Finite Group Databasebeta

← C31×#23888 #21480647

Subgroups — C31×#23888 #21480647

Order 7936.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#577C211yesmaximal, characteristic, complemented
2C2×C31×#576C211yesmaximal, characteristic, complemented
3C2×C31×#454C211yesmaximal, characteristic, complemented
4C2×C31×#455C211yesmaximal, characteristic, complemented
5C31×#3013C211yesmaximal, characteristic, complemented
6C31×#3012C211yesmaximal, characteristic, complemented
7C31×#2019C211yesmaximal, characteristic, complemented
8C31×#2018C211yesmaximal, characteristic, complemented
9C31×#2012C211yesmaximal, characteristic, complemented
10C31×#2006C211yesmaximal, characteristic, complemented
11C31×#1908C211yesmaximal, characteristic, complemented
12C31×#1907C211yesmaximal, characteristic, complemented
13C31×#1876C211yesmaximal, characteristic, complemented
14C31×#1876C211yesmaximal, characteristic, complemented
15C31×#1792C211yesmaximal, characteristic, complemented
16C2×C31×2−1+4C2211yescharacteristic, complemented
17C2×C31×H(5,𝔽2)C2211yescharacteristic
18C2×C31×H(5,𝔽2)C2211yescharacteristic
19C31×#577—24no—
20C31×#577—24no—
21C31×#576—24no—
22C31×#576—24no—
23C2×C31×#137—21no—
24C2×C31×#137C2211yescharacteristic
25C2×C31×#137C2211yescharacteristic, complemented
26C2×C31×AGL(1,ℤ/8)—21no—
27C2×C31×AGL(1,ℤ/8)—21no—
28C2×C31×AGL(1,ℤ/8)—21no—
29C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
30C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
31C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
32C2×C31×AGL(1,ℤ/8)C2211yescharacteristic, complemented
33C2×C31×#135—21no—
34C2×C31×#135—21no—
35C2×C31×#135C2211yescharacteristic
36C2×C31×#135C2211yescharacteristic
37C22×SD16×C31—21no—
38C22×SD16×C31C2211yescharacteristic, complemented
39C22×D8×C31—21no—
40C22×D8×C31C2211yescharacteristic
41C2×C31×#131C2211yescharacteristic
42C2×C31×#131C2211yescharacteristic, complemented
43C31×#537C2211yescharacteristic, complemented
44C2×C31×#124C2211yescharacteristic, complemented
45C31×#455—24no—
46C31×#454—24no—
47C31×#452—21no—
48C31×#452—21no—
49C31×#451—21no—
50C31×#450—21no—
51C31×#449—21no—
52C31×#449—21no—
53C31×#448—21no—
54C31×#447—21no—
55C2×C31×#104C2211yescharacteristic
56C2×C31×#104C2211yescharacteristic, complemented
57C2×C31×#104C2211yescharacteristic, complemented
58C2×C31×#104C2211yescharacteristic, complemented
59C31×#417C2211yescharacteristic
60C31×#417C2211yescharacteristic, complemented
61C2×C31×#103C2211yescharacteristic, complemented
62C2×C31×#102C2211yescharacteristic, complemented
63C2×C31×#101C2211yescharacteristic, complemented
64C2×C31×#100C2211yescharacteristic, complemented
65C2×C31×#100C2211yescharacteristic, complemented
66C31×#408C2211yescharacteristic, complemented
67C31×#408C2211yescharacteristic, complemented
68C31×#390C2211yescharacteristic, complemented
69C31×#343C2211yescharacteristic, complemented
70C31×#341C2211yescharacteristic, complemented
71C31×#341C2211yescharacteristic, complemented
72C31×#336C2211yescharacteristic, complemented
73C31×2−1+4—22no—
74C31×2−1+4—22no—
75C31×2−1+4—22no—
76C31×2−1+4—41no—
77C31×H(5,𝔽2)—22no—
78C31×H(5,𝔽2)—22no—
79C31×H(5,𝔽2)—22no—
80C31×H(5,𝔽2)—22no—
81C31×H(5,𝔽2)—22no—
82C31×H(5,𝔽2)—41no—
83C31×H(5,𝔽2)—41no—
84C31×H(5,𝔽2)D414yescomplemented
85C2×#41×C31—21no—
86C2×#41×C31—21no—
87C2×#41×C31—21no—
88C2×#41×C31—21no—
89C2×#41×C31—21no—
90C2×#41×C31—21no—
91C2×#41×C31—41no—
92C2×#41×C31C2311yescharacteristic
93C2×#41×C31C2311yescharacteristic
94C2×#41×C31C2311yescharacteristic
95C2×#41×C31C2311yescharacteristic
96C22×Q8×C31—21no—
97C22×Q8×C31—21no—
98C22×Q8×C31C2311yescharacteristic
99C22×D4×C31—21no—
100C22×D4×C31—21no—
101C22×D4×C31—21no—
102C22×D4×C31—21no—
103C22×D4×C31—41no—
104C22×D4×C31—41no—
105C22×D4×C31C2311yescharacteristic
106C22×D4×C31C2311yescharacteristic
107C31×#137—28no—
108C31×#137—22no—
109C31×#137—22no—
110C31×#137—41no—
111C31×#137D414yescomplemented
112C31×AGL(1,ℤ/8)—28no—
113C31×AGL(1,ℤ/8)—28no—
114C31×AGL(1,ℤ/8)—28no—
115C31×AGL(1,ℤ/8)—22no—
116C31×AGL(1,ℤ/8)—22no—
117C31×AGL(1,ℤ/8)—22no—
118C31×AGL(1,ℤ/8)—22no—
119C31×AGL(1,ℤ/8)—22no—
120C31×AGL(1,ℤ/8)—22no—
121C31×AGL(1,ℤ/8)—41no—
122C31×AGL(1,ℤ/8)D414yescomplemented
123C31×#135—28no—
124C31×#135—28no—
125C31×#135—22no—
126C31×#135—22no—
127C31×#135—22no—
128C31×#135—22no—
129C2×Q16×C31—21no—
130C2×Q16×C31—21no—
131C2×Q16×C31D411yescharacteristic
132C2×Q16×C31D411yescharacteristic
133C2×SD16×C31—28no—
134C2×SD16×C31—21no—
135C2×SD16×C31—22no—
136C2×SD16×C31—21no—
137C2×SD16×C31—21no—
138C2×SD16×C31—21no—
139C2×SD16×C31—22no—
140C2×SD16×C31—21no—
141C2×SD16×C31—21no—
142C2×SD16×C31—21no—
143C2×SD16×C31—21no—
144C2×SD16×C31D411yescharacteristic
145C2×SD16×C31D411yescharacteristic
146C2×SD16×C31D411yescharacteristic
147C2×SD16×C31D411yescharacteristic
148C2×D8×C31—28no—
149C2×D8×C31—21no—
150C2×D8×C31—21no—
151C2×D8×C31—22no—
152C2×D8×C31—22no—
153C2×D8×C31—21no—
154C2×D8×C31—21no—
155C2×D8×C31—21no—
156C2×D8×C31—21no—
157C2×D8×C31D411yescharacteristic
158C2×D8×C31D411yescharacteristic
159C31×#131—22no—
160C31×#131—22no—
161C31×#131—22no—
162C31×#131—22no—
163C2×M16×C31—21no—
164C2×M16×C31—21no—
165C2×M16×C31C2311yescharacteristic
166C2×M16×C31C2311yescharacteristic
167C2×M16×C31C2311yescharacteristic
168C2×M16×C31C2311yescharacteristic
169C22×C8×C31—21no—
170C22×C8×C31—21no—
171C22×C8×C31C2311yescharacteristic
172C22×C8×C31C2311yescharacteristic
173C31×#124—22no—
174C31×#124—22no—
175C31×C22⋊Q8—21no—
176C31×C22⋊Q8—21no—
177C31×#121—21no—
178C31×#121—21no—
179C31×#121—41no—
180C2×C4⋊C4×C31C2311yescharacteristic
181C2×C22⋊C4×C31—41no—
182C2×C22⋊C4×C31—41no—
183C2×C42×C31C2311yescharacteristic
184C31×#104—22no—
185C31×#104—22no—
186C31×#104—22no—
187C31×#104—22no—
188C31×#103—21no—
189C31×#103—21no—
190C31×#103—21no—
191C31×#103—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×#102—21no—
195C31×#102—21no—
196C31×#101—22no—
197C31×#100—22no—
198C31×#100—41no—
199C31×C22⋊C8—21no—
200C31×C22⋊C8—21no—
201C31×C22⋊C8—21no—
202C31×C22⋊C8—21no—
203C24×C31—21no—
204C24×C31—21no—
205C24×C31—41no—
206C24×C31—41no—
207#41×C31—21no—
208#41×C31—21no—
209#41×C31—21no—
210#41×C31—21no—
211#41×C31—24no—
212#41×C31—24no—
213#41×C31—24no—
214#41×C31—24no—
215#41×C31—21no—
216#41×C31—21no—
217#41×C31—21no—
218#41×C31—21no—
219#41×C31—21no—
220#41×C31—21no—
221#41×C31—21no—
222#41×C31—21no—
223#41×C31—42no—
224#41×C31—44no—
225#41×C31—42no—
226#41×C31—42no—
227#41×C31—42no—
228#41×C31—42no—
229#41×C31—42no—
230#41×C31—44no—
231#41×C31—42no—
232#41×C31—42no—
233#41×C31C2×D412yes—
234#41×C31C2×D412yes—
235#41×C31C2×D412yes—
236#41×C31C2×D412yes—
237C2×Q8×C31—21no—
238C2×Q8×C31—24no—
239C2×Q8×C31—21no—
240C2×Q8×C31—21no—
241C2×Q8×C31—21no—
242C2×Q8×C31—21no—
243C2×Q8×C31—41no—
244C2×Q8×C31—42no—
245C2×Q8×C31—42no—
246C2×Q8×C31—42no—
247C2×Q8×C31C2×D411yescharacteristic
248C2×Q8×C31C2×D411yescharacteristic
249C2×Q8×C31C2×D412yes—
250C2×Q8×C31C2×D411yescharacteristic
251C2×Q8×C31C2×D411yescharacteristic
252C2×D4×C31—21no—
253C2×D4×C31—21no—
254C2×D4×C31—24no—
255C2×D4×C31—24no—
256C2×D4×C31—24no—
257C2×D4×C31—21no—
258C2×D4×C31—21no—
259C2×D4×C31—21no—
260C2×D4×C31—21no—
261C2×D4×C31—21no—
262C2×D4×C31—21no—
263C2×D4×C31—21no—
264C2×D4×C31—21no—
265C2×D4×C31—21no—
266C2×D4×C31—21no—
267C2×D4×C31—21no—
268C2×D4×C31—21no—
269C2×D4×C31—42no—
270C2×D4×C31—42no—
271C2×D4×C31—42no—
272C2×D4×C31—41no—
273C2×D4×C31—41no—
274C2×D4×C31—41no—
275C2×D4×C31—41no—
276C2×D4×C31—44no—
277C2×D4×C31—42no—
278C2×D4×C31—44no—
279C2×D4×C31—44no—
280C2×D4×C31—44no—
281C2×D4×C31—41no—
282C2×D4×C31—42no—
283C2×D4×C31—41no—
284C2×D4×C31C2×D411yescharacteristic
285C2×D4×C31C2×D411yescharacteristic
286C2×D4×C31C2×D412yes—
287C2×D4×C31C2×D412yes—
288C2×D4×C31C2×D411yescharacteristic
289C2×D4×C31C2×D411yescharacteristic
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—41no—
298C22×C4×C31—41no—
299C22×C4×C31—41no—
300C22×C4×C31—41no—
301C22×C4×C31C2411yescharacteristic
302Q16×C31—24no—
303Q16×C31—22no—
304Q16×C31—22no—
305Q16×C31—42no—
306SD16×C31—24no—
307SD16×C31—24no—
308SD16×C31—24no—
309SD16×C31—24no—
310SD16×C31—24no—
311SD16×C31—22no—
312SD16×C31—22no—
313SD16×C31—22no—
314SD16×C31—24no—
315SD16×C31—22no—
316SD16×C31—42no—
317SD16×C31—42no—
318D8×C31—24no—
319D8×C31—24no—
320D8×C31—24no—
321D8×C31—24no—
322D8×C31—22no—
323D8×C31—24no—
324D8×C31—22no—
325D8×C31—42no—
326M16×C31—24no—
327M16×C31—24no—
328M16×C31—21no—
329M16×C31—21no—
330M16×C31—21no—
331M16×C31—21no—
332M16×C31—21no—
333M16×C31—21no—
334M16×C31C2×D412yes—
335M16×C31C2×D412yes—
336C2×C8×C31—24no—
337C2×C8×C31—24no—
338C2×C8×C31—21no—
339C2×C8×C31—21no—
340C2×C8×C31—21no—
341C2×C8×C31—21no—
342C2×C8×C31—21no—
343C2×C8×C31—21no—
344C2×C8×C31—21no—
345C2×C8×C31—21no—
346C2×C8×C31C2×D411yescharacteristic
347C2×C8×C31C2×D411yescharacteristic
348C2×C8×C31C2×D411yescharacteristic
349C2×C8×C31C2×D411yescharacteristic
350C4⋊C4×C31—21no—
351C4⋊C4×C31—21no—
352C4⋊C4×C31—41no—
353C22⋊C4×C31—44no—
354C22⋊C4×C31—41no—
355C22⋊C4×C31—41no—
356C22⋊C4×C31—82no—
357C42×C31—21no—
358C42×C31—21no—
359#23888C3111yesmaximal, characteristic, direct product factor, Sylow
360C23×C31—21no—
361C23×C31—21no—
362C23×C31—21no—
363C23×C31—21no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—44no—
367C23×C31—44no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—81no—
373C23×C31—81no—
374C23×C31—81no—
375C23×C31—81no—
376C23×C31—161no—
377C23×C31—161no—
378C23×C31—161no—
379C23×C31—161no—
380C23×C31H(5,𝔽2)11yescharacteristic
381Q8×C31—21no—
382Q8×C31—21no—
383Q8×C31—22no—
384Q8×C31—21no—
385Q8×C31—21no—
386Q8×C31—21no—
387Q8×C31—22no—
388Q8×C31—21no—
389Q8×C31—44no—
390Q8×C31—41no—
391Q8×C31—41no—
392Q8×C31#12012yes—
393Q8×C31#12012yes—
394D4×C31—22no—
395D4×C31—22no—
396D4×C31—22no—
397D4×C31—22no—
398D4×C31—22no—
399D4×C31—22no—
400D4×C31—21no—
401D4×C31—21no—
402D4×C31—22no—
403D4×C31—21no—
404D4×C31—21no—
405D4×C31—21no—
406D4×C31—22no—
407D4×C31—21no—
408D4×C31—44no—
409D4×C31—44no—
410D4×C31—44no—
411D4×C31—44no—
412D4×C31—44no—
413D4×C31—41no—
414D4×C31—41no—
415D4×C31—41no—
416D4×C31—41no—
417D4×C31—41no—
418D4×C31—41no—
419D4×C31—41no—
420D4×C31—41no—
421D4×C31—161no—
422D4×C31#12012yes—
423D4×C31#12012yes—
424C2×C4×C31—21no—
425C2×C4×C31—21no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—21no—
432C2×C4×C31—21no—
433C2×C4×C31—44no—
434C2×C4×C31—44no—
435C2×C4×C31—44no—
436C2×C4×C31—44no—
437C2×C4×C31—41no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—81no—
448C2×C4×C31C22×D411yescharacteristic
449C2×C4×C31C22×D411yescharacteristic
450C2×C4×C31C22×D411yescharacteristic
451C2×C4×C31C22×D411yescharacteristic
452C2×C4×C31C22×D411yescharacteristic
453C2×C4×C31H(5,𝔽2)11yescharacteristic
454C8×C31—21no—
455C8×C31—21no—
456C8×C31—22no—
457C8×C31—22no—
458C8×C31—21no—
459C8×C31—21no—
460C8×C31—41no—
461C8×C31—41no—
462C2×#577C2×C3111yescharacteristic, complemented
463C2×#576C2×C3111yescharacteristic, complemented
464C2×#454C2×C3111yescharacteristic, complemented
465C2×#455C2×C3111yescharacteristic, complemented
466#3013C2×C3111yescharacteristic, complemented
467#3012C2×C3111yescharacteristic, complemented
468#2019C2×C3111yescharacteristic, complemented
469#2018C2×C3111yescharacteristic, complemented
470#2012C2×C3111yescharacteristic, complemented
471#2006C2×C3111yescharacteristic, complemented
472#1908C2×C3111yescharacteristic, complemented
473#1907C2×C3111yescharacteristic, complemented
474#1876C2×C3111yescharacteristic, complemented
475#1876C2×C3111yescharacteristic, complemented
476#1792C2×C3111yescharacteristic, complemented
477C22×C31—21no—
478C22×C31—21no—
479C22×C31—22no—
480C22×C31—22no—
481C22×C31—41no—
482C22×C31—41no—
483C22×C31—41no—
484C22×C31—41no—
485C22×C31—41no—
486C22×C31—41no—
487C22×C31—42no—
488C22×C31—42no—
489C22×C31—41no—
490C22×C31—41no—
491C22×C31—41no—
492C22×C31—41no—
493C22×C31—82no—
494C22×C31—82no—
495C22×C31—81no—
496C22×C31—81no—
497C22×C31—81no—
498C22×C31—81no—
499C22×C31—161no—
500C22×C31—161no—
501C22×C31—164no—
502C22×C31—164no—
503C22×C31#53411yescharacteristic
504C22×C31D4211yescharacteristic
505C22×C31D4211yescharacteristic
506C4×C31—22no—
507C4×C31—22no—
508C4×C31—41no—
509C4×C31—42no—
510C4×C31—41no—
511C4×C31—81no—
512C4×C31—81no—
513C4×C31C2×#12011yescharacteristic
514C4×C31C2×#12011yescharacteristic
515C4×C31D4211yescharacteristic
516C4×C31D4211yescharacteristic
517C2×2−1+4C22×C3111yescharacteristic, complemented
518C2×H(5,𝔽2)C22×C3111yescharacteristic
519C2×H(5,𝔽2)C22×C3111yescharacteristic
520#577—24no—
521#577—24no—
522#576—24no—
523#576—24no—
524C2×#137—21no—
525C2×#137C22×C3111yescharacteristic
526C2×#137C22×C3111yescharacteristic, complemented
527C2×AGL(1,ℤ/8)—21no—
528C2×AGL(1,ℤ/8)—21no—
529C2×AGL(1,ℤ/8)—21no—
530C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
531C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
532C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
533C2×AGL(1,ℤ/8)C22×C3111yescharacteristic, complemented
534C2×#135—21no—
535C2×#135—21no—
536C2×#135C22×C3111yescharacteristic
537C2×#135C22×C3111yescharacteristic
538C22×SD16—21no—
539C22×SD16C22×C3111yescharacteristic, complemented
540C22×D8—21no—
541C22×D8C22×C3111yescharacteristic
542C2×#131C22×C3111yescharacteristic
543C2×#131C22×C3111yescharacteristic, complemented
544#537C22×C3111yescharacteristic, complemented
545C2×#124C22×C3111yescharacteristic, complemented
546#455—24no—
547#454—24no—
548#452—21no—
549#452—21no—
550#451—21no—
551#450—21no—
552#449—21no—
553#449—21no—
554#448—21no—
555#447—21no—
556C2×#104C22×C3111yescharacteristic
557C2×#104C22×C3111yescharacteristic, complemented
558C2×#104C22×C3111yescharacteristic, complemented
559C2×#104C22×C3111yescharacteristic, complemented
560#417C22×C3111yescharacteristic
561#417C22×C3111yescharacteristic, complemented
562C2×#103C22×C3111yescharacteristic, complemented
563C2×#102C22×C3111yescharacteristic, complemented
564C2×#101C22×C3111yescharacteristic, complemented
565C2×#100C22×C3111yescharacteristic, complemented
566C2×#100C22×C3111yescharacteristic, complemented
567#408C22×C3111yescharacteristic, complemented
568#408C22×C3111yescharacteristic, complemented
569#390C22×C3111yescharacteristic, complemented
570#343C22×C3111yescharacteristic, complemented
571#341C22×C3111yescharacteristic, complemented
572#341C22×C3111yescharacteristic, complemented
573#336C22×C3111yescharacteristic, complemented
574C2×C31—21no—
575C2×C31—21no—
576C2×C31—42no—
577C2×C31—42no—
578C2×C31—81no—
579C2×C31—81no—
580C2×C31—82no—
581C2×C31—82no—
582C2×C31#240311yescharacteristic
583C2×C31#328811yescharacteristic
584C2×C31#329011yescharacteristic
5852−1+4—22no—
5862−1+4—22no—
5872−1+4—22no—
5882−1+4—41no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—22no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—22no—
593H(5,𝔽2)—22no—
594H(5,𝔽2)—41no—
595H(5,𝔽2)—41no—
596H(5,𝔽2)D4×C3114yescomplemented
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—41no—
604C2×#41C23×C3111yescharacteristic
605C2×#41C23×C3111yescharacteristic
606C2×#41C23×C3111yescharacteristic
607C2×#41C23×C3111yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C3111yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—21no—
614C22×D4—21no—
615C22×D4—41no—
616C22×D4—41no—
617C22×D4C23×C3111yescharacteristic
618C22×D4C23×C3111yescharacteristic
619#137—28no—
620#137—22no—
621#137—22no—
622#137—41no—
623#137D4×C3114yescomplemented
624AGL(1,ℤ/8)—28no—
625AGL(1,ℤ/8)—28no—
626AGL(1,ℤ/8)—28no—
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—22no—
631AGL(1,ℤ/8)—22no—
632AGL(1,ℤ/8)—22no—
633AGL(1,ℤ/8)—41no—
634AGL(1,ℤ/8)D4×C3114yescomplemented
635#135—28no—
636#135—28no—
637#135—22no—
638#135—22no—
639#135—22no—
640#135—22no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×Q16D4×C3111yescharacteristic
644C2×Q16D4×C3111yescharacteristic
645C2×SD16—28no—
646C2×SD16—21no—
647C2×SD16—22no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—22no—
652C2×SD16—21no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16D4×C3111yescharacteristic
657C2×SD16D4×C3111yescharacteristic
658C2×SD16D4×C3111yescharacteristic
659C2×SD16D4×C3111yescharacteristic
660C2×D8—28no—
661C2×D8—21no—
662C2×D8—21no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—21no—
666C2×D8—21no—
667C2×D8—21no—
668C2×D8—21no—
669C2×D8D4×C3111yescharacteristic
670C2×D8D4×C3111yescharacteristic
671#131—22no—
672#131—22no—
673#131—22no—
674#131—22no—
675C2×M16—21no—
676C2×M16—21no—
677C2×M16C23×C3111yescharacteristic
678C2×M16C23×C3111yescharacteristic
679C2×M16C23×C3111yescharacteristic
680C2×M16C23×C3111yescharacteristic
681C22×C8—21no—
682C22×C8—21no—
683C22×C8C23×C3111yescharacteristic
684C22×C8C23×C3111yescharacteristic
685#124—22no—
686#124—22no—
687C22⋊Q8—21no—
688C22⋊Q8—21no—
689#121—21no—
690#121—21no—
691#121—41no—
692C2×C4⋊C4C23×C3111yescharacteristic
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C42C23×C3111yescharacteristic
696#104—22no—
697#104—22no—
698#104—22no—
699#104—22no—
700#103—21no—
701#103—21no—
702#103—21no—
703#103—21no—
704#102—21no—
705#102—21no—
706#102—21no—
707#102—21no—
708#101—22no—
709#100—22no—
710#100—41no—
711C22⋊C8—21no—
712C22⋊C8—21no—
713C22⋊C8—21no—
714C22⋊C8—21no—
715C31#2388811yescharacteristic, direct product factor, Sylow
716C24—21no—
717C24—21no—
718C24—41no—
719C24—41no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—24no—
725#41—24no—
726#41—24no—
727#41—24no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—42no—
737#41—44no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—42no—
743#41—44no—
744#41—42no—
745#41—42no—
746#41C2×D4×C3112yes—
747#41C2×D4×C3112yes—
748#41C2×D4×C3112yes—
749#41C2×D4×C3112yes—
750C2×Q8—21no—
751C2×Q8—24no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—41no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8C2×D4×C3111yescharacteristic
761C2×Q8C2×D4×C3111yescharacteristic
762C2×Q8C2×D4×C3112yes—
763C2×Q8C2×D4×C3111yescharacteristic
764C2×Q8C2×D4×C3111yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—44no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—41no—
795C2×D4—42no—
796C2×D4—41no—
797C2×D4C2×D4×C3111yescharacteristic
798C2×D4C2×D4×C3111yescharacteristic
799C2×D4C2×D4×C3112yes—
800C2×D4C2×D4×C3112yes—
801C2×D4C2×D4×C3111yescharacteristic
802C2×D4C2×D4×C3111yescharacteristic
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4C24×C3111yescharacteristic
815Q16—24no—
816Q16—22no—
817Q16—22no—
818Q16—42no—
819SD16—24no—
820SD16—24no—
821SD16—24no—
822SD16—24no—
823SD16—24no—
824SD16—22no—
825SD16—22no—
826SD16—22no—
827SD16—24no—
828SD16—22no—
829SD16—42no—
830SD16—42no—
831D8—24no—
832D8—24no—
833D8—24no—
834D8—24no—
835D8—22no—
836D8—24no—
837D8—22no—
838D8—42no—
839M16—24no—
840M16—24no—
841M16—21no—
842M16—21no—
843M16—21no—
844M16—21no—
845M16—21no—
846M16—21no—
847M16C2×D4×C3112yes—
848M16C2×D4×C3112yes—
849C2×C8—24no—
850C2×C8—24no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C3111yescharacteristic
860C2×C8C2×D4×C3111yescharacteristic
861C2×C8C2×D4×C3111yescharacteristic
862C2×C8C2×D4×C3111yescharacteristic
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—41no—
866C22⋊C4—44no—
867C22⋊C4—41no—
868C22⋊C4—41no—
869C22⋊C4—82no—
870C42—21no—
871C42—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—22no—
877C23—22no—
878C23—44no—
879C23—44no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—81no—
885C23—81no—
886C23—81no—
887C23—81no—
888C23—161no—
889C23—161no—
890C23—161no—
891C23—161no—
892C23C31×H(5,𝔽2)11yescharacteristic
893Q8—21no—
894Q8—21no—
895Q8—22no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—22no—
900Q8—21no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8C31×#12012yes—
905Q8C31×#12012yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—22no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—22no—
919D4—21no—
920D4—44no—
921D4—44no—
922D4—44no—
923D4—44no—
924D4—44no—
925D4—41no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—161no—
934D4C31×#12012yes—
935D4C31×#12012yes—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—81no—
960C2×C4C22×D4×C3111yescharacteristic
961C2×C4C22×D4×C3111yescharacteristic
962C2×C4C22×D4×C3111yescharacteristic
963C2×C4C22×D4×C3111yescharacteristic
964C2×C4C22×D4×C3111yescharacteristic
965C2×C4C31×H(5,𝔽2)11yescharacteristic
966C8—21no—
967C8—21no—
968C8—22no—
969C8—22no—
970C8—21no—
971C8—21no—
972C8—41no—
973C8—41no—
974C22—21no—
975C22—21no—
976C22—22no—
977C22—22no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—42no—
985C22—42no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—82no—
991C22—82no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—161no—
997C22—161no—
998C22—164no—
999C22—164no—
1000C22C31×#53411yescharacteristic
1001C22D42×C3111yescharacteristic
1002C22D42×C3111yescharacteristic
1003C4—22no—
1004C4—22no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—81no—
1009C4—81no—
1010C4C2×C31×#12011yescharacteristic
1011C4C2×C31×#12011yescharacteristic
1012C4D42×C3111yescharacteristic
1013C4D42×C3111yescharacteristic
1014C2—21no—
1015C2—21no—
1016C2—42no—
1017C2—42no—
1018C2—81no—
1019C2—81no—
1020C2—82no—
1021C2—82no—
1022C2C31×#240311yescharacteristic
1023C2C31×#328811yescharacteristic
1024C2C31×#329011yescharacteristic
subgroupG/H
center, socleC22×C31D42
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#577C2semidirect
2. C2×C31×#576C2semidirect
3. C2×C31×#454C2semidirect
4. C2×C31×#455C2semidirect
5. C31×#3013C2semidirect
6. C31×#3012C2semidirect
7. C31×#2019C2semidirect
8. C31×#2018C2semidirect
9. C31×#2012C2semidirect
10. C31×#2006C2semidirect
11. C31×#1908C2semidirect
12. C31×#1907C2semidirect
13. C31×#1876C2semidirect
14. C31×#1876C2semidirect
15. C31×#1792C2semidirect
16. C2×C31×2−1+4C22semidirect
25. C2×C31×#137C22semidirect
31. C2×C31×AGL(1,ℤ/8)C22semidirect
32. C2×C31×AGL(1,ℤ/8)C22semidirect
38. C22×SD16×C31C22semidirect
42. C2×C31×#131C22semidirect
43. C31×#537C22semidirect
44. C2×C31×#124C22semidirect
56. C2×C31×#104C22semidirect
57. C2×C31×#104C22semidirect
58. C2×C31×#104C22semidirect
60. C31×#417C22semidirect
61. C2×C31×#103C22semidirect
62. C2×C31×#102C22semidirect
63. C2×C31×#101C22semidirect
64. C2×C31×#100C22semidirect
65. C2×C31×#100C22semidirect
66. C31×#408C22semidirect
67. C31×#408C22semidirect
68. C31×#390C22semidirect
69. C31×#343C22semidirect
70. C31×#341C22semidirect
71. C31×#341C22semidirect
72. C31×#336C22semidirect
84. C31×H(5,𝔽2)D4semidirect
111. C31×#137D4semidirect
122. C31×AGL(1,ℤ/8)D4semidirect
359. #23888C31direct (N × H)
462. C2×#577C2×C31semidirect
463. C2×#576C2×C31semidirect
464. C2×#454C2×C31semidirect
465. C2×#455C2×C31semidirect
466. #3013C2×C31semidirect
467. #3012C2×C31semidirect
468. #2019C2×C31semidirect
469. #2018C2×C31semidirect
470. #2012C2×C31semidirect
471. #2006C2×C31semidirect
472. #1908C2×C31semidirect
473. #1907C2×C31semidirect
474. #1876C2×C31semidirect
475. #1876C2×C31semidirect
476. #1792C2×C31semidirect
517. C2×2−1+4C22×C31semidirect
526. C2×#137C22×C31semidirect
532. C2×AGL(1,ℤ/8)C22×C31semidirect
533. C2×AGL(1,ℤ/8)C22×C31semidirect
539. C22×SD16C22×C31semidirect
543. C2×#131C22×C31semidirect
544. #537C22×C31semidirect
545. C2×#124C22×C31semidirect
557. C2×#104C22×C31semidirect
558. C2×#104C22×C31semidirect
559. C2×#104C22×C31semidirect
561. #417C22×C31semidirect
562. C2×#103C22×C31semidirect
563. C2×#102C22×C31semidirect
564. C2×#101C22×C31semidirect
565. C2×#100C22×C31semidirect
566. C2×#100C22×C31semidirect
567. #408C22×C31semidirect
568. #408C22×C31semidirect
569. #390C22×C31semidirect
570. #343C22×C31semidirect
571. #341C22×C31semidirect
572. #341C22×C31semidirect
573. #336C22×C31semidirect
596. H(5,𝔽2)D4×C31semidirect
623. #137D4×C31semidirect
634. AGL(1,ℤ/8)D4×C31semidirect
715. C31#23888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5772
C2×C31×#5762
C2×C31×#4542
C2×C31×#4552
C31×#30132
C31×#30122
C31×#20192
C31×#20182
C31×#20122
C31×#20062
C31×#19082
C31×#19072
C31×#18762
C31×#17922
#2388831