Finite Group Databasebeta

← C31×#24257 #21481016

Subgroups — C31×#24257 #21481016

Order 7936.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#447C211yesmaximal, characteristic, complemented
5C2×C31×#442C211yesmaximal, characteristic, complemented
6C31×#2537C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1959C211yesmaximal, characteristic, complemented
12C31×#1955C211yesmaximal, characteristic, complemented
13C31×#1802C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic, complemented
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C31×#546—24no—
22C31×#546—24no—
23C2×C31×#124C2211yescharacteristic
24C2×C31×#123—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121—21no—
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic, complemented
31C2×C31×#120—21no—
32C2×C4×D4×C31C2211yescharacteristic
33C2×C4×D4×C31C2211yescharacteristic
34C2×C4×D4×C31C2211yescharacteristic, complemented
35C22×C22⋊C4×C31—21no—
36C31×#463—24no—
37C31×#449—24no—
38C31×#447—24no—
39C31×#442—24no—
40C2×C31×#106C2211yescharacteristic, complemented
41C2×C31×C4⋊C8C2211yescharacteristic, complemented
42C2×C31×#103C2211yescharacteristic, complemented
43C2×C31×#103C2211yescharacteristic, complemented
44C2×C31×#103C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×#102C2211yescharacteristic, complemented
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic, complemented
55C2×C31×C22⋊C8C2211yescharacteristic, complemented
56C2×C31×#97C2211yescharacteristic, complemented
57C31×#394—21no—
58C31×#394—21no—
59C31×#384C2211yescharacteristic, complemented
60C31×#380—21no—
61C31×#380C2211yescharacteristic
62C31×#380C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, complemented
65C25×C31—21no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—22no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—41no—
83C22×D4×C31—41no—
84C22×D4×C31D411yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C22×D4×C31C2311yescharacteristic
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31—21no—
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—41no—
96C2×D8×C31—22no—
97C2×D8×C31—22no—
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—41no—
101C2×D8×C31D414yescomplemented
102C22×C8×C31C2311yescharacteristic
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C31×#124—22no—
107C31×#124D414yescomplemented
108C31×#123—28no—
109C31×C22⋊Q8—22no—
110C31×C22⋊Q8—22no—
111C31×#121—28no—
112C31×#121—22no—
113C31×#121—22no—
114C31×#121—22no—
115C31×#121—22no—
116C31×#121—41no—
117C31×#121—41no—
118C31×#121—44no—
119C31×#120—28no—
120C4×D4×C31—22no—
121C4×D4×C31—22no—
122C4×D4×C31—22no—
123C4×D4×C31—22no—
124C4×D4×C31—22no—
125C4×D4×C31D414yescomplemented
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31D411yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C4⋊C4×C31C2311yescharacteristic
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C22⋊C4×C31—28no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31D411yescharacteristic
146C2×C22⋊C4×C31D411yescharacteristic
147C2×C42×C31C2311yescharacteristic
148C31×#106—22no—
149C31×C4⋊C8—22no—
150C31×#103—22no—
151C31×#103—22no—
152C31×#103—41no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—41no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8—41no—
163C31×C22⋊C8—41no—
164C31×#97—22no—
165C31×#95—21no—
166C31×#95—21no—
167C24×C31—21no—
168C24×C31—24no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—42no—
172C24×C31—42no—
173C24×C31—42no—
174C24×C31—42no—
175C24×C31—81no—
176C24×C31—81no—
177C24×C31C2×D411yescharacteristic
178C24×C31C2×D411yescharacteristic
179#41×C31—44no—
180#41×C31—44no—
181#41×C31—44no—
182#41×C31—44no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31C2×D412yes—
189C2×D4×C31—24no—
190C2×D4×C31—24no—
191C2×D4×C31—22no—
192C2×D4×C31—24no—
193C2×D4×C31—22no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—41no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—44no—
211C2×D4×C31—44no—
212C2×D4×C31—44no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—44no—
216C2×D4×C31—42no—
217C2×D4×C31—42no—
218C2×D4×C31—42no—
219C2×D4×C31—42no—
220C2×D4×C31—81no—
221C2×D4×C31—81no—
222C2×D4×C31—81no—
223C2×D4×C31—81no—
224C2×D4×C31C2×D412yes—
225C2×D4×C31C2×D412yes—
226C2×D4×C31C2×D412yes—
227C2×D4×C31C2×D412yes—
228C2×D4×C31#4112yes—
229C22×C4×C31—24no—
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—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—24no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—42no—
249C22×C4×C31—42no—
250C22×C4×C31—42no—
251C22×C4×C31—42no—
252C22×C4×C31—42no—
253C22×C4×C31—81no—
254C22×C4×C31—81no—
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2×D411yescharacteristic
259C22×C4×C31C2411yescharacteristic
260SD16×C31—44no—
261D8×C31—28no—
262D8×C31—44no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31—21no—
268C2×C8×C31—21no—
269C2×C8×C31—21no—
270C2×C8×C31—21no—
271C2×C8×C31—21no—
272C2×C8×C31—21no—
273C2×C8×C31—21no—
274C2×C8×C31C2×D412yes—
275C4⋊C4×C31—24no—
276C4⋊C4×C31—22no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—42no—
285C4⋊C4×C31—81no—
286C4⋊C4×C31C2×D412yes—
287C22⋊C4×C31—24no—
288C22⋊C4×C31—24no—
289C22⋊C4×C31—22no—
290C22⋊C4×C31—24no—
291C22⋊C4×C31—24no—
292C22⋊C4×C31—24no—
293C22⋊C4×C31—22no—
294C22⋊C4×C31—42no—
295C22⋊C4×C31—42no—
296C22⋊C4×C31—42no—
297C22⋊C4×C31—42no—
298C22⋊C4×C31—42no—
299C42×C31C2×D412yes—
300C42×C31C2×D412yes—
301#24257C3111yesmaximal, characteristic, direct product factor, Sylow
302C23×C31—21no—
303C23×C31—22no—
304C23×C31—21no—
305C23×C31—22no—
306C23×C31—21no—
307C23×C31—22no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—22no—
312C23×C31—21no—
313C23×C31—22no—
314C23×C31—21no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—48no—
321C23×C31—48no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
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—84no—
339C23×C31—84no—
340C23×C31—84no—
341C23×C31—84no—
342C23×C31—84no—
343C23×C31AGL(1,ℤ/8)12yes—
344C23×C31C22×D411yescharacteristic
345Q8×C31—22no—
346Q8×C31—22no—
347Q8×C31—41no—
348Q8×C31—41no—
349D4×C31—22no—
350D4×C31—22no—
351D4×C31—22no—
352D4×C31—22no—
353D4×C31—22no—
354D4×C31—22no—
355D4×C31—22no—
356D4×C31—44no—
357D4×C31—48no—
358D4×C31—48no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—41no—
362D4×C31—41no—
363D4×C31—84no—
364D4×C31—84no—
365D4×C31—84no—
366D4×C31#12114yescomplemented
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—21no—
371C2×C4×C31—22no—
372C2×C4×C31—21no—
373C2×C4×C31—22no—
374C2×C4×C31—21no—
375C2×C4×C31—21no—
376C2×C4×C31—21no—
377C2×C4×C31—21no—
378C2×C4×C31—21no—
379C2×C4×C31—48no—
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—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—84no—
402C2×C4×C31—84no—
403C2×C4×C31#12012yes—
404C2×C4×C31#12012yes—
405C2×C4×C31C22×D411yescharacteristic
406C2×C4×C31C22×D411yescharacteristic
407C2×C4×C31C22×D411yescharacteristic
408C2×C4×C31C2×#4111yescharacteristic
409C2×C4×C31H(5,𝔽2)11yescharacteristic
410C2×C4×C31H(5,𝔽2)11yescharacteristic
411C8×C31—22no—
412C8×C31—41no—
413C8×C31—41no—
414C8×C31—41no—
415C2×#546C2×C3111yescharacteristic, complemented
416C2×#463C2×C3111yescharacteristic, complemented
417C2×#449C2×C3111yescharacteristic, complemented
418C2×#447C2×C3111yescharacteristic, complemented
419C2×#442C2×C3111yescharacteristic, complemented
420#2537C2×C3111yescharacteristic, complemented
421#2035C2×C3111yescharacteristic, complemented
422#2034C2×C3111yescharacteristic, complemented
423#2000C2×C3111yescharacteristic, complemented
424#1999C2×C3111yescharacteristic, complemented
425#1959C2×C3111yescharacteristic, complemented
426#1955C2×C3111yescharacteristic, complemented
427#1802C2×C3111yescharacteristic, complemented
428#1788C2×C3111yescharacteristic, complemented
429#1786C2×C3111yescharacteristic, complemented
430C22×C31—24no—
431C22×C31—22no—
432C22×C31—22no—
433C22×C31—22no—
434C22×C31—41no—
435C22×C31—42no—
436C22×C31—42no—
437C22×C31—41no—
438C22×C31—42no—
439C22×C31—42no—
440C22×C31—41no—
441C22×C31—42no—
442C22×C31—41no—
443C22×C31—42no—
444C22×C31—41no—
445C22×C31—42no—
446C22×C31—42no—
447C22×C31—41no—
448C22×C31—42no—
449C22×C31—41no—
450C22×C31—42no—
451C22×C31—41no—
452C22×C31—42no—
453C22×C31—41no—
454C22×C31—42no—
455C22×C31—41no—
456C22×C31—41no—
457C22×C31—816no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31—81no—
463C22×C31—81no—
464C22×C31—81no—
465C22×C31—81no—
466C22×C31C2×#12011yescharacteristic
467C22×C31D4211yescharacteristic
468C22×C31#54611yescharacteristic
469C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C31#57511yescharacteristic
471C22×C31#57611yescharacteristic
472C22×C31#57711yescharacteristic
473C4×C31—22no—
474C4×C31—22no—
475C4×C31—41no—
476C4×C31—41no—
477C4×C31—42no—
478C4×C31—42no—
479C4×C31—81no—
480C4×C31—81no—
481C4×C31—81no—
482C4×C31C2×#12111yescharacteristic
483C4×C31#53511yescharacteristic
484C4×C31D4211yescharacteristic
485C4×C31#54611yescharacteristic
486C22×#41C22×C3111yescharacteristic
487C23×D4C22×C3111yescharacteristic
488C22×SD16C22×C3111yescharacteristic, complemented
489C22×D8C22×C3111yescharacteristic
490C22×D8C22×C3111yescharacteristic
491#546—24no—
492#546—24no—
493C2×#124C22×C3111yescharacteristic
494C2×#123—21no—
495C2×C22⋊Q8C22×C3111yescharacteristic
496C2×#121—21no—
497C2×#121—21no—
498C2×#121C22×C3111yescharacteristic
499C2×#121C22×C3111yescharacteristic
500C2×#121C22×C3111yescharacteristic, complemented
501C2×#120—21no—
502C2×C4×D4C22×C3111yescharacteristic
503C2×C4×D4C22×C3111yescharacteristic
504C2×C4×D4C22×C3111yescharacteristic, complemented
505C22×C22⋊C4—21no—
506#463—24no—
507#449—24no—
508#447—24no—
509#442—24no—
510C2×#106C22×C3111yescharacteristic, complemented
511C2×C4⋊C8C22×C3111yescharacteristic, complemented
512C2×#103C22×C3111yescharacteristic, complemented
513C2×#103C22×C3111yescharacteristic, complemented
514C2×#103C22×C3111yescharacteristic, complemented
515C2×#102C22×C3111yescharacteristic
516C2×#102C22×C3111yescharacteristic
517C2×#102C22×C3111yescharacteristic
518C2×#102C22×C3111yescharacteristic
519C2×#102C22×C3111yescharacteristic
520C2×#102C22×C3111yescharacteristic
521C2×#102C22×C3111yescharacteristic, complemented
522C2×C22⋊C8C22×C3111yescharacteristic
523C2×C22⋊C8C22×C3111yescharacteristic
524C2×C22⋊C8C22×C3111yescharacteristic, complemented
525C2×C22⋊C8C22×C3111yescharacteristic, complemented
526C2×#97C22×C3111yescharacteristic, complemented
527#394—21no—
528#394—21no—
529#384C22×C3111yescharacteristic, complemented
530#380—21no—
531#380C22×C3111yescharacteristic
532#380C22×C3111yescharacteristic, complemented
533#340C22×C3111yescharacteristic, complemented
534#340C22×C3111yescharacteristic, complemented
535C2×C31—42no—
536C2×C31—44no—
537C2×C31—81no—
538C2×C31—82no—
539C2×C31—82no—
540C2×C31#240811yescharacteristic
541C2×C31#300611yescharacteristic
542C2×C31#301211yescharacteristic
543C2×C31#326411yescharacteristic
544C2×C31#326711yescharacteristic
545C2×C31#330611yescharacteristic
546C2×C31#331911yescharacteristic
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C3111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—41no—
565C22×D4—41no—
566C22×D4D4×C3111yescharacteristic
567C22×D4C23×C3111yescharacteristic
568C22×D4C23×C3111yescharacteristic
569C22×D4C23×C3111yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C3111yescharacteristic
574C23×C4C23×C3111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—41no—
583C2×D8D4×C3114yescomplemented
584C22×C8C23×C3111yescharacteristic
585C22×C8C23×C3111yescharacteristic
586C22×C8C23×C3111yescharacteristic
587C22×C8C23×C3111yescharacteristic
588#124—22no—
589#124D4×C3114yescomplemented
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121—41no—
600#121—44no—
601#120—28no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4D4×C3114yescomplemented
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4D4×C3111yescharacteristic
612C2×C4⋊C4C23×C3111yescharacteristic
613C2×C4⋊C4C23×C3111yescharacteristic
614C2×C4⋊C4C23×C3111yescharacteristic
615C2×C4⋊C4C23×C3111yescharacteristic
616C2×C22⋊C4—28no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4D4×C3111yescharacteristic
628C2×C22⋊C4D4×C3111yescharacteristic
629C2×C42C23×C3111yescharacteristic
630#106—22no—
631C4⋊C8—22no—
632#103—22no—
633#103—22no—
634#103—41no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—41no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8—41no—
645C22⋊C8—41no—
646#97—22no—
647#95—21no—
648#95—21no—
649C31#2425711yescharacteristic, direct product factor, Sylow
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C3111yescharacteristic
661C24C2×D4×C3111yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C3112yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C3112yes—
708C2×D4C2×D4×C3112yes—
709C2×D4C2×D4×C3112yes—
710C2×D4C2×D4×C3112yes—
711C2×D4#41×C3112yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C3111yescharacteristic
739C22×C4C2×D4×C3111yescharacteristic
740C22×C4C2×D4×C3111yescharacteristic
741C22×C4C2×D4×C3111yescharacteristic
742C22×C4C24×C3111yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C3112yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C3112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C3112yes—
783C42C2×D4×C3112yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23C31×AGL(1,ℤ/8)12yes—
826C23C22×D4×C3111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4C31×#12114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4C31×#12012yes—
886C2×C4C31×#12012yes—
887C2×C4C22×D4×C3111yescharacteristic
888C2×C4C22×D4×C3111yescharacteristic
889C2×C4C22×D4×C3111yescharacteristic
890C2×C4C2×#41×C3111yescharacteristic
891C2×C4C31×H(5,𝔽2)11yescharacteristic
892C2×C4C31×H(5,𝔽2)11yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×C31×#12011yescharacteristic
934C22D42×C3111yescharacteristic
935C22C31×#54611yescharacteristic
936C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
937C22C31×#57511yescharacteristic
938C22C31×#57611yescharacteristic
939C22C31×#57711yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×C31×#12111yescharacteristic
950C4C31×#53511yescharacteristic
951C4D42×C3111yescharacteristic
952C4C31×#54611yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C31×#240811yescharacteristic
959C2C31×#300611yescharacteristic
960C2C31×#301211yescharacteristic
961C2C31×#326411yescharacteristic
962C2C31×#326711yescharacteristic
963C2C31×#330611yescharacteristic
964C2C31×#331911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C2×C31×#546C2semidirect
2. C2×C31×#463C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#447C2semidirect
5. C2×C31×#442C2semidirect
6. C31×#2537C2semidirect
7. C31×#2035C2semidirect
8. C31×#2034C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1959C2semidirect
12. C31×#1955C2semidirect
13. C31×#1802C2semidirect
14. C31×#1788C2semidirect
15. C31×#1786C2semidirect
18. C22×SD16×C31C22semidirect
30. C2×C31×#121C22semidirect
34. C2×C4×D4×C31C22semidirect
40. C2×C31×#106C22semidirect
41. C2×C31×C4⋊C8C22semidirect
42. C2×C31×#103C22semidirect
43. C2×C31×#103C22semidirect
44. C2×C31×#103C22semidirect
51. C2×C31×#102C22semidirect
54. C2×C31×C22⋊C8C22semidirect
55. C2×C31×C22⋊C8C22semidirect
56. C2×C31×#97C22semidirect
59. C31×#384C22semidirect
62. C31×#380C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
101. C2×D8×C31D4semidirect
107. C31×#124D4semidirect
125. C4×D4×C31D4semidirect
301. #24257C31direct (N × H)
366. D4×C31#121semidirect
415. C2×#546C2×C31semidirect
416. C2×#463C2×C31semidirect
417. C2×#449C2×C31semidirect
418. C2×#447C2×C31semidirect
419. C2×#442C2×C31semidirect
420. #2537C2×C31semidirect
421. #2035C2×C31semidirect
422. #2034C2×C31semidirect
423. #2000C2×C31semidirect
424. #1999C2×C31semidirect
425. #1959C2×C31semidirect
426. #1955C2×C31semidirect
427. #1802C2×C31semidirect
428. #1788C2×C31semidirect
429. #1786C2×C31semidirect
488. C22×SD16C22×C31semidirect
500. C2×#121C22×C31semidirect
504. C2×C4×D4C22×C31semidirect
510. C2×#106C22×C31semidirect
511. C2×C4⋊C8C22×C31semidirect
512. C2×#103C22×C31semidirect
513. C2×#103C22×C31semidirect
514. C2×#103C22×C31semidirect
521. C2×#102C22×C31semidirect
524. C2×C22⋊C8C22×C31semidirect
525. C2×C22⋊C8C22×C31semidirect
526. C2×#97C22×C31semidirect
529. #384C22×C31semidirect
532. #380C22×C31semidirect
533. #340C22×C31semidirect
534. #340C22×C31semidirect
583. C2×D8D4×C31semidirect
589. #124D4×C31semidirect
607. C4×D4D4×C31semidirect
649. C31#24257direct (N × H)
848. D4C31×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5462
C2×C31×#4632
C2×C31×#4492
C2×C31×#4472
C2×C31×#4422
C31×#25372
C31×#20352
C31×#20342
C31×#20002
C31×#19992
C31×#19592
C31×#19552
C31×#18022
C31×#17882
C31×#17862
#2425731