Finite Group Databasebeta

← C31×#24044 #21480803

Subgroups — C31×#24044 #21480803

Order 7936.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C31C211yesmaximal, characteristic
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C31×#2485C211yesmaximal, characteristic, complemented
5C31×#2041C211yesmaximal, characteristic, complemented
6C31×#2041C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1895C211yesmaximal, characteristic, complemented
10C31×#1870C211yesmaximal, characteristic, complemented
11C31×#1864C211yesmaximal, characteristic, complemented
12C31×#1862C211yesmaximal, characteristic, complemented
13C31×#1786C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31—21no—
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic, complemented
20D42×C31—24no—
21D42×C31—24no—
22C2×C31×#127C2211yescharacteristic
23C2×C31×#121—21no—
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C31×#120—21no—
27C2×C31×#120—21no—
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic, complemented
31C31×#482—24no—
32C2×C31×#107C2211yescharacteristic, complemented
33C2×C31×#106C2211yescharacteristic, complemented
34C31×#418—24no—
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic, complemented
40C2×C31×#102C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×C22⋊C8C2211yescharacteristic, complemented
48C2×C31×C22⋊C8C2211yescharacteristic, complemented
49C2×C31×C22⋊C8C2211yescharacteristic, complemented
50C31×#397—21no—
51C31×#394—21no—
52C31×#389C2211yescharacteristic, complemented
53C31×#389C2211yescharacteristic, complemented
54C31×#388—21no—
55C31×#387—21no—
56C31×#380C2211yescharacteristic, complemented
57C31×#380C2211yescharacteristic, complemented
58C31×#380C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C25×C31—21no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—28no—
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—22no—
78C22×D4×C31—21no—
79C22×D4×C31—41no—
80C22×D4×C31—41no—
81C22×D4×C31—41no—
82C22×D4×C31—41no—
83C22×D4×C31—44no—
84C22×D4×C31—44no—
85C22×D4×C31D411yescharacteristic
86C22×D4×C31D414yes—
87C22×D4×C31C2311yescharacteristic
88C22×D4×C31C2311yescharacteristic
89C22×D4×C31C2311yescharacteristic
90C23×C4×C31—21no—
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C2×M16×C31—22no—
94C2×M16×C31—41no—
95C2×M16×C31—41no—
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C22×C8×C31C2311yescharacteristic
100C31×#127—22no—
101C31×#127—22no—
102C31×#121—28no—
103C31×#121—22no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121D414yes—
107C31×#120—28no—
108C31×#120—28no—
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C31×#117—22no—
114C31×#117—22no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31D411yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C22⋊C4×C31D411yescharacteristic
132C2×C42×C31—21no—
133C2×C42×C31C2311yescharacteristic
134C31×#107—22no—
135C31×#106—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—41no—
145C31×#102—41no—
146C31×#102—41no—
147C31×#102—41no—
148C31×C22⋊C8—22no—
149C31×C22⋊C8—41no—
150C31×C22⋊C8—41no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C31×#95—21no—
155C31×#95—21no—
156C24×C31—21no—
157C24×C31—24no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—24no—
161C24×C31—42no—
162C24×C31—42no—
163C24×C31—42no—
164C24×C31—42no—
165C24×C31—42no—
166C24×C31—42no—
167C24×C31—42no—
168C24×C31—42no—
169C24×C31—81no—
170C24×C31—81no—
171C24×C31—81no—
172C24×C31—81no—
173C24×C31C2×D411yescharacteristic
174C24×C31C2×D411yescharacteristic
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—28no—
178C2×D4×C31—24no—
179C2×D4×C31—24no—
180C2×D4×C31—24no—
181C2×D4×C31—24no—
182C2×D4×C31—24no—
183C2×D4×C31—24no—
184C2×D4×C31—22no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—44no—
199C2×D4×C31—44no—
200C2×D4×C31—44no—
201C2×D4×C31—42no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C2×D4×C31—432no—
209C2×D4×C31—44no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—44no—
215C2×D4×C31—42no—
216C2×D4×C31—81no—
217C2×D4×C31—81no—
218C2×D4×C31C2×D412yes—
219C2×D4×C31C2×D412yes—
220C2×D4×C31C2×D412yes—
221C2×D4×C31#4112yes—
222C2×D4×C31#4112yes—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—24no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—42no—
240C22×C4×C31—42no—
241C22×C4×C31C2×D411yescharacteristic
242C22×C4×C31C2×D411yescharacteristic
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D412yes—
245C22×C4×C31C2×D412yes—
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2411yescharacteristic
248M16×C31—44no—
249C2×C8×C31—21no—
250C2×C8×C31—21no—
251C2×C8×C31—21no—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C4⋊C4×C31—22no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—42no—
272C4⋊C4×C31—81no—
273C4⋊C4×C31C2×D412yes—
274C22⋊C4×C31—24no—
275C22⋊C4×C31—24no—
276C22⋊C4×C31—22no—
277C22⋊C4×C31—24no—
278C22⋊C4×C31—22no—
279C22⋊C4×C31—42no—
280C22⋊C4×C31—42no—
281C22⋊C4×C31—81no—
282C22⋊C4×C31—81no—
283C42×C31—21no—
284C42×C31—21no—
285C42×C31—42no—
286#24044C3111yesmaximal, characteristic, direct product factor, Sylow
287C23×C31—21no—
288C23×C31—22no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—21no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—48no—
305C23×C31—48no—
306C23×C31—48no—
307C23×C31—48no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—84no—
325C23×C31—84no—
326C23×C31—84no—
327C23×C31—84no—
328C23×C31—84no—
329C23×C31—84no—
330C23×C31—84no—
331C23×C31—84no—
332C23×C31—84no—
333C23×C31—84no—
334C23×C31#12012yes—
335C23×C31AGL(1,ℤ/8)12yes—
336C23×C31C22×D411yescharacteristic
337D4×C31—28no—
338D4×C31—22no—
339D4×C31—22no—
340D4×C31—22no—
341D4×C31—22no—
342D4×C31—22no—
343D4×C31—22no—
344D4×C31—22no—
345D4×C31—48no—
346D4×C31—48no—
347D4×C31—48no—
348D4×C31—48no—
349D4×C31—48no—
350D4×C31—41no—
351D4×C31—41no—
352D4×C31—41no—
353D4×C31—41no—
354D4×C31—84no—
355D4×C31#12314yes—
356C2×C4×C31—21no—
357C2×C4×C31—21no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—22no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—21no—
371C2×C4×C31—48no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31#12012yes—
391C2×C4×C31AGL(1,ℤ/8)12yes—
392C2×C4×C31C22×D411yescharacteristic
393C2×C4×C31C22×D411yescharacteristic
394C2×C4×C31C2×#4111yescharacteristic
395C2×C4×C31C2×#4111yescharacteristic
396C2×C4×C31H(5,𝔽2)11yescharacteristic
397C2×C4×C31H(5,𝔽2)11yescharacteristic
398C8×C31—41no—
399C8×C31—41no—
400C8×C31—41no—
401C8×C31—41no—
402C2×D42C2×C3111yescharacteristic
403C2×#482C2×C3111yescharacteristic, complemented
404C2×#418C2×C3111yescharacteristic, complemented
405#2485C2×C3111yescharacteristic, complemented
406#2041C2×C3111yescharacteristic, complemented
407#2041C2×C3111yescharacteristic, complemented
408#2034C2×C3111yescharacteristic, complemented
409#2033C2×C3111yescharacteristic, complemented
410#1895C2×C3111yescharacteristic, complemented
411#1870C2×C3111yescharacteristic, complemented
412#1864C2×C3111yescharacteristic, complemented
413#1862C2×C3111yescharacteristic, complemented
414#1786C2×C3111yescharacteristic, complemented
415#1786C2×C3111yescharacteristic, complemented
416#1786C2×C3111yescharacteristic, complemented
417C22×C31—22no—
418C22×C31—24no—
419C22×C31—22no—
420C22×C31—22no—
421C22×C31—22no—
422C22×C31—22no—
423C22×C31—22no—
424C22×C31—41no—
425C22×C31—42no—
426C22×C31—41no—
427C22×C31—42no—
428C22×C31—41no—
429C22×C31—42no—
430C22×C31—41no—
431C22×C31—42no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—42no—
435C22×C31—41no—
436C22×C31—41no—
437C22×C31—42no—
438C22×C31—42no—
439C22×C31—42no—
440C22×C31—42no—
441C22×C31—42no—
442C22×C31—42no—
443C22×C31—42no—
444C22×C31—816no—
445C22×C31—816no—
446C22×C31—81no—
447C22×C31—81no—
448C22×C31—81no—
449C22×C31—81no—
450C22×C31—81no—
451C22×C31—81no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31C2×#12011yescharacteristic
455C22×C31#54611yescharacteristic
456C22×C31#54611yescharacteristic
457C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
458C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
459C22×C31#57611yescharacteristic
460C22×C31#57711yescharacteristic
461C4×C31—22no—
462C4×C31—22no—
463C4×C31—41no—
464C4×C31—42no—
465C4×C31—41no—
466C4×C31—81no—
467C4×C31—81no—
468C4×C31—81no—
469C4×C31—81no—
470C4×C31C2×#12311yescharacteristic
471C4×C31#53411yescharacteristic
472C4×C31#54611yescharacteristic
473C4×C31#54611yescharacteristic
474C23×D4—21no—
475C23×D4C22×C3111yescharacteristic
476C23×D4C22×C3111yescharacteristic
477C22×M16C22×C3111yescharacteristic, complemented
478D42—24no—
479D42—24no—
480C2×#127C22×C3111yescharacteristic
481C2×#121—21no—
482C2×#121C22×C3111yescharacteristic
483C2×#121C22×C3111yescharacteristic
484C2×#120—21no—
485C2×#120—21no—
486C2×C4×D4C22×C3111yescharacteristic
487C2×C4×D4C22×C3111yescharacteristic
488C2×#117C22×C3111yescharacteristic, complemented
489#482—24no—
490C2×#107C22×C3111yescharacteristic, complemented
491C2×#106C22×C3111yescharacteristic, complemented
492#418—24no—
493C2×#102C22×C3111yescharacteristic
494C2×#102C22×C3111yescharacteristic
495C2×#102C22×C3111yescharacteristic
496C2×#102C22×C3111yescharacteristic
497C2×#102C22×C3111yescharacteristic, complemented
498C2×#102C22×C3111yescharacteristic, complemented
499C2×#102C22×C3111yescharacteristic, complemented
500C2×#102C22×C3111yescharacteristic, complemented
501C2×#102C22×C3111yescharacteristic, complemented
502C2×#102C22×C3111yescharacteristic, complemented
503C2×#102C22×C3111yescharacteristic, complemented
504C2×#102C22×C3111yescharacteristic, complemented
505C2×C22⋊C8C22×C3111yescharacteristic, complemented
506C2×C22⋊C8C22×C3111yescharacteristic, complemented
507C2×C22⋊C8C22×C3111yescharacteristic, complemented
508#397—21no—
509#394—21no—
510#389C22×C3111yescharacteristic, complemented
511#389C22×C3111yescharacteristic, complemented
512#388—21no—
513#387—21no—
514#380C22×C3111yescharacteristic, complemented
515#380C22×C3111yescharacteristic, complemented
516#380C22×C3111yescharacteristic, complemented
517#340C22×C3111yescharacteristic, complemented
518#340C22×C3111yescharacteristic, complemented
519#336C22×C3111yescharacteristic, complemented
520#336C22×C3111yescharacteristic, complemented
521C2×C31—42no—
522C2×C31—42no—
523C2×C31—44no—
524C2×C31—82no—
525C2×C31—82no—
526C2×C31#240511yescharacteristic
527C2×C31#300311yescharacteristic
528C2×C31#301211yescharacteristic
529C2×C31#331011yescharacteristic
530C2×C31#331811yescharacteristic
531C2×C31#332411yescharacteristic
532C2×C31#332511yescharacteristic
533C25—21no—
534C25—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—28no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—22no—
548C22×D4—21no—
549C22×D4—41no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—44no—
554C22×D4—44no—
555C22×D4D4×C3111yescharacteristic
556C22×D4D4×C3114yes—
557C22×D4C23×C3111yescharacteristic
558C22×D4C23×C3111yescharacteristic
559C22×D4C23×C3111yescharacteristic
560C23×C4—21no—
561C23×C4C23×C3111yescharacteristic
562C23×C4C23×C3111yescharacteristic
563C2×M16—22no—
564C2×M16—41no—
565C2×M16—41no—
566C22×C8C23×C3111yescharacteristic
567C22×C8C23×C3111yescharacteristic
568C22×C8C23×C3111yescharacteristic
569C22×C8C23×C3111yescharacteristic
570#127—22no—
571#127—22no—
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121D4×C3114yes—
577#120—28no—
578#120—28no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583#117—22no—
584#117—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C3111yescharacteristic
588C2×C4⋊C4C23×C3111yescharacteristic
589C2×C4⋊C4C23×C3111yescharacteristic
590C2×C4⋊C4C23×C3111yescharacteristic
591C2×C4⋊C4C23×C3111yescharacteristic
592C2×C4⋊C4C23×C3111yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4D4×C3111yescharacteristic
601C2×C22⋊C4D4×C3111yescharacteristic
602C2×C42—21no—
603C2×C42C23×C3111yescharacteristic
604#107—22no—
605#106—22no—
606#102—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615#102—41no—
616#102—41no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C31#2404411yescharacteristic, direct product factor, Sylow
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C3111yescharacteristic
645C24C2×D4×C3111yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C3112yes—
690C2×D4C2×D4×C3112yes—
691C2×D4C2×D4×C3112yes—
692C2×D4#41×C3112yes—
693C2×D4#41×C3112yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C3111yescharacteristic
713C22×C4C2×D4×C3111yescharacteristic
714C22×C4C2×D4×C3111yescharacteristic
715C22×C4C2×D4×C3112yes—
716C22×C4C2×D4×C3112yes—
717C22×C4C2×D4×C3111yescharacteristic
718C22×C4C24×C3111yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C3112yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23C31×#12012yes—
805C23C31×AGL(1,ℤ/8)12yes—
806C23C22×D4×C3111yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4C31×#12314yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4C31×#12012yes—
861C2×C4C31×AGL(1,ℤ/8)12yes—
862C2×C4C22×D4×C3111yescharacteristic
863C2×C4C22×D4×C3111yescharacteristic
864C2×C4C2×#41×C3111yescharacteristic
865C2×C4C2×#41×C3111yescharacteristic
866C2×C4C31×H(5,𝔽2)11yescharacteristic
867C2×C4C31×H(5,𝔽2)11yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×C31×#12011yescharacteristic
910C22C31×#54611yescharacteristic
911C22C31×#54611yescharacteristic
912C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
913C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
914C22C31×#57611yescharacteristic
915C22C31×#57711yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×C31×#12311yescharacteristic
926C4C31×#53411yescharacteristic
927C4C31×#54611yescharacteristic
928C4C31×#54611yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C31×#240511yescharacteristic
935C2C31×#300311yescharacteristic
936C2C31×#301211yescharacteristic
937C2C31×#331011yescharacteristic
938C2C31×#331811yescharacteristic
939C2C31×#332411yescharacteristic
940C2C31×#332511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×D42×C31C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#482C2semidirect
3. C2×C31×#418C2semidirect
4. C31×#2485C2semidirect
5. C31×#2041C2semidirect
6. C31×#2041C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1895C2semidirect
10. C31×#1870C2semidirect
11. C31×#1864C2semidirect
12. C31×#1862C2semidirect
13. C31×#1786C2semidirect
14. C31×#1786C2semidirect
15. C31×#1786C2semidirect
19. C22×M16×C31C22semidirect
30. C2×C31×#117C22semidirect
32. C2×C31×#107C22semidirect
33. C2×C31×#106C22semidirect
39. C2×C31×#102C22semidirect
40. C2×C31×#102C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
47. C2×C31×C22⋊C8C22semidirect
48. C2×C31×C22⋊C8C22semidirect
49. C2×C31×C22⋊C8C22semidirect
52. C31×#389C22semidirect
53. C31×#389C22semidirect
56. C31×#380C22semidirect
57. C31×#380C22semidirect
58. C31×#380C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
286. #24044C31direct (N × H)
403. C2×#482C2×C31semidirect
404. C2×#418C2×C31semidirect
405. #2485C2×C31semidirect
406. #2041C2×C31semidirect
407. #2041C2×C31semidirect
408. #2034C2×C31semidirect
409. #2033C2×C31semidirect
410. #1895C2×C31semidirect
411. #1870C2×C31semidirect
412. #1864C2×C31semidirect
413. #1862C2×C31semidirect
414. #1786C2×C31semidirect
415. #1786C2×C31semidirect
416. #1786C2×C31semidirect
477. C22×M16C22×C31semidirect
488. C2×#117C22×C31semidirect
490. C2×#107C22×C31semidirect
491. C2×#106C22×C31semidirect
497. C2×#102C22×C31semidirect
498. C2×#102C22×C31semidirect
499. C2×#102C22×C31semidirect
500. C2×#102C22×C31semidirect
501. C2×#102C22×C31semidirect
502. C2×#102C22×C31semidirect
503. C2×#102C22×C31semidirect
504. C2×#102C22×C31semidirect
505. C2×C22⋊C8C22×C31semidirect
506. C2×C22⋊C8C22×C31semidirect
507. C2×C22⋊C8C22×C31semidirect
510. #389C22×C31semidirect
511. #389C22×C31semidirect
514. #380C22×C31semidirect
515. #380C22×C31semidirect
516. #380C22×C31semidirect
517. #340C22×C31semidirect
518. #340C22×C31semidirect
519. #336C22×C31semidirect
520. #336C22×C31semidirect
626. C31#24044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C312
C2×C31×#4822
C2×C31×#4182
C31×#24852
C31×#20412
C31×#20342
C31×#20332
C31×#18952
C31×#18702
C31×#18642
C31×#18622
C31×#17862
#2404431