Finite Group Databasebeta

← C31×#25128 #21481887

Subgroups — C31×#25128 #21481887

Order 7936.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic, complemented
2C2×C31×#450C211yesmaximal, characteristic, complemented
3C2×C31×#435C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic, complemented
5C31×#2417C211yesmaximal, characteristic, complemented
6C31×#2408C211yesmaximal, characteristic
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1973C211yesmaximal, characteristic, complemented
12C31×#1936C211yesmaximal, characteristic, complemented
13C31×#1895C211yesmaximal, characteristic, complemented
14C31×#1892C211yesmaximal, characteristic, complemented
15C31×#1852C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic, complemented
20C23×C8×C31C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic, complemented
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C31×#468—24no—
29C31×#450—24no—
30C31×#435—24no—
31C2×C31×#107C2211yescharacteristic, complemented
32C2×C31×#107C2211yescharacteristic, complemented
33C2×C31×C4⋊C8C2211yescharacteristic, complemented
34C2×C31×#103C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#102—24no—
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic, complemented
45C2×C31×#97C2211yescharacteristic, complemented
46C31×#398—21no—
47C31×#396—21no—
48C31×#394—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic, complemented
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#389C2211yescharacteristic, complemented
54C31×#386—21no—
55C31×#380—21no—
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic, complemented
58C31×#379—21no—
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—21no—
69C22×D4×C31—22no—
70C22×D4×C31—21no—
71C22×D4×C31—22no—
72C22×D4×C31—41no—
73C22×D4×C31—41no—
74C22×D4×C31D411yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C23×C4×C31—21no—
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—41no—
85C2×SD16×C31—41no—
86C2×M16×C31—22no—
87C2×M16×C31—22no—
88C2×M16×C31—41no—
89C22×C8×C31—22no—
90C22×C8×C31—22no—
91C22×C8×C31—41no—
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—41no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—41no—
103C31×#121—41no—
104C31×#120—44no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—41no—
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×#107—41no—
134C31×C4⋊C8—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102D414yescomplemented
143C31×C22⋊C8—22no—
144C31×C22⋊C8D414yescomplemented
145C31×#97—22no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—42no—
154C24×C31—42no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—81no—
159C24×C31—81no—
160C24×C31C2×D411yescharacteristic
161C24×C31C2×D411yescharacteristic
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×D4×C31—28no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—22no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—44no—
183C2×D4×C31—44no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—44no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—81no—
193C2×D4×C31—81no—
194C2×D4×C31C2×D412yes—
195C2×D4×C31#4112yes—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—42no—
213C22×C4×C31—42no—
214C22×C4×C31—81no—
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D412yes—
220C22×C4×C31#4112yes—
221C22×C4×C31C2411yescharacteristic
222SD16×C31—44no—
223SD16×C31—44no—
224M16×C31—44no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—44no—
235C2×C8×C31C2×D412yes—
236C2×C8×C31C2×D412yes—
237C2×C8×C31C2×D412yes—
238C4⋊C4×C31—22no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—42no—
249C4⋊C4×C31—42no—
250C4⋊C4×C31—42no—
251C4⋊C4×C31—81no—
252C4⋊C4×C31C2×D412yes—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—42no—
261C22⋊C4×C31—42no—
262C22⋊C4×C31—81no—
263C22⋊C4×C31—81no—
264C22⋊C4×C31—81no—
265C42×C31—21no—
266C42×C31—21no—
267#25128C3111yesmaximal, characteristic, direct product factor, Sylow
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—48no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—84no—
295C23×C31—84no—
296C23×C31—84no—
297C23×C31—84no—
298C23×C31—84no—
299C23×C31—84no—
300C23×C31#12112yes—
301C23×C31AGL(1,ℤ/8)12yes—
302C23×C31#13712yes—
303C23×C31C22×D411yescharacteristic
304Q8×C31—41no—
305Q8×C31—41no—
306Q8×C31—41no—
307Q8×C31—41no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—22no—
311D4×C31—22no—
312D4×C31—48no—
313D4×C31—44no—
314D4×C31—41no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—84no—
319D4×C31—84no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—22no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—84no—
358C2×C4×C31#12112yes—
359C2×C4×C31C22×D411yescharacteristic
360C2×C4×C31C22×D411yescharacteristic
361C2×C4×C31C2×#4111yescharacteristic
362C2×C4×C31C2×#4111yescharacteristic
363C2×C4×C31H(5,𝔽2)11yescharacteristic
364C2×C4×C31H(5,𝔽2)11yescharacteristic
365C8×C31—22no—
366C8×C31—22no—
367C8×C31—22no—
368C8×C31—41no—
369C2×#468C2×C3111yescharacteristic, complemented
370C2×#450C2×C3111yescharacteristic, complemented
371C2×#435C2×C3111yescharacteristic, complemented
372C22×#102C2×C3111yescharacteristic, complemented
373#2417C2×C3111yescharacteristic, complemented
374#2408C2×C3111yescharacteristic
375#2067C2×C3111yescharacteristic, complemented
376#2055C2×C3111yescharacteristic, complemented
377#2033C2×C3111yescharacteristic, complemented
378#2000C2×C3111yescharacteristic, complemented
379#1973C2×C3111yescharacteristic, complemented
380#1936C2×C3111yescharacteristic, complemented
381#1895C2×C3111yescharacteristic, complemented
382#1892C2×C3111yescharacteristic, complemented
383#1852C2×C3111yescharacteristic, complemented
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—22no—
387C22×C31—22no—
388C22×C31—22no—
389C22×C31—22no—
390C22×C31—41no—
391C22×C31—42no—
392C22×C31—42no—
393C22×C31—41no—
394C22×C31—42no—
395C22×C31—41no—
396C22×C31—42no—
397C22×C31—41no—
398C22×C31—41no—
399C22×C31—42no—
400C22×C31—41no—
401C22×C31—42no—
402C22×C31—41no—
403C22×C31—816no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31#46814yescomplemented
413C22×C31C2×#12111yescharacteristic
414C22×C31D4211yescharacteristic
415C22×C31#54611yescharacteristic
416C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C31C2×#13711yescharacteristic
418C22×C31#57611yescharacteristic
419C22×C31#57711yescharacteristic
420C4×C31—22no—
421C4×C31—41no—
422C4×C31—42no—
423C4×C31—41no—
424C4×C31—41no—
425C4×C31—81no—
426C4×C31—81no—
427C4×C31—81no—
428C4×C31—81no—
429C4×C31—81no—
430C4×C31#52511yescharacteristic
431C4×C31#53811yescharacteristic
432C4×C31D4211yescharacteristic
433C4×C31#54611yescharacteristic
434C23×D4C22×C3111yescharacteristic
435C22×SD16C22×C3111yescharacteristic
436C22×SD16C22×C3111yescharacteristic
437C22×M16C22×C3111yescharacteristic, complemented
438C23×C8C22×C3111yescharacteristic
439C2×C22⋊Q8C22×C3111yescharacteristic
440C2×C22⋊Q8C22×C3111yescharacteristic, complemented
441C2×#121C22×C3111yescharacteristic
442C2×#121C22×C3111yescharacteristic
443C2×#120—21no—
444C2×C4×D4C22×C3111yescharacteristic
445C22×C4⋊C4C22×C3111yescharacteristic
446#468—24no—
447#450—24no—
448#435—24no—
449C2×#107C22×C3111yescharacteristic, complemented
450C2×#107C22×C3111yescharacteristic, complemented
451C2×C4⋊C8C22×C3111yescharacteristic, complemented
452C2×#103C22×C3111yescharacteristic, complemented
453C2×#103C22×C3111yescharacteristic, complemented
454C2×#102—24no—
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×#102C22×C3111yescharacteristic
459C2×#102C22×C3111yescharacteristic
460C2×#102C22×C3111yescharacteristic
461C2×C22⋊C8C22×C3111yescharacteristic
462C2×C22⋊C8C22×C3111yescharacteristic, complemented
463C2×#97C22×C3111yescharacteristic, complemented
464#398—21no—
465#396—21no—
466#394—21no—
467#392—21no—
468#391C22×C3111yescharacteristic, complemented
469#390C22×C3111yescharacteristic
470#390C22×C3111yescharacteristic
471#389C22×C3111yescharacteristic, complemented
472#386—21no—
473#380—21no—
474#380C22×C3111yescharacteristic
475#380C22×C3111yescharacteristic, complemented
476#379—21no—
477#340C22×C3111yescharacteristic, complemented
478#340C22×C3111yescharacteristic, complemented
479#340C22×C3111yescharacteristic, complemented
480#340C22×C3111yescharacteristic, complemented
481C2×C31—24no—
482C2×C31—81no—
483C2×C31—82no—
484C2×C31—82no—
485C2×C31#242411yescharacteristic
486C2×C31C2×#46811yescharacteristic
487C2×C31#306211yescharacteristic
488C2×C31#326411yescharacteristic
489C2×C31#326611yescharacteristic
490C2×C31#331011yescharacteristic
491C2×C31#331411yescharacteristic
492C25—21no—
493C22×Q8C23×C3111yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4D4×C3111yescharacteristic
504C22×D4C23×C3111yescharacteristic
505C22×D4C23×C3111yescharacteristic
506C23×C4—21no—
507C23×C4C23×C3111yescharacteristic
508C23×C4C23×C3111yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—41no—
521C22×C8C23×C3111yescharacteristic
522C22×C8C23×C3111yescharacteristic
523C22×C8C23×C3111yescharacteristic
524C22×C8C23×C3111yescharacteristic
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—22no—
531#121—41no—
532#121—41no—
533#120—44no—
534C4×D4—22no—
535C4×D4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4D4×C3111yescharacteristic
543C2×C4⋊C4C23×C3111yescharacteristic
544C2×C4⋊C4C23×C3111yescharacteristic
545C2×C4⋊C4C23×C3111yescharacteristic
546C2×C4⋊C4C23×C3111yescharacteristic
547C2×C4⋊C4C23×C3111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4D4×C3111yescharacteristic
559C2×C22⋊C4D4×C3111yescharacteristic
560C2×C42C23×C3111yescharacteristic
561#107—22no—
562#107—41no—
563C4⋊C8—22no—
564#103—22no—
565#103—41no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102D4×C3114yescomplemented
572C22⋊C8—22no—
573C22⋊C8D4×C3114yescomplemented
574#97—22no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580C31#2512811yescharacteristic, direct product factor, Sylow
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C3111yescharacteristic
591C24C2×D4×C3111yescharacteristic
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×D4—28no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C3112yes—
625C2×D4#41×C3112yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C2×D4×C3111yescharacteristic
646C22×C4C2×D4×C3111yescharacteristic
647C22×C4C2×D4×C3111yescharacteristic
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3112yes—
650C22×C4#41×C3112yes—
651C22×C4C24×C3111yescharacteristic
652SD16—44no—
653SD16—44no—
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8C2×D4×C3112yes—
666C2×C8C2×D4×C3112yes—
667C2×C8C2×D4×C3112yes—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4C2×D4×C3112yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23C31×#12112yes—
730C23C31×AGL(1,ℤ/8)12yes—
731C23C31×#13712yes—
732C23C22×D4×C3111yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4C31×#12112yes—
788C2×C4C22×D4×C3111yescharacteristic
789C2×C4C22×D4×C3111yescharacteristic
790C2×C4C2×#41×C3111yescharacteristic
791C2×C4C2×#41×C3111yescharacteristic
792C2×C4C31×H(5,𝔽2)11yescharacteristic
793C2×C4C31×H(5,𝔽2)11yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22C31×#46814yescomplemented
827C22C2×C31×#12111yescharacteristic
828C22D42×C3111yescharacteristic
829C22C31×#54611yescharacteristic
830C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
831C22C2×C31×#13711yescharacteristic
832C22C31×#57611yescharacteristic
833C22C31×#57711yescharacteristic
834C4—22no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—41no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4C31×#52511yescharacteristic
845C4C31×#53811yescharacteristic
846C4D42×C3111yescharacteristic
847C4C31×#54611yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2C31×#242411yescharacteristic
853C2C2×C31×#46811yescharacteristic
854C2C31×#306211yescharacteristic
855C2C31×#326411yescharacteristic
856C2C31×#326611yescharacteristic
857C2C31×#331011yescharacteristic
858C2C31×#331411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2408C2
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×#468C2semidirect
2. C2×C31×#450C2semidirect
3. C2×C31×#435C2semidirect
4. C22×C31×#102C2semidirect
5. C31×#2417C2semidirect
7. C31×#2067C2semidirect
8. C31×#2055C2semidirect
9. C31×#2033C2semidirect
10. C31×#2000C2semidirect
11. C31×#1973C2semidirect
12. C31×#1936C2semidirect
13. C31×#1895C2semidirect
14. C31×#1892C2semidirect
15. C31×#1852C2semidirect
19. C22×M16×C31C22semidirect
22. C2×C31×C22⋊Q8C22semidirect
31. C2×C31×#107C22semidirect
32. C2×C31×#107C22semidirect
33. C2×C31×C4⋊C8C22semidirect
34. C2×C31×#103C22semidirect
35. C2×C31×#103C22semidirect
44. C2×C31×C22⋊C8C22semidirect
45. C2×C31×#97C22semidirect
50. C31×#391C22semidirect
53. C31×#389C22semidirect
57. C31×#380C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
142. C31×#102D4semidirect
144. C31×C22⋊C8D4semidirect
267. #25128C31direct (N × H)
369. C2×#468C2×C31semidirect
370. C2×#450C2×C31semidirect
371. C2×#435C2×C31semidirect
372. C22×#102C2×C31semidirect
373. #2417C2×C31semidirect
375. #2067C2×C31semidirect
376. #2055C2×C31semidirect
377. #2033C2×C31semidirect
378. #2000C2×C31semidirect
379. #1973C2×C31semidirect
380. #1936C2×C31semidirect
381. #1895C2×C31semidirect
382. #1892C2×C31semidirect
383. #1852C2×C31semidirect
412. C22×C31#468semidirect
437. C22×M16C22×C31semidirect
440. C2×C22⋊Q8C22×C31semidirect
449. C2×#107C22×C31semidirect
450. C2×#107C22×C31semidirect
451. C2×C4⋊C8C22×C31semidirect
452. C2×#103C22×C31semidirect
453. C2×#103C22×C31semidirect
462. C2×C22⋊C8C22×C31semidirect
463. C2×#97C22×C31semidirect
468. #391C22×C31semidirect
471. #389C22×C31semidirect
475. #380C22×C31semidirect
477. #340C22×C31semidirect
478. #340C22×C31semidirect
479. #340C22×C31semidirect
480. #340C22×C31semidirect
571. #102D4×C31semidirect
573. C22⋊C8D4×C31semidirect
580. C31#25128direct (N × H)
826. C22C31×#468semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4502
C2×C31×#4352
C22×C31×#1022
C31×#24172
C31×#24082
C31×#20672
C31×#20552
C31×#20332
C31×#20002
C31×#19732
C31×#19362
C31×#18952
C31×#18922
C31×#18522
#2512831