Finite Group Databasebeta

← C31×#24977 #21481736

Subgroups — C31×#24977 #21481736

Order 7936.

892 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2535C211yesmaximal, characteristic
2D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
3C31×#2077C211yesmaximal, characteristic, complemented
4C31×#2076C211yesmaximal, characteristic, complemented
5C31×#2034C211yesmaximal, characteristic, complemented
6C31×#2033C211yesmaximal, characteristic, complemented
7C31×#1955C211yesmaximal, characteristic, complemented
8C31×#1949C211yesmaximal, characteristic, complemented
9C31×#1874C211yesmaximal, characteristic, complemented
10C31×#1874C211yesmaximal, characteristic, complemented
11C31×#1836C211yesmaximal, characteristic, complemented
12C31×#1824C211yesmaximal, characteristic, complemented
13C31×#1823C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1762C211yesmaximal, characteristic, complemented
16C2×C31×#121C2211yescharacteristic
17C2×C31×#121C2211yescharacteristic
18C2×C4×D4×C31—21no—
19C2×C4×D4×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C2×C31×#107C2211yescharacteristic
24C2×C31×#106C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C2×C31×#102C2211yescharacteristic
27C2×C31×#102C2211yescharacteristic
28C2×C31×#102C2211yescharacteristic
29C2×C31×#102C2211yescharacteristic
30C2×C31×C22⋊C8C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×#97C2211yescharacteristic
35C31×#397—21no—
36C31×#392—21no—
37C31×#389—21no—
38C31×#386—21no—
39C31×#386—21no—
40C31×#385—21no—
41C31×#385—21no—
42C31×#384C2211yescharacteristic
43C31×#382C2211yescharacteristic
44C31×#380C2211yescharacteristic
45C31×#380C2211yescharacteristic
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C4×C4⋊C4×C31C2211yescharacteristic
49C31×#340C2211yescharacteristic
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C22×D4×C31—21no—
60C22×D4×C31—21no—
61C22×D4×C31D411yescharacteristic
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C31×#121—22no—
73C31×#121—22no—
74C31×#121—41no—
75C31×#121—41no—
76C4×D4×C31—22no—
77C4×D4×C31—22no—
78C4×D4×C31—22no—
79C4×D4×C31—22no—
80C4×D4×C31—44no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—41no—
88C2×C4⋊C4×C31—41no—
89C2×C4⋊C4×C31D411yescharacteristic
90C2×C4⋊C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31D411yescharacteristic
105C2×C22⋊C4×C31D411yescharacteristic
106C2×C42×C31—21no—
107C2×C42×C31C2311yescharacteristic
108C31×#107—41no—
109C31×#106—41no—
110C31×C4⋊C8—22no—
111C31×#102—22no—
112C31×#102—22no—
113C31×#102—41no—
114C31×#102—41no—
115C31×C22⋊C8—41no—
116C31×C22⋊C8—41no—
117C31×C22⋊C8—41no—
118C31×C22⋊C8—41no—
119C31×#97—22no—
120C31×#95—21no—
121C31×#95—21no—
122C31×#95—21no—
123C31×#95—21no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C24×C31—21no—
128C24×C31C2×D411yescharacteristic
129C24×C31C2×D411yescharacteristic
130C2×D4×C31—22no—
131C2×D4×C31—22no—
132C2×D4×C31—22no—
133C2×D4×C31—21no—
134C2×D4×C31—21no—
135C2×D4×C31—21no—
136C2×D4×C31—21no—
137C2×D4×C31—21no—
138C2×D4×C31—42no—
139C2×D4×C31—42no—
140C2×D4×C31—42no—
141C2×D4×C31—42no—
142C2×D4×C31—81no—
143C2×D4×C31—81no—
144C2×D4×C31#4112yes—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—42no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—81no—
170C22×C4×C31—81no—
171C22×C4×C31—81no—
172C22×C4×C31—81no—
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2411yescharacteristic
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C4⋊C4×C31—22no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—81no—
208C4⋊C4×C31#4112yes—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—22no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—81no—
217C22⋊C4×C31—81no—
218C42×C31—42no—
219C42×C31#4112yes—
220C42×C31#4112yes—
221#24977C3111yesmaximal, characteristic, direct product factor, Sylow
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—22no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31AGL(1,ℤ/8)12yes—
242C23×C31#13712yes—
243C23×C31C22×D411yescharacteristic
244D4×C31—28no—
245D4×C31—22no—
246D4×C31—22no—
247D4×C31—41no—
248D4×C31—41no—
249D4×C31—84no—
250D4×C31—84no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—84no—
291C2×C4×C31—84no—
292C2×C4×C31—84no—
293C2×C4×C31#12312yes—
294C2×C4×C31#12312yes—
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C31C2×#4111yescharacteristic
297C2×C4×C31C2×#4111yescharacteristic
298C2×C4×C31C2×#4111yescharacteristic
299C2×C4×C31H(5,𝔽2)11yescharacteristic
300C2×C4×C31H(5,𝔽2)11yescharacteristic
301C8×C31—41no—
302C8×C31—41no—
303C8×C31—41no—
304C8×C31—41no—
305#2535C2×C3111yescharacteristic
306D4×C4⋊C4C2×C3111yescharacteristic, complemented
307#2077C2×C3111yescharacteristic, complemented
308#2076C2×C3111yescharacteristic, complemented
309#2034C2×C3111yescharacteristic, complemented
310#2033C2×C3111yescharacteristic, complemented
311#1955C2×C3111yescharacteristic, complemented
312#1949C2×C3111yescharacteristic, complemented
313#1874C2×C3111yescharacteristic, complemented
314#1874C2×C3111yescharacteristic, complemented
315#1836C2×C3111yescharacteristic, complemented
316#1824C2×C3111yescharacteristic, complemented
317#1823C2×C3111yescharacteristic, complemented
318#1802C2×C3111yescharacteristic, complemented
319#1762C2×C3111yescharacteristic, complemented
320C22×C31—22no—
321C22×C31—22no—
322C22×C31—22no—
323C22×C31—22no—
324C22×C31—22no—
325C22×C31—22no—
326C22×C31—41no—
327C22×C31—41no—
328C22×C31—41no—
329C22×C31—41no—
330C22×C31—41no—
331C22×C31—41no—
332C22×C31—41no—
333C22×C31—41no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—81no—
338C22×C31—81no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31C2×#12311yescharacteristic
342C22×C31#54611yescharacteristic
343C22×C31#54611yescharacteristic
344C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C31C2×#13711yescharacteristic
346C22×C31#57611yescharacteristic
347C22×C31#57711yescharacteristic
348C4×C31—22no—
349C4×C31—22no—
350C4×C31—41no—
351C4×C31—41no—
352C4×C31—42no—
353C4×C31—81no—
354C4×C31—81no—
355C4×C31—81no—
356C4×C31—81no—
357C4×C31—81no—
358C4×C31—81no—
359C4×C31#52911yescharacteristic
360C4×C31#54011yescharacteristic
361C4×C31#55311yescharacteristic
362C4×C31#55511yescharacteristic
363C2×#121C22×C3111yescharacteristic
364C2×#121C22×C3111yescharacteristic
365C2×C4×D4—21no—
366C2×C4×D4C22×C3111yescharacteristic
367C2×C4×D4C22×C3111yescharacteristic
368C22×C4⋊C4C22×C3111yescharacteristic
369C22×C4⋊C4C22×C3111yescharacteristic
370C2×#107C22×C3111yescharacteristic
371C2×#106C22×C3111yescharacteristic
372C2×C4⋊C8C22×C3111yescharacteristic
373C2×#102C22×C3111yescharacteristic
374C2×#102C22×C3111yescharacteristic
375C2×#102C22×C3111yescharacteristic
376C2×#102C22×C3111yescharacteristic
377C2×C22⋊C8C22×C3111yescharacteristic
378C2×C22⋊C8C22×C3111yescharacteristic
379C2×C22⋊C8C22×C3111yescharacteristic
380C2×C22⋊C8C22×C3111yescharacteristic
381C2×#97C22×C3111yescharacteristic
382#397—21no—
383#392—21no—
384#389—21no—
385#386—21no—
386#386—21no—
387#385—21no—
388#385—21no—
389#384C22×C3111yescharacteristic
390#382C22×C3111yescharacteristic
391#380C22×C3111yescharacteristic
392#380C22×C3111yescharacteristic
393#380C22×C3111yescharacteristic
394#380C22×C3111yescharacteristic
395C4×C4⋊C4C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#340C22×C3111yescharacteristic
398#340C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406C2×C31—42no—
407C2×C31—42no—
408C2×C31—82no—
409C2×C31#242011yescharacteristic
410C2×C31#309211yescharacteristic
411C2×C31#309611yescharacteristic
412C2×C31#330611yescharacteristic
413C2×C31#331411yescharacteristic
414C2×C31#331811yescharacteristic
415C2×C31#332011yescharacteristic
416C22×D4—21no—
417C22×D4—21no—
418C22×D4D4×C3111yescharacteristic
419C22×D4C23×C3111yescharacteristic
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—21no—
423C23×C4C23×C3111yescharacteristic
424C23×C4C23×C3111yescharacteristic
425C22×C8C23×C3111yescharacteristic
426C22×C8C23×C3111yescharacteristic
427C22×C8C23×C3111yescharacteristic
428C22×C8C23×C3111yescharacteristic
429#121—22no—
430#121—22no—
431#121—41no—
432#121—41no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—44no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4D4×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C4⋊C4C23×C3111yescharacteristic
452C2×C4⋊C4C23×C3111yescharacteristic
453C2×C4⋊C4C23×C3111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C3111yescharacteristic
462C2×C22⋊C4D4×C3111yescharacteristic
463C2×C42—21no—
464C2×C42C23×C3111yescharacteristic
465#107—41no—
466#106—41no—
467C4⋊C8—22no—
468#102—22no—
469#102—22no—
470#102—41no—
471#102—41no—
472C22⋊C8—41no—
473C22⋊C8—41no—
474C22⋊C8—41no—
475C22⋊C8—41no—
476#97—22no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484C31#2497711yescharacteristic, direct product factor, Sylow
485C24—21no—
486C24C2×D4×C3111yescharacteristic
487C24C2×D4×C3111yescharacteristic
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4#41×C3112yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4C2×D4×C3111yescharacteristic
532C22×C4C2×D4×C3111yescharacteristic
533C22×C4C2×D4×C3111yescharacteristic
534C22×C4C2×D4×C3111yescharacteristic
535C22×C4C24×C3111yescharacteristic
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4#41×C3112yes—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—42no—
577C42#41×C3112yes—
578C42#41×C3112yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C31×AGL(1,ℤ/8)12yes—
599C23C31×#13712yes—
600C23C22×D4×C3111yescharacteristic
601D4—28no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4C31×#12312yes—
651C2×C4C31×#12312yes—
652C2×C4C2×#41×C3111yescharacteristic
653C2×C4C2×#41×C3111yescharacteristic
654C2×C4C2×#41×C3111yescharacteristic
655C2×C4C2×#41×C3111yescharacteristic
656C2×C4C31×H(5,𝔽2)11yescharacteristic
657C2×C4C31×H(5,𝔽2)11yescharacteristic
658C8—41no—
659C8—41no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C2×C31×#12311yescharacteristic
684C22C31×#54611yescharacteristic
685C22C31×#54611yescharacteristic
686C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
687C22C2×C31×#13711yescharacteristic
688C22C31×#57611yescharacteristic
689C22C31×#57711yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4C31×#52911yescharacteristic
702C4C31×#54011yescharacteristic
703C4C31×#55311yescharacteristic
704C4C31×#55511yescharacteristic
705C2—42no—
706C2—42no—
707C2—82no—
708C2C31×#242011yescharacteristic
709C2C31×#309211yescharacteristic
710C2C31×#309611yescharacteristic
711C2C31×#330611yescharacteristic
712C2C31×#331411yescharacteristic
713C2C31×#331811yescharacteristic
714C2C31×#332011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2535C2
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
2. D4×C4⋊C4×C31C2semidirect
3. C31×#2077C2semidirect
4. C31×#2076C2semidirect
5. C31×#2034C2semidirect
6. C31×#2033C2semidirect
7. C31×#1955C2semidirect
8. C31×#1949C2semidirect
9. C31×#1874C2semidirect
10. C31×#1874C2semidirect
11. C31×#1836C2semidirect
12. C31×#1824C2semidirect
13. C31×#1823C2semidirect
14. C31×#1802C2semidirect
15. C31×#1762C2semidirect
221. #24977C31direct (N × H)
306. D4×C4⋊C4C2×C31semidirect
307. #2077C2×C31semidirect
308. #2076C2×C31semidirect
309. #2034C2×C31semidirect
310. #2033C2×C31semidirect
311. #1955C2×C31semidirect
312. #1949C2×C31semidirect
313. #1874C2×C31semidirect
314. #1874C2×C31semidirect
315. #1836C2×C31semidirect
316. #1824C2×C31semidirect
317. #1823C2×C31semidirect
318. #1802C2×C31semidirect
319. #1762C2×C31semidirect
484. C31#24977direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25352
D4×C4⋊C4×C312
C31×#20772
C31×#20762
C31×#20342
C31×#20332
C31×#19552
C31×#19492
C31×#18742
C31×#18362
C31×#18242
C31×#18232
C31×#18022
C31×#17622
#2497731