Finite Group Databasebeta

← C31×#25890 #21482649

Subgroups — C31×#25890 #21482649

Order 7936.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#488C211yesmaximal, characteristic, complemented
3C2×C31×#478C211yesmaximal, characteristic, complemented
4C31×#2562C211yesmaximal, characteristic, complemented
5C31×#2036C211yesmaximal, characteristic, complemented
6C31×#2035C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1983C211yesmaximal, characteristic, complemented
10C31×#1954C211yesmaximal, characteristic, complemented
11C31×#1788C211yesmaximal, characteristic, complemented
12C31×#1788C211yesmaximal, characteristic, complemented
13C31×#1786C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C31×#546—24no—
19C31×#546—24no—
20C2×C31×#125C2211yescharacteristic, complemented
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
29C22×C22⋊C4×C31—21no—
30C31×#488—24no—
31C31×#478—24no—
32C2×C31×#107C2211yescharacteristic, complemented
33C2×C31×#106C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
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
50C2×C31×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C8×C31C2211yescharacteristic, complemented
52C31×#400—21no—
53C31×#394—21no—
54C31×#388—21no—
55C31×#388—21no—
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic, complemented
59C31×#380C2211yescharacteristic, complemented
60C4×C4⋊C4×C31C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C25×C31—21no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
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×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C31×#125—22no—
92C31×#125—22no—
93C31×#124—22no—
94C31×#124D414yes—
95C31×#123—28no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×#121—28no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#120—28no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31D414yes—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C22⋊C4×C31—28no—
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×C31D411yescharacteristic
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C42×C31—21no—
128C2×C42×C31C2311yescharacteristic
129C31×#107—22no—
130C31×#106—22no—
131C31×C4⋊C8—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—41no—
135C31×#103—41no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×#102—41no—
144C31×C22⋊C8—41no—
145C31×C22⋊C8—41no—
146C31×C22⋊C8—41no—
147C31×C22⋊C8—41no—
148C4×C8×C31—22no—
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—44no—
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—24no—
177C2×D4×C31—22no—
178C2×D4×C31—24no—
179C2×D4×C31—22no—
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—24no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
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—24no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—81no—
226C22×C4×C31—81no—
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
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—
244C4⋊C4×C31—24no—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—21no—
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—42no—
256C4⋊C4×C31—42no—
257C4⋊C4×C31C2×D412yes—
258C22⋊C4×C31—24no—
259C22⋊C4×C31—24no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—24no—
262C22⋊C4×C31—24no—
263C22⋊C4×C31—24no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—81no—
268C22⋊C4×C31—81no—
269C42×C31—81no—
270C42×C31C2×D412yes—
271C42×C31C2×D412yes—
272#25890C3111yesmaximal, characteristic, direct product factor, Sylow
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—22no—
278C23×C31—22no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—22no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
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#13512yes—
308C23×C31C22×D411yescharacteristic
309Q8×C31—22no—
310Q8×C31—22no—
311Q8×C31—41no—
312Q8×C31—41no—
313D4×C31—22no—
314D4×C31—22no—
315D4×C31—22no—
316D4×C31—22no—
317D4×C31—22no—
318D4×C31—44no—
319D4×C31—48no—
320D4×C31—48no—
321D4×C31—41no—
322D4×C31—41no—
323D4×C31—84no—
324D4×C31#12414yes—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—22no—
330C2×C4×C31—21no—
331C2×C4×C31—22no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—48no—
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—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—84no—
363C2×C4×C31#12012yes—
364C2×C4×C31#12012yes—
365C2×C4×C31C22×D411yescharacteristic
366C2×C4×C31C22×D411yescharacteristic
367C2×C4×C31C2×#4111yescharacteristic
368C2×C4×C31C2×#4111yescharacteristic
369C2×C4×C31H(5,𝔽2)11yescharacteristic
370C2×C4×C31H(5,𝔽2)11yescharacteristic
371C8×C31—41no—
372C8×C31—41no—
373C8×C31—41no—
374C8×C31—41no—
375C2×#546C2×C3111yescharacteristic
376C2×#488C2×C3111yescharacteristic, complemented
377C2×#478C2×C3111yescharacteristic, complemented
378#2562C2×C3111yescharacteristic, complemented
379#2036C2×C3111yescharacteristic, complemented
380#2035C2×C3111yescharacteristic, complemented
381#2034C2×C3111yescharacteristic, complemented
382#2033C2×C3111yescharacteristic, complemented
383#1983C2×C3111yescharacteristic, complemented
384#1954C2×C3111yescharacteristic, complemented
385#1788C2×C3111yescharacteristic, complemented
386#1788C2×C3111yescharacteristic, complemented
387#1786C2×C3111yescharacteristic, complemented
388#1786C2×C3111yescharacteristic, complemented
389C4×#102C2×C3111yescharacteristic, complemented
390C22×C31—24no—
391C22×C31—22no—
392C22×C31—22no—
393C22×C31—22no—
394C22×C31—41no—
395C22×C31—42no—
396C22×C31—42no—
397C22×C31—41no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—41no—
401C22×C31—42no—
402C22×C31—41no—
403C22×C31—42no—
404C22×C31—41no—
405C22×C31—42no—
406C22×C31—41no—
407C22×C31—42no—
408C22×C31—41no—
409C22×C31—42no—
410C22×C31—41no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—816no—
415C22×C31—81no—
416C22×C31—81no—
417C22×C31—81no—
418C22×C31—81no—
419C22×C31C2×#12011yescharacteristic
420C22×C31#54611yescharacteristic
421C22×C31#54611yescharacteristic
422C22×C31C2×#13511yescharacteristic
423C22×C31#57511yescharacteristic
424C22×C31#57611yescharacteristic
425C22×C31#57711yescharacteristic
426C4×C31—22no—
427C4×C31—22no—
428C4×C31—41no—
429C4×C31—41no—
430C4×C31—42no—
431C4×C31—42no—
432C4×C31—81no—
433C4×C31—81no—
434C4×C31—81no—
435C4×C31—81no—
436C4×C31C2×#12411yescharacteristic
437C4×C31#53511yescharacteristic
438C4×C31#54611yescharacteristic
439C4×C31#54611yescharacteristic
440C22×#41C22×C3111yescharacteristic
441C23×D4C22×C3111yescharacteristic
442#546—24no—
443#546—24no—
444C2×#125C22×C3111yescharacteristic, complemented
445C2×#124C22×C3111yescharacteristic
446C2×#123—21no—
447C2×C22⋊Q8C22×C3111yescharacteristic
448C2×#121—21no—
449C2×#121C22×C3111yescharacteristic
450C2×#120—21no—
451C2×C4×D4C22×C3111yescharacteristic
452C2×C4×D4C22×C3111yescharacteristic
453C22×C22⋊C4—21no—
454#488—24no—
455#478—24no—
456C2×#107C22×C3111yescharacteristic, complemented
457C2×#106C22×C3111yescharacteristic, complemented
458C2×C4⋊C8C22×C3111yescharacteristic, complemented
459C2×#103C22×C3111yescharacteristic, complemented
460C2×#103C22×C3111yescharacteristic, complemented
461C2×#103C22×C3111yescharacteristic, complemented
462C2×#103C22×C3111yescharacteristic, complemented
463C2×#102C22×C3111yescharacteristic
464C2×#102C22×C3111yescharacteristic
465C2×#102C22×C3111yescharacteristic
466C2×#102C22×C3111yescharacteristic
467C2×#102C22×C3111yescharacteristic
468C2×#102C22×C3111yescharacteristic
469C2×#102C22×C3111yescharacteristic
470C2×#102C22×C3111yescharacteristic
471C2×C22⋊C8C22×C3111yescharacteristic
472C2×C22⋊C8C22×C3111yescharacteristic
473C2×C22⋊C8C22×C3111yescharacteristic, complemented
474C2×C22⋊C8C22×C3111yescharacteristic, complemented
475C2×C4×C8C22×C3111yescharacteristic, complemented
476#400—21no—
477#394—21no—
478#388—21no—
479#388—21no—
480#380C22×C3111yescharacteristic
481#380C22×C3111yescharacteristic
482#380C22×C3111yescharacteristic, complemented
483#380C22×C3111yescharacteristic, complemented
484C4×C4⋊C4C22×C3111yescharacteristic, complemented
485#340C22×C3111yescharacteristic, complemented
486#340C22×C3111yescharacteristic, complemented
487C2×C31—42no—
488C2×C31—44no—
489C2×C31—81no—
490C2×C31—82no—
491C2×C31#243511yescharacteristic
492C2×C31#300211yescharacteristic
493C2×C31#301211yescharacteristic
494C2×C31#329611yescharacteristic
495C2×C31#329711yescharacteristic
496C2×C31#332211yescharacteristic
497C2×C31#332311yescharacteristic
498C25—21no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C22×Q8C23×C3111yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4D4×C3111yescharacteristic
516C22×D4C23×C3111yescharacteristic
517C22×D4C23×C3111yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C23×C3111yescharacteristic
521C23×C4C23×C3111yescharacteristic
522C22×C8C23×C3111yescharacteristic
523C22×C8C23×C3111yescharacteristic
524C22×C8C23×C3111yescharacteristic
525C22×C8C23×C3111yescharacteristic
526#125—22no—
527#125—22no—
528#124—22no—
529#124D4×C3114yes—
530#123—28no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533#121—28no—
534#121—22no—
535#121—22no—
536#120—28no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4D4×C3114yes—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4D4×C3111yescharacteristic
545C2×C4⋊C4C23×C3111yescharacteristic
546C2×C4⋊C4C23×C3111yescharacteristic
547C2×C4⋊C4C23×C3111yescharacteristic
548C2×C4⋊C4C23×C3111yescharacteristic
549C2×C4⋊C4C23×C3111yescharacteristic
550C2×C22⋊C4—28no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4D4×C3111yescharacteristic
561C2×C22⋊C4D4×C3111yescharacteristic
562C2×C42—21no—
563C2×C42C23×C3111yescharacteristic
564#107—22no—
565#106—22no—
566C4⋊C8—22no—
567#103—22no—
568#103—22no—
569#103—41no—
570#103—41no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C4×C8—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C31#2589011yescharacteristic, direct product factor, Sylow
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C3111yescharacteristic
600C24C2×D4×C3111yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C3112yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C3112yes—
636C2×D4C2×D4×C3112yes—
637C2×D4#41×C3112yes—
638C2×D4#41×C3112yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C3111yescharacteristic
664C22×C4C2×D4×C3111yescharacteristic
665C22×C4C2×D4×C3111yescharacteristic
666C22×C4C2×D4×C3111yescharacteristic
667C22×C4C24×C3111yescharacteristic
668C2×C8—21no—
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—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C3112yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C3112yes—
707C42C2×D4×C3112yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23C31×#13512yes—
743C23C22×D4×C3111yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4C31×#12414yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
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—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—84no—
798C2×C4C31×#12012yes—
799C2×C4C31×#12012yes—
800C2×C4C22×D4×C3111yescharacteristic
801C2×C4C22×D4×C3111yescharacteristic
802C2×C4C2×#41×C3111yescharacteristic
803C2×C4C2×#41×C3111yescharacteristic
804C2×C4C31×H(5,𝔽2)11yescharacteristic
805C2×C4C31×H(5,𝔽2)11yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—24no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×C31×#12011yescharacteristic
840C22C31×#54611yescharacteristic
841C22C31×#54611yescharacteristic
842C22C2×C31×#13511yescharacteristic
843C22C31×#57511yescharacteristic
844C22C31×#57611yescharacteristic
845C22C31×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×C31×#12411yescharacteristic
857C4C31×#53511yescharacteristic
858C4C31×#54611yescharacteristic
859C4C31×#54611yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2C31×#243511yescharacteristic
865C2C31×#300211yescharacteristic
866C2C31×#301211yescharacteristic
867C2C31×#329611yescharacteristic
868C2C31×#329711yescharacteristic
869C2C31×#332211yescharacteristic
870C2C31×#332311yescharacteristic
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×#488C2semidirect
3. C2×C31×#478C2semidirect
4. C31×#2562C2semidirect
5. C31×#2036C2semidirect
6. C31×#2035C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1983C2semidirect
10. C31×#1954C2semidirect
11. C31×#1788C2semidirect
12. C31×#1788C2semidirect
13. C31×#1786C2semidirect
14. C31×#1786C2semidirect
15. C4×C31×#102C2semidirect
20. C2×C31×#125C22semidirect
32. C2×C31×#107C22semidirect
33. C2×C31×#106C22semidirect
34. C2×C31×C4⋊C8C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
37. C2×C31×#103C22semidirect
38. C2×C31×#103C22semidirect
49. C2×C31×C22⋊C8C22semidirect
50. C2×C31×C22⋊C8C22semidirect
51. C2×C4×C8×C31C22semidirect
58. C31×#380C22semidirect
59. C31×#380C22semidirect
60. C4×C4⋊C4×C31C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
272. #25890C31direct (N × H)
376. C2×#488C2×C31semidirect
377. C2×#478C2×C31semidirect
378. #2562C2×C31semidirect
379. #2036C2×C31semidirect
380. #2035C2×C31semidirect
381. #2034C2×C31semidirect
382. #2033C2×C31semidirect
383. #1983C2×C31semidirect
384. #1954C2×C31semidirect
385. #1788C2×C31semidirect
386. #1788C2×C31semidirect
387. #1786C2×C31semidirect
388. #1786C2×C31semidirect
389. C4×#102C2×C31semidirect
444. C2×#125C22×C31semidirect
456. C2×#107C22×C31semidirect
457. C2×#106C22×C31semidirect
458. C2×C4⋊C8C22×C31semidirect
459. C2×#103C22×C31semidirect
460. C2×#103C22×C31semidirect
461. C2×#103C22×C31semidirect
462. C2×#103C22×C31semidirect
473. C2×C22⋊C8C22×C31semidirect
474. C2×C22⋊C8C22×C31semidirect
475. C2×C4×C8C22×C31semidirect
482. #380C22×C31semidirect
483. #380C22×C31semidirect
484. C4×C4⋊C4C22×C31semidirect
485. #340C22×C31semidirect
486. #340C22×C31semidirect
589. C31#25890direct (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×#4882
C2×C31×#4782
C31×#25622
C31×#20362
C31×#20352
C31×#20342
C31×#20332
C31×#19832
C31×#19542
C31×#17882
C31×#17862
C4×C31×#1022
#2589031