Finite Group Databasebeta

← C31×#23972 #21480731

Subgroups — C31×#23972 #21480731

Order 7936.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#547C211yesmaximal, characteristic, complemented
2C2×C31×#449C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C31×#2407C211yesmaximal, characteristic, complemented
5C31×#2024C211yesmaximal, characteristic, complemented
6C31×#2023C211yesmaximal, characteristic, complemented
7C31×#2000C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1895C211yesmaximal, characteristic, complemented
10C31×#1879C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1872C211yesmaximal, characteristic, complemented
14C31×#1870C211yesmaximal, characteristic, complemented
15C31×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C31—21no—
17C22×#41×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C31×#547—24no—
22C31×#547—24no—
23C2×C31×C4⋊Q8C2211yescharacteristic
24C2×C31×#123—21no—
25C2×C31×#123—21no—
26C2×C31×C22⋊Q8—21no—
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C31×#449—24no—
36C31×#417—24no—
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#394—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#386—21no—
53C31×#385—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—28no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C2×#41×C31—44no—
71C2×#41×C31—44no—
72C22×Q8×C31—21no—
73C22×Q8×C31C2311yescharacteristic
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31D411yescharacteristic
79C22×D4×C31C2311yescharacteristic
80C22×D4×C31C2311yescharacteristic
81C23×C4×C31—21no—
82C23×C4×C31—21no—
83C23×C4×C31—21no—
84C23×C4×C31—21no—
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C2×SD16×C31—22no—
88C2×SD16×C31—22no—
89C2×SD16×C31—41no—
90C2×D8×C31—22no—
91C2×D8×C31—22no—
92C2×D8×C31—41no—
93C2×M16×C31—22no—
94C2×M16×C31—41no—
95C2×M16×C31—41no—
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C22×C8×C31C2311yescharacteristic
100C31×C4⋊Q8—22no—
101C31×C4⋊Q8—22no—
102C31×#123—28no—
103C31×#123—28no—
104C31×C22⋊Q8—28no—
105C31×C22⋊Q8—22no—
106C31×C22⋊Q8—41no—
107C31×#121—22no—
108C31×#121—22no—
109C31×#121—22no—
110C31×#121—22no—
111C31×#121—41no—
112C31×#121D414yescomplemented
113C4×D4×C31—22no—
114C4×D4×C31—22no—
115C4×D4×C31—22no—
116C4×D4×C31—22no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—21no—
119C2×C4⋊C4×C31—22no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31—22no—
122C2×C4⋊C4×C31—22no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31D411yescharacteristic
125C2×C4⋊C4×C31D414yescomplemented
126C2×C4⋊C4×C31C2311yescharacteristic
127C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
140C2×C22⋊C4×C31D411yescharacteristic
141C2×C42×C31C2311yescharacteristic
142C31×#103—22no—
143C31×#103—22no—
144C31×#103—22no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—41no—
149C31×#102—41no—
150C31×C22⋊C8—22no—
151C31×C22⋊C8—41no—
152C31×C22⋊C8—41no—
153C31×#95—21no—
154C31×#95—21no—
155C31×#95—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31C2×D411yescharacteristic
159C24×C31C2×D411yescharacteristic
160#41×C31—28no—
161#41×C31—44no—
162#41×C31—44no—
163#41×C31—44no—
164#41×C31—432no—
165C2×Q8×C31—24no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—42no—
172C2×Q8×C31—42no—
173C2×Q8×C31#4112yescomplemented
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—24no—
177C2×D4×C31—24no—
178C2×D4×C31—22no—
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—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—42no—
193C2×D4×C31—42no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—42no—
198C2×D4×C31—81no—
199C2×D4×C31C2×D412yes—
200C2×D4×C31#4112yescomplemented
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—24no—
206C22×C4×C31—24no—
207C22×C4×C31—24no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—42no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—42no—
227C22×C4×C31—42no—
228C22×C4×C31—42no—
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D412yes—
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2×D411yescharacteristic
235C22×C4×C31C2411yescharacteristic
236SD16×C31—44no—
237D8×C31—44no—
238M16×C31—44no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—21no—
250C2×C8×C31—21no—
251C4⋊C4×C31—24no—
252C4⋊C4×C31—24no—
253C4⋊C4×C31—24no—
254C4⋊C4×C31—22no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—42no—
263C4⋊C4×C31C2×D412yes—
264C4⋊C4×C31C2×D412yes—
265C4⋊C4×C31C2×D412yes—
266C22⋊C4×C31—24no—
267C22⋊C4×C31—24no—
268C22⋊C4×C31—22no—
269C22⋊C4×C31—24no—
270C22⋊C4×C31—22no—
271C22⋊C4×C31—42no—
272C22⋊C4×C31—42no—
273C22⋊C4×C31—42no—
274C22⋊C4×C31—81no—
275C22⋊C4×C31—81no—
276C42×C31—21no—
277C42×C31—21no—
278#23972C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31#12012yes—
306C23×C31AGL(1,ℤ/8)12yes—
307C23×C31C22×D411yescharacteristic
308Q8×C31—22no—
309Q8×C31—22no—
310Q8×C31—48no—
311Q8×C31—41no—
312Q8×C31—41no—
313D4×C31—28no—
314D4×C31—22no—
315D4×C31—22no—
316D4×C31—22no—
317D4×C31—22no—
318D4×C31—48no—
319D4×C31—48no—
320D4×C31—48no—
321D4×C31—41no—
322D4×C31—41no—
323D4×C31—41no—
324D4×C31—41no—
325D4×C31—84no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—21no—
340C2×C4×C31—22no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—48no—
345C2×C4×C31—48no—
346C2×C4×C31—48no—
347C2×C4×C31—48no—
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—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31#12012yes—
367C2×C4×C31AGL(1,ℤ/8)12yes—
368C2×C4×C31C22×D411yescharacteristic
369C2×C4×C31C22×D411yescharacteristic
370C2×C4×C31C2×#4111yescharacteristic
371C2×C4×C31C2×#4111yescharacteristic
372C2×C4×C31H(5,𝔽2)11yescharacteristic
373C2×C4×C31H(5,𝔽2)11yescharacteristic
374C8×C31—41no—
375C8×C31—41no—
376C8×C31—41no—
377C8×C31—41no—
378C2×#547C2×C3111yescharacteristic, complemented
379C2×#449C2×C3111yescharacteristic, complemented
380C2×#417C2×C3111yescharacteristic, complemented
381#2407C2×C3111yescharacteristic, complemented
382#2024C2×C3111yescharacteristic, complemented
383#2023C2×C3111yescharacteristic, complemented
384#2000C2×C3111yescharacteristic, complemented
385#1999C2×C3111yescharacteristic, complemented
386#1895C2×C3111yescharacteristic, complemented
387#1879C2×C3111yescharacteristic, complemented
388#1877C2×C3111yescharacteristic, complemented
389#1874C2×C3111yescharacteristic, complemented
390#1872C2×C3111yescharacteristic, complemented
391#1870C2×C3111yescharacteristic, complemented
392#1824C2×C3111yescharacteristic, complemented
393C22×C31—22no—
394C22×C31—22no—
395C22×C31—22no—
396C22×C31—22no—
397C22×C31—22no—
398C22×C31—22no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—41no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—81no—
414C22×C31—81no—
415C22×C31—81no—
416C22×C31—81no—
417C22×C31—81no—
418C22×C31—81no—
419C22×C31—81no—
420C22×C31—81no—
421C22×C31C2×#12011yescharacteristic
422C22×C31#54611yescharacteristic
423C22×C31#54611yescharacteristic
424C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
425C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
426C22×C31#57711yescharacteristic
427C22×C31#57811yescharacteristic
428C4×C31—22no—
429C4×C31—22no—
430C4×C31—41no—
431C4×C31—42no—
432C4×C31—42no—
433C4×C31—42no—
434C4×C31—42no—
435C4×C31—41no—
436C4×C31—81no—
437C4×C31—81no—
438C4×C31#52511yescharacteristic
439C4×C31#53511yescharacteristic
440C4×C31#54611yescharacteristic
441C4×C31#54611yescharacteristic
442C22×#41—21no—
443C22×#41C22×C3111yescharacteristic
444C22×SD16C22×C3111yescharacteristic
445C22×D8C22×C3111yescharacteristic
446C22×M16C22×C3111yescharacteristic
447#547—24no—
448#547—24no—
449C2×C4⋊Q8C22×C3111yescharacteristic
450C2×#123—21no—
451C2×#123—21no—
452C2×C22⋊Q8—21no—
453C2×C22⋊Q8C22×C3111yescharacteristic
454C2×#121C22×C3111yescharacteristic
455C2×#121C22×C3111yescharacteristic
456C2×#121C22×C3111yescharacteristic
457C2×C4×D4C22×C3111yescharacteristic
458C2×C4×D4C22×C3111yescharacteristic
459C22×C4⋊C4C22×C3111yescharacteristic
460C22×C4⋊C4C22×C3111yescharacteristic
461#449—24no—
462#417—24no—
463C2×#103C22×C3111yescharacteristic
464C2×#103C22×C3111yescharacteristic
465C2×#103C22×C3111yescharacteristic
466C2×#102C22×C3111yescharacteristic
467C2×#102C22×C3111yescharacteristic
468C2×#102C22×C3111yescharacteristic
469C2×#102C22×C3111yescharacteristic
470C2×#102C22×C3111yescharacteristic
471C2×C22⋊C8C22×C3111yescharacteristic
472C2×C22⋊C8C22×C3111yescharacteristic
473C2×C22⋊C8C22×C3111yescharacteristic
474#394—21no—
475#392—21no—
476#391C22×C3111yescharacteristic
477#390C22×C3111yescharacteristic
478#386—21no—
479#385—21no—
480#380C22×C3111yescharacteristic
481#340C22×C3111yescharacteristic
482#340C22×C3111yescharacteristic
483#340C22×C3111yescharacteristic
484#340C22×C3111yescharacteristic
485#340C22×C3111yescharacteristic
486#340C22×C3111yescharacteristic
487#336C22×C3111yescharacteristic
488#336C22×C3111yescharacteristic
489C2×C31—42no—
490C2×C31—42no—
491C2×C31—82no—
492C2×C31—82no—
493C2×C31#240411yescharacteristic
494C2×C31#300311yescharacteristic
495C2×C31#301311yescharacteristic
496C2×C31#330611yescharacteristic
497C2×C31#330811yescharacteristic
498C2×C31#333011yescharacteristic
499C2×C31#333211yescharacteristic
500C2×#41—28no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—44no—
508C2×#41—44no—
509C22×Q8—21no—
510C22×Q8C23×C3111yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C3111yescharacteristic
516C22×D4C23×C3111yescharacteristic
517C22×D4C23×C3111yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C3111yescharacteristic
523C23×C4C23×C3111yescharacteristic
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—41no—
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—41no—
530C2×M16—22no—
531C2×M16—41no—
532C2×M16—41no—
533C22×C8C23×C3111yescharacteristic
534C22×C8C23×C3111yescharacteristic
535C22×C8C23×C3111yescharacteristic
536C22×C8C23×C3111yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539#123—28no—
540#123—28no—
541C22⋊Q8—28no—
542C22⋊Q8—22no—
543C22⋊Q8—41no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121D4×C3114yescomplemented
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4D4×C3111yescharacteristic
562C2×C4⋊C4D4×C3114yescomplemented
563C2×C4⋊C4C23×C3111yescharacteristic
564C2×C4⋊C4C23×C3111yescharacteristic
565C2×C4⋊C4C23×C3111yescharacteristic
566C2×C4⋊C4C23×C3111yescharacteristic
567C2×C4⋊C4C23×C3111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4D4×C3111yescharacteristic
577C2×C22⋊C4D4×C3111yescharacteristic
578C2×C42C23×C3111yescharacteristic
579#103—22no—
580#103—22no—
581#103—22no—
582#102—22no—
583#102—22no—
584#102—22no—
585#102—41no—
586#102—41no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593C31#2397211yescharacteristic, direct product factor, Sylow
594C24—21no—
595C24—21no—
596C24C2×D4×C3111yescharacteristic
597C24C2×D4×C3111yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C3112yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C3112yes—
638C2×D4#41×C3112yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C3111yescharacteristic
668C22×C4C2×D4×C3111yescharacteristic
669C22×C4C2×D4×C3111yescharacteristic
670C22×C4C2×D4×C3112yes—
671C22×C4C2×D4×C3112yes—
672C22×C4C2×D4×C3111yescharacteristic
673C22×C4C24×C3111yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C3112yes—
702C4⋊C4C2×D4×C3112yes—
703C4⋊C4C2×D4×C3112yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23C31×#12012yes—
743C23C31×AGL(1,ℤ/8)12yes—
744C23C22×D4×C3111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4C31×#12012yes—
804C2×C4C31×AGL(1,ℤ/8)12yes—
805C2×C4C22×D4×C3111yescharacteristic
806C2×C4C22×D4×C3111yescharacteristic
807C2×C4C2×#41×C3111yescharacteristic
808C2×C4C2×#41×C3111yescharacteristic
809C2×C4C31×H(5,𝔽2)11yescharacteristic
810C2×C4C31×H(5,𝔽2)11yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×C31×#12011yescharacteristic
844C22C31×#54611yescharacteristic
845C22C31×#54611yescharacteristic
846C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
847C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
848C22C31×#57711yescharacteristic
849C22C31×#57811yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4C31×#52511yescharacteristic
861C4C31×#53511yescharacteristic
862C4C31×#54611yescharacteristic
863C4C31×#54611yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C31×#240411yescharacteristic
869C2C31×#300311yescharacteristic
870C2C31×#301311yescharacteristic
871C2C31×#330611yescharacteristic
872C2C31×#330811yescharacteristic
873C2C31×#333011yescharacteristic
874C2C31×#333211yescharacteristic
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×#547C2semidirect
2. C2×C31×#449C2semidirect
3. C2×C31×#417C2semidirect
4. C31×#2407C2semidirect
5. C31×#2024C2semidirect
6. C31×#2023C2semidirect
7. C31×#2000C2semidirect
8. C31×#1999C2semidirect
9. C31×#1895C2semidirect
10. C31×#1879C2semidirect
11. C31×#1877C2semidirect
12. C31×#1874C2semidirect
13. C31×#1872C2semidirect
14. C31×#1870C2semidirect
15. C31×#1824C2semidirect
112. C31×#121D4semidirect
125. C2×C4⋊C4×C31D4semidirect
173. C2×Q8×C31#41semidirect
200. C2×D4×C31#41semidirect
278. #23972C31direct (N × H)
378. C2×#547C2×C31semidirect
379. C2×#449C2×C31semidirect
380. C2×#417C2×C31semidirect
381. #2407C2×C31semidirect
382. #2024C2×C31semidirect
383. #2023C2×C31semidirect
384. #2000C2×C31semidirect
385. #1999C2×C31semidirect
386. #1895C2×C31semidirect
387. #1879C2×C31semidirect
388. #1877C2×C31semidirect
389. #1874C2×C31semidirect
390. #1872C2×C31semidirect
391. #1870C2×C31semidirect
392. #1824C2×C31semidirect
549. #121D4×C31semidirect
562. C2×C4⋊C4D4×C31semidirect
593. C31#23972direct (N × H)
611. C2×Q8#41×C31semidirect
638. C2×D4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5472
C2×C31×#4492
C2×C31×#4172
C31×#24072
C31×#20242
C31×#20232
C31×#20002
C31×#19992
C31×#18952
C31×#18792
C31×#18772
C31×#18742
C31×#18722
C31×#18702
C31×#18242
#2397231