Finite Group Databasebeta

← C31×#25164 #21481923

Subgroups — C31×#25164 #21481923

Order 7936.

1296 conjugacy classes of subgroups.

The subgroup lattice has 856 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×C31×#440C211yesmaximal, characteristic, complemented
5C31×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#1972C211yesmaximal, characteristic, complemented
12C31×#1924C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1879C211yesmaximal, 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×Q8×C31C2211yescharacteristic, complemented
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C22×C22⋊C4×C31—21no—
28C31×#463—24no—
29C31×#450—24no—
30C31×#447—24no—
31C31×#440—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×C31×#97C2211yescharacteristic, complemented
46C31×#396—21no—
47C31×#394—21no—
48C31×#390—21no—
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic, complemented
52C31×#389C2211yescharacteristic, complemented
53C31×#388—21no—
54C31×#386—21no—
55C31×#386—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×C31C2311yescharacteristic
79C2×SD16×C31—22no—
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—41no—
84C2×SD16×C31D414yescomplemented
85C2×D8×C31—22no—
86C2×D8×C31—22no—
87C2×D8×C31—22no—
88C2×D8×C31—22no—
89C2×D8×C31—22no—
90C2×D8×C31—41no—
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C31×#124—22no—
96C31×#124—41no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—41no—
99C31×#121—22no—
100C31×#121—41no—
101C4×Q8×C31—22no—
102C4×Q8×C31—41no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—41no—
106C4×D4×C31—41no—
107C2×C4⋊C4×C31—21no—
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—21no—
127C2×C22⋊C4×C31—44no—
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C42×C31—21no—
131C2×C42×C31C2311yescharacteristic
132C2×C42×C31C2311yescharacteristic
133C31×#107—22no—
134C31×#106—41no—
135C31×C4⋊C8—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×#102D414yes—
144C31×C22⋊C8—22no—
145C31×C22⋊C8—22no—
146C31×#97—22no—
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×C31C2×D412yes—
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—21no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C2×D4×C31—44no—
189C2×D4×C31—44no—
190C2×D4×C31—42no—
191C2×D4×C31—81no—
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—81no—
212C22×C4×C31—81no—
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2411yescharacteristic
219SD16×C31—28no—
220SD16×C31—44no—
221D8×C31—44no—
222D8×C31—44no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
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×C31C2×D412yes—
234C2×C8×C31C2×D412yes—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—42no—
243C4⋊C4×C31—42no—
244C4⋊C4×C31—81no—
245C4⋊C4×C31C2×D412yes—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—41no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
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—81no—
259C22⋊C4×C31—81no—
260C22⋊C4×C31—81no—
261C42×C31—21no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—42no—
266#25164C3111yesmaximal, 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—48no—
278C23×C31—48no—
279C23×C31—41no—
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×C31AGL(1,ℤ/8)12yes—
302C23×C31C22×D411yescharacteristic
303Q8×C31—22no—
304Q8×C31—22no—
305Q8×C31—41no—
306Q8×C31—41no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—22no—
311D4×C31—22no—
312D4×C31—48no—
313D4×C31—41no—
314D4×C31—41no—
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—22no—
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—21no—
337C2×C4×C31—21no—
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—41no—
355C2×C4×C31—84no—
356C2×C4×C31—84no—
357C2×C4×C31C22×D411yescharacteristic
358C2×C4×C31C22×D411yescharacteristic
359C2×C4×C31C2×#4111yescharacteristic
360C2×C4×C31C2×#4111yescharacteristic
361C2×C4×C31H(5,𝔽2)11yescharacteristic
362C2×C4×C31H(5,𝔽2)11yescharacteristic
363C8×C31—22no—
364C8×C31—22no—
365C8×C31—41no—
366C8×C31—41no—
367C2×#463C2×C3111yescharacteristic, complemented
368C2×#450C2×C3111yescharacteristic, complemented
369C2×#447C2×C3111yescharacteristic
370C2×#440C2×C3111yescharacteristic, complemented
371#2426C2×C3111yescharacteristic, complemented
372D4×C22⋊C4C2×C3111yescharacteristic, complemented
373#2067C2×C3111yescharacteristic, complemented
374#2035C2×C3111yescharacteristic, complemented
375#2033C2×C3111yescharacteristic, complemented
376#2012C2×C3111yescharacteristic, complemented
377#1972C2×C3111yescharacteristic, complemented
378#1924C2×C3111yescharacteristic, complemented
379#1880C2×C3111yescharacteristic, complemented
380#1879C2×C3111yescharacteristic, complemented
381#1864C2×C3111yescharacteristic, complemented
382C22×C31—22no—
383C22×C31—24no—
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—42no—
387C22×C31—41no—
388C22×C31—42no—
389C22×C31—41no—
390C22×C31—42no—
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—816no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31#52511yescharacteristic
412C22×C31D4211yescharacteristic
413C22×C31D4211yescharacteristic
414C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C31#57511yescharacteristic
416C22×C31#57611yescharacteristic
417C22×C31#57711yescharacteristic
418C4×C31—41no—
419C4×C31—42no—
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×C31C2×#12111yescharacteristic
429C4×C31#53811yescharacteristic
430C4×C31#54611yescharacteristic
431C4×C31#54611yescharacteristic
432C23×D4C22×C3111yescharacteristic
433C22×SD16C22×C3111yescharacteristic
434C22×SD16C22×C3111yescharacteristic
435C22×D8C22×C3111yescharacteristic
436C22×D8C22×C3111yescharacteristic
437C2×#124C22×C3111yescharacteristic, complemented
438C2×C22⋊Q8C22×C3111yescharacteristic
439C2×#121C22×C3111yescharacteristic
440C2×C4×Q8C22×C3111yescharacteristic, complemented
441C2×C4×D4C22×C3111yescharacteristic
442C2×C4×D4C22×C3111yescharacteristic
443C22×C22⋊C4—21no—
444#463—24no—
445#450—24no—
446#447—24no—
447#440—24no—
448C2×#107C22×C3111yescharacteristic, complemented
449C2×#106C22×C3111yescharacteristic, complemented
450C2×C4⋊C8C22×C3111yescharacteristic, complemented
451C2×#103C22×C3111yescharacteristic, complemented
452C2×#103C22×C3111yescharacteristic, complemented
453C2×#102C22×C3111yescharacteristic
454C2×#102C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic, complemented
458C2×#102C22×C3111yescharacteristic, complemented
459C2×C22⋊C8C22×C3111yescharacteristic
460C2×C22⋊C8C22×C3111yescharacteristic
461C2×#97C22×C3111yescharacteristic, complemented
462#396—21no—
463#394—21no—
464#390—21no—
465#390C22×C3111yescharacteristic
466#390C22×C3111yescharacteristic
467#390C22×C3111yescharacteristic, complemented
468#389C22×C3111yescharacteristic, complemented
469#388—21no—
470#386—21no—
471#386—21no—
472#380C22×C3111yescharacteristic
473#379—21no—
474C4×C22⋊C4C22×C3111yescharacteristic
475#340C22×C3111yescharacteristic, complemented
476#340C22×C3111yescharacteristic, complemented
477#336C22×C3111yescharacteristic, complemented
478#336C22×C3111yescharacteristic, complemented
479C2×C31—42no—
480C2×C31—44no—
481C2×C31—82no—
482C2×C31—161no—
483C2×C31#242411yescharacteristic
484C2×C31#311411yescharacteristic
485C2×C31#311811yescharacteristic
486C2×C31#326411yescharacteristic
487C2×C31#326511yescharacteristic
488C2×C31#326811yescharacteristic
489C2×C31#327511yescharacteristic
490C25—21no—
491C22×Q8C23×C3111yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C3111yescharacteristic
501C22×D4C23×C3111yescharacteristic
502C22×D4C23×C3111yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C3111yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16D4×C3114yescomplemented
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—41no—
518C22×C8C23×C3111yescharacteristic
519C22×C8C23×C3111yescharacteristic
520C22×C8C23×C3111yescharacteristic
521C22×C8C23×C3111yescharacteristic
522#124—22no—
523#124—41no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—41no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—41no—
533C4×D4—41no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4C23×C3111yescharacteristic
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C4⋊C4C23×C3111yescharacteristic
541C2×C22⋊C4—21no—
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×C42—21no—
558C2×C42C23×C3111yescharacteristic
559C2×C42C23×C3111yescharacteristic
560#107—22no—
561#106—41no—
562C4⋊C8—22no—
563#103—22no—
564#103—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—41no—
570#102D4×C3114yes—
571C22⋊C8—22no—
572C22⋊C8—22no—
573#97—22no—
574#95—21no—
575#95—21no—
576#95D4×C3111yescharacteristic
577#95D4×C3111yescharacteristic
578C31#2516411yescharacteristic, direct product factor, Sylow
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C3111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C3112yes—
596C2×D4—24no—
597C2×D4—21no—
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—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C3112yes—
621C2×D4C2×D4×C3112yes—
622C2×D4#41×C3112yes—
623C2×D4#41×C3112yes—
624C22×C4—21no—
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—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3111yescharacteristic
645C22×C4C2×D4×C3111yescharacteristic
646C22×C4C24×C3111yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C3112yes—
662C2×C8C2×D4×C3112yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C3112yes—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
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—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23C31×AGL(1,ℤ/8)12yes—
729C23C22×D4×C3111yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4C31×#12114yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
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—21no—
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×C4C22×D4×C3111yescharacteristic
785C2×C4C22×D4×C3111yescharacteristic
786C2×C4C2×#41×C3111yescharacteristic
787C2×C4C2×#41×C3111yescharacteristic
788C2×C4C31×H(5,𝔽2)11yescharacteristic
789C2×C4C31×H(5,𝔽2)11yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22C31×#52511yescharacteristic
824C22D42×C3111yescharacteristic
825C22D42×C3111yescharacteristic
826C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
827C22C31×#57511yescharacteristic
828C22C31×#57611yescharacteristic
829C22C31×#57711yescharacteristic
830C4—41no—
831C4—42no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×C31×#12111yescharacteristic
841C4C31×#53811yescharacteristic
842C4C31×#54611yescharacteristic
843C4C31×#54611yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C31×#242411yescharacteristic
849C2C31×#311411yescharacteristic
850C2C31×#311811yescharacteristic
851C2C31×#326411yescharacteristic
852C2C31×#326511yescharacteristic
853C2C31×#326811yescharacteristic
854C2C31×#327511yescharacteristic
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×C31×#440C2semidirect
5. C31×#2426C2semidirect
6. D4×C22⋊C4×C31C2semidirect
7. C31×#2067C2semidirect
8. C31×#2035C2semidirect
9. C31×#2033C2semidirect
10. C31×#2012C2semidirect
11. C31×#1972C2semidirect
12. C31×#1924C2semidirect
13. C31×#1880C2semidirect
14. C31×#1879C2semidirect
15. C31×#1864C2semidirect
21. C2×C31×#124C22semidirect
24. C2×C4×Q8×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×C31×#97C22semidirect
51. C31×#390C22semidirect
52. C31×#389C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
84. C2×SD16×C31D4semidirect
266. #25164C31direct (N × H)
367. C2×#463C2×C31semidirect
368. C2×#450C2×C31semidirect
370. C2×#440C2×C31semidirect
371. #2426C2×C31semidirect
372. D4×C22⋊C4C2×C31semidirect
373. #2067C2×C31semidirect
374. #2035C2×C31semidirect
375. #2033C2×C31semidirect
376. #2012C2×C31semidirect
377. #1972C2×C31semidirect
378. #1924C2×C31semidirect
379. #1880C2×C31semidirect
380. #1879C2×C31semidirect
381. #1864C2×C31semidirect
437. C2×#124C22×C31semidirect
440. C2×C4×Q8C22×C31semidirect
448. C2×#107C22×C31semidirect
449. C2×#106C22×C31semidirect
450. C2×C4⋊C8C22×C31semidirect
451. C2×#103C22×C31semidirect
452. C2×#103C22×C31semidirect
457. C2×#102C22×C31semidirect
458. C2×#102C22×C31semidirect
461. C2×#97C22×C31semidirect
467. #390C22×C31semidirect
468. #389C22×C31semidirect
475. #340C22×C31semidirect
476. #340C22×C31semidirect
477. #336C22×C31semidirect
478. #336C22×C31semidirect
511. C2×SD16D4×C31semidirect
578. C31#25164direct (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×C31×#4402
C31×#24262
D4×C22⋊C4×C312
C31×#20672
C31×#20352
C31×#20332
C31×#20122
C31×#19722
C31×#19242
C31×#18802
C31×#18792
C31×#18642
#2516431