Finite Group Databasebeta

← C31×#24921 #21481680

Subgroups — C31×#24921 #21481680

Order 7936.

1150 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#450C211yesmaximal, characteristic
2C2×C31×#440C211yesmaximal, characteristic, complemented
3C31×#2423C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C31C211yesmaximal, characteristic
5C31×#2093C211yesmaximal, characteristic, complemented
6C31×#2076C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2036C211yesmaximal, characteristic, complemented
9C31×#1936C211yesmaximal, characteristic, complemented
10C31×#1924C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1877C211yesmaximal, characteristic, complemented
13C31×#1862C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic, complemented
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C22×C22⋊C4×C31—21no—
24C31×#450—24no—
25C31×#440—24no—
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#107C2211yescharacteristic, complemented
28C2×C31×C4⋊C8C2211yescharacteristic, complemented
29C2×C31×#103C2211yescharacteristic, complemented
30C2×C31×#103C2211yescharacteristic, complemented
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×#97C2211yescharacteristic, complemented
40C31×#399—21no—
41C31×#398—21no—
42C31×#391C2211yescharacteristic, complemented
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic, complemented
46C31×#388—21no—
47C31×#387—21no—
48C31×#386—21no—
49C31×#386—21no—
50C31×#384C2211yescharacteristic, complemented
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#379—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31—21no—
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2311yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C2×SD16×C31—22no—
76C2×SD16×C31—22no—
77C2×SD16×C31—22no—
78C2×SD16×C31—22no—
79C2×SD16×C31—41no—
80C2×SD16×C31D414yes—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8—41no—
87C4×Q8×C31—22no—
88C4×Q8×C31—41no—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—41no—
92C4×D4×C31—41no—
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×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—44no—
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C42×C31—21no—
116C2×C42×C31C2311yescharacteristic
117C2×C42×C31C2311yescharacteristic
118C31×#107—22no—
119C31×#107—41no—
120C31×C4⋊C8—41no—
121C31×#103—22no—
122C31×#103—41no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—41no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—41no—
131C31×#97—22no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95D411yescharacteristic
138C31×#95D411yescharacteristic
139C24×C31—21no—
140C24×C31—24no—
141C24×C31—21no—
142C24×C31—42no—
143C24×C31—42no—
144C24×C31—42no—
145C24×C31—42no—
146C24×C31—81no—
147C24×C31—81no—
148C24×C31C2×D411yescharacteristic
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31C2×D412yes—
155C2×D4×C31—24no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31—44no—
167C2×D4×C31—44no—
168C2×D4×C31—44no—
169C2×D4×C31—44no—
170C2×D4×C31C2×D412yes—
171C2×D4×C31#4112yes—
172C2×D4×C31#4112yes—
173C2×D4×C31#4112yes—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—42no—
187C22×C4×C31—42no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—81no—
191C22×C4×C31—81no—
192C22×C4×C31C2×D411yescharacteristic
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2411yescharacteristic
198SD16×C31—28no—
199SD16×C31—44no—
200C2×C8×C31—21no—
201C2×C8×C31—21no—
202C2×C8×C31—21no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31C2×D412yes—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—42no—
223C4⋊C4×C31—42no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—81no—
226C4⋊C4×C31—81no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—81no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31—81no—
238C42×C31—21no—
239C42×C31—21no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—42no—
243#24921C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—21no—
245C23×C31—22no—
246C23×C31—21no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—22no—
254C23×C31—48no—
255C23×C31—48no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—84no—
267C23×C31—84no—
268C23×C31—84no—
269C23×C31—84no—
270C23×C31—84no—
271C23×C31#13712yes—
272C23×C31C22×D411yescharacteristic
273Q8×C31—22no—
274Q8×C31—22no—
275Q8×C31—41no—
276Q8×C31—41no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—22no—
280D4×C31—22no—
281D4×C31—22no—
282D4×C31—48no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31#12314yes—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—22no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—84no—
323C2×C4×C31—84no—
324C2×C4×C31AGL(1,ℤ/8)12yes—
325C2×C4×C31C22×D411yescharacteristic
326C2×C4×C31C2×#4111yescharacteristic
327C2×C4×C31C2×#4111yescharacteristic
328C2×C4×C31C2×#4111yescharacteristic
329C2×C4×C31H(5,𝔽2)11yescharacteristic
330C2×C4×C31H(5,𝔽2)11yescharacteristic
331C8×C31—22no—
332C8×C31—41no—
333C8×C31—41no—
334C8×C31—41no—
335C2×#450C2×C3111yescharacteristic
336C2×#440C2×C3111yescharacteristic, complemented
337#2423C2×C3111yescharacteristic, complemented
338D4×C22⋊C4C2×C3111yescharacteristic
339#2093C2×C3111yescharacteristic, complemented
340#2076C2×C3111yescharacteristic, complemented
341#2055C2×C3111yescharacteristic, complemented
342#2036C2×C3111yescharacteristic, complemented
343#1936C2×C3111yescharacteristic, complemented
344#1924C2×C3111yescharacteristic, complemented
345#1880C2×C3111yescharacteristic, complemented
346#1877C2×C3111yescharacteristic, complemented
347#1862C2×C3111yescharacteristic, complemented
348#1802C2×C3111yescharacteristic, complemented
349#1786C2×C3111yescharacteristic
350C22×C31—22no—
351C22×C31—24no—
352C22×C31—22no—
353C22×C31—22no—
354C22×C31—42no—
355C22×C31—41no—
356C22×C31—42no—
357C22×C31—41no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—41no—
361C22×C31—42no—
362C22×C31—41no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—816no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31#52511yescharacteristic
373C22×C31D4211yescharacteristic
374C22×C31#54611yescharacteristic
375C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C31C2×#13711yescharacteristic
377C22×C31#57611yescharacteristic
378C22×C31#57711yescharacteristic
379C4×C31—22no—
380C4×C31—41no—
381C4×C31—42no—
382C4×C31—41no—
383C4×C31—41no—
384C4×C31—41no—
385C4×C31—81no—
386C4×C31—81no—
387C4×C31—81no—
388C4×C31—81no—
389C4×C31—81no—
390C4×C31C2×#12311yescharacteristic
391C4×C31#53811yescharacteristic
392C4×C31#54611yescharacteristic
393C4×C31#55111yescharacteristic
394C23×D4C22×C3111yescharacteristic
395C22×SD16C22×C3111yescharacteristic
396C22×SD16C22×C3111yescharacteristic
397C2×C22⋊Q8C22×C3111yescharacteristic
398C2×C4×Q8C22×C3111yescharacteristic, complemented
399C2×C4×D4C22×C3111yescharacteristic
400C2×C4×D4C22×C3111yescharacteristic
401C22×C22⋊C4—21no—
402#450—24no—
403#440—24no—
404C2×#107C22×C3111yescharacteristic, complemented
405C2×#107C22×C3111yescharacteristic, complemented
406C2×C4⋊C8C22×C3111yescharacteristic, complemented
407C2×#103C22×C3111yescharacteristic, complemented
408C2×#103C22×C3111yescharacteristic, complemented
409C2×#102C22×C3111yescharacteristic
410C2×#102C22×C3111yescharacteristic
411C2×#102C22×C3111yescharacteristic
412C2×#102C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×C22⋊C8C22×C3111yescharacteristic
416C2×C22⋊C8C22×C3111yescharacteristic
417C2×#97C22×C3111yescharacteristic, complemented
418#399—21no—
419#398—21no—
420#391C22×C3111yescharacteristic, complemented
421#390C22×C3111yescharacteristic
422#390C22×C3111yescharacteristic
423#389C22×C3111yescharacteristic, complemented
424#388—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#384C22×C3111yescharacteristic, complemented
429#380C22×C3111yescharacteristic
430#380C22×C3111yescharacteristic
431#379—21no—
432C4×C22⋊C4C22×C3111yescharacteristic
433#340C22×C3111yescharacteristic, complemented
434#340C22×C3111yescharacteristic, complemented
435#340C22×C3111yescharacteristic, complemented
436#340C22×C3111yescharacteristic, complemented
437#336C22×C3111yescharacteristic, complemented
438#336C22×C3111yescharacteristic, complemented
439C2×C31—42no—
440C2×C31—44no—
441C2×C31—82no—
442C2×C31#241811yescharacteristic
443C2×C31#311011yescharacteristic
444C2×C31#311811yescharacteristic
445C2×C31#326611yescharacteristic
446C2×C31#327411yescharacteristic
447C2×C31#331011yescharacteristic
448C2×C31#331411yescharacteristic
449C25—21no—
450C22×Q8C23×C3111yescharacteristic
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—21no—
456C22×D4—41no—
457C22×D4—41no—
458C22×D4C23×C3111yescharacteristic
459C22×D4C23×C3111yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4C23×C3111yescharacteristic
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—41no—
468C2×SD16D4×C3114yes—
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472C22×C8C23×C3111yescharacteristic
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475C4×Q8—22no—
476C4×Q8—41no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—41no—
480C4×D4—41no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4C23×C3111yescharacteristic
487C2×C4⋊C4C23×C3111yescharacteristic
488C2×C4⋊C4C23×C3111yescharacteristic
489C2×C4⋊C4C23×C3111yescharacteristic
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—44no—
501C2×C22⋊C4D4×C3111yescharacteristic
502C2×C22⋊C4D4×C3111yescharacteristic
503C2×C42—21no—
504C2×C42C23×C3111yescharacteristic
505C2×C42C23×C3111yescharacteristic
506#107—22no—
507#107—41no—
508C4⋊C8—41no—
509#103—22no—
510#103—41no—
511#102—22no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—41no—
517C22⋊C8—22no—
518C22⋊C8—41no—
519#97—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95D4×C3111yescharacteristic
526#95D4×C3111yescharacteristic
527C31#2492111yescharacteristic, direct product factor, Sylow
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C3111yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C3112yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C3112yes—
560C2×D4#41×C3112yes—
561C2×D4#41×C3112yes—
562C2×D4#41×C3112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C24×C3111yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C3112yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C31×#13712yes—
660C23C22×D4×C3111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4C31×#12314yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4C31×AGL(1,ℤ/8)12yes—
713C2×C4C22×D4×C3111yescharacteristic
714C2×C4C2×#41×C3111yescharacteristic
715C2×C4C2×#41×C3111yescharacteristic
716C2×C4C2×#41×C3111yescharacteristic
717C2×C4C31×H(5,𝔽2)11yescharacteristic
718C2×C4C31×H(5,𝔽2)11yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—24no—
725C22—22no—
726C22—22no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C31×#52511yescharacteristic
746C22D42×C3111yescharacteristic
747C22C31×#54611yescharacteristic
748C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
749C22C2×C31×#13711yescharacteristic
750C22C31×#57611yescharacteristic
751C22C31×#57711yescharacteristic
752C4—22no—
753C4—41no—
754C4—42no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×C31×#12311yescharacteristic
764C4C31×#53811yescharacteristic
765C4C31×#54611yescharacteristic
766C4C31×#55111yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2C31×#241811yescharacteristic
771C2C31×#311011yescharacteristic
772C2C31×#311811yescharacteristic
773C2C31×#326611yescharacteristic
774C2C31×#327411yescharacteristic
775C2C31×#331011yescharacteristic
776C2C31×#331411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
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×C31×#440C2semidirect
3. C31×#2423C2semidirect
5. C31×#2093C2semidirect
6. C31×#2076C2semidirect
7. C31×#2055C2semidirect
8. C31×#2036C2semidirect
9. C31×#1936C2semidirect
10. C31×#1924C2semidirect
11. C31×#1880C2semidirect
12. C31×#1877C2semidirect
13. C31×#1862C2semidirect
14. C31×#1802C2semidirect
20. C2×C4×Q8×C31C22semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#107C22semidirect
28. C2×C31×C4⋊C8C22semidirect
29. C2×C31×#103C22semidirect
30. C2×C31×#103C22semidirect
39. C2×C31×#97C22semidirect
42. C31×#391C22semidirect
45. C31×#389C22semidirect
50. C31×#384C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
243. #24921C31direct (N × H)
336. C2×#440C2×C31semidirect
337. #2423C2×C31semidirect
339. #2093C2×C31semidirect
340. #2076C2×C31semidirect
341. #2055C2×C31semidirect
342. #2036C2×C31semidirect
343. #1936C2×C31semidirect
344. #1924C2×C31semidirect
345. #1880C2×C31semidirect
346. #1877C2×C31semidirect
347. #1862C2×C31semidirect
348. #1802C2×C31semidirect
398. C2×C4×Q8C22×C31semidirect
404. C2×#107C22×C31semidirect
405. C2×#107C22×C31semidirect
406. C2×C4⋊C8C22×C31semidirect
407. C2×#103C22×C31semidirect
408. C2×#103C22×C31semidirect
417. C2×#97C22×C31semidirect
420. #391C22×C31semidirect
423. #389C22×C31semidirect
428. #384C22×C31semidirect
433. #340C22×C31semidirect
434. #340C22×C31semidirect
435. #340C22×C31semidirect
436. #340C22×C31semidirect
437. #336C22×C31semidirect
438. #336C22×C31semidirect
527. C31#24921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4502
C2×C31×#4402
C31×#24232
D4×C22⋊C4×C312
C31×#20932
C31×#20762
C31×#20552
C31×#20362
C31×#19362
C31×#19242
C31×#18802
C31×#18772
C31×#18622
C31×#18022
C31×#17862
#2492131