Finite Group Databasebeta

← C31×#24100 #21480859

Subgroups — C31×#24100 #21480859

Order 7936.

1300 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#547C211yesmaximal, characteristic
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#428C211yesmaximal, characteristic, complemented
4C31×#2485C211yesmaximal, characteristic, complemented
5C31×#2058C211yesmaximal, characteristic, complemented
6C31×#2057C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1895C211yesmaximal, characteristic, complemented
10C31×#1870C211yesmaximal, characteristic, complemented
11C31×#1864C211yesmaximal, characteristic, complemented
12C31×#1862C211yesmaximal, characteristic, complemented
13C31×#1853C211yesmaximal, characteristic, complemented
14C31×#1852C211yesmaximal, characteristic, complemented
15C31×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C31—21no—
17C22×M16×C31C2211yescharacteristic
18C31×#547—24no—
19C31×#547—24no—
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×#123—21no—
22C2×C31×#123—21no—
23C2×C31×C22⋊Q8—21no—
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#482—24no—
32C31×#428—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#107C2211yescharacteristic
35C2×C31×#107C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×#106C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C31×#397—21no—
47C31×#394—21no—
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#388—21no—
51C31×#387—21no—
52C31×#380C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—28no—
64C2×#41×C31—44no—
65C2×#41×C31—44no—
66C22×Q8×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31D411yescharacteristic
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C2×M16×C31—22no—
77C2×M16×C31—22no—
78C2×M16×C31—22no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×C4⋊Q8—22no—
84C31×C4⋊Q8—22no—
85C31×#123—28no—
86C31×#123—28no—
87C31×C22⋊Q8—28no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121D414yes—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C31×#117—22no—
97C31×#117—22no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31D411yescharacteristic
107C2×C4⋊C4×C31D414yes—
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31D411yescharacteristic
123C2×C22⋊C4×C31D411yescharacteristic
124C2×C42×C31—21no—
125C2×C42×C31C2311yescharacteristic
126C31×#107—22no—
127C31×#107—22no—
128C31×#107—22no—
129C31×#106—22no—
130C31×#106—22no—
131C31×#106—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×C22⋊C8—22no—
137C31×C22⋊C8—22no—
138C31×C22⋊C8—22no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C24×C31—21no—
145C24×C31C2×D411yescharacteristic
146C24×C31C2×D411yescharacteristic
147#41×C31—432no—
148C2×Q8×C31—24no—
149C2×Q8×C31—42no—
150C2×Q8×C31—42no—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—24no—
154C2×D4×C31—24no—
155C2×D4×C31—22no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—42no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31C2×D412yes—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—24no—
171C22×C4×C31—24no—
172C22×C4×C31—24no—
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—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—42no—
187C22×C4×C31—42no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D412yes—
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2411yescharacteristic
199M16×C31—28no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31#4112yescomplemented
211C2×C8×C31#4112yescomplemented
212C4⋊C4×C31—24no—
213C4⋊C4×C31—24no—
214C4⋊C4×C31—24no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—81no—
229C4⋊C4×C31C2×D412yes—
230C4⋊C4×C31C2×D412yes—
231C4⋊C4×C31C2×D412yes—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—24no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—81no—
240C22⋊C4×C31—81no—
241C42×C31—21no—
242C42×C31—21no—
243C42×C31—42no—
244#24100C3111yesmaximal, characteristic, direct product factor, Sylow
245C23×C31—21no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—22no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31#12012yes—
265C23×C31AGL(1,ℤ/8)12yes—
266C23×C31C22×D411yescharacteristic
267Q8×C31—48no—
268D4×C31—28no—
269D4×C31—22no—
270D4×C31—22no—
271D4×C31—48no—
272D4×C31—48no—
273D4×C31—41no—
274D4×C31—41no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—48no—
293C2×C4×C31—48no—
294C2×C4×C31—48no—
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—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31#12012yes—
318C2×C4×C31AGL(1,ℤ/8)12yes—
319C2×C4×C31C22×D411yescharacteristic
320C2×C4×C31C22×D411yescharacteristic
321C2×C4×C31C2×#4111yescharacteristic
322C2×C4×C31C2×#4111yescharacteristic
323C2×C4×C312−1+411yescharacteristic
324C2×C4×C312−1+411yescharacteristic
325C8×C31—22no—
326C8×C31—22no—
327C8×C31—41no—
328C8×C31—41no—
329C2×#547C2×C3111yescharacteristic
330C2×#482C2×C3111yescharacteristic, complemented
331C2×#428C2×C3111yescharacteristic, complemented
332#2485C2×C3111yescharacteristic, complemented
333#2058C2×C3111yescharacteristic, complemented
334#2057C2×C3111yescharacteristic, complemented
335#2034C2×C3111yescharacteristic, complemented
336#2033C2×C3111yescharacteristic, complemented
337#1895C2×C3111yescharacteristic, complemented
338#1870C2×C3111yescharacteristic, complemented
339#1864C2×C3111yescharacteristic, complemented
340#1862C2×C3111yescharacteristic, complemented
341#1853C2×C3111yescharacteristic, complemented
342#1852C2×C3111yescharacteristic, complemented
343#1824C2×C3111yescharacteristic, complemented
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—22no—
347C22×C31—22no—
348C22×C31—22no—
349C22×C31—22no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—41no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—42no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31C2×#12011yescharacteristic
366C22×C31#54711yescharacteristic
367C22×C31#54711yescharacteristic
368C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C31#57711yescharacteristic
371C22×C31#57811yescharacteristic
372C4×C31—22no—
373C4×C31—22no—
374C4×C31—41no—
375C4×C31—42no—
376C4×C31—42no—
377C4×C31—42no—
378C4×C31—41no—
379C4×C31—81no—
380C4×C31—81no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31#52511yescharacteristic
384C4×C31#53611yescharacteristic
385C4×C31#54711yescharacteristic
386C4×C31#54711yescharacteristic
387C22×#41—21no—
388C22×M16C22×C3111yescharacteristic
389#547—24no—
390#547—24no—
391C2×C4⋊Q8C22×C3111yescharacteristic
392C2×#123—21no—
393C2×#123—21no—
394C2×C22⋊Q8—21no—
395C2×#121C22×C3111yescharacteristic
396C2×#121C22×C3111yescharacteristic
397C2×C4×D4C22×C3111yescharacteristic
398C2×C4×D4C22×C3111yescharacteristic
399C2×#117C22×C3111yescharacteristic
400C22×C4⋊C4C22×C3111yescharacteristic
401C22×C4⋊C4C22×C3111yescharacteristic
402#482—24no—
403#428—24no—
404C2×#107C22×C3111yescharacteristic
405C2×#107C22×C3111yescharacteristic
406C2×#107C22×C3111yescharacteristic
407C2×#106C22×C3111yescharacteristic
408C2×#106C22×C3111yescharacteristic
409C2×#106C22×C3111yescharacteristic
410C2×#102C22×C3111yescharacteristic
411C2×#102C22×C3111yescharacteristic
412C2×#102C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×C22⋊C8C22×C3111yescharacteristic
415C2×C22⋊C8C22×C3111yescharacteristic
416C2×C22⋊C8C22×C3111yescharacteristic
417#397—21no—
418#394—21no—
419#389C22×C3111yescharacteristic
420#389C22×C3111yescharacteristic
421#388—21no—
422#387—21no—
423#380C22×C3111yescharacteristic
424#380C22×C3111yescharacteristic
425#380C22×C3111yescharacteristic
426#340C22×C3111yescharacteristic
427#340C22×C3111yescharacteristic
428#340C22×C3111yescharacteristic
429#340C22×C3111yescharacteristic
430#340C22×C3111yescharacteristic
431#340C22×C3111yescharacteristic
432#336C22×C3111yescharacteristic
433#336C22×C3111yescharacteristic
434C2×C31—42no—
435C2×C31—42no—
436C2×C31—82no—
437C2×C31#240611yescharacteristic
438C2×C31#300311yescharacteristic
439C2×C31#301311yescharacteristic
440C2×C31#334311yescharacteristic
441C2×C31#334511yescharacteristic
442C2×C31#335311yescharacteristic
443C2×C31#335411yescharacteristic
444C2×#41—28no—
445C2×#41—44no—
446C2×#41—44no—
447C22×Q8—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4D4×C3111yescharacteristic
451C22×D4C23×C3111yescharacteristic
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—21no—
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C22×C8C23×C3111yescharacteristic
461C22×C8C23×C3111yescharacteristic
462C22×C8C23×C3111yescharacteristic
463C22×C8C23×C3111yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8—22no—
466#123—28no—
467#123—28no—
468C22⋊Q8—28no—
469#121—22no—
470#121—22no—
471#121—22no—
472#121D4×C3114yes—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4—22no—
476C4×D4—22no—
477#117—22no—
478#117—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4D4×C3111yescharacteristic
488C2×C4⋊C4D4×C3114yes—
489C2×C4⋊C4C23×C3111yescharacteristic
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C4⋊C4C23×C3111yescharacteristic
492C2×C4⋊C4C23×C3111yescharacteristic
493C2×C4⋊C4C23×C3111yescharacteristic
494C2×C4⋊C4C23×C3111yescharacteristic
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4D4×C3111yescharacteristic
504C2×C22⋊C4D4×C3111yescharacteristic
505C2×C42—21no—
506C2×C42C23×C3111yescharacteristic
507#107—22no—
508#107—22no—
509#107—22no—
510#106—22no—
511#106—22no—
512#106—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525C31#2410011yescharacteristic, direct product factor, Sylow
526C24—21no—
527C24C2×D4×C3111yescharacteristic
528C24C2×D4×C3111yescharacteristic
529#41—432no—
530C2×Q8—24no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C2×D4×C3112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4C2×D4×C3111yescharacteristic
575C22×C4C2×D4×C3111yescharacteristic
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3112yes—
578C22×C4C2×D4×C3112yes—
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C24×C3111yescharacteristic
581M16—28no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8#41×C3112yescomplemented
593C2×C8#41×C3112yescomplemented
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—81no—
611C4⋊C4C2×D4×C3112yes—
612C4⋊C4C2×D4×C3112yes—
613C4⋊C4C2×D4×C3112yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—22no—
617C22⋊C4—24no—
618C22⋊C4—22no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C42—21no—
624C42—21no—
625C42—42no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C31×#12012yes—
646C23C31×AGL(1,ℤ/8)12yes—
647C23C22×D4×C3111yescharacteristic
648Q8—48no—
649D4—28no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—48no—
654D4—41no—
655D4—41no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—48no—
675C2×C4—48no—
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—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4C31×#12012yes—
699C2×C4C31×AGL(1,ℤ/8)12yes—
700C2×C4C22×D4×C3111yescharacteristic
701C2×C4C22×D4×C3111yescharacteristic
702C2×C4C2×#41×C3111yescharacteristic
703C2×C4C2×#41×C3111yescharacteristic
704C2×C4C31×2−1+411yescharacteristic
705C2×C4C31×2−1+411yescharacteristic
706C8—22no—
707C8—22no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×C31×#12011yescharacteristic
732C22C31×#54711yescharacteristic
733C22C31×#54711yescharacteristic
734C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
735C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
736C22C31×#57711yescharacteristic
737C22C31×#57811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C31×#52511yescharacteristic
750C4C31×#53611yescharacteristic
751C4C31×#54711yescharacteristic
752C4C31×#54711yescharacteristic
753C2—42no—
754C2—42no—
755C2—82no—
756C2C31×#240611yescharacteristic
757C2C31×#300311yescharacteristic
758C2C31×#301311yescharacteristic
759C2C31×#334311yescharacteristic
760C2C31×#334511yescharacteristic
761C2C31×#335311yescharacteristic
762C2C31×#335411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#547C2
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. C2×C31×#482C2semidirect
3. C2×C31×#428C2semidirect
4. C31×#2485C2semidirect
5. C31×#2058C2semidirect
6. C31×#2057C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1895C2semidirect
10. C31×#1870C2semidirect
11. C31×#1864C2semidirect
12. C31×#1862C2semidirect
13. C31×#1853C2semidirect
14. C31×#1852C2semidirect
15. C31×#1824C2semidirect
210. C2×C8×C31#41semidirect
211. C2×C8×C31#41semidirect
244. #24100C31direct (N × H)
330. C2×#482C2×C31semidirect
331. C2×#428C2×C31semidirect
332. #2485C2×C31semidirect
333. #2058C2×C31semidirect
334. #2057C2×C31semidirect
335. #2034C2×C31semidirect
336. #2033C2×C31semidirect
337. #1895C2×C31semidirect
338. #1870C2×C31semidirect
339. #1864C2×C31semidirect
340. #1862C2×C31semidirect
341. #1853C2×C31semidirect
342. #1852C2×C31semidirect
343. #1824C2×C31semidirect
525. C31#24100direct (N × H)
592. C2×C8#41×C31semidirect
593. C2×C8#41×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5472
C2×C31×#4822
C2×C31×#4282
C31×#24852
C31×#20582
C31×#20572
C31×#20342
C31×#20332
C31×#18952
C31×#18702
C31×#18642
C31×#18622
C31×#18532
C31×#18522
C31×#18242
#2410031