Finite Group Databasebeta

← C31×#24337 #21481096

Subgroups — C31×#24337 #21481096

Order 7936.

1070 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic
2C2×C31×#479C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C31C211yesmaximal, characteristic
4C31×#2581C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2058C211yesmaximal, characteristic, complemented
7C31×#2026C211yesmaximal, characteristic, complemented
8C31×#2024C211yesmaximal, characteristic, complemented
9C31×#1991C211yesmaximal, characteristic, complemented
10C31×#1984C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic
12C31×#1877C211yesmaximal, characteristic
13C31×#1864C211yesmaximal, characteristic
14C31×#1862C211yesmaximal, characteristic
15C31×#1804C211yesmaximal, characteristic
16C22×SD16×C31C2211yescharacteristic
17C31×#554—24no—
18C31×#554—24no—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#125C2211yescharacteristic
21C2×C31×#125C2211yescharacteristic
22C2×C31×C22⋊Q8—21no—
23C2×C31×C22⋊Q8—21no—
24C2×C31×C22⋊Q8—21no—
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C22×C4⋊C4×C31—21no—
31C31×#479—24no—
32C4×SD16×C31—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#106C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C4×C8×C31C2211yescharacteristic
44C31×#400—21no—
45C31×#395—21no—
46C31×#391C2211yescharacteristic
47C31×#391C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#387—21no—
51C31×#387—21no—
52C31×#382C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31D411yescharacteristic
65C22×Q8×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×C31Q814yescomplemented
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×C4⋊Q8—22no—
78C31×C4⋊Q8—22no—
79C31×#125—22no—
80C31×#125—22no—
81C31×#125—22no—
82C31×#125D414yes—
83C31×C22⋊Q8—28no—
84C31×C22⋊Q8—28no—
85C31×C22⋊Q8—28no—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31D414yes—
96C2×C4⋊C4×C31—28no—
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×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31D411yescharacteristic
107C2×C4⋊C4×C31D411yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
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×#107—22no—
122C31×#106—22no—
123C31×#106—22no—
124C31×C4⋊C8—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103—22no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—22no—
131C4×C8×C31—22no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C24×C31—21no—
141C2×Q8×C31—24no—
142C2×Q8×C31—22no—
143C2×Q8×C31—22no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—41no—
150C2×Q8×C31—81no—
151C2×Q8×C31—81no—
152C2×Q8×C31C2×Q812yes—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31C2×D412yes—
157C2×D4×C31C2×Q812yes—
158C2×D4×C31#4112yes—
159C22×C4×C31—24no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—24no—
165C22×C4×C31—24no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—81no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31—81no—
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2411yescharacteristic
182SD16×C31—28no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31C2×Q812yes—
195C4⋊C4×C31—24no—
196C4⋊C4×C31—24no—
197C4⋊C4×C31—24no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—42no—
215C4⋊C4×C31C2×D412yes—
216C4⋊C4×C31C2×D412yes—
217C4⋊C4×C31C2×D412yes—
218C22⋊C4×C31—24no—
219C22⋊C4×C31—24no—
220C22⋊C4×C31—24no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—42no—
226C42×C31C2×D412yes—
227C42×C31C2×D412yes—
228#24337C3111yesmaximal, characteristic, direct product factor, Sylow
229C23×C31—22no—
230C23×C31—22no—
231C23×C31—22no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31C22×D411yescharacteristic
237Q8×C31—22no—
238Q8×C31—22no—
239Q8×C31—44no—
240Q8×C31—41no—
241Q8×C31—41no—
242Q8×C31—84no—
243D4×C31—22no—
244D4×C31—22no—
245D4×C31—22no—
246D4×C31C22⋊Q814yes—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—48no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—84no—
285C2×C4×C31—84no—
286C2×C4×C31#12012yes—
287C2×C4×C31#12012yes—
288C2×C4×C31#13512yes—
289C2×C4×C31C22×D411yescharacteristic
290C2×C4×C31C22×D411yescharacteristic
291C2×C4×C31C22×Q811yescharacteristic
292C2×C4×C31C2×#4111yescharacteristic
293C2×C4×C312−1+411yescharacteristic
294C2×C4×C312−1+411yescharacteristic
295C8×C31—22no—
296C8×C31—41no—
297C8×C31—41no—
298C8×C31—41no—
299C2×#554C2×C3111yescharacteristic
300C2×#479C2×C3111yescharacteristic, complemented
301C2×C4×SD16C2×C3111yescharacteristic
302#2581C2×C3111yescharacteristic, complemented
303#2059C2×C3111yescharacteristic, complemented
304#2058C2×C3111yescharacteristic, complemented
305#2026C2×C3111yescharacteristic, complemented
306#2024C2×C3111yescharacteristic, complemented
307#1991C2×C3111yescharacteristic, complemented
308#1984C2×C3111yescharacteristic, complemented
309#1877C2×C3111yescharacteristic
310#1877C2×C3111yescharacteristic
311#1864C2×C3111yescharacteristic
312#1862C2×C3111yescharacteristic
313#1804C2×C3111yescharacteristic
314C22×C31—24no—
315C22×C31—42no—
316C22×C31—42no—
317C22×C31—42no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31C2×#12011yescharacteristic
322C22×C31#54811yescharacteristic
323C22×C31D4×Q811yescharacteristic
324C22×C31C2×#13511yescharacteristic
325C22×C31#57511yescharacteristic
326C22×C31#57711yescharacteristic
327C22×C31#57711yescharacteristic
328C4×C31—22no—
329C4×C31—22no—
330C4×C31—22no—
331C4×C31—42no—
332C4×C31—41no—
333C4×C31—42no—
334C4×C31—41no—
335C4×C31—41no—
336C4×C31—42no—
337C4×C31—42no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31—81no—
341C4×C31C2×C22⋊Q811yescharacteristic
342C4×C31#53611yescharacteristic
343C4×C31#54811yescharacteristic
344C4×C31D4×Q811yescharacteristic
345C22×SD16C22×C3111yescharacteristic
346#554—24no—
347#554—24no—
348C2×C4⋊Q8C22×C3111yescharacteristic
349C2×#125C22×C3111yescharacteristic
350C2×#125C22×C3111yescharacteristic
351C2×C22⋊Q8—21no—
352C2×C22⋊Q8—21no—
353C2×C22⋊Q8—21no—
354C2×C4×Q8C22×C3111yescharacteristic
355C2×C4×Q8C22×C3111yescharacteristic
356C2×C4×D4C22×C3111yescharacteristic
357C2×C4×D4C22×C3111yescharacteristic
358C2×C4×D4C22×C3111yescharacteristic
359C22×C4⋊C4—21no—
360#479—24no—
361C4×SD16—24no—
362C2×#107C22×C3111yescharacteristic
363C2×#106C22×C3111yescharacteristic
364C2×#106C22×C3111yescharacteristic
365C2×C4⋊C8C22×C3111yescharacteristic
366C2×#103C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×#103C22×C3111yescharacteristic
369C2×#102C22×C3111yescharacteristic
370C2×#102C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×C4×C8C22×C3111yescharacteristic
373#400—21no—
374#395—21no—
375#391C22×C3111yescharacteristic
376#391C22×C3111yescharacteristic
377#389C22×C3111yescharacteristic
378#389C22×C3111yescharacteristic
379#387—21no—
380#387—21no—
381#382C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#336C22×C3111yescharacteristic
389#336C22×C3111yescharacteristic
390#336C22×C3111yescharacteristic
391#336C22×C3111yescharacteristic
392C2×C31—44no—
393C2×C31#240911yescharacteristic
394C2×C31#300211yescharacteristic
395C2×C31#300911yescharacteristic
396C2×C31#336011yescharacteristic
397C2×C31#337611yescharacteristic
398C2×C31#338111yescharacteristic
399C2×C31#338811yescharacteristic
400C22×Q8—21no—
401C22×Q8D4×C3111yescharacteristic
402C22×Q8C23×C3111yescharacteristic
403C22×D4C23×C3111yescharacteristic
404C23×C4—21no—
405C23×C4—21no—
406C23×C4—21no—
407C2×SD16—22no—
408C2×SD16—22no—
409C2×SD16Q8×C3114yescomplemented
410C22×C8C23×C3111yescharacteristic
411C22×C8C23×C3111yescharacteristic
412C22×C8C23×C3111yescharacteristic
413C22×C8C23×C3111yescharacteristic
414C4⋊Q8—22no—
415C4⋊Q8—22no—
416#125—22no—
417#125—22no—
418#125—22no—
419#125D4×C3114yes—
420C22⋊Q8—28no—
421C22⋊Q8—28no—
422C22⋊Q8—28no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4D4×C3114yes—
433C2×C4⋊C4—28no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4D4×C3111yescharacteristic
443C2×C4⋊C4D4×C3111yescharacteristic
444C2×C4⋊C4D4×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—21no—
455C2×C42C23×C3111yescharacteristic
456C2×C42C23×C3111yescharacteristic
457C2×C42C23×C3111yescharacteristic
458#107—22no—
459#106—22no—
460#106—22no—
461C4⋊C8—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#102—22no—
466#102—22no—
467#102—22no—
468C4×C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477C31#2433711yescharacteristic, direct product factor, Sylow
478C24—21no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—41no—
488C2×Q8—81no—
489C2×Q8—81no—
490C2×Q8C2×Q8×C3112yes—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×D4×C3112yes—
495C2×D4C2×Q8×C3112yes—
496C2×D4#41×C3112yes—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4C2×D4×C3111yescharacteristic
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3111yescharacteristic
517C22×C4C2×D4×C3111yescharacteristic
518C22×C4C2×D4×C3111yescharacteristic
519C22×C4C24×C3111yescharacteristic
520SD16—28no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8C2×Q8×C3112yes—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4C2×D4×C3112yes—
554C4⋊C4C2×D4×C3112yes—
555C4⋊C4C2×D4×C3112yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—42no—
564C42C2×D4×C3112yes—
565C42C2×D4×C3112yes—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C22×D4×C3111yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—44no—
577Q8—41no—
578Q8—41no—
579Q8—84no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4C31×C22⋊Q814yes—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—48no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4C31×#12012yes—
624C2×C4C31×#12012yes—
625C2×C4C31×#13512yes—
626C2×C4C22×D4×C3111yescharacteristic
627C2×C4C22×D4×C3111yescharacteristic
628C2×C4C22×Q8×C3111yescharacteristic
629C2×C4C2×#41×C3111yescharacteristic
630C2×C4C31×2−1+411yescharacteristic
631C2×C4C31×2−1+411yescharacteristic
632C8—22no—
633C8—41no—
634C8—41no—
635C8—41no—
636C22—24no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22C2×C31×#12011yescharacteristic
644C22C31×#54811yescharacteristic
645C22D4×Q8×C3111yescharacteristic
646C22C2×C31×#13511yescharacteristic
647C22C31×#57511yescharacteristic
648C22C31×#57711yescharacteristic
649C22C31×#57711yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4C2×C31×C22⋊Q811yescharacteristic
664C4C31×#53611yescharacteristic
665C4C31×#54811yescharacteristic
666C4D4×Q8×C3111yescharacteristic
667C2—44no—
668C2C31×#240911yescharacteristic
669C2C31×#300211yescharacteristic
670C2C31×#300911yescharacteristic
671C2C31×#336011yescharacteristic
672C2C31×#337611yescharacteristic
673C2C31×#338111yescharacteristic
674C2C31×#338811yescharacteristic
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
2. C2×C31×#479C2semidirect
4. C31×#2581C2semidirect
5. C31×#2059C2semidirect
6. C31×#2058C2semidirect
7. C31×#2026C2semidirect
8. C31×#2024C2semidirect
9. C31×#1991C2semidirect
10. C31×#1984C2semidirect
72. C2×SD16×C31Q8semidirect
228. #24337C31direct (N × H)
300. C2×#479C2×C31semidirect
302. #2581C2×C31semidirect
303. #2059C2×C31semidirect
304. #2058C2×C31semidirect
305. #2026C2×C31semidirect
306. #2024C2×C31semidirect
307. #1991C2×C31semidirect
308. #1984C2×C31semidirect
409. C2×SD16Q8×C31semidirect
477. C31#24337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5542
C2×C31×#4792
C2×C4×SD16×C312
C31×#25812
C31×#20592
C31×#20582
C31×#20262
C31×#20242
C31×#19912
C31×#19842
C31×#18772
C31×#18642
C31×#18622
C31×#18042
#2433731