Finite Group Databasebeta

← C31×#25654 #21482413

Subgroups — C31×#25654 #21482413

Order 7936.

1018 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#556C211yesmaximal, characteristic
2C2×C31×#488C211yesmaximal, characteristic
3C2×C31×#479C211yesmaximal, characteristic, complemented
4C31×#2584C211yesmaximal, characteristic, complemented
5C31×#2043C211yesmaximal, characteristic, complemented
6C31×#2043C211yesmaximal, characteristic, complemented
7C31×#2042C211yesmaximal, characteristic
8C31×#2042C211yesmaximal, characteristic
9C31×#1984C211yesmaximal, characteristic, complemented
10C31×#1983C211yesmaximal, characteristic
11C31×#1865C211yesmaximal, characteristic, complemented
12C31×#1864C211yesmaximal, characteristic
13C31×#1863C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic
15C4×C31×#103C211yesmaximal, characteristic, complemented
16C31×#556—24no—
17C31×#556—24no—
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#126—21no—
20C2×C31×#126—21no—
21C2×C31×#125C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×#124C2211yescharacteristic
24C2×C31×C22⋊Q8—21no—
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117—21no—
30C31×#488—24no—
31C31×#479—24no—
32C2×C31×#107C2211yescharacteristic
33C2×C31×#106C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C4×C8×C31C2211yescharacteristic
48C31×#398—21no—
49C31×#395—21no—
50C31×#389—21no—
51C31×#389—21no—
52C31×#389C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#389C2211yescharacteristic
55C31×#389C2211yescharacteristic
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C31×C4⋊Q8—22no—
73C31×C4⋊Q8—22no—
74C31×#126—28no—
75C31×#126—28no—
76C31×#125—22no—
77C31×#125—22no—
78C31×#124—22no—
79C31×#124—22no—
80C31×#124—22no—
81C31×#124D414yes—
82C31×C22⋊Q8—28no—
83C4×Q8×C31—22no—
84C4×Q8×C31—22no—
85C4×Q8×C31—22no—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×Q8×C31D414yes—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C31×#117—28no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
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×C31D411yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
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×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31C2311yescharacteristic
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×#107—22no—
122C31×#106—22no—
123C31×C4⋊C8—22no—
124C31×#103—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C4×C8×C31—22no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C24×C31—21no—
143C2×Q8×C31—22no—
144C2×Q8×C31—22no—
145C2×Q8×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—41no—
156C2×Q8×C31C2×D412yes—
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×C31C2×D412yes—
164C22×C4×C31—24no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2411yescharacteristic
181C2×C8×C31—21no—
182C2×C8×C31—21no—
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—
193C4⋊C4×C31—24no—
194C4⋊C4×C31—24no—
195C4⋊C4×C31—24no—
196C4⋊C4×C31—24no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—81no—
212C4⋊C4×C31—81no—
213C4⋊C4×C31C2×D412yes—
214C4⋊C4×C31#4112yes—
215C4⋊C4×C31#4112yes—
216C22⋊C4×C31—24no—
217C22⋊C4×C31—24no—
218C22⋊C4×C31—24no—
219C22⋊C4×C31—24no—
220C22⋊C4×C31—24no—
221C42×C31—24no—
222C42×C31—24no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—21no—
227C42×C31—81no—
228C42×C31C2×D412yes—
229C42×C31C2×D412yes—
230#25654C3111yesmaximal, characteristic, direct product factor, Sylow
231C23×C31—22no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31C22×D411yescharacteristic
239Q8×C31—22no—
240Q8×C31—22no—
241Q8×C31—22no—
242Q8×C31—22no—
243Q8×C31—44no—
244Q8×C31—41no—
245Q8×C31—41no—
246Q8×C31—41no—
247Q8×C31—41no—
248D4×C31—22no—
249D4×C31—22no—
250D4×C31—41no—
251D4×C31—41no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—21no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
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—48no—
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—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31#12012yes—
290C2×C4×C31#12012yes—
291C2×C4×C31#13512yes—
292C2×C4×C31C22×D411yescharacteristic
293C2×C4×C31C22×D411yescharacteristic
294C2×C4×C31C2×#4111yescharacteristic
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C312−1+411yescharacteristic
297C2×C4×C312−1+411yescharacteristic
298C8×C31—41no—
299C8×C31—41no—
300C8×C31—41no—
301C8×C31—41no—
302C2×#556C2×C3111yescharacteristic
303C2×#488C2×C3111yescharacteristic
304C2×#479C2×C3111yescharacteristic, complemented
305#2584C2×C3111yescharacteristic, complemented
306#2043C2×C3111yescharacteristic, complemented
307#2043C2×C3111yescharacteristic, complemented
308#2042C2×C3111yescharacteristic
309#2042C2×C3111yescharacteristic
310#1984C2×C3111yescharacteristic, complemented
311#1983C2×C3111yescharacteristic
312#1865C2×C3111yescharacteristic, complemented
313#1864C2×C3111yescharacteristic
314#1863C2×C3111yescharacteristic, complemented
315#1862C2×C3111yescharacteristic
316C4×#103C2×C3111yescharacteristic, complemented
317C22×C31—42no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—81no—
321C22×C31—81no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31C2×#12011yescharacteristic
325C22×C31#54811yescharacteristic
326C22×C31#54811yescharacteristic
327C22×C31C2×#13511yescharacteristic
328C22×C31#57511yescharacteristic
329C22×C31#57711yescharacteristic
330C22×C31#57811yescharacteristic
331C4×C31—22no—
332C4×C31—22no—
333C4×C31—22no—
334C4×C31—42no—
335C4×C31—42no—
336C4×C31—42no—
337C4×C31—42no—
338C4×C31—41no—
339C4×C31—42no—
340C4×C31—41no—
341C4×C31—41no—
342C4×C31—81no—
343C4×C31—81no—
344C4×C31#53211yescharacteristic
345C4×C31#53611yescharacteristic
346C4×C31#54711yescharacteristic
347C4×C31#54711yescharacteristic
348#556—24no—
349#556—24no—
350C2×C4⋊Q8C22×C3111yescharacteristic
351C2×#126—21no—
352C2×#126—21no—
353C2×#125C22×C3111yescharacteristic
354C2×#124C22×C3111yescharacteristic
355C2×#124C22×C3111yescharacteristic
356C2×C22⋊Q8—21no—
357C2×C4×Q8C22×C3111yescharacteristic
358C2×C4×Q8C22×C3111yescharacteristic
359C2×C4×Q8C22×C3111yescharacteristic
360C2×C4×D4C22×C3111yescharacteristic
361C2×#117—21no—
362#488—24no—
363#479—24no—
364C2×#107C22×C3111yescharacteristic
365C2×#106C22×C3111yescharacteristic
366C2×C4⋊C8C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×#103C22×C3111yescharacteristic
369C2×#103C22×C3111yescharacteristic
370C2×#103C22×C3111yescharacteristic
371C2×#103C22×C3111yescharacteristic
372C2×#103C22×C3111yescharacteristic
373C2×#103C22×C3111yescharacteristic
374C2×#103C22×C3111yescharacteristic
375C2×#102C22×C3111yescharacteristic
376C2×#102C22×C3111yescharacteristic
377C2×#102C22×C3111yescharacteristic
378C2×#102C22×C3111yescharacteristic
379C2×C4×C8C22×C3111yescharacteristic
380#398—21no—
381#395—21no—
382#389—21no—
383#389—21no—
384#389C22×C3111yescharacteristic
385#389C22×C3111yescharacteristic
386#389C22×C3111yescharacteristic
387#389C22×C3111yescharacteristic
388C4×C4⋊C4C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#340C22×C3111yescharacteristic
391#336C22×C3111yescharacteristic
392#336C22×C3111yescharacteristic
393#336C22×C3111yescharacteristic
394#336C22×C3111yescharacteristic
395C2×C31—82no—
396C2×C31#243211yescharacteristic
397C2×C31#300211yescharacteristic
398C2×C31#301311yescharacteristic
399C2×C31#336011yescharacteristic
400C2×C31#336411yescharacteristic
401C2×C31#337611yescharacteristic
402C2×C31#337711yescharacteristic
403C22×Q8D4×C3111yescharacteristic
404C22×Q8C23×C3111yescharacteristic
405C22×Q8C23×C3111yescharacteristic
406C22×D4C23×C3111yescharacteristic
407C23×C4—21no—
408C22×C8C23×C3111yescharacteristic
409C22×C8C23×C3111yescharacteristic
410C22×C8C23×C3111yescharacteristic
411C22×C8C23×C3111yescharacteristic
412C4⋊Q8—22no—
413C4⋊Q8—22no—
414#126—28no—
415#126—28no—
416#125—22no—
417#125—22no—
418#124—22no—
419#124—22no—
420#124—22no—
421#124D4×C3114yes—
422C22⋊Q8—28no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8D4×C3114yes—
429C4×D4—22no—
430C4×D4—22no—
431#117—28no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
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×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C23×C3111yescharacteristic
459C2×C42C23×C3111yescharacteristic
460C2×C42C23×C3111yescharacteristic
461#107—22no—
462#106—22no—
463C4⋊C8—22no—
464#103—22no—
465#103—22no—
466#103—22no—
467#103—22no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476C4×C8—22no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482C31#2565411yescharacteristic, direct product factor, Sylow
483C24—21no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8C2×D4×C3112yes—
498C2×Q8C2×D4×C3112yes—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C3112yes—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3111yescharacteristic
517C22×C4C2×D4×C3111yescharacteristic
518C22×C4C2×D4×C3111yescharacteristic
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C24×C3111yescharacteristic
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×C8—21no—
533C2×C8—21no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
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—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C2×D4×C3112yes—
555C4⋊C4#41×C3112yes—
556C4⋊C4#41×C3112yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C42—24no—
563C42—24no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—81no—
569C42C2×D4×C3112yes—
570C42C2×D4×C3112yes—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×D4×C3111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—44no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588D4—22no—
589D4—22no—
590D4—41no—
591D4—41no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—48no—
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—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4C31×#12012yes—
630C2×C4C31×#12012yes—
631C2×C4C31×#13512yes—
632C2×C4C22×D4×C3111yescharacteristic
633C2×C4C22×D4×C3111yescharacteristic
634C2×C4C2×#41×C3111yescharacteristic
635C2×C4C2×#41×C3111yescharacteristic
636C2×C4C31×2−1+411yescharacteristic
637C2×C4C31×2−1+411yescharacteristic
638C8—41no—
639C8—41no—
640C8—41no—
641C8—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×C31×#12011yescharacteristic
650C22C31×#54811yescharacteristic
651C22C31×#54811yescharacteristic
652C22C2×C31×#13511yescharacteristic
653C22C31×#57511yescharacteristic
654C22C31×#57711yescharacteristic
655C22C31×#57811yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—42no—
663C4—41no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4C31×#53211yescharacteristic
670C4C31×#53611yescharacteristic
671C4C31×#54711yescharacteristic
672C4C31×#54711yescharacteristic
673C2—82no—
674C2C31×#243211yescharacteristic
675C2C31×#300211yescharacteristic
676C2C31×#301311yescharacteristic
677C2C31×#336011yescharacteristic
678C2C31×#336411yescharacteristic
679C2C31×#337611yescharacteristic
680C2C31×#337711yescharacteristic
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×C31×#479C2semidirect
4. C31×#2584C2semidirect
5. C31×#2043C2semidirect
6. C31×#2043C2semidirect
9. C31×#1984C2semidirect
11. C31×#1865C2semidirect
13. C31×#1863C2semidirect
15. C4×C31×#103C2semidirect
230. #25654C31direct (N × H)
304. C2×#479C2×C31semidirect
305. #2584C2×C31semidirect
306. #2043C2×C31semidirect
307. #2043C2×C31semidirect
310. #1984C2×C31semidirect
312. #1865C2×C31semidirect
314. #1863C2×C31semidirect
316. C4×#103C2×C31semidirect
482. C31#25654direct (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×#4882
C2×C31×#4792
C31×#25842
C31×#20432
C31×#20422
C31×#19842
C31×#19832
C31×#18652
C31×#18642
C31×#18632
C31×#18622
C4×C31×#1032
#2565431