Finite Group Databasebeta

← C31×#23902 #21480661

Subgroups — C31×#23902 #21480661

Order 7936.

1992 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3485C211yesmaximal, characteristic, complemented
2C2×C31×#525C211yesmaximal, characteristic, complemented
3C2×C31×#458C211yesmaximal, characteristic, complemented
4C2×C31×B(4,𝔽2)C211yesmaximal, characteristic, complemented
5C31×#2849C212yesmaximal, complemented
6C31×#2022C212yesmaximal, complemented
7C31×#2021C212yesmaximal, complemented
8C31×#1899C212yesmaximal, complemented
9C31×#1890C211yesmaximal, characteristic, complemented
10C31×#1889C211yesmaximal, characteristic, complemented
11C31×#1782C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic, complemented
15C31×#547—24no—
16C31×#546—24no—
17C31×#536—21no—
18C31×#534—21no—
19C31×#534C2212yes—
20C31×#525—21no—
21C31×#525—24no—
22C31×#525—24no—
23C2×C31×#123—21no—
24C2×C31×#123C2212yes—
25C2×C31×#123C2211yescharacteristic
26C2×C31×#123C2212yes—
27C2×C31×#123C2211yescharacteristic, complemented
28C2×C31×C22⋊Q8—21no—
29C2×C31×#121—21no—
30C2×C31×#120C2212yes—
31C2×C31×#120C2211yescharacteristic
32C2×C31×#120C2211yescharacteristic, complemented
33C31×#518C2211yescharacteristic
34C2×C4×D4×C31—21no—
35C2×C4×D4×C31—21no—
36C2×C31×#117C2211yescharacteristic, complemented
37C31×#458—24no—
38C31×B(4,𝔽2)—24no—
39C2×C31×#99C2211yescharacteristic
40C2×C31×#99C2211yescharacteristic
41C2×C31×#99C2212yes—
42C2×C31×#99C2212yes—
43C2×C31×#99C2212yescomplemented
44C31×#386—24no—
45C31×#385—24no—
46C31×#381C2212yescomplemented
47C31×#381C2212yescomplemented
48C31×#379C2212yescomplemented
49C31×#342C2212yescomplemented
50C31×#342C2212yescomplemented
51C25×C31C2311yescharacteristic
52C31×H(5,𝔽2)—22no—
53C31×H(5,𝔽2)—22no—
54C31×H(5,𝔽2)—42no—
55C2×#41×C31—22no—
56C2×#41×C31—22no—
57C2×#41×C31—21no—
58C2×#41×C31—24no—
59C2×#41×C31—22no—
60C2×#41×C31—42no—
61C22×Q8×C31D411yescharacteristic, complemented
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31D411yescharacteristic, complemented
68C22×D4×C31C2312yes—
69C22×D4×C31C2311yescharacteristic
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—22no—
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31—22no—
75C23×C4×C31—24no—
76C23×C4×C31—42no—
77C23×C4×C31D411yescharacteristic, complemented
78C23×C4×C31D411yescharacteristic, complemented
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C31×C4⋊Q8—22no—
82C31×#124—22no—
83C31×#123—24no—
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—22no—
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—24no—
90C31×#123—22no—
91C31×#123—22no—
92C31×#123—22no—
93C31×#123—24no—
94C31×#123—42no—
95C31×#123D414yescomplemented
96C31×C22⋊Q8—28no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—24no—
99C31×#121—28no—
100C31×#121—22no—
101C31×#121—24no—
102C31×#121—24no—
103C31×#120—22no—
104C31×#120—22no—
105C31×#120—22no—
106C31×#120—22no—
107C31×#120—22no—
108C31×#120—22no—
109C31×#120—24no—
110C31×#120—42no—
111C31×#120D414yescomplemented
112C4×D4×C31—28no—
113C4×D4×C31—28no—
114C4×D4×C31—24no—
115C4×D4×C31—24no—
116C31×#117—21no—
117C31×#117—22no—
118C31×#117—22no—
119C2×C4⋊C4×C31—22no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31—21no—
123C2×C4⋊C4×C31—22no—
124C2×C4⋊C4×C31D414yescomplemented
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—24no—
134C2×C22⋊C4×C31D414yescomplemented
135C2×C22⋊C4×C31C2312yes—
136C2×C22⋊C4×C31C2312yes—
137C2×C22⋊C4×C31C2312yes—
138C2×C22⋊C4×C31C2311yescharacteristic
139C2×C22⋊C4×C31C2311yescharacteristic
140C2×C42×C31—21no—
141C31×#99—22no—
142C31×#99—22no—
143C31×#99—24no—
144C31×#99—24no—
145C31×#99—42no—
146C31×#95—24no—
147C31×#95—24no—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—22no—
153C24×C31—44no—
154C24×C31C2×D412yes—
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D412yes—
157C24×C31C2×D411yescharacteristic
158C24×C31C2411yescharacteristic
159#41×C31—48no—
160#41×C31—48no—
161#41×C31—44no—
162#41×C31—44no—
163#41×C31—42no—
164#41×C31—42no—
165C2×Q8×C31—21no—
166C2×Q8×C31—22no—
167C2×Q8×C31—22no—
168C2×Q8×C31—41no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—24no—
172C2×D4×C31—22no—
173C2×D4×C31—21no—
174C2×D4×C31—24no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—24no—
187C2×D4×C31—22no—
188C2×D4×C31—41no—
189C2×D4×C31—44no—
190C2×D4×C31—44no—
191C2×D4×C31—44no—
192C2×D4×C31—44no—
193C2×D4×C31—42no—
194C2×D4×C31—42no—
195C2×D4×C31—44no—
196C2×D4×C31—48no—
197C2×D4×C31C2×D412yes—
198C2×D4×C31C2×D412yes—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—22no—
202C22×C4×C31—21no—
203C22×C4×C31—24no—
204C22×C4×C31—22no—
205C22×C4×C31—24no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—41no—
220C22×C4×C31—41no—
221C22×C4×C31—48no—
222C22×C4×C31—48no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—42no—
227C22×C4×C31C2×D412yes—
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D412yes—
230C22×C4×C31C2×D414yes—
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D414yes—
235C4⋊C4×C31—24no—
236C4⋊C4×C31—24no—
237C4⋊C4×C31—24no—
238C4⋊C4×C31—22no—
239C4⋊C4×C31—24no—
240C4⋊C4×C31—24no—
241C4⋊C4×C31—24no—
242C4⋊C4×C31—44no—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—24no—
246C22⋊C4×C31—24no—
247C22⋊C4×C31—24no—
248C22⋊C4×C31—24no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—24no—
255C22⋊C4×C31—24no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—22no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—44no—
261C22⋊C4×C31—44no—
262C22⋊C4×C31—48no—
263C22⋊C4×C31C2×D412yes—
264C22⋊C4×C31C2×D412yes—
265C42×C31—24no—
266C42×C31—22no—
267#23902C3111yesmaximal, characteristic, direct product factor, Sylow
268C23×C31—28no—
269C23×C31—24no—
270C23×C31—22no—
271C23×C31—21no—
272C23×C31—24no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—22no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—22no—
279C23×C31—22no—
280C23×C31—44no—
281C23×C31—42no—
282C23×C31—44no—
283C23×C31—42no—
284C23×C31—44no—
285C23×C31—48no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—44no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—42no—
293C23×C31—82no—
294C23×C31#12012yes—
295C23×C31C22×D411yescharacteristic
296C23×C31C22×D412yes—
297C23×C31C22×D411yescharacteristic
298C23×C31C22×D411yescharacteristic
299C23×C31H(5,𝔽2)12yes—
300Q8×C31—44no—
301Q8×C31—42no—
302D4×C31—24no—
303D4×C31—24no—
304D4×C31—44no—
305D4×C31—42no—
306D4×C31—48no—
307D4×C31—48no—
308D4×C31—44no—
309D4×C31—42no—
310D4×C31—42no—
311D4×C31—42no—
312D4×C31—42no—
313D4×C31—42no—
314D4×C31—42no—
315D4×C31—84no—
316D4×C31—88no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—24no—
324C2×C4×C31—24no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—24no—
330C2×C4×C31—21no—
331C2×C4×C31—22no—
332C2×C4×C31—21no—
333C2×C4×C31—22no—
334C2×C4×C31—24no—
335C2×C4×C31—22no—
336C2×C4×C31—44no—
337C2×C4×C31—44no—
338C2×C4×C31—48no—
339C2×C4×C31—48no—
340C2×C4×C31—44no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—42no—
347C2×C4×C31—44no—
348C2×C4×C31—44no—
349C2×C4×C31—44no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31—82no—
353C2×C4×C31#12012yes—
354C2×C4×C31#12012yes—
355C2×C4×C31#12012yes—
356#3485C2×C3111yescharacteristic, complemented
357C2×#525C2×C3111yescharacteristic, complemented
358C2×#458C2×C3111yescharacteristic, complemented
359C2×B(4,𝔽2)C2×C3111yescharacteristic, complemented
360#2849C2×C3112yescomplemented
361#2022C2×C3112yescomplemented
362#2021C2×C3112yescomplemented
363#1899C2×C3112yescomplemented
364#1890C2×C3111yescharacteristic, complemented
365#1889C2×C3111yescharacteristic, complemented
366#1782C2×C3111yescharacteristic, complemented
367C22×C31—24no—
368C22×C31—22no—
369C22×C31—24no—
370C22×C31—28no—
371C22×C31—22no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—44no—
378C22×C31—48no—
379C22×C31—44no—
380C22×C31—42no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—44no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—44no—
388C22×C31—81no—
389C22×C31—82no—
390C22×C31—82no—
391C22×C31—81no—
392C22×C31—162no—
393C22×C31C2×#12011yescharacteristic
394C22×C31C2×#12011yescharacteristic
395C22×C31#53411yescharacteristic
396C22×C31D4212yes—
397C22×C31D4212yes—
398C4×C31—22no—
399C4×C31—22no—
400C4×C31—22no—
401C4×C31—42no—
402C4×C31—42no—
403C4×C31—42no—
404C4×C31—42no—
405C4×C31—41no—
406C4×C31—44no—
407C4×C31—82no—
408C4×C31—82no—
409C2×H(5,𝔽2)C22×C3111yescharacteristic
410C22×#41C22×C3111yescharacteristic
411C24×C4C22×C3111yescharacteristic, complemented
412#547—24no—
413#546—24no—
414#536—21no—
415#534—21no—
416#534C22×C3112yes—
417#525—21no—
418#525—24no—
419#525—24no—
420C2×#123—21no—
421C2×#123C22×C3112yes—
422C2×#123C22×C3111yescharacteristic
423C2×#123C22×C3112yes—
424C2×#123C22×C3111yescharacteristic, complemented
425C2×C22⋊Q8—21no—
426C2×#121—21no—
427C2×#120C22×C3112yes—
428C2×#120C22×C3111yescharacteristic
429C2×#120C22×C3111yescharacteristic, complemented
430#518C22×C3111yescharacteristic
431C2×C4×D4—21no—
432C2×C4×D4—21no—
433C2×#117C22×C3111yescharacteristic, complemented
434#458—24no—
435B(4,𝔽2)—24no—
436C2×#99C22×C3111yescharacteristic
437C2×#99C22×C3111yescharacteristic
438C2×#99C22×C3112yes—
439C2×#99C22×C3112yes—
440C2×#99C22×C3112yescomplemented
441#386—24no—
442#385—24no—
443#381C22×C3112yescomplemented
444#381C22×C3112yescomplemented
445#379C22×C3112yescomplemented
446#342C22×C3112yescomplemented
447#342C22×C3112yescomplemented
448C2×C31—21no—
449C2×C31—22no—
450C2×C31—22no—
451C2×C31—21no—
452C2×C31—44no—
453C2×C31—42no—
454C2×C31—81no—
455C2×C31—82no—
456C2×C31#240311yescharacteristic
457C2×C31#302512yes—
458C25C23×C3111yescharacteristic
459H(5,𝔽2)—22no—
460H(5,𝔽2)—22no—
461H(5,𝔽2)—42no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—21no—
465C2×#41—24no—
466C2×#41—22no—
467C2×#41—42no—
468C22×Q8D4×C3111yescharacteristic, complemented
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4D4×C3111yescharacteristic, complemented
475C22×D4C23×C3112yes—
476C22×D4C23×C3111yescharacteristic
477C22×D4C23×C3111yescharacteristic
478C23×C4—22no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—22no—
482C23×C4—24no—
483C23×C4—42no—
484C23×C4D4×C3111yescharacteristic, complemented
485C23×C4D4×C3111yescharacteristic, complemented
486C23×C4C23×C3111yescharacteristic
487C23×C4C23×C3111yescharacteristic
488C4⋊Q8—22no—
489#124—22no—
490#123—24no—
491#123—22no—
492#123—22no—
493#123—22no—
494#123—22no—
495#123—22no—
496#123—24no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—24no—
501#123—42no—
502#123D4×C3114yescomplemented
503C22⋊Q8—28no—
504C22⋊Q8—22no—
505C22⋊Q8—24no—
506#121—28no—
507#121—22no—
508#121—24no—
509#121—24no—
510#120—22no—
511#120—22no—
512#120—22no—
513#120—22no—
514#120—22no—
515#120—22no—
516#120—24no—
517#120—42no—
518#120D4×C3114yescomplemented
519C4×D4—28no—
520C4×D4—28no—
521C4×D4—24no—
522C4×D4—24no—
523#117—21no—
524#117—22no—
525#117—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4D4×C3114yescomplemented
532C2×C22⋊C4—22no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4D4×C3114yescomplemented
542C2×C22⋊C4C23×C3112yes—
543C2×C22⋊C4C23×C3112yes—
544C2×C22⋊C4C23×C3112yes—
545C2×C22⋊C4C23×C3111yescharacteristic
546C2×C22⋊C4C23×C3111yescharacteristic
547C2×C42—21no—
548#99—22no—
549#99—22no—
550#99—24no—
551#99—24no—
552#99—42no—
553#95—24no—
554#95—24no—
555C31#2390211yescharacteristic, direct product factor, Sylow
556C24—22no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24—22no—
561C24—44no—
562C24C2×D4×C3112yes—
563C24C2×D4×C3111yescharacteristic
564C24C2×D4×C3112yes—
565C24C2×D4×C3111yescharacteristic
566C24C24×C3111yescharacteristic
567#41—48no—
568#41—48no—
569#41—44no—
570#41—44no—
571#41—42no—
572#41—42no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—41no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—24no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—41no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—44no—
604C2×D4—48no—
605C2×D4C2×D4×C3112yes—
606C2×D4C2×D4×C3112yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4C2×D4×C3112yes—
636C22×C4C2×D4×C3111yescharacteristic
637C22×C4C2×D4×C3112yes—
638C22×C4C2×D4×C3114yes—
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3114yes—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—44no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—22no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—22no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—48no—
671C22⋊C4C2×D4×C3112yes—
672C22⋊C4C2×D4×C3112yes—
673C42—24no—
674C42—22no—
675C23—28no—
676C23—24no—
677C23—22no—
678C23—21no—
679C23—24no—
680C23—21no—
681C23—22no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—44no—
692C23—48no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—82no—
701C23C31×#12012yes—
702C23C22×D4×C3111yescharacteristic
703C23C22×D4×C3112yes—
704C23C22×D4×C3111yescharacteristic
705C23C22×D4×C3111yescharacteristic
706C23C31×H(5,𝔽2)12yes—
707Q8—44no—
708Q8—42no—
709D4—24no—
710D4—24no—
711D4—44no—
712D4—42no—
713D4—48no—
714D4—48no—
715D4—44no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—84no—
723D4—88no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—48no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—82no—
760C2×C4C31×#12012yes—
761C2×C4C31×#12012yes—
762C2×C4C31×#12012yes—
763C22—24no—
764C22—22no—
765C22—24no—
766C22—28no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—44no—
774C22—48no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—81no—
785C22—82no—
786C22—82no—
787C22—81no—
788C22—162no—
789C22C2×C31×#12011yescharacteristic
790C22C2×C31×#12011yescharacteristic
791C22C31×#53411yescharacteristic
792C22D42×C3112yes—
793C22D42×C3112yes—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—44no—
803C4—82no—
804C4—82no—
805C2—21no—
806C2—22no—
807C2—22no—
808C2—21no—
809C2—44no—
810C2—42no—
811C2—81no—
812C2—82no—
813C2C31×#240311yescharacteristic
814C2C31×#302512yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ 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×#3485C2semidirect
2. C2×C31×#525C2semidirect
3. C2×C31×#458C2semidirect
4. C2×C31×B(4,𝔽2)C2semidirect
5. C31×#2849C2semidirect
6. C31×#2022C2semidirect
7. C31×#2021C2semidirect
8. C31×#1899C2semidirect
9. C31×#1890C2semidirect
10. C31×#1889C2semidirect
11. C31×#1782C2semidirect
14. C24×C4×C31C22semidirect
27. C2×C31×#123C22semidirect
32. C2×C31×#120C22semidirect
36. C2×C31×#117C22semidirect
43. C2×C31×#99C22semidirect
46. C31×#381C22semidirect
47. C31×#381C22semidirect
48. C31×#379C22semidirect
49. C31×#342C22semidirect
50. C31×#342C22semidirect
61. C22×Q8×C31D4semidirect
67. C22×D4×C31D4semidirect
77. C23×C4×C31D4semidirect
78. C23×C4×C31D4semidirect
95. C31×#123D4semidirect
111. C31×#120D4semidirect
124. C2×C4⋊C4×C31D4semidirect
134. C2×C22⋊C4×C31D4semidirect
267. #23902C31direct (N × H)
356. #3485C2×C31semidirect
357. C2×#525C2×C31semidirect
358. C2×#458C2×C31semidirect
359. C2×B(4,𝔽2)C2×C31semidirect
360. #2849C2×C31semidirect
361. #2022C2×C31semidirect
362. #2021C2×C31semidirect
363. #1899C2×C31semidirect
364. #1890C2×C31semidirect
365. #1889C2×C31semidirect
366. #1782C2×C31semidirect
411. C24×C4C22×C31semidirect
424. C2×#123C22×C31semidirect
429. C2×#120C22×C31semidirect
433. C2×#117C22×C31semidirect
440. C2×#99C22×C31semidirect
443. #381C22×C31semidirect
444. #381C22×C31semidirect
445. #379C22×C31semidirect
446. #342C22×C31semidirect
447. #342C22×C31semidirect
468. C22×Q8D4×C31semidirect
474. C22×D4D4×C31semidirect
484. C23×C4D4×C31semidirect
485. C23×C4D4×C31semidirect
502. #123D4×C31semidirect
518. #120D4×C31semidirect
531. C2×C4⋊C4D4×C31semidirect
541. C2×C22⋊C4D4×C31semidirect
555. C31#23902direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34852
C2×C31×#5252
C2×C31×#4582
C2×C31×B(4,𝔽2)2
C31×#28492
C31×#20222
C31×#20212
C31×#18992
C31×#18902
C31×#18892
C31×#17822
#2390231