Finite Group Databasebeta

← C31×#32961 #21489720

Subgroups — C31×#32961 #21489720

Order 7936.

1320 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C31C211yesmaximal, characteristic
2C2×C31×#479C211yesmaximal, characteristic, complemented
3C2×C31×#478C211yesmaximal, characteristic, complemented
4C31×#2851C211yesmaximal, characteristic, complemented
5C31×#1865C211yesmaximal, characteristic, complemented
6C31×#1864C211yesmaximal, characteristic, complemented
7C31×#1863C211yesmaximal, characteristic, complemented
8C31×#1862C211yesmaximal, characteristic, complemented
9C31×#1854C211yesmaximal, characteristic, complemented
10C31×#1854C211yesmaximal, characteristic, complemented
11C31×#1805C211yesmaximal, characteristic, complemented
12C31×#1804C211yesmaximal, characteristic, complemented
13C31×#1797C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic
15C31×#1788C211yesmaximal, characteristic
16C22×#41×C31C2211yescharacteristic
17C2×C31×#125C2211yescharacteristic
18C4×#41×C31—24no—
19C4×#41×C31—24no—
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×D4×C31—21no—
23C2×C4×D4×C31—21no—
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C31×#117—21no—
27C2×C31×#117C2211yescharacteristic
28C22×C42×C31—21no—
29C22×C42×C31C2211yescharacteristic
30C31×#479—24no—
31C31×#478—24no—
32C2×C31×#107C2211yescharacteristic
33C2×C31×#107C2211yescharacteristic
34C2×C31×#106C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#387—21no—
51C31×#387—21no—
52C31×#385—21no—
53C31×#385—21no—
54C31×#382C2211yescharacteristic
55C31×#380C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31Q814yes—
69C22×Q8×C31C2311yescharacteristic
70C22×D4×C31—21no—
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31D411yescharacteristic
76C23×C4×C31D411yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×#125—22no—
83C31×#125—22no—
84C4×Q8×C31—22no—
85C4×Q8×C31—22no—
86C4×Q8×C31—22no—
87C4×Q8×C31D414yes—
88C4×D4×C31—28no—
89C4×D4×C31—28no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31D414yes—
94C31×#117—28no—
95C31×#117—22no—
96C31×#117—22no—
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×C31—21no—
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
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×C42×C31—28no—
115C2×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31—22no—
119C2×C42×C31—22no—
120C2×C42×C31D411yescharacteristic
121C2×C42×C31D411yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#107—22no—
125C31×#107—22no—
126C31×#106—22no—
127C31×#106—22no—
128C31×C4⋊C8—22no—
129C31×C4⋊C8—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×C22⋊C8—22no—
139C31×C22⋊C8—22no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C24×C31—21no—
147C24×C31C2×D411yescharacteristic
148#41×C31—28no—
149#41×C31—28no—
150#41×C31—28no—
151#41×C31—28no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31C2×D412yes—
156C2×Q8×C31C2×Q812yes—
157C2×Q8×C31#4112yes—
158C2×D4×C31—24no—
159C2×D4×C31—24no—
160C2×D4×C31—24no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31C2×D412yes—
165C2×D4×C31C2×Q812yes—
166C2×D4×C31#4112yes—
167C22×C4×C31—24no—
168C22×C4×C31—24no—
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—24no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—24no—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—41no—
187C22×C4×C31—41no—
188C22×C4×C31—41no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×Q812yes—
199C22×C4×C31#4112yes—
200C22×C4×C31C2411yescharacteristic
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—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C4⋊C4×C31—24no—
214C4⋊C4×C31—24no—
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—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—42no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31C2×D412yes—
230C4⋊C4×C31C2×D412yes—
231C22⋊C4×C31—24no—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—24no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C42×C31—24no—
237C42×C31—24no—
238C42×C31—22no—
239C42×C31—24no—
240C42×C31—22no—
241C42×C31—21no—
242C42×C31—21no—
243C42×C31C2×D412yes—
244C42×C31C2×D412yes—
245#32961C3111yesmaximal, characteristic, direct product factor, Sylow
246C23×C31—21no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—21no—
250C23×C31—22no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31C22⋊Q812yes—
260C23×C31C22×D411yescharacteristic
261Q8×C31—22no—
262Q8×C31—22no—
263Q8×C31—22no—
264Q8×C31C22⋊Q814yes—
265D4×C31—216no—
266D4×C31—22no—
267D4×C31—22no—
268D4×C31—22no—
269D4×C31C22⋊Q814yes—
270C2×C4×C31—216no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—21no—
276C2×C4×C31—22no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—44no—
292C2×C4×C31—48no—
293C2×C4×C31—44no—
294C2×C4×C31—48no—
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—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31#12012yes—
312C2×C4×C31#12012yes—
313C2×C4×C31C22⋊Q812yes—
314C2×C4×C31#13512yes—
315C2×C4×C31C22×D411yescharacteristic
316C2×C4×C31C22×D411yescharacteristic
317C2×C4×C31C22×Q811yescharacteristic
318C2×C4×C31C2×#4111yescharacteristic
319C2×C4×C31C2×#4111yescharacteristic
320C2×C4×C31C2×#4111yescharacteristic
321C8×C31—41no—
322C8×C31—41no—
323C8×C31—41no—
324C8×C31—41no—
325C2×C4×#41C2×C3111yescharacteristic
326C2×#479C2×C3111yescharacteristic, complemented
327C2×#478C2×C3111yescharacteristic, complemented
328#2851C2×C3111yescharacteristic, complemented
329#1865C2×C3111yescharacteristic, complemented
330#1864C2×C3111yescharacteristic, complemented
331#1863C2×C3111yescharacteristic, complemented
332#1862C2×C3111yescharacteristic, complemented
333#1854C2×C3111yescharacteristic, complemented
334#1854C2×C3111yescharacteristic, complemented
335#1805C2×C3111yescharacteristic, complemented
336#1804C2×C3111yescharacteristic, complemented
337#1797C2×C3111yescharacteristic, complemented
338#1788C2×C3111yescharacteristic
339#1788C2×C3111yescharacteristic
340C22×C31—22no—
341C22×C31—22no—
342C22×C31—22no—
343C22×C31—24no—
344C22×C31—42no—
345C22×C31—42no—
346C22×C31—41no—
347C22×C31—42no—
348C22×C31—41no—
349C22×C31—42no—
350C22×C31—41no—
351C22×C31—42no—
352C22×C31—41no—
353C22×C31—42no—
354C22×C31C2×#12011yescharacteristic
355C22×C31C2×C22⋊Q811yescharacteristic
356C22×C31#52511yescharacteristic
357C22×C31C2×#13511yescharacteristic
358C22×C31#57511yescharacteristic
359C22×C31#57511yescharacteristic
360C22×C31#57511yescharacteristic
361C4×C31—22no—
362C4×C31—24no—
363C4×C31—22no—
364C4×C31—22no—
365C4×C31—22no—
366C4×C31—42no—
367C4×C31—41no—
368C4×C31—42no—
369C4×C31—81no—
370C4×C31—81no—
371C4×C31—81no—
372C4×C31—81no—
373C4×C31C2×C22⋊Q811yescharacteristic
374C4×C31C2×C22⋊Q811yescharacteristic
375C4×C31#52511yescharacteristic
376C4×C31#52511yescharacteristic
377C22×#41C22×C3111yescharacteristic
378C2×#125C22×C3111yescharacteristic
379C4×#41—24no—
380C4×#41—24no—
381C2×C4×Q8C22×C3111yescharacteristic
382C2×C4×Q8C22×C3111yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4—21no—
385C2×C4×D4C22×C3111yescharacteristic
386C2×C4×D4C22×C3111yescharacteristic
387C2×#117—21no—
388C2×#117C22×C3111yescharacteristic
389C22×C42—21no—
390C22×C42C22×C3111yescharacteristic
391#479—24no—
392#478—24no—
393C2×#107C22×C3111yescharacteristic
394C2×#107C22×C3111yescharacteristic
395C2×#106C22×C3111yescharacteristic
396C2×#106C22×C3111yescharacteristic
397C2×C4⋊C8C22×C3111yescharacteristic
398C2×C4⋊C8C22×C3111yescharacteristic
399C2×#103C22×C3111yescharacteristic
400C2×#103C22×C3111yescharacteristic
401C2×#103C22×C3111yescharacteristic
402C2×#103C22×C3111yescharacteristic
403C2×#102C22×C3111yescharacteristic
404C2×#102C22×C3111yescharacteristic
405C2×#102C22×C3111yescharacteristic
406C2×#102C22×C3111yescharacteristic
407C2×C22⋊C8C22×C3111yescharacteristic
408C2×C22⋊C8C22×C3111yescharacteristic
409#389C22×C3111yescharacteristic
410#389C22×C3111yescharacteristic
411#387—21no—
412#387—21no—
413#385—21no—
414#385—21no—
415#382C22×C3111yescharacteristic
416#380C22×C3111yescharacteristic
417#380C22×C3111yescharacteristic
418#340C22×C3111yescharacteristic
419#340C22×C3111yescharacteristic
420#340C22×C3111yescharacteristic
421#340C22×C3111yescharacteristic
422#336C22×C3111yescharacteristic
423#336C22×C3111yescharacteristic
424C2×C31—42no—
425C2×C31—44no—
426C2×C31#284811yescharacteristic
427C2×C31#300211yescharacteristic
428C2×C31#300511yescharacteristic
429C2×C31#307611yescharacteristic
430C2×C31#308011yescharacteristic
431C2×C31#310211yescharacteristic
432C2×C31#311111yescharacteristic
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—22no—
437C2×#41—22no—
438C2×#41Q8×C3114yes—
439C22×Q8C23×C3111yescharacteristic
440C22×D4—21no—
441C22×D4C23×C3111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—21no—
445C23×C4D4×C3111yescharacteristic
446C23×C4D4×C3111yescharacteristic
447C23×C4C23×C3111yescharacteristic
448C22×C8C23×C3111yescharacteristic
449C22×C8C23×C3111yescharacteristic
450C22×C8C23×C3111yescharacteristic
451C22×C8C23×C3111yescharacteristic
452#125—22no—
453#125—22no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8D4×C3114yes—
458C4×D4—28no—
459C4×D4—28no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4D4×C3114yes—
464#117—28no—
465#117—22no—
466#117—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4C23×C3111yescharacteristic
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C4⋊C4C23×C3111yescharacteristic
476C2×C4⋊C4C23×C3111yescharacteristic
477C2×C4⋊C4C23×C3111yescharacteristic
478C2×C4⋊C4C23×C3111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C42—28no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42D4×C3111yescharacteristic
491C2×C42D4×C3111yescharacteristic
492C2×C42C23×C3111yescharacteristic
493C2×C42C23×C3111yescharacteristic
494#107—22no—
495#107—22no—
496#106—22no—
497#106—22no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500#103—22no—
501#103—22no—
502#103—22no—
503#103—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C31#3296111yescharacteristic, direct product factor, Sylow
517C24—21no—
518C24C2×D4×C3111yescharacteristic
519#41—28no—
520#41—28no—
521#41—28no—
522#41—28no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8C2×D4×C3112yes—
527C2×Q8C2×Q8×C3112yes—
528C2×Q8#41×C3112yes—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4C2×D4×C3112yes—
536C2×D4C2×Q8×C3112yes—
537C2×D4#41×C3112yes—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4C2×D4×C3111yescharacteristic
565C22×C4C2×D4×C3111yescharacteristic
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C2×Q8×C3112yes—
570C22×C4#41×C3112yes—
571C22×C4C24×C3111yescharacteristic
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4C2×D4×C3112yes—
601C4⋊C4C2×D4×C3112yes—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C42—24no—
608C42—24no—
609C42—22no—
610C42—24no—
611C42—22no—
612C42—21no—
613C42—21no—
614C42C2×D4×C3112yes—
615C42C2×D4×C3112yes—
616C23—21no—
617C23—22no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C31×C22⋊Q812yes—
630C23C22×D4×C3111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8C31×C22⋊Q814yes—
635D4—216no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4C31×C22⋊Q814yes—
640C2×C4—216no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—44no—
662C2×C4—48no—
663C2×C4—44no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4C31×#12012yes—
682C2×C4C31×#12012yes—
683C2×C4C31×C22⋊Q812yes—
684C2×C4C31×#13512yes—
685C2×C4C22×D4×C3111yescharacteristic
686C2×C4C22×D4×C3111yescharacteristic
687C2×C4C22×Q8×C3111yescharacteristic
688C2×C4C2×#41×C3111yescharacteristic
689C2×C4C2×#41×C3111yescharacteristic
690C2×C4C2×#41×C3111yescharacteristic
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—24no—
699C22—42no—
700C22—42no—
701C22—41no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—41no—
708C22—42no—
709C22C2×C31×#12011yescharacteristic
710C22C2×C31×C22⋊Q811yescharacteristic
711C22C31×#52511yescharacteristic
712C22C2×C31×#13511yescharacteristic
713C22C31×#57511yescharacteristic
714C22C31×#57511yescharacteristic
715C22C31×#57511yescharacteristic
716C4—22no—
717C4—24no—
718C4—22no—
719C4—22no—
720C4—22no—
721C4—42no—
722C4—41no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4C2×C31×C22⋊Q811yescharacteristic
729C4C2×C31×C22⋊Q811yescharacteristic
730C4C31×#52511yescharacteristic
731C4C31×#52511yescharacteristic
732C2—42no—
733C2—44no—
734C2C31×#284811yescharacteristic
735C2C31×#300211yescharacteristic
736C2C31×#300511yescharacteristic
737C2C31×#307611yescharacteristic
738C2C31×#308011yescharacteristic
739C2C31×#310211yescharacteristic
740C2C31×#311111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#479C2semidirect
3. C2×C31×#478C2semidirect
4. C31×#2851C2semidirect
5. C31×#1865C2semidirect
6. C31×#1864C2semidirect
7. C31×#1863C2semidirect
8. C31×#1862C2semidirect
9. C31×#1854C2semidirect
10. C31×#1854C2semidirect
11. C31×#1805C2semidirect
12. C31×#1804C2semidirect
13. C31×#1797C2semidirect
245. #32961C31direct (N × H)
326. C2×#479C2×C31semidirect
327. C2×#478C2×C31semidirect
328. #2851C2×C31semidirect
329. #1865C2×C31semidirect
330. #1864C2×C31semidirect
331. #1863C2×C31semidirect
332. #1862C2×C31semidirect
333. #1854C2×C31semidirect
334. #1854C2×C31semidirect
335. #1805C2×C31semidirect
336. #1804C2×C31semidirect
337. #1797C2×C31semidirect
516. C31#32961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#41×C312
C2×C31×#4792
C2×C31×#4782
C31×#28512
C31×#18652
C31×#18642
C31×#18632
C31×#18622
C31×#18542
C31×#18052
C31×#18042
C31×#17972
C31×#17882
#3296131