Finite Group Databasebeta

← C31×#24195 #21480954

Subgroups — C31×#24195 #21480954

Order 7936.

1074 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#556C211yesmaximal, characteristic
2C2×C31×#464C211yesmaximal, characteristic
3C2×C4×Q16×C31C211yesmaximal, characteristic, complemented
4C31×#2581C211yesmaximal, characteristic, complemented
5C31×#2043C211yesmaximal, characteristic, complemented
6C31×#2042C211yesmaximal, characteristic
7C31×#2016C211yesmaximal, characteristic, complemented
8C31×#2015C211yesmaximal, characteristic
9C31×#1984C211yesmaximal, characteristic, complemented
10C31×#1958C211yesmaximal, characteristic
11C31×#1878C211yesmaximal, characteristic, complemented
12C31×#1877C211yesmaximal, characteristic
13C31×#1863C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic
15C31×#1805C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C31×#556—24no—
20C31×#556—24no—
21C2×C31×C4⋊Q8C2211yescharacteristic
22C2×C31×#126—21no—
23C2×C31×#126—21no—
24C2×C31×#124C2211yescharacteristic
25C2×C31×#124C2211yescharacteristic
26C2×C31×C22⋊Q8—21no—
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×Q8×C31C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117—21no—
33C31×#464—24no—
34C4×Q16×C31—24no—
35C2×C31×#107C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C4×C8×C31C2211yescharacteristic
48C31×#400—21no—
49C31×#395—21no—
50C31×#391C2211yescharacteristic
51C31×#391C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#387—21no—
55C31×#387—21no—
56C31×#382C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×Q8×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C23×C4×C31—21no—
69C2×Q16×C31—22no—
70C2×Q16×C31—22no—
71C2×Q16×C31—22no—
72C2×Q16×C31—22no—
73C2×Q16×C31—22no—
74C2×Q16×C31—41no—
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×SD16×C31—41no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×C4⋊Q8—22no—
83C31×C4⋊Q8—22no—
84C31×#126—28no—
85C31×#126—28no—
86C31×#124—22no—
87C31×#124—22no—
88C31×#124—22no—
89C31×#124D414yes—
90C31×C22⋊Q8—28no—
91C4×Q8×C31—22no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31—22no—
97C4×Q8×C31—22no—
98C4×Q8×C31D414yes—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C31×#117—28no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31D411yescharacteristic
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
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×C42×C31—21no—
122C2×C42×C31—21no—
123C2×C42×C31—21no—
124C2×C42×C31C2311yescharacteristic
125C2×C42×C31C2311yescharacteristic
126C2×C42×C31C2311yescharacteristic
127C31×#107—22no—
128C31×C4⋊C8—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—41no—
134C31×#103—41no—
135C31×#103—41no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—41no—
139C4×C8×C31—22no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C2×Q8×C31—22no—
150C2×Q8×C31—22no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—41no—
167C2×Q8×C31C2×D412yes—
168C2×Q8×C31C2×D412yes—
169C2×Q8×C31#4112yes—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31C2×D412yes—
176C22×C4×C31—24no—
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—21no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2×D411yescharacteristic
192C22×C4×C31C2411yescharacteristic
193Q16×C31—28no—
194Q16×C31—44no—
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×C31#4112yes—
208C4⋊C4×C31—24no—
209C4⋊C4×C31—24no—
210C4⋊C4×C31—24no—
211C4⋊C4×C31—24no—
212C4⋊C4×C31—22no—
213C4⋊C4×C31—22no—
214C4⋊C4×C31—22no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—42no—
223C4⋊C4×C31—42no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31C2×D412yes—
226C22⋊C4×C31—24no—
227C22⋊C4×C31—24no—
228C22⋊C4×C31—24no—
229C22⋊C4×C31—24no—
230C22⋊C4×C31—24no—
231C42×C31—24no—
232C42×C31—24no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—21no—
236C42×C31—21no—
237C42×C31—42no—
238C42×C31C2×D412yes—
239C42×C31C2×D412yes—
240#24195C3111yesmaximal, characteristic, direct product factor, Sylow
241C23×C31—22no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31C22×D411yescharacteristic
249Q8×C31—22no—
250Q8×C31—22no—
251Q8×C31—22no—
252Q8×C31—22no—
253Q8×C31—22no—
254Q8×C31—22no—
255Q8×C31—44no—
256Q8×C31—41no—
257Q8×C31—41no—
258Q8×C31—41no—
259Q8×C31—41no—
260Q8×C31—41no—
261Q8×C31—41no—
262D4×C31—22no—
263D4×C31—22no—
264D4×C31—41no—
265D4×C31—41no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—22no—
274C2×C4×C31—21no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—21no—
278C2×C4×C31—22no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—48no—
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#12012yes—
304C2×C4×C31#12012yes—
305C2×C4×C31#13512yes—
306C2×C4×C31C22×D411yescharacteristic
307C2×C4×C31C22×D411yescharacteristic
308C2×C4×C31C2×#4111yescharacteristic
309C2×C4×C31C2×#4111yescharacteristic
310C2×C4×C31H(5,𝔽2)11yescharacteristic
311C2×C4×C312−1+411yescharacteristic
312C8×C31—22no—
313C8×C31—41no—
314C8×C31—41no—
315C8×C31—41no—
316C2×#556C2×C3111yescharacteristic
317C2×#464C2×C3111yescharacteristic
318C2×C4×Q16C2×C3111yescharacteristic, complemented
319#2581C2×C3111yescharacteristic, complemented
320#2043C2×C3111yescharacteristic, complemented
321#2042C2×C3111yescharacteristic
322#2016C2×C3111yescharacteristic, complemented
323#2015C2×C3111yescharacteristic
324#1984C2×C3111yescharacteristic, complemented
325#1958C2×C3111yescharacteristic
326#1878C2×C3111yescharacteristic, complemented
327#1877C2×C3111yescharacteristic
328#1863C2×C3111yescharacteristic, complemented
329#1862C2×C3111yescharacteristic
330#1805C2×C3111yescharacteristic, complemented
331C22×C31—42no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31—81no—
337C22×C31—81no—
338C22×C31C2×#12011yescharacteristic
339C22×C31#54811yescharacteristic
340C22×C31#55011yescharacteristic
341C22×C31C2×#13511yescharacteristic
342C22×C31#57511yescharacteristic
343C22×C31#57811yescharacteristic
344C22×C31#57811yescharacteristic
345C4×C31—22no—
346C4×C31—22no—
347C4×C31—22no—
348C4×C31—42no—
349C4×C31—42no—
350C4×C31—42no—
351C4×C31—41no—
352C4×C31—42no—
353C4×C31—41no—
354C4×C31—41no—
355C4×C31—81no—
356C4×C31—81no—
357C4×C31—81no—
358C4×C31#52511yescharacteristic
359C4×C31#53711yescharacteristic
360C4×C31#54611yescharacteristic
361C4×C31#54711yescharacteristic
362C22×Q16C22×C3111yescharacteristic
363C22×Q16C22×C3111yescharacteristic
364C22×SD16C22×C3111yescharacteristic
365#556—24no—
366#556—24no—
367C2×C4⋊Q8C22×C3111yescharacteristic
368C2×#126—21no—
369C2×#126—21no—
370C2×#124C22×C3111yescharacteristic
371C2×#124C22×C3111yescharacteristic
372C2×C22⋊Q8—21no—
373C2×C4×Q8C22×C3111yescharacteristic
374C2×C4×Q8C22×C3111yescharacteristic
375C2×C4×Q8C22×C3111yescharacteristic
376C2×C4×Q8C22×C3111yescharacteristic
377C2×C4×D4C22×C3111yescharacteristic
378C2×#117—21no—
379#464—24no—
380C4×Q16—24no—
381C2×#107C22×C3111yescharacteristic
382C2×C4⋊C8C22×C3111yescharacteristic
383C2×#103C22×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×#102C22×C3111yescharacteristic
393C2×C4×C8C22×C3111yescharacteristic
394#400—21no—
395#395—21no—
396#391C22×C3111yescharacteristic
397#391C22×C3111yescharacteristic
398#389C22×C3111yescharacteristic
399#389C22×C3111yescharacteristic
400#387—21no—
401#387—21no—
402#382C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#336C22×C3111yescharacteristic
406#336C22×C3111yescharacteristic
407#336C22×C3111yescharacteristic
408#336C22×C3111yescharacteristic
409C2×C31—82no—
410C2×C31#240711yescharacteristic
411C2×C31#300211yescharacteristic
412C2×C31#301111yescharacteristic
413C2×C31#336411yescharacteristic
414C2×C31#337711yescharacteristic
415C2×C31#339311yescharacteristic
416C2×C31#340211yescharacteristic
417C22×Q8D4×C3111yescharacteristic
418C22×Q8C23×C3111yescharacteristic
419C22×Q8C23×C3111yescharacteristic
420C22×Q8C23×C3111yescharacteristic
421C22×D4C23×C3111yescharacteristic
422C23×C4—21no—
423C2×Q16—22no—
424C2×Q16—22no—
425C2×Q16—22no—
426C2×Q16—22no—
427C2×Q16—22no—
428C2×Q16—41no—
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—41no—
432C22×C8C23×C3111yescharacteristic
433C22×C8C23×C3111yescharacteristic
434C22×C8C23×C3111yescharacteristic
435C22×C8C23×C3111yescharacteristic
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438#126—28no—
439#126—28no—
440#124—22no—
441#124—22no—
442#124—22no—
443#124D4×C3114yes—
444C22⋊Q8—28no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8D4×C3114yes—
453C4×D4—22no—
454C4×D4—22no—
455#117—28no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C3111yescharacteristic
464C2×C4⋊C4D4×C3111yescharacteristic
465C2×C4⋊C4D4×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C3111yescharacteristic
479C2×C42C23×C3111yescharacteristic
480C2×C42C23×C3111yescharacteristic
481#107—22no—
482C4⋊C8—22no—
483#103—22no—
484#103—22no—
485#103—22no—
486#103—22no—
487#103—41no—
488#103—41no—
489#103—41no—
490#102—22no—
491#102—22no—
492#102—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#95—21no—
502C31#2419511yescharacteristic, direct product factor, Sylow
503C24—21no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—21no—
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—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—41no—
522C2×Q8C2×D4×C3112yes—
523C2×Q8C2×D4×C3112yes—
524C2×Q8#41×C3112yes—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4C2×D4×C3112yes—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C2×D4×C3111yescharacteristic
543C22×C4C2×D4×C3111yescharacteristic
544C22×C4C2×D4×C3111yescharacteristic
545C22×C4C2×D4×C3111yescharacteristic
546C22×C4C2×D4×C3111yescharacteristic
547C22×C4C24×C3111yescharacteristic
548Q16—28no—
549Q16—44no—
550SD16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8#41×C3112yes—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4C2×D4×C3112yes—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C42—24no—
587C42—24no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42C2×D4×C3112yes—
594C42C2×D4×C3112yes—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23C22×D4×C3111yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—22no—
609Q8—44no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—22no—
617D4—22no—
618D4—41no—
619D4—41no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
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×C4C31×#12012yes—
658C2×C4C31×#12012yes—
659C2×C4C31×#13512yes—
660C2×C4C22×D4×C3111yescharacteristic
661C2×C4C22×D4×C3111yescharacteristic
662C2×C4C2×#41×C3111yescharacteristic
663C2×C4C2×#41×C3111yescharacteristic
664C2×C4C31×H(5,𝔽2)11yescharacteristic
665C2×C4C31×2−1+411yescharacteristic
666C8—22no—
667C8—41no—
668C8—41no—
669C8—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×C31×#12011yescharacteristic
678C22C31×#54811yescharacteristic
679C22C31×#55011yescharacteristic
680C22C2×C31×#13511yescharacteristic
681C22C31×#57511yescharacteristic
682C22C31×#57811yescharacteristic
683C22C31×#57811yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—41no—
691C4—42no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C31×#52511yescharacteristic
698C4C31×#53711yescharacteristic
699C4C31×#54611yescharacteristic
700C4C31×#54711yescharacteristic
701C2—82no—
702C2C31×#240711yescharacteristic
703C2C31×#300211yescharacteristic
704C2C31×#301111yescharacteristic
705C2C31×#336411yescharacteristic
706C2C31×#337711yescharacteristic
707C2C31×#339311yescharacteristic
708C2C31×#340211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q16×C31C2semidirect
4. C31×#2581C2semidirect
5. C31×#2043C2semidirect
7. C31×#2016C2semidirect
9. C31×#1984C2semidirect
11. C31×#1878C2semidirect
13. C31×#1863C2semidirect
15. C31×#1805C2semidirect
240. #24195C31direct (N × H)
318. C2×C4×Q16C2×C31semidirect
319. #2581C2×C31semidirect
320. #2043C2×C31semidirect
322. #2016C2×C31semidirect
324. #1984C2×C31semidirect
326. #1878C2×C31semidirect
328. #1863C2×C31semidirect
330. #1805C2×C31semidirect
502. C31#24195direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5562
C2×C31×#4642
C2×C4×Q16×C312
C31×#25812
C31×#20432
C31×#20422
C31×#20162
C31×#20152
C31×#19842
C31×#19582
C31×#18782
C31×#18772
C31×#18632
C31×#18622
C31×#18052
#2419531