Finite Group Databasebeta

← C31×#24898 #21481657

Subgroups — C31×#24898 #21481657

Order 7936.

1016 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#448C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C31×#2422C211yesmaximal, characteristic
4Q8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2096C211yesmaximal, characteristic, complemented
6C31×#2077C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic
9C31×#1933C211yesmaximal, characteristic, complemented
10C31×#1923C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1877C211yesmaximal, characteristic, complemented
13C31×#1865C211yesmaximal, characteristic, complemented
14C31×#1803C211yesmaximal, characteristic, complemented
15C31×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×#123—21no—
20C2×C31×#121C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#448—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×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic
40C31×#397—21no—
41C31×#394—21no—
42C31×#391—21no—
43C31×#391—21no—
44C31×#391C2211yescharacteristic
45C31×#391C2211yescharacteristic
46C31×#390C2211yescharacteristic
47C31×#389C2211yescharacteristic
48C31×#385—21no—
49C31×#384C2211yescharacteristic
50C31×#380—21no—
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C4×C22⋊C4×C31—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31—22no—
62C22×Q8×C31—22no—
63C22×Q8×C31—21no—
64C22×Q8×C31—22no—
65C22×Q8×C31—22no—
66C22×Q8×C31—41no—
67C22×Q8×C31—41no—
68C22×Q8×C31C2311yescharacteristic
69C22×Q8×C31C2311yescharacteristic
70C22×D4×C31—21no—
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—41no—
80C2×SD16×C31D414yes—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×#123—44no—
86C31×#121—22no—
87C31×#121—41no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×Q8×C31—41no—
91C4×Q8×C31—41no—
92C4×D4×C31—22no—
93C4×D4×C31—41no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31D411yescharacteristic
111C2×C22⋊C4×C31D411yescharacteristic
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×#106—22no—
117C31×#106—41no—
118C31×C4⋊C8—41no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—22no—
122C31×#103—22no—
123C31×#103—22no—
124C31×#103—41no—
125C31×#102—22no—
126C31×#102—41no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—41no—
129C4×C8×C31—22no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95D411yescharacteristic
138C31×#95D411yescharacteristic
139C24×C31—21no—
140C24×C31C2×D411yescharacteristic
141C2×Q8×C31—24no—
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—42no—
151C2×Q8×C31—42no—
152C2×Q8×C31—44no—
153C2×Q8×C31—44no—
154C2×Q8×C31—44no—
155C2×Q8×C31—44no—
156C2×Q8×C31C2×D412yes—
157C2×Q8×C31#4112yes—
158C2×Q8×C31#4112yes—
159C2×Q8×C31#4112yes—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—42no—
166C2×D4×C31—42no—
167C2×D4×C31—81no—
168C2×D4×C31C2×D412yes—
169C22×C4×C31—21no—
170C22×C4×C31—24no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—42no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—42no—
187C22×C4×C31—81no—
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2411yescharacteristic
194SD16×C31—28no—
195SD16×C31—44no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31C2×D412yes—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—42no—
220C4⋊C4×C31—42no—
221C4⋊C4×C31—42no—
222C4⋊C4×C31—81no—
223C22⋊C4×C31—41no—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—42no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31SD1614yescomplemented
231C42×C31—21no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—42no—
236C42×C31—42no—
237#24898C3111yesmaximal, characteristic, direct product factor, Sylow
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—21no—
244C23×C31—22no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31C2×SD1612yes—
252C23×C31C22×D411yescharacteristic
253Q8×C31—22no—
254Q8×C31—22no—
255Q8×C31—22no—
256Q8×C31—22no—
257Q8×C31—22no—
258Q8×C31—48no—
259Q8×C31—41no—
260Q8×C31—41no—
261Q8×C31#12314yescomplemented
262D4×C31—22no—
263D4×C31—22no—
264D4×C31—41no—
265D4×C31—41no—
266D4×C31—84no—
267C2×C4×C31—22no—
268C2×C4×C31—21no—
269C2×C4×C31—22no—
270C2×C4×C31—21no—
271C2×C4×C31—22no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—22no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—48no—
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—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—84no—
307C2×C4×C31C2×SD1612yes—
308C2×C4×C31C2×SD1612yes—
309C2×C4×C31C22×D411yescharacteristic
310C2×C4×C31C2×#4111yescharacteristic
311C2×C4×C31C2×#4111yescharacteristic
312C2×C4×C31C2×#4111yescharacteristic
313C2×C4×C31H(5,𝔽2)11yescharacteristic
314C2×C4×C31H(5,𝔽2)11yescharacteristic
315C8×C31—22no—
316C8×C31—41no—
317C8×C31—41no—
318C8×C31—41no—
319C2×#448C2×C3111yescharacteristic
320C2×C4×SD16C2×C3111yescharacteristic, complemented
321#2422C2×C3111yescharacteristic
322Q8×C22⋊C4C2×C3111yescharacteristic, complemented
323#2096C2×C3111yescharacteristic, complemented
324#2077C2×C3111yescharacteristic, complemented
325#2055C2×C3111yescharacteristic, complemented
326#2034C2×C3111yescharacteristic
327#1933C2×C3111yescharacteristic, complemented
328#1923C2×C3111yescharacteristic, complemented
329#1880C2×C3111yescharacteristic, complemented
330#1877C2×C3111yescharacteristic, complemented
331#1865C2×C3111yescharacteristic, complemented
332#1803C2×C3111yescharacteristic, complemented
333#1787C2×C3111yescharacteristic, complemented
334C22×C31—22no—
335C22×C31—22no—
336C22×C31—22no—
337C22×C31—41no—
338C22×C31—41no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—42no—
342C22×C31—42no—
343C22×C31—42no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31#52511yescharacteristic
349C22×C31D4211yescharacteristic
350C22×C31#54611yescharacteristic
351C22×C31C22×SD1611yescharacteristic
352C22×C31#57511yescharacteristic
353C22×C31#57711yescharacteristic
354C22×C31#57811yescharacteristic
355C4×C31—24no—
356C4×C31—22no—
357C4×C31—22no—
358C4×C31—41no—
359C4×C31—42no—
360C4×C31—41no—
361C4×C31—41no—
362C4×C31—81no—
363C4×C31—81no—
364C4×C31—81no—
365C4×C31—81no—
366C4×C31—81no—
367C4×C31C2×#12311yescharacteristic
368C4×C31#53811yescharacteristic
369C4×C31#54611yescharacteristic
370C4×C31#55111yescharacteristic
371C23×Q8C22×C3111yescharacteristic
372C22×SD16C22×C3111yescharacteristic
373C22×SD16C22×C3111yescharacteristic
374C2×#123—21no—
375C2×#121C22×C3111yescharacteristic
376C2×C4×Q8C22×C3111yescharacteristic
377C2×C4×Q8C22×C3111yescharacteristic
378C2×C4×D4C22×C3111yescharacteristic
379#448—24no—
380C4×SD16—24no—
381C2×#106C22×C3111yescharacteristic
382C2×#106C22×C3111yescharacteristic
383C2×C4⋊C8C22×C3111yescharacteristic
384C2×#103C22×C3111yescharacteristic
385C2×#103C22×C3111yescharacteristic
386C2×#103C22×C3111yescharacteristic
387C2×#103C22×C3111yescharacteristic
388C2×#103C22×C3111yescharacteristic
389C2×#103C22×C3111yescharacteristic
390C2×#102C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×C22⋊C8C22×C3111yescharacteristic
393C2×C22⋊C8C22×C3111yescharacteristic
394C2×C4×C8C22×C3111yescharacteristic
395#397—21no—
396#394—21no—
397#391—21no—
398#391—21no—
399#391C22×C3111yescharacteristic
400#391C22×C3111yescharacteristic
401#390C22×C3111yescharacteristic
402#389C22×C3111yescharacteristic
403#385—21no—
404#384C22×C3111yescharacteristic
405#380—21no—
406#380C22×C3111yescharacteristic
407#380C22×C3111yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414#336C22×C3111yescharacteristic
415#336C22×C3111yescharacteristic
416C2×C31—42no—
417C2×C31—82no—
418C2×C31#241811yescharacteristic
419C2×C31#310311yescharacteristic
420C2×C31#312111yescharacteristic
421C2×C31#326911yescharacteristic
422C2×C31D4×SD1611yescharacteristic
423C2×C31#329811yescharacteristic
424C2×C31#332611yescharacteristic
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—21no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—41no—
431C22×Q8—41no—
432C22×Q8C23×C3111yescharacteristic
433C22×Q8C23×C3111yescharacteristic
434C22×D4—21no—
435C22×D4C23×C3111yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C23×C3111yescharacteristic
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—41no—
444C2×SD16D4×C3114yes—
445C22×C8C23×C3111yescharacteristic
446C22×C8C23×C3111yescharacteristic
447C22×C8C23×C3111yescharacteristic
448C22×C8C23×C3111yescharacteristic
449#123—44no—
450#121—22no—
451#121—41no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—41no—
455C4×Q8—41no—
456C4×D4—22no—
457C4×D4—41no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4C23×C3111yescharacteristic
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4D4×C3111yescharacteristic
475C2×C22⋊C4D4×C3111yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C3111yescharacteristic
479C2×C42C23×C3111yescharacteristic
480#106—22no—
481#106—41no—
482C4⋊C8—41no—
483#103—22no—
484#103—22no—
485#103—22no—
486#103—22no—
487#103—22no—
488#103—41no—
489#102—22no—
490#102—41no—
491C22⋊C8—22no—
492C22⋊C8—41no—
493C4×C8—22no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95D4×C3111yescharacteristic
502#95D4×C3111yescharacteristic
503C31#2489811yescharacteristic, direct product factor, Sylow
504C24—21no—
505C24C2×D4×C3111yescharacteristic
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8C2×D4×C3112yes—
522C2×Q8#41×C3112yes—
523C2×Q8#41×C3112yes—
524C2×Q8#41×C3112yes—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4C2×D4×C3112yes—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4C2×D4×C3111yescharacteristic
554C22×C4C2×D4×C3111yescharacteristic
555C22×C4C2×D4×C3111yescharacteristic
556C22×C4C2×D4×C3111yescharacteristic
557C22×C4C2×D4×C3111yescharacteristic
558C22×C4C24×C3111yescharacteristic
559SD16—28no—
560SD16—44no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8C2×D4×C3112yes—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—81no—
588C22⋊C4—41no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4SD16×C3114yescomplemented
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23C2×SD16×C3112yes—
616C23C22×D4×C3111yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8C31×#12314yescomplemented
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—84no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4C2×SD16×C3112yes—
672C2×C4C2×SD16×C3112yes—
673C2×C4C22×D4×C3111yescharacteristic
674C2×C4C2×#41×C3111yescharacteristic
675C2×C4C2×#41×C3111yescharacteristic
676C2×C4C2×#41×C3111yescharacteristic
677C2×C4C31×H(5,𝔽2)11yescharacteristic
678C2×C4C31×H(5,𝔽2)11yescharacteristic
679C8—22no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C31×#52511yescharacteristic
698C22D42×C3111yescharacteristic
699C22C31×#54611yescharacteristic
700C22C22×SD16×C3111yescharacteristic
701C22C31×#57511yescharacteristic
702C22C31×#57711yescharacteristic
703C22C31×#57811yescharacteristic
704C4—24no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—81no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C2×C31×#12311yescharacteristic
717C4C31×#53811yescharacteristic
718C4C31×#54611yescharacteristic
719C4C31×#55111yescharacteristic
720C2—42no—
721C2—82no—
722C2C31×#241811yescharacteristic
723C2C31×#310311yescharacteristic
724C2C31×#312111yescharacteristic
725C2C31×#326911yescharacteristic
726C2D4×SD16×C3111yescharacteristic
727C2C31×#329811yescharacteristic
728C2C31×#332611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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
2. C2×C4×SD16×C31C2semidirect
4. Q8×C22⋊C4×C31C2semidirect
5. C31×#2096C2semidirect
6. C31×#2077C2semidirect
7. C31×#2055C2semidirect
9. C31×#1933C2semidirect
10. C31×#1923C2semidirect
11. C31×#1880C2semidirect
12. C31×#1877C2semidirect
13. C31×#1865C2semidirect
14. C31×#1803C2semidirect
15. C31×#1787C2semidirect
230. C22⋊C4×C31SD16semidirect
237. #24898C31direct (N × H)
261. Q8×C31#123semidirect
320. C2×C4×SD16C2×C31semidirect
322. Q8×C22⋊C4C2×C31semidirect
323. #2096C2×C31semidirect
324. #2077C2×C31semidirect
325. #2055C2×C31semidirect
327. #1933C2×C31semidirect
328. #1923C2×C31semidirect
329. #1880C2×C31semidirect
330. #1877C2×C31semidirect
331. #1865C2×C31semidirect
332. #1803C2×C31semidirect
333. #1787C2×C31semidirect
503. C31#24898direct (N × H)
595. C22⋊C4SD16×C31semidirect
625. Q8C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4482
C2×C4×SD16×C312
C31×#24222
Q8×C22⋊C4×C312
C31×#20962
C31×#20772
C31×#20552
C31×#20342
C31×#19332
C31×#19232
C31×#18802
C31×#18772
C31×#18652
C31×#18032
C31×#17872
#2489831