Finite Group Databasebeta

← C31×#24310 #21481069

Subgroups — C31×#24310 #21481069

Order 7936.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic
2C2×C31×#479C211yesmaximal, characteristic, complemented
3C2×C31×#475C211yesmaximal, characteristic, complemented
4C31×#2323C211yesmaximal, characteristic
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2058C211yesmaximal, characteristic, complemented
7C31×#2026C211yesmaximal, characteristic, complemented
8C31×#2024C211yesmaximal, characteristic, complemented
9C31×#1989C211yesmaximal, characteristic, complemented
10C31×#1987C211yesmaximal, characteristic, complemented
11C31×#1873C211yesmaximal, characteristic
12C31×#1872C211yesmaximal, characteristic
13C31×#1854C211yesmaximal, characteristic
14C31×#1853C211yesmaximal, characteristic
15C31×#1798C211yesmaximal, characteristic
16C31×#544—24no—
17C31×#544—24no—
18C2×C31×C4⋊Q8—21no—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×#125—21no—
22C2×C31×#125C2211yescharacteristic
23C2×C31×#125C2211yescharacteristic
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#479—24no—
32C31×#475—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#106C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×C4⋊C8C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C31×#391C2211yescharacteristic
46C31×#389—21no—
47C31×#389C2211yescharacteristic
48C31×#388—21no—
49C31×#388—21no—
50C31×#387—21no—
51C31×#380C2211yescharacteristic
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31—21no—
65C22×Q8×C31C2311yescharacteristic
66C23×C4×C31—21no—
67C23×C4×C31C2311yescharacteristic
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C31×C4⋊Q8—28no—
73C31×C4⋊Q8—22no—
74C31×C4⋊Q8—22no—
75C31×C4⋊Q8—22no—
76C31×C4⋊Q8D414yes—
77C31×#125—28no—
78C31×#125—22no—
79C31×#125—22no—
80C31×#125—22no—
81C31×#125D414yes—
82C31×C22⋊Q8—28no—
83C31×C22⋊Q8—28no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8Q814yescomplemented
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C31×#117—22no—
89C31×#117—22no—
90C31×#117—22no—
91C31×#117—22no—
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—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31D411yescharacteristic
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C31×#107—22no—
124C31×#106—22no—
125C31×#106—22no—
126C31×#106—22no—
127C31×C4⋊C8—22no—
128C31×C4⋊C8—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×C22⋊C8—22no—
134C31×C22⋊C8—22no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C24×C31C2×D411yescharacteristic
141C2×Q8×C31—24no—
142C2×Q8×C31—24no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—81no—
149C2×Q8×C31—81no—
150C2×Q8×C31—81no—
151C2×Q8×C31—81no—
152C2×Q8×C31C2×Q812yes—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—24no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—81no—
167C22×C4×C31—81no—
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×Q812yes—
174C22×C4×C31#4112yes—
175C22×C4×C31C2411yescharacteristic
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
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—
188C4⋊C4×C31—24no—
189C4⋊C4×C31—24no—
190C4⋊C4×C31—24no—
191C4⋊C4×C31—24no—
192C4⋊C4×C31—24no—
193C4⋊C4×C31—24no—
194C4⋊C4×C31—24no—
195C4⋊C4×C31—22no—
196C4⋊C4×C31—22no—
197C4⋊C4×C31—24no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
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—81no—
209C4⋊C4×C31C2×D412yes—
210C4⋊C4×C31C2×D412yes—
211C4⋊C4×C31C2×D412yes—
212C4⋊C4×C31C2×D412yes—
213C4⋊C4×C31C2×Q812yes—
214C22⋊C4×C31—24no—
215C22⋊C4×C31—24no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—81no—
219C42×C31—24no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—42no—
223C42×C31—81no—
224C42×C31C2×D412yes—
225C42×C31C2×D412yes—
226#24310C3111yesmaximal, characteristic, direct product factor, Sylow
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31C22⋊Q812yes—
234C23×C31C22×D411yescharacteristic
235Q8×C31—22no—
236Q8×C31—22no—
237Q8×C31—41no—
238Q8×C31—41no—
239Q8×C31—84no—
240Q8×C31—84no—
241C2×C4×C31—21no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—22no—
251C2×C4×C31—21no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
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—84no—
282C2×C4×C31#12012yes—
283C2×C4×C31#12012yes—
284C2×C4×C31C22⋊Q812yes—
285C2×C4×C31C22×D411yescharacteristic
286C2×C4×C31C22×D411yescharacteristic
287C2×C4×C31C22×Q811yescharacteristic
288C2×C4×C31C2×#4111yescharacteristic
289C2×C4×C312−1+411yescharacteristic
290C2×C4×C312−1+411yescharacteristic
291C8×C31—41no—
292C8×C31—41no—
293C8×C31—41no—
294C8×C31—41no—
295C2×#544C2×C3111yescharacteristic
296C2×#479C2×C3111yescharacteristic, complemented
297C2×#475C2×C3111yescharacteristic, complemented
298#2323C2×C3111yescharacteristic
299#2059C2×C3111yescharacteristic, complemented
300#2058C2×C3111yescharacteristic, complemented
301#2026C2×C3111yescharacteristic, complemented
302#2024C2×C3111yescharacteristic, complemented
303#1989C2×C3111yescharacteristic, complemented
304#1987C2×C3111yescharacteristic, complemented
305#1873C2×C3111yescharacteristic
306#1872C2×C3111yescharacteristic
307#1854C2×C3111yescharacteristic
308#1853C2×C3111yescharacteristic
309#1798C2×C3111yescharacteristic
310C22×C31—22no—
311C22×C31—22no—
312C22×C31—22no—
313C22×C31—41no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31C2×#12011yescharacteristic
318C22×C31C2×C22⋊Q811yescharacteristic
319C22×C31#53611yescharacteristic
320C22×C31#57711yescharacteristic
321C22×C31#57711yescharacteristic
322C22×C31#57711yescharacteristic
323C22×C31#57811yescharacteristic
324C4×C31—22no—
325C4×C31—22no—
326C4×C31—22no—
327C4×C31—42no—
328C4×C31—42no—
329C4×C31—41no—
330C4×C31—42no—
331C4×C31—42no—
332C4×C31—42no—
333C4×C31—41no—
334C4×C31—42no—
335C4×C31—81no—
336C4×C31—81no—
337C4×C31#54811yescharacteristic
338C4×C31#54811yescharacteristic
339C4×C31D4×Q811yescharacteristic
340C4×C31D4×Q811yescharacteristic
341#544—24no—
342#544—24no—
343C2×C4⋊Q8—21no—
344C2×C4⋊Q8C22×C3111yescharacteristic
345C2×C4⋊Q8C22×C3111yescharacteristic
346C2×#125—21no—
347C2×#125C22×C3111yescharacteristic
348C2×#125C22×C3111yescharacteristic
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8C22×C3111yescharacteristic
352C2×C4×Q8C22×C3111yescharacteristic
353C2×#117C22×C3111yescharacteristic
354C2×#117C22×C3111yescharacteristic
355C22×C4⋊C4C22×C3111yescharacteristic
356#479—24no—
357#475—24no—
358C2×#107C22×C3111yescharacteristic
359C2×#106C22×C3111yescharacteristic
360C2×#106C22×C3111yescharacteristic
361C2×#106C22×C3111yescharacteristic
362C2×C4⋊C8C22×C3111yescharacteristic
363C2×C4⋊C8C22×C3111yescharacteristic
364C2×#103C22×C3111yescharacteristic
365C2×#103C22×C3111yescharacteristic
366C2×#103C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×C22⋊C8C22×C3111yescharacteristic
369C2×C22⋊C8C22×C3111yescharacteristic
370#391C22×C3111yescharacteristic
371#389—21no—
372#389C22×C3111yescharacteristic
373#388—21no—
374#388—21no—
375#387—21no—
376#380C22×C3111yescharacteristic
377C4×C4⋊C4C22×C3111yescharacteristic
378#340C22×C3111yescharacteristic
379#340C22×C3111yescharacteristic
380#340C22×C3111yescharacteristic
381#340C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#336C22×C3111yescharacteristic
387#336C22×C3111yescharacteristic
388C2×C31—42no—
389C2×C31#240911yescharacteristic
390C2×C31#300911yescharacteristic
391C2×C31#301311yescharacteristic
392C2×C31#308211yescharacteristic
393C2×C31#308411yescharacteristic
394C2×C31#324211yescharacteristic
395C2×C31#324411yescharacteristic
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8C23×C3111yescharacteristic
399C23×C4—21no—
400C23×C4C23×C3111yescharacteristic
401C22×C8C23×C3111yescharacteristic
402C22×C8C23×C3111yescharacteristic
403C22×C8C23×C3111yescharacteristic
404C22×C8C23×C3111yescharacteristic
405C4⋊Q8—28no—
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8D4×C3114yes—
410#125—28no—
411#125—22no—
412#125—22no—
413#125—22no—
414#125D4×C3114yes—
415C22⋊Q8—28no—
416C22⋊Q8—28no—
417C22⋊Q8—22no—
418C22⋊Q8Q8×C3114yescomplemented
419C4×Q8—22no—
420C4×Q8—22no—
421#117—22no—
422#117—22no—
423#117—22no—
424#117—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4D4×C3111yescharacteristic
438C2×C4⋊C4D4×C3111yescharacteristic
439C2×C4⋊C4C23×C3111yescharacteristic
440C2×C4⋊C4C23×C3111yescharacteristic
441C2×C4⋊C4C23×C3111yescharacteristic
442C2×C4⋊C4C23×C3111yescharacteristic
443C2×C4⋊C4C23×C3111yescharacteristic
444C2×C4⋊C4C23×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4D4×C3111yescharacteristic
450C2×C22⋊C4D4×C3111yescharacteristic
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C3111yescharacteristic
455C2×C42C23×C3111yescharacteristic
456#107—22no—
457#106—22no—
458#106—22no—
459#106—22no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#103—22no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473C31#2431011yescharacteristic, direct product factor, Sylow
474C24C2×D4×C3111yescharacteristic
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—81no—
483C2×Q8—81no—
484C2×Q8—81no—
485C2×Q8—81no—
486C2×Q8C2×Q8×C3112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C3111yescharacteristic
503C22×C4C2×D4×C3111yescharacteristic
504C22×C4C2×D4×C3111yescharacteristic
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C2×D4×C3111yescharacteristic
507C22×C4C2×Q8×C3112yes—
508C22×C4#41×C3112yes—
509C22×C4C24×C3111yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4C2×D4×C3112yes—
544C4⋊C4C2×D4×C3112yes—
545C4⋊C4C2×D4×C3112yes—
546C4⋊C4C2×D4×C3112yes—
547C4⋊C4C2×Q8×C3112yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—81no—
553C42—24no—
554C42—21no—
555C42—21no—
556C42—42no—
557C42—81no—
558C42C2×D4×C3112yes—
559C42C2×D4×C3112yes—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C31×C22⋊Q812yes—
567C23C22×D4×C3111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573Q8—84no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
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—84no—
615C2×C4C31×#12012yes—
616C2×C4C31×#12012yes—
617C2×C4C31×C22⋊Q812yes—
618C2×C4C22×D4×C3111yescharacteristic
619C2×C4C22×D4×C3111yescharacteristic
620C2×C4C22×Q8×C3111yescharacteristic
621C2×C4C2×#41×C3111yescharacteristic
622C2×C4C31×2−1+411yescharacteristic
623C2×C4C31×2−1+411yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×C31×#12011yescharacteristic
636C22C2×C31×C22⋊Q811yescharacteristic
637C22C31×#53611yescharacteristic
638C22C31×#57711yescharacteristic
639C22C31×#57711yescharacteristic
640C22C31×#57711yescharacteristic
641C22C31×#57811yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4C31×#54811yescharacteristic
656C4C31×#54811yescharacteristic
657C4D4×Q8×C3111yescharacteristic
658C4D4×Q8×C3111yescharacteristic
659C2—42no—
660C2C31×#240911yescharacteristic
661C2C31×#300911yescharacteristic
662C2C31×#301311yescharacteristic
663C2C31×#308211yescharacteristic
664C2C31×#308411yescharacteristic
665C2C31×#324211yescharacteristic
666C2C31×#324411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#479C2semidirect
3. C2×C31×#475C2semidirect
5. C31×#2059C2semidirect
6. C31×#2058C2semidirect
7. C31×#2026C2semidirect
8. C31×#2024C2semidirect
9. C31×#1989C2semidirect
10. C31×#1987C2semidirect
85. C31×C22⋊Q8Q8semidirect
226. #24310C31direct (N × H)
296. C2×#479C2×C31semidirect
297. C2×#475C2×C31semidirect
299. #2059C2×C31semidirect
300. #2058C2×C31semidirect
301. #2026C2×C31semidirect
302. #2024C2×C31semidirect
303. #1989C2×C31semidirect
304. #1987C2×C31semidirect
418. C22⋊Q8Q8×C31semidirect
473. C31#24310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C2×C31×#4792
C2×C31×#4752
C31×#23232
C31×#20592
C31×#20582
C31×#20262
C31×#20242
C31×#19892
C31×#19872
C31×#18732
C31×#18722
C31×#18542
C31×#18532
C31×#17982
#2431031