Finite Group Databasebeta

← C31×#24561 #21481320

Subgroups — C31×#24561 #21481320

Order 7936.

1084 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#485C211yesmaximal, characteristic, complemented
2C2×C31×#407C211yesmaximal, characteristic
3C31×#2848C211yesmaximal, characteristic
4C31×#2280C211yesmaximal, characteristic
5C31×#2077C211yesmaximal, characteristic, complemented
6C31×#2076C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1894C211yesmaximal, characteristic, complemented
10C31×#1894C211yesmaximal, characteristic, complemented
11C31×#1873C211yesmaximal, characteristic, complemented
12C31×#1854C211yesmaximal, characteristic, complemented
13C31×#1825C211yesmaximal, characteristic, complemented
14C31×#1809C211yesmaximal, characteristic, complemented
15C31×#1809C211yesmaximal, characteristic, complemented
16C24×C4×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C2×C31×#117C2211yescharacteristic
24C31×#485—24no—
25C2×C31×#107C2211yescharacteristic, complemented
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×#106C2211yescharacteristic, complemented
29C2×C31×#103C2211yescharacteristic, complemented
30C2×C31×#103C2211yescharacteristic, complemented
31C2×C31×#103C2211yescharacteristic, complemented
32C2×C31×#103C2211yescharacteristic, complemented
33C31×#407—24no—
34C2×C31×C22⋊C8C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C31×#385—21no—
39C31×#385—21no—
40C31×#385—21no—
41C31×#381—21no—
42C31×#380C2211yescharacteristic
43C31×#380C2211yescharacteristic
44C31×#380C2211yescharacteristic
45C31×#380C2211yescharacteristic
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C31×#379—21no—
50C31×#379—21no—
51C4×C22⋊C4×C31—21no—
52C4×C22⋊C4×C31—21no—
53C31×#340C2211yescharacteristic, complemented
54C31×#340C2211yescharacteristic, complemented
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C25×C31D411yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—41no—
68C23×C4×C31—41no—
69C23×C4×C31D411yescharacteristic
70C23×C4×C31D411yescharacteristic
71C23×C4×C31D411yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C2×M16×C31—22no—
76C2×M16×C31—22no—
77C2×M16×C31—22no—
78C2×M16×C31—22no—
79C2×M16×C31—41no—
80C2×M16×C31—41no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—41no—
90C31×C22⋊Q8—41no—
91C31×#117—22no—
92C31×#117—22no—
93C31×#117—41no—
94C31×#117—41no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
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×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C31×#107—22no—
120C31×#107—41no—
121C31×#106—22no—
122C31×#106—41no—
123C31×#103—22no—
124C31×#103—22no—
125C31×#103—41no—
126C31×#103—41no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8D414yes—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C24×C31—22no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—41no—
142C24×C31—41no—
143C24×C31—41no—
144C24×C31—41no—
145C24×C31C2×D411yescharacteristic
146C24×C31C2×D411yescharacteristic
147C24×C31C2×D411yescharacteristic
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×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—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
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—41no—
183C22×C4×C31—41no—
184C22×C4×C31—41no—
185C22×C4×C31—44no—
186C22×C4×C31—44no—
187C22×C4×C31—44no—
188C22×C4×C31—44no—
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D412yes—
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31#4112yes—
194C22×C4×C31#4112yes—
195C22×C4×C31#4112yes—
196C22×C4×C31C2411yescharacteristic
197M16×C31—44no—
198M16×C31—44no—
199C2×C8×C31—21no—
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×C31C2×D412yes—
210C2×C8×C31C2×D412yes—
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—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—42no—
226C4⋊C4×C31—42no—
227C4⋊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—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C42×C31—42no—
241C42×C31—42no—
242#24561C3111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—44no—
262C23×C31—44no—
263C23×C31—44no—
264C23×C31—44no—
265C23×C31—44no—
266C23×C31—44no—
267C23×C31—44no—
268C23×C31#12112yes—
269C23×C31#12312yes—
270C23×C31#13712yes—
271C23×C31C22×D411yescharacteristic
272Q8×C31—41no—
273Q8×C31—41no—
274Q8×C31—41no—
275Q8×C31—41no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
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—44no—
292C2×C4×C31—44no—
293C2×C4×C31—44no—
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—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31#12112yes—
323C2×C4×C31#12312yes—
324C2×C4×C31C22×D411yescharacteristic
325C2×C4×C31C2×#4111yescharacteristic
326C2×C4×C31C2×#4111yescharacteristic
327C2×C4×C31C2×#4111yescharacteristic
328C2×C4×C31H(5,𝔽2)11yescharacteristic
329C2×C4×C31H(5,𝔽2)11yescharacteristic
330C8×C31—22no—
331C8×C31—22no—
332C8×C31—41no—
333C8×C31—41no—
334C2×#485C2×C3111yescharacteristic, complemented
335C2×#407C2×C3111yescharacteristic
336#2848C2×C3111yescharacteristic
337#2280C2×C3111yescharacteristic
338#2077C2×C3111yescharacteristic, complemented
339#2076C2×C3111yescharacteristic, complemented
340#2036C2×C3111yescharacteristic, complemented
341#2035C2×C3111yescharacteristic, complemented
342#1894C2×C3111yescharacteristic, complemented
343#1894C2×C3111yescharacteristic, complemented
344#1873C2×C3111yescharacteristic, complemented
345#1854C2×C3111yescharacteristic, complemented
346#1825C2×C3111yescharacteristic, complemented
347#1809C2×C3111yescharacteristic, complemented
348#1809C2×C3111yescharacteristic, complemented
349C22×C31—22no—
350C22×C31—22no—
351C22×C31—22no—
352C22×C31—22no—
353C22×C31—22no—
354C22×C31—22no—
355C22×C31—22no—
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—416no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—41no—
363C22×C31—41no—
364C22×C31—41no—
365C22×C31—41no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31C2×#12111yescharacteristic
372C22×C31C2×#12311yescharacteristic
373C22×C31#53411yescharacteristic
374C22×C31C2×#13711yescharacteristic
375C22×C31#57511yescharacteristic
376C22×C31#57511yescharacteristic
377C22×C31#57511yescharacteristic
378C4×C31—22no—
379C4×C31—22no—
380C4×C31—41no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31—81no—
386C4×C31—81no—
387C4×C31—81no—
388C4×C31—81no—
389C4×C31#54611yescharacteristic
390C4×C31#54611yescharacteristic
391C4×C31#55111yescharacteristic
392C4×C31#55111yescharacteristic
393C24×C4C22×C3111yescharacteristic
394C22×M16C22×C3111yescharacteristic
395C22×M16C22×C3111yescharacteristic
396C2×C22⋊Q8C22×C3111yescharacteristic
397C2×C22⋊Q8C22×C3111yescharacteristic
398C2×C22⋊Q8C22×C3111yescharacteristic
399C2×#117C22×C3111yescharacteristic
400C2×#117C22×C3111yescharacteristic
401#485—24no—
402C2×#107C22×C3111yescharacteristic, complemented
403C2×#107C22×C3111yescharacteristic, complemented
404C2×#106C22×C3111yescharacteristic, complemented
405C2×#106C22×C3111yescharacteristic, complemented
406C2×#103C22×C3111yescharacteristic, complemented
407C2×#103C22×C3111yescharacteristic, complemented
408C2×#103C22×C3111yescharacteristic, complemented
409C2×#103C22×C3111yescharacteristic, complemented
410#407—24no—
411C2×C22⋊C8C22×C3111yescharacteristic
412C2×C22⋊C8C22×C3111yescharacteristic
413C2×C22⋊C8C22×C3111yescharacteristic
414C2×C22⋊C8C22×C3111yescharacteristic
415#385—21no—
416#385—21no—
417#385—21no—
418#381—21no—
419#380C22×C3111yescharacteristic
420#380C22×C3111yescharacteristic
421#380C22×C3111yescharacteristic
422#380C22×C3111yescharacteristic
423#380C22×C3111yescharacteristic
424#380C22×C3111yescharacteristic
425#380C22×C3111yescharacteristic
426#379—21no—
427#379—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430#340C22×C3111yescharacteristic, complemented
431#340C22×C3111yescharacteristic, complemented
432#340C22×C3111yescharacteristic, complemented
433#340C22×C3111yescharacteristic, complemented
434#340C22×C3111yescharacteristic, complemented
435#340C22×C3111yescharacteristic, complemented
436#340C22×C3111yescharacteristic, complemented
437#340C22×C3111yescharacteristic, complemented
438C2×C31—42no—
439C2×C31—42no—
440C2×C31—42no—
441C2×C31#241211yescharacteristic
442C2×C31#305411yescharacteristic
443C2×C31#305611yescharacteristic
444C2×C31#309311yescharacteristic
445C2×C31#309511yescharacteristic
446C2×C31#319611yescharacteristic
447C2×C31#319711yescharacteristic
448C25D4×C3111yescharacteristic
449C22×Q8C23×C3111yescharacteristic
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—41no—
455C23×C4—41no—
456C23×C4D4×C3111yescharacteristic
457C23×C4D4×C3111yescharacteristic
458C23×C4D4×C3111yescharacteristic
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3111yescharacteristic
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—22no—
466C2×M16—41no—
467C2×M16—41no—
468C22×C8C23×C3111yescharacteristic
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—41no—
477C22⋊Q8—41no—
478#117—22no—
479#117—22no—
480#117—41no—
481#117—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4C23×C3111yescharacteristic
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C4⋊C4C23×C3111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
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⋊C4—21no—
504C2×C42—21no—
505C2×C42—21no—
506#107—22no—
507#107—41no—
508#106—22no—
509#106—41no—
510#103—22no—
511#103—22no—
512#103—41no—
513#103—41no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8D4×C3114yes—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525C31#2456111yescharacteristic, direct product factor, Sylow
526C24—22no—
527C24—22no—
528C24—22no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24C2×D4×C3111yescharacteristic
534C24C2×D4×C3111yescharacteristic
535C24C2×D4×C3111yescharacteristic
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—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—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
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—21no—
569C22×C4—21no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3112yes—
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4#41×C3112yes—
582C22×C4#41×C3112yes—
583C22×C4#41×C3112yes—
584C22×C4C24×C3111yescharacteristic
585M16—44no—
586M16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8C2×D4×C3112yes—
598C2×C8C2×D4×C3112yes—
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—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C42—42no—
629C42—42no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23C31×#12112yes—
656C23C31×#12312yes—
657C23C31×#13712yes—
658C23C22×D4×C3111yescharacteristic
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
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×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4C31×#12112yes—
710C2×C4C31×#12312yes—
711C2×C4C22×D4×C3111yescharacteristic
712C2×C4C2×#41×C3111yescharacteristic
713C2×C4C2×#41×C3111yescharacteristic
714C2×C4C2×#41×C3111yescharacteristic
715C2×C4C31×H(5,𝔽2)11yescharacteristic
716C2×C4C31×H(5,𝔽2)11yescharacteristic
717C8—22no—
718C8—22no—
719C8—41no—
720C8—41no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—416no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22C2×C31×#12111yescharacteristic
744C22C2×C31×#12311yescharacteristic
745C22C31×#53411yescharacteristic
746C22C2×C31×#13711yescharacteristic
747C22C31×#57511yescharacteristic
748C22C31×#57511yescharacteristic
749C22C31×#57511yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C31×#54611yescharacteristic
762C4C31×#54611yescharacteristic
763C4C31×#55111yescharacteristic
764C4C31×#55111yescharacteristic
765C2—42no—
766C2—42no—
767C2—42no—
768C2C31×#241211yescharacteristic
769C2C31×#305411yescharacteristic
770C2C31×#305611yescharacteristic
771C2C31×#309311yescharacteristic
772C2C31×#309511yescharacteristic
773C2C31×#319611yescharacteristic
774C2C31×#319711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#485C2semidirect
5. C31×#2077C2semidirect
6. C31×#2076C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
9. C31×#1894C2semidirect
10. C31×#1894C2semidirect
11. C31×#1873C2semidirect
12. C31×#1854C2semidirect
13. C31×#1825C2semidirect
14. C31×#1809C2semidirect
15. C31×#1809C2semidirect
25. C2×C31×#107C22semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×#106C22semidirect
29. C2×C31×#103C22semidirect
30. C2×C31×#103C22semidirect
31. C2×C31×#103C22semidirect
32. C2×C31×#103C22semidirect
53. C31×#340C22semidirect
54. C31×#340C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
242. #24561C31direct (N × H)
334. C2×#485C2×C31semidirect
338. #2077C2×C31semidirect
339. #2076C2×C31semidirect
340. #2036C2×C31semidirect
341. #2035C2×C31semidirect
342. #1894C2×C31semidirect
343. #1894C2×C31semidirect
344. #1873C2×C31semidirect
345. #1854C2×C31semidirect
346. #1825C2×C31semidirect
347. #1809C2×C31semidirect
348. #1809C2×C31semidirect
402. C2×#107C22×C31semidirect
403. C2×#107C22×C31semidirect
404. C2×#106C22×C31semidirect
405. C2×#106C22×C31semidirect
406. C2×#103C22×C31semidirect
407. C2×#103C22×C31semidirect
408. C2×#103C22×C31semidirect
409. C2×#103C22×C31semidirect
430. #340C22×C31semidirect
431. #340C22×C31semidirect
432. #340C22×C31semidirect
433. #340C22×C31semidirect
434. #340C22×C31semidirect
435. #340C22×C31semidirect
436. #340C22×C31semidirect
437. #340C22×C31semidirect
525. C31#24561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4852
C2×C31×#4072
C31×#28482
C31×#22802
C31×#20772
C31×#20762
C31×#20362
C31×#20352
C31×#18942
C31×#18732
C31×#18542
C31×#18252
C31×#18092
#2456131