Finite Group Databasebeta

← C31×#26251 #21483010

Subgroups — C31×#26251 #21483010

Order 7936.

880 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#495C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C31×#2448C211yesmaximal, characteristic, complemented
4C31×#2447C211yesmaximal, characteristic, complemented
5C31×#2056C211yesmaximal, characteristic, complemented
6C31×#2054C211yesmaximal, characteristic
7C31×#2042C211yesmaximal, characteristic, complemented
8C31×#2042C211yesmaximal, characteristic, complemented
9C31×#1968C211yesmaximal, characteristic, complemented
10C31×#1968C211yesmaximal, characteristic, complemented
11C31×#1968C211yesmaximal, characteristic, complemented
12C31×#1941C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic
14C31×#1878C211yesmaximal, characteristic, complemented
15C8×C4⋊C4×C31C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#495—24no—
25C4×SD16×C31—24no—
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C4×C8×C31C2211yescharacteristic
38C2×C4×C8×C31C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic
40C31×#399—21no—
41C31×#397—21no—
42C31×#397—21no—
43C31×#397—21no—
44C31×#391C2211yescharacteristic
45C31×#391C2211yescharacteristic
46C31×#391C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#388—21no—
53C31×#388—21no—
54C31×#385—21no—
55C31×#381—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31C2311yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C2×Q16×C31—22no—
67C2×Q16×C31—22no—
68C2×Q16×C31—41no—
69C2×SD16×C31—22no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31D414yes—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—41no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×#124—22no—
83C31×#124—22no—
84C31×#124—41no—
85C31×#124—41no—
86C4×Q8×C31—22no—
87C4×Q8×C31—41no—
88C4×D4×C31—22no—
89C4×D4×C31—41no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31D411yescharacteristic
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C42×C31—21no—
111C2×C42×C31C2311yescharacteristic
112C2×C42×C31C2311yescharacteristic
113C2×C42×C31C2311yescharacteristic
114C31×#106—22no—
115C31×#106—22no—
116C31×C4⋊C8—22no—
117C31×#103—22no—
118C31×#103—41no—
119C31×#103—41no—
120C31×#103—41no—
121C31×#102—22no—
122C31×#102—41no—
123C31×#102—41no—
124C31×#102—41no—
125C4×C8×C31—22no—
126C4×C8×C31—22no—
127C4×C8×C31—22no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95D411yescharacteristic
137C31×#95D411yescharacteristic
138C24×C31—21no—
139C24×C31—21no—
140C2×Q8×C31—21no—
141C2×Q8×C31—21no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31C2×D412yes—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31C2×D412yes—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—81no—
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2411yescharacteristic
180Q16×C31—44no—
181SD16×C31—28no—
182SD16×C31—44no—
183D8×C31—44no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31C2×D412yes—
193C2×C8×C31#4112yes—
194C2×C8×C31#4112yes—
195C2×C8×C31#4112yes—
196C4⋊C4×C31—22no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—81no—
208C4⋊C4×C31—81no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—81no—
218C22⋊C4×C31—81no—
219C22⋊C4×C31—81no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—42no—
227#26251C3111yesmaximal, characteristic, direct product factor, Sylow
228C23×C31—22no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31C22×D411yescharacteristic
243Q8×C31—22no—
244Q8×C31—22no—
245Q8×C31—41no—
246Q8×C31—41no—
247Q8×C31—41no—
248Q8×C31—41no—
249Q8×C31—41no—
250Q8×C31—41no—
251D4×C31—22no—
252D4×C31—22no—
253D4×C31—41no—
254D4×C31—41no—
255D4×C31—41no—
256D4×C31—41no—
257D4×C31—41no—
258D4×C31—41no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—22no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—84no—
294C2×C4×C31#13512yes—
295C2×C4×C31#13512yes—
296C2×C4×C31C22×D411yescharacteristic
297C2×C4×C31C2×#4111yescharacteristic
298C2×C4×C31C2×#4111yescharacteristic
299C2×C4×C31C2×#4111yescharacteristic
300C2×C4×C31H(5,𝔽2)11yescharacteristic
301C2×C4×C31H(5,𝔽2)11yescharacteristic
302C8×C31—22no—
303C8×C31—41no—
304C8×C31—41no—
305C8×C31#12314yes—
306C2×#495C2×C3111yescharacteristic
307C2×C4×SD16C2×C3111yescharacteristic, complemented
308#2448C2×C3111yescharacteristic, complemented
309#2447C2×C3111yescharacteristic, complemented
310#2056C2×C3111yescharacteristic, complemented
311#2054C2×C3111yescharacteristic
312#2042C2×C3111yescharacteristic, complemented
313#2042C2×C3111yescharacteristic, complemented
314#1968C2×C3111yescharacteristic, complemented
315#1968C2×C3111yescharacteristic, complemented
316#1968C2×C3111yescharacteristic, complemented
317#1941C2×C3111yescharacteristic, complemented
318#1879C2×C3111yescharacteristic
319#1878C2×C3111yescharacteristic, complemented
320C8×C4⋊C4C2×C3111yescharacteristic, complemented
321C22×C31—42no—
322C22×C31—42no—
323C22×C31—42no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31—81no—
329C22×C31—81no—
330C22×C31—81no—
331C22×C31—81no—
332C22×C31—81no—
333C22×C31—81no—
334C22×C31—81no—
335C22×C31#53211yescharacteristic
336C22×C31D4211yescharacteristic
337C22×C31#55011yescharacteristic
338C22×C31C2×#13511yescharacteristic
339C22×C31C2×#13511yescharacteristic
340C22×C31#57711yescharacteristic
341C22×C31#57711yescharacteristic
342C4×C31—22no—
343C4×C31—22no—
344C4×C31—41no—
345C4×C31—42no—
346C4×C31—41no—
347C4×C31—41no—
348C4×C31—41no—
349C4×C31—81no—
350C4×C31—81no—
351C4×C31—81no—
352C4×C31—81no—
353C4×C31—81no—
354C4×C31C2×#12311yescharacteristic
355C4×C31#54011yescharacteristic
356C4×C31#54611yescharacteristic
357C4×C31#55911yescharacteristic
358C22×Q16C22×C3111yescharacteristic
359C22×SD16C22×C3111yescharacteristic
360C22×SD16C22×C3111yescharacteristic
361C22×D8C22×C3111yescharacteristic
362C2×#124C22×C3111yescharacteristic
363C2×#124C22×C3111yescharacteristic
364C2×C4×Q8C22×C3111yescharacteristic
365C2×C4×D4C22×C3111yescharacteristic
366#495—24no—
367C4×SD16—24no—
368C2×#106C22×C3111yescharacteristic
369C2×#106C22×C3111yescharacteristic
370C2×C4⋊C8C22×C3111yescharacteristic
371C2×#103C22×C3111yescharacteristic
372C2×#103C22×C3111yescharacteristic
373C2×#103C22×C3111yescharacteristic
374C2×#103C22×C3111yescharacteristic
375C2×#102C22×C3111yescharacteristic
376C2×#102C22×C3111yescharacteristic
377C2×#102C22×C3111yescharacteristic
378C2×#102C22×C3111yescharacteristic
379C2×C4×C8C22×C3111yescharacteristic
380C2×C4×C8C22×C3111yescharacteristic
381C2×C4×C8C22×C3111yescharacteristic
382#399—21no—
383#397—21no—
384#397—21no—
385#397—21no—
386#391C22×C3111yescharacteristic
387#391C22×C3111yescharacteristic
388#391C22×C3111yescharacteristic
389#390C22×C3111yescharacteristic
390#390C22×C3111yescharacteristic
391#390C22×C3111yescharacteristic
392#389C22×C3111yescharacteristic
393#389C22×C3111yescharacteristic
394#388—21no—
395#388—21no—
396#385—21no—
397#381—21no—
398C4×C4⋊C4C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#336C22×C3111yescharacteristic
402#336C22×C3111yescharacteristic
403C2×C31—82no—
404C2×C31—161no—
405C2×C31#244511yescharacteristic
406C2×C31#316811yescharacteristic
407C2×C31#317311yescharacteristic
408C2×C31#328211yescharacteristic
409C2×C31#328411yescharacteristic
410C2×C31#339411yescharacteristic
411C2×C31#339411yescharacteristic
412C22×Q8C23×C3111yescharacteristic
413C22×Q8C23×C3111yescharacteristic
414C22×D4C23×C3111yescharacteristic
415C22×D4C23×C3111yescharacteristic
416C23×C4—21no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—41no—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16D4×C3114yes—
426C2×D8—22no—
427C2×D8—22no—
428C2×D8—41no—
429C22×C8C23×C3111yescharacteristic
430C22×C8C23×C3111yescharacteristic
431C22×C8C23×C3111yescharacteristic
432C22×C8C23×C3111yescharacteristic
433#124—22no—
434#124—22no—
435#124—41no—
436#124—41no—
437C4×Q8—22no—
438C4×Q8—41no—
439C4×D4—22no—
440C4×D4—41no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4D4×C3111yescharacteristic
445C2×C4⋊C4D4×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C42—21no—
462C2×C42C23×C3111yescharacteristic
463C2×C42C23×C3111yescharacteristic
464C2×C42C23×C3111yescharacteristic
465#106—22no—
466#106—22no—
467C4⋊C8—22no—
468#103—22no—
469#103—41no—
470#103—41no—
471#103—41no—
472#102—22no—
473#102—41no—
474#102—41no—
475#102—41no—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8—22no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95D4×C3111yescharacteristic
488#95D4×C3111yescharacteristic
489C31#2625111yescharacteristic, direct product factor, Sylow
490C24—21no—
491C24—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×D4×C3112yes—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4C2×D4×C3112yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3111yescharacteristic
527C22×C4C2×D4×C3111yescharacteristic
528C22×C4C2×D4×C3111yescharacteristic
529C22×C4C2×D4×C3111yescharacteristic
530C22×C4C2×D4×C3111yescharacteristic
531C22×C4C24×C3111yescharacteristic
532Q16—44no—
533SD16—28no—
534SD16—44no—
535D8—44no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C2×D4×C3112yes—
545C2×C8#41×C3112yes—
546C2×C8#41×C3112yes—
547C2×C8#41×C3112yes—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—42no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C22×D4×C3111yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—84no—
645C2×C4C31×#13512yes—
646C2×C4C31×#13512yes—
647C2×C4C22×D4×C3111yescharacteristic
648C2×C4C2×#41×C3111yescharacteristic
649C2×C4C2×#41×C3111yescharacteristic
650C2×C4C2×#41×C3111yescharacteristic
651C2×C4C31×H(5,𝔽2)11yescharacteristic
652C2×C4C31×H(5,𝔽2)11yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8C31×#12314yes—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22C31×#53211yescharacteristic
672C22D42×C3111yescharacteristic
673C22C31×#55011yescharacteristic
674C22C2×C31×#13511yescharacteristic
675C22C2×C31×#13511yescharacteristic
676C22C31×#57711yescharacteristic
677C22C31×#57711yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—42no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4C2×C31×#12311yescharacteristic
691C4C31×#54011yescharacteristic
692C4C31×#54611yescharacteristic
693C4C31×#55911yescharacteristic
694C2—82no—
695C2—161no—
696C2C31×#244511yescharacteristic
697C2C31×#316811yescharacteristic
698C2C31×#317311yescharacteristic
699C2C31×#328211yescharacteristic
700C2C31×#328411yescharacteristic
701C2C31×#339411yescharacteristic
702C2C31×#339411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C31C2semidirect
3. C31×#2448C2semidirect
4. C31×#2447C2semidirect
5. C31×#2056C2semidirect
7. C31×#2042C2semidirect
8. C31×#2042C2semidirect
9. C31×#1968C2semidirect
10. C31×#1968C2semidirect
11. C31×#1968C2semidirect
12. C31×#1941C2semidirect
14. C31×#1878C2semidirect
15. C8×C4⋊C4×C31C2semidirect
227. #26251C31direct (N × H)
307. C2×C4×SD16C2×C31semidirect
308. #2448C2×C31semidirect
309. #2447C2×C31semidirect
310. #2056C2×C31semidirect
312. #2042C2×C31semidirect
313. #2042C2×C31semidirect
314. #1968C2×C31semidirect
315. #1968C2×C31semidirect
316. #1968C2×C31semidirect
317. #1941C2×C31semidirect
319. #1878C2×C31semidirect
320. C8×C4⋊C4C2×C31semidirect
489. C31#26251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4952
C2×C4×SD16×C312
C31×#24482
C31×#24472
C31×#20562
C31×#20542
C31×#20422
C31×#19682
C31×#19412
C31×#18792
C31×#18782
C8×C4⋊C4×C312
#2625131