Finite Group Databasebeta

← C31×#24737 #21481496

Subgroups — C31×#24737 #21481496

Order 7936.

1000 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×#463C211yesmaximal, characteristic
2C2×C31×#463C211yesmaximal, characteristic
3C2×C31×#461C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
5C31×#2545C211yesmaximal, characteristic, complemented
6C31×#2349C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic, complemented
9C31×#2043C211yesmaximal, characteristic, complemented
10C31×#2042C211yesmaximal, characteristic, complemented
11C31×#1958C211yesmaximal, characteristic, complemented
12C31×#1939C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1805C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C31×#463—24no—
27C31×#463—24no—
28C31×#461—24no—
29C4×SD16×C31—24no—
30C2×C31×#106C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C4×C8×C31C2211yescharacteristic
45C31×#396—21no—
46C31×#396—21no—
47C31×#391C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#388—21no—
52C31×#388—21no—
53C31×#385—21no—
54C31×#385—21no—
55C31×#382C2211yescharacteristic
56C31×#380—21no—
57C4×C4⋊C4×C31C2211yescharacteristic
58C2×C31×#95—21no—
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31D414yes—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×C4⋊Q8—22no—
84C31×C4⋊Q8—41no—
85C31×#124—22no—
86C31×#124—22no—
87C31×#124—22no—
88C31×#124—41no—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—41no—
95C4×D4×C31—41no—
96C4×D4×C31D414yes—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31D411yescharacteristic
103C2×C4⋊C4×C31D411yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31C2311yescharacteristic
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×#106—22no—
122C31×C4⋊C8—22no—
123C31×C4⋊C8—22no—
124C31×C4⋊C8—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—41no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—41no—
135C4×C8×C31—22no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
145C24×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
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×C31C2×D412yes—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31C2×D412yes—
168C2×D4×C31C2×D412yes—
169C2×D4×C31#4112yes—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—24no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—42no—
178C22×C4×C31—42no—
179C22×C4×C31—42no—
180C22×C4×C31—42no—
181C22×C4×C31—81no—
182C22×C4×C31—81no—
183C22×C4×C31—81no—
184C22×C4×C31—81no—
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D411yescharacteristic
187C22×C4×C31C2×D411yescharacteristic
188C22×C4×C31C2×D411yescharacteristic
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D411yescharacteristic
191C22×C4×C31C2411yescharacteristic
192SD16×C31—28no—
193SD16×C31—44no—
194D8×C31—44no—
195C2×C8×C31—21no—
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×C31C2×D412yes—
207C4⋊C4×C31—22no—
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—41no—
216C4⋊C4×C31—42no—
217C4⋊C4×C31—42no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—81no—
220C4⋊C4×C31—81no—
221C4⋊C4×C31C2×D412yes—
222C22⋊C4×C31—24no—
223C22⋊C4×C31—42no—
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×C31—42no—
231C42×C31—21no—
232C42×C31—21no—
233C42×C31—21no—
234C42×C31—21no—
235C42×C31—42no—
236C42×C31C2×D412yes—
237C42×C31#4112yes—
238#24737C3111yesmaximal, characteristic, direct product factor, Sylow
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31C22×D411yescharacteristic
254Q8×C31—22no—
255Q8×C31—22no—
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—22no—
265D4×C31—41no—
266D4×C31—41no—
267D4×C31—41no—
268D4×C31—41no—
269D4×C31#12114yes—
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—22no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—22no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
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—84no—
304C2×C4×C31—84no—
305C2×C4×C31—84no—
306C2×C4×C31#12112yes—
307C2×C4×C31#12112yes—
308C2×C4×C31#13512yes—
309C2×C4×C31C22×D411yescharacteristic
310C2×C4×C31C22×D411yescharacteristic
311C2×C4×C31C2×#4111yescharacteristic
312C2×C4×C31C2×#4111yescharacteristic
313C2×C4×C31H(5,𝔽2)11yescharacteristic
314C2×C4×C312−1+411yescharacteristic
315C8×C31—22no—
316C8×C31—41no—
317C8×C31—41no—
318C8×C31—41no—
319C2×#463C2×C3111yescharacteristic
320C2×#463C2×C3111yescharacteristic
321C2×#461C2×C3111yescharacteristic, complemented
322C2×C4×SD16C2×C3111yescharacteristic, complemented
323#2545C2×C3111yescharacteristic, complemented
324#2349C2×C3111yescharacteristic, complemented
325#2066C2×C3111yescharacteristic, complemented
326#2065C2×C3111yescharacteristic, complemented
327#2043C2×C3111yescharacteristic, complemented
328#2042C2×C3111yescharacteristic, complemented
329#1958C2×C3111yescharacteristic, complemented
330#1939C2×C3111yescharacteristic, complemented
331#1879C2×C3111yescharacteristic
332#1877C2×C3111yescharacteristic, complemented
333#1805C2×C3111yescharacteristic, complemented
334C22×C31—24no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31C2×#12111yescharacteristic
349C22×C31D4211yescharacteristic
350C22×C31#54811yescharacteristic
351C22×C31C2×#13511yescharacteristic
352C22×C31#57511yescharacteristic
353C22×C31#57711yescharacteristic
354C22×C31#57711yescharacteristic
355C4×C31—22no—
356C4×C31—22no—
357C4×C31—22no—
358C4×C31—42no—
359C4×C31—41no—
360C4×C31—41no—
361C4×C31—41no—
362C4×C31—42no—
363C4×C31—81no—
364C4×C31—81no—
365C4×C31—81no—
366C4×C31—81no—
367C4×C31C2×#12111yescharacteristic
368C4×C31#53711yescharacteristic
369C4×C31#54711yescharacteristic
370C4×C31#55311yescharacteristic
371C22×SD16C22×C3111yescharacteristic
372C22×SD16C22×C3111yescharacteristic
373C22×D8C22×C3111yescharacteristic
374C2×C4⋊Q8C22×C3111yescharacteristic
375C2×#124C22×C3111yescharacteristic
376C2×#124C22×C3111yescharacteristic
377C2×C4×Q8C22×C3111yescharacteristic
378C2×C4×D4C22×C3111yescharacteristic
379C2×C4×D4C22×C3111yescharacteristic
380C2×C4×D4C22×C3111yescharacteristic
381#463—24no—
382#463—24no—
383#461—24no—
384C4×SD16—24no—
385C2×#106C22×C3111yescharacteristic
386C2×C4⋊C8C22×C3111yescharacteristic
387C2×C4⋊C8C22×C3111yescharacteristic
388C2×C4⋊C8C22×C3111yescharacteristic
389C2×#103C22×C3111yescharacteristic
390C2×#103C22×C3111yescharacteristic
391C2×#103C22×C3111yescharacteristic
392C2×#103C22×C3111yescharacteristic
393C2×#103C22×C3111yescharacteristic
394C2×#103C22×C3111yescharacteristic
395C2×#102C22×C3111yescharacteristic
396C2×#102C22×C3111yescharacteristic
397C2×#102C22×C3111yescharacteristic
398C2×#102C22×C3111yescharacteristic
399C2×C4×C8C22×C3111yescharacteristic
400#396—21no—
401#396—21no—
402#391C22×C3111yescharacteristic
403#390C22×C3111yescharacteristic
404#389C22×C3111yescharacteristic
405#389C22×C3111yescharacteristic
406#388—21no—
407#388—21no—
408#385—21no—
409#385—21no—
410#382C22×C3111yescharacteristic
411#380—21no—
412C4×C4⋊C4C22×C3111yescharacteristic
413C2×#95—21no—
414#340C22×C3111yescharacteristic
415#340C22×C3111yescharacteristic
416#336C22×C3111yescharacteristic
417#336C22×C3111yescharacteristic
418C2×C31—44no—
419C2×C31—161no—
420C2×C31#241611yescharacteristic
421C2×C31#303511yescharacteristic
422C2×C31#304211yescharacteristic
423C2×C31#327511yescharacteristic
424C2×C31#328211yescharacteristic
425C2×C31#336011yescharacteristic
426C2×C31#337611yescharacteristic
427C22×Q8C23×C3111yescharacteristic
428C22×Q8C23×C3111yescharacteristic
429C22×D4C23×C3111yescharacteristic
430C22×D4C23×C3111yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16D4×C3114yes—
440C2×D8—22no—
441C2×D8—22no—
442C2×D8—22no—
443C22×C8C23×C3111yescharacteristic
444C22×C8C23×C3111yescharacteristic
445C22×C8C23×C3111yescharacteristic
446C22×C8C23×C3111yescharacteristic
447C4⋊Q8—22no—
448C4⋊Q8—41no—
449#124—22no—
450#124—22no—
451#124—22no—
452#124—41no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—41no—
459C4×D4—41no—
460C4×D4D4×C3114yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4D4×C3111yescharacteristic
467C2×C4⋊C4D4×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C4⋊C4C23×C3111yescharacteristic
471C2×C4⋊C4C23×C3111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C42—21no—
482C2×C42C23×C3111yescharacteristic
483C2×C42C23×C3111yescharacteristic
484C2×C42C23×C3111yescharacteristic
485#106—22no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—22no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—41no—
499C4×C8—22no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95D4×C3111yescharacteristic
507#95D4×C3111yescharacteristic
508C31#2473711yescharacteristic, direct product factor, Sylow
509C24—21no—
510C24—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—21no—
522C2×Q8C2×D4×C3112yes—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4C2×D4×C3112yes—
533C2×D4C2×D4×C3112yes—
534C2×D4#41×C3112yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4C2×D4×C3111yescharacteristic
551C22×C4C2×D4×C3111yescharacteristic
552C22×C4C2×D4×C3111yescharacteristic
553C22×C4C2×D4×C3111yescharacteristic
554C22×C4C2×D4×C3111yescharacteristic
555C22×C4C2×D4×C3111yescharacteristic
556C22×C4C24×C3111yescharacteristic
557SD16—28no—
558SD16—44no—
559D8—44no—
560C2×C8—21no—
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×C8C2×D4×C3112yes—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—41no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4C2×D4×C3112yes—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42C2×D4×C3112yes—
602C42#41×C3112yes—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C3111yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—41no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626D4—22no—
627D4—22no—
628D4—22no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4C31×#12114yes—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
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—84no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4C31×#12112yes—
671C2×C4C31×#12112yes—
672C2×C4C31×#13512yes—
673C2×C4C22×D4×C3111yescharacteristic
674C2×C4C22×D4×C3111yescharacteristic
675C2×C4C2×#41×C3111yescharacteristic
676C2×C4C2×#41×C3111yescharacteristic
677C2×C4C31×H(5,𝔽2)11yescharacteristic
678C2×C4C31×2−1+411yescharacteristic
679C8—22no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—24no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C2×C31×#12111yescharacteristic
698C22D42×C3111yescharacteristic
699C22C31×#54811yescharacteristic
700C22C2×C31×#13511yescharacteristic
701C22C31×#57511yescharacteristic
702C22C31×#57711yescharacteristic
703C22C31×#57711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—42no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—42no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C2×C31×#12111yescharacteristic
717C4C31×#53711yescharacteristic
718C4C31×#54711yescharacteristic
719C4C31×#55311yescharacteristic
720C2—44no—
721C2—161no—
722C2C31×#241611yescharacteristic
723C2C31×#303511yescharacteristic
724C2C31×#304211yescharacteristic
725C2C31×#327511yescharacteristic
726C2C31×#328211yescharacteristic
727C2C31×#336011yescharacteristic
728C2C31×#337611yescharacteristic
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
3. C2×C31×#461C2semidirect
4. C2×C4×SD16×C31C2semidirect
5. C31×#2545C2semidirect
6. C31×#2349C2semidirect
7. C31×#2066C2semidirect
8. C31×#2065C2semidirect
9. C31×#2043C2semidirect
10. C31×#2042C2semidirect
11. C31×#1958C2semidirect
12. C31×#1939C2semidirect
14. C31×#1877C2semidirect
15. C31×#1805C2semidirect
238. #24737C31direct (N × H)
321. C2×#461C2×C31semidirect
322. C2×C4×SD16C2×C31semidirect
323. #2545C2×C31semidirect
324. #2349C2×C31semidirect
325. #2066C2×C31semidirect
326. #2065C2×C31semidirect
327. #2043C2×C31semidirect
328. #2042C2×C31semidirect
329. #1958C2×C31semidirect
330. #1939C2×C31semidirect
332. #1877C2×C31semidirect
333. #1805C2×C31semidirect
508. C31#24737direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C2×C31×#4612
C2×C4×SD16×C312
C31×#25452
C31×#23492
C31×#20662
C31×#20652
C31×#20432
C31×#20422
C31×#19582
C31×#19392
C31×#18792
C31×#18772
C31×#18052
#2473731