Finite Group Databasebeta

← C31×#25088 #21481847

Subgroups — C31×#25088 #21481847

Order 7936.

1310 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#465C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic
4C22×C31×#102C211yesmaximal, characteristic, complemented
5C31×#2435C211yesmaximal, characteristic, complemented
6C31×#2361C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2042C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1926C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1872C211yesmaximal, characteristic, complemented
15C31×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic, complemented
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C23×C8×C31C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31C2211yescharacteristic, complemented
27C22×C4⋊C4×C31C2211yescharacteristic
28C31×#465—24no—
29C31×#463—24no—
30C31×#447—24no—
31C2×C31×#106C2211yescharacteristic, complemented
32C2×C31×C4⋊C8C2211yescharacteristic, complemented
33C2×C31×C4⋊C8C2211yescharacteristic, complemented
34C2×C31×#103C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
37C2×C31×#102—24no—
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×C22⋊C8C2211yescharacteristic
46C31×#394—21no—
47C31×#394—21no—
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic, complemented
51C31×#389C2211yescharacteristic, complemented
52C31×#388—21no—
53C31×#386—21no—
54C31×#385—21no—
55C31×#379—21no—
56C31×#379—21no—
57C4×C4⋊C4×C31C2211yescharacteristic, complemented
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—22no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C23×C4×C31—21no—
77C23×C4×C31—21no—
78C23×C4×C31C2311yescharacteristic
79C2×SD16×C31—22no—
80C2×SD16×C31—22no—
81C2×SD16×C31—41no—
82C2×D8×C31—22no—
83C2×D8×C31—22no—
84C2×D8×C31—22no—
85C2×D8×C31—22no—
86C2×D8×C31—41no—
87C2×D8×C31—41no—
88C22×C8×C31—22no—
89C22×C8×C31—22no—
90C22×C8×C31—41no—
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C31×#124—22no—
96C31×#124—22no—
97C31×#124—41no—
98C31×#124—41no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8—22no—
101C31×#121—22no—
102C31×#121D414yes—
103C4×D4×C31—22no—
104C4×D4×C31—41no—
105C4×D4×C31—44no—
106C2×C4⋊C4×C31—22no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—41no—
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C42×C31—21no—
131C2×C42×C31C2311yescharacteristic
132C2×C42×C31C2311yescharacteristic
133C31×#106—22no—
134C31×C4⋊C8—22no—
135C31×C4⋊C8—41no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#103—41no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102D414yescomplemented
146C31×C22⋊C8—22no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95D411yescharacteristic
150C31×#95D411yescharacteristic
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—42no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—81no—
160C24×C31—81no—
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—24no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
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—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—44no—
186C2×D4×C31—44no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—44no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—42no—
193C2×D4×C31C2×D412yes—
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—42no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31—42no—
209C22×C4×C31—81no—
210C22×C4×C31—81no—
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D412yes—
217C22×C4×C31#4112yes—
218C22×C4×C31C2411yescharacteristic
219SD16×C31—44no—
220D8×C31—44no—
221D8×C31—44no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
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—44no—
234C2×C8×C31C2×D412yes—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—42no—
242C4⋊C4×C31—42no—
243C4⋊C4×C31—42no—
244C4⋊C4×C31C2×D412yes—
245C4⋊C4×C31C2×D412yes—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—24no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—81no—
257C22⋊C4×C31—81no—
258C22⋊C4×C31—81no—
259C22⋊C4×C31—81no—
260C22⋊C4×C31—81no—
261C42×C31—21no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—42no—
266#25088C3111yesmaximal, characteristic, direct product factor, Sylow
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—48no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
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—84no—
294C23×C31—84no—
295C23×C31—84no—
296C23×C31—84no—
297C23×C31—84no—
298C23×C31—84no—
299C23×C31#12112yes—
300C23×C31#13512yes—
301C23×C31AGL(1,ℤ/8)12yes—
302C23×C31C22×D411yescharacteristic
303Q8×C31—41no—
304Q8×C31—41no—
305Q8×C31—41no—
306Q8×C31—41no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—22no—
311D4×C31—22no—
312D4×C31—22no—
313D4×C31—48no—
314D4×C31—48no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—41no—
319D4×C31—41no—
320D4×C31—41no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
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—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
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—84no—
355C2×C4×C31—84no—
356C2×C4×C31#12112yes—
357C2×C4×C31C22×D411yescharacteristic
358C2×C4×C31C22×D411yescharacteristic
359C2×C4×C31C2×#4111yescharacteristic
360C2×C4×C31C2×#4111yescharacteristic
361C2×C4×C31H(5,𝔽2)11yescharacteristic
362C2×C4×C31H(5,𝔽2)11yescharacteristic
363C8×C31—22no—
364C8×C31—41no—
365C8×C31—41no—
366C8×C31—41no—
367C2×#465C2×C3111yescharacteristic, complemented
368C2×#463C2×C3111yescharacteristic, complemented
369C2×#447C2×C3111yescharacteristic
370C22×#102C2×C3111yescharacteristic, complemented
371#2435C2×C3111yescharacteristic, complemented
372#2361C2×C3111yescharacteristic, complemented
373#2065C2×C3111yescharacteristic, complemented
374#2054C2×C3111yescharacteristic, complemented
375#2042C2×C3111yescharacteristic, complemented
376#2012C2×C3111yescharacteristic, complemented
377#1983C2×C3111yescharacteristic, complemented
378#1926C2×C3111yescharacteristic, complemented
379#1879C2×C3111yescharacteristic, complemented
380#1872C2×C3111yescharacteristic, complemented
381#1850C2×C3111yescharacteristic, complemented
382C22×C31—22no—
383C22×C31—22no—
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—22no—
387C22×C31—22no—
388C22×C31—42no—
389C22×C31—42no—
390C22×C31—42no—
391C22×C31—42no—
392C22×C31—42no—
393C22×C31—42no—
394C22×C31—42no—
395C22×C31—42no—
396C22×C31—42no—
397C22×C31—816no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31#46314yescomplemented
411C22×C31C2×#12111yescharacteristic
412C22×C31D4211yescharacteristic
413C22×C31#54611yescharacteristic
414C22×C31C2×#13511yescharacteristic
415C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C31#57611yescharacteristic
417C22×C31#57711yescharacteristic
418C4×C31—22no—
419C4×C31—41no—
420C4×C31—42no—
421C4×C31—41no—
422C4×C31—42no—
423C4×C31—41no—
424C4×C31—41no—
425C4×C31—81no—
426C4×C31—81no—
427C4×C31—81no—
428C4×C31#52511yescharacteristic
429C4×C31#53811yescharacteristic
430C4×C31D4211yescharacteristic
431C4×C31#54611yescharacteristic
432C23×D4C22×C3111yescharacteristic
433C22×SD16C22×C3111yescharacteristic, complemented
434C22×D8C22×C3111yescharacteristic
435C22×D8C22×C3111yescharacteristic
436C23×C8C22×C3111yescharacteristic
437C2×#124C22×C3111yescharacteristic
438C2×#124C22×C3111yescharacteristic
439C2×C22⋊Q8C22×C3111yescharacteristic
440C2×#121C22×C3111yescharacteristic
441C2×C4×D4—21no—
442C2×C4×D4C22×C3111yescharacteristic, complemented
443C22×C4⋊C4C22×C3111yescharacteristic
444#465—24no—
445#463—24no—
446#447—24no—
447C2×#106C22×C3111yescharacteristic, complemented
448C2×C4⋊C8C22×C3111yescharacteristic, complemented
449C2×C4⋊C8C22×C3111yescharacteristic, complemented
450C2×#103C22×C3111yescharacteristic, complemented
451C2×#103C22×C3111yescharacteristic, complemented
452C2×#103C22×C3111yescharacteristic, complemented
453C2×#102—24no—
454C2×#102C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×#102C22×C3111yescharacteristic
459C2×#102C22×C3111yescharacteristic
460C2×#102C22×C3111yescharacteristic, complemented
461C2×C22⋊C8C22×C3111yescharacteristic
462#394—21no—
463#394—21no—
464#390C22×C3111yescharacteristic
465#390C22×C3111yescharacteristic
466#390C22×C3111yescharacteristic, complemented
467#389C22×C3111yescharacteristic, complemented
468#388—21no—
469#386—21no—
470#385—21no—
471#379—21no—
472#379—21no—
473C4×C4⋊C4C22×C3111yescharacteristic, complemented
474C4×C22⋊C4C22×C3111yescharacteristic
475#340C22×C3111yescharacteristic, complemented
476#340C22×C3111yescharacteristic, complemented
477#336C22×C3111yescharacteristic, complemented
478#336C22×C3111yescharacteristic, complemented
479C2×C31—24no—
480C2×C31—82no—
481C2×C31—82no—
482C2×C31—82no—
483C2×C31#242411yescharacteristic
484C2×C31C2×#46311yescharacteristic
485C2×C31#304511yescharacteristic
486C2×C31#326411yescharacteristic
487C2×C31#328211yescharacteristic
488C2×C31#329711yescharacteristic
489C2×C31#330611yescharacteristic
490C25—21no—
491C22×Q8C23×C3111yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C3111yescharacteristic
501C22×D4C23×C3111yescharacteristic
502C22×D4C23×C3111yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C3111yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C22×C8—22no—
516C22×C8—22no—
517C22×C8—41no—
518C22×C8C23×C3111yescharacteristic
519C22×C8C23×C3111yescharacteristic
520C22×C8C23×C3111yescharacteristic
521C22×C8C23×C3111yescharacteristic
522#124—22no—
523#124—22no—
524#124—41no—
525#124—41no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528#121—22no—
529#121D4×C3114yes—
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—44no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C4⋊C4C23×C3111yescharacteristic
541C2×C4⋊C4C23×C3111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
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⋊C4D4×C3111yescharacteristic
556C2×C22⋊C4D4×C3111yescharacteristic
557C2×C42—21no—
558C2×C42C23×C3111yescharacteristic
559C2×C42C23×C3111yescharacteristic
560#106—22no—
561C4⋊C8—22no—
562C4⋊C8—41no—
563#103—22no—
564#103—22no—
565#103—41no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102D4×C3114yescomplemented
573C22⋊C8—22no—
574#95—21no—
575#95—21no—
576#95D4×C3111yescharacteristic
577#95D4×C3111yescharacteristic
578C31#2508811yescharacteristic, direct product factor, Sylow
579C24—21no—
580C24—21no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C3111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×D4—28no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
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—21no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×D4×C3112yes—
622C2×D4C2×D4×C3112yes—
623C2×D4#41×C3112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4C2×D4×C3111yescharacteristic
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3112yes—
645C22×C4#41×C3112yes—
646C22×C4C24×C3111yescharacteristic
647SD16—44no—
648D8—44no—
649D8—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—44no—
662C2×C8C2×D4×C3112yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C3112yes—
673C4⋊C4C2×D4×C3112yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—24no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—81no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—48no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23C31×#12112yes—
727C23C31×#13512yes—
728C23C31×AGL(1,ℤ/8)12yes—
729C23C22×D4×C3111yescharacteristic
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—48no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
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—84no—
782C2×C4—84no—
783C2×C4C31×#12112yes—
784C2×C4C22×D4×C3111yescharacteristic
785C2×C4C22×D4×C3111yescharacteristic
786C2×C4C2×#41×C3111yescharacteristic
787C2×C4C2×#41×C3111yescharacteristic
788C2×C4C31×H(5,𝔽2)11yescharacteristic
789C2×C4C31×H(5,𝔽2)11yescharacteristic
790C8—22no—
791C8—41no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—816no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22C31×#46314yescomplemented
823C22C2×C31×#12111yescharacteristic
824C22D42×C3111yescharacteristic
825C22C31×#54611yescharacteristic
826C22C2×C31×#13511yescharacteristic
827C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
828C22C31×#57611yescharacteristic
829C22C31×#57711yescharacteristic
830C4—22no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C31×#52511yescharacteristic
841C4C31×#53811yescharacteristic
842C4D42×C3111yescharacteristic
843C4C31×#54611yescharacteristic
844C2—24no—
845C2—82no—
846C2—82no—
847C2—82no—
848C2C31×#242411yescharacteristic
849C2C2×C31×#46311yescharacteristic
850C2C31×#304511yescharacteristic
851C2C31×#326411yescharacteristic
852C2C31×#328211yescharacteristic
853C2C31×#329711yescharacteristic
854C2C31×#330611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
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. C2×C31×#465C2semidirect
2. C2×C31×#463C2semidirect
4. C22×C31×#102C2semidirect
5. C31×#2435C2semidirect
6. C31×#2361C2semidirect
7. C31×#2065C2semidirect
8. C31×#2054C2semidirect
9. C31×#2042C2semidirect
10. C31×#2012C2semidirect
11. C31×#1983C2semidirect
12. C31×#1926C2semidirect
13. C31×#1879C2semidirect
14. C31×#1872C2semidirect
15. C31×#1850C2semidirect
17. C22×SD16×C31C22semidirect
26. C2×C4×D4×C31C22semidirect
31. C2×C31×#106C22semidirect
32. C2×C31×C4⋊C8C22semidirect
33. C2×C31×C4⋊C8C22semidirect
34. C2×C31×#103C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
44. C2×C31×#102C22semidirect
50. C31×#390C22semidirect
51. C31×#389C22semidirect
57. C4×C4⋊C4×C31C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
145. C31×#102D4semidirect
266. #25088C31direct (N × H)
367. C2×#465C2×C31semidirect
368. C2×#463C2×C31semidirect
370. C22×#102C2×C31semidirect
371. #2435C2×C31semidirect
372. #2361C2×C31semidirect
373. #2065C2×C31semidirect
374. #2054C2×C31semidirect
375. #2042C2×C31semidirect
376. #2012C2×C31semidirect
377. #1983C2×C31semidirect
378. #1926C2×C31semidirect
379. #1879C2×C31semidirect
380. #1872C2×C31semidirect
381. #1850C2×C31semidirect
410. C22×C31#463semidirect
433. C22×SD16C22×C31semidirect
442. C2×C4×D4C22×C31semidirect
447. C2×#106C22×C31semidirect
448. C2×C4⋊C8C22×C31semidirect
449. C2×C4⋊C8C22×C31semidirect
450. C2×#103C22×C31semidirect
451. C2×#103C22×C31semidirect
452. C2×#103C22×C31semidirect
460. C2×#102C22×C31semidirect
466. #390C22×C31semidirect
467. #389C22×C31semidirect
473. C4×C4⋊C4C22×C31semidirect
475. #340C22×C31semidirect
476. #340C22×C31semidirect
477. #336C22×C31semidirect
478. #336C22×C31semidirect
572. #102D4×C31semidirect
578. C31#25088direct (N × H)
822. C22C31×#463semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4652
C2×C31×#4632
C2×C31×#4472
C22×C31×#1022
C31×#24352
C31×#23612
C31×#20652
C31×#20542
C31×#20422
C31×#20122
C31×#19832
C31×#19262
C31×#18792
C31×#18722
C31×#18502
#2508831