Finite Group Databasebeta

← C31×#24366 #21481125

Subgroups — C31×#24366 #21481125

Order 7936.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 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
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#459C211yesmaximal, characteristic, complemented
4C2×C31×#447C211yesmaximal, characteristic, complemented
5C31×#2431C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2012C211yesmaximal, characteristic, complemented
10C31×#2011C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1851C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)—24no—
19C2×C31×AGL(1,ℤ/8)—24no—
20C2×C31×AGL(1,ℤ/8)—24no—
21C22×SD16×C31C2211yescharacteristic
22C22×SD16×C31C2211yescharacteristic
23C22×D8×C31C2211yescharacteristic
24C22×D8×C31C2211yescharacteristic
25C22×D8×C31C2211yescharacteristic
26C22×D8×C31C2211yescharacteristic
27C22×M16×C31C2211yescharacteristic
28C2×C31×#127C2211yescharacteristic, complemented
29C2×C31×#124C2211yescharacteristic, complemented
30C2×C31×#121C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C22×C22⋊C4×C31—21no—
34C31×#463—24no—
35C31×#459—24no—
36C31×#447—24no—
37C2×C31×C4⋊C8C2211yescharacteristic, complemented
38C2×C31×C4⋊C8C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#392—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic, complemented
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#390C2211yescharacteristic, complemented
54C31×#386—21no—
55C31×#386—21no—
56C31×#386—21no—
57C31×#386—21no—
58C31×#380C2211yescharacteristic
59C31×#379—21no—
60C4×C22⋊C4×C31C2211yescharacteristic
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, 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—22no—
74C22×D4×C31—22no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—22no—
81C22×D4×C31—41no—
82C22×D4×C31—41no—
83C22×D4×C31D414yescomplemented
84C22×D4×C31C2311yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C22×D4×C31C2311yescharacteristic
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31—21no—
91C23×C4×C31C2311yescharacteristic
92C31×AGL(1,ℤ/8)—232no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31D414yescomplemented
99C2×D8×C31—22no—
100C2×D8×C31—22no—
101C2×D8×C31—22no—
102C2×D8×C31—22no—
103C2×D8×C31—22no—
104C2×D8×C31—22no—
105C2×D8×C31—22no—
106C2×D8×C31—22no—
107C2×D8×C31—22no—
108C2×D8×C31—41no—
109C2×D8×C31—41no—
110C2×D8×C31D414yescomplemented
111C2×M16×C31—22no—
112C2×M16×C31—22no—
113C2×M16×C31—22no—
114C22×C8×C31C2311yescharacteristic
115C22×C8×C31C2311yescharacteristic
116C22×C8×C31C2311yescharacteristic
117C22×C8×C31C2311yescharacteristic
118C31×#127—22no—
119C31×#127—41no—
120C31×#124—22no—
121C31×#124—41no—
122C31×#121—22no—
123C31×#121—22no—
124C4×D4×C31—22no—
125C4×D4×C31—22no—
126C4×D4×C31—41no—
127C4×D4×C31—41no—
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C4⋊C4×C31C2311yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
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—44no—
144C2×C22⋊C4×C31D411yescharacteristic
145C2×C22⋊C4×C31D411yescharacteristic
146C2×C42×C31C2311yescharacteristic
147C2×C42×C31C2311yescharacteristic
148C31×C4⋊C8—22no—
149C31×C4⋊C8—22no—
150C31×#103—22no—
151C31×#103—41no—
152C31×#102—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—41no—
158C31×C22⋊C8—22no—
159C31×#95—21no—
160C31×#95—21no—
161C31×#95—21no—
162C31×#95D411yescharacteristic
163C31×#95D411yescharacteristic
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—24no—
168C24×C31—21no—
169C24×C31—42no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—42no—
173C24×C31—81no—
174C24×C31—81no—
175C24×C31C2×D411yescharacteristic
176#41×C31—28no—
177#41×C31—44no—
178#41×C31—44no—
179#41×C31—44no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31C2×D412yes—
186C2×D4×C31—28no—
187C2×D4×C31—24no—
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—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—44no—
208C2×D4×C31—44no—
209C2×D4×C31—44no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
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×C31C2×D412yes—
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—42no—
238C22×C4×C31—42no—
239C22×C4×C31—42no—
240C22×C4×C31—42no—
241C22×C4×C31—42no—
242C22×C4×C31—42no—
243C22×C4×C31—42no—
244C22×C4×C31—81no—
245C22×C4×C31—81no—
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D412yes—
251C22×C4×C31C2×D411yescharacteristic
252C22×C4×C31#4112yes—
253C22×C4×C31C2411yescharacteristic
254SD16×C31—28no—
255SD16×C31—28no—
256D8×C31—28no—
257D8×C31—28no—
258D8×C31—44no—
259D8×C31—44no—
260M16×C31—28no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
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×C31C2×D412yes—
272C2×C8×C31C2×D412yes—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C22⋊C4×C31—22no—
280C22⋊C4×C31—41no—
281C22⋊C4×C31—42no—
282C22⋊C4×C31—42no—
283C22⋊C4×C31—42no—
284C22⋊C4×C31—42no—
285C22⋊C4×C31—42no—
286C22⋊C4×C31—42no—
287C22⋊C4×C31—42no—
288C22⋊C4×C31—42no—
289C22⋊C4×C31—81no—
290C22⋊C4×C31—81no—
291C22⋊C4×C31—81no—
292C22⋊C4×C31—81no—
293C42×C31—21no—
294C42×C31—21no—
295C42×C31—21no—
296C42×C31—21no—
297#24366C3111yesmaximal, characteristic, direct product factor, Sylow
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—48no—
310C23×C31—48no—
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—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—84no—
335C23×C31—84no—
336C23×C31—84no—
337C23×C31—84no—
338C23×C31—84no—
339C23×C31#12112yes—
340C23×C31C22×D411yescharacteristic
341Q8×C31—22no—
342Q8×C31—22no—
343Q8×C31—41no—
344Q8×C31—41no—
345D4×C31—22no—
346D4×C31—22no—
347D4×C31—22no—
348D4×C31—22no—
349D4×C31—22no—
350D4×C31—22no—
351D4×C31—22no—
352D4×C31—48no—
353D4×C31—48no—
354D4×C31—41no—
355D4×C31—41no—
356D4×C31—41no—
357D4×C31—41no—
358D4×C31—41no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—41no—
362D4×C31—84no—
363D4×C31—84no—
364D4×C31—84no—
365D4×C31#12014yes—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—21no—
375C2×C4×C31—21no—
376C2×C4×C31—21no—
377C2×C4×C31—22no—
378C2×C4×C31—21no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—48no—
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—84no—
397C2×C4×C31—84no—
398C2×C4×C31#12112yes—
399C2×C4×C31AGL(1,ℤ/8)12yescomplemented
400C2×C4×C31C22×D411yescharacteristic
401C2×C4×C31C22×D411yescharacteristic
402C2×C4×C31C22×D411yescharacteristic
403C2×C4×C31C2×#4111yescharacteristic
404C2×C4×C31H(5,𝔽2)11yescharacteristic
405C2×C4×C31H(5,𝔽2)11yescharacteristic
406C8×C31—22no—
407C8×C31—22no—
408C8×C31—41no—
409C8×C31—41no—
410C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
411C2×#463C2×C3111yescharacteristic, complemented
412C2×#459C2×C3111yescharacteristic, complemented
413C2×#447C2×C3111yescharacteristic, complemented
414#2431C2×C3111yescharacteristic, complemented
415D4×C22⋊C4C2×C3111yescharacteristic, complemented
416#2055C2×C3111yescharacteristic, complemented
417#2054C2×C3111yescharacteristic, complemented
418#2012C2×C3111yescharacteristic, complemented
419#2011C2×C3111yescharacteristic, complemented
420#1895C2×C3111yescharacteristic, complemented
421#1879C2×C3111yescharacteristic, complemented
422#1877C2×C3111yescharacteristic, complemented
423#1851C2×C3111yescharacteristic, complemented
424#1788C2×C3111yescharacteristic, complemented
425C22×C31—22no—
426C22×C31—24no—
427C22×C31—22no—
428C22×C31—22no—
429C22×C31—42no—
430C22×C31—41no—
431C22×C31—41no—
432C22×C31—42no—
433C22×C31—41no—
434C22×C31—42no—
435C22×C31—42no—
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—42no—
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×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31C2×#12111yescharacteristic
462C22×C31D4211yescharacteristic
463C22×C31D4211yescharacteristic
464C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
465C22×C31#57511yescharacteristic
466C22×C31#57611yescharacteristic
467C22×C31#57611yescharacteristic
468C4×C31—22no—
469C4×C31—22no—
470C4×C31—42no—
471C4×C31—41no—
472C4×C31—41no—
473C4×C31—41no—
474C4×C31—81no—
475C4×C31—81no—
476C4×C31—81no—
477C4×C31C2×#12011yescharacteristic
478C4×C31#53411yescharacteristic
479C4×C31#54611yescharacteristic
480C4×C31#54611yescharacteristic
481C22×#41C22×C3111yescharacteristic
482C23×D4C22×C3111yescharacteristic
483C2×AGL(1,ℤ/8)—24no—
484C2×AGL(1,ℤ/8)—24no—
485C2×AGL(1,ℤ/8)—24no—
486C22×SD16C22×C3111yescharacteristic
487C22×SD16C22×C3111yescharacteristic
488C22×D8C22×C3111yescharacteristic
489C22×D8C22×C3111yescharacteristic
490C22×D8C22×C3111yescharacteristic
491C22×D8C22×C3111yescharacteristic
492C22×M16C22×C3111yescharacteristic
493C2×#127C22×C3111yescharacteristic, complemented
494C2×#124C22×C3111yescharacteristic, complemented
495C2×#121C22×C3111yescharacteristic
496C2×C4×D4C22×C3111yescharacteristic
497C2×C4×D4C22×C3111yescharacteristic
498C22×C22⋊C4—21no—
499#463—24no—
500#459—24no—
501#447—24no—
502C2×C4⋊C8C22×C3111yescharacteristic, complemented
503C2×C4⋊C8C22×C3111yescharacteristic, complemented
504C2×#103C22×C3111yescharacteristic, complemented
505C2×#103C22×C3111yescharacteristic, complemented
506C2×#102C22×C3111yescharacteristic
507C2×#102C22×C3111yescharacteristic
508C2×#102C22×C3111yescharacteristic, complemented
509C2×#102C22×C3111yescharacteristic, complemented
510C2×#102C22×C3111yescharacteristic, complemented
511C2×#102C22×C3111yescharacteristic, complemented
512C2×C22⋊C8C22×C3111yescharacteristic
513#392—21no—
514#392—21no—
515#391C22×C3111yescharacteristic, complemented
516#390C22×C3111yescharacteristic
517#390C22×C3111yescharacteristic
518#390C22×C3111yescharacteristic, complemented
519#386—21no—
520#386—21no—
521#386—21no—
522#386—21no—
523#380C22×C3111yescharacteristic
524#379—21no—
525C4×C22⋊C4C22×C3111yescharacteristic
526#340C22×C3111yescharacteristic, complemented
527#340C22×C3111yescharacteristic, complemented
528#336C22×C3111yescharacteristic, complemented
529#336C22×C3111yescharacteristic, complemented
530C2×C31—42no—
531C2×C31—44no—
532C2×C31—82no—
533C2×C31—82no—
534C2×C31—161no—
535C2×C31#241011yescharacteristic
536C2×C31#303611yescharacteristic
537C2×C31#304111yescharacteristic
538C2×C31#326411yescharacteristic
539C2×C31#326811yescharacteristic
540C2×C31#327311yescharacteristic
541C2×C31#327411yescharacteristic
542C25—21no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—41no—
548C2×#41—41no—
549C22×Q8C23×C3111yescharacteristic
550C22×D4—22no—
551C22×D4—22no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—41no—
559C22×D4—41no—
560C22×D4D4×C3114yescomplemented
561C22×D4C23×C3111yescharacteristic
562C22×D4C23×C3111yescharacteristic
563C22×D4C23×C3111yescharacteristic
564C22×D4C23×C3111yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4—21no—
568C23×C4C23×C3111yescharacteristic
569AGL(1,ℤ/8)—232no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16D4×C3114yescomplemented
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×D8—41no—
587C2×D8D4×C3114yescomplemented
588C2×M16—22no—
589C2×M16—22no—
590C2×M16—22no—
591C22×C8C23×C3111yescharacteristic
592C22×C8C23×C3111yescharacteristic
593C22×C8C23×C3111yescharacteristic
594C22×C8C23×C3111yescharacteristic
595#127—22no—
596#127—41no—
597#124—22no—
598#124—41no—
599#121—22no—
600#121—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C2×C4⋊C4C23×C3111yescharacteristic
606C2×C4⋊C4C23×C3111yescharacteristic
607C2×C4⋊C4C23×C3111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4D4×C3111yescharacteristic
622C2×C22⋊C4D4×C3111yescharacteristic
623C2×C42C23×C3111yescharacteristic
624C2×C42C23×C3111yescharacteristic
625C4⋊C8—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—41no—
629#102—22no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—41no—
635C22⋊C8—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95D4×C3111yescharacteristic
640#95D4×C3111yescharacteristic
641C31#2436611yescharacteristic, direct product factor, Sylow
642C24—21no—
643C24—21no—
644C24—21no—
645C24—24no—
646C24—21no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—81no—
652C24—81no—
653C24C2×D4×C3111yescharacteristic
654#41—28no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8C2×D4×C3112yes—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
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—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C3112yes—
703C2×D4C2×D4×C3112yes—
704C2×D4C2×D4×C3112yes—
705C2×D4C2×D4×C3112yes—
706C2×D4C2×D4×C3112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4C2×D4×C3111yescharacteristic
725C22×C4C2×D4×C3111yescharacteristic
726C22×C4C2×D4×C3111yescharacteristic
727C22×C4C2×D4×C3111yescharacteristic
728C22×C4C2×D4×C3112yes—
729C22×C4C2×D4×C3111yescharacteristic
730C22×C4#41×C3112yes—
731C22×C4C24×C3111yescharacteristic
732SD16—28no—
733SD16—28no—
734D8—28no—
735D8—28no—
736D8—44no—
737D8—44no—
738M16—28no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8C2×D4×C3112yes—
750C2×C8C2×D4×C3112yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C22⋊C4—81no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23C31×#12112yes—
817C23C22×D4×C3111yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4C31×#12014yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
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—84no—
874C2×C4—84no—
875C2×C4C31×#12112yes—
876C2×C4C31×AGL(1,ℤ/8)12yescomplemented
877C2×C4C22×D4×C3111yescharacteristic
878C2×C4C22×D4×C3111yescharacteristic
879C2×C4C22×D4×C3111yescharacteristic
880C2×C4C2×#41×C3111yescharacteristic
881C2×C4C31×H(5,𝔽2)11yescharacteristic
882C2×C4C31×H(5,𝔽2)11yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—24no—
889C22—22no—
890C22—22no—
891C22—42no—
892C22—41no—
893C22—41no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×C31×#12111yescharacteristic
924C22D42×C3111yescharacteristic
925C22D42×C3111yescharacteristic
926C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
927C22C31×#57511yescharacteristic
928C22C31×#57611yescharacteristic
929C22C31×#57611yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×C31×#12011yescharacteristic
940C4C31×#53411yescharacteristic
941C4C31×#54611yescharacteristic
942C4C31×#54611yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2C31×#241011yescharacteristic
949C2C31×#303611yescharacteristic
950C2C31×#304111yescharacteristic
951C2C31×#326411yescharacteristic
952C2C31×#326811yescharacteristic
953C2C31×#327311yescharacteristic
954C2C31×#327411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×AGL(1,ℤ/8)C2semidirect
2. C2×C31×#463C2semidirect
3. C2×C31×#459C2semidirect
4. C2×C31×#447C2semidirect
5. C31×#2431C2semidirect
6. D4×C22⋊C4×C31C2semidirect
7. C31×#2055C2semidirect
8. C31×#2054C2semidirect
9. C31×#2012C2semidirect
10. C31×#2011C2semidirect
11. C31×#1895C2semidirect
12. C31×#1879C2semidirect
13. C31×#1877C2semidirect
14. C31×#1851C2semidirect
15. C31×#1788C2semidirect
28. C2×C31×#127C22semidirect
29. C2×C31×#124C22semidirect
37. C2×C31×C4⋊C8C22semidirect
38. C2×C31×C4⋊C8C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#103C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
50. C31×#391C22semidirect
53. C31×#390C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
83. C22×D4×C31D4semidirect
98. C2×SD16×C31D4semidirect
110. C2×D8×C31D4semidirect
297. #24366C31direct (N × H)
399. C2×C4×C31AGL(1,ℤ/8)semidirect
410. C22×AGL(1,ℤ/8)C2×C31semidirect
411. C2×#463C2×C31semidirect
412. C2×#459C2×C31semidirect
413. C2×#447C2×C31semidirect
414. #2431C2×C31semidirect
415. D4×C22⋊C4C2×C31semidirect
416. #2055C2×C31semidirect
417. #2054C2×C31semidirect
418. #2012C2×C31semidirect
419. #2011C2×C31semidirect
420. #1895C2×C31semidirect
421. #1879C2×C31semidirect
422. #1877C2×C31semidirect
423. #1851C2×C31semidirect
424. #1788C2×C31semidirect
493. C2×#127C22×C31semidirect
494. C2×#124C22×C31semidirect
502. C2×C4⋊C8C22×C31semidirect
503. C2×C4⋊C8C22×C31semidirect
504. C2×#103C22×C31semidirect
505. C2×#103C22×C31semidirect
508. C2×#102C22×C31semidirect
509. C2×#102C22×C31semidirect
510. C2×#102C22×C31semidirect
511. C2×#102C22×C31semidirect
515. #391C22×C31semidirect
518. #390C22×C31semidirect
526. #340C22×C31semidirect
527. #340C22×C31semidirect
528. #336C22×C31semidirect
529. #336C22×C31semidirect
560. C22×D4D4×C31semidirect
575. C2×SD16D4×C31semidirect
587. C2×D8D4×C31semidirect
641. C31#24366direct (N × H)
876. C2×C4C31×AGL(1,ℤ/8)semidirect

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
C2×C31×#4632
C2×C31×#4592
C2×C31×#4472
C31×#24312
D4×C22⋊C4×C312
C31×#20552
C31×#20542
C31×#20122
C31×#20112
C31×#18952
C31×#18792
C31×#18772
C31×#18512
C31×#17882
#2436631