Finite Group Databasebeta

← C31×#23876 #21480635

Subgroups — C31×#23876 #21480635

Order 7936.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C31×#3488C211yesmaximal, characteristic, complemented
3C2×C31×#453C212yesmaximal, complemented
4C31×#3003C211yesmaximal, characteristic, complemented
5C31×#2433C211yesmaximal, characteristic, complemented
6C31×#2006C212yesmaximal, complemented
7C31×#2002C212yesmaximal, complemented
8C31×#1900C211yesmaximal, characteristic, complemented
9C31×#1883C212yesmaximal, complemented
10C31×#1871C211yesmaximal, characteristic, complemented
11C31×#1789C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic, complemented
13C22×#41×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic, complemented
15C2×C31×AGL(1,ℤ/8)—21no—
16C2×C31×AGL(1,ℤ/8)—21no—
17C2×C31×AGL(1,ℤ/8)—28no—
18C2×C31×AGL(1,ℤ/8)C2212yes—
19C2×C31×AGL(1,ℤ/8)C2212yescomplemented
20C2×C31×AGL(1,ℤ/8)C2212yescomplemented
21C22×SD16×C31—21no—
22C22×D8×C31—21no—
23C22×M16×C31C2211yescharacteristic, complemented
24C31×#550—21no—
25C31×#548—21no—
26C31×#546—21no—
27C31×#546—22no—
28D42×C31—22no—
29D42×C31—21no—
30C31×#537—21no—
31C31×#537C2211yescharacteristic, complemented
32C31×#535—21no—
33C31×#535C2211yescharacteristic, complemented
34C2×C31×#127C2212yescomplemented
35C31×#525—21no—
36C31×#525C2211yescharacteristic
37C2×C31×#121—21no—
38C2×C31×#121C2211yescharacteristic
39C2×C31×#120—22no—
40C31×#520C2211yescharacteristic, complemented
41C31×#453—28no—
42C31×#450—21no—
43C31×#450—21no—
44C31×#447—21no—
45C31×#447—21no—
46C2×C31×#104C2212yescomplemented
47C2×C31×#104C2212yescomplemented
48C2×C31×#104C2212yescomplemented
49C31×#418C2212yescomplemented
50C2×C31×#100C2212yescomplemented
51C31×#407C2211yescharacteristic, complemented
52C31×#392—22no—
53C31×#390C2212yescomplemented
54C4×C22⋊C4×C31C2211yescharacteristic, complemented
55C31×#343C2212yescomplemented
56C31×#339C2212yescomplemented
57C25×C31—21no—
58C31×H(5,𝔽2)—24no—
59C31×H(5,𝔽2)—42no—
60C2×#41×C31—21no—
61C2×#41×C31—21no—
62C2×#41×C31—21no—
63C2×#41×C31—21no—
64C2×#41×C31—24no—
65C2×#41×C31—42no—
66C2×#41×C31D411yescharacteristic, complemented
67C2×#41×C31D411yescharacteristic, complemented
68C2×#41×C31C2311yescharacteristic
69C2×#41×C31C2311yescharacteristic
70C2×#41×C31C2311yescharacteristic
71C22×Q8×C31D411yescharacteristic, complemented
72C22×D4×C31—24no—
73C22×D4×C31—21no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—24no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31—42no—
85C22×D4×C31D412yes—
86C22×D4×C31D411yescharacteristic, complemented
87C22×D4×C31C2311yescharacteristic
88C22×D4×C31C2312yes—
89C23×C4×C31—21no—
90C23×C4×C31C2311yescharacteristic
91C31×AGL(1,ℤ/8)—28no—
92C31×AGL(1,ℤ/8)—28no—
93C31×AGL(1,ℤ/8)—24no—
94C31×AGL(1,ℤ/8)—24no—
95C31×AGL(1,ℤ/8)—24no—
96C31×AGL(1,ℤ/8)—24no—
97C31×AGL(1,ℤ/8)—42no—
98C31×AGL(1,ℤ/8)D418yescomplemented
99C2×SD16×C31—28no—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31—22no—
103C2×D8×C31—28no—
104C2×D8×C31—22no—
105C2×D8×C31—22no—
106C2×D8×C31—22no—
107C2×M16×C31—21no—
108C2×M16×C31—24no—
109C2×M16×C31C2312yes—
110C2×M16×C31C2312yes—
111C22×C8×C31—21no—
112C31×#127—22no—
113C31×#127—21no—
114C31×#127—24no—
115C31×#127—42no—
116C31×#124—22no—
117C31×#124—21no—
118C31×#123—22no—
119C31×#123—21no—
120C31×C22⋊Q8—22no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8—21no—
123C31×C22⋊Q8D411yescharacteristic, complemented
124C31×C22⋊Q8D411yescharacteristic, complemented
125C31×#121—22no—
126C31×#121—22no—
127C31×#121—22no—
128C31×#121—22no—
129C31×#121—22no—
130C31×#121—21no—
131C31×#121—21no—
132C31×#121—21no—
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—22no—
137C31×#121—21no—
138C31×#121—21no—
139C31×#121D411yescharacteristic, complemented
140C31×#121D411yescharacteristic, complemented
141C31×#120—22no—
142C31×#120—22no—
143C31×#120—22no—
144C31×#120—21no—
145C31×#120—22no—
146C31×#120—48no—
147C4×Q8×C31—21no—
148C4×D4×C31—22no—
149C4×D4×C31—22no—
150C4×D4×C31—21no—
151C4×D4×C31—22no—
152C4×D4×C31—21no—
153C4×D4×C31—21no—
154C31×#117—21no—
155C31×#117C2311yescharacteristic
156C2×C4⋊C4×C31—21no—
157C2×C4⋊C4×C31C2311yescharacteristic
158C2×C22⋊C4×C31—22no—
159C2×C22⋊C4×C31—21no—
160C2×C22⋊C4×C31—24no—
161C2×C22⋊C4×C31D412yes—
162C2×C42×C31C2312yes—
163C31×#104—24no—
164C31×#104—24no—
165C31×#104—42no—
166C31×#102—22no—
167C31×#102—22no—
168C31×#100—24no—
169C31×C22⋊C8—21no—
170C31×C22⋊C8—21no—
171C31×#95—21no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—21no—
175C24×C31—44no—
176C24×C31—44no—
177C24×C31—41no—
178C24×C31—41no—
179C24×C31—82no—
180C24×C31C2×D411yescharacteristic
181C24×C31C2×D412yes—
182#41×C31—22no—
183#41×C31—22no—
184#41×C31—22no—
185#41×C31—22no—
186#41×C31—22no—
187#41×C31—22no—
188#41×C31—22no—
189#41×C31—44no—
190#41×C31—41no—
191#41×C31—41no—
192#41×C31—44no—
193#41×C31—44no—
194#41×C31—42no—
195#41×C31—42no—
196#41×C31C2×D414yes—
197C2×Q8×C31—21no—
198C2×Q8×C31—22no—
199C2×Q8×C31—41no—
200C2×Q8×C31C2×D411yescharacteristic
201C2×Q8×C31C2×D411yescharacteristic
202C2×Q8×C31C2×D411yescharacteristic
203C2×D4×C31—21no—
204C2×D4×C31—24no—
205C2×D4×C31—24no—
206C2×D4×C31—22no—
207C2×D4×C31—22no—
208C2×D4×C31—22no—
209C2×D4×C31—22no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—21no—
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—22no—
216C2×D4×C31—22no—
217C2×D4×C31—22no—
218C2×D4×C31—21no—
219C2×D4×C31—22no—
220C2×D4×C31—21no—
221C2×D4×C31—22no—
222C2×D4×C31—22no—
223C2×D4×C31—22no—
224C2×D4×C31—22no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—22no—
228C2×D4×C31—22no—
229C2×D4×C31—22no—
230C2×D4×C31—41no—
231C2×D4×C31—44no—
232C2×D4×C31—44no—
233C2×D4×C31—44no—
234C2×D4×C31—44no—
235C2×D4×C31—42no—
236C2×D4×C31—42no—
237C2×D4×C31—48no—
238C2×D4×C31—44no—
239C2×D4×C31—48no—
240C2×D4×C31—42no—
241C2×D4×C31—42no—
242C2×D4×C31—44no—
243C2×D4×C31—48no—
244C2×D4×C31—41no—
245C2×D4×C31—41no—
246C2×D4×C31—84no—
247C2×D4×C31—84no—
248C2×D4×C31C2×D411yescharacteristic
249C2×D4×C31C2×D411yescharacteristic
250C2×D4×C31C2×D411yescharacteristic
251C2×D4×C31C2×D414yescomplemented
252C22×C4×C31—21no—
253C22×C4×C31—22no—
254C22×C4×C31—22no—
255C22×C4×C31—22no—
256C22×C4×C31—21no—
257C22×C4×C31—22no—
258C22×C4×C31—22no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—44no—
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31C2×D411yescharacteristic
266C22×C4×C31C2×D411yescharacteristic
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2×D411yescharacteristic
269C22×C4×C31C2×D412yes—
270C22×C4×C31C2411yescharacteristic
271SD16×C31—28no—
272SD16×C31—28no—
273SD16×C31—44no—
274D8×C31—28no—
275D8×C31—28no—
276D8×C31—44no—
277M16×C31—24no—
278M16×C31—22no—
279M16×C31—22no—
280M16×C31—22no—
281M16×C31C2×D414yescomplemented
282C2×C8×C31—24no—
283C2×C8×C31—22no—
284C2×C8×C31—22no—
285C4⋊C4×C31—22no—
286C4⋊C4×C31—22no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31C2×D411yescharacteristic
292C4⋊C4×C31C2×D411yescharacteristic
293C22⋊C4×C31—22no—
294C22⋊C4×C31—22no—
295C22⋊C4×C31—24no—
296C22⋊C4×C31—22no—
297C22⋊C4×C31—22no—
298C22⋊C4×C31—22no—
299C22⋊C4×C31—21no—
300C22⋊C4×C31—21no—
301C22⋊C4×C31—21no—
302C22⋊C4×C31—21no—
303C22⋊C4×C31—22no—
304C22⋊C4×C31—22no—
305C22⋊C4×C31—21no—
306C22⋊C4×C31—48no—
307C42×C31—22no—
308C42×C31—21no—
309C42×C31—22no—
310C42×C31—22no—
311#23876C3111yesmaximal, characteristic, direct product factor, Sylow
312C23×C31—21no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—22no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—24no—
319C23×C31—24no—
320C23×C31—41no—
321C23×C31—42no—
322C23×C31—44no—
323C23×C31—44no—
324C23×C31—44no—
325C23×C31—44no—
326C23×C31—44no—
327C23×C31—42no—
328C23×C31—42no—
329C23×C31—42no—
330C23×C31—42no—
331C23×C31—42no—
332C23×C31—81no—
333C23×C31—82no—
334C23×C31—82no—
335C23×C31—82no—
336C23×C31—82no—
337C23×C31—82no—
338C23×C31—816no—
339C23×C31—82no—
340C23×C31#12011yescharacteristic
341C23×C31#12011yescharacteristic
342C23×C31C22×D411yescharacteristic
343Q8×C31—21no—
344Q8×C31—21no—
345Q8×C31—21no—
346Q8×C31—22no—
347Q8×C31—42no—
348Q8×C31#12012yescomplemented
349D4×C31—24no—
350D4×C31—21no—
351D4×C31—24no—
352D4×C31—21no—
353D4×C31—21no—
354D4×C31—22no—
355D4×C31—24no—
356D4×C31—42no—
357D4×C31—42no—
358D4×C31—44no—
359D4×C31—44no—
360D4×C31—44no—
361D4×C31—42no—
362D4×C31—44no—
363D4×C31—42no—
364D4×C31—42no—
365D4×C31—44no—
366D4×C31—42no—
367D4×C31—41no—
368D4×C31—42no—
369D4×C31—41no—
370D4×C31—42no—
371D4×C31—42no—
372D4×C31—81no—
373D4×C31—82no—
374D4×C31—82no—
375D4×C31—82no—
376D4×C31—82no—
377D4×C31—816no—
378D4×C31#12012yescomplemented
379C2×C4×C31—21no—
380C2×C4×C31—22no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—24no—
388C2×C4×C31—24no—
389C2×C4×C31—21no—
390C2×C4×C31—22no—
391C2×C4×C31—21no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—42no—
395C2×C4×C31—42no—
396C2×C4×C31—42no—
397C2×C4×C31—44no—
398C2×C4×C31—42no—
399C2×C4×C31—42no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—42no—
403C2×C4×C31—42no—
404C2×C4×C31—82no—
405C2×C4×C31#12011yescharacteristic
406C2×C4×C31#12011yescharacteristic
407C2×C4×C31C22×D411yescharacteristic
408C2×C4×C31C22×D412yes—
409C2×C4×C31C22×D411yescharacteristic
410C2×C4×C31H(5,𝔽2)12yes—
411C8×C31—24no—
412C8×C31—42no—
413C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
414#3488C2×C3111yescharacteristic, complemented
415C2×#453C2×C3112yescomplemented
416#3003C2×C3111yescharacteristic, complemented
417#2433C2×C3111yescharacteristic, complemented
418#2006C2×C3112yescomplemented
419#2002C2×C3112yescomplemented
420#1900C2×C3111yescharacteristic, complemented
421#1883C2×C3112yescomplemented
422#1871C2×C3111yescharacteristic, complemented
423#1789C2×C3111yescharacteristic, complemented
424C22×C31—21no—
425C22×C31—21no—
426C22×C31—21no—
427C22×C31—21no—
428C22×C31—21no—
429C22×C31—22no—
430C22×C31—21no—
431C22×C31—21no—
432C22×C31—44no—
433C22×C31—48no—
434C22×C31—41no—
435C22×C31—41no—
436C22×C31—41no—
437C22×C31—41no—
438C22×C31—42no—
439C22×C31—44no—
440C22×C31—42no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—41no—
444C22×C31—42no—
445C22×C31—41no—
446C22×C31—84no—
447C22×C31—84no—
448C22×C31—84no—
449C22×C31—88no—
450C22×C31—88no—
451C22×C31—82no—
452C22×C31—82no—
453C22×C31—164no—
454C22×C31#45312yescomplemented
455C22×C31C2×#12011yescharacteristic
456C22×C31D4212yes—
457C4×C31—21no—
458C4×C31—21no—
459C4×C31—22no—
460C4×C31—44no—
461C4×C31—41no—
462C4×C31—41no—
463C4×C31—42no—
464C4×C31—41no—
465C4×C31—41no—
466C4×C31C2×#12011yescharacteristic
467C4×C31#53411yescharacteristic
468C4×C31D4212yes—
469C2×H(5,𝔽2)C22×C3111yescharacteristic, complemented
470C22×#41C22×C3111yescharacteristic
471C23×D4C22×C3111yescharacteristic, complemented
472C2×AGL(1,ℤ/8)—21no—
473C2×AGL(1,ℤ/8)—21no—
474C2×AGL(1,ℤ/8)—28no—
475C2×AGL(1,ℤ/8)C22×C3112yes—
476C2×AGL(1,ℤ/8)C22×C3112yescomplemented
477C2×AGL(1,ℤ/8)C22×C3112yescomplemented
478C22×SD16—21no—
479C22×D8—21no—
480C22×M16C22×C3111yescharacteristic, complemented
481#550—21no—
482#548—21no—
483#546—21no—
484#546—22no—
485D42—22no—
486D42—21no—
487#537—21no—
488#537C22×C3111yescharacteristic, complemented
489#535—21no—
490#535C22×C3111yescharacteristic, complemented
491C2×#127C22×C3112yescomplemented
492#525—21no—
493#525C22×C3111yescharacteristic
494C2×#121—21no—
495C2×#121C22×C3111yescharacteristic
496C2×#120—22no—
497#520C22×C3111yescharacteristic, complemented
498#453—28no—
499#450—21no—
500#450—21no—
501#447—21no—
502#447—21no—
503C2×#104C22×C3112yescomplemented
504C2×#104C22×C3112yescomplemented
505C2×#104C22×C3112yescomplemented
506#418C22×C3112yescomplemented
507C2×#100C22×C3112yescomplemented
508#407C22×C3111yescharacteristic, complemented
509#392—22no—
510#390C22×C3112yescomplemented
511C4×C22⋊C4C22×C3111yescharacteristic, complemented
512#343C22×C3112yescomplemented
513#339C22×C3112yescomplemented
514C2×C31—22no—
515C2×C31—22no—
516C2×C31—41no—
517C2×C31—42no—
518C2×C31—81no—
519C2×C31—84no—
520C2×C31—82no—
521C2×C31—81no—
522C2×C31#240311yescharacteristic
523C2×C31C2×#45311yescharacteristic
524C2×C31#302111yescharacteristic
525C25—21no—
526H(5,𝔽2)—24no—
527H(5,𝔽2)—42no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—24no—
533C2×#41—42no—
534C2×#41D4×C3111yescharacteristic, complemented
535C2×#41D4×C3111yescharacteristic, complemented
536C2×#41C23×C3111yescharacteristic
537C2×#41C23×C3111yescharacteristic
538C2×#41C23×C3111yescharacteristic
539C22×Q8D4×C3111yescharacteristic, complemented
540C22×D4—24no—
541C22×D4—21no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—24no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—42no—
553C22×D4D4×C3112yes—
554C22×D4D4×C3111yescharacteristic, complemented
555C22×D4C23×C3111yescharacteristic
556C22×D4C23×C3112yes—
557C23×C4—21no—
558C23×C4C23×C3111yescharacteristic
559AGL(1,ℤ/8)—28no—
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—24no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—42no—
566AGL(1,ℤ/8)D4×C3118yescomplemented
567C2×SD16—28no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×D8—28no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×M16—21no—
576C2×M16—24no—
577C2×M16C23×C3112yes—
578C2×M16C23×C3112yes—
579C22×C8—21no—
580#127—22no—
581#127—21no—
582#127—24no—
583#127—42no—
584#124—22no—
585#124—21no—
586#123—22no—
587#123—21no—
588C22⋊Q8—22no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8D4×C3111yescharacteristic, complemented
592C22⋊Q8D4×C3111yescharacteristic, complemented
593#121—22no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—22no—
605#121—21no—
606#121—21no—
607#121D4×C3111yescharacteristic, complemented
608#121D4×C3111yescharacteristic, complemented
609#120—22no—
610#120—22no—
611#120—22no—
612#120—21no—
613#120—22no—
614#120—48no—
615C4×Q8—21no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—21no—
619C4×D4—22no—
620C4×D4—21no—
621C4×D4—21no—
622#117—21no—
623#117C23×C3111yescharacteristic
624C2×C4⋊C4—21no—
625C2×C4⋊C4C23×C3111yescharacteristic
626C2×C22⋊C4—22no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—24no—
629C2×C22⋊C4D4×C3112yes—
630C2×C42C23×C3112yes—
631#104—24no—
632#104—24no—
633#104—42no—
634#102—22no—
635#102—22no—
636#100—24no—
637C22⋊C8—21no—
638C22⋊C8—21no—
639#95—21no—
640C31#2387611yescharacteristic, direct product factor, Sylow
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C3111yescharacteristic
650C24C2×D4×C3112yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C3114yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C3111yescharacteristic
670C2×Q8C2×D4×C3111yescharacteristic
671C2×Q8C2×D4×C3111yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C3111yescharacteristic
718C2×D4C2×D4×C3111yescharacteristic
719C2×D4C2×D4×C3111yescharacteristic
720C2×D4C2×D4×C3114yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C3111yescharacteristic
734C22×C4C2×D4×C3111yescharacteristic
735C22×C4C2×D4×C3111yescharacteristic
736C22×C4C2×D4×C3111yescharacteristic
737C22×C4C2×D4×C3111yescharacteristic
738C22×C4C2×D4×C3112yes—
739C22×C4C24×C3111yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C3114yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C3111yescharacteristic
761C4⋊C4C2×D4×C3111yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23C31×#12011yescharacteristic
809C23C31×#12011yescharacteristic
810C23C22×D4×C3111yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8C31×#12012yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—81no—
841D4—82no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4C31×#12012yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4C31×#12011yescharacteristic
874C2×C4C31×#12011yescharacteristic
875C2×C4C22×D4×C3111yescharacteristic
876C2×C4C22×D4×C3112yes—
877C2×C4C22×D4×C3111yescharacteristic
878C2×C4C31×H(5,𝔽2)12yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22C31×#45312yescomplemented
912C22C2×C31×#12011yescharacteristic
913C22D42×C3112yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×C31×#12011yescharacteristic
924C4C31×#53411yescharacteristic
925C4D42×C3112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C31×#240311yescharacteristic
935C2C2×C31×#45311yescharacteristic
936C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×AGL(1,ℤ/8)C2semidirect
2. C31×#3488C2semidirect
3. C2×C31×#453C2semidirect
4. C31×#3003C2semidirect
5. C31×#2433C2semidirect
6. C31×#2006C2semidirect
7. C31×#2002C2semidirect
8. C31×#1900C2semidirect
9. C31×#1883C2semidirect
10. C31×#1871C2semidirect
11. C31×#1789C2semidirect
12. C2×C31×H(5,𝔽2)C22semidirect
14. C23×D4×C31C22semidirect
19. C2×C31×AGL(1,ℤ/8)C22semidirect
20. C2×C31×AGL(1,ℤ/8)C22semidirect
23. C22×M16×C31C22semidirect
31. C31×#537C22semidirect
33. C31×#535C22semidirect
34. C2×C31×#127C22semidirect
40. C31×#520C22semidirect
46. C2×C31×#104C22semidirect
47. C2×C31×#104C22semidirect
48. C2×C31×#104C22semidirect
49. C31×#418C22semidirect
50. C2×C31×#100C22semidirect
51. C31×#407C22semidirect
53. C31×#390C22semidirect
54. C4×C22⋊C4×C31C22semidirect
55. C31×#343C22semidirect
56. C31×#339C22semidirect
66. C2×#41×C31D4semidirect
67. C2×#41×C31D4semidirect
71. C22×Q8×C31D4semidirect
86. C22×D4×C31D4semidirect
98. C31×AGL(1,ℤ/8)D4semidirect
123. C31×C22⋊Q8D4semidirect
124. C31×C22⋊Q8D4semidirect
139. C31×#121D4semidirect
140. C31×#121D4semidirect
251. C2×D4×C31C2×D4semidirect
281. M16×C31C2×D4semidirect
311. #23876C31direct (N × H)
348. Q8×C31#120semidirect
378. D4×C31#120semidirect
413. C22×AGL(1,ℤ/8)C2×C31semidirect
414. #3488C2×C31semidirect
415. C2×#453C2×C31semidirect
416. #3003C2×C31semidirect
417. #2433C2×C31semidirect
418. #2006C2×C31semidirect
419. #2002C2×C31semidirect
420. #1900C2×C31semidirect
421. #1883C2×C31semidirect
422. #1871C2×C31semidirect
423. #1789C2×C31semidirect
454. C22×C31#453semidirect
469. C2×H(5,𝔽2)C22×C31semidirect
471. C23×D4C22×C31semidirect
476. C2×AGL(1,ℤ/8)C22×C31semidirect
477. C2×AGL(1,ℤ/8)C22×C31semidirect
480. C22×M16C22×C31semidirect
488. #537C22×C31semidirect
490. #535C22×C31semidirect
491. C2×#127C22×C31semidirect
497. #520C22×C31semidirect
503. C2×#104C22×C31semidirect
504. C2×#104C22×C31semidirect
505. C2×#104C22×C31semidirect
506. #418C22×C31semidirect
507. C2×#100C22×C31semidirect
508. #407C22×C31semidirect
510. #390C22×C31semidirect
511. C4×C22⋊C4C22×C31semidirect
512. #343C22×C31semidirect
513. #339C22×C31semidirect
534. C2×#41D4×C31semidirect
535. C2×#41D4×C31semidirect
539. C22×Q8D4×C31semidirect
554. C22×D4D4×C31semidirect
566. AGL(1,ℤ/8)D4×C31semidirect
591. C22⋊Q8D4×C31semidirect
592. C22⋊Q8D4×C31semidirect
607. #121D4×C31semidirect
608. #121D4×C31semidirect
640. C31#23876direct (N × H)
720. C2×D4C2×D4×C31semidirect
750. M16C2×D4×C31semidirect
816. Q8C31×#120semidirect
846. D4C31×#120semidirect
911. C22C31×#453semidirect

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C31×#34882
C2×C31×#4532
C31×#30032
C31×#24332
C31×#20062
C31×#20022
C31×#19002
C31×#18832
C31×#18712
C31×#17892
#2387631