Finite Group Databasebeta

← C31×#24560 #21481319

Subgroups — C31×#24560 #21481319

Order 7936.

1162 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#482C211yesmaximal, characteristic, complemented
2C2×C31×#407C211yesmaximal, characteristic, complemented
3C31×#2847C211yesmaximal, characteristic
4C31×#2280C211yesmaximal, characteristic, complemented
5C31×#2077C211yesmaximal, characteristic, complemented
6C31×#2075C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1895C211yesmaximal, characteristic, complemented
10C31×#1895C211yesmaximal, characteristic, complemented
11C31×#1875C211yesmaximal, 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×#121C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C31×#120—21no—
23C2×C31×#117C2211yescharacteristic
24C2×C31×#117C2211yescharacteristic
25C31×#482—24no—
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#107C2211yescharacteristic, complemented
28C2×C31×#106C2211yescharacteristic, complemented
29C2×C31×#106C2211yescharacteristic, complemented
30C2×C31×#102C2211yescharacteristic, complemented
31C2×C31×#102C2211yescharacteristic, complemented
32C2×C31×#102C2211yescharacteristic, complemented
33C2×C31×#102C2211yescharacteristic, complemented
34C31×#407—24no—
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C31×#386—21no—
40C31×#386—21no—
41C31×#386—21no—
42C31×#381—21no—
43C31×#380C2211yescharacteristic
44C31×#380C2211yescharacteristic
45C31×#380C2211yescharacteristic
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C31×#380C2211yescharacteristic
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×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31C2311yescharacteristic
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—41no—
71C23×C4×C31—41no—
72C23×C4×C31D411yescharacteristic
73C23×C4×C31D411yescharacteristic
74C23×C4×C31D411yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C2×M16×C31—22no—
79C2×M16×C31—22no—
80C2×M16×C31—22no—
81C2×M16×C31—22no—
82C2×M16×C31—41no—
83C2×M16×C31—41no—
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—41no—
93C31×#121—41no—
94C31×#120—44no—
95C31×#117—22no—
96C31×#117—22no—
97C31×#117—41no—
98C31×#117—41no—
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×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C31×#107—22no—
121C31×#107—41no—
122C31×#106—22no—
123C31×#106—41no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—41no—
127C31×#102—41no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—22no—
131C31×C22⋊C8D414yescomplemented
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—21no—
143C24×C31—41no—
144C24×C31—41no—
145C24×C31—41no—
146C24×C31—41no—
147C24×C31C2×D411yescharacteristic
148C24×C31C2×D411yescharacteristic
149C24×C31C2×D411yescharacteristic
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—42no—
157C2×D4×C31—42no—
158C2×D4×C31—42no—
159C2×D4×C31—42no—
160C2×D4×C31—42no—
161C2×D4×C31—42no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
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—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
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—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—41no—
193C22×C4×C31—41no—
194C22×C4×C31—41no—
195C22×C4×C31—44no—
196C22×C4×C31—44no—
197C22×C4×C31—44no—
198C22×C4×C31—44no—
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31#4112yes—
204C22×C4×C31#4112yes—
205C22×C4×C31#4112yes—
206C22×C4×C31C2411yescharacteristic
207M16×C31—44no—
208M16×C31—44no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31C2×D412yes—
220C2×C8×C31C2×D412yes—
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—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—42no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C42×C31—42no—
248C42×C31—42no—
249#24560C3111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—44no—
269C23×C31—44no—
270C23×C31—44no—
271C23×C31—44no—
272C23×C31—44no—
273C23×C31—44no—
274C23×C31—44no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31#12112yes—
283C23×C31#12312yes—
284C23×C31AGL(1,ℤ/8)12yes—
285C23×C31C22×D411yescharacteristic
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—41no—
289D4×C31—41no—
290D4×C31—84no—
291D4×C31—84no—
292D4×C31—84no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—44no—
309C2×C4×C31—44no—
310C2×C4×C31—44no—
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—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31#12112yes—
337C2×C4×C31#12312yes—
338C2×C4×C31C22×D411yescharacteristic
339C2×C4×C31C2×#4111yescharacteristic
340C2×C4×C31C2×#4111yescharacteristic
341C2×C4×C31C2×#4111yescharacteristic
342C2×C4×C31H(5,𝔽2)11yescharacteristic
343C2×C4×C31H(5,𝔽2)11yescharacteristic
344C8×C31—22no—
345C8×C31—22no—
346C8×C31—41no—
347C8×C31—41no—
348C2×#482C2×C3111yescharacteristic, complemented
349C2×#407C2×C3111yescharacteristic, complemented
350#2847C2×C3111yescharacteristic
351#2280C2×C3111yescharacteristic, complemented
352#2077C2×C3111yescharacteristic, complemented
353#2075C2×C3111yescharacteristic, complemented
354#2034C2×C3111yescharacteristic, complemented
355#2033C2×C3111yescharacteristic, complemented
356#1895C2×C3111yescharacteristic, complemented
357#1895C2×C3111yescharacteristic, complemented
358#1875C2×C3111yescharacteristic, complemented
359#1854C2×C3111yescharacteristic, complemented
360#1825C2×C3111yescharacteristic, complemented
361#1809C2×C3111yescharacteristic, complemented
362#1809C2×C3111yescharacteristic, complemented
363C22×C31—22no—
364C22×C31—22no—
365C22×C31—22no—
366C22×C31—22no—
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—22no—
370C22×C31—22no—
371C22×C31—22no—
372C22×C31—416no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—41no—
376C22×C31—41no—
377C22×C31—41no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31C2×#12111yescharacteristic
393C22×C31C2×#12311yescharacteristic
394C22×C31#53411yescharacteristic
395C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C31#57511yescharacteristic
397C22×C31#57511yescharacteristic
398C22×C31#57511yescharacteristic
399C4×C31—22no—
400C4×C31—22no—
401C4×C31—41no—
402C4×C31—81no—
403C4×C31—81no—
404C4×C31—81no—
405C4×C31—81no—
406C4×C31—81no—
407C4×C31—81no—
408C4×C31—81no—
409C4×C31#54611yescharacteristic
410C4×C31#54611yescharacteristic
411C4×C31#55111yescharacteristic
412C4×C31#55111yescharacteristic
413C24×C4C22×C3111yescharacteristic
414C22×M16C22×C3111yescharacteristic
415C22×M16C22×C3111yescharacteristic
416C2×#121C22×C3111yescharacteristic
417C2×#121C22×C3111yescharacteristic
418C2×#121C22×C3111yescharacteristic
419C2×#120—21no—
420C2×#117C22×C3111yescharacteristic
421C2×#117C22×C3111yescharacteristic
422#482—24no—
423C2×#107C22×C3111yescharacteristic, complemented
424C2×#107C22×C3111yescharacteristic, complemented
425C2×#106C22×C3111yescharacteristic, complemented
426C2×#106C22×C3111yescharacteristic, complemented
427C2×#102C22×C3111yescharacteristic, complemented
428C2×#102C22×C3111yescharacteristic, complemented
429C2×#102C22×C3111yescharacteristic, complemented
430C2×#102C22×C3111yescharacteristic, complemented
431#407—24no—
432C2×C22⋊C8C22×C3111yescharacteristic
433C2×C22⋊C8C22×C3111yescharacteristic
434C2×C22⋊C8C22×C3111yescharacteristic
435C2×C22⋊C8C22×C3111yescharacteristic
436#386—21no—
437#386—21no—
438#386—21no—
439#381—21no—
440#380C22×C3111yescharacteristic
441#380C22×C3111yescharacteristic
442#380C22×C3111yescharacteristic
443#380C22×C3111yescharacteristic
444#380C22×C3111yescharacteristic
445#380C22×C3111yescharacteristic
446#380C22×C3111yescharacteristic
447#379—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450#340C22×C3111yescharacteristic, complemented
451#340C22×C3111yescharacteristic, complemented
452#340C22×C3111yescharacteristic, complemented
453#340C22×C3111yescharacteristic, complemented
454#340C22×C3111yescharacteristic, complemented
455#340C22×C3111yescharacteristic, complemented
456#340C22×C3111yescharacteristic, complemented
457#340C22×C3111yescharacteristic, complemented
458C2×C31—42no—
459C2×C31—42no—
460C2×C31—42no—
461C2×C31—161no—
462C2×C31#241211yescharacteristic
463C2×C31#305411yescharacteristic
464C2×C31#305511yescharacteristic
465C2×C31#309311yescharacteristic
466C2×C31#309411yescharacteristic
467C2×C31#319411yescharacteristic
468C2×C31#319711yescharacteristic
469C25D4×C3111yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4C23×C3111yescharacteristic
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—41no—
479C23×C4—41no—
480C23×C4D4×C3111yescharacteristic
481C23×C4D4×C3111yescharacteristic
482C23×C4D4×C3111yescharacteristic
483C23×C4C23×C3111yescharacteristic
484C23×C4C23×C3111yescharacteristic
485C23×C4C23×C3111yescharacteristic
486C2×M16—22no—
487C2×M16—22no—
488C2×M16—22no—
489C2×M16—22no—
490C2×M16—41no—
491C2×M16—41no—
492C22×C8C23×C3111yescharacteristic
493C22×C8C23×C3111yescharacteristic
494C22×C8C23×C3111yescharacteristic
495C22×C8C23×C3111yescharacteristic
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—41no—
501#121—41no—
502#120—44no—
503#117—22no—
504#117—22no—
505#117—41no—
506#117—41no—
507C2×C4⋊C4C23×C3111yescharacteristic
508C2×C4⋊C4C23×C3111yescharacteristic
509C2×C4⋊C4C23×C3111yescharacteristic
510C2×C4⋊C4C23×C3111yescharacteristic
511C2×C4⋊C4C23×C3111yescharacteristic
512C2×C4⋊C4C23×C3111yescharacteristic
513C2×C4⋊C4C23×C3111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C42—21no—
527C2×C42—21no—
528#107—22no—
529#107—41no—
530#106—22no—
531#106—41no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8D4×C3114yescomplemented
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547C31#2456011yescharacteristic, direct product factor, Sylow
548C24—22no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—41no—
553C24—41no—
554C24—41no—
555C24—41no—
556C24C2×D4×C3111yescharacteristic
557C24C2×D4×C3111yescharacteristic
558C24C2×D4×C3111yescharacteristic
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4C2×D4×C3111yescharacteristic
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3112yes—
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4#41×C3112yes—
613C22×C4#41×C3112yes—
614C22×C4#41×C3112yes—
615C22×C4C24×C3111yescharacteristic
616M16—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8C2×D4×C3112yes—
629C2×C8C2×D4×C3112yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C42—42no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23C31×#12112yes—
691C23C31×#12312yes—
692C23C31×AGL(1,ℤ/8)12yes—
693C23C22×D4×C3111yescharacteristic
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4C31×#12112yes—
745C2×C4C31×#12312yes—
746C2×C4C22×D4×C3111yescharacteristic
747C2×C4C2×#41×C3111yescharacteristic
748C2×C4C2×#41×C3111yescharacteristic
749C2×C4C2×#41×C3111yescharacteristic
750C2×C4C31×H(5,𝔽2)11yescharacteristic
751C2×C4C31×H(5,𝔽2)11yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—416no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×C31×#12111yescharacteristic
786C22C2×C31×#12311yescharacteristic
787C22C31×#53411yescharacteristic
788C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
789C22C31×#57511yescharacteristic
790C22C31×#57511yescharacteristic
791C22C31×#57511yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C31×#54611yescharacteristic
803C4C31×#54611yescharacteristic
804C4C31×#55111yescharacteristic
805C4C31×#55111yescharacteristic
806C2—42no—
807C2—42no—
808C2—42no—
809C2—161no—
810C2C31×#241211yescharacteristic
811C2C31×#305411yescharacteristic
812C2C31×#305511yescharacteristic
813C2C31×#309311yescharacteristic
814C2C31×#309411yescharacteristic
815C2C31×#319411yescharacteristic
816C2C31×#319711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2847C2
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×#482C2semidirect
2. C2×C31×#407C2semidirect
4. C31×#2280C2semidirect
5. C31×#2077C2semidirect
6. C31×#2075C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1895C2semidirect
10. C31×#1895C2semidirect
11. C31×#1875C2semidirect
12. C31×#1854C2semidirect
13. C31×#1825C2semidirect
14. C31×#1809C2semidirect
15. C31×#1809C2semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#107C22semidirect
28. C2×C31×#106C22semidirect
29. C2×C31×#106C22semidirect
30. C2×C31×#102C22semidirect
31. C2×C31×#102C22semidirect
32. C2×C31×#102C22semidirect
33. C2×C31×#102C22semidirect
53. C31×#340C22semidirect
54. C31×#340C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
131. C31×C22⋊C8D4semidirect
249. #24560C31direct (N × H)
348. C2×#482C2×C31semidirect
349. C2×#407C2×C31semidirect
351. #2280C2×C31semidirect
352. #2077C2×C31semidirect
353. #2075C2×C31semidirect
354. #2034C2×C31semidirect
355. #2033C2×C31semidirect
356. #1895C2×C31semidirect
357. #1895C2×C31semidirect
358. #1875C2×C31semidirect
359. #1854C2×C31semidirect
360. #1825C2×C31semidirect
361. #1809C2×C31semidirect
362. #1809C2×C31semidirect
423. C2×#107C22×C31semidirect
424. C2×#107C22×C31semidirect
425. C2×#106C22×C31semidirect
426. C2×#106C22×C31semidirect
427. C2×#102C22×C31semidirect
428. C2×#102C22×C31semidirect
429. C2×#102C22×C31semidirect
430. C2×#102C22×C31semidirect
450. #340C22×C31semidirect
451. #340C22×C31semidirect
452. #340C22×C31semidirect
453. #340C22×C31semidirect
454. #340C22×C31semidirect
455. #340C22×C31semidirect
456. #340C22×C31semidirect
457. #340C22×C31semidirect
539. C22⋊C8D4×C31semidirect
547. C31#24560direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4822
C2×C31×#4072
C31×#28472
C31×#22802
C31×#20772
C31×#20752
C31×#20342
C31×#20332
C31×#18952
C31×#18752
C31×#18542
C31×#18252
C31×#18092
#2456031