Finite Group Databasebeta

← C31×#25601 #21482360

Subgroups — C31×#25601 #21482360

Order 7936.

1216 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic, complemented
2C2×C31×#495C211yesmaximal, characteristic, complemented
3C2×C31×#488C211yesmaximal, characteristic, complemented
4C31×#2850C211yesmaximal, characteristic, complemented
5C31×#2001C211yesmaximal, characteristic, complemented
6C31×#2000C211yesmaximal, characteristic, complemented
7C31×#2000C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic
9C31×#1991C211yesmaximal, characteristic, complemented
10C31×#1958C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C31×#529—24no—
21C31×#529—24no—
22C2×C31×#126—21no—
23C2×C31×#125C2211yescharacteristic
24C2×C31×#124C2211yescharacteristic
25C2×C31×#124C2211yescharacteristic
26C2×C31×#123—21no—
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×C22⋊Q8C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C4×Q8×C31C2211yescharacteristic
32C2×C4×D4×C31—21no—
33C2×C4×D4×C31C2211yescharacteristic
34C2×C31×#117—21no—
35C22×C42×C31C2211yescharacteristic
36C31×#495—24no—
37C31×#488—24no—
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C4×C8×C31C2211yescharacteristic
49C2×C4×C8×C31C2211yescharacteristic
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#388—21no—
53C31×#388—21no—
54C31×#386—21no—
55C31×#386—21no—
56C31×#382C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31D411yescharacteristic
71C23×C4×C31D411yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C2×Q16×C31—22no—
74C2×Q16×C31—22no—
75C2×Q16×C31—41no—
76C2×SD16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—22no—
80C2×SD16×C31—41no—
81C2×SD16×C31—41no—
82C2×D8×C31—22no—
83C2×D8×C31—22no—
84C2×D8×C31—41no—
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C31×#126—28no—
90C31×#125—22no—
91C31×#125D414yescomplemented
92C31×#124—22no—
93C31×#124—22no—
94C31×#124—22no—
95C31×#124D414yescomplemented
96C31×#123—28no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—41no—
100C31×C22⋊Q8—41no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—41no—
104C31×#121—41no—
105C4×Q8×C31—22no—
106C4×Q8×C31—22no—
107C4×D4×C31—28no—
108C4×D4×C31—22no—
109C4×D4×C31—22no—
110C31×#117—28no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
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×C42×C31—21no—
132C2×C42×C31—22no—
133C2×C42×C31—22no—
134C2×C42×C31D411yescharacteristic
135C2×C42×C31D411yescharacteristic
136C2×C42×C31C2311yescharacteristic
137C2×C42×C31C2311yescharacteristic
138C31×#103—22no—
139C31×#103—22no—
140C31×#103—41no—
141C31×#103—41no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—41no—
145C31×#102—41no—
146C31×C22⋊C8—22no—
147C31×C22⋊C8—22no—
148C4×C8×C31—22no—
149C4×C8×C31—22no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—21no—
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—24no—
170C2×D4×C31—21no—
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—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—42no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31C2×D412yes—
187C22×C4×C31—24no—
188C22×C4×C31—22no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
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—41no—
205C22×C4×C31—41no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2411yescharacteristic
214Q16×C31—44no—
215SD16×C31—44no—
216SD16×C31—44no—
217D8×C31—44no—
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—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31#4112yes—
229C2×C8×C31#4112yes—
230C4⋊C4×C31—24no—
231C4⋊C4×C31—24no—
232C4⋊C4×C31—24no—
233C4⋊C4×C31—24no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—42no—
241C4⋊C4×C31C2×D412yes—
242C4⋊C4×C31C2×D412yes—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—24no—
245C22⋊C4×C31—24no—
246C22⋊C4×C31—24no—
247C22⋊C4×C31—24no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
254C42×C31—24no—
255C42×C31—22no—
256C42×C31—22no—
257C42×C31—21no—
258C42×C31—21no—
259C42×C31C2×D412yes—
260C42×C31C2×D412yes—
261#25601C3111yesmaximal, characteristic, direct product factor, Sylow
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—22no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31#13512yes—
283C23×C31C22×D411yescharacteristic
284Q8×C31—22no—
285Q8×C31—22no—
286Q8×C31—41no—
287Q8×C31—41no—
288Q8×C31—41no—
289Q8×C31—41no—
290Q8×C31—41no—
291Q8×C31—41no—
292D4×C31—22no—
293D4×C31—22no—
294D4×C31—48no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—41no—
298D4×C31—41no—
299D4×C31—41no—
300D4×C31—41no—
301D4×C31—84no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—44no—
318C2×C4×C31—44no—
319C2×C4×C31—48no—
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—41no—
339C2×C4×C31#12012yes—
340C2×C4×C31#12012yes—
341C2×C4×C31#13512yes—
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C22×D411yescharacteristic
344C2×C4×C31C2×#4111yescharacteristic
345C2×C4×C31C2×#4111yescharacteristic
346C2×C4×C31H(5,𝔽2)11yescharacteristic
347C2×C4×C31H(5,𝔽2)11yescharacteristic
348C8×C31—22no—
349C8×C31—22no—
350C8×C31—41no—
351C8×C31—41no—
352C2×#529C2×C3111yescharacteristic, complemented
353C2×#495C2×C3111yescharacteristic, complemented
354C2×#488C2×C3111yescharacteristic, complemented
355#2850C2×C3111yescharacteristic, complemented
356#2001C2×C3111yescharacteristic, complemented
357#2000C2×C3111yescharacteristic, complemented
358#2000C2×C3111yescharacteristic, complemented
359#1999C2×C3111yescharacteristic
360#1991C2×C3111yescharacteristic, complemented
361#1958C2×C3111yescharacteristic, complemented
362#1880C2×C3111yescharacteristic, complemented
363#1879C2×C3111yescharacteristic, complemented
364#1878C2×C3111yescharacteristic, complemented
365#1877C2×C3111yescharacteristic, complemented
366C4×C22⋊C8C2×C3111yescharacteristic, complemented
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—22no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—81no—
378C22×C31—81no—
379C22×C31—81no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31C2×#12011yescharacteristic
389C22×C31#53211yescharacteristic
390C22×C31#53511yescharacteristic
391C22×C31C2×#13511yescharacteristic
392C22×C31C2×#13511yescharacteristic
393C22×C31#57511yescharacteristic
394C22×C31#57511yescharacteristic
395C4×C31—22no—
396C4×C31—22no—
397C4×C31—22no—
398C4×C31—41no—
399C4×C31—42no—
400C4×C31—41no—
401C4×C31—42no—
402C4×C31—42no—
403C4×C31—81no—
404C4×C31—81no—
405C4×C31—81no—
406C4×C31#54611yescharacteristic
407C4×C31#54611yescharacteristic
408C4×C31#55011yescharacteristic
409C4×C31#55011yescharacteristic
410C22×Q16C22×C3111yescharacteristic
411C22×SD16C22×C3111yescharacteristic
412C22×SD16C22×C3111yescharacteristic
413C22×D8C22×C3111yescharacteristic
414#529—24no—
415#529—24no—
416C2×#126—21no—
417C2×#125C22×C3111yescharacteristic
418C2×#124C22×C3111yescharacteristic
419C2×#124C22×C3111yescharacteristic
420C2×#123—21no—
421C2×C22⋊Q8C22×C3111yescharacteristic
422C2×C22⋊Q8C22×C3111yescharacteristic
423C2×#121C22×C3111yescharacteristic
424C2×#121C22×C3111yescharacteristic
425C2×C4×Q8C22×C3111yescharacteristic
426C2×C4×D4—21no—
427C2×C4×D4C22×C3111yescharacteristic
428C2×#117—21no—
429C22×C42C22×C3111yescharacteristic
430#495—24no—
431#488—24no—
432C2×#103C22×C3111yescharacteristic
433C2×#103C22×C3111yescharacteristic
434C2×#103C22×C3111yescharacteristic
435C2×#103C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic
440C2×C22⋊C8C22×C3111yescharacteristic
441C2×C22⋊C8C22×C3111yescharacteristic
442C2×C4×C8C22×C3111yescharacteristic
443C2×C4×C8C22×C3111yescharacteristic
444#391C22×C3111yescharacteristic
445#390C22×C3111yescharacteristic
446#388—21no—
447#388—21no—
448#386—21no—
449#386—21no—
450#382C22×C3111yescharacteristic
451#340C22×C3111yescharacteristic
452#340C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic
454#340C22×C3111yescharacteristic
455#336C22×C3111yescharacteristic
456#336C22×C3111yescharacteristic
457C2×C31—42no—
458C2×C31—82no—
459C2×C31—161no—
460C2×C31#243111yescharacteristic
461C2×C31#300211yescharacteristic
462C2×C31#300211yescharacteristic
463C2×C31#316811yescharacteristic
464C2×C31#318311yescharacteristic
465C2×C31#321111yescharacteristic
466C2×C31#321211yescharacteristic
467C22×Q8C23×C3111yescharacteristic
468C22×Q8C23×C3111yescharacteristic
469C22×D4—21no—
470C22×D4—21no—
471C22×D4C23×C3111yescharacteristic
472C22×D4C23×C3111yescharacteristic
473C23×C4—21no—
474C23×C4D4×C3111yescharacteristic
475C23×C4D4×C3111yescharacteristic
476C23×C4C23×C3111yescharacteristic
477C2×Q16—22no—
478C2×Q16—22no—
479C2×Q16—41no—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—41no—
485C2×SD16—41no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—41no—
489C22×C8C23×C3111yescharacteristic
490C22×C8C23×C3111yescharacteristic
491C22×C8C23×C3111yescharacteristic
492C22×C8C23×C3111yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C3114yescomplemented
496#124—22no—
497#124—22no—
498#124—22no—
499#124D4×C3114yescomplemented
500#123—28no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505#121—22no—
506#121—22no—
507#121—41no—
508#121—41no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×D4—28no—
512C4×D4—22no—
513C4×D4—22no—
514#117—28no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4C23×C3111yescharacteristic
521C2×C4⋊C4C23×C3111yescharacteristic
522C2×C4⋊C4C23×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
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×C42—21no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42D4×C3111yescharacteristic
539C2×C42D4×C3111yescharacteristic
540C2×C42C23×C3111yescharacteristic
541C2×C42C23×C3111yescharacteristic
542#103—22no—
543#103—22no—
544#103—41no—
545#103—41no—
546#102—22no—
547#102—22no—
548#102—41no—
549#102—41no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C4×C8—22no—
553C4×C8—22no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558C31#2560111yescharacteristic, direct product factor, Sylow
559C24—21no—
560C24—21no—
561C24C2×D4×C3111yescharacteristic
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×Q8—21no—
572C2×Q8—21no—
573C2×Q8C2×D4×C3112yes—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4C2×D4×C3112yes—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4C2×D4×C3111yescharacteristic
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C24×C3111yescharacteristic
619Q16—44no—
620SD16—44no—
621SD16—44no—
622D8—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C3112yes—
634C2×C8#41×C3112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4C2×D4×C3112yes—
647C4⋊C4C2×D4×C3112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C42—24no—
660C42—22no—
661C42—22no—
662C42—21no—
663C42—21no—
664C42C2×D4×C3112yes—
665C42C2×D4×C3112yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23C31×#13512yes—
687C23C22×D4×C3111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696D4—22no—
697D4—22no—
698D4—48no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—84no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—48no—
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×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4C31×#12012yes—
744C2×C4C31×#12012yes—
745C2×C4C31×#13512yes—
746C2×C4C22×D4×C3111yescharacteristic
747C2×C4C22×D4×C3111yescharacteristic
748C2×C4C2×#41×C3111yescharacteristic
749C2×C4C2×#41×C3111yescharacteristic
750C2×C4C31×H(5,𝔽2)11yescharacteristic
751C2×C4C31×H(5,𝔽2)11yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×C31×#12011yescharacteristic
778C22C31×#53211yescharacteristic
779C22C31×#53511yescharacteristic
780C22C2×C31×#13511yescharacteristic
781C22C2×C31×#13511yescharacteristic
782C22C31×#57511yescharacteristic
783C22C31×#57511yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4C31×#54611yescharacteristic
796C4C31×#54611yescharacteristic
797C4C31×#55011yescharacteristic
798C4C31×#55011yescharacteristic
799C2—42no—
800C2—82no—
801C2—161no—
802C2C31×#243111yescharacteristic
803C2C31×#300211yescharacteristic
804C2C31×#300211yescharacteristic
805C2C31×#316811yescharacteristic
806C2C31×#318311yescharacteristic
807C2C31×#321111yescharacteristic
808C2C31×#321211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#529C2semidirect
2. C2×C31×#495C2semidirect
3. C2×C31×#488C2semidirect
4. C31×#2850C2semidirect
5. C31×#2001C2semidirect
6. C31×#2000C2semidirect
7. C31×#2000C2semidirect
9. C31×#1991C2semidirect
10. C31×#1958C2semidirect
11. C31×#1880C2semidirect
12. C31×#1879C2semidirect
13. C31×#1878C2semidirect
14. C31×#1877C2semidirect
15. C4×C31×C22⋊C8C2semidirect
91. C31×#125D4semidirect
95. C31×#124D4semidirect
261. #25601C31direct (N × H)
352. C2×#529C2×C31semidirect
353. C2×#495C2×C31semidirect
354. C2×#488C2×C31semidirect
355. #2850C2×C31semidirect
356. #2001C2×C31semidirect
357. #2000C2×C31semidirect
358. #2000C2×C31semidirect
360. #1991C2×C31semidirect
361. #1958C2×C31semidirect
362. #1880C2×C31semidirect
363. #1879C2×C31semidirect
364. #1878C2×C31semidirect
365. #1877C2×C31semidirect
366. C4×C22⋊C8C2×C31semidirect
495. #125D4×C31semidirect
499. #124D4×C31semidirect
558. C31#25601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C2×C31×#4952
C2×C31×#4882
C31×#28502
C31×#20012
C31×#20002
C31×#19992
C31×#19912
C31×#19582
C31×#18802
C31×#18792
C31×#18782
C31×#18772
C4×C31×C22⋊C82
#2560131