Finite Group Databasebeta

← C31×#24256 #21481015

Subgroups — C31×#24256 #21481015

Order 7936.

1510 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#548C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#448C211yesmaximal, characteristic, complemented
5C2×C31×#440C211yesmaximal, characteristic, complemented
6C31×#2537C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1959C211yesmaximal, characteristic, complemented
12C31×#1955C211yesmaximal, characteristic, complemented
13C31×#1803C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic, complemented
15C31×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C31×#548—24no—
22C31×#548—24no—
23C2×C31×#124—21no—
24C2×C31×#124C2211yescharacteristic
25C2×C31×C22⋊Q8—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×#121—21no—
28C2×C31×#121—21no—
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C2×C4×D4×C31—21no—
34C2×C4×D4×C31C2211yescharacteristic
35C2×C4×D4×C31C2211yescharacteristic
36C31×#463—24no—
37C31×#449—24no—
38C31×#448—24no—
39C31×#440—24no—
40C2×C31×#107C2211yescharacteristic
41C2×C31×C4⋊C8C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#103C2211yescharacteristic
45C2×C31×#103C2211yescharacteristic
46C2×C31×#103C2211yescharacteristic
47C2×C31×#103C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×#102C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C2×C31×C22⋊C8C2211yescharacteristic
56C2×C31×#97C2211yescharacteristic
57C31×#394—21no—
58C31×#394—21no—
59C31×#384C2211yescharacteristic
60C31×#380—21no—
61C31×#380C2211yescharacteristic
62C31×#380C2211yescharacteristic
63C31×#340C2211yescharacteristic
64C31×#340C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—41no—
70C2×#41×C31—41no—
71C22×Q8×C31—22no—
72C22×Q8×C31—22no—
73C22×Q8×C31—21no—
74C22×Q8×C31—22no—
75C22×Q8×C31—22no—
76C22×Q8×C31—41no—
77C22×Q8×C31—41no—
78C22×Q8×C31C2311yescharacteristic
79C22×Q8×C31C2311yescharacteristic
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31D411yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C2×SD16×C31—22no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—41no—
97C2×SD16×C31D414yescomplemented
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—41no—
101C22×C8×C31C2311yescharacteristic
102C22×C8×C31C2311yescharacteristic
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C31×#124—28no—
106C31×#124—22no—
107C31×#124D414yescomplemented
108C31×C22⋊Q8—28no—
109C31×C22⋊Q8—22no—
110C31×C22⋊Q8—22no—
111C31×#121—28no—
112C31×#121—22no—
113C31×#121—22no—
114C31×#121—22no—
115C31×#121—22no—
116C31×#121—41no—
117C31×#121—41no—
118C31×#121—44no—
119C4×Q8×C31—22no—
120C4×Q8×C31D414yescomplemented
121C4×D4×C31—28no—
122C4×D4×C31—22no—
123C4×D4×C31—22no—
124C4×D4×C31—22no—
125C4×D4×C31—22no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31D411yescharacteristic
131C2×C4⋊C4×C31C2311yescharacteristic
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31D411yescharacteristic
145C2×C22⋊C4×C31D411yescharacteristic
146C2×C42×C31—21no—
147C2×C42×C31C2311yescharacteristic
148C31×#107—22no—
149C31×C4⋊C8—22no—
150C31×#103—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#103—22no—
155C31×#103—41no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—41no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8—41no—
163C31×C22⋊C8—41no—
164C31×#97—22no—
165C31×#95—21no—
166C31×#95—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31C2×D411yescharacteristic
170C24×C31C2×D411yescharacteristic
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175C2×Q8×C31—24no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—42no—
185C2×Q8×C31—42no—
186C2×Q8×C31—44no—
187C2×Q8×C31—44no—
188C2×Q8×C31—44no—
189C2×Q8×C31—44no—
190C2×Q8×C31C2×D412yes—
191C2×Q8×C31C2×D412yes—
192C2×Q8×C31C2×D412yes—
193C2×Q8×C31#4112yes—
194C2×D4×C31—24no—
195C2×D4×C31—24no—
196C2×D4×C31—22no—
197C2×D4×C31—22no—
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—41no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—42no—
217C2×D4×C31—81no—
218C2×D4×C31—81no—
219C2×D4×C31C2×D412yes—
220C2×D4×C31C2×D412yes—
221C22×C4×C31—21no—
222C22×C4×C31—24no—
223C22×C4×C31—24no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
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—21no—
241C22×C4×C31—42no—
242C22×C4×C31—42no—
243C22×C4×C31—42no—
244C22×C4×C31—42no—
245C22×C4×C31—42no—
246C22×C4×C31—42no—
247C22×C4×C31—42no—
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D411yescharacteristic
251C22×C4×C31C2×D411yescharacteristic
252C22×C4×C31C2411yescharacteristic
253SD16×C31—28no—
254SD16×C31—44no—
255D8×C31—44no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31C2×D412yes—
268C4⋊C4×C31—24no—
269C4⋊C4×C31—24no—
270C4⋊C4×C31—22no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—42no—
279C4⋊C4×C31—81no—
280C4⋊C4×C31C2×D412yes—
281C22⋊C4×C31—24no—
282C22⋊C4×C31—24no—
283C22⋊C4×C31—24no—
284C22⋊C4×C31—24no—
285C22⋊C4×C31—22no—
286C22⋊C4×C31—22no—
287C22⋊C4×C31—42no—
288C22⋊C4×C31—42no—
289C22⋊C4×C31—42no—
290C22⋊C4×C31—42no—
291C22⋊C4×C31—42no—
292C42×C31—24no—
293C42×C31C2×D412yes—
294C42×C31C2×D412yes—
295#24256C3111yesmaximal, characteristic, direct product factor, Sylow
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31AGL(1,ℤ/8)12yes—
324C23×C31C22×D411yescharacteristic
325Q8×C31—22no—
326Q8×C31—22no—
327Q8×C31—22no—
328Q8×C31—22no—
329Q8×C31—22no—
330Q8×C31—48no—
331Q8×C31—41no—
332Q8×C31—41no—
333Q8×C31#12114yescomplemented
334D4×C31—22no—
335D4×C31—22no—
336D4×C31—22no—
337D4×C31—22no—
338D4×C31—44no—
339D4×C31—48no—
340D4×C31—48no—
341D4×C31—41no—
342D4×C31—41no—
343D4×C31—41no—
344D4×C31—41no—
345D4×C31—84no—
346D4×C31—84no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—21no—
357C2×C4×C31—21no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—21no—
362C2×C4×C31—48no—
363C2×C4×C31—48no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—84no—
386C2×C4×C31#12012yes—
387C2×C4×C31#12012yes—
388C2×C4×C31C22×D411yescharacteristic
389C2×C4×C31C22×D411yescharacteristic
390C2×C4×C31C22×D411yescharacteristic
391C2×C4×C31C2×#4111yescharacteristic
392C2×C4×C31H(5,𝔽2)11yescharacteristic
393C2×C4×C31H(5,𝔽2)11yescharacteristic
394C8×C31—22no—
395C8×C31—41no—
396C8×C31—41no—
397C8×C31—41no—
398C2×#548C2×C3111yescharacteristic, complemented
399C2×#463C2×C3111yescharacteristic, complemented
400C2×#449C2×C3111yescharacteristic, complemented
401C2×#448C2×C3111yescharacteristic, complemented
402C2×#440C2×C3111yescharacteristic, complemented
403#2537C2×C3111yescharacteristic, complemented
404#2036C2×C3111yescharacteristic, complemented
405#2033C2×C3111yescharacteristic, complemented
406#2000C2×C3111yescharacteristic, complemented
407#1999C2×C3111yescharacteristic, complemented
408#1959C2×C3111yescharacteristic, complemented
409#1955C2×C3111yescharacteristic, complemented
410#1803C2×C3111yescharacteristic, complemented
411#1788C2×C3111yescharacteristic, complemented
412#1787C2×C3111yescharacteristic, complemented
413C22×C31—22no—
414C22×C31—22no—
415C22×C31—22no—
416C22×C31—41no—
417C22×C31—41no—
418C22×C31—41no—
419C22×C31—41no—
420C22×C31—42no—
421C22×C31—41no—
422C22×C31—42no—
423C22×C31—41no—
424C22×C31—42no—
425C22×C31—41no—
426C22×C31—42no—
427C22×C31—41no—
428C22×C31—42no—
429C22×C31—41no—
430C22×C31—42no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31—81no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31—81no—
439C22×C31—81no—
440C22×C31—81no—
441C22×C31C2×#12011yescharacteristic
442C22×C31D4211yescharacteristic
443C22×C31#54611yescharacteristic
444C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
445C22×C31#57511yescharacteristic
446C22×C31#57711yescharacteristic
447C22×C31#57811yescharacteristic
448C4×C31—24no—
449C4×C31—22no—
450C4×C31—22no—
451C4×C31—41no—
452C4×C31—41no—
453C4×C31—42no—
454C4×C31—42no—
455C4×C31—81no—
456C4×C31—81no—
457C4×C31—81no—
458C4×C31C2×#12111yescharacteristic
459C4×C31#53511yescharacteristic
460C4×C31D4211yescharacteristic
461C4×C31#54611yescharacteristic
462C22×#41C22×C3111yescharacteristic
463C23×Q8C22×C3111yescharacteristic
464C22×SD16C22×C3111yescharacteristic
465C22×SD16C22×C3111yescharacteristic
466C22×D8C22×C3111yescharacteristic
467#548—24no—
468#548—24no—
469C2×#124—21no—
470C2×#124C22×C3111yescharacteristic
471C2×C22⋊Q8—21no—
472C2×C22⋊Q8C22×C3111yescharacteristic
473C2×#121—21no—
474C2×#121—21no—
475C2×#121C22×C3111yescharacteristic
476C2×#121C22×C3111yescharacteristic
477C2×#121C22×C3111yescharacteristic
478C2×C4×Q8C22×C3111yescharacteristic
479C2×C4×D4—21no—
480C2×C4×D4C22×C3111yescharacteristic
481C2×C4×D4C22×C3111yescharacteristic
482#463—24no—
483#449—24no—
484#448—24no—
485#440—24no—
486C2×#107C22×C3111yescharacteristic
487C2×C4⋊C8C22×C3111yescharacteristic
488C2×#103C22×C3111yescharacteristic
489C2×#103C22×C3111yescharacteristic
490C2×#103C22×C3111yescharacteristic
491C2×#103C22×C3111yescharacteristic
492C2×#103C22×C3111yescharacteristic
493C2×#103C22×C3111yescharacteristic
494C2×#102C22×C3111yescharacteristic
495C2×#102C22×C3111yescharacteristic
496C2×#102C22×C3111yescharacteristic
497C2×#102C22×C3111yescharacteristic
498C2×C22⋊C8C22×C3111yescharacteristic
499C2×C22⋊C8C22×C3111yescharacteristic
500C2×C22⋊C8C22×C3111yescharacteristic
501C2×C22⋊C8C22×C3111yescharacteristic
502C2×#97C22×C3111yescharacteristic
503#394—21no—
504#394—21no—
505#384C22×C3111yescharacteristic
506#380—21no—
507#380C22×C3111yescharacteristic
508#380C22×C3111yescharacteristic
509#340C22×C3111yescharacteristic
510#340C22×C3111yescharacteristic
511C2×C31—42no—
512C2×C31—81no—
513C2×C31—82no—
514C2×C31—82no—
515C2×C31#240811yescharacteristic
516C2×C31#300611yescharacteristic
517C2×C31#301311yescharacteristic
518C2×C31#326511yescharacteristic
519C2×C31#326911yescharacteristic
520C2×C31#330811yescharacteristic
521C2×C31#332111yescharacteristic
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—21no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8C23×C3111yescharacteristic
536C22×Q8C23×C3111yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C3111yescharacteristic
542C22×D4C23×C3111yescharacteristic
543C22×D4C23×C3111yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4C23×C3111yescharacteristic
548C23×C4C23×C3111yescharacteristic
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16D4×C3114yescomplemented
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—41no—
558C22×C8C23×C3111yescharacteristic
559C22×C8C23×C3111yescharacteristic
560C22×C8C23×C3111yescharacteristic
561C22×C8C23×C3111yescharacteristic
562#124—28no—
563#124—22no—
564#124D4×C3114yescomplemented
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568#121—28no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—41no—
574#121—41no—
575#121—44no—
576C4×Q8—22no—
577C4×Q8D4×C3114yescomplemented
578C4×D4—28no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C3111yescharacteristic
588C2×C4⋊C4C23×C3111yescharacteristic
589C2×C4⋊C4C23×C3111yescharacteristic
590C2×C4⋊C4C23×C3111yescharacteristic
591C2×C4⋊C4C23×C3111yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C3111yescharacteristic
602C2×C22⋊C4D4×C3111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C3111yescharacteristic
605#107—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621#97—22no—
622#95—21no—
623#95—21no—
624C31#2425611yescharacteristic, direct product factor, Sylow
625C24—21no—
626C24—21no—
627C24C2×D4×C3111yescharacteristic
628C24C2×D4×C3111yescharacteristic
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—24no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8C2×D4×C3112yes—
649C2×Q8C2×D4×C3112yes—
650C2×Q8C2×D4×C3112yes—
651C2×Q8#41×C3112yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C3112yes—
678C2×D4C2×D4×C3112yes—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4C2×D4×C3111yescharacteristic
707C22×C4C2×D4×C3111yescharacteristic
708C22×C4C2×D4×C3111yescharacteristic
709C22×C4C2×D4×C3111yescharacteristic
710C22×C4C24×C3111yescharacteristic
711SD16—28no—
712SD16—44no—
713D8—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8C2×D4×C3112yes—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—81no—
738C4⋊C4C2×D4×C3112yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C42—24no—
751C42C2×D4×C3112yes—
752C42C2×D4×C3112yes—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23C31×AGL(1,ℤ/8)12yes—
781C23C22×D4×C3111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—41no—
789Q8—41no—
790Q8C31×#12114yescomplemented
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—84no—
843C2×C4C31×#12012yes—
844C2×C4C31×#12012yes—
845C2×C4C22×D4×C3111yescharacteristic
846C2×C4C22×D4×C3111yescharacteristic
847C2×C4C22×D4×C3111yescharacteristic
848C2×C4C2×#41×C3111yescharacteristic
849C2×C4C31×H(5,𝔽2)11yescharacteristic
850C2×C4C31×H(5,𝔽2)11yescharacteristic
851C8—22no—
852C8—41no—
853C8—41no—
854C8—41no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×C31×#12011yescharacteristic
884C22D42×C3111yescharacteristic
885C22C31×#54611yescharacteristic
886C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
887C22C31×#57511yescharacteristic
888C22C31×#57711yescharacteristic
889C22C31×#57811yescharacteristic
890C4—24no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×C31×#12111yescharacteristic
901C4C31×#53511yescharacteristic
902C4D42×C3111yescharacteristic
903C4C31×#54611yescharacteristic
904C2—42no—
905C2—81no—
906C2—82no—
907C2—82no—
908C2C31×#240811yescharacteristic
909C2C31×#300611yescharacteristic
910C2C31×#301311yescharacteristic
911C2C31×#326511yescharacteristic
912C2C31×#326911yescharacteristic
913C2C31×#330811yescharacteristic
914C2C31×#332111yescharacteristic
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. C2×C31×#548C2semidirect
2. C2×C31×#463C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#448C2semidirect
5. C2×C31×#440C2semidirect
6. C31×#2537C2semidirect
7. C31×#2036C2semidirect
8. C31×#2033C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1959C2semidirect
12. C31×#1955C2semidirect
13. C31×#1803C2semidirect
14. C31×#1788C2semidirect
15. C31×#1787C2semidirect
97. C2×SD16×C31D4semidirect
107. C31×#124D4semidirect
120. C4×Q8×C31D4semidirect
295. #24256C31direct (N × H)
333. Q8×C31#121semidirect
398. C2×#548C2×C31semidirect
399. C2×#463C2×C31semidirect
400. C2×#449C2×C31semidirect
401. C2×#448C2×C31semidirect
402. C2×#440C2×C31semidirect
403. #2537C2×C31semidirect
404. #2036C2×C31semidirect
405. #2033C2×C31semidirect
406. #2000C2×C31semidirect
407. #1999C2×C31semidirect
408. #1959C2×C31semidirect
409. #1955C2×C31semidirect
410. #1803C2×C31semidirect
411. #1788C2×C31semidirect
412. #1787C2×C31semidirect
554. C2×SD16D4×C31semidirect
564. #124D4×C31semidirect
577. C4×Q8D4×C31semidirect
624. C31#24256direct (N × H)
790. Q8C31×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5482
C2×C31×#4632
C2×C31×#4492
C2×C31×#4482
C2×C31×#4402
C31×#25372
C31×#20362
C31×#20332
C31×#20002
C31×#19992
C31×#19592
C31×#19552
C31×#18032
C31×#17882
C31×#17872
#2425631