Finite Group Databasebeta

← C31×#25635 #21482394

Subgroups — C31×#25635 #21482394

Order 7936.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#559C211yesmaximal, characteristic, complemented
2C2×C31×#495C211yesmaximal, characteristic, complemented
3C2×C31×#463C211yesmaximal, characteristic, complemented
4C31×#2592C211yesmaximal, characteristic, complemented
5C31×#2015C211yesmaximal, characteristic, complemented
6C31×#2014C211yesmaximal, characteristic, complemented
7C31×#2012C211yesmaximal, characteristic, complemented
8C31×#2011C211yesmaximal, characteristic
9C31×#1984C211yesmaximal, characteristic, complemented
10C31×#1983C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C22×D8×C31C2211yescharacteristic
22C31×#559—24no—
23C31×#559—24no—
24C2×C31×#127C2211yescharacteristic
25C2×C31×#124—21no—
26C2×C31×#124C2211yescharacteristic
27C2×C31×#124C2211yescharacteristic
28C2×C31×#124C2211yescharacteristic
29C2×C31×#123—21no—
30C2×C31×#123—21no—
31C2×C4×Q8×C31C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C2×C4×D4×C31—21no—
34C2×C4×D4×C31C2211yescharacteristic
35C2×C4×D4×C31C2211yescharacteristic
36C31×#495—24no—
37C31×#463—24no—
38C2×C31×C4⋊C8C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C4×C8×C31C2211yescharacteristic
48C31×#397—21no—
49C31×#393—21no—
50C31×#391C2211yescharacteristic
51C31×#391C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#390C2211yescharacteristic
54C31×#388—21no—
55C31×#388—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31C2311yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
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—22no—
81C2×SD16×C31—41no—
82C2×SD16×C31—41no—
83C2×SD16×C31—41no—
84C2×SD16×C31—41no—
85C2×D8×C31—22no—
86C2×D8×C31—22no—
87C2×D8×C31—22no—
88C2×D8×C31—41no—
89C2×D8×C31—41no—
90C2×D8×C31—41no—
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C31×#127—22no—
96C31×#127—22no—
97C31×#124—28no—
98C31×#124—22no—
99C31×#124—22no—
100C31×#124—22no—
101C31×#124—22no—
102C31×#124—22no—
103C31×#124D414yes—
104C31×#123—28no—
105C31×#123—28no—
106C4×Q8×C31—22no—
107C4×Q8×C31—22no—
108C4×Q8×C31—22no—
109C4×Q8×C31—22no—
110C4×D4×C31—28no—
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C4×D4×C31—22no—
114C4×D4×C31D414yes—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31D411yescharacteristic
117C2×C4⋊C4×C31D411yescharacteristic
118C2×C4⋊C4×C31D411yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C42×C31—21no—
135C2×C42×C31—21no—
136C2×C42×C31C2311yescharacteristic
137C2×C42×C31C2311yescharacteristic
138C2×C42×C31C2311yescharacteristic
139C31×C4⋊C8—22no—
140C31×#103—22no—
141C31×#103—41no—
142C31×#103—41no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—41no—
147C31×#102—41no—
148C4×C8×C31—22no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C2×Q8×C31—22no—
158C2×Q8×C31—22no—
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×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—41no—
171C2×Q8×C31C2×D412yes—
172C2×D4×C31—24no—
173C2×D4×C31—24no—
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—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—81no—
193C2×D4×C31—81no—
194C2×D4×C31C2×D412yes—
195C2×D4×C31C2×D412yes—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—24no—
199C22×C4×C31—24no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—81no—
204C22×C4×C31—81no—
205C22×C4×C31—81no—
206C22×C4×C31—81no—
207C22×C4×C31C2×D411yescharacteristic
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—
217SD16×C31—44no—
218D8×C31—44no—
219D8×C31—44no—
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—21no—
229C2×C8×C31—21no—
230C2×C8×C31#4112yes—
231C2×C8×C31#4112yes—
232C4⋊C4×C31—24no—
233C4⋊C4×C31—22no—
234C4⋊C4×C31—22no—
235C4⋊C4×C31—22no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31C2×D412yes—
242C22⋊C4×C31—24no—
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—81no—
253C22⋊C4×C31—81no—
254C42×C31—24no—
255C42×C31—21no—
256C42×C31—21no—
257C42×C31—21no—
258C42×C31—21no—
259C42×C31—81no—
260C42×C31C2×D412yes—
261C42×C31C2×D412yes—
262#25635C3111yesmaximal, characteristic, direct product factor, Sylow
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
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—41no—
283C23×C31—41no—
284C23×C31C22×D411yescharacteristic
285Q8×C31—22no—
286Q8×C31—22no—
287Q8×C31—44no—
288Q8×C31—41no—
289Q8×C31—41no—
290Q8×C31—41no—
291Q8×C31—41no—
292Q8×C31—41no—
293Q8×C31—41no—
294D4×C31—22no—
295D4×C31—22no—
296D4×C31—22no—
297D4×C31—22no—
298D4×C31—48no—
299D4×C31—41no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—84no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
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—84no—
339C2×C4×C31—84no—
340C2×C4×C31#12012yes—
341C2×C4×C31#12012yes—
342C2×C4×C31#13512yes—
343C2×C4×C31C22×D411yescharacteristic
344C2×C4×C31C22×D411yescharacteristic
345C2×C4×C31C2×#4111yescharacteristic
346C2×C4×C31C2×#4111yescharacteristic
347C2×C4×C31H(5,𝔽2)11yescharacteristic
348C2×C4×C31H(5,𝔽2)11yescharacteristic
349C8×C31—22no—
350C8×C31—22no—
351C8×C31—41no—
352C8×C31—41no—
353C2×#559C2×C3111yescharacteristic, complemented
354C2×#495C2×C3111yescharacteristic, complemented
355C2×#463C2×C3111yescharacteristic, complemented
356#2592C2×C3111yescharacteristic, complemented
357#2015C2×C3111yescharacteristic, complemented
358#2014C2×C3111yescharacteristic, complemented
359#2012C2×C3111yescharacteristic, complemented
360#2011C2×C3111yescharacteristic
361#1984C2×C3111yescharacteristic, complemented
362#1983C2×C3111yescharacteristic, complemented
363#1880C2×C3111yescharacteristic, complemented
364#1879C2×C3111yescharacteristic, complemented
365#1878C2×C3111yescharacteristic, complemented
366#1877C2×C3111yescharacteristic, complemented
367C4×#102C2×C3111yescharacteristic, complemented
368C22×C31—42no—
369C22×C31—42no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—42no—
373C22×C31—42no—
374C22×C31—81no—
375C22×C31—81no—
376C22×C31—81no—
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×C31—81no—
389C22×C31C2×#12011yescharacteristic
390C22×C31#55011yescharacteristic
391C22×C31#55011yescharacteristic
392C22×C31C2×#13511yescharacteristic
393C22×C31#57511yescharacteristic
394C22×C31#57611yescharacteristic
395C22×C31#57711yescharacteristic
396C4×C31—22no—
397C4×C31—22no—
398C4×C31—22no—
399C4×C31—42no—
400C4×C31—41no—
401C4×C31—41no—
402C4×C31—41no—
403C4×C31—42no—
404C4×C31—81no—
405C4×C31—81no—
406C4×C31—81no—
407C4×C31#53211yescharacteristic
408C4×C31#53511yescharacteristic
409C4×C31#54611yescharacteristic
410C4×C31#54611yescharacteristic
411C22×Q16C22×C3111yescharacteristic
412C22×SD16C22×C3111yescharacteristic
413C22×SD16C22×C3111yescharacteristic
414C22×SD16C22×C3111yescharacteristic
415C22×D8C22×C3111yescharacteristic
416C22×D8C22×C3111yescharacteristic
417#559—24no—
418#559—24no—
419C2×#127C22×C3111yescharacteristic
420C2×#124—21no—
421C2×#124C22×C3111yescharacteristic
422C2×#124C22×C3111yescharacteristic
423C2×#124C22×C3111yescharacteristic
424C2×#123—21no—
425C2×#123—21no—
426C2×C4×Q8C22×C3111yescharacteristic
427C2×C4×Q8C22×C3111yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4C22×C3111yescharacteristic
430C2×C4×D4C22×C3111yescharacteristic
431#495—24no—
432#463—24no—
433C2×C4⋊C8C22×C3111yescharacteristic
434C2×#103C22×C3111yescharacteristic
435C2×#103C22×C3111yescharacteristic
436C2×#103C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×C4×C8C22×C3111yescharacteristic
443#397—21no—
444#393—21no—
445#391C22×C3111yescharacteristic
446#391C22×C3111yescharacteristic
447#390C22×C3111yescharacteristic
448#390C22×C3111yescharacteristic
449#388—21no—
450#388—21no—
451C4×C4⋊C4C22×C3111yescharacteristic
452#340C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic
454#336C22×C3111yescharacteristic
455#336C22×C3111yescharacteristic
456#336C22×C3111yescharacteristic
457#336C22×C3111yescharacteristic
458C2×C31—82no—
459C2×C31—82no—
460C2×C31—161no—
461C2×C31#243111yescharacteristic
462C2×C31#300211yescharacteristic
463C2×C31#301211yescharacteristic
464C2×C31#339411yescharacteristic
465C2×C31#339611yescharacteristic
466C2×C31#340111yescharacteristic
467C2×C31#340311yescharacteristic
468C22×Q8D4×C3111yescharacteristic
469C22×Q8C23×C3111yescharacteristic
470C22×Q8C23×C3111yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4C23×C3111yescharacteristic
474C22×D4C23×C3111yescharacteristic
475C22×D4C23×C3111yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C2×Q16—22no—
479C2×Q16—22no—
480C2×Q16—41no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—41no—
487C2×SD16—41no—
488C2×SD16—41no—
489C2×SD16—41no—
490C2×D8—22no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C2×D8—41no—
495C2×D8—41no—
496C22×C8C23×C3111yescharacteristic
497C22×C8C23×C3111yescharacteristic
498C22×C8C23×C3111yescharacteristic
499C22×C8C23×C3111yescharacteristic
500#127—22no—
501#127—22no—
502#124—28no—
503#124—22no—
504#124—22no—
505#124—22no—
506#124—22no—
507#124—22no—
508#124D4×C3114yes—
509#123—28no—
510#123—28no—
511C4×Q8—22no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—22no—
515C4×D4—28no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4D4×C3114yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4D4×C3111yescharacteristic
522C2×C4⋊C4D4×C3111yescharacteristic
523C2×C4⋊C4D4×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C4⋊C4C23×C3111yescharacteristic
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⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C3111yescharacteristic
542C2×C42C23×C3111yescharacteristic
543C2×C42C23×C3111yescharacteristic
544C4⋊C8—22no—
545#103—22no—
546#103—41no—
547#103—41no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C4×C8—22no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559C31#2563511yescharacteristic, direct product factor, Sylow
560C24—21no—
561C24—21no—
562C24—21no—
563C2×Q8—22no—
564C2×Q8—22no—
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×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—41no—
577C2×Q8C2×D4×C3112yes—
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C3112yes—
601C2×D4C2×D4×C3112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4C2×D4×C3111yescharacteristic
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C24×C3111yescharacteristic
620Q16—44no—
621SD16—44no—
622SD16—44no—
623SD16—44no—
624D8—44no—
625D8—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8#41×C3112yes—
637C2×C8#41×C3112yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4C2×D4×C3112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C42—24no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—81no—
666C42C2×D4×C3112yes—
667C42C2×D4×C3112yes—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
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—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C22×D4×C3111yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—44no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
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×C4—84no—
744C2×C4—84no—
745C2×C4C31×#12012yes—
746C2×C4C31×#12012yes—
747C2×C4C31×#13512yes—
748C2×C4C22×D4×C3111yescharacteristic
749C2×C4C22×D4×C3111yescharacteristic
750C2×C4C2×#41×C3111yescharacteristic
751C2×C4C2×#41×C3111yescharacteristic
752C2×C4C31×H(5,𝔽2)11yescharacteristic
753C2×C4C31×H(5,𝔽2)11yescharacteristic
754C8—22no—
755C8—22no—
756C8—41no—
757C8—41no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×C31×#12011yescharacteristic
780C22C31×#55011yescharacteristic
781C22C31×#55011yescharacteristic
782C22C2×C31×#13511yescharacteristic
783C22C31×#57511yescharacteristic
784C22C31×#57611yescharacteristic
785C22C31×#57711yescharacteristic
786C4—22no—
787C4—22no—
788C4—22no—
789C4—42no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4C31×#53211yescharacteristic
798C4C31×#53511yescharacteristic
799C4C31×#54611yescharacteristic
800C4C31×#54611yescharacteristic
801C2—82no—
802C2—82no—
803C2—161no—
804C2C31×#243111yescharacteristic
805C2C31×#300211yescharacteristic
806C2C31×#301211yescharacteristic
807C2C31×#339411yescharacteristic
808C2C31×#339611yescharacteristic
809C2C31×#340111yescharacteristic
810C2C31×#340311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#559C2semidirect
2. C2×C31×#495C2semidirect
3. C2×C31×#463C2semidirect
4. C31×#2592C2semidirect
5. C31×#2015C2semidirect
6. C31×#2014C2semidirect
7. C31×#2012C2semidirect
9. C31×#1984C2semidirect
10. C31×#1983C2semidirect
11. C31×#1880C2semidirect
12. C31×#1879C2semidirect
13. C31×#1878C2semidirect
14. C31×#1877C2semidirect
15. C4×C31×#102C2semidirect
262. #25635C31direct (N × H)
353. C2×#559C2×C31semidirect
354. C2×#495C2×C31semidirect
355. C2×#463C2×C31semidirect
356. #2592C2×C31semidirect
357. #2015C2×C31semidirect
358. #2014C2×C31semidirect
359. #2012C2×C31semidirect
361. #1984C2×C31semidirect
362. #1983C2×C31semidirect
363. #1880C2×C31semidirect
364. #1879C2×C31semidirect
365. #1878C2×C31semidirect
366. #1877C2×C31semidirect
367. C4×#102C2×C31semidirect
559. C31#25635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5592
C2×C31×#4952
C2×C31×#4632
C31×#25922
C31×#20152
C31×#20142
C31×#20122
C31×#20112
C31×#19842
C31×#19832
C31×#18802
C31×#18792
C31×#18782
C31×#18772
C4×C31×#1022
#2563531