Finite Group Databasebeta

← C31×#23860 #21480619

Subgroups — C31×#23860 #21480619

Order 7936.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 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
2C2×D42×C31C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#447C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic, complemented
7C31×#2014C211yesmaximal, characteristic, complemented
8C31×#2011C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1870C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic, complemented
17C23×D4×C31—21no—
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C2×C31×AGL(1,ℤ/8)—24no—
21C2×C31×AGL(1,ℤ/8)—24no—
22C2×C31×AGL(1,ℤ/8)—24no—
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic, complemented
25C22×SD16×C31C2211yescharacteristic, complemented
26C22×D8×C31C2211yescharacteristic
27C22×D8×C31C2211yescharacteristic, complemented
28C22×D8×C31C2211yescharacteristic, complemented
29C22×M16×C31C2211yescharacteristic, complemented
30D42×C31—24no—
31D42×C31—24no—
32C2×C31×#127C2211yescharacteristic
33C2×C31×C22⋊Q8C2211yescharacteristic, complemented
34C2×C31×#121—21no—
35C2×C31×#121C2211yescharacteristic
36C2×C31×#121C2211yescharacteristic
37C2×C31×#121C2211yescharacteristic, complemented
38C2×C31×#120—21no—
39C2×C31×#120—21no—
40C2×C4×D4×C31C2211yescharacteristic
41C2×C4×D4×C31C2211yescharacteristic
42C31×#450—24no—
43C31×#449—24no—
44C31×#447—24no—
45C2×C31×#103C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic, complemented
49C2×C31×#102C2211yescharacteristic, complemented
50C2×C31×#102C2211yescharacteristic, complemented
51C2×C31×#102C2211yescharacteristic, complemented
52C2×C31×#102C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C2×C31×C22⋊C8C2211yescharacteristic, complemented
55C2×C31×C22⋊C8C2211yescharacteristic, complemented
56C31×#394—21no—
57C31×#392—21no—
58C31×#391C2211yescharacteristic, complemented
59C31×#390C2211yescharacteristic, complemented
60C31×#386—21no—
61C31×#385—21no—
62C31×#380C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, complemented
65C31×#336C2211yescharacteristic, complemented
66C31×#336C2211yescharacteristic, complemented
67C25×C31—21no—
68C25×C31—21no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C22×Q8×C31C2311yescharacteristic
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—28no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—22no—
82C22×D4×C31—22no—
83C22×D4×C31—22no—
84C22×D4×C31—22no—
85C22×D4×C31—21no—
86C22×D4×C31—21no—
87C22×D4×C31—21no—
88C22×D4×C31—21no—
89C22×D4×C31—21no—
90C22×D4×C31—22no—
91C22×D4×C31—21no—
92C22×D4×C31—41no—
93C22×D4×C31—41no—
94C22×D4×C31—41no—
95C22×D4×C31—41no—
96C22×D4×C31—44no—
97C22×D4×C31—44no—
98C22×D4×C31D411yescharacteristic
99C22×D4×C31D414yescomplemented
100C22×D4×C31C2311yescharacteristic
101C22×D4×C31C2311yescharacteristic
102C22×D4×C31C2311yescharacteristic
103C22×D4×C31C2311yescharacteristic
104C23×C4×C31—21no—
105C23×C4×C31—21no—
106C23×C4×C31C2311yescharacteristic
107C23×C4×C31C2311yescharacteristic
108C31×AGL(1,ℤ/8)—232no—
109C2×SD16×C31—22no—
110C2×SD16×C31—22no—
111C2×SD16×C31—22no—
112C2×SD16×C31—22no—
113C2×SD16×C31—22no—
114C2×SD16×C31—22no—
115C2×SD16×C31—22no—
116C2×SD16×C31—41no—
117C2×SD16×C31D414yescomplemented
118C2×D8×C31—22no—
119C2×D8×C31—22no—
120C2×D8×C31—22no—
121C2×D8×C31—22no—
122C2×D8×C31—22no—
123C2×D8×C31—22no—
124C2×D8×C31—22no—
125C2×D8×C31—41no—
126C2×D8×C31D414yescomplemented
127C2×M16×C31—22no—
128C2×M16×C31—22no—
129C2×M16×C31—22no—
130C22×C8×C31C2311yescharacteristic
131C22×C8×C31C2311yescharacteristic
132C22×C8×C31C2311yescharacteristic
133C22×C8×C31C2311yescharacteristic
134C31×#127—22no—
135C31×#127—22no—
136C31×C22⋊Q8—22no—
137C31×C22⋊Q8—41no—
138C31×#121—28no—
139C31×#121—22no—
140C31×#121—22no—
141C31×#121—22no—
142C31×#121—22no—
143C31×#121—41no—
144C31×#121D414yescomplemented
145C31×#120—28no—
146C31×#120—28no—
147C4×D4×C31—22no—
148C4×D4×C31—22no—
149C4×D4×C31—22no—
150C4×D4×C31—22no—
151C2×C4⋊C4×C31—21no—
152C2×C4⋊C4×C31D411yescharacteristic
153C2×C4⋊C4×C31C2311yescharacteristic
154C2×C4⋊C4×C31C2311yescharacteristic
155C2×C4⋊C4×C31C2311yescharacteristic
156C2×C22⋊C4×C31—21no—
157C2×C22⋊C4×C31—21no—
158C2×C22⋊C4×C31—21no—
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—21no—
161C2×C22⋊C4×C31—21no—
162C2×C22⋊C4×C31—21no—
163C2×C22⋊C4×C31—21no—
164C2×C22⋊C4×C31D411yescharacteristic
165C2×C22⋊C4×C31D411yescharacteristic
166C2×C42×C31C2311yescharacteristic
167C31×#103—22no—
168C31×#102—22no—
169C31×#102—22no—
170C31×#102—22no—
171C31×#102—22no—
172C31×#102—22no—
173C31×#102—41no—
174C31×#102—41no—
175C31×C22⋊C8—22no—
176C31×C22⋊C8—22no—
177C31×C22⋊C8—22no—
178C31×#95—21no—
179C31×#95—21no—
180C31×#95—21no—
181C24×C31—21no—
182C24×C31—24no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—24no—
187C24×C31—42no—
188C24×C31—42no—
189C24×C31—42no—
190C24×C31—42no—
191C24×C31—42no—
192C24×C31—42no—
193C24×C31—42no—
194C24×C31—42no—
195C24×C31—81no—
196C24×C31—81no—
197C24×C31—81no—
198C24×C31—81no—
199C24×C31C2×D411yescharacteristic
200C24×C31C2×D411yescharacteristic
201#41×C31—28no—
202#41×C31—44no—
203#41×C31—44no—
204#41×C31—44no—
205C2×Q8×C31—21no—
206C2×Q8×C31—21no—
207C2×Q8×C31—21no—
208C2×Q8×C31—21no—
209C2×Q8×C31—21no—
210C2×Q8×C31C2×D412yescomplemented
211C2×D4×C31—22no—
212C2×D4×C31—22no—
213C2×D4×C31—28no—
214C2×D4×C31—24no—
215C2×D4×C31—24no—
216C2×D4×C31—24no—
217C2×D4×C31—24no—
218C2×D4×C31—24no—
219C2×D4×C31—24no—
220C2×D4×C31—22no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—21no—
232C2×D4×C31—21no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—21no—
236C2×D4×C31—21no—
237C2×D4×C31—21no—
238C2×D4×C31—21no—
239C2×D4×C31—44no—
240C2×D4×C31—44no—
241C2×D4×C31—44no—
242C2×D4×C31—42no—
243C2×D4×C31—42no—
244C2×D4×C31—42no—
245C2×D4×C31—42no—
246C2×D4×C31—42no—
247C2×D4×C31—42no—
248C2×D4×C31—44no—
249C2×D4×C31—44no—
250C2×D4×C31—432no—
251C2×D4×C31—44no—
252C2×D4×C31—42no—
253C2×D4×C31—42no—
254C2×D4×C31—42no—
255C2×D4×C31—42no—
256C2×D4×C31—42no—
257C2×D4×C31—42no—
258C2×D4×C31—44no—
259C2×D4×C31—42no—
260C2×D4×C31—42no—
261C2×D4×C31—42no—
262C2×D4×C31—81no—
263C2×D4×C31—81no—
264C2×D4×C31—81no—
265C2×D4×C31C2×D412yes—
266C2×D4×C31C2×D412yes—
267C2×D4×C31C2×D412yes—
268C2×D4×C31C2×D412yes—
269C2×D4×C31C2×D412yes—
270C2×D4×C31C2×D412yescomplemented
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—24no—
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—42no—
287C22×C4×C31—42no—
288C22×C4×C31—42no—
289C22×C4×C31—42no—
290C22×C4×C31—42no—
291C22×C4×C31C2×D411yescharacteristic
292C22×C4×C31C2×D411yescharacteristic
293C22×C4×C31C2×D411yescharacteristic
294C22×C4×C31C2×D412yes—
295C22×C4×C31C2×D412yes—
296C22×C4×C31C2×D411yescharacteristic
297C22×C4×C31C2411yescharacteristic
298SD16×C31—28no—
299SD16×C31—28no—
300SD16×C31—44no—
301D8×C31—28no—
302D8×C31—28no—
303D8×C31—44no—
304M16×C31—28no—
305C2×C8×C31—21no—
306C2×C8×C31—21no—
307C2×C8×C31—21no—
308C2×C8×C31—21no—
309C2×C8×C31—21no—
310C2×C8×C31—21no—
311C2×C8×C31—21no—
312C2×C8×C31—21no—
313C2×C8×C31—21no—
314C2×C8×C31—21no—
315C2×C8×C31C2×D412yescomplemented
316C2×C8×C31C2×D412yescomplemented
317C4⋊C4×C31—22no—
318C4⋊C4×C31—21no—
319C4⋊C4×C31—21no—
320C4⋊C4×C31—21no—
321C4⋊C4×C31—21no—
322C4⋊C4×C31—21no—
323C4⋊C4×C31—42no—
324C4⋊C4×C31C2×D412yes—
325C22⋊C4×C31—24no—
326C22⋊C4×C31—24no—
327C22⋊C4×C31—22no—
328C22⋊C4×C31—24no—
329C22⋊C4×C31—22no—
330C22⋊C4×C31—42no—
331C22⋊C4×C31—42no—
332C22⋊C4×C31—42no—
333C22⋊C4×C31—81no—
334C22⋊C4×C31—81no—
335C42×C31—21no—
336C42×C31—21no—
337#23860C3111yesmaximal, characteristic, direct product factor, Sylow
338C23×C31—21no—
339C23×C31—22no—
340C23×C31—21no—
341C23×C31—21no—
342C23×C31—21no—
343C23×C31—21no—
344C23×C31—22no—
345C23×C31—22no—
346C23×C31—21no—
347C23×C31—21no—
348C23×C31—21no—
349C23×C31—21no—
350C23×C31—21no—
351C23×C31—21no—
352C23×C31—21no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—48no—
357C23×C31—48no—
358C23×C31—48no—
359C23×C31—48no—
360C23×C31—41no—
361C23×C31—41no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—41no—
366C23×C31—41no—
367C23×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—84no—
383C23×C31—84no—
384C23×C31—84no—
385C23×C31—84no—
386C23×C31—84no—
387C23×C31—84no—
388C23×C31—84no—
389C23×C31—84no—
390C23×C31—84no—
391C23×C31—84no—
392C23×C31#12012yes—
393C23×C31AGL(1,ℤ/8)12yescomplemented
394C23×C31C22×D411yescharacteristic
395Q8×C31—22no—
396Q8×C31—22no—
397Q8×C31—41no—
398Q8×C31—41no—
399D4×C31—28no—
400D4×C31—22no—
401D4×C31—22no—
402D4×C31—22no—
403D4×C31—22no—
404D4×C31—22no—
405D4×C31—22no—
406D4×C31—22no—
407D4×C31—22no—
408D4×C31—22no—
409D4×C31—48no—
410D4×C31—48no—
411D4×C31—48no—
412D4×C31—48no—
413D4×C31—48no—
414D4×C31—48no—
415D4×C31—41no—
416D4×C31—41no—
417D4×C31—41no—
418D4×C31—41no—
419D4×C31—41no—
420D4×C31—41no—
421D4×C31—84no—
422D4×C31—84no—
423D4×C31#12014yes—
424C2×C4×C31—21no—
425C2×C4×C31—21no—
426C2×C4×C31—21no—
427C2×C4×C31—21no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—21no—
433C2×C4×C31—21no—
434C2×C4×C31—22no—
435C2×C4×C31—21no—
436C2×C4×C31—22no—
437C2×C4×C31—21no—
438C2×C4×C31—21no—
439C2×C4×C31—21no—
440C2×C4×C31—48no—
441C2×C4×C31—48no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31#12012yes—
457C2×C4×C31AGL(1,ℤ/8)12yescomplemented
458C2×C4×C31C22×D411yescharacteristic
459C2×C4×C31C22×D411yescharacteristic
460C2×C4×C31C22×D411yescharacteristic
461C2×C4×C31C22×D411yescharacteristic
462C2×C4×C31H(5,𝔽2)11yescharacteristic
463C2×C4×C31H(5,𝔽2)11yescharacteristic
464C8×C31—22no—
465C8×C31—22no—
466C8×C31—41no—
467C8×C31—41no—
468C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
469C2×D42C2×C3111yescharacteristic, complemented
470C2×#449C2×C3111yescharacteristic, complemented
471C2×#450C2×C3111yescharacteristic, complemented
472C2×#447C2×C3111yescharacteristic, complemented
473#2407C2×C3111yescharacteristic, complemented
474#2014C2×C3111yescharacteristic, complemented
475#2011C2×C3111yescharacteristic, complemented
476#2000C2×C3111yescharacteristic, complemented
477#1999C2×C3111yescharacteristic, complemented
478#1895C2×C3111yescharacteristic, complemented
479#1879C2×C3111yescharacteristic, complemented
480#1877C2×C3111yescharacteristic, complemented
481#1870C2×C3111yescharacteristic, complemented
482#1786C2×C3111yescharacteristic, complemented
483C22×C31—22no—
484C22×C31—24no—
485C22×C31—22no—
486C22×C31—22no—
487C22×C31—22no—
488C22×C31—22no—
489C22×C31—22no—
490C22×C31—41no—
491C22×C31—42no—
492C22×C31—41no—
493C22×C31—42no—
494C22×C31—41no—
495C22×C31—42no—
496C22×C31—41no—
497C22×C31—42no—
498C22×C31—41no—
499C22×C31—41no—
500C22×C31—42no—
501C22×C31—41no—
502C22×C31—41no—
503C22×C31—42no—
504C22×C31—42no—
505C22×C31—42no—
506C22×C31—42no—
507C22×C31—42no—
508C22×C31—42no—
509C22×C31—42no—
510C22×C31—42no—
511C22×C31—42no—
512C22×C31—42no—
513C22×C31—816no—
514C22×C31—816no—
515C22×C31—81no—
516C22×C31—81no—
517C22×C31—81no—
518C22×C31—81no—
519C22×C31—81no—
520C22×C31—81no—
521C22×C31—81no—
522C22×C31—81no—
523C22×C31—81no—
524C22×C31—81no—
525C22×C31—81no—
526C22×C31—81no—
527C22×C31C2×#12011yescharacteristic
528C22×C31D4211yescharacteristic
529C22×C31D4211yescharacteristic
530C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
531C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
532C22×C31#57611yescharacteristic
533C22×C31#57711yescharacteristic
534C4×C31—22no—
535C4×C31—22no—
536C4×C31—41no—
537C4×C31—42no—
538C4×C31—42no—
539C4×C31—41no—
540C4×C31—81no—
541C4×C31—81no—
542C4×C31C2×#12011yescharacteristic
543C4×C31#53411yescharacteristic
544C4×C31D4211yescharacteristic
545C4×C31D4211yescharacteristic
546C22×#41C22×C3111yescharacteristic, complemented
547C23×D4—21no—
548C23×D4C22×C3111yescharacteristic
549C23×D4C22×C3111yescharacteristic
550C2×AGL(1,ℤ/8)—24no—
551C2×AGL(1,ℤ/8)—24no—
552C2×AGL(1,ℤ/8)—24no—
553C22×SD16C22×C3111yescharacteristic
554C22×SD16C22×C3111yescharacteristic, complemented
555C22×SD16C22×C3111yescharacteristic, complemented
556C22×D8C22×C3111yescharacteristic
557C22×D8C22×C3111yescharacteristic, complemented
558C22×D8C22×C3111yescharacteristic, complemented
559C22×M16C22×C3111yescharacteristic, complemented
560D42—24no—
561D42—24no—
562C2×#127C22×C3111yescharacteristic
563C2×C22⋊Q8C22×C3111yescharacteristic, complemented
564C2×#121—21no—
565C2×#121C22×C3111yescharacteristic
566C2×#121C22×C3111yescharacteristic
567C2×#121C22×C3111yescharacteristic, complemented
568C2×#120—21no—
569C2×#120—21no—
570C2×C4×D4C22×C3111yescharacteristic
571C2×C4×D4C22×C3111yescharacteristic
572#450—24no—
573#449—24no—
574#447—24no—
575C2×#103C22×C3111yescharacteristic, complemented
576C2×#102C22×C3111yescharacteristic
577C2×#102C22×C3111yescharacteristic
578C2×#102C22×C3111yescharacteristic, complemented
579C2×#102C22×C3111yescharacteristic, complemented
580C2×#102C22×C3111yescharacteristic, complemented
581C2×#102C22×C3111yescharacteristic, complemented
582C2×#102C22×C3111yescharacteristic, complemented
583C2×C22⋊C8C22×C3111yescharacteristic, complemented
584C2×C22⋊C8C22×C3111yescharacteristic, complemented
585C2×C22⋊C8C22×C3111yescharacteristic, complemented
586#394—21no—
587#392—21no—
588#391C22×C3111yescharacteristic, complemented
589#390C22×C3111yescharacteristic, complemented
590#386—21no—
591#385—21no—
592#380C22×C3111yescharacteristic, complemented
593#340C22×C3111yescharacteristic, complemented
594#340C22×C3111yescharacteristic, complemented
595#336C22×C3111yescharacteristic, complemented
596#336C22×C3111yescharacteristic, complemented
597C2×C31—42no—
598C2×C31—42no—
599C2×C31—44no—
600C2×C31—82no—
601C2×C31—82no—
602C2×C31—82no—
603C2×C31#240311yescharacteristic
604C2×C31#300311yescharacteristic
605C2×C31#301211yescharacteristic
606C2×C31#326411yescharacteristic
607C2×C31#326511yescharacteristic
608C2×C31#327211yescharacteristic
609C2×C31#327411yescharacteristic
610C25—21no—
611C25—21no—
612C2×#41—22no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—41no—
617C2×#41—41no—
618C22×Q8C23×C3111yescharacteristic
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—28no—
622C22×D4—21no—
623C22×D4—21no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—21no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—22no—
634C22×D4—21no—
635C22×D4—41no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—44no—
640C22×D4—44no—
641C22×D4D4×C3111yescharacteristic
642C22×D4D4×C3114yescomplemented
643C22×D4C23×C3111yescharacteristic
644C22×D4C23×C3111yescharacteristic
645C22×D4C23×C3111yescharacteristic
646C22×D4C23×C3111yescharacteristic
647C23×C4—21no—
648C23×C4—21no—
649C23×C4C23×C3111yescharacteristic
650C23×C4C23×C3111yescharacteristic
651AGL(1,ℤ/8)—232no—
652C2×SD16—22no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—41no—
660C2×SD16D4×C3114yescomplemented
661C2×D8—22no—
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—41no—
669C2×D8D4×C3114yescomplemented
670C2×M16—22no—
671C2×M16—22no—
672C2×M16—22no—
673C22×C8C23×C3111yescharacteristic
674C22×C8C23×C3111yescharacteristic
675C22×C8C23×C3111yescharacteristic
676C22×C8C23×C3111yescharacteristic
677#127—22no—
678#127—22no—
679C22⋊Q8—22no—
680C22⋊Q8—41no—
681#121—28no—
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—41no—
687#121D4×C3114yescomplemented
688#120—28no—
689#120—28no—
690C4×D4—22no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4D4×C3111yescharacteristic
696C2×C4⋊C4C23×C3111yescharacteristic
697C2×C4⋊C4C23×C3111yescharacteristic
698C2×C4⋊C4C23×C3111yescharacteristic
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4D4×C3111yescharacteristic
708C2×C22⋊C4D4×C3111yescharacteristic
709C2×C42C23×C3111yescharacteristic
710#103—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—41no—
717#102—41no—
718C22⋊C8—22no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721#95—21no—
722#95—21no—
723#95—21no—
724C31#2386011yescharacteristic, direct product factor, Sylow
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C3111yescharacteristic
744C24C2×D4×C3111yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C3112yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C3112yes—
810C2×D4C2×D4×C3112yes—
811C2×D4C2×D4×C3112yes—
812C2×D4C2×D4×C3112yes—
813C2×D4C2×D4×C3112yes—
814C2×D4C2×D4×C3112yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C3111yescharacteristic
836C22×C4C2×D4×C3111yescharacteristic
837C22×C4C2×D4×C3111yescharacteristic
838C22×C4C2×D4×C3112yes—
839C22×C4C2×D4×C3112yes—
840C22×C4C2×D4×C3111yescharacteristic
841C22×C4C24×C3111yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C3112yescomplemented
860C2×C8C2×D4×C3112yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C3112yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23C31×#12012yes—
936C23C31×AGL(1,ℤ/8)12yescomplemented
937C23C22×D4×C3111yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4C31×#12014yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4C31×#12012yes—
1000C2×C4C31×AGL(1,ℤ/8)12yescomplemented
1001C2×C4C22×D4×C3111yescharacteristic
1002C2×C4C22×D4×C3111yescharacteristic
1003C2×C4C22×D4×C3111yescharacteristic
1004C2×C4C22×D4×C3111yescharacteristic
1005C2×C4C31×H(5,𝔽2)11yescharacteristic
1006C2×C4C31×H(5,𝔽2)11yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×C31×#12011yescharacteristic
1056C22D42×C3111yescharacteristic
1057C22D42×C3111yescharacteristic
1058C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
1059C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
1060C22C31×#57611yescharacteristic
1061C22C31×#57711yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—81no—
1069C4—81no—
1070C4C2×C31×#12011yescharacteristic
1071C4C31×#53411yescharacteristic
1072C4D42×C3111yescharacteristic
1073C4D42×C3111yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2C31×#240311yescharacteristic
1081C2C31×#300311yescharacteristic
1082C2C31×#301211yescharacteristic
1083C2C31×#326411yescharacteristic
1084C2C31×#326511yescharacteristic
1085C2C31×#327211yescharacteristic
1086C2C31×#327411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×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. C2×D42×C31C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#447C2semidirect
6. C31×#2407C2semidirect
7. C31×#2014C2semidirect
8. C31×#2011C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1895C2semidirect
12. C31×#1879C2semidirect
13. C31×#1877C2semidirect
14. C31×#1870C2semidirect
15. C31×#1786C2semidirect
16. C22×#41×C31C22semidirect
24. C22×SD16×C31C22semidirect
25. C22×SD16×C31C22semidirect
27. C22×D8×C31C22semidirect
28. C22×D8×C31C22semidirect
29. C22×M16×C31C22semidirect
33. C2×C31×C22⋊Q8C22semidirect
37. C2×C31×#121C22semidirect
45. C2×C31×#103C22semidirect
48. C2×C31×#102C22semidirect
49. C2×C31×#102C22semidirect
50. C2×C31×#102C22semidirect
51. C2×C31×#102C22semidirect
52. C2×C31×#102C22semidirect
53. C2×C31×C22⋊C8C22semidirect
54. C2×C31×C22⋊C8C22semidirect
55. C2×C31×C22⋊C8C22semidirect
58. C31×#391C22semidirect
59. C31×#390C22semidirect
62. C31×#380C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
65. C31×#336C22semidirect
66. C31×#336C22semidirect
99. C22×D4×C31D4semidirect
117. C2×SD16×C31D4semidirect
126. C2×D8×C31D4semidirect
144. C31×#121D4semidirect
210. C2×Q8×C31C2×D4semidirect
270. C2×D4×C31C2×D4semidirect
315. C2×C8×C31C2×D4semidirect
316. C2×C8×C31C2×D4semidirect
337. #23860C31direct (N × H)
393. C23×C31AGL(1,ℤ/8)semidirect
457. C2×C4×C31AGL(1,ℤ/8)semidirect
468. C22×AGL(1,ℤ/8)C2×C31semidirect
469. C2×D42C2×C31semidirect
470. C2×#449C2×C31semidirect
471. C2×#450C2×C31semidirect
472. C2×#447C2×C31semidirect
473. #2407C2×C31semidirect
474. #2014C2×C31semidirect
475. #2011C2×C31semidirect
476. #2000C2×C31semidirect
477. #1999C2×C31semidirect
478. #1895C2×C31semidirect
479. #1879C2×C31semidirect
480. #1877C2×C31semidirect
481. #1870C2×C31semidirect
482. #1786C2×C31semidirect
546. C22×#41C22×C31semidirect
554. C22×SD16C22×C31semidirect
555. C22×SD16C22×C31semidirect
557. C22×D8C22×C31semidirect
558. C22×D8C22×C31semidirect
559. C22×M16C22×C31semidirect
563. C2×C22⋊Q8C22×C31semidirect
567. C2×#121C22×C31semidirect
575. C2×#103C22×C31semidirect
578. C2×#102C22×C31semidirect
579. C2×#102C22×C31semidirect
580. C2×#102C22×C31semidirect
581. C2×#102C22×C31semidirect
582. C2×#102C22×C31semidirect
583. C2×C22⋊C8C22×C31semidirect
584. C2×C22⋊C8C22×C31semidirect
585. C2×C22⋊C8C22×C31semidirect
588. #391C22×C31semidirect
589. #390C22×C31semidirect
592. #380C22×C31semidirect
593. #340C22×C31semidirect
594. #340C22×C31semidirect
595. #336C22×C31semidirect
596. #336C22×C31semidirect
642. C22×D4D4×C31semidirect
660. C2×SD16D4×C31semidirect
669. C2×D8D4×C31semidirect
687. #121D4×C31semidirect
724. C31#23860direct (N × H)
754. C2×Q8C2×D4×C31semidirect
814. C2×D4C2×D4×C31semidirect
859. C2×C8C2×D4×C31semidirect
860. C2×C8C2×D4×C31semidirect
936. C23C31×AGL(1,ℤ/8)semidirect
1000. C2×C4C31×AGL(1,ℤ/8)semidirect

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
C2×D42×C312
C2×C31×#4492
C2×C31×#4502
C2×C31×#4472
C31×#24072
C31×#20142
C31×#20112
C31×#20002
C31×#19992
C31×#18952
C31×#18792
C31×#18772
C31×#18702
C31×#17862
#2386031