Finite Group Databasebeta

← C31×#25030 #21481789

Subgroups — C31×#25030 #21481789

Order 7936.

886 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#465C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C31×#2423C211yesmaximal, characteristic, complemented
4C31×#2422C211yesmaximal, characteristic
5C31×#2072C211yesmaximal, characteristic, complemented
6C31×#2071C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic
9C31×#1968C211yesmaximal, characteristic, complemented
10C31×#1941C211yesmaximal, characteristic, complemented
11C31×#1865C211yesmaximal, characteristic, complemented
12C31×#1864C211yesmaximal, characteristic, complemented
13C31×#1844C211yesmaximal, characteristic, complemented
14C31×#1807C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×#123—21no—
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C31×#465—24no—
24C4×SD16×C31—24no—
25C2×C31×#106C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C4×C8×C31C2211yescharacteristic
38C2×C4×C8×C31C2211yescharacteristic
39C31×#399—21no—
40C31×#398—21no—
41C31×#397—21no—
42C31×#394—21no—
43C31×#391C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#388—21no—
48C31×#387—21no—
49C31×#385—21no—
50C31×#384C2211yescharacteristic
51C31×#384C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31C2311yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31C2311yescharacteristic
66C2×SD16×C31—22no—
67C2×SD16×C31—22no—
68C2×SD16×C31D414yes—
69C22×C8×C31—22no—
70C22×C8×C31—22no—
71C22×C8×C31—22no—
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C31×#123—44no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—41no—
79C31×#121—22no—
80C31×#121—41no—
81C4×Q8×C31—22no—
82C4×Q8×C31—41no—
83C4×D4×C31—22no—
84C4×D4×C31—41no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31D411yescharacteristic
107C2×C22⋊C4×C31D411yescharacteristic
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C2×C42×C31C2311yescharacteristic
111C31×#106—22no—
112C31×#106—22no—
113C31×#106—22no—
114C31×#106—41no—
115C31×#106—41no—
116C31×#103—22no—
117C31×#103—22no—
118C31×#103—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×C22⋊C8—22no—
123C4×C8×C31—22no—
124C4×C8×C31—22no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95D411yescharacteristic
132C31×#95D411yescharacteristic
133C24×C31—21no—
134C24×C31C2×D411yescharacteristic
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31C2×D412yes—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—42no—
147C2×D4×C31—42no—
148C2×D4×C31—81no—
149C2×D4×C31C2×D412yes—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
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—42no—
164C22×C4×C31—42no—
165C22×C4×C31—81no—
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2411yescharacteristic
172SD16×C31—28no—
173C2×C8×C31—21no—
174C2×C8×C31—21no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—44no—
182C2×C8×C31C2×D412yes—
183C2×C8×C31#4112yes—
184C2×C8×C31#4112yes—
185C2×C8×C31#4112yes—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—81no—
204C4⋊C4×C31—81no—
205C4⋊C4×C31—81no—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—81no—
214C22⋊C4×C31SD1614yescomplemented
215C42×C31—21no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—42no—
220#25030C3111yesmaximal, characteristic, direct product factor, Sylow
221C23×C31—21no—
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—22no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31C2×SD1612yes—
235C23×C31C22×D411yescharacteristic
236Q8×C31—22no—
237Q8×C31—22no—
238Q8×C31—41no—
239Q8×C31—41no—
240D4×C31—22no—
241D4×C31—22no—
242D4×C31—41no—
243D4×C31—41no—
244D4×C31—84no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
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—22no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
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—41no—
282C2×C4×C31—84no—
283C2×C4×C31C2×SD1612yes—
284C2×C4×C31C2×SD1612yes—
285C2×C4×C31#13512yes—
286C2×C4×C31C22×D411yescharacteristic
287C2×C4×C31C2×#4111yescharacteristic
288C2×C4×C31C2×#4111yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31H(5,𝔽2)11yescharacteristic
291C2×C4×C312−1+411yescharacteristic
292C8×C31—22no—
293C8×C31—41no—
294C8×C31—41no—
295C8×C31#12314yescomplemented
296C2×#465C2×C3111yescharacteristic
297C2×C4×SD16C2×C3111yescharacteristic, complemented
298#2423C2×C3111yescharacteristic, complemented
299#2422C2×C3111yescharacteristic
300#2072C2×C3111yescharacteristic, complemented
301#2071C2×C3111yescharacteristic, complemented
302#2035C2×C3111yescharacteristic, complemented
303#2034C2×C3111yescharacteristic
304#1968C2×C3111yescharacteristic, complemented
305#1941C2×C3111yescharacteristic, complemented
306#1865C2×C3111yescharacteristic, complemented
307#1864C2×C3111yescharacteristic, complemented
308#1844C2×C3111yescharacteristic, complemented
309#1807C2×C3111yescharacteristic, complemented
310C8×C22⋊C4C2×C3111yescharacteristic, complemented
311C22×C31—22no—
312C22×C31—22no—
313C22×C31—22no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—81no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31—81no—
325C22×C31#53211yescharacteristic
326C22×C31D4211yescharacteristic
327C22×C31#54711yescharacteristic
328C22×C31C22×SD1611yescharacteristic
329C22×C31C2×#13511yescharacteristic
330C22×C31#57711yescharacteristic
331C22×C31#57711yescharacteristic
332C4×C31—22no—
333C4×C31—22no—
334C4×C31—22no—
335C4×C31—41no—
336C4×C31—42no—
337C4×C31—41no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31—81no—
341C4×C31—81no—
342C4×C31—81no—
343C4×C31—81no—
344C4×C31C2×#12311yescharacteristic
345C4×C31#54211yescharacteristic
346C4×C31#54711yescharacteristic
347C4×C31#55311yescharacteristic
348C22×SD16C22×C3111yescharacteristic
349C23×C8C22×C3111yescharacteristic
350C2×#123—21no—
351C2×C22⋊Q8C22×C3111yescharacteristic
352C2×#121C22×C3111yescharacteristic
353C2×C4×Q8C22×C3111yescharacteristic
354C2×C4×D4C22×C3111yescharacteristic
355#465—24no—
356C4×SD16—24no—
357C2×#106C22×C3111yescharacteristic
358C2×#106C22×C3111yescharacteristic
359C2×#106C22×C3111yescharacteristic
360C2×#106C22×C3111yescharacteristic
361C2×#106C22×C3111yescharacteristic
362C2×#103C22×C3111yescharacteristic
363C2×#103C22×C3111yescharacteristic
364C2×#103C22×C3111yescharacteristic
365C2×#102C22×C3111yescharacteristic
366C2×#102C22×C3111yescharacteristic
367C2×#102C22×C3111yescharacteristic
368C2×C22⋊C8C22×C3111yescharacteristic
369C2×C4×C8C22×C3111yescharacteristic
370C2×C4×C8C22×C3111yescharacteristic
371#399—21no—
372#398—21no—
373#397—21no—
374#394—21no—
375#391C22×C3111yescharacteristic
376#390C22×C3111yescharacteristic
377#389C22×C3111yescharacteristic
378#389C22×C3111yescharacteristic
379#388—21no—
380#387—21no—
381#385—21no—
382#384C22×C3111yescharacteristic
383#384C22×C3111yescharacteristic
384#380C22×C3111yescharacteristic
385#380C22×C3111yescharacteristic
386C4×C22⋊C4C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#340C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#340C22×C3111yescharacteristic
391#336C22×C3111yescharacteristic
392#336C22×C3111yescharacteristic
393C2×C31—42no—
394C2×C31—82no—
395C2×C31#242211yescharacteristic
396C2×C31#316711yescharacteristic
397C2×C31#317311yescharacteristic
398C2×C31D4×SD1611yescharacteristic
399C2×C31#328411yescharacteristic
400C2×C31#333511yescharacteristic
401C2×C31#333711yescharacteristic
402C22×Q8C23×C3111yescharacteristic
403C22×D4—21no—
404C22×D4C23×C3111yescharacteristic
405C23×C4—21no—
406C23×C4C23×C3111yescharacteristic
407C2×SD16—22no—
408C2×SD16—22no—
409C2×SD16D4×C3114yes—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8C23×C3111yescharacteristic
414C22×C8C23×C3111yescharacteristic
415C22×C8C23×C3111yescharacteristic
416C22×C8C23×C3111yescharacteristic
417#123—44no—
418C22⋊Q8—22no—
419C22⋊Q8—41no—
420#121—22no—
421#121—41no—
422C4×Q8—22no—
423C4×Q8—41no—
424C4×D4—22no—
425C4×D4—41no—
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—21no—
434C2×C4⋊C4C23×C3111yescharacteristic
435C2×C4⋊C4C23×C3111yescharacteristic
436C2×C4⋊C4C23×C3111yescharacteristic
437C2×C4⋊C4C23×C3111yescharacteristic
438C2×C4⋊C4C23×C3111yescharacteristic
439C2×C4⋊C4C23×C3111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C3111yescharacteristic
448C2×C22⋊C4D4×C3111yescharacteristic
449C2×C42—21no—
450C2×C42C23×C3111yescharacteristic
451C2×C42C23×C3111yescharacteristic
452#106—22no—
453#106—22no—
454#106—22no—
455#106—41no—
456#106—41no—
457#103—22no—
458#103—22no—
459#103—22no—
460#102—22no—
461#102—22no—
462#102—22no—
463C22⋊C8—22no—
464C4×C8—22no—
465C4×C8—22no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C3111yescharacteristic
473#95D4×C3111yescharacteristic
474C31#2503011yescharacteristic, direct product factor, Sylow
475C24—21no—
476C24C2×D4×C3111yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8C2×D4×C3112yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—81no—
491C2×D4C2×D4×C3112yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4C2×D4×C3111yescharacteristic
509C22×C4C2×D4×C3111yescharacteristic
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C24×C3111yescharacteristic
514SD16—28no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—44no—
524C2×C8C2×D4×C3112yes—
525C2×C8#41×C3112yes—
526C2×C8#41×C3112yes—
527C2×C8#41×C3112yes—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
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—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C22⋊C4—22no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4SD16×C3114yescomplemented
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23C2×SD16×C3112yes—
576C23C22×D4×C3111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581D4—22no—
582D4—22no—
583D4—41no—
584D4—41no—
585D4—84no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
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—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—84no—
624C2×C4C2×SD16×C3112yes—
625C2×C4C2×SD16×C3112yes—
626C2×C4C31×#13512yes—
627C2×C4C22×D4×C3111yescharacteristic
628C2×C4C2×#41×C3111yescharacteristic
629C2×C4C2×#41×C3111yescharacteristic
630C2×C4C2×#41×C3111yescharacteristic
631C2×C4C31×H(5,𝔽2)11yescharacteristic
632C2×C4C31×2−1+411yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8C31×#12314yescomplemented
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22C31×#53211yescharacteristic
652C22D42×C3111yescharacteristic
653C22C31×#54711yescharacteristic
654C22C22×SD16×C3111yescharacteristic
655C22C2×C31×#13511yescharacteristic
656C22C31×#57711yescharacteristic
657C22C31×#57711yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4C2×C31×#12311yescharacteristic
671C4C31×#54211yescharacteristic
672C4C31×#54711yescharacteristic
673C4C31×#55311yescharacteristic
674C2—42no—
675C2—82no—
676C2C31×#242211yescharacteristic
677C2C31×#316711yescharacteristic
678C2C31×#317311yescharacteristic
679C2D4×SD16×C3111yescharacteristic
680C2C31×#328411yescharacteristic
681C2C31×#333511yescharacteristic
682C2C31×#333711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C31C2semidirect
3. C31×#2423C2semidirect
5. C31×#2072C2semidirect
6. C31×#2071C2semidirect
7. C31×#2035C2semidirect
9. C31×#1968C2semidirect
10. C31×#1941C2semidirect
11. C31×#1865C2semidirect
12. C31×#1864C2semidirect
13. C31×#1844C2semidirect
14. C31×#1807C2semidirect
15. C8×C22⋊C4×C31C2semidirect
214. C22⋊C4×C31SD16semidirect
220. #25030C31direct (N × H)
295. C8×C31#123semidirect
297. C2×C4×SD16C2×C31semidirect
298. #2423C2×C31semidirect
300. #2072C2×C31semidirect
301. #2071C2×C31semidirect
302. #2035C2×C31semidirect
304. #1968C2×C31semidirect
305. #1941C2×C31semidirect
306. #1865C2×C31semidirect
307. #1864C2×C31semidirect
308. #1844C2×C31semidirect
309. #1807C2×C31semidirect
310. C8×C22⋊C4C2×C31semidirect
474. C31#25030direct (N × H)
556. C22⋊C4SD16×C31semidirect
636. C8C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4652
C2×C4×SD16×C312
C31×#24232
C31×#24222
C31×#20722
C31×#20712
C31×#20352
C31×#20342
C31×#19682
C31×#19412
C31×#18652
C31×#18642
C31×#18442
C31×#18072
C8×C22⋊C4×C312
#2503031