Finite Group Databasebeta

← C31×#24441 #21481200

Subgroups — C31×#24441 #21481200

Order 7936.

1522 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#548C211yesmaximal, characteristic, complemented
2C2×C31×#468C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic, complemented
4C2×C31×#448C211yesmaximal, characteristic, complemented
5C2×C31×#417C211yesmaximal, characteristic, complemented
6C31×#2416C211yesmaximal, characteristic, complemented
7C31×#2042C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2012C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1872C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic, complemented
14C31×#1863C211yesmaximal, characteristic, complemented
15C31×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C31×#548—24no—
23C31×#548—24no—
24C2×C31×#124—21no—
25C2×C31×#124C2211yescharacteristic
26C2×C31×C22⋊Q8—21no—
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×#121—21no—
29C2×C31×#121—21no—
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C31×#121C2211yescharacteristic
33C2×C4×Q8×C31C2211yescharacteristic
34C2×C4×D4×C31—21no—
35C2×C4×D4×C31C2211yescharacteristic
36C22×C4⋊C4×C31C2211yescharacteristic
37C31×#468—24no—
38C31×#449—24no—
39C31×#448—24no—
40C2×C31×#107C2211yescharacteristic
41C31×#417—24no—
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#103C2211yescharacteristic
45C2×C31×#103C2211yescharacteristic
46C2×C31×#103C2211yescharacteristic
47C2×C31×#103C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×#102C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C31×#396—21no—
56C31×#394—21no—
57C31×#390C2211yescharacteristic
58C31×#389C2211yescharacteristic
59C31×#386—21no—
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C2×#41×C31D414yescomplemented
71C22×Q8×C31—22no—
72C22×Q8×C31—22no—
73C22×Q8×C31—21no—
74C22×Q8×C31—22no—
75C22×Q8×C31—22no—
76C22×Q8×C31—41no—
77C22×Q8×C31—41no—
78C22×Q8×C31C2311yescharacteristic
79C22×Q8×C31C2311yescharacteristic
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31D411yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C2×SD16×C31—22no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—41no—
98C2×D8×C31—22no—
99C2×D8×C31—41no—
100C2×D8×C31—41no—
101C2×M16×C31—22no—
102C2×M16×C31—22no—
103C2×M16×C31—41no—
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C22×C8×C31C2311yescharacteristic
108C31×#124—28no—
109C31×#124—22no—
110C31×#124—22no—
111C31×C22⋊Q8—28no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8D414yescomplemented
114C31×#121—28no—
115C31×#121—22no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—41no—
121C31×#121—44no—
122C4×Q8×C31—22no—
123C4×Q8×C31—22no—
124C4×D4×C31—28no—
125C4×D4×C31—22no—
126C4×D4×C31—22no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—22no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31—41no—
133C2×C4⋊C4×C31D411yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31D411yescharacteristic
148C2×C22⋊C4×C31D411yescharacteristic
149C2×C42×C31—21no—
150C2×C42×C31C2311yescharacteristic
151C31×#107—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#103—22no—
155C31×#103—22no—
156C31×#103—41no—
157C31×#103D414yescomplemented
158C31×#102—22no—
159C31×#102—22no—
160C31×#102—22no—
161C31×#102—22no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8—22no—
164C31×C22⋊C8—41no—
165C31×#95—21no—
166C31×#95—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31C2×D411yescharacteristic
170C24×C31C2×D411yescharacteristic
171#41×C31—28no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175C2×Q8×C31—24no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—42no—
185C2×Q8×C31—42no—
186C2×Q8×C31—44no—
187C2×Q8×C31—44no—
188C2×Q8×C31—44no—
189C2×Q8×C31—44no—
190C2×Q8×C31C2×D412yes—
191C2×Q8×C31C2×D412yes—
192C2×Q8×C31C2×D412yes—
193C2×Q8×C31#4112yes—
194C2×D4×C31—24no—
195C2×D4×C31—22no—
196C2×D4×C31—24no—
197C2×D4×C31—22no—
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—21no—
208C2×D4×C31—21no—
209C2×D4×C31—41no—
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—81no—
220C2×D4×C31C2×D412yes—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—24no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—24no—
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—42no—
240C22×C4×C31—42no—
241C22×C4×C31—42no—
242C22×C4×C31—42no—
243C22×C4×C31—42no—
244C22×C4×C31—42no—
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×D412yes—
252C22×C4×C31C2411yescharacteristic
253SD16×C31—44no—
254SD16×C31—44no—
255D8×C31—44no—
256M16×C31—44no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
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×C31C2×D412yes—
269C4⋊C4×C31—24no—
270C4⋊C4×C31—24no—
271C4⋊C4×C31—22no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—42no—
279C4⋊C4×C31—42no—
280C4⋊C4×C31C2×D412yes—
281C4⋊C4×C31C2×D412yes—
282C22⋊C4×C31—24no—
283C22⋊C4×C31—24no—
284C22⋊C4×C31—24no—
285C22⋊C4×C31—24no—
286C22⋊C4×C31—22no—
287C22⋊C4×C31—22no—
288C22⋊C4×C31—42no—
289C22⋊C4×C31—42no—
290C22⋊C4×C31—42no—
291C22⋊C4×C31—42no—
292C22⋊C4×C31—81no—
293C42×C31—24no—
294C42×C31—21no—
295C42×C31—21no—
296#24441C3111yesmaximal, characteristic, direct product factor, Sylow
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—22no—
310C23×C31—41no—
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#12012yes—
324C23×C31AGL(1,ℤ/8)12yes—
325C23×C31C22×D411yescharacteristic
326Q8×C31—22no—
327Q8×C31—22no—
328Q8×C31—22no—
329Q8×C31—22no—
330Q8×C31—22no—
331Q8×C31—48no—
332Q8×C31—41no—
333Q8×C31—41no—
334Q8×C31#12114yescomplemented
335D4×C31—22no—
336D4×C31—22no—
337D4×C31—48no—
338D4×C31—44no—
339D4×C31—48no—
340D4×C31—41no—
341D4×C31—41no—
342D4×C31—41no—
343D4×C31—41no—
344D4×C31—41no—
345D4×C31—41no—
346D4×C31—84no—
347D4×C31—84no—
348C2×C4×C31—22no—
349C2×C4×C31—21no—
350C2×C4×C31—22no—
351C2×C4×C31—21no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—21no—
358C2×C4×C31—21no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—22no—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—48no—
370C2×C4×C31—48no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
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—84no—
388C2×C4×C31#12012yes—
389C2×C4×C31C22×D411yescharacteristic
390C2×C4×C31C22×D411yescharacteristic
391C2×C4×C31C22×D411yescharacteristic
392C2×C4×C31C2×#4111yescharacteristic
393C2×C4×C31H(5,𝔽2)11yescharacteristic
394C2×C4×C31H(5,𝔽2)11yescharacteristic
395C8×C31—22no—
396C8×C31—41no—
397C8×C31—41no—
398C8×C31—41no—
399C2×#548C2×C3111yescharacteristic, complemented
400C2×#468C2×C3111yescharacteristic, complemented
401C2×#449C2×C3111yescharacteristic, complemented
402C2×#448C2×C3111yescharacteristic, complemented
403C2×#417C2×C3111yescharacteristic, complemented
404#2416C2×C3111yescharacteristic, complemented
405#2042C2×C3111yescharacteristic, complemented
406#2033C2×C3111yescharacteristic, complemented
407#2012C2×C3111yescharacteristic, complemented
408#1999C2×C3111yescharacteristic, complemented
409#1880C2×C3111yescharacteristic, complemented
410#1872C2×C3111yescharacteristic, complemented
411#1870C2×C3111yescharacteristic, complemented
412#1863C2×C3111yescharacteristic, complemented
413#1787C2×C3111yescharacteristic, complemented
414C22×C31—22no—
415C22×C31—22no—
416C22×C31—22no—
417C22×C31—22no—
418C22×C31—22no—
419C22×C31—22no—
420C22×C31—41no—
421C22×C31—41no—
422C22×C31—41no—
423C22×C31—41no—
424C22×C31—41no—
425C22×C31—41no—
426C22×C31—41no—
427C22×C31—41no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31—81no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31—81no—
439C22×C31—81no—
440C22×C31—81no—
441C22×C31—81no—
442C22×C31C2×#12011yescharacteristic
443C22×C31D4211yescharacteristic
444C22×C31#54611yescharacteristic
445C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C31#57511yescharacteristic
447C22×C31#57711yescharacteristic
448C22×C31#57811yescharacteristic
449C4×C31—22no—
450C4×C31—24no—
451C4×C31—41no—
452C4×C31—42no—
453C4×C31—41no—
454C4×C31—42no—
455C4×C31—42no—
456C4×C31—41no—
457C4×C31—81no—
458C4×C31—81no—
459C4×C31C2×#12111yescharacteristic
460C4×C31#53411yescharacteristic
461C4×C31D4211yescharacteristic
462C4×C31#54611yescharacteristic
463C22×#41C22×C3111yescharacteristic
464C23×Q8C22×C3111yescharacteristic
465C22×SD16C22×C3111yescharacteristic
466C22×SD16C22×C3111yescharacteristic
467C22×D8C22×C3111yescharacteristic
468C22×M16C22×C3111yescharacteristic
469#548—24no—
470#548—24no—
471C2×#124—21no—
472C2×#124C22×C3111yescharacteristic
473C2×C22⋊Q8—21no—
474C2×C22⋊Q8C22×C3111yescharacteristic
475C2×#121—21no—
476C2×#121—21no—
477C2×#121C22×C3111yescharacteristic
478C2×#121C22×C3111yescharacteristic
479C2×#121C22×C3111yescharacteristic
480C2×C4×Q8C22×C3111yescharacteristic
481C2×C4×D4—21no—
482C2×C4×D4C22×C3111yescharacteristic
483C22×C4⋊C4C22×C3111yescharacteristic
484#468—24no—
485#449—24no—
486#448—24no—
487C2×#107C22×C3111yescharacteristic
488#417—24no—
489C2×#103C22×C3111yescharacteristic
490C2×#103C22×C3111yescharacteristic
491C2×#103C22×C3111yescharacteristic
492C2×#103C22×C3111yescharacteristic
493C2×#103C22×C3111yescharacteristic
494C2×#103C22×C3111yescharacteristic
495C2×#102C22×C3111yescharacteristic
496C2×#102C22×C3111yescharacteristic
497C2×#102C22×C3111yescharacteristic
498C2×#102C22×C3111yescharacteristic
499C2×C22⋊C8C22×C3111yescharacteristic
500C2×C22⋊C8C22×C3111yescharacteristic
501C2×C22⋊C8C22×C3111yescharacteristic
502#396—21no—
503#394—21no—
504#390C22×C3111yescharacteristic
505#389C22×C3111yescharacteristic
506#386—21no—
507#380C22×C3111yescharacteristic
508#340C22×C3111yescharacteristic
509#340C22×C3111yescharacteristic
510#336C22×C3111yescharacteristic
511#336C22×C3111yescharacteristic
512C2×C31—42no—
513C2×C31—42no—
514C2×C31—82no—
515C2×C31—161no—
516C2×C31#241011yescharacteristic
517C2×C31#300611yescharacteristic
518C2×C31#301311yescharacteristic
519C2×C31#326511yescharacteristic
520C2×C31#327711yescharacteristic
521C2×C31#330811yescharacteristic
522C2×C31#332611yescharacteristic
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—41no—
527C2×#41—41no—
528C2×#41D4×C3114yescomplemented
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
536C22×Q8C23×C3111yescharacteristic
537C22×Q8C23×C3111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4D4×C3111yescharacteristic
543C22×D4C23×C3111yescharacteristic
544C22×D4C23×C3111yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C3111yescharacteristic
549C23×C4C23×C3111yescharacteristic
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—41no—
556C2×D8—22no—
557C2×D8—41no—
558C2×D8—41no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—41no—
562C22×C8C23×C3111yescharacteristic
563C22×C8C23×C3111yescharacteristic
564C22×C8C23×C3111yescharacteristic
565C22×C8C23×C3111yescharacteristic
566#124—28no—
567#124—22no—
568#124—22no—
569C22⋊Q8—28no—
570C22⋊Q8—22no—
571C22⋊Q8D4×C3114yescomplemented
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—41no—
579#121—44no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×D4—28no—
583C4×D4—22no—
584C4×D4—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4D4×C3111yescharacteristic
592C2×C4⋊C4C23×C3111yescharacteristic
593C2×C4⋊C4C23×C3111yescharacteristic
594C2×C4⋊C4C23×C3111yescharacteristic
595C2×C4⋊C4C23×C3111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C3111yescharacteristic
606C2×C22⋊C4D4×C3111yescharacteristic
607C2×C42—21no—
608C2×C42C23×C3111yescharacteristic
609#107—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—41no—
615#103D4×C3114yescomplemented
616#102—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620C22⋊C8—22no—
621C22⋊C8—22no—
622C22⋊C8—41no—
623#95—21no—
624#95—21no—
625C31#2444111yescharacteristic, direct product factor, Sylow
626C24—21no—
627C24—21no—
628C24C2×D4×C3111yescharacteristic
629C24C2×D4×C3111yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—24no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—42no—
644C2×Q8—42no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8C2×D4×C3112yes—
650C2×Q8C2×D4×C3112yes—
651C2×Q8C2×D4×C3112yes—
652C2×Q8#41×C3112yes—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—81no—
679C2×D4C2×D4×C3112yes—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—81no—
705C22×C4C2×D4×C3111yescharacteristic
706C22×C4C2×D4×C3111yescharacteristic
707C22×C4C2×D4×C3111yescharacteristic
708C22×C4C2×D4×C3111yescharacteristic
709C22×C4C2×D4×C3112yes—
710C22×C4C2×D4×C3112yes—
711C22×C4C24×C3111yescharacteristic
712SD16—44no—
713SD16—44no—
714D8—44no—
715M16—44no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8C2×D4×C3112yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C3112yes—
740C4⋊C4C2×D4×C3112yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C42—24no—
753C42—21no—
754C42—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—22no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23C31×#12012yes—
782C23C31×AGL(1,ℤ/8)12yes—
783C23C22×D4×C3111yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—22no—
789Q8—48no—
790Q8—41no—
791Q8—41no—
792Q8C31×#12114yescomplemented
793D4—22no—
794D4—22no—
795D4—48no—
796D4—44no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—84no—
805D4—84no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—48no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—84no—
846C2×C4C31×#12012yes—
847C2×C4C22×D4×C3111yescharacteristic
848C2×C4C22×D4×C3111yescharacteristic
849C2×C4C22×D4×C3111yescharacteristic
850C2×C4C2×#41×C3111yescharacteristic
851C2×C4C31×H(5,𝔽2)11yescharacteristic
852C2×C4C31×H(5,𝔽2)11yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×C31×#12011yescharacteristic
886C22D42×C3111yescharacteristic
887C22C31×#54611yescharacteristic
888C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
889C22C31×#57511yescharacteristic
890C22C31×#57711yescharacteristic
891C22C31×#57811yescharacteristic
892C4—22no—
893C4—24no—
894C4—41no—
895C4—42no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—41no—
900C4—81no—
901C4—81no—
902C4C2×C31×#12111yescharacteristic
903C4C31×#53411yescharacteristic
904C4D42×C3111yescharacteristic
905C4C31×#54611yescharacteristic
906C2—42no—
907C2—42no—
908C2—82no—
909C2—161no—
910C2C31×#241011yescharacteristic
911C2C31×#300611yescharacteristic
912C2C31×#301311yescharacteristic
913C2C31×#326511yescharacteristic
914C2C31×#327711yescharacteristic
915C2C31×#330811yescharacteristic
916C2C31×#332611yescharacteristic
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×#548C2semidirect
2. C2×C31×#468C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#448C2semidirect
5. C2×C31×#417C2semidirect
6. C31×#2416C2semidirect
7. C31×#2042C2semidirect
8. C31×#2033C2semidirect
9. C31×#2012C2semidirect
10. C31×#1999C2semidirect
11. C31×#1880C2semidirect
12. C31×#1872C2semidirect
13. C31×#1870C2semidirect
14. C31×#1863C2semidirect
15. C31×#1787C2semidirect
70. C2×#41×C31D4semidirect
113. C31×C22⋊Q8D4semidirect
157. C31×#103D4semidirect
296. #24441C31direct (N × H)
334. Q8×C31#121semidirect
399. C2×#548C2×C31semidirect
400. C2×#468C2×C31semidirect
401. C2×#449C2×C31semidirect
402. C2×#448C2×C31semidirect
403. C2×#417C2×C31semidirect
404. #2416C2×C31semidirect
405. #2042C2×C31semidirect
406. #2033C2×C31semidirect
407. #2012C2×C31semidirect
408. #1999C2×C31semidirect
409. #1880C2×C31semidirect
410. #1872C2×C31semidirect
411. #1870C2×C31semidirect
412. #1863C2×C31semidirect
413. #1787C2×C31semidirect
528. C2×#41D4×C31semidirect
571. C22⋊Q8D4×C31semidirect
615. #103D4×C31semidirect
625. C31#24441direct (N × H)
792. Q8C31×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5482
C2×C31×#4682
C2×C31×#4492
C2×C31×#4482
C2×C31×#4172
C31×#24162
C31×#20422
C31×#20332
C31×#20122
C31×#19992
C31×#18802
C31×#18722
C31×#18702
C31×#18632
C31×#17872
#2444131