Finite Group Databasebeta

← C31×#24385 #21481144

Subgroups — C31×#24385 #21481144

Order 7936.

1892 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#468C212yesmaximal, complemented
3C2×C31×#450C211yesmaximal, characteristic, complemented
4C2×C31×#407C211yesmaximal, characteristic, complemented
5C31×#2848C211yesmaximal, characteristic, complemented
6C31×#2033C212yesmaximal, complemented
7C31×#2000C212yesmaximal, complemented
8C31×#1895C212yesmaximal, complemented
9C31×#1872C211yesmaximal, characteristic, complemented
10C31×#1852C211yesmaximal, characteristic, complemented
11C31×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C31—21no—
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C22×SD16×C31C2212yescomplemented
16C22×M16×C31C2212yescomplemented
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic, complemented
19C2×C31×C22⋊Q8C2211yescharacteristic, complemented
20C2×C31×#121—21no—
21C2×C31×#121—21no—
22C2×C31×#121—28no—
23C2×C31×#121C2212yes—
24C2×C31×#121C2212yes—
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31—21no—
27C31×#468—28no—
28C31×#450—24no—
29C2×C31×#107C2212yescomplemented
30C2×C31×#103C2212yescomplemented
31C2×C31×#102C2212yescomplemented
32C2×C31×#102C2212yescomplemented
33C2×C31×#102C2212yescomplemented
34C31×#407—24no—
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2212yescomplemented
38C31×#385—21no—
39C31×#385—21no—
40C31×#385—21no—
41C31×#380C2211yescharacteristic
42C31×#380C2211yescharacteristic, complemented
43C31×#380C2211yescharacteristic, complemented
44C31×#379—21no—
45C31×#340C2212yescomplemented
46C31×#340C2212yescomplemented
47C25×C31—21no—
48C25×C31D411yescharacteristic
49C22×Q8×C31C2311yescharacteristic
50C22×D4×C31—28no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—24no—
54C22×D4×C31—21no—
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—42no—
58C22×D4×C31—44no—
59C22×D4×C31—44no—
60C22×D4×C31C2312yes—
61C23×C4×C31—21no—
62C23×C4×C31—22no—
63C23×C4×C31—24no—
64C23×C4×C31—22no—
65C23×C4×C31—42no—
66C23×C4×C31D411yescharacteristic
67C23×C4×C31D411yescharacteristic
68C23×C4×C31D411yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C2×SD16×C31—24no—
73C2×SD16×C31—24no—
74C2×SD16×C31—42no—
75C2×M16×C31—24no—
76C2×M16×C31—24no—
77C2×M16×C31—42no—
78C22×C8×C31C2312yes—
79C22×C8×C31C2312yes—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—24no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—42no—
84C31×#121—28no—
85C31×#121—28no—
86C31×#121—24no—
87C31×#121—24no—
88C31×#121—24no—
89C31×#121D418yes—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—24no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2312yes—
99C2×C22⋊C4×C31—28no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C31×#107—24no—
109C31×#103—24no—
110C31×#102—24no—
111C31×#102—24no—
112C31×#102—42no—
113C31×C22⋊C8—22no—
114C31×C22⋊C8—24no—
115C31×C22⋊C8D414yescomplemented
116C31×#95—21no—
117C31×#95—21no—
118C31×#95—21no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—24no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—41no—
127C24×C31—41no—
128C24×C31—42no—
129C24×C31—42no—
130C24×C31—42no—
131C24×C31—42no—
132C24×C31—42no—
133C24×C31—42no—
134C24×C31C2×D411yescharacteristic
135C24×C31C2×D411yescharacteristic
136C24×C31C2×D411yescharacteristic
137C2×Q8×C31—22no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31—22no—
141C2×D4×C31—24no—
142C2×D4×C31—28no—
143C2×D4×C31—28no—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—22no—
147C2×D4×C31—22no—
148C2×D4×C31—22no—
149C2×D4×C31—48no—
150C2×D4×C31—48no—
151C2×D4×C31—42no—
152C2×D4×C31—432no—
153C2×D4×C31—44no—
154C2×D4×C31—44no—
155C2×D4×C31—44no—
156C2×D4×C31—44no—
157C2×D4×C31—42no—
158C2×D4×C31C2×D414yes—
159C22×C4×C31—22no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—24no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—21no—
173C22×C4×C31—22no—
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—41no—
181C22×C4×C31—41no—
182C22×C4×C31—41no—
183C22×C4×C31—48no—
184C22×C4×C31—48no—
185C22×C4×C31—42no—
186C22×C4×C31—42no—
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D414yes—
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D412yes—
192C22×C4×C31#4112yes—
193C22×C4×C31C2411yescharacteristic
194SD16×C31—48no—
195M16×C31—48no—
196C2×C8×C31—22no—
197C2×C8×C31—22no—
198C2×C8×C31—22no—
199C2×C8×C31—22no—
200C2×C8×C31—22no—
201C2×C8×C31C2×D414yescomplemented
202C4⋊C4×C31—24no—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—22no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31C2×D414yes—
212C22⋊C4×C31—28no—
213C22⋊C4×C31—28no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220#24385C3111yesmaximal, characteristic, direct product factor, Sylow
221C23×C31—21no—
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—28no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—24no—
239C23×C31—44no—
240C23×C31—44no—
241C23×C31—44no—
242C23×C31—44no—
243C23×C31—44no—
244C23×C31—48no—
245C23×C31—48no—
246C23×C31—48no—
247C23×C31—44no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—84no—
255C23×C31—84no—
256C23×C31—84no—
257C23×C31—84no—
258C23×C31#12012yes—
259C23×C31#12112yes—
260C23×C31AGL(1,ℤ/8)12yes—
261C23×C31AGL(1,ℤ/8)12yes—
262C23×C31#13712yes—
263C23×C31C22×D411yescharacteristic
264Q8×C31—42no—
265Q8×C31—42no—
266D4×C31—24no—
267D4×C31—24no—
268D4×C31—48no—
269D4×C31—416no—
270D4×C31—416no—
271D4×C31—42no—
272D4×C31—42no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—24no—
278C2×C4×C31—24no—
279C2×C4×C31—24no—
280C2×C4×C31—24no—
281C2×C4×C31—21no—
282C2×C4×C31—24no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—44no—
286C2×C4×C31—44no—
287C2×C4×C31—44no—
288C2×C4×C31—48no—
289C2×C4×C31—42no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31#12012yes—
306C2×C4×C31#12112yes—
307C2×C4×C31C22×D411yescharacteristic
308C2×C4×C31C22×D412yes—
309C2×C4×C31C2×#4111yescharacteristic
310C2×C4×C31H(5,𝔽2)12yes—
311C8×C31—24no—
312C8×C31—42no—
313C22×#121C2×C3111yescharacteristic
314C2×#468C2×C3112yescomplemented
315C2×#450C2×C3111yescharacteristic, complemented
316C2×#407C2×C3111yescharacteristic, complemented
317#2848C2×C3111yescharacteristic, complemented
318#2033C2×C3112yescomplemented
319#2000C2×C3112yescomplemented
320#1895C2×C3112yescomplemented
321#1872C2×C3111yescharacteristic, complemented
322#1852C2×C3111yescharacteristic, complemented
323#1786C2×C3111yescharacteristic, complemented
324C22×C31—22no—
325C22×C31—22no—
326C22×C31—22no—
327C22×C31—22no—
328C22×C31—22no—
329C22×C31—22no—
330C22×C31—22no—
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—22no—
335C22×C31—22no—
336C22×C31—416no—
337C22×C31—41no—
338C22×C31—41no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—41no—
342C22×C31—41no—
343C22×C31—41no—
344C22×C31—41no—
345C22×C31—44no—
346C22×C31—44no—
347C22×C31—44no—
348C22×C31—816no—
349C22×C31—82no—
350C22×C31—82no—
351C22×C31—82no—
352C22×C31—82no—
353C22×C31#46814yescomplemented
354C22×C31C2×#12011yescharacteristic
355C22×C31C2×#12111yescharacteristic
356C22×C31#53411yescharacteristic
357C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C31C2×#13711yescharacteristic
360C22×C31#57511yescharacteristic
361C4×C31—22no—
362C4×C31—22no—
363C4×C31—41no—
364C4×C31—44no—
365C4×C31—81no—
366C4×C31—81no—
367C4×C31—81no—
368C4×C31—81no—
369C4×C31D4212yes—
370C4×C31#54612yes—
371C23×D4—21no—
372C23×D4C22×C3111yescharacteristic
373C24×C4C22×C3111yescharacteristic
374C22×SD16C22×C3112yescomplemented
375C22×M16C22×C3112yescomplemented
376C2×C22⋊Q8C22×C3111yescharacteristic
377C2×C22⋊Q8C22×C3111yescharacteristic, complemented
378C2×C22⋊Q8C22×C3111yescharacteristic, complemented
379C2×#121—21no—
380C2×#121—21no—
381C2×#121—28no—
382C2×#121C22×C3112yes—
383C2×#121C22×C3112yes—
384C22×C4⋊C4C22×C3111yescharacteristic
385C22×C22⋊C4—21no—
386#468—28no—
387#450—24no—
388C2×#107C22×C3112yescomplemented
389C2×#103C22×C3112yescomplemented
390C2×#102C22×C3112yescomplemented
391C2×#102C22×C3112yescomplemented
392C2×#102C22×C3112yescomplemented
393#407—24no—
394C2×C22⋊C8C22×C3111yescharacteristic
395C2×C22⋊C8C22×C3111yescharacteristic
396C2×C22⋊C8C22×C3112yescomplemented
397#385—21no—
398#385—21no—
399#385—21no—
400#380C22×C3111yescharacteristic
401#380C22×C3111yescharacteristic, complemented
402#380C22×C3111yescharacteristic, complemented
403#379—21no—
404#340C22×C3112yescomplemented
405#340C22×C3112yescomplemented
406C2×C31—24no—
407C2×C31—42no—
408C2×C31—42no—
409C2×C31—84no—
410C2×C31#241011yescharacteristic
411C2×C31#300311yescharacteristic
412C2×C31#300711yescharacteristic
413C2×C31C2×#46811yescharacteristic
414C2×C31#305511yescharacteristic
415C2×C31#319311yescharacteristic
416C2×C31#319411yescharacteristic
417C25—21no—
418C25D4×C3111yescharacteristic
419C22×Q8C23×C3111yescharacteristic
420C22×D4—28no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—24no—
424C22×D4—21no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—42no—
428C22×D4—44no—
429C22×D4—44no—
430C22×D4C23×C3112yes—
431C23×C4—21no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—42no—
436C23×C4D4×C3111yescharacteristic
437C23×C4D4×C3111yescharacteristic
438C23×C4D4×C3111yescharacteristic
439C23×C4C23×C3111yescharacteristic
440C23×C4C23×C3111yescharacteristic
441C23×C4C23×C3111yescharacteristic
442C2×SD16—24no—
443C2×SD16—24no—
444C2×SD16—42no—
445C2×M16—24no—
446C2×M16—24no—
447C2×M16—42no—
448C22×C8C23×C3112yes—
449C22×C8C23×C3112yes—
450C22⋊Q8—22no—
451C22⋊Q8—24no—
452C22⋊Q8—22no—
453C22⋊Q8—42no—
454#121—28no—
455#121—28no—
456#121—24no—
457#121—24no—
458#121—24no—
459#121D4×C3118yes—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3112yes—
469C2×C22⋊C4—28no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478#107—24no—
479#103—24no—
480#102—24no—
481#102—24no—
482#102—42no—
483C22⋊C8—22no—
484C22⋊C8—24no—
485C22⋊C8D4×C3114yescomplemented
486#95—21no—
487#95—21no—
488#95—21no—
489C31#2438511yescharacteristic, direct product factor, Sylow
490C24—22no—
491C24—22no—
492C24—22no—
493C24—24no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—41no—
498C24—41no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24C2×D4×C3111yescharacteristic
506C24C2×D4×C3111yescharacteristic
507C24C2×D4×C3111yescharacteristic
508C2×Q8—22no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—22no—
512C2×D4—24no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—42no—
523C2×D4—432no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—42no—
529C2×D4C2×D4×C3114yes—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4C2×D4×C3111yescharacteristic
559C22×C4C2×D4×C3111yescharacteristic
560C22×C4C2×D4×C3114yes—
561C22×C4C2×D4×C3111yescharacteristic
562C22×C4C2×D4×C3112yes—
563C22×C4#41×C3112yes—
564C22×C4C24×C3111yescharacteristic
565SD16—48no—
566M16—48no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8C2×D4×C3114yescomplemented
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—22no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4C2×D4×C3114yes—
583C22⋊C4—28no—
584C22⋊C4—28no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—28no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—24no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—48no—
615C23—48no—
616C23—48no—
617C23—44no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23C31×#12012yes—
629C23C31×#12112yes—
630C23C31×AGL(1,ℤ/8)12yes—
631C23C31×AGL(1,ℤ/8)12yes—
632C23C31×#13712yes—
633C23C22×D4×C3111yescharacteristic
634Q8—42no—
635Q8—42no—
636D4—24no—
637D4—24no—
638D4—48no—
639D4—416no—
640D4—416no—
641D4—42no—
642D4—42no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—21no—
652C2×C4—24no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4C31×#12012yes—
676C2×C4C31×#12112yes—
677C2×C4C22×D4×C3111yescharacteristic
678C2×C4C22×D4×C3112yes—
679C2×C4C2×#41×C3111yescharacteristic
680C2×C4C31×H(5,𝔽2)12yes—
681C8—24no—
682C8—42no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—416no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—816no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22C31×#46814yescomplemented
713C22C2×C31×#12011yescharacteristic
714C22C2×C31×#12111yescharacteristic
715C22C31×#53411yescharacteristic
716C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
717C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
718C22C2×C31×#13711yescharacteristic
719C22C31×#57511yescharacteristic
720C4—22no—
721C4—22no—
722C4—41no—
723C4—44no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4D42×C3112yes—
729C4C31×#54612yes—
730C2—24no—
731C2—42no—
732C2—42no—
733C2—84no—
734C2C31×#241011yescharacteristic
735C2C31×#300311yescharacteristic
736C2C31×#300711yescharacteristic
737C2C2×C31×#46811yescharacteristic
738C2C31×#305511yescharacteristic
739C2C31×#319311yescharacteristic
740C2C31×#319411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#468C2semidirect
3. C2×C31×#450C2semidirect
4. C2×C31×#407C2semidirect
5. C31×#2848C2semidirect
6. C31×#2033C2semidirect
7. C31×#2000C2semidirect
8. C31×#1895C2semidirect
9. C31×#1872C2semidirect
10. C31×#1852C2semidirect
11. C31×#1786C2semidirect
15. C22×SD16×C31C22semidirect
16. C22×M16×C31C22semidirect
18. C2×C31×C22⋊Q8C22semidirect
19. C2×C31×C22⋊Q8C22semidirect
29. C2×C31×#107C22semidirect
30. C2×C31×#103C22semidirect
31. C2×C31×#102C22semidirect
32. C2×C31×#102C22semidirect
33. C2×C31×#102C22semidirect
37. C2×C31×C22⋊C8C22semidirect
42. C31×#380C22semidirect
43. C31×#380C22semidirect
45. C31×#340C22semidirect
46. C31×#340C22semidirect
115. C31×C22⋊C8D4semidirect
201. C2×C8×C31C2×D4semidirect
220. #24385C31direct (N × H)
314. C2×#468C2×C31semidirect
315. C2×#450C2×C31semidirect
316. C2×#407C2×C31semidirect
317. #2848C2×C31semidirect
318. #2033C2×C31semidirect
319. #2000C2×C31semidirect
320. #1895C2×C31semidirect
321. #1872C2×C31semidirect
322. #1852C2×C31semidirect
323. #1786C2×C31semidirect
353. C22×C31#468semidirect
374. C22×SD16C22×C31semidirect
375. C22×M16C22×C31semidirect
377. C2×C22⋊Q8C22×C31semidirect
378. C2×C22⋊Q8C22×C31semidirect
388. C2×#107C22×C31semidirect
389. C2×#103C22×C31semidirect
390. C2×#102C22×C31semidirect
391. C2×#102C22×C31semidirect
392. C2×#102C22×C31semidirect
396. C2×C22⋊C8C22×C31semidirect
401. #380C22×C31semidirect
402. #380C22×C31semidirect
404. #340C22×C31semidirect
405. #340C22×C31semidirect
485. C22⋊C8D4×C31semidirect
489. C31#24385direct (N × H)
572. C2×C8C2×D4×C31semidirect
712. C22C31×#468semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#4682
C2×C31×#4502
C2×C31×#4072
C31×#28482
C31×#20332
C31×#20002
C31×#18952
C31×#18722
C31×#18522
C31×#17862
#2438531