Finite Group Databasebeta

← C31×#13885 #21470644

Subgroups — C31×#13885 #21470644

Order 7936.

1342 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#382C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
4C31×#1445C212yesmaximal
5C31×#1443C212yesmaximal
6C31×#1436C212yesmaximal
7C31×C4⋊#95C211yesmaximal, characteristic
8C31×C4⋊#95C211yesmaximal, characteristic
9C31×C4⋊#95C211yesmaximal, characteristic
10C31×C4⋊#95C211yesmaximal, characteristic
11C31×#1434C212yesmaximal
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2212yes—
19C22×C42×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C31×#382—24no—
23C4×C4⋊C4×C31—24no—
24C4×C4⋊C4×C31C418yescomplemented
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C23×C4×C31C2312yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31C2×C414yes—
64C2×C4⋊C4×C31C2×C414yes—
65C2×C4⋊C4×C31D414yes—
66C2×C4⋊C4×C31Q814yes—
67C2×C42×C31—22no—
68C2×C42×C31—22no—
69C2×C42×C31—22no—
70C2×C42×C31—22no—
71C2×C42×C31—22no—
72C2×C42×C31—22no—
73C2×C42×C31—24no—
74C2×C42×C31—24no—
75C2×C42×C31—42no—
76C2×C42×C31C2×C414yes—
77C2×C42×C31C2×C414yes—
78C2×C42×C31C2×C414yes—
79C31×#95—24no—
80C31×#95—24no—
81C31×#95—24no—
82C31×#95—24no—
83C31×#95—24no—
84C31×#95—24no—
85C31×#95—42no—
86C31×#95—42no—
87C31×#95—42no—
88C31×#95—42no—
89C31×#95—42no—
90C31×#95C2×C414yes—
91C31×#95C2×C414yes—
92C24×C31C2411yescharacteristic
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—21no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31C22×C412yes—
152C22×C4×C31C22×C412yes—
153C22×C4×C31C22×C412yes—
154C22×C4×C31C22×C412yes—
155C22×C4×C31C22×C412yes—
156C22×C4×C31C22×C412yes—
157C22×C4×C31C22×C412yes—
158C22×C4×C31C2×D414yes—
159C22×C4×C31C2×D412yes—
160C22×C4×C31C2×Q814yes—
161C22×C4×C31C2×Q812yes—
162C22×C4×C31#4112yes—
163C22×C4×C31#4112yes—
164C22×C4×C31#4112yes—
165C22×C4×C31#4112yes—
166C22×C4×C31#4112yes—
167C22×C4×C31#4112yes—
168C22×C4×C31#4112yes—
169C22×C4×C31#4112yes—
170C4⋊C4×C31—28no—
171C4⋊C4×C31—28no—
172C4⋊C4×C31—28no—
173C4⋊C4×C31—28no—
174C4⋊C4×C31—44no—
175C4⋊C4×C31—44no—
176C42×C31—28no—
177C42×C31—28no—
178C42×C31—28no—
179C42×C31—48no—
180#13885C3111yesmaximal, characteristic, direct product factor, Sylow
181C23×C31C23×C411yescharacteristic
182C23×C31C22×D411yescharacteristic
183C23×C31C22×Q811yescharacteristic
184C23×C31C2×#4111yescharacteristic
185C23×C31C2×#4111yescharacteristic
186C23×C31C2×#4111yescharacteristic
187C23×C31C2×#4111yescharacteristic
188C23×C31C2×#4111yescharacteristic
189C23×C31C2×#4111yescharacteristic
190C23×C31C2×#4111yescharacteristic
191C23×C31C2×#4111yescharacteristic
192C23×C31H(5,𝔽2)11yescharacteristic
193C23×C31H(5,𝔽2)11yescharacteristic
194C23×C312−1+411yescharacteristic
195C23×C312−1+411yescharacteristic
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—24no—
221C2×C4×C31—24no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—24no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—41no—
236C2×C4×C31—41no—
237C2×C4×C31—41no—
238C2×C4×C31—41no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—42no—
242C2×C4×C31—41no—
243C2×C4×C31—41no—
244C2×C4×C31—41no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31—42no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31—42no—
263C2×C4×C31—42no—
264C2×C4×C31#11714yes—
265C2×C4×C31#11714yes—
266C2×C4×C31#11714yes—
267C2×C4×C31C4×D414yes—
268C2×C4×C31C4×Q814yes—
269C2×C4×C31C22⋊Q814yes—
270C2×C4×C31#12314yes—
271C2×C4×C31#12514yes—
272C2×C4×C31#12614yes—
273C2×#382C2×C3111yescharacteristic
274C2×C4×C4⋊C4C2×C3111yescharacteristic
275C2×C4×C4⋊C4C2×C3111yescharacteristic
276#1445C2×C3112yes—
277#1443C2×C3112yes—
278#1436C2×C3112yes—
279C4⋊#95C2×C3111yescharacteristic
280C4⋊#95C2×C3111yescharacteristic
281C4⋊#95C2×C3111yescharacteristic
282C4⋊#95C2×C3111yescharacteristic
283#1434C2×C3112yes—
284C22×C31C2×#11711yescharacteristic
285C22×C31C2×#11711yescharacteristic
286C22×C31C2×#11711yescharacteristic
287C22×C31C2×C4×D411yescharacteristic
288C22×C31C2×C4×Q811yescharacteristic
289C22×C31#52011yescharacteristic
290C22×C31#52011yescharacteristic
291C22×C31C2×C22⋊Q811yescharacteristic
292C22×C31C2×#12311yescharacteristic
293C22×C31C2×#12511yescharacteristic
294C22×C31C2×#12611yescharacteristic
295C22×C31#52911yescharacteristic
296C22×C31#52911yescharacteristic
297C22×C31#52911yescharacteristic
298C22×C31#52911yescharacteristic
299C22×C31#54011yescharacteristic
300C22×C31#54111yescharacteristic
301C22×C31#54211yescharacteristic
302C22×C31#54211yescharacteristic
303C22×C31#54611yescharacteristic
304C22×C31#54711yescharacteristic
305C22×C31#54811yescharacteristic
306C22×C31#55011yescharacteristic
307C22×C31#55211yescharacteristic
308C22×C31#55311yescharacteristic
309C22×C31#55411yescharacteristic
310C22×C31#55411yescharacteristic
311C22×C31#55511yescharacteristic
312C22×C31#55611yescharacteristic
313C22×C31#55611yescharacteristic
314C22×C31#55611yescharacteristic
315C22×C31#55711yescharacteristic
316C22×C31#55711yescharacteristic
317C22×C31#55911yescharacteristic
318C22×C31#55911yescharacteristic
319C4×C31—24no—
320C4×C31—24no—
321C4×C31—42no—
322C4×C31—42no—
323C4×C31—42no—
324C4×C31—42no—
325C4×C31—44no—
326C4×C31—44no—
327C4×C31—82no—
328C4×C31—82no—
329C4×C31#38718yes—
330C22×C4⋊C4C22×C3111yescharacteristic
331C22×C4⋊C4C22×C3111yescharacteristic
332C22×C4⋊C4C22×C3111yescharacteristic
333C22×C4⋊C4C22×C3111yescharacteristic
334C22×C4⋊C4C22×C3111yescharacteristic
335C22×C4⋊C4C22×C3111yescharacteristic
336C22×C42C22×C3112yes—
337C22×C42C22×C3111yescharacteristic
338C22×C42C22×C3111yescharacteristic
339C22×C42C22×C3111yescharacteristic
340#382—24no—
341C4×C4⋊C4—24no—
342C4×C4⋊C4C4×C3118yescomplemented
343C2×#95C22×C3112yes—
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3112yes—
347C2×#95C22×C3112yes—
348C2×#95C22×C3112yes—
349C2×#95C22×C3112yes—
350C2×#95C22×C3112yes—
351C2×#95C22×C3112yes—
352C2×#95C22×C3112yes—
353C2×#95C22×C3112yes—
354C2×#95C22×C3111yescharacteristic
355C2×#95C22×C3111yescharacteristic
356C2×C31#228311yescharacteristic
357C2×C31C2×#38711yescharacteristic
358C2×C31#231411yescharacteristic
359C2×C31#235211yescharacteristic
360C2×C31#235411yescharacteristic
361C2×C31#235511yescharacteristic
362C2×C31#235511yescharacteristic
363C2×C31#244711yescharacteristic
364C2×C31#244811yescharacteristic
365C2×C31#245311yescharacteristic
366C2×C31#245411yescharacteristic
367C2×C31#250811yescharacteristic
368C2×C31#250911yescharacteristic
369C2×C31#251311yescharacteristic
370C2×C31#251411yescharacteristic
371C23×C4C23×C3112yes—
372C23×C4C23×C3112yes—
373C23×C4C23×C3111yescharacteristic
374C23×C4C23×C3111yescharacteristic
375C23×C4C23×C3111yescharacteristic
376C23×C4C23×C3111yescharacteristic
377C23×C4C23×C3112yes—
378C23×C4C23×C3112yes—
379C23×C4C23×C3111yescharacteristic
380C23×C4C23×C3111yescharacteristic
381C23×C4C23×C3111yescharacteristic
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4C2×C4×C3114yes—
397C2×C4⋊C4C2×C4×C3114yes—
398C2×C4⋊C4D4×C3114yes—
399C2×C4⋊C4Q8×C3114yes—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—42no—
409C2×C42C2×C4×C3114yes—
410C2×C42C2×C4×C3114yes—
411C2×C42C2×C4×C3114yes—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95C2×C4×C3114yes—
424#95C2×C4×C3114yes—
425C31#1388511yescharacteristic, direct product factor, Sylow
426C24C24×C3111yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4C22×C4×C3112yes—
486C22×C4C22×C4×C3112yes—
487C22×C4C22×C4×C3112yes—
488C22×C4C22×C4×C3112yes—
489C22×C4C22×C4×C3112yes—
490C22×C4C22×C4×C3112yes—
491C22×C4C22×C4×C3112yes—
492C22×C4C2×D4×C3114yes—
493C22×C4C2×D4×C3112yes—
494C22×C4C2×Q8×C3114yes—
495C22×C4C2×Q8×C3112yes—
496C22×C4#41×C3112yes—
497C22×C4#41×C3112yes—
498C22×C4#41×C3112yes—
499C22×C4#41×C3112yes—
500C22×C4#41×C3112yes—
501C22×C4#41×C3112yes—
502C22×C4#41×C3112yes—
503C22×C4#41×C3112yes—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—28no—
507C4⋊C4—28no—
508C4⋊C4—44no—
509C4⋊C4—44no—
510C42—28no—
511C42—28no—
512C42—28no—
513C42—48no—
514C23C23×C4×C3111yescharacteristic
515C23C22×D4×C3111yescharacteristic
516C23C22×Q8×C3111yescharacteristic
517C23C2×#41×C3111yescharacteristic
518C23C2×#41×C3111yescharacteristic
519C23C2×#41×C3111yescharacteristic
520C23C2×#41×C3111yescharacteristic
521C23C2×#41×C3111yescharacteristic
522C23C2×#41×C3111yescharacteristic
523C23C2×#41×C3111yescharacteristic
524C23C2×#41×C3111yescharacteristic
525C23C31×H(5,𝔽2)11yescharacteristic
526C23C31×H(5,𝔽2)11yescharacteristic
527C23C31×2−1+411yescharacteristic
528C23C31×2−1+411yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4C31×#11714yes—
598C2×C4C31×#11714yes—
599C2×C4C31×#11714yes—
600C2×C4C4×D4×C3114yes—
601C2×C4C4×Q8×C3114yes—
602C2×C4C31×C22⋊Q814yes—
603C2×C4C31×#12314yes—
604C2×C4C31×#12514yes—
605C2×C4C31×#12614yes—
606C22C2×C31×#11711yescharacteristic
607C22C2×C31×#11711yescharacteristic
608C22C2×C31×#11711yescharacteristic
609C22C2×C4×D4×C3111yescharacteristic
610C22C2×C4×Q8×C3111yescharacteristic
611C22C31×#52011yescharacteristic
612C22C31×#52011yescharacteristic
613C22C2×C31×C22⋊Q811yescharacteristic
614C22C2×C31×#12311yescharacteristic
615C22C2×C31×#12511yescharacteristic
616C22C2×C31×#12611yescharacteristic
617C22C31×#52911yescharacteristic
618C22C31×#52911yescharacteristic
619C22C31×#52911yescharacteristic
620C22C31×#52911yescharacteristic
621C22C31×#54011yescharacteristic
622C22C31×#54111yescharacteristic
623C22C31×#54211yescharacteristic
624C22C31×#54211yescharacteristic
625C22C31×#54611yescharacteristic
626C22C31×#54711yescharacteristic
627C22C31×#54811yescharacteristic
628C22C31×#55011yescharacteristic
629C22C31×#55211yescharacteristic
630C22C31×#55311yescharacteristic
631C22C31×#55411yescharacteristic
632C22C31×#55411yescharacteristic
633C22C31×#55511yescharacteristic
634C22C31×#55611yescharacteristic
635C22C31×#55611yescharacteristic
636C22C31×#55611yescharacteristic
637C22C31×#55711yescharacteristic
638C22C31×#55711yescharacteristic
639C22C31×#55911yescharacteristic
640C22C31×#55911yescharacteristic
641C4—24no—
642C4—24no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—44no—
648C4—44no—
649C4—82no—
650C4—82no—
651C4C31×#38718yes—
652C2C31×#228311yescharacteristic
653C2C2×C31×#38711yescharacteristic
654C2C31×#231411yescharacteristic
655C2C31×#235211yescharacteristic
656C2C31×#235411yescharacteristic
657C2C31×#235511yescharacteristic
658C2C31×#235511yescharacteristic
659C2C31×#244711yescharacteristic
660C2C31×#244811yescharacteristic
661C2C31×#245311yescharacteristic
662C2C31×#245411yescharacteristic
663C2C31×#250811yescharacteristic
664C2C31×#250911yescharacteristic
665C2C31×#251311yescharacteristic
666C2C31×#251411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
24. C4×C4⋊C4×C31C4semidirect
180. #13885C31direct (N × H)
342. C4×C4⋊C4C4×C31semidirect
425. C31#13885direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3822
C2×C4×C4⋊C4×C312
C31×#14452
C31×#14432
C31×#14362
C31×C4⋊#952
C31×#14342
#1388531