic
902C22C31×#57612yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C31×#300811yescharacteristic
925C2C31×#302111yescharacteristic
926C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C31×#3534C2semidirect
2. C31×#3003C2semidirect
3. C2×C31×#447C2semidirect
4. C31×#2613C2semidirect
5. C31×#1600C2semidirect
6. C31×#1598C2semidirect
7. C31×#1597C2semidirect
8. C31×#1595C2semidirect
9. C31×#1516C2semidirect
10. C31×#1510C2semidirect
11. C31×#1468C2semidirect
12. C23×D4×C31C22semidirect
25. C31×#539C22semidirect
27. C31×#538C22semidirect
28. C31×#537C22semidirect
30. C31×#534C22semidirect
36. C31×#450C22semidirect
41. C31×#447C22semidirect
42. C31×#447C22semidirect
45. C31×#407C22semidirect
46. C2×C31×C22⋊C8C22semidirect
48. C31×#394C22semidirect
50. C31×#392C22semidirect
51. C31×#381C22semidirect
53. C31×#328C22semidirect
54. C31×#327C22semidirect
55. C31×#327C22semidirect
56. C31×#327C22semidirect
57. C31×#324C22semidirect
58. C31×#323C22semidirect
61. C2×#41×C31D4semidirect
73. C22×D4×C31D4semidirect
113. C31×C22⋊Q8D4semidirect
130. C31×#121D4semidirect
131. C31×#121D4semidirect
132. C31×#121D4semidirect
154. C31×#117D4semidirect
156. C2×C4⋊C4×C31D4semidirect
308. #18224C31direct (N × H)
405. #3534C2×C31semidirect
406. #3003C2×C31semidirect
407. C2×#447C2×C31semidirect
408. #2613C2×C31semidirect
409. #1600C2×C31semidirect
410. #1598C2×C31semidirect
411. #1597C2×C31semidirect
412. #1595C2×C31semidirect
413. #1516C2×C31semidirect
414. #1510C2×C31semidirect
415. #1468C2×C31semidirect
464. C23×D4C22×C31semidirect
477. #539C22×C31semidirect
479. #538C22×C31semidirect
480. #537C22×C31semidirect
482. #534C22×C31semidirect
488. #450C22×C31semidirect
493. #447C22×C31semidirect
494. #447C22×C31semidirect
497. #407C22×C31semidirect
498. C2×C22⋊C8C22×C31semidirect
500. #394C22×C31semidirect
502. #392C22×C31semidirect
503. #381C22×C31semidirect
505. #328C22×C31semidirect
506. #327C22×C31semidirect
507. #327C22×C31semidirect
508. #327C22×C31semidirect
509. #324C22×C31semidirect
510. #323C22×C31semidirect
524. C2×#41D4×C31semidirect
536. C22×D4D4×C31semidirect
576. C22⋊Q8D4×C31semidirect
593. #121D4×C31semidirect
594. #121D4×C31semidirect
595. #121D4×C31semidirect
617. #117D4×C31semidirect
619. C2×C4⋊C4D4×C31semidirect
641. C31#18224direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35342
C31×#30032
C2×C31×#4472
C31×#26132
C31×#16002
C31×#15982
C31×#15972
C31×#15952
C31×#15162
C31×#15102
C31×#14682
#1822431