Finite Group Databasebeta

← C31×#24103 #21480862

Subgroups — C31×#24103 #21480862

Order 7936.

1110 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#428C211yesmaximal, characteristic, complemented
4C31×#2485C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2059C211yesmaximal, 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×#1854C211yesmaximal, characteristic, complemented
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1823C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C31×#553—24no—
18C31×#553—24no—
19C2×C31×#126—21no—
20C2×C31×#125C2211yescharacteristic
21C2×C31×#123—21no—
22C2×C31×#121—21no—
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
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
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31D411yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C2×M16×C31—22no—
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C31×#126—28no—
79C31×#125—22no—
80C31×#125—22no—
81C31×#123—28no—
82C31×#121—28no—
83C31×#121—22no—
84C31×#121—22no—
85C31×#121—22no—
86C31×#121D414yes—
87C4×D4×C31—28no—
88C4×D4×C31—22no—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C31×#117—22no—
93C31×#117—22no—
94C31×#117—22no—
95C31×#117—22no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31D411yescharacteristic
103C2×C4⋊C4×C31D414yes—
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31D411yescharacteristic
120C2×C22⋊C4×C31D411yescharacteristic
121C2×C42×C31—21no—
122C2×C42×C31—21no—
123C2×C42×C31C2311yescharacteristic
124C31×#107—22no—
125C31×#107—22no—
126C31×#107—22no—
127C31×#106—22no—
128C31×#106—22no—
129C31×#106—22no—
130C31×#102—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×C22⋊C8—22no—
135C31×C22⋊C8—22no—
136C31×C22⋊C8—22no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C24×C31—21no—
143C24×C31C2×D411yescharacteristic
144C24×C31C2×D411yescharacteristic
145C2×D4×C31—22no—
146C2×D4×C31—24no—
147C2×D4×C31—24no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—41no—
154C2×D4×C31—41no—
155C2×D4×C31—42no—
156C2×D4×C31—42no—
157C2×D4×C31—81no—
158C2×D4×C31—81no—
159C2×D4×C31C2×D412yes—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—24no—
168C22×C4×C31—24no—
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—81no—
180C22×C4×C31—81no—
181C22×C4×C31—81no—
182C22×C4×C31—81no—
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D411yescharacteristic
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2411yescharacteristic
190M16×C31—28no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
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#4112yes—
202C2×C8×C31#4112yes—
203C4⋊C4×C31—24no—
204C4⋊C4×C31—24no—
205C4⋊C4×C31—24no—
206C4⋊C4×C31—22no—
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—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—81no—
220C4⋊C4×C31C2×D412yes—
221C4⋊C4×C31C2×D412yes—
222C4⋊C4×C31C2×D412yes—
223C22⋊C4×C31—24no—
224C22⋊C4×C31—24no—
225C22⋊C4×C31—24no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—24no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—81no—
232C22⋊C4×C31—81no—
233C42×C31—24no—
234C42×C31—21no—
235C42×C31—21no—
236C42×C31—42no—
237#24103C3111yesmaximal, characteristic, direct product factor, Sylow
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—22no—
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31#12012yes—
259C23×C31C22×D411yescharacteristic
260D4×C31—22no—
261D4×C31—22no—
262D4×C31—44no—
263D4×C31—48no—
264D4×C31—41no—
265D4×C31—41no—
266D4×C31—84no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—22no—
276C2×C4×C31—21no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
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—84no—
308C2×C4×C31—84no—
309C2×C4×C31#12012yes—
310C2×C4×C31C22×D411yescharacteristic
311C2×C4×C31C22×D411yescharacteristic
312C2×C4×C31C2×#4111yescharacteristic
313C2×C4×C31C2×#4111yescharacteristic
314C2×C4×C312−1+411yescharacteristic
315C2×C4×C312−1+411yescharacteristic
316C8×C31—22no—
317C8×C31—22no—
318C8×C31—41no—
319C8×C31—41no—
320C2×#553C2×C3111yescharacteristic
321C2×#482C2×C3111yescharacteristic, complemented
322C2×#428C2×C3111yescharacteristic, complemented
323#2485C2×C3111yescharacteristic, complemented
324#2059C2×C3111yescharacteristic, complemented
325#2059C2×C3111yescharacteristic, complemented
326#2034C2×C3111yescharacteristic, complemented
327#2033C2×C3111yescharacteristic, complemented
328#1895C2×C3111yescharacteristic, complemented
329#1870C2×C3111yescharacteristic, complemented
330#1864C2×C3111yescharacteristic, complemented
331#1862C2×C3111yescharacteristic, complemented
332#1854C2×C3111yescharacteristic, complemented
333#1854C2×C3111yescharacteristic, complemented
334#1823C2×C3111yescharacteristic, complemented
335C22×C31—22no—
336C22×C31—22no—
337C22×C31—22no—
338C22×C31—41no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—41no—
342C22×C31—41no—
343C22×C31—41no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—41no—
347C22×C31—42no—
348C22×C31—41no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—41no—
352C22×C31—81no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31C2×#12011yescharacteristic
357C22×C31#54711yescharacteristic
358C22×C31#54711yescharacteristic
359C22×C31#57511yescharacteristic
360C22×C31#57511yescharacteristic
361C22×C31#57611yescharacteristic
362C22×C31#57711yescharacteristic
363C4×C31—22no—
364C4×C31—41no—
365C4×C31—41no—
366C4×C31—42no—
367C4×C31—41no—
368C4×C31—42no—
369C4×C31—42no—
370C4×C31—81no—
371C4×C31—81no—
372C4×C31—81no—
373C4×C31—81no—
374C4×C31#52511yescharacteristic
375C4×C31#53611yescharacteristic
376C4×C31#54711yescharacteristic
377C4×C31#54711yescharacteristic
378C22×M16C22×C3111yescharacteristic
379#553—24no—
380#553—24no—
381C2×#126—21no—
382C2×#125C22×C3111yescharacteristic
383C2×#123—21no—
384C2×#121—21no—
385C2×#121C22×C3111yescharacteristic
386C2×#121C22×C3111yescharacteristic
387C2×C4×D4—21no—
388C2×C4×D4C22×C3111yescharacteristic
389C2×C4×D4C22×C3111yescharacteristic
390C2×#117C22×C3111yescharacteristic
391C2×#117C22×C3111yescharacteristic
392C22×C4⋊C4C22×C3111yescharacteristic
393#482—24no—
394#428—24no—
395C2×#107C22×C3111yescharacteristic
396C2×#107C22×C3111yescharacteristic
397C2×#107C22×C3111yescharacteristic
398C2×#106C22×C3111yescharacteristic
399C2×#106C22×C3111yescharacteristic
400C2×#106C22×C3111yescharacteristic
401C2×#102C22×C3111yescharacteristic
402C2×#102C22×C3111yescharacteristic
403C2×#102C22×C3111yescharacteristic
404C2×#102C22×C3111yescharacteristic
405C2×C22⋊C8C22×C3111yescharacteristic
406C2×C22⋊C8C22×C3111yescharacteristic
407C2×C22⋊C8C22×C3111yescharacteristic
408#397—21no—
409#394—21no—
410#389C22×C3111yescharacteristic
411#389C22×C3111yescharacteristic
412#388—21no—
413#387—21no—
414#380C22×C3111yescharacteristic
415#380C22×C3111yescharacteristic
416#380C22×C3111yescharacteristic
417#340C22×C3111yescharacteristic
418#340C22×C3111yescharacteristic
419#340C22×C3111yescharacteristic
420#340C22×C3111yescharacteristic
421#340C22×C3111yescharacteristic
422#340C22×C3111yescharacteristic
423#336C22×C3111yescharacteristic
424#336C22×C3111yescharacteristic
425C2×C31—42no—
426C2×C31—81no—
427C2×C31—82no—
428C2×C31#240611yescharacteristic
429C2×C31#300511yescharacteristic
430C2×C31#301211yescharacteristic
431C2×C31#334711yescharacteristic
432C2×C31#335011yescharacteristic
433C2×C31#335111yescharacteristic
434C2×C31#335511yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4D4×C3111yescharacteristic
438C22×D4C23×C3111yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4C23×C3111yescharacteristic
442C23×C4C23×C3111yescharacteristic
443C2×M16—22no—
444C2×M16—22no—
445C2×M16—22no—
446C22×C8C23×C3111yescharacteristic
447C22×C8C23×C3111yescharacteristic
448C22×C8C23×C3111yescharacteristic
449C22×C8C23×C3111yescharacteristic
450#126—28no—
451#125—22no—
452#125—22no—
453#123—28no—
454#121—28no—
455#121—22no—
456#121—22no—
457#121—22no—
458#121D4×C3114yes—
459C4×D4—28no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464#117—22no—
465#117—22no—
466#117—22no—
467#117—22no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4D4×C3111yescharacteristic
475C2×C4⋊C4D4×C3114yes—
476C2×C4⋊C4C23×C3111yescharacteristic
477C2×C4⋊C4C23×C3111yescharacteristic
478C2×C4⋊C4C23×C3111yescharacteristic
479C2×C4⋊C4C23×C3111yescharacteristic
480C2×C4⋊C4C23×C3111yescharacteristic
481C2×C4⋊C4C23×C3111yescharacteristic
482C2×C4⋊C4C23×C3111yescharacteristic
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⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4D4×C3111yescharacteristic
492C2×C22⋊C4D4×C3111yescharacteristic
493C2×C42—21no—
494C2×C42—21no—
495C2×C42C23×C3111yescharacteristic
496#107—22no—
497#107—22no—
498#107—22no—
499#106—22no—
500#106—22no—
501#106—22no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514C31#2410311yescharacteristic, direct product factor, Sylow
515C24—21no—
516C24C2×D4×C3111yescharacteristic
517C24C2×D4×C3111yescharacteristic
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4C2×D4×C3112yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—24no—
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—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4C2×D4×C3111yescharacteristic
557C22×C4C2×D4×C3111yescharacteristic
558C22×C4C2×D4×C3111yescharacteristic
559C22×C4C2×D4×C3111yescharacteristic
560C22×C4C2×D4×C3112yes—
561C22×C4C2×D4×C3112yes—
562C22×C4C24×C3111yescharacteristic
563M16—28no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8#41×C3112yes—
575C2×C8#41×C3112yes—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—81no—
593C4⋊C4C2×D4×C3112yes—
594C4⋊C4C2×D4×C3112yes—
595C4⋊C4C2×D4×C3112yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—24no—
601C22⋊C4—22no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42—42no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23C31×#12012yes—
631C23C22×D4×C3111yescharacteristic
632D4—22no—
633D4—22no—
634D4—44no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—84no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
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—84no—
680C2×C4—84no—
681C2×C4C31×#12012yes—
682C2×C4C22×D4×C3111yescharacteristic
683C2×C4C22×D4×C3111yescharacteristic
684C2×C4C2×#41×C3111yescharacteristic
685C2×C4C2×#41×C3111yescharacteristic
686C2×C4C31×2−1+411yescharacteristic
687C2×C4C31×2−1+411yescharacteristic
688C8—22no—
689C8—22no—
690C8—41no—
691C8—41no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—42no—
708C22—41no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×C31×#12011yescharacteristic
714C22C31×#54711yescharacteristic
715C22C31×#54711yescharacteristic
716C22C31×#57511yescharacteristic
717C22C31×#57511yescharacteristic
718C22C31×#57611yescharacteristic
719C22C31×#57711yescharacteristic
720C4—22no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4C31×#52511yescharacteristic
732C4C31×#53611yescharacteristic
733C4C31×#54711yescharacteristic
734C4C31×#54711yescharacteristic
735C2—42no—
736C2—81no—
737C2—82no—
738C2C31×#240611yescharacteristic
739C2C31×#300511yescharacteristic
740C2C31×#301211yescharacteristic
741C2C31×#334711yescharacteristic
742C2C31×#335011yescharacteristic
743C2C31×#335111yescharacteristic
744C2C31×#335511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#553C2
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×#2059C2semidirect
6. C31×#2059C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1895C2semidirect
10. C31×#1870C2semidirect
11. C31×#1864C2semidirect
12. C31×#1862C2semidirect
13. C31×#1854C2semidirect
14. C31×#1854C2semidirect
15. C31×#1823C2semidirect
237. #24103C31direct (N × H)
321. C2×#482C2×C31semidirect
322. C2×#428C2×C31semidirect
323. #2485C2×C31semidirect
324. #2059C2×C31semidirect
325. #2059C2×C31semidirect
326. #2034C2×C31semidirect
327. #2033C2×C31semidirect
328. #1895C2×C31semidirect
329. #1870C2×C31semidirect
330. #1864C2×C31semidirect
331. #1862C2×C31semidirect
332. #1854C2×C31semidirect
333. #1854C2×C31semidirect
334. #1823C2×C31semidirect
514. C31#24103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5532
C2×C31×#4822
C2×C31×#4282
C31×#24852
C31×#20592
C31×#20342
C31×#20332
C31×#18952
C31×#18702
C31×#18642
C31×#18622
C31×#18542
C31×#18232
#2410331