Finite Group Databasebeta

← C31×#25576 #21482335

Subgroups — C31×#25576 #21482335

Order 7936.

1174 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#552C211yesmaximal, characteristic, complemented
2C2×C31×#488C211yesmaximal, characteristic, complemented
3C2×C31×#464C211yesmaximal, characteristic, complemented
4C31×#2540C211yesmaximal, characteristic
5C31×#2001C211yesmaximal, characteristic, complemented
6C31×#2001C211yesmaximal, characteristic, complemented
7C31×#2000C211yesmaximal, characteristic, complemented
8C31×#2000C211yesmaximal, characteristic, complemented
9C31×#1989C211yesmaximal, characteristic, complemented
10C31×#1954C211yesmaximal, characteristic, complemented
11C31×#1875C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1873C211yesmaximal, characteristic, complemented
14C31×#1872C211yesmaximal, characteristic, complemented
15C4×C31×#103C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C31×#552—24no—
19C31×#552—24no—
20C2×C31×#126—21no—
21C2×C31×#125—21no—
22C2×C31×#125C2211yescharacteristic
23C2×C31×#124C2211yescharacteristic
24C2×C31×#123—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×C22⋊Q8C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C4×Q8×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C2×C31×#117—21no—
34C2×C31×#117C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic
36C31×#488—24no—
37C31×#464—24no—
38C2×C31×C4⋊C8C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C4×C8×C31C2211yescharacteristic
52C31×#399—21no—
53C31×#392—21no—
54C31×#390—21no—
55C31×#390—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31D411yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C2×Q16×C31—22no—
73C2×Q16×C31—41no—
74C2×Q16×C31—41no—
75C2×SD16×C31—22no—
76C2×SD16×C31—41no—
77C2×SD16×C31—41no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×#126—28no—
83C31×#125—28no—
84C31×#125—22no—
85C31×#125D414yescomplemented
86C31×#124—22no—
87C31×#124—22no—
88C31×#123—28no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—41no—
96C31×C22⋊Q8—41no—
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—41no—
100C31×#121—41no—
101C4×Q8×C31—22no—
102C4×Q8×C31D414yescomplemented
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C31×#117—28no—
106C31×#117—22no—
107C31×#117—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—22no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31D411yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
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—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31D411yescharacteristic
134C2×C22⋊C4×C31D411yescharacteristic
135C2×C42×C31—21no—
136C2×C42×C31—21no—
137C2×C42×C31—21no—
138C2×C42×C31C2311yescharacteristic
139C31×C4⋊C8—22no—
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—22no—
143C31×#103—22no—
144C31×#103—22no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×C22⋊C8—41no—
149C31×C22⋊C8—41no—
150C31×C22⋊C8—41no—
151C31×C22⋊C8—41no—
152C4×C8×C31—22no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D411yescharacteristic
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31C2×D412yes—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—41no—
178C2×D4×C31—42no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31—81no—
183C2×D4×C31—81no—
184C22×C4×C31—24no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—42no—
205C22×C4×C31—42no—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2411yescharacteristic
211Q16×C31—44no—
212SD16×C31—44no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C4⋊C4×C31—24no—
226C4⋊C4×C31—24no—
227C4⋊C4×C31—24no—
228C4⋊C4×C31—24no—
229C4⋊C4×C31—24no—
230C4⋊C4×C31—24no—
231C4⋊C4×C31—22no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31—42no—
239C4⋊C4×C31C2×D412yes—
240C4⋊C4×C31C2×D412yes—
241C4⋊C4×C31C2×D412yes—
242C4⋊C4×C31#4112yes—
243C4⋊C4×C31#4112yes—
244C22⋊C4×C31—24no—
245C22⋊C4×C31—24no—
246C22⋊C4×C31—24no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C42×C31—24no—
256C42×C31—24no—
257C42×C31—81no—
258C42×C31C2×D412yes—
259C42×C31C2×D412yes—
260#25576C3111yesmaximal, characteristic, direct product factor, Sylow
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31#13512yes—
282C23×C31C22×D411yescharacteristic
283Q8×C31—22no—
284Q8×C31—22no—
285Q8×C31—41no—
286Q8×C31—41no—
287Q8×C31—41no—
288Q8×C31—41no—
289Q8×C31—41no—
290Q8×C31—41no—
291D4×C31—44no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—41no—
296D4×C31—84no—
297D4×C31—84no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—21no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—48no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31#12012yes—
339C2×C4×C31#12012yes—
340C2×C4×C31C22×D411yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C2×#4111yescharacteristic
343C2×C4×C31C2×#4111yescharacteristic
344C2×C4×C31H(5,𝔽2)11yescharacteristic
345C2×C4×C31H(5,𝔽2)11yescharacteristic
346C8×C31—41no—
347C8×C31—41no—
348C8×C31—41no—
349C8×C31—41no—
350C2×#552C2×C3111yescharacteristic, complemented
351C2×#488C2×C3111yescharacteristic, complemented
352C2×#464C2×C3111yescharacteristic, complemented
353#2540C2×C3111yescharacteristic
354#2001C2×C3111yescharacteristic, complemented
355#2001C2×C3111yescharacteristic, complemented
356#2000C2×C3111yescharacteristic, complemented
357#2000C2×C3111yescharacteristic, complemented
358#1989C2×C3111yescharacteristic, complemented
359#1954C2×C3111yescharacteristic, complemented
360#1875C2×C3111yescharacteristic, complemented
361#1874C2×C3111yescharacteristic, complemented
362#1873C2×C3111yescharacteristic, complemented
363#1872C2×C3111yescharacteristic, complemented
364C4×#103C2×C3111yescharacteristic, complemented
365C22×C31—22no—
366C22×C31—22no—
367C22×C31—22no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—41no—
376C22×C31—41no—
377C22×C31—41no—
378C22×C31—41no—
379C22×C31—81no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31C2×#12011yescharacteristic
387C22×C31#54611yescharacteristic
388C22×C31#54611yescharacteristic
389C22×C31C2×#13511yescharacteristic
390C22×C31#57511yescharacteristic
391C22×C31#57711yescharacteristic
392C22×C31#57811yescharacteristic
393C4×C31—22no—
394C4×C31—22no—
395C4×C31—41no—
396C4×C31—41no—
397C4×C31—42no—
398C4×C31—42no—
399C4×C31—42no—
400C4×C31—42no—
401C4×C31—42no—
402C4×C31—42no—
403C4×C31—81no—
404C4×C31#53211yescharacteristic
405C4×C31#53511yescharacteristic
406C4×C31#55011yescharacteristic
407C4×C31#55011yescharacteristic
408C22×Q16C22×C3111yescharacteristic
409C22×SD16C22×C3111yescharacteristic
410#552—24no—
411#552—24no—
412C2×#126—21no—
413C2×#125—21no—
414C2×#125C22×C3111yescharacteristic
415C2×#124C22×C3111yescharacteristic
416C2×#123—21no—
417C2×C22⋊Q8C22×C3111yescharacteristic
418C2×C22⋊Q8C22×C3111yescharacteristic
419C2×C22⋊Q8C22×C3111yescharacteristic
420C2×C22⋊Q8C22×C3111yescharacteristic
421C2×#121C22×C3111yescharacteristic
422C2×#121C22×C3111yescharacteristic
423C2×C4×Q8C22×C3111yescharacteristic
424C2×C4×D4C22×C3111yescharacteristic
425C2×#117—21no—
426C2×#117C22×C3111yescharacteristic
427C22×C4⋊C4C22×C3111yescharacteristic
428#488—24no—
429#464—24no—
430C2×C4⋊C8C22×C3111yescharacteristic
431C2×#103C22×C3111yescharacteristic
432C2×#103C22×C3111yescharacteristic
433C2×#103C22×C3111yescharacteristic
434C2×#103C22×C3111yescharacteristic
435C2×#103C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×C22⋊C8C22×C3111yescharacteristic
440C2×C22⋊C8C22×C3111yescharacteristic
441C2×C22⋊C8C22×C3111yescharacteristic
442C2×C22⋊C8C22×C3111yescharacteristic
443C2×C4×C8C22×C3111yescharacteristic
444#399—21no—
445#392—21no—
446#390—21no—
447#390—21no—
448C4×C4⋊C4C22×C3111yescharacteristic
449#340C22×C3111yescharacteristic
450#340C22×C3111yescharacteristic
451#340C22×C3111yescharacteristic
452#340C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic
454#340C22×C3111yescharacteristic
455C2×C31—42no—
456C2×C31—81no—
457C2×C31—161no—
458C2×C31#243111yescharacteristic
459C2×C31#300211yescharacteristic
460C2×C31#301311yescharacteristic
461C2×C31#329611yescharacteristic
462C2×C31#330011yescharacteristic
463C2×C31#332311yescharacteristic
464C2×C31#332711yescharacteristic
465C22×Q8C23×C3111yescharacteristic
466C22×Q8C23×C3111yescharacteristic
467C22×D4—21no—
468C22×D4—21no—
469C22×D4D4×C3111yescharacteristic
470C22×D4C23×C3111yescharacteristic
471C23×C4—21no—
472C23×C4C23×C3111yescharacteristic
473C23×C4C23×C3111yescharacteristic
474C2×Q16—22no—
475C2×Q16—41no—
476C2×Q16—41no—
477C2×SD16—22no—
478C2×SD16—41no—
479C2×SD16—41no—
480C22×C8C23×C3111yescharacteristic
481C22×C8C23×C3111yescharacteristic
482C22×C8C23×C3111yescharacteristic
483C22×C8C23×C3111yescharacteristic
484#126—28no—
485#125—28no—
486#125—22no—
487#125D4×C3114yescomplemented
488#124—22no—
489#124—22no—
490#123—28no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—41no—
498C22⋊Q8—41no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×Q8—22no—
504C4×Q8D4×C3114yescomplemented
505C4×D4—22no—
506C4×D4—22no—
507#117—28no—
508#117—22no—
509#117—22no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C3111yescharacteristic
521C2×C4⋊C4C23×C3111yescharacteristic
522C2×C4⋊C4C23×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4D4×C3111yescharacteristic
536C2×C22⋊C4D4×C3111yescharacteristic
537C2×C42—21no—
538C2×C42—21no—
539C2×C42—21no—
540C2×C42C23×C3111yescharacteristic
541C4⋊C8—22no—
542#103—22no—
543#103—22no—
544#103—22no—
545#103—22no—
546#103—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550C22⋊C8—41no—
551C22⋊C8—41no—
552C22⋊C8—41no—
553C22⋊C8—41no—
554C4×C8—22no—
555#95—21no—
556C31#2557611yescharacteristic, direct product factor, Sylow
557C24—21no—
558C24C2×D4×C3111yescharacteristic
559C24C2×D4×C3111yescharacteristic
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C2×D4×C3112yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3111yescharacteristic
613C22×C4C24×C3111yescharacteristic
614Q16—44no—
615SD16—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4C2×D4×C3112yes—
643C4⋊C4C2×D4×C3112yes—
644C4⋊C4C2×D4×C3112yes—
645C4⋊C4#41×C3112yes—
646C4⋊C4#41×C3112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C42—24no—
659C42—24no—
660C42—81no—
661C42C2×D4×C3112yes—
662C42C2×D4×C3112yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23C31×#13512yes—
684C23C22×D4×C3111yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4C31×#12012yes—
741C2×C4C31×#12012yes—
742C2×C4C22×D4×C3111yescharacteristic
743C2×C4C22×D4×C3111yescharacteristic
744C2×C4C2×#41×C3111yescharacteristic
745C2×C4C2×#41×C3111yescharacteristic
746C2×C4C31×H(5,𝔽2)11yescharacteristic
747C2×C4C31×H(5,𝔽2)11yescharacteristic
748C8—41no—
749C8—41no—
750C8—41no—
751C8—41no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22C2×C31×#12011yescharacteristic
774C22C31×#54611yescharacteristic
775C22C31×#54611yescharacteristic
776C22C2×C31×#13511yescharacteristic
777C22C31×#57511yescharacteristic
778C22C31×#57711yescharacteristic
779C22C31×#57811yescharacteristic
780C4—22no—
781C4—22no—
782C4—41no—
783C4—41no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—81no—
791C4C31×#53211yescharacteristic
792C4C31×#53511yescharacteristic
793C4C31×#55011yescharacteristic
794C4C31×#55011yescharacteristic
795C2—42no—
796C2—81no—
797C2—161no—
798C2C31×#243111yescharacteristic
799C2C31×#300211yescharacteristic
800C2C31×#301311yescharacteristic
801C2C31×#329611yescharacteristic
802C2C31×#330011yescharacteristic
803C2C31×#332311yescharacteristic
804C2C31×#332711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2540C2
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×#552C2semidirect
2. C2×C31×#488C2semidirect
3. C2×C31×#464C2semidirect
5. C31×#2001C2semidirect
6. C31×#2001C2semidirect
7. C31×#2000C2semidirect
8. C31×#2000C2semidirect
9. C31×#1989C2semidirect
10. C31×#1954C2semidirect
11. C31×#1875C2semidirect
12. C31×#1874C2semidirect
13. C31×#1873C2semidirect
14. C31×#1872C2semidirect
15. C4×C31×#103C2semidirect
85. C31×#125D4semidirect
102. C4×Q8×C31D4semidirect
260. #25576C31direct (N × H)
350. C2×#552C2×C31semidirect
351. C2×#488C2×C31semidirect
352. C2×#464C2×C31semidirect
354. #2001C2×C31semidirect
355. #2001C2×C31semidirect
356. #2000C2×C31semidirect
357. #2000C2×C31semidirect
358. #1989C2×C31semidirect
359. #1954C2×C31semidirect
360. #1875C2×C31semidirect
361. #1874C2×C31semidirect
362. #1873C2×C31semidirect
363. #1872C2×C31semidirect
364. C4×#103C2×C31semidirect
487. #125D4×C31semidirect
504. C4×Q8D4×C31semidirect
556. C31#25576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5522
C2×C31×#4882
C2×C31×#4642
C31×#25402
C31×#20012
C31×#20002
C31×#19892
C31×#19542
C31×#18752
C31×#18742
C31×#18732
C31×#18722
C4×C31×#1032
#2557631