Finite Group Databasebeta

← C31×#24037 #21480796

Subgroups — C31×#24037 #21480796

Order 7936.

1462 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#416C211yesmaximal, characteristic, complemented
4C31×#2485C211yesmaximal, characteristic, complemented
5C31×#2042C211yesmaximal, characteristic, complemented
6C31×#2042C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#1893C211yesmaximal, characteristic, complemented
10C31×#1869C211yesmaximal, characteristic, complemented
11C31×#1864C211yesmaximal, characteristic, complemented
12C31×#1862C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×C8×C31C2211yescharacteristic, complemented
19C31×#546—24no—
20C31×#546—24no—
21C2×C31×#124C2211yescharacteristic
22C2×C31×#123—21no—
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121—21no—
25C2×C31×#121C2211yescharacteristic
26C2×C31×#120—21no—
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic, complemented
30C22×C22⋊C4×C31—21no—
31C31×#482—24no—
32C2×C31×#107C2211yescharacteristic, complemented
33C2×C31×#106C2211yescharacteristic, complemented
34C31×#416—24no—
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
37C2×C31×#103C2211yescharacteristic, complemented
38C2×C31×#103C2211yescharacteristic, complemented
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic, complemented
50C31×#397—21no—
51C31×#394—21no—
52C31×#389C2211yescharacteristic, complemented
53C31×#389C2211yescharacteristic, complemented
54C31×#388—21no—
55C31×#387—21no—
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C2×#41×C31D414yes—
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—21no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31D411yescharacteristic
81C22×D4×C31C2311yescharacteristic
82C22×D4×C31C2311yescharacteristic
83C23×C4×C31—21no—
84C23×C4×C31—21no—
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C22×C8×C31—22no—
88C22×C8×C31—41no—
89C22×C8×C31—41no—
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C31×#124—22no—
95C31×#124—22no—
96C31×#123—28no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×#121—28no—
100C31×#121—22no—
101C31×#121D414yes—
102C31×#120—28no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C31×#117—22no—
108C31×#117—22no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31D411yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—28no—
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—21no—
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C42×C31—21no—
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×#106—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#103—41no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—41no—
145C31×#102—41no—
146C31×C22⋊C8—22no—
147C31×C22⋊C8—41no—
148C31×C22⋊C8—41no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—24no—
156C24×C31—21no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—42no—
160C24×C31—42no—
161C24×C31—81no—
162C24×C31—81no—
163C24×C31C2×D411yescharacteristic
164C24×C31C2×D411yescharacteristic
165#41×C31—28no—
166#41×C31—44no—
167#41×C31—44no—
168#41×C31—44no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31C2×D412yes—
175C2×D4×C31—24no—
176C2×D4×C31—22no—
177C2×D4×C31—24no—
178C2×D4×C31—22no—
179C2×D4×C31—24no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—41no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—44no—
192C2×D4×C31—44no—
193C2×D4×C31—44no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—44no—
197C2×D4×C31—81no—
198C2×D4×C31—81no—
199C2×D4×C31C2×D412yes—
200C2×D4×C31C2×D412yes—
201C2×D4×C31#4112yes—
202C2×D4×C31#4112yes—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—24no—
210C22×C4×C31—24no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—81no—
224C22×C4×C31—81no—
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D412yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2411yescharacteristic
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—44no—
245C4⋊C4×C31—24no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—42no—
257C4⋊C4×C31—81no—
258C4⋊C4×C31C2×D412yes—
259C22⋊C4×C31—24no—
260C22⋊C4×C31—24no—
261C22⋊C4×C31—24no—
262C22⋊C4×C31—24no—
263C22⋊C4×C31—22no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—24no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—81no—
269C22⋊C4×C31—81no—
270C42×C31—21no—
271C42×C31—21no—
272C42×C31—42no—
273#24037C3111yesmaximal, characteristic, direct product factor, Sylow
274C23×C31—21no—
275C23×C31—22no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—22no—
290C23×C31—48no—
291C23×C31—48no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—84no—
303C23×C31—84no—
304C23×C31—84no—
305C23×C31—84no—
306C23×C31—84no—
307C23×C31#12012yes—
308C23×C31#13512yes—
309C23×C31C22×D411yescharacteristic
310Q8×C31—22no—
311Q8×C31—22no—
312Q8×C31—41no—
313Q8×C31—41no—
314D4×C31—22no—
315D4×C31—22no—
316D4×C31—22no—
317D4×C31—22no—
318D4×C31—22no—
319D4×C31—44no—
320D4×C31—48no—
321D4×C31—48no—
322D4×C31—41no—
323D4×C31—41no—
324D4×C31—84no—
325D4×C31#12314yes—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—48no—
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—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—84no—
365C2×C4×C31#12012yes—
366C2×C4×C31C22×D411yescharacteristic
367C2×C4×C31C22×D411yescharacteristic
368C2×C4×C31C2×#4111yescharacteristic
369C2×C4×C31C2×#4111yescharacteristic
370C2×C4×C31H(5,𝔽2)11yescharacteristic
371C2×C4×C31H(5,𝔽2)11yescharacteristic
372C8×C31—41no—
373C8×C31—41no—
374C8×C31—41no—
375C8×C31—41no—
376C2×#546C2×C3111yescharacteristic
377C2×#482C2×C3111yescharacteristic, complemented
378C2×#416C2×C3111yescharacteristic, complemented
379#2485C2×C3111yescharacteristic, complemented
380#2042C2×C3111yescharacteristic, complemented
381#2042C2×C3111yescharacteristic, complemented
382#2036C2×C3111yescharacteristic, complemented
383#2035C2×C3111yescharacteristic, complemented
384#1893C2×C3111yescharacteristic, complemented
385#1869C2×C3111yescharacteristic, complemented
386#1864C2×C3111yescharacteristic, complemented
387#1862C2×C3111yescharacteristic, complemented
388#1788C2×C3111yescharacteristic, complemented
389#1786C2×C3111yescharacteristic, complemented
390#1786C2×C3111yescharacteristic, complemented
391C22×C31—22no—
392C22×C31—24no—
393C22×C31—22no—
394C22×C31—22no—
395C22×C31—22no—
396C22×C31—22no—
397C22×C31—22no—
398C22×C31—41no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—41no—
402C22×C31—41no—
403C22×C31—42no—
404C22×C31—41no—
405C22×C31—42no—
406C22×C31—41no—
407C22×C31—41no—
408C22×C31—42no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—816no—
416C22×C31—81no—
417C22×C31—81no—
418C22×C31—81no—
419C22×C31—81no—
420C22×C31C2×#12011yescharacteristic
421C22×C31#54611yescharacteristic
422C22×C31#54611yescharacteristic
423C22×C31C2×#13511yescharacteristic
424C22×C31#57511yescharacteristic
425C22×C31#57611yescharacteristic
426C22×C31#57711yescharacteristic
427C4×C31—22no—
428C4×C31—41no—
429C4×C31—42no—
430C4×C31—41no—
431C4×C31—41no—
432C4×C31—42no—
433C4×C31—81no—
434C4×C31—81no—
435C4×C31—81no—
436C4×C31—81no—
437C4×C31C2×#12311yescharacteristic
438C4×C31#53411yescharacteristic
439C4×C31#54611yescharacteristic
440C4×C31#54611yescharacteristic
441C22×#41C22×C3111yescharacteristic
442C23×D4C22×C3111yescharacteristic
443C23×C8C22×C3111yescharacteristic, complemented
444#546—24no—
445#546—24no—
446C2×#124C22×C3111yescharacteristic
447C2×#123—21no—
448C2×C22⋊Q8C22×C3111yescharacteristic
449C2×#121—21no—
450C2×#121C22×C3111yescharacteristic
451C2×#120—21no—
452C2×C4×D4C22×C3111yescharacteristic
453C2×C4×D4C22×C3111yescharacteristic
454C2×#117C22×C3111yescharacteristic, complemented
455C22×C22⋊C4—21no—
456#482—24no—
457C2×#107C22×C3111yescharacteristic, complemented
458C2×#106C22×C3111yescharacteristic, complemented
459#416—24no—
460C2×#103C22×C3111yescharacteristic, complemented
461C2×#103C22×C3111yescharacteristic, complemented
462C2×#103C22×C3111yescharacteristic, complemented
463C2×#103C22×C3111yescharacteristic, complemented
464C2×#102C22×C3111yescharacteristic
465C2×#102C22×C3111yescharacteristic
466C2×#102C22×C3111yescharacteristic
467C2×#102C22×C3111yescharacteristic
468C2×#102C22×C3111yescharacteristic
469C2×#102C22×C3111yescharacteristic
470C2×#102C22×C3111yescharacteristic
471C2×#102C22×C3111yescharacteristic
472C2×C22⋊C8C22×C3111yescharacteristic
473C2×C22⋊C8C22×C3111yescharacteristic
474C2×C22⋊C8C22×C3111yescharacteristic, complemented
475#397—21no—
476#394—21no—
477#389C22×C3111yescharacteristic, complemented
478#389C22×C3111yescharacteristic, complemented
479#388—21no—
480#387—21no—
481#380C22×C3111yescharacteristic
482#380C22×C3111yescharacteristic
483#380C22×C3111yescharacteristic, complemented
484#340C22×C3111yescharacteristic, complemented
485#340C22×C3111yescharacteristic, complemented
486#336C22×C3111yescharacteristic, complemented
487#336C22×C3111yescharacteristic, complemented
488C2×C31—42no—
489C2×C31—42no—
490C2×C31—44no—
491C2×C31—82no—
492C2×C31#240511yescharacteristic
493C2×C31#300211yescharacteristic
494C2×C31#301211yescharacteristic
495C2×C31#329611yescharacteristic
496C2×C31#329711yescharacteristic
497C2×C31#331111yescharacteristic
498C2×C31#331911yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41D4×C3114yes—
506C22×Q8C23×C3111yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C3111yescharacteristic
517C22×D4C23×C3111yescharacteristic
518C22×D4C23×C3111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C3111yescharacteristic
522C23×C4C23×C3111yescharacteristic
523C22×C8—22no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8C23×C3111yescharacteristic
527C22×C8C23×C3111yescharacteristic
528C22×C8C23×C3111yescharacteristic
529C22×C8C23×C3111yescharacteristic
530#124—22no—
531#124—22no—
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535#121—28no—
536#121—22no—
537#121D4×C3114yes—
538#120—28no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543#117—22no—
544#117—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4D4×C3111yescharacteristic
549C2×C4⋊C4C23×C3111yescharacteristic
550C2×C4⋊C4C23×C3111yescharacteristic
551C2×C4⋊C4C23×C3111yescharacteristic
552C2×C4⋊C4C23×C3111yescharacteristic
553C2×C4⋊C4C23×C3111yescharacteristic
554C2×C22⋊C4—28no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4D4×C3111yescharacteristic
565C2×C22⋊C4D4×C3111yescharacteristic
566C2×C42—21no—
567C2×C42C23×C3111yescharacteristic
568#107—22no—
569#106—22no—
570#103—22no—
571#103—22no—
572#103—41no—
573#103—41no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—41no—
581#102—41no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C31#2403711yescharacteristic, direct product factor, Sylow
591C24—21no—
592C24—24no—
593C24—21no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C3111yescharacteristic
601C24C2×D4×C3111yescharacteristic
602#41—28no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C3112yes—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—41no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C3112yes—
637C2×D4C2×D4×C3112yes—
638C2×D4#41×C3112yes—
639C2×D4#41×C3112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C3111yescharacteristic
663C22×C4C2×D4×C3111yescharacteristic
664C22×C4C2×D4×C3111yescharacteristic
665C22×C4C2×D4×C3111yescharacteristic
666C22×C4C2×D4×C3112yes—
667C22×C4C2×D4×C3112yes—
668C22×C4C24×C3111yescharacteristic
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—44no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C3112yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—24no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—21no—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—48no—
727C23—48no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23C31×#12012yes—
744C23C31×#13512yes—
745C23C22×D4×C3111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—44no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4C31×#12314yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4C31×#12012yes—
802C2×C4C22×D4×C3111yescharacteristic
803C2×C4C22×D4×C3111yescharacteristic
804C2×C4C2×#41×C3111yescharacteristic
805C2×C4C2×#41×C3111yescharacteristic
806C2×C4C31×H(5,𝔽2)11yescharacteristic
807C2×C4C31×H(5,𝔽2)11yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×C31×#12011yescharacteristic
842C22C31×#54611yescharacteristic
843C22C31×#54611yescharacteristic
844C22C2×C31×#13511yescharacteristic
845C22C31×#57511yescharacteristic
846C22C31×#57611yescharacteristic
847C22C31×#57711yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×C31×#12311yescharacteristic
859C4C31×#53411yescharacteristic
860C4C31×#54611yescharacteristic
861C4C31×#54611yescharacteristic
862C2—42no—
863C2—42no—
864C2—44no—
865C2—82no—
866C2C31×#240511yescharacteristic
867C2C31×#300211yescharacteristic
868C2C31×#301211yescharacteristic
869C2C31×#329611yescharacteristic
870C2C31×#329711yescharacteristic
871C2C31×#331111yescharacteristic
872C2C31×#331911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#546C2
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×#416C2semidirect
4. C31×#2485C2semidirect
5. C31×#2042C2semidirect
6. C31×#2042C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
9. C31×#1893C2semidirect
10. C31×#1869C2semidirect
11. C31×#1864C2semidirect
12. C31×#1862C2semidirect
13. C31×#1788C2semidirect
14. C31×#1786C2semidirect
15. C31×#1786C2semidirect
18. C23×C8×C31C22semidirect
29. C2×C31×#117C22semidirect
32. C2×C31×#107C22semidirect
33. C2×C31×#106C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
37. C2×C31×#103C22semidirect
38. C2×C31×#103C22semidirect
49. C2×C31×C22⋊C8C22semidirect
52. C31×#389C22semidirect
53. C31×#389C22semidirect
58. C31×#380C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
273. #24037C31direct (N × H)
377. C2×#482C2×C31semidirect
378. C2×#416C2×C31semidirect
379. #2485C2×C31semidirect
380. #2042C2×C31semidirect
381. #2042C2×C31semidirect
382. #2036C2×C31semidirect
383. #2035C2×C31semidirect
384. #1893C2×C31semidirect
385. #1869C2×C31semidirect
386. #1864C2×C31semidirect
387. #1862C2×C31semidirect
388. #1788C2×C31semidirect
389. #1786C2×C31semidirect
390. #1786C2×C31semidirect
443. C23×C8C22×C31semidirect
454. C2×#117C22×C31semidirect
457. C2×#107C22×C31semidirect
458. C2×#106C22×C31semidirect
460. C2×#103C22×C31semidirect
461. C2×#103C22×C31semidirect
462. C2×#103C22×C31semidirect
463. C2×#103C22×C31semidirect
474. C2×C22⋊C8C22×C31semidirect
477. #389C22×C31semidirect
478. #389C22×C31semidirect
483. #380C22×C31semidirect
484. #340C22×C31semidirect
485. #340C22×C31semidirect
486. #336C22×C31semidirect
487. #336C22×C31semidirect
590. C31#24037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5462
C2×C31×#4822
C2×C31×#4162
C31×#24852
C31×#20422
C31×#20362
C31×#20352
C31×#18932
C31×#18692
C31×#18642
C31×#18622
C31×#17882
C31×#17862
#2403731