Finite Group Databasebeta

← C31×#25160 #21481919

Subgroups — C31×#25160 #21481919

Order 7936.

1316 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#463C211yesmaximal, characteristic, complemented
2C2×C31×#450C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic
4C2×C4×D8×C31C211yesmaximal, characteristic, complemented
5C31×#2427C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2036C211yesmaximal, characteristic, complemented
9C31×#2034C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#1968C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic, complemented
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic, complemented
27C22×C22⋊C4×C31—21no—
28C31×#463—24no—
29C31×#450—24no—
30C31×#447—24no—
31C4×D8×C31—24no—
32C2×C31×#107C2211yescharacteristic, complemented
33C2×C31×#106C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C4×C8×C31C2211yescharacteristic, complemented
46C31×#397—21no—
47C31×#394—21no—
48C31×#391C2211yescharacteristic, complemented
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic, complemented
52C31×#386—21no—
53C31×#386—21no—
54C31×#386—21no—
55C31×#380—21no—
56C31×#380C2211yescharacteristic
57C31×#379—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C23×C4×C31—21no—
77C23×C4×C31—21no—
78C23×C4×C31—21no—
79C23×C4×C31C2311yescharacteristic
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—41no—
86C2×D8×C31—22no—
87C2×D8×C31—22no—
88C2×D8×C31—22no—
89C2×D8×C31—22no—
90C2×D8×C31—41no—
91C2×D8×C31D414yes—
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C31×#124—22no—
97C31×#124—41no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—41no—
100C31×#121—22no—
101C31×#121—41no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—41no—
106C4×D4×C31—41no—
107C4×D4×C31—41no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—44no—
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C42×C31C2311yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C31×#107—22no—
132C31×#106—41no—
133C31×C4⋊C8—22no—
134C31×#103—22no—
135C31×#103—41no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102D414yescomplemented
142C31×C22⋊C8—22no—
143C31×C22⋊C8—22no—
144C4×C8×C31—22no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95D411yescharacteristic
150C31×#95D411yescharacteristic
151C24×C31—21no—
152C24×C31—24no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—81no—
160C24×C31—81no—
161C24×C31C2×D411yescharacteristic
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×D4×C31—24no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—44no—
185C2×D4×C31—44no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—81no—
191C2×D4×C31C2×D412yes—
192C2×D4×C31C2×D412yes—
193C2×D4×C31C2×D412yes—
194C2×D4×C31#4112yes—
195C2×D4×C31#4112yes—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—42no—
208C22×C4×C31—42no—
209C22×C4×C31—42no—
210C22×C4×C31—42no—
211C22×C4×C31—42no—
212C22×C4×C31—42no—
213C22×C4×C31—81no—
214C22×C4×C31—81no—
215C22×C4×C31—81no—
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2411yescharacteristic
222SD16×C31—44no—
223SD16×C31—44no—
224D8×C31—28no—
225D8×C31—44no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31C2×D412yes—
237C2×C8×C31C2×D412yes—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—42no—
246C4⋊C4×C31—81no—
247C4⋊C4×C31C2×D412yes—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—81no—
261C22⋊C4×C31—81no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—21no—
266#25160C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—21no—
268C23×C31—22no—
269C23×C31—21no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—48no—
279C23×C31—48no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—84no—
297C23×C31—84no—
298C23×C31—84no—
299C23×C31—84no—
300C23×C31—84no—
301C23×C31#13512yes—
302C23×C31C22×D411yescharacteristic
303Q8×C31—41no—
304Q8×C31—41no—
305Q8×C31—41no—
306Q8×C31—41no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—22no—
311D4×C31—22no—
312D4×C31—22no—
313D4×C31—22no—
314D4×C31—48no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—41no—
319D4×C31—84no—
320D4×C31#12114yes—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—84no—
355C2×C4×C31—84no—
356C2×C4×C31—84no—
357C2×C4×C31AGL(1,ℤ/8)12yes—
358C2×C4×C31C22×D411yescharacteristic
359C2×C4×C31C22×D411yescharacteristic
360C2×C4×C31C2×#4111yescharacteristic
361C2×C4×C31C2×#4111yescharacteristic
362C2×C4×C31H(5,𝔽2)11yescharacteristic
363C2×C4×C31H(5,𝔽2)11yescharacteristic
364C8×C31—22no—
365C8×C31—22no—
366C8×C31—41no—
367C8×C31—41no—
368C2×#463C2×C3111yescharacteristic, complemented
369C2×#450C2×C3111yescharacteristic, complemented
370C2×#447C2×C3111yescharacteristic
371C2×C4×D8C2×C3111yescharacteristic, complemented
372#2427C2×C3111yescharacteristic, complemented
373D4×C22⋊C4C2×C3111yescharacteristic, complemented
374#2067C2×C3111yescharacteristic, complemented
375#2036C2×C3111yescharacteristic, complemented
376#2034C2×C3111yescharacteristic, complemented
377#2012C2×C3111yescharacteristic, complemented
378#1968C2×C3111yescharacteristic, complemented
379#1923C2×C3111yescharacteristic, complemented
380#1879C2×C3111yescharacteristic, complemented
381#1877C2×C3111yescharacteristic, complemented
382#1864C2×C3111yescharacteristic, complemented
383C22×C31—22no—
384C22×C31—24no—
385C22×C31—22no—
386C22×C31—22no—
387C22×C31—42no—
388C22×C31—41no—
389C22×C31—42no—
390C22×C31—41no—
391C22×C31—42no—
392C22×C31—41no—
393C22×C31—42no—
394C22×C31—41no—
395C22×C31—42no—
396C22×C31—42no—
397C22×C31—42no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—816no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31#52511yescharacteristic
413C22×C31D4211yescharacteristic
414C22×C31D4211yescharacteristic
415C22×C31C2×#13511yescharacteristic
416C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C31#57611yescharacteristic
418C22×C31#57711yescharacteristic
419C4×C31—22no—
420C4×C31—41no—
421C4×C31—42no—
422C4×C31—41no—
423C4×C31—41no—
424C4×C31—41no—
425C4×C31—81no—
426C4×C31—81no—
427C4×C31—81no—
428C4×C31—81no—
429C4×C31C2×#12111yescharacteristic
430C4×C31#53811yescharacteristic
431C4×C31#54611yescharacteristic
432C4×C31#54611yescharacteristic
433C23×D4C22×C3111yescharacteristic
434C22×SD16C22×C3111yescharacteristic
435C22×SD16C22×C3111yescharacteristic
436C22×D8C22×C3111yescharacteristic
437C22×D8C22×C3111yescharacteristic
438C2×#124C22×C3111yescharacteristic, complemented
439C2×C22⋊Q8C22×C3111yescharacteristic
440C2×#121C22×C3111yescharacteristic
441C2×C4×D4C22×C3111yescharacteristic
442C2×C4×D4C22×C3111yescharacteristic
443C2×C4×D4C22×C3111yescharacteristic, complemented
444C22×C22⋊C4—21no—
445#463—24no—
446#450—24no—
447#447—24no—
448C4×D8—24no—
449C2×#107C22×C3111yescharacteristic, complemented
450C2×#106C22×C3111yescharacteristic, complemented
451C2×C4⋊C8C22×C3111yescharacteristic, complemented
452C2×#103C22×C3111yescharacteristic, complemented
453C2×#103C22×C3111yescharacteristic, complemented
454C2×#102C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×#102C22×C3111yescharacteristic, complemented
459C2×#102C22×C3111yescharacteristic, complemented
460C2×C22⋊C8C22×C3111yescharacteristic
461C2×C22⋊C8C22×C3111yescharacteristic
462C2×C4×C8C22×C3111yescharacteristic, complemented
463#397—21no—
464#394—21no—
465#391C22×C3111yescharacteristic, complemented
466#390C22×C3111yescharacteristic
467#390C22×C3111yescharacteristic
468#389C22×C3111yescharacteristic, complemented
469#386—21no—
470#386—21no—
471#386—21no—
472#380—21no—
473#380C22×C3111yescharacteristic
474#379—21no—
475C4×C22⋊C4C22×C3111yescharacteristic
476#340C22×C3111yescharacteristic, complemented
477#340C22×C3111yescharacteristic, complemented
478#336C22×C3111yescharacteristic, complemented
479#336C22×C3111yescharacteristic, complemented
480C2×C31—42no—
481C2×C31—44no—
482C2×C31—82no—
483C2×C31—82no—
484C2×C31#242411yescharacteristic
485C2×C31#310511yescharacteristic
486C2×C31#311811yescharacteristic
487C2×C31#326411yescharacteristic
488C2×C31#327211yescharacteristic
489C2×C31#328011yescharacteristic
490C2×C31#328211yescharacteristic
491C25—21no—
492C22×Q8C23×C3111yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C3111yescharacteristic
502C22×D4C23×C3111yescharacteristic
503C22×D4C23×C3111yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C3111yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8D4×C3114yes—
520C22×C8C23×C3111yescharacteristic
521C22×C8C23×C3111yescharacteristic
522C22×C8C23×C3111yescharacteristic
523C22×C8C23×C3111yescharacteristic
524#124—22no—
525#124—41no—
526C22⋊Q8—22no—
527C22⋊Q8—41no—
528#121—22no—
529#121—41no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—41no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C4⋊C4C23×C3111yescharacteristic
541C2×C4⋊C4C23×C3111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—44no—
555C2×C22⋊C4D4×C3111yescharacteristic
556C2×C22⋊C4D4×C3111yescharacteristic
557C2×C42C23×C3111yescharacteristic
558C2×C42C23×C3111yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C3114yescomplemented
570C22⋊C8—22no—
571C22⋊C8—22no—
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95D4×C3111yescharacteristic
578#95D4×C3111yescharacteristic
579C31#2516011yescharacteristic, direct product factor, Sylow
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C3111yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C3112yes—
621C2×D4C2×D4×C3112yes—
622C2×D4C2×D4×C3112yes—
623C2×D4#41×C3112yes—
624C2×D4#41×C3112yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C3111yescharacteristic
646C22×C4C2×D4×C3111yescharacteristic
647C22×C4C2×D4×C3111yescharacteristic
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3111yescharacteristic
650C22×C4C24×C3111yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C3112yes—
666C2×C8C2×D4×C3112yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C3112yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23C31×#13512yes—
730C23C22×D4×C3111yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4C31×#12114yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C31×AGL(1,ℤ/8)12yes—
786C2×C4C22×D4×C3111yescharacteristic
787C2×C4C22×D4×C3111yescharacteristic
788C2×C4C2×#41×C3111yescharacteristic
789C2×C4C2×#41×C3111yescharacteristic
790C2×C4C31×H(5,𝔽2)11yescharacteristic
791C2×C4C31×H(5,𝔽2)11yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—24no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C31×#52511yescharacteristic
826C22D42×C3111yescharacteristic
827C22D42×C3111yescharacteristic
828C22C2×C31×#13511yescharacteristic
829C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
830C22C31×#57611yescharacteristic
831C22C31×#57711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×C31×#12111yescharacteristic
843C4C31×#53811yescharacteristic
844C4C31×#54611yescharacteristic
845C4C31×#54611yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2C31×#242411yescharacteristic
851C2C31×#310511yescharacteristic
852C2C31×#311811yescharacteristic
853C2C31×#326411yescharacteristic
854C2C31×#327211yescharacteristic
855C2C31×#328011yescharacteristic
856C2C31×#328211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#463C2semidirect
2. C2×C31×#450C2semidirect
4. C2×C4×D8×C31C2semidirect
5. C31×#2427C2semidirect
6. D4×C22⋊C4×C31C2semidirect
7. C31×#2067C2semidirect
8. C31×#2036C2semidirect
9. C31×#2034C2semidirect
10. C31×#2012C2semidirect
11. C31×#1968C2semidirect
12. C31×#1923C2semidirect
13. C31×#1879C2semidirect
14. C31×#1877C2semidirect
15. C31×#1864C2semidirect
21. C2×C31×#124C22semidirect
26. C2×C4×D4×C31C22semidirect
32. C2×C31×#107C22semidirect
33. C2×C31×#106C22semidirect
34. C2×C31×C4⋊C8C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
45. C2×C4×C8×C31C22semidirect
48. C31×#391C22semidirect
51. C31×#389C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
141. C31×#102D4semidirect
266. #25160C31direct (N × H)
368. C2×#463C2×C31semidirect
369. C2×#450C2×C31semidirect
371. C2×C4×D8C2×C31semidirect
372. #2427C2×C31semidirect
373. D4×C22⋊C4C2×C31semidirect
374. #2067C2×C31semidirect
375. #2036C2×C31semidirect
376. #2034C2×C31semidirect
377. #2012C2×C31semidirect
378. #1968C2×C31semidirect
379. #1923C2×C31semidirect
380. #1879C2×C31semidirect
381. #1877C2×C31semidirect
382. #1864C2×C31semidirect
438. C2×#124C22×C31semidirect
443. C2×C4×D4C22×C31semidirect
449. C2×#107C22×C31semidirect
450. C2×#106C22×C31semidirect
451. C2×C4⋊C8C22×C31semidirect
452. C2×#103C22×C31semidirect
453. C2×#103C22×C31semidirect
458. C2×#102C22×C31semidirect
459. C2×#102C22×C31semidirect
462. C2×C4×C8C22×C31semidirect
465. #391C22×C31semidirect
468. #389C22×C31semidirect
476. #340C22×C31semidirect
477. #340C22×C31semidirect
478. #336C22×C31semidirect
479. #336C22×C31semidirect
569. #102D4×C31semidirect
579. C31#25160direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C2×C31×#4502
C2×C31×#4472
C2×C4×D8×C312
C31×#24272
D4×C22⋊C4×C312
C31×#20672
C31×#20362
C31×#20342
C31×#20122
C31×#19682
C31×#19232
C31×#18792
C31×#18772
C31×#18642
#2516031