Finite Group Databasebeta

← C31×#24432 #21481191

Subgroups — C31×#24432 #21481191

Order 7936.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C31C211yesmaximal, characteristic
2C2×C31×#465C211yesmaximal, characteristic, complemented
3C2×C31×#450C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C22×C31×#102C211yesmaximal, characteristic, complemented
6C31×#2417C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2014C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31—21no—
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic, complemented
21C22×SD16×C31C2211yescharacteristic, complemented
22C23×C8×C31C2211yescharacteristic, complemented
23D42×C31—24no—
24D42×C31—24no—
25C2×C31×#127C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic, complemented
27C2×C31×C22⋊Q8C2211yescharacteristic, complemented
28C2×C31×#121—21no—
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#120—21no—
32C2×C31×#120—21no—
33C2×C4×D4×C31C2211yescharacteristic
34C2×C4×D4×C31C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic, complemented
36C31×#465—24no—
37C31×#450—24no—
38C31×#450—24no—
39C2×C31×#106C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#102—24no—
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×#102C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic, complemented
49C2×C31×#102C2211yescharacteristic, complemented
50C2×C31×#102C2211yescharacteristic, complemented
51C2×C31×C22⋊C8C2211yescharacteristic, complemented
52C2×C31×C22⋊C8C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#398—21no—
55C31×#396—21no—
56C31×#391C2211yescharacteristic, complemented
57C31×#389C2211yescharacteristic, complemented
58C31×#386—21no—
59C31×#380—21no—
60C31×#380C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, complemented
65C25×C31—21no—
66C25×C31—21no—
67C22×Q8×C31C2311yescharacteristic
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—28no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—22no—
81C22×D4×C31—21no—
82C22×D4×C31—41no—
83C22×D4×C31—41no—
84C22×D4×C31—41no—
85C22×D4×C31—41no—
86C22×D4×C31—44no—
87C22×D4×C31—44no—
88C22×D4×C31D411yescharacteristic
89C22×D4×C31D414yes—
90C22×D4×C31C2311yescharacteristic
91C22×D4×C31C2311yescharacteristic
92C22×D4×C31C2311yescharacteristic
93C23×C4×C31—21no—
94C23×C4×C31—21no—
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31—22no—
103C2×SD16×C31—41no—
104C2×SD16×C31—41no—
105C2×SD16×C31—41no—
106C22×C8×C31—22no—
107C22×C8×C31—22no—
108C22×C8×C31—41no—
109C22×C8×C31C2311yescharacteristic
110C22×C8×C31C2311yescharacteristic
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C31×#127—22no—
114C31×#127—22no—
115C31×C22⋊Q8—22no—
116C31×C22⋊Q8—22no—
117C31×C22⋊Q8—22no—
118C31×C22⋊Q8—41no—
119C31×#121—28no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—22no—
123C31×#121D414yes—
124C31×#120—28no—
125C31×#120—28no—
126C4×D4×C31—22no—
127C4×D4×C31—22no—
128C4×D4×C31—22no—
129C4×D4×C31—22no—
130C2×C4⋊C4×C31—22no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31—21no—
134C2×C4⋊C4×C31—21no—
135C2×C4⋊C4×C31—41no—
136C2×C4⋊C4×C31D411yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C4⋊C4×C31C2311yescharacteristic
139C2×C4⋊C4×C31C2311yescharacteristic
140C2×C4⋊C4×C31C2311yescharacteristic
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31D411yescharacteristic
148C2×C22⋊C4×C31D411yescharacteristic
149C2×C42×C31C2311yescharacteristic
150C31×#106—22no—
151C31×#103—22no—
152C31×#102—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—41no—
160C31×#102D414yescomplemented
161C31×C22⋊C8—22no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8—41no—
164C31×#95—21no—
165C31×#95—21no—
166C31×#95—21no—
167C31×#95—21no—
168C24×C31—21no—
169C24×C31—24no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—24no—
173C24×C31—42no—
174C24×C31—42no—
175C24×C31—42no—
176C24×C31—42no—
177C24×C31—42no—
178C24×C31—42no—
179C24×C31—42no—
180C24×C31—42no—
181C24×C31—81no—
182C24×C31—81no—
183C24×C31—81no—
184C24×C31—81no—
185C24×C31C2×D411yescharacteristic
186C24×C31C2×D411yescharacteristic
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31—21no—
191C2×Q8×C31—21no—
192C2×Q8×C31—21no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—28no—
196C2×D4×C31—24no—
197C2×D4×C31—24no—
198C2×D4×C31—24no—
199C2×D4×C31—24no—
200C2×D4×C31—24no—
201C2×D4×C31—24no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—21no—
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—44no—
216C2×D4×C31—44no—
217C2×D4×C31—44no—
218C2×D4×C31—42no—
219C2×D4×C31—42no—
220C2×D4×C31—42no—
221C2×D4×C31—42no—
222C2×D4×C31—42no—
223C2×D4×C31—44no—
224C2×D4×C31—44no—
225C2×D4×C31—432no—
226C2×D4×C31—44no—
227C2×D4×C31—42no—
228C2×D4×C31—42no—
229C2×D4×C31—42no—
230C2×D4×C31—42no—
231C2×D4×C31—44no—
232C2×D4×C31—42no—
233C2×D4×C31—81no—
234C2×D4×C31—81no—
235C2×D4×C31SD1614yescomplemented
236C2×D4×C31C2×D412yes—
237C2×D4×C31C2×D412yes—
238C2×D4×C31C2×D412yes—
239C2×D4×C31C2×D412yes—
240C2×D4×C31#4112yes—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—24no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—42no—
258C22×C4×C31—42no—
259C22×C4×C31—42no—
260C22×C4×C31—42no—
261C22×C4×C31—81no—
262C22×C4×C31C2×D411yescharacteristic
263C22×C4×C31C2×D411yescharacteristic
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31C2×D412yes—
266C22×C4×C31C2×D412yes—
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2411yescharacteristic
269SD16×C31—44no—
270SD16×C31—44no—
271SD16×C31—44no—
272C2×C8×C31—21no—
273C2×C8×C31—21no—
274C2×C8×C31—21no—
275C2×C8×C31—21no—
276C2×C8×C31—21no—
277C2×C8×C31—21no—
278C2×C8×C31—21no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31—21no—
282C2×C8×C31—21no—
283C2×C8×C31—44no—
284C2×C8×C31C2×D412yescomplemented
285C4⋊C4×C31—22no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—42no—
293C4⋊C4×C31—42no—
294C4⋊C4×C31—42no—
295C4⋊C4×C31—81no—
296C4⋊C4×C31C2×D412yes—
297C4⋊C4×C31C2×D412yescomplemented
298C22⋊C4×C31—24no—
299C22⋊C4×C31—24no—
300C22⋊C4×C31—22no—
301C22⋊C4×C31—24no—
302C22⋊C4×C31—22no—
303C22⋊C4×C31—42no—
304C22⋊C4×C31—42no—
305C22⋊C4×C31—81no—
306C42×C31—21no—
307C42×C31—21no—
308#24432C3111yesmaximal, characteristic, direct product factor, Sylow
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—22no—
315C23×C31—21no—
316C23×C31—22no—
317C23×C31—21no—
318C23×C31—22no—
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—21no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—48no—
325C23×C31—48no—
326C23×C31—48no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—48no—
344C23×C31—84no—
345C23×C31—84no—
346C23×C31—84no—
347C23×C31—84no—
348C23×C31—84no—
349C23×C31—84no—
350C23×C31—84no—
351C23×C31—84no—
352C23×C31—84no—
353C23×C31—84no—
354C23×C31#12012yes—
355C23×C31C2×SD1612yes—
356C23×C31C2×SD1612yes—
357C23×C31AGL(1,ℤ/8)12yes—
358C23×C31C22×D411yescharacteristic
359Q8×C31—41no—
360Q8×C31—41no—
361Q8×C31—41no—
362Q8×C31—41no—
363D4×C31—28no—
364D4×C31—22no—
365D4×C31—22no—
366D4×C31—22no—
367D4×C31—22no—
368D4×C31—22no—
369D4×C31—22no—
370D4×C31—22no—
371D4×C31—48no—
372D4×C31—48no—
373D4×C31—48no—
374D4×C31—48no—
375D4×C31—48no—
376D4×C31—41no—
377D4×C31—41no—
378D4×C31—41no—
379D4×C31—41no—
380D4×C31—84no—
381D4×C31#12114yes—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—21no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—21no—
391C2×C4×C31—21no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—21no—
397C2×C4×C31—21no—
398C2×C4×C31—48no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—84no—
417C2×C4×C31#12012yes—
418C2×C4×C31C2×SD1612yes—
419C2×C4×C31C22×D411yescharacteristic
420C2×C4×C31C22×D411yescharacteristic
421C2×C4×C31C22×D411yescharacteristic
422C2×C4×C31C2×#4111yescharacteristic
423C2×C4×C31H(5,𝔽2)11yescharacteristic
424C2×C4×C31H(5,𝔽2)11yescharacteristic
425C8×C31—22no—
426C8×C31—41no—
427C8×C31—41no—
428C8×C31—41no—
429C2×D42C2×C3111yescharacteristic
430C2×#465C2×C3111yescharacteristic, complemented
431C2×#450C2×C3111yescharacteristic, complemented
432C2×#450C2×C3111yescharacteristic, complemented
433C22×#102C2×C3111yescharacteristic, complemented
434#2417C2×C3111yescharacteristic, complemented
435#2041C2×C3111yescharacteristic, complemented
436#2034C2×C3111yescharacteristic, complemented
437#2014C2×C3111yescharacteristic, complemented
438#2000C2×C3111yescharacteristic, complemented
439#1877C2×C3111yescharacteristic, complemented
440#1874C2×C3111yescharacteristic, complemented
441#1869C2×C3111yescharacteristic, complemented
442#1864C2×C3111yescharacteristic, complemented
443#1786C2×C3111yescharacteristic, complemented
444C22×C31—22no—
445C22×C31—22no—
446C22×C31—22no—
447C22×C31—22no—
448C22×C31—22no—
449C22×C31—22no—
450C22×C31—24no—
451C22×C31—22no—
452C22×C31—22no—
453C22×C31—22no—
454C22×C31—41no—
455C22×C31—42no—
456C22×C31—41no—
457C22×C31—42no—
458C22×C31—41no—
459C22×C31—42no—
460C22×C31—42no—
461C22×C31—42no—
462C22×C31—41no—
463C22×C31—42no—
464C22×C31—42no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—42no—
468C22×C31—42no—
469C22×C31—42no—
470C22×C31—816no—
471C22×C31—816no—
472C22×C31—81no—
473C22×C31—81no—
474C22×C31—81no—
475C22×C31—81no—
476C22×C31—81no—
477C22×C31—81no—
478C22×C31—81no—
479C22×C31—81no—
480C22×C31#45014yescomplemented
481C22×C31C2×#12011yescharacteristic
482C22×C31D4211yescharacteristic
483C22×C31#54611yescharacteristic
484C22×C31C22×SD1611yescharacteristic
485C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C31#57611yescharacteristic
487C22×C31#57711yescharacteristic
488C4×C31—22no—
489C4×C31—22no—
490C4×C31—41no—
491C4×C31—42no—
492C4×C31—42no—
493C4×C31—41no—
494C4×C31—81no—
495C4×C31—81no—
496C4×C31—81no—
497C4×C31C2×#12111yescharacteristic
498C4×C31#53411yescharacteristic
499C4×C31D4211yescharacteristic
500C4×C31#54611yescharacteristic
501C23×D4—21no—
502C23×D4C22×C3111yescharacteristic
503C23×D4C22×C3111yescharacteristic
504C22×SD16C22×C3111yescharacteristic
505C22×SD16C22×C3111yescharacteristic, complemented
506C22×SD16C22×C3111yescharacteristic, complemented
507C23×C8C22×C3111yescharacteristic, complemented
508D42—24no—
509D42—24no—
510C2×#127C22×C3111yescharacteristic
511C2×C22⋊Q8C22×C3111yescharacteristic, complemented
512C2×C22⋊Q8C22×C3111yescharacteristic, complemented
513C2×#121—21no—
514C2×#121C22×C3111yescharacteristic
515C2×#121C22×C3111yescharacteristic
516C2×#120—21no—
517C2×#120—21no—
518C2×C4×D4C22×C3111yescharacteristic
519C2×C4×D4C22×C3111yescharacteristic
520C22×C4⋊C4C22×C3111yescharacteristic, complemented
521#465—24no—
522#450—24no—
523#450—24no—
524C2×#106C22×C3111yescharacteristic, complemented
525C2×#103C22×C3111yescharacteristic, complemented
526C2×#102—24no—
527C2×#102C22×C3111yescharacteristic
528C2×#102C22×C3111yescharacteristic
529C2×#102C22×C3111yescharacteristic
530C2×#102C22×C3111yescharacteristic, complemented
531C2×#102C22×C3111yescharacteristic, complemented
532C2×#102C22×C3111yescharacteristic, complemented
533C2×#102C22×C3111yescharacteristic, complemented
534C2×#102C22×C3111yescharacteristic, complemented
535C2×#102C22×C3111yescharacteristic, complemented
536C2×C22⋊C8C22×C3111yescharacteristic, complemented
537C2×C22⋊C8C22×C3111yescharacteristic, complemented
538C2×C22⋊C8C22×C3111yescharacteristic, complemented
539#398—21no—
540#396—21no—
541#391C22×C3111yescharacteristic, complemented
542#389C22×C3111yescharacteristic, complemented
543#386—21no—
544#380—21no—
545#380C22×C3111yescharacteristic, complemented
546#340C22×C3111yescharacteristic, complemented
547#340C22×C3111yescharacteristic, complemented
548#336C22×C3111yescharacteristic, complemented
549#336C22×C3111yescharacteristic, complemented
550C2×C31—24no—
551C2×C31—42no—
552C2×C31—44no—
553C2×C31—82no—
554C2×C31—82no—
555C2×C31#241011yescharacteristic
556C2×C31C2×#45011yescharacteristic
557C2×C31#301211yescharacteristic
558C2×C31#326411yescharacteristic
559C2×C31D4×SD1611yescharacteristic
560C2×C31#329511yescharacteristic
561C2×C31#331011yescharacteristic
562C25—21no—
563C25—21no—
564C22×Q8C23×C3111yescharacteristic
565C22×D4—22no—
566C22×D4—22no—
567C22×D4—28no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—22no—
578C22×D4—21no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—44no—
584C22×D4—44no—
585C22×D4D4×C3111yescharacteristic
586C22×D4D4×C3114yes—
587C22×D4C23×C3111yescharacteristic
588C22×D4C23×C3111yescharacteristic
589C22×D4C23×C3111yescharacteristic
590C23×C4—21no—
591C23×C4—21no—
592C23×C4C23×C3111yescharacteristic
593C23×C4C23×C3111yescharacteristic
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16—41no—
602C2×SD16—41no—
603C22×C8—22no—
604C22×C8—22no—
605C22×C8—41no—
606C22×C8C23×C3111yescharacteristic
607C22×C8C23×C3111yescharacteristic
608C22×C8C23×C3111yescharacteristic
609C22×C8C23×C3111yescharacteristic
610#127—22no—
611#127—22no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—41no—
616#121—28no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121D4×C3114yes—
621#120—28no—
622#120—28no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4D4×C3111yescharacteristic
634C2×C4⋊C4C23×C3111yescharacteristic
635C2×C4⋊C4C23×C3111yescharacteristic
636C2×C4⋊C4C23×C3111yescharacteristic
637C2×C4⋊C4C23×C3111yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4D4×C3111yescharacteristic
645C2×C22⋊C4D4×C3111yescharacteristic
646C2×C42C23×C3111yescharacteristic
647#106—22no—
648#103—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—41no—
657#102D4×C3114yescomplemented
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—41no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665C31#2443211yescharacteristic, direct product factor, Sylow
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C3111yescharacteristic
684C24C2×D4×C3111yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C3114yescomplemented
734C2×D4C2×D4×C3112yes—
735C2×D4C2×D4×C3112yes—
736C2×D4C2×D4×C3112yes—
737C2×D4C2×D4×C3112yes—
738C2×D4#41×C3112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C3111yescharacteristic
761C22×C4C2×D4×C3111yescharacteristic
762C22×C4C2×D4×C3111yescharacteristic
763C22×C4C2×D4×C3112yes—
764C22×C4C2×D4×C3112yes—
765C22×C4C2×D4×C3111yescharacteristic
766C22×C4C24×C3111yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C3112yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C3112yes—
795C4⋊C4C2×D4×C3112yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23C31×#12012yes—
852C23C2×SD16×C3112yes—
853C23C2×SD16×C3112yes—
854C23C31×AGL(1,ℤ/8)12yes—
855C23C22×D4×C3111yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4C31×#12114yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4C31×#12012yes—
915C2×C4C2×SD16×C3112yes—
916C2×C4C22×D4×C3111yescharacteristic
917C2×C4C22×D4×C3111yescharacteristic
918C2×C4C22×D4×C3111yescharacteristic
919C2×C4C2×#41×C3111yescharacteristic
920C2×C4C31×H(5,𝔽2)11yescharacteristic
921C2×C4C31×H(5,𝔽2)11yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C31×#45014yescomplemented
963C22C2×C31×#12011yescharacteristic
964C22D42×C3111yescharacteristic
965C22C31×#54611yescharacteristic
966C22C22×SD16×C3111yescharacteristic
967C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
968C22C31×#57611yescharacteristic
969C22C31×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×C31×#12111yescharacteristic
980C4C31×#53411yescharacteristic
981C4D42×C3111yescharacteristic
982C4C31×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C31×#241011yescharacteristic
989C2C2×C31×#45011yescharacteristic
990C2C31×#301211yescharacteristic
991C2C31×#326411yescharacteristic
992C2D4×SD16×C3111yescharacteristic
993C2C31×#329511yescharacteristic
994C2C31×#331011yescharacteristic
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×#465C2semidirect
3. C2×C31×#450C2semidirect
4. C2×C31×#450C2semidirect
5. C22×C31×#102C2semidirect
6. C31×#2417C2semidirect
7. C31×#2041C2semidirect
8. C31×#2034C2semidirect
9. C31×#2014C2semidirect
10. C31×#2000C2semidirect
11. C31×#1877C2semidirect
12. C31×#1874C2semidirect
13. C31×#1869C2semidirect
14. C31×#1864C2semidirect
15. C31×#1786C2semidirect
20. C22×SD16×C31C22semidirect
21. C22×SD16×C31C22semidirect
22. C23×C8×C31C22semidirect
26. C2×C31×C22⋊Q8C22semidirect
27. C2×C31×C22⋊Q8C22semidirect
35. C22×C4⋊C4×C31C22semidirect
39. C2×C31×#106C22semidirect
40. C2×C31×#103C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
47. C2×C31×#102C22semidirect
48. C2×C31×#102C22semidirect
49. C2×C31×#102C22semidirect
50. C2×C31×#102C22semidirect
51. C2×C31×C22⋊C8C22semidirect
52. C2×C31×C22⋊C8C22semidirect
53. C2×C31×C22⋊C8C22semidirect
56. C31×#391C22semidirect
57. C31×#389C22semidirect
60. C31×#380C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
160. C31×#102D4semidirect
235. C2×D4×C31SD16semidirect
284. C2×C8×C31C2×D4semidirect
297. C4⋊C4×C31C2×D4semidirect
308. #24432C31direct (N × H)
430. C2×#465C2×C31semidirect
431. C2×#450C2×C31semidirect
432. C2×#450C2×C31semidirect
433. C22×#102C2×C31semidirect
434. #2417C2×C31semidirect
435. #2041C2×C31semidirect
436. #2034C2×C31semidirect
437. #2014C2×C31semidirect
438. #2000C2×C31semidirect
439. #1877C2×C31semidirect
440. #1874C2×C31semidirect
441. #1869C2×C31semidirect
442. #1864C2×C31semidirect
443. #1786C2×C31semidirect
480. C22×C31#450semidirect
505. C22×SD16C22×C31semidirect
506. C22×SD16C22×C31semidirect
507. C23×C8C22×C31semidirect
511. C2×C22⋊Q8C22×C31semidirect
512. C2×C22⋊Q8C22×C31semidirect
520. C22×C4⋊C4C22×C31semidirect
524. C2×#106C22×C31semidirect
525. C2×#103C22×C31semidirect
530. C2×#102C22×C31semidirect
531. C2×#102C22×C31semidirect
532. C2×#102C22×C31semidirect
533. C2×#102C22×C31semidirect
534. C2×#102C22×C31semidirect
535. C2×#102C22×C31semidirect
536. C2×C22⋊C8C22×C31semidirect
537. C2×C22⋊C8C22×C31semidirect
538. C2×C22⋊C8C22×C31semidirect
541. #391C22×C31semidirect
542. #389C22×C31semidirect
545. #380C22×C31semidirect
546. #340C22×C31semidirect
547. #340C22×C31semidirect
548. #336C22×C31semidirect
549. #336C22×C31semidirect
657. #102D4×C31semidirect
665. C31#24432direct (N × H)
733. C2×D4SD16×C31semidirect
782. C2×C8C2×D4×C31semidirect
795. C4⋊C4C2×D4×C31semidirect
962. C22C31×#450semidirect

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×#4652
C2×C31×#4502
C22×C31×#1022
C31×#24172
C31×#20412
C31×#20342
C31×#20142
C31×#20002
C31×#18772
C31×#18742
C31×#18692
C31×#18642
C31×#17862
#2443231