Finite Group Databasebeta

← C31×#24766 #21481525

Subgroups — C31×#24766 #21481525

Order 7936.

960 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic
2C2×C31×#465C211yesmaximal, characteristic
3C2×C31×#461C211yesmaximal, characteristic, complemented
4C2×C31×#424C211yesmaximal, characteristic, complemented
5C31×#2621C211yesmaximal, characteristic, complemented
6C31×#2324C211yesmaximal, characteristic
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2066C211yesmaximal, characteristic, complemented
9C31×#2055C211yesmaximal, characteristic, complemented
10C31×#2055C211yesmaximal, characteristic, complemented
11C31×#1981C211yesmaximal, characteristic, complemented
12C31×#1949C211yesmaximal, characteristic, complemented
13C31×#1894C211yesmaximal, characteristic, complemented
14C31×#1892C211yesmaximal, characteristic, complemented
15C31×#1804C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C31×#117C2211yescharacteristic
26C31×#468—24no—
27C31×#465—24no—
28C31×#461—24no—
29C2×C31×#107C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C31×#424—24no—
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×C4⋊C8C2211yescharacteristic
35C2×C31×C4⋊C8C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C31×#398—21no—
45C31×#398—21no—
46C31×#397—21no—
47C31×#397—21no—
48C31×#391C2211yescharacteristic
49C31×#391C2211yescharacteristic
50C31×#390—21no—
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#386—21no—
55C31×#385—21no—
56C31×#382C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C2×SD16×C31—22no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—41no—
74C2×SD16×C31—41no—
75C2×M16×C31—22no—
76C2×M16×C31—22no—
77C2×M16×C31—41no—
78C22×C8×C31—22no—
79C22×C8×C31—22no—
80C22×C8×C31—41no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×C4⋊Q8—22no—
86C31×C4⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×#121—22no—
92C31×#121D414yes—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C31×#117—22no—
96C31×#117—22no—
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×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C22⋊C4×C31—21no—
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×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31D411yescharacteristic
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C42×C31—21no—
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×#107—22no—
122C31×#106—22no—
123C31×C4⋊C8—22no—
124C31×C4⋊C8—22no—
125C31×C4⋊C8—22no—
126C31×C4⋊C8D414yescomplemented
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—41no—
132C31×#103—41no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C24×C31—21no—
145C24×C31C2×D411yescharacteristic
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—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×D4×C31—24no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—81no—
165C2×D4×C31—81no—
166C2×D4×C31C2×D412yes—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—42no—
179C22×C4×C31—81no—
180C22×C4×C31—81no—
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D411yescharacteristic
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D412yes—
187C22×C4×C31#4112yes—
188C22×C4×C31C2411yescharacteristic
189SD16×C31—44no—
190SD16×C31—44no—
191M16×C31—44no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31—21no—
199C2×C8×C31—21no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—44no—
203C2×C8×C31C2×D412yes—
204C2×C8×C31C2×D412yes—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—42no—
217C4⋊C4×C31—42no—
218C4⋊C4×C31—42no—
219C4⋊C4×C31—42no—
220C4⋊C4×C31—81no—
221C4⋊C4×C31C2×D412yes—
222C22⋊C4×C31—24no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—42no—
226C22⋊C4×C31—42no—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—81no—
229C22⋊C4×C31—81no—
230C22⋊C4×C31—81no—
231C42×C31—21no—
232C42×C31—21no—
233C42×C31—81no—
234C42×C31C2×D412yes—
235C42×C31#4112yes—
236#24766C3111yesmaximal, characteristic, direct product factor, Sylow
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—21no—
243C23×C31—22no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31#12112yes—
251C23×C31C22×D411yescharacteristic
252Q8×C31—41no—
253Q8×C31—41no—
254Q8×C31—41no—
255Q8×C31—41no—
256Q8×C31—41no—
257Q8×C31—41no—
258Q8×C31—41no—
259Q8×C31—41no—
260D4×C31—22no—
261D4×C31—22no—
262D4×C31—41no—
263D4×C31—41no—
264D4×C31—84no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—22no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
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—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
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—84no—
303C2×C4×C31#12112yes—
304C2×C4×C31#12112yes—
305C2×C4×C31#12112yes—
306C2×C4×C31C22×D411yescharacteristic
307C2×C4×C31C22×D411yescharacteristic
308C2×C4×C31C2×#4111yescharacteristic
309C2×C4×C31C2×#4111yescharacteristic
310C2×C4×C31H(5,𝔽2)11yescharacteristic
311C2×C4×C312−1+411yescharacteristic
312C8×C31—22no—
313C8×C31—22no—
314C8×C31—41no—
315C8×C31—41no—
316C2×#468C2×C3111yescharacteristic
317C2×#465C2×C3111yescharacteristic
318C2×#461C2×C3111yescharacteristic, complemented
319C2×#424C2×C3111yescharacteristic, complemented
320#2621C2×C3111yescharacteristic, complemented
321#2324C2×C3111yescharacteristic
322#2068C2×C3111yescharacteristic, complemented
323#2066C2×C3111yescharacteristic, complemented
324#2055C2×C3111yescharacteristic, complemented
325#2055C2×C3111yescharacteristic, complemented
326#1981C2×C3111yescharacteristic, complemented
327#1949C2×C3111yescharacteristic, complemented
328#1894C2×C3111yescharacteristic, complemented
329#1892C2×C3111yescharacteristic, complemented
330#1804C2×C3111yescharacteristic, complemented
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—41no—
335C22×C31—41no—
336C22×C31—41no—
337C22×C31—41no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31C2×#12111yescharacteristic
346C22×C31C2×#12111yescharacteristic
347C22×C31#53711yescharacteristic
348C22×C31#57711yescharacteristic
349C22×C31#57711yescharacteristic
350C22×C31#57711yescharacteristic
351C22×C31#57811yescharacteristic
352C4×C31—22no—
353C4×C31—22no—
354C4×C31—22no—
355C4×C31—42no—
356C4×C31—41no—
357C4×C31—41no—
358C4×C31—81no—
359C4×C31—81no—
360C4×C31—81no—
361C4×C31—81no—
362C4×C31—81no—
363C4×C31—81no—
364C4×C31D4211yescharacteristic
365C4×C31#54711yescharacteristic
366C4×C31#54811yescharacteristic
367C4×C31#55311yescharacteristic
368C22×SD16C22×C3111yescharacteristic
369C22×SD16C22×C3111yescharacteristic
370C22×M16C22×C3111yescharacteristic
371C23×C8C22×C3111yescharacteristic
372C2×C4⋊Q8C22×C3111yescharacteristic
373C2×C22⋊Q8C22×C3111yescharacteristic
374C2×C22⋊Q8C22×C3111yescharacteristic
375C2×#121C22×C3111yescharacteristic
376C2×C4×D4C22×C3111yescharacteristic
377C2×#117C22×C3111yescharacteristic
378#468—24no—
379#465—24no—
380#461—24no—
381C2×#107C22×C3111yescharacteristic
382C2×#106C22×C3111yescharacteristic
383#424—24no—
384C2×C4⋊C8C22×C3111yescharacteristic
385C2×C4⋊C8C22×C3111yescharacteristic
386C2×C4⋊C8C22×C3111yescharacteristic
387C2×C4⋊C8C22×C3111yescharacteristic
388C2×#103C22×C3111yescharacteristic
389C2×#103C22×C3111yescharacteristic
390C2×#103C22×C3111yescharacteristic
391C2×#103C22×C3111yescharacteristic
392C2×#103C22×C3111yescharacteristic
393C2×#103C22×C3111yescharacteristic
394C2×#102C22×C3111yescharacteristic
395C2×#102C22×C3111yescharacteristic
396#398—21no—
397#398—21no—
398#397—21no—
399#397—21no—
400#391C22×C3111yescharacteristic
401#391C22×C3111yescharacteristic
402#390—21no—
403#390C22×C3111yescharacteristic
404#389C22×C3111yescharacteristic
405#388—21no—
406#386—21no—
407#385—21no—
408#382C22×C3111yescharacteristic
409#380C22×C3111yescharacteristic
410C4×C4⋊C4C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414#340C22×C3111yescharacteristic
415C2×C31—42no—
416C2×C31—82no—
417C2×C31#241611yescharacteristic
418C2×C31#304211yescharacteristic
419C2×C31#304611yescharacteristic
420C2×C31#305711yescharacteristic
421C2×C31#306311yescharacteristic
422C2×C31#325811yescharacteristic
423C2×C31#326011yescharacteristic
424C22×Q8C23×C3111yescharacteristic
425C22×Q8C23×C3111yescharacteristic
426C22×D4—21no—
427C22×D4C23×C3111yescharacteristic
428C23×C4—21no—
429C23×C4C23×C3111yescharacteristic
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—41no—
435C2×SD16—41no—
436C2×M16—22no—
437C2×M16—22no—
438C2×M16—41no—
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8C23×C3111yescharacteristic
443C22×C8C23×C3111yescharacteristic
444C22×C8C23×C3111yescharacteristic
445C22×C8C23×C3111yescharacteristic
446C4⋊Q8—22no—
447C4⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452#121—22no—
453#121D4×C3114yes—
454C4×D4—22no—
455C4×D4—22no—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C3111yescharacteristic
464C2×C4⋊C4D4×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4D4×C3111yescharacteristic
478C2×C22⋊C4D4×C3111yescharacteristic
479C2×C42—21no—
480C2×C42C23×C3111yescharacteristic
481C2×C42C23×C3111yescharacteristic
482#107—22no—
483#106—22no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8D4×C3114yescomplemented
488#103—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—41no—
493#103—41no—
494#102—22no—
495#102—22no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505C31#2476611yescharacteristic, direct product factor, Sylow
506C24—21no—
507C24C2×D4×C3111yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4C2×D4×C3112yes—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4C2×D4×C3111yescharacteristic
544C22×C4C2×D4×C3111yescharacteristic
545C22×C4C2×D4×C3111yescharacteristic
546C22×C4C2×D4×C3111yescharacteristic
547C22×C4C2×D4×C3111yescharacteristic
548C22×C4C2×D4×C3112yes—
549C22×C4#41×C3112yes—
550C22×C4C24×C3111yescharacteristic
551SD16—44no—
552SD16—44no—
553M16—44no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—44no—
565C2×C8C2×D4×C3112yes—
566C2×C8C2×D4×C3112yes—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—81no—
583C4⋊C4C2×D4×C3112yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—81no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C42—21no—
594C42—21no—
595C42—81no—
596C42C2×D4×C3112yes—
597C42#41×C3112yes—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23C31×#12112yes—
612C23C22×D4×C3111yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—22no—
622D4—22no—
623D4—41no—
624D4—41no—
625D4—84no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4C31×#12112yes—
665C2×C4C31×#12112yes—
666C2×C4C31×#12112yes—
667C2×C4C22×D4×C3111yescharacteristic
668C2×C4C22×D4×C3111yescharacteristic
669C2×C4C2×#41×C3111yescharacteristic
670C2×C4C2×#41×C3111yescharacteristic
671C2×C4C31×H(5,𝔽2)11yescharacteristic
672C2×C4C31×2−1+411yescharacteristic
673C8—22no—
674C8—22no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×C31×#12111yescharacteristic
692C22C2×C31×#12111yescharacteristic
693C22C31×#53711yescharacteristic
694C22C31×#57711yescharacteristic
695C22C31×#57711yescharacteristic
696C22C31×#57711yescharacteristic
697C22C31×#57811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4D42×C3111yescharacteristic
711C4C31×#54711yescharacteristic
712C4C31×#54811yescharacteristic
713C4C31×#55311yescharacteristic
714C2—42no—
715C2—82no—
716C2C31×#241611yescharacteristic
717C2C31×#304211yescharacteristic
718C2C31×#304611yescharacteristic
719C2C31×#305711yescharacteristic
720C2C31×#306311yescharacteristic
721C2C31×#325811yescharacteristic
722C2C31×#326011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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
3. C2×C31×#461C2semidirect
4. C2×C31×#424C2semidirect
5. C31×#2621C2semidirect
7. C31×#2068C2semidirect
8. C31×#2066C2semidirect
9. C31×#2055C2semidirect
10. C31×#2055C2semidirect
11. C31×#1981C2semidirect
12. C31×#1949C2semidirect
13. C31×#1894C2semidirect
14. C31×#1892C2semidirect
15. C31×#1804C2semidirect
126. C31×C4⋊C8D4semidirect
236. #24766C31direct (N × H)
318. C2×#461C2×C31semidirect
319. C2×#424C2×C31semidirect
320. #2621C2×C31semidirect
322. #2068C2×C31semidirect
323. #2066C2×C31semidirect
324. #2055C2×C31semidirect
325. #2055C2×C31semidirect
326. #1981C2×C31semidirect
327. #1949C2×C31semidirect
328. #1894C2×C31semidirect
329. #1892C2×C31semidirect
330. #1804C2×C31semidirect
487. C4⋊C8D4×C31semidirect
505. C31#24766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4652
C2×C31×#4612
C2×C31×#4242
C31×#26212
C31×#23242
C31×#20682
C31×#20662
C31×#20552
C31×#19812
C31×#19492
C31×#18942
C31×#18922
C31×#18042
#2476631