Finite Group Databasebeta

← C31×#26244 #21483003

Subgroups — C31×#26244 #21483003

Order 7936.

970 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#484C211yesmaximal, characteristic, complemented
2C2×C31×#480C211yesmaximal, characteristic, complemented
3C31×#2540C211yesmaximal, characteristic
4D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2036C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1983C211yesmaximal, characteristic, complemented
10C31×#1959C211yesmaximal, characteristic, complemented
11C31×#1955C211yesmaximal, characteristic, complemented
12C31×#1947C211yesmaximal, characteristic, complemented
13C31×#1874C211yesmaximal, characteristic, complemented
14C31×#1872C211yesmaximal, characteristic, complemented
15C31×#1776C211yesmaximal, characteristic, complemented
16C2×C31×#124C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C31×#484—24no—
26C31×#480—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#107C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×C22⋊C8C2211yescharacteristic
41C2×C31×C22⋊C8C2211yescharacteristic
42C2×C31×C22⋊C8C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×#97C2211yescharacteristic
45C31×#399—21no—
46C31×#392—21no—
47C31×#390—21no—
48C31×#390—21no—
49C31×#389—21no—
50C31×#385—21no—
51C31×#385—21no—
52C31×#384C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C31×#380C2211yescharacteristic
55C4×C4⋊C4×C31C2211yescharacteristic
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31D411yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C31×#124—22no—
75C31×#124—22no—
76C31×C22⋊Q8—22no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—41no—
79C31×C22⋊Q8—41no—
80C31×#121—22no—
81C31×#121—22no—
82C31×#121—41no—
83C31×#121—41no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—44no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31D411yescharacteristic
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C42×C31—21no—
115C2×C42×C31—21no—
116C2×C42×C31C2311yescharacteristic
117C31×#107—22no—
118C31×#107—22no—
119C31×#107D414yescomplemented
120C31×#106—22no—
121C31×C4⋊C8—22no—
122C31×#103—22no—
123C31×#103—22no—
124C31×#103—41no—
125C31×#103—41no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—41no—
129C31×#102—41no—
130C31×C22⋊C8—22no—
131C31×C22⋊C8—22no—
132C31×C22⋊C8—41no—
133C31×C22⋊C8—41no—
134C31×#97—22no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C24×C31—21no—
140C24×C31C2×D411yescharacteristic
141C24×C31C2×D411yescharacteristic
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×D4×C31—22no—
149C2×D4×C31—22no—
150C2×D4×C31—22no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—42no—
158C2×D4×C31—42no—
159C2×D4×C31—42no—
160C2×D4×C31—42no—
161C2×D4×C31—81no—
162C2×D4×C31—81no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—42no—
183C22×C4×C31—42no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—81no—
187C22×C4×C31—81no—
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2411yescharacteristic
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31C2×D412yes—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—42no—
216C4⋊C4×C31—42no—
217C4⋊C4×C31—42no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—42no—
220C4⋊C4×C31—81no—
221C4⋊C4×C31C2×D412yes—
222C4⋊C4×C31C2×D412yes—
223C4⋊C4×C31#4112yes—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C42×C31—42no—
235C42×C31—81no—
236C42×C31#4112yes—
237C42×C31#4112yes—
238#26244C3111yesmaximal, characteristic, direct product factor, Sylow
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31AGL(1,ℤ/8)12yes—
259C23×C31#13712yes—
260C23×C31C22×D411yescharacteristic
261Q8×C31—41no—
262Q8×C31—41no—
263Q8×C31—41no—
264Q8×C31—41no—
265D4×C31—28no—
266D4×C31—41no—
267D4×C31—41no—
268D4×C31—41no—
269D4×C31—41no—
270D4×C31—84no—
271D4×C31—84no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—22no—
279C2×C4×C31—21no—
280C2×C4×C31—22no—
281C2×C4×C31—21no—
282C2×C4×C31—22no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—84no—
312C2×C4×C31—84no—
313C2×C4×C31#12312yes—
314C2×C4×C31#12312yes—
315C2×C4×C31C22×D411yescharacteristic
316C2×C4×C31C2×#4111yescharacteristic
317C2×C4×C31C2×#4111yescharacteristic
318C2×C4×C31C2×#4111yescharacteristic
319C2×C4×C31H(5,𝔽2)11yescharacteristic
320C2×C4×C31H(5,𝔽2)11yescharacteristic
321C8×C31—22no—
322C8×C31—41no—
323C8×C31—41no—
324C8×C31—41no—
325C2×#484C2×C3111yescharacteristic, complemented
326C2×#480C2×C3111yescharacteristic, complemented
327#2540C2×C3111yescharacteristic
328D4×C4⋊C4C2×C3111yescharacteristic, complemented
329#2036C2×C3111yescharacteristic, complemented
330#2035C2×C3111yescharacteristic, complemented
331#2034C2×C3111yescharacteristic, complemented
332#2033C2×C3111yescharacteristic, complemented
333#1983C2×C3111yescharacteristic, complemented
334#1959C2×C3111yescharacteristic, complemented
335#1955C2×C3111yescharacteristic, complemented
336#1947C2×C3111yescharacteristic, complemented
337#1874C2×C3111yescharacteristic, complemented
338#1872C2×C3111yescharacteristic, complemented
339#1776C2×C3111yescharacteristic, complemented
340C22×C31—22no—
341C22×C31—22no—
342C22×C31—22no—
343C22×C31—22no—
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—81no—
358C22×C31—81no—
359C22×C31—81no—
360C22×C31—81no—
361C22×C31C2×#12311yescharacteristic
362C22×C31D4211yescharacteristic
363C22×C31#54611yescharacteristic
364C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C31C2×#13711yescharacteristic
366C22×C31#57611yescharacteristic
367C22×C31#57811yescharacteristic
368C4×C31—22no—
369C4×C31—22no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—42no—
373C4×C31—42no—
374C4×C31—42no—
375C4×C31—81no—
376C4×C31—81no—
377C4×C31—81no—
378C4×C31—81no—
379C4×C31#53211yescharacteristic
380C4×C31#54011yescharacteristic
381C4×C31#55011yescharacteristic
382C4×C31#55911yescharacteristic
383C2×#124C22×C3111yescharacteristic
384C2×C22⋊Q8C22×C3111yescharacteristic
385C2×C22⋊Q8C22×C3111yescharacteristic
386C2×#121C22×C3111yescharacteristic
387C2×#121C22×C3111yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4C22×C3111yescharacteristic
390C22×C4⋊C4C22×C3111yescharacteristic
391C22×C4⋊C4C22×C3111yescharacteristic
392#484—24no—
393#480—24no—
394C2×#107C22×C3111yescharacteristic
395C2×#107C22×C3111yescharacteristic
396C2×#107C22×C3111yescharacteristic
397C2×#106C22×C3111yescharacteristic
398C2×C4⋊C8C22×C3111yescharacteristic
399C2×#103C22×C3111yescharacteristic
400C2×#103C22×C3111yescharacteristic
401C2×#103C22×C3111yescharacteristic
402C2×#103C22×C3111yescharacteristic
403C2×#102C22×C3111yescharacteristic
404C2×#102C22×C3111yescharacteristic
405C2×#102C22×C3111yescharacteristic
406C2×#102C22×C3111yescharacteristic
407C2×C22⋊C8C22×C3111yescharacteristic
408C2×C22⋊C8C22×C3111yescharacteristic
409C2×C22⋊C8C22×C3111yescharacteristic
410C2×C22⋊C8C22×C3111yescharacteristic
411C2×#97C22×C3111yescharacteristic
412#399—21no—
413#392—21no—
414#390—21no—
415#390—21no—
416#389—21no—
417#385—21no—
418#385—21no—
419#384C22×C3111yescharacteristic
420#380C22×C3111yescharacteristic
421#380C22×C3111yescharacteristic
422C4×C4⋊C4C22×C3111yescharacteristic
423C4×C4⋊C4C22×C3111yescharacteristic
424#340C22×C3111yescharacteristic
425#340C22×C3111yescharacteristic
426#340C22×C3111yescharacteristic
427#340C22×C3111yescharacteristic
428C2×C31—42no—
429C2×C31—42no—
430C2×C31—161no—
431C2×C31#244511yescharacteristic
432C2×C31#309211yescharacteristic
433C2×C31#309811yescharacteristic
434C2×C31#326411yescharacteristic
435C2×C31#327011yescharacteristic
436C2×C31#330811yescharacteristic
437C2×C31#331411yescharacteristic
438C22×Q8C23×C3111yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4D4×C3111yescharacteristic
442C22×D4C23×C3111yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4C23×C3111yescharacteristic
446C23×C4C23×C3111yescharacteristic
447C22×C8C23×C3111yescharacteristic
448C22×C8C23×C3111yescharacteristic
449C22×C8C23×C3111yescharacteristic
450C22×C8C23×C3111yescharacteristic
451#124—22no—
452#124—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—41no—
456C22⋊Q8—41no—
457#121—22no—
458#121—22no—
459#121—41no—
460#121—41no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—44no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4D4×C3111yescharacteristic
475C2×C4⋊C4C23×C3111yescharacteristic
476C2×C4⋊C4C23×C3111yescharacteristic
477C2×C4⋊C4C23×C3111yescharacteristic
478C2×C4⋊C4C23×C3111yescharacteristic
479C2×C4⋊C4C23×C3111yescharacteristic
480C2×C4⋊C4C23×C3111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4D4×C3111yescharacteristic
490C2×C22⋊C4D4×C3111yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42C23×C3111yescharacteristic
494#107—22no—
495#107—22no—
496#107D4×C3114yescomplemented
497#106—22no—
498C4⋊C8—22no—
499#103—22no—
500#103—22no—
501#103—41no—
502#103—41no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—41no—
510C22⋊C8—41no—
511#97—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C31#2624411yescharacteristic, direct product factor, Sylow
517C24—21no—
518C24C2×D4×C3111yescharacteristic
519C24C2×D4×C3111yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—81no—
540C2×D4—81no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C24×C3111yescharacteristic
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8C2×D4×C3112yes—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—81no—
599C4⋊C4C2×D4×C3112yes—
600C4⋊C4C2×D4×C3112yes—
601C4⋊C4#41×C3112yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C42—42no—
613C42—81no—
614C42#41×C3112yes—
615C42#41×C3112yes—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C31×AGL(1,ℤ/8)12yes—
636C23C31×#13712yes—
637C23C22×D4×C3111yescharacteristic
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642D4—28no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—84no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4C31×#12312yes—
691C2×C4C31×#12312yes—
692C2×C4C22×D4×C3111yescharacteristic
693C2×C4C2×#41×C3111yescharacteristic
694C2×C4C2×#41×C3111yescharacteristic
695C2×C4C2×#41×C3111yescharacteristic
696C2×C4C31×H(5,𝔽2)11yescharacteristic
697C2×C4C31×H(5,𝔽2)11yescharacteristic
698C8—22no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×C31×#12311yescharacteristic
724C22D42×C3111yescharacteristic
725C22C31×#54611yescharacteristic
726C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
727C22C2×C31×#13711yescharacteristic
728C22C31×#57611yescharacteristic
729C22C31×#57811yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4C31×#53211yescharacteristic
742C4C31×#54011yescharacteristic
743C4C31×#55011yescharacteristic
744C4C31×#55911yescharacteristic
745C2—42no—
746C2—42no—
747C2—161no—
748C2C31×#244511yescharacteristic
749C2C31×#309211yescharacteristic
750C2C31×#309811yescharacteristic
751C2C31×#326411yescharacteristic
752C2C31×#327011yescharacteristic
753C2C31×#330811yescharacteristic
754C2C31×#331411yescharacteristic
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×#484C2semidirect
2. C2×C31×#480C2semidirect
4. D4×C4⋊C4×C31C2semidirect
5. C31×#2036C2semidirect
6. C31×#2035C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1983C2semidirect
10. C31×#1959C2semidirect
11. C31×#1955C2semidirect
12. C31×#1947C2semidirect
13. C31×#1874C2semidirect
14. C31×#1872C2semidirect
15. C31×#1776C2semidirect
119. C31×#107D4semidirect
238. #26244C31direct (N × H)
325. C2×#484C2×C31semidirect
326. C2×#480C2×C31semidirect
328. D4×C4⋊C4C2×C31semidirect
329. #2036C2×C31semidirect
330. #2035C2×C31semidirect
331. #2034C2×C31semidirect
332. #2033C2×C31semidirect
333. #1983C2×C31semidirect
334. #1959C2×C31semidirect
335. #1955C2×C31semidirect
336. #1947C2×C31semidirect
337. #1874C2×C31semidirect
338. #1872C2×C31semidirect
339. #1776C2×C31semidirect
496. #107D4×C31semidirect
516. C31#26244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4842
C2×C31×#4802
C31×#25402
D4×C4⋊C4×C312
C31×#20362
C31×#20352
C31×#20342
C31×#20332
C31×#19832
C31×#19592
C31×#19552
C31×#19472
C31×#18742
C31×#18722
C31×#17762
#2624431