Finite Group Databasebeta

← C31×#23578 #21480337

Subgroups — C31×#23578 #21480337

Order 7936.

1176 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic
2C2×C31×#441C211yesmaximal, characteristic, complemented
3C2×C31×#440C211yesmaximal, characteristic, complemented
4C4×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2042C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic
9C31×#2026C211yesmaximal, characteristic, complemented
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#2001C211yesmaximal, characteristic, complemented
12C31×#2000C211yesmaximal, characteristic
13C31×#1763C211yesmaximal, characteristic, complemented
14C31×#1762C211yesmaximal, characteristic, complemented
15C31×#1749C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C31×#529—24no—
19C31×#529—24no—
20C2×C31×#126—21no—
21C2×C31×#125C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C2×C4×D4×C31—21no—
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117—21no—
32C22×C42×C31C2211yescharacteristic
33C31×#441—24no—
34C31×#440—24no—
35C2×C31×#107C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×#97C2211yescharacteristic
48C2×C31×#97C2211yescharacteristic
49C31×#391C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#387—21no—
52C31×#385—21no—
53C31×#380C2211yescharacteristic
54C4×C4⋊C4×C31—21no—
55C4×C4⋊C4×C31C2211yescharacteristic
56C4×C22⋊C4×C31—21no—
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31D411yescharacteristic
69C23×C4×C31D411yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C2×Q16×C31—22no—
72C2×Q16×C31—22no—
73C2×Q16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C31×#126—28no—
82C31×#125—22no—
83C31×#125—22no—
84C31×#124—22no—
85C31×#124—22no—
86C31×#123—28no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×#121—22no—
92C31×#121—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31D414yes—
97C4×D4×C31—28no—
98C4×D4×C31—22no—
99C4×D4×C31D414yes—
100C31×#117—28no—
101C2×C4⋊C4×C31—21no—
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×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31—22no—
122C2×C42×C31—22no—
123C2×C42×C31—21no—
124C2×C42×C31—21no—
125C2×C42×C31D411yescharacteristic
126C2×C42×C31D411yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C2×C42×C31C2311yescharacteristic
129C31×#107—22no—
130C31×#106—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×C22⋊C8—22no—
140C31×C22⋊C8—22no—
141C31×#97—22no—
142C31×#97—22no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31C2×D411yescharacteristic
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×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31C2×D412yes—
161C2×Q8×C31#4112yes—
162C2×D4×C31—24no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31C2×D412yes—
171C22×C4×C31—22no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—24no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—41no—
189C22×C4×C31—41no—
190C22×C4×C31—41no—
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×C31C2411yescharacteristic
199Q16×C31—28no—
200SD16×C31—28no—
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#4112yes—
212C2×C8×C31#4112yes—
213C4⋊C4×C31—24no—
214C4⋊C4×C31—24no—
215C4⋊C4×C31—24no—
216C4⋊C4×C31—24no—
217C4⋊C4×C31—24no—
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×C31C2×D412yes—
228C4⋊C4×C31C2×D412yes—
229C4⋊C4×C31#4112yes—
230C22⋊C4×C31—24no—
231C22⋊C4×C31—24no—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—24no—
234C22⋊C4×C31—24no—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—42no—
237C42×C31—22no—
238C42×C31—22no—
239C42×C31—24no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—42no—
243C42×C31—42no—
244C42×C31C2×D412yes—
245C42×C31C2×D412yes—
246#23578C3111yesmaximal, characteristic, direct product factor, Sylow
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—22no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31#13712yes—
261C23×C31C22×D411yescharacteristic
262Q8×C31—22no—
263Q8×C31—22no—
264Q8×C31—22no—
265Q8×C31—22no—
266Q8×C31—41no—
267Q8×C31—41no—
268Q8×C31—41no—
269Q8×C31—41no—
270D4×C31—22no—
271D4×C31—22no—
272D4×C31—48no—
273D4×C31—41no—
274D4×C31—41no—
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—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—44no—
294C2×C4×C31—44no—
295C2×C4×C31—48no—
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—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31#12012yes—
317C2×C4×C31#12012yes—
318C2×C4×C31C22×D411yescharacteristic
319C2×C4×C31C22×D411yescharacteristic
320C2×C4×C31C2×#4111yescharacteristic
321C2×C4×C31C2×#4111yescharacteristic
322C2×C4×C31C2×#4111yescharacteristic
323C2×C4×C31C2×#4111yescharacteristic
324C8×C31—22no—
325C8×C31—22no—
326C8×C31—41no—
327C8×C31—41no—
328C2×#529C2×C3111yescharacteristic
329C2×#441C2×C3111yescharacteristic, complemented
330C2×#440C2×C3111yescharacteristic, complemented
331C4×C22⋊Q8C2×C3111yescharacteristic, complemented
332#2059C2×C3111yescharacteristic, complemented
333#2042C2×C3111yescharacteristic, complemented
334#2036C2×C3111yescharacteristic, complemented
335#2034C2×C3111yescharacteristic
336#2026C2×C3111yescharacteristic, complemented
337#2015C2×C3111yescharacteristic, complemented
338#2001C2×C3111yescharacteristic, complemented
339#2000C2×C3111yescharacteristic
340#1763C2×C3111yescharacteristic, complemented
341#1762C2×C3111yescharacteristic, complemented
342#1749C2×C3111yescharacteristic, complemented
343C22×C31—22no—
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—41no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—42no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31C2×#12011yescharacteristic
358C22×C31#52511yescharacteristic
359C22×C31#53211yescharacteristic
360C22×C31C2×#13711yescharacteristic
361C22×C31#57511yescharacteristic
362C22×C31#57511yescharacteristic
363C22×C31#57511yescharacteristic
364C4×C31—22no—
365C4×C31—22no—
366C4×C31—42no—
367C4×C31—41no—
368C4×C31—42no—
369C4×C31—42no—
370C4×C31—41no—
371C4×C31—42no—
372C4×C31—41no—
373C4×C31—42no—
374C4×C31—81no—
375C4×C31—81no—
376C4×C31#52511yescharacteristic
377C4×C31#52511yescharacteristic
378C4×C31#53211yescharacteristic
379C4×C31#53211yescharacteristic
380C22×Q16C22×C3111yescharacteristic
381C22×SD16C22×C3111yescharacteristic
382#529—24no—
383#529—24no—
384C2×#126—21no—
385C2×#125C22×C3111yescharacteristic
386C2×#124C22×C3111yescharacteristic
387C2×#123—21no—
388C2×C22⋊Q8C22×C3111yescharacteristic
389C2×C22⋊Q8C22×C3111yescharacteristic
390C2×#121C22×C3111yescharacteristic
391C2×C4×Q8C22×C3111yescharacteristic
392C2×C4×Q8C22×C3111yescharacteristic
393C2×C4×D4—21no—
394C2×C4×D4C22×C3111yescharacteristic
395C2×#117—21no—
396C22×C42C22×C3111yescharacteristic
397#441—24no—
398#440—24no—
399C2×#107C22×C3111yescharacteristic
400C2×#106C22×C3111yescharacteristic
401C2×#103C22×C3111yescharacteristic
402C2×#103C22×C3111yescharacteristic
403C2×#103C22×C3111yescharacteristic
404C2×#103C22×C3111yescharacteristic
405C2×#103C22×C3111yescharacteristic
406C2×#102C22×C3111yescharacteristic
407C2×#102C22×C3111yescharacteristic
408C2×#102C22×C3111yescharacteristic
409C2×C22⋊C8C22×C3111yescharacteristic
410C2×C22⋊C8C22×C3111yescharacteristic
411C2×#97C22×C3111yescharacteristic
412C2×#97C22×C3111yescharacteristic
413#391C22×C3111yescharacteristic
414#389C22×C3111yescharacteristic
415#387—21no—
416#385—21no—
417#380C22×C3111yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4C22×C3111yescharacteristic
420C4×C22⋊C4—21no—
421#340C22×C3111yescharacteristic
422#340C22×C3111yescharacteristic
423#340C22×C3111yescharacteristic
424#340C22×C3111yescharacteristic
425#336C22×C3111yescharacteristic
426#336C22×C3111yescharacteristic
427C2×C31—42no—
428C2×C31—82no—
429C2×C31#238811yescharacteristic
430C2×C31#300511yescharacteristic
431C2×C31#300711yescharacteristic
432C2×C31#311111yescharacteristic
433C2×C31#311711yescharacteristic
434C2×C31#318111yescharacteristic
435C2×C31#318311yescharacteristic
436C22×Q8C23×C3111yescharacteristic
437C22×Q8C23×C3111yescharacteristic
438C22×D4—21no—
439C22×D4C23×C3111yescharacteristic
440C23×C4—21no—
441C23×C4D4×C3111yescharacteristic
442C23×C4D4×C3111yescharacteristic
443C23×C4C23×C3111yescharacteristic
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16—22no—
447C2×SD16—22no—
448C2×SD16—22no—
449C2×SD16—22no—
450C22×C8C23×C3111yescharacteristic
451C22×C8C23×C3111yescharacteristic
452C22×C8C23×C3111yescharacteristic
453C22×C8C23×C3111yescharacteristic
454#126—28no—
455#125—22no—
456#125—22no—
457#124—22no—
458#124—22no—
459#123—28no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464#121—22no—
465#121—22no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8D4×C3114yes—
470C4×D4—28no—
471C4×D4—22no—
472C4×D4D4×C3114yes—
473#117—28no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4C23×C3111yescharacteristic
482C2×C4⋊C4C23×C3111yescharacteristic
483C2×C4⋊C4C23×C3111yescharacteristic
484C2×C4⋊C4C23×C3111yescharacteristic
485C2×C4⋊C4C23×C3111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C42—21no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42D4×C3111yescharacteristic
499C2×C42D4×C3111yescharacteristic
500C2×C42C23×C3111yescharacteristic
501C2×C42C23×C3111yescharacteristic
502#107—22no—
503#106—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—22no—
508#103—22no—
509#102—22no—
510#102—22no—
511#102—22no—
512C22⋊C8—22no—
513C22⋊C8—22no—
514#97—22no—
515#97—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521C31#2357811yescharacteristic, direct product factor, Sylow
522C24—21no—
523C24C2×D4×C3111yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8C2×D4×C3112yes—
535C2×Q8#41×C3112yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4C2×D4×C3112yes—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C2×D4×C3111yescharacteristic
570C22×C4C2×D4×C3111yescharacteristic
571C22×C4C2×D4×C3111yescharacteristic
572C22×C4C24×C3111yescharacteristic
573Q16—28no—
574SD16—28no—
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—
584C2×C8—21no—
585C2×C8#41×C3112yes—
586C2×C8#41×C3112yes—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4C2×D4×C3112yes—
602C4⋊C4C2×D4×C3112yes—
603C4⋊C4#41×C3112yes—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—42no—
611C42—22no—
612C42—22no—
613C42—24no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42C2×D4×C3112yes—
619C42C2×D4×C3112yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C31×#13712yes—
634C23C22×D4×C3111yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—48no—
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×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4C31×#12012yes—
690C2×C4C31×#12012yes—
691C2×C4C22×D4×C3111yescharacteristic
692C2×C4C22×D4×C3111yescharacteristic
693C2×C4C2×#41×C3111yescharacteristic
694C2×C4C2×#41×C3111yescharacteristic
695C2×C4C2×#41×C3111yescharacteristic
696C2×C4C2×#41×C3111yescharacteristic
697C8—22no—
698C8—22no—
699C8—41no—
700C8—41no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×C31×#12011yescharacteristic
716C22C31×#52511yescharacteristic
717C22C31×#53211yescharacteristic
718C22C2×C31×#13711yescharacteristic
719C22C31×#57511yescharacteristic
720C22C31×#57511yescharacteristic
721C22C31×#57511yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—41no—
726C4—42no—
727C4—42no—
728C4—41no—
729C4—42no—
730C4—41no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4C31×#52511yescharacteristic
735C4C31×#52511yescharacteristic
736C4C31×#53211yescharacteristic
737C4C31×#53211yescharacteristic
738C2—42no—
739C2—82no—
740C2C31×#238811yescharacteristic
741C2C31×#300511yescharacteristic
742C2C31×#300711yescharacteristic
743C2C31×#311111yescharacteristic
744C2C31×#311711yescharacteristic
745C2C31×#318111yescharacteristic
746C2C31×#318311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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×#441C2semidirect
3. C2×C31×#440C2semidirect
4. C4×C31×C22⋊Q8C2semidirect
5. C31×#2059C2semidirect
6. C31×#2042C2semidirect
7. C31×#2036C2semidirect
9. C31×#2026C2semidirect
10. C31×#2015C2semidirect
11. C31×#2001C2semidirect
13. C31×#1763C2semidirect
14. C31×#1762C2semidirect
15. C31×#1749C2semidirect
246. #23578C31direct (N × H)
329. C2×#441C2×C31semidirect
330. C2×#440C2×C31semidirect
331. C4×C22⋊Q8C2×C31semidirect
332. #2059C2×C31semidirect
333. #2042C2×C31semidirect
334. #2036C2×C31semidirect
336. #2026C2×C31semidirect
337. #2015C2×C31semidirect
338. #2001C2×C31semidirect
340. #1763C2×C31semidirect
341. #1762C2×C31semidirect
342. #1749C2×C31semidirect
521. C31#23578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C2×C31×#4412
C2×C31×#4402
C4×C31×C22⋊Q82
C31×#20592
C31×#20422
C31×#20362
C31×#20342
C31×#20262
C31×#20152
C31×#20012
C31×#20002
C31×#17632
C31×#17622
C31×#17492
#2357831