Finite Group Databasebeta

← C31×#26130 #21482889

Subgroups — C31×#26130 #21482889

Order 7936.

1008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#481C211yesmaximal, characteristic, complemented
2C22×C31×#106C211yesmaximal, characteristic, complemented
3C31×#2416C211yesmaximal, characteristic
4D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2084C211yesmaximal, characteristic, complemented
7C31×#2077C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#1926C211yesmaximal, characteristic, complemented
10C31×#1919C211yesmaximal, characteristic, complemented
11C31×#1893C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic, complemented
14C31×#1853C211yesmaximal, characteristic, complemented
15C31×#1853C211yesmaximal, characteristic, complemented
16C23×C8×C31C2211yescharacteristic
17C2×C31×#121—21no—
18C2×C31×#121C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C31×#481—24no—
26C2×C31×#106—24no—
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×#106C2211yescharacteristic
32C2×C31×#106C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C31×#396—21no—
41C31×#394—21no—
42C31×#390C2211yescharacteristic
43C31×#389—21no—
44C31×#389C2211yescharacteristic
45C31×#386—21no—
46C31×#385—21no—
47C31×#385—21no—
48C31×#384C2211yescharacteristic
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31D411yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C22×C8×C31—22no—
71C22×C8×C31—22no—
72C22×C8×C31—22no—
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×#121—22no—
78C31×#121—22no—
79C31×#121—22no—
80C31×#121—41no—
81C31×#121—44no—
82C4×D4×C31—22no—
83C4×D4×C31—22no—
84C4×D4×C31—44no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31D411yescharacteristic
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C42×C31—21no—
115C2×C42×C31C2311yescharacteristic
116C31×#106—22no—
117C31×#106—22no—
118C31×#106—22no—
119C31×#106—22no—
120C31×#106—41no—
121C31×#106D414yescomplemented
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—41no—
126C31×C22⋊C8—22no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C24×C31—21no—
135C24×C31C2×D411yescharacteristic
136C24×C31C2×D411yescharacteristic
137C2×D4×C31—22no—
138C2×D4×C31—22no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—42no—
146C2×D4×C31—42no—
147C2×D4×C31—42no—
148C2×D4×C31—42no—
149C2×D4×C31—42no—
150C2×D4×C31—81no—
151C2×D4×C31SD1614yes—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31—42no—
175C22×C4×C31—81no—
176C22×C4×C31—81no—
177C22×C4×C31—81no—
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31#4112yes—
183C22×C4×C31#4112yes—
184C22×C4×C31C2411yescharacteristic
185C2×C8×C31—28no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31C2×D412yes—
197C2×C8×C31#4112yes—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—42no—
215C4⋊C4×C31—42no—
216C4⋊C4×C31—81no—
217C4⋊C4×C31C2×D412yes—
218C4⋊C4×C31C2×D412yes—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
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—81no—
228C42×C31—21no—
229C42×C31—21no—
230C42×C31—42no—
231#26130C3111yesmaximal, characteristic, direct product factor, Sylow
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31#12312yes—
250C23×C31C2×SD1612yes—
251C23×C31C2×SD1612yes—
252C23×C31AGL(1,ℤ/8)12yes—
253C23×C31C22×D411yescharacteristic
254D4×C31—28no—
255D4×C31—41no—
256D4×C31—41no—
257D4×C31—41no—
258D4×C31—41no—
259D4×C31—84no—
260D4×C31—84no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—84no—
301C2×C4×C31—84no—
302C2×C4×C31—84no—
303C2×C4×C31#12312yes—
304C2×C4×C31C2×SD1612yes—
305C2×C4×C31C22×D411yescharacteristic
306C2×C4×C31C2×#4111yescharacteristic
307C2×C4×C31C2×#4111yescharacteristic
308C2×C4×C31C2×#4111yescharacteristic
309C2×C4×C31H(5,𝔽2)11yescharacteristic
310C2×C4×C312−1+411yescharacteristic
311C8×C31—22no—
312C8×C31—22no—
313C8×C31—41no—
314C8×C31—41no—
315C2×#481C2×C3111yescharacteristic, complemented
316C22×#106C2×C3111yescharacteristic, complemented
317#2416C2×C3111yescharacteristic
318D4×C4⋊C4C2×C3111yescharacteristic, complemented
319#2094C2×C3111yescharacteristic, complemented
320#2084C2×C3111yescharacteristic, complemented
321#2077C2×C3111yescharacteristic, complemented
322#2034C2×C3111yescharacteristic, complemented
323#1926C2×C3111yescharacteristic, complemented
324#1919C2×C3111yescharacteristic, complemented
325#1893C2×C3111yescharacteristic, complemented
326#1874C2×C3111yescharacteristic, complemented
327#1869C2×C3111yescharacteristic, complemented
328#1853C2×C3111yescharacteristic, complemented
329#1853C2×C3111yescharacteristic, complemented
330C22×C31—22no—
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—22no—
335C22×C31—22no—
336C22×C31—22no—
337C22×C31—22no—
338C22×C31—22no—
339C22×C31—41no—
340C22×C31—41no—
341C22×C31—41no—
342C22×C31—41no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31—81no—
349C22×C31—81no—
350C22×C31#48114yescomplemented
351C22×C31C2×#12311yescharacteristic
352C22×C31D4211yescharacteristic
353C22×C31#54711yescharacteristic
354C22×C31C22×SD1611yescharacteristic
355C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C31#57711yescharacteristic
357C22×C31#57711yescharacteristic
358C4×C31—22no—
359C4×C31—22no—
360C4×C31—41no—
361C4×C31—41no—
362C4×C31—42no—
363C4×C31—42no—
364C4×C31—81no—
365C4×C31—81no—
366C4×C31—81no—
367C4×C31—81no—
368C4×C31—81no—
369C4×C31#52511yescharacteristic
370C4×C31#53911yescharacteristic
371C4×C31#54811yescharacteristic
372C4×C31#55311yescharacteristic
373C23×C8C22×C3111yescharacteristic
374C2×#121—21no—
375C2×#121C22×C3111yescharacteristic
376C2×#121C22×C3111yescharacteristic
377C2×C4×D4—21no—
378C2×C4×D4C22×C3111yescharacteristic
379C22×C4⋊C4C22×C3111yescharacteristic
380C22×C4⋊C4C22×C3111yescharacteristic
381C22×C4⋊C4C22×C3111yescharacteristic
382#481—24no—
383C2×#106—24no—
384C2×#106C22×C3111yescharacteristic
385C2×#106C22×C3111yescharacteristic
386C2×#106C22×C3111yescharacteristic
387C2×#106C22×C3111yescharacteristic
388C2×#106C22×C3111yescharacteristic
389C2×#106C22×C3111yescharacteristic
390C2×#102C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×#102C22×C3111yescharacteristic
393C2×#102C22×C3111yescharacteristic
394C2×C22⋊C8C22×C3111yescharacteristic
395C2×C22⋊C8C22×C3111yescharacteristic
396C2×C22⋊C8C22×C3111yescharacteristic
397#396—21no—
398#394—21no—
399#390C22×C3111yescharacteristic
400#389—21no—
401#389C22×C3111yescharacteristic
402#386—21no—
403#385—21no—
404#385—21no—
405#384C22×C3111yescharacteristic
406#380C22×C3111yescharacteristic
407#380C22×C3111yescharacteristic
408#380C22×C3111yescharacteristic
409C4×C4⋊C4C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414#340C22×C3111yescharacteristic
415#340C22×C3111yescharacteristic
416#336C22×C3111yescharacteristic
417#336C22×C3111yescharacteristic
418C2×C31—24no—
419C2×C31—42no—
420C2×C31—161no—
421C2×C31#244311yescharacteristic
422C2×C31C2×#48111yescharacteristic
423C2×C31#309911yescharacteristic
424C2×C31#326511yescharacteristic
425C2×C31D4×SD1611yescharacteristic
426C2×C31#333511yescharacteristic
427C2×C31#334511yescharacteristic
428C22×D4—21no—
429C22×D4—21no—
430C22×D4D4×C3111yescharacteristic
431C22×D4C23×C3111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4C23×C3111yescharacteristic
436C23×C4C23×C3111yescharacteristic
437C22×C8—22no—
438C22×C8—22no—
439C22×C8—22no—
440C22×C8C23×C3111yescharacteristic
441C22×C8C23×C3111yescharacteristic
442C22×C8C23×C3111yescharacteristic
443C22×C8C23×C3111yescharacteristic
444#121—22no—
445#121—22no—
446#121—22no—
447#121—41no—
448#121—44no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—44no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4D4×C3111yescharacteristic
465C2×C4⋊C4C23×C3111yescharacteristic
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C4⋊C4C23×C3111yescharacteristic
471C2×C4⋊C4C23×C3111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4D4×C3111yescharacteristic
480C2×C22⋊C4D4×C3111yescharacteristic
481C2×C42—21no—
482C2×C42C23×C3111yescharacteristic
483#106—22no—
484#106—22no—
485#106—22no—
486#106—22no—
487#106—41no—
488#106D4×C3114yescomplemented
489#102—22no—
490#102—22no—
491#102—22no—
492#102—41no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501C31#2613011yescharacteristic, direct product factor, Sylow
502C24—21no—
503C24C2×D4×C3111yescharacteristic
504C24C2×D4×C3111yescharacteristic
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4SD16×C3114yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×D4×C3111yescharacteristic
547C22×C4C2×D4×C3111yescharacteristic
548C22×C4C2×D4×C3111yescharacteristic
549C22×C4C2×D4×C3111yescharacteristic
550C22×C4#41×C3112yes—
551C22×C4#41×C3112yes—
552C22×C4C24×C3111yescharacteristic
553C2×C8—28no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8C2×D4×C3112yes—
565C2×C8#41×C3112yes—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—81no—
585C4⋊C4C2×D4×C3112yes—
586C4⋊C4C2×D4×C3112yes—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C42—21no—
597C42—21no—
598C42—42no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23C31×#12312yes—
617C23C2×SD16×C3112yes—
618C23C2×SD16×C3112yes—
619C23C31×AGL(1,ℤ/8)12yes—
620C23C22×D4×C3111yescharacteristic
621D4—28no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—84no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4C31×#12312yes—
671C2×C4C2×SD16×C3112yes—
672C2×C4C22×D4×C3111yescharacteristic
673C2×C4C2×#41×C3111yescharacteristic
674C2×C4C2×#41×C3111yescharacteristic
675C2×C4C2×#41×C3111yescharacteristic
676C2×C4C31×H(5,𝔽2)11yescharacteristic
677C2×C4C31×2−1+411yescharacteristic
678C8—22no—
679C8—22no—
680C8—41no—
681C8—41no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22C31×#48114yescomplemented
703C22C2×C31×#12311yescharacteristic
704C22D42×C3111yescharacteristic
705C22C31×#54711yescharacteristic
706C22C22×SD16×C3111yescharacteristic
707C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
708C22C31×#57711yescharacteristic
709C22C31×#57711yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—42no—
716C4—81no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4C31×#52511yescharacteristic
722C4C31×#53911yescharacteristic
723C4C31×#54811yescharacteristic
724C4C31×#55311yescharacteristic
725C2—24no—
726C2—42no—
727C2—161no—
728C2C31×#244311yescharacteristic
729C2C2×C31×#48111yescharacteristic
730C2C31×#309911yescharacteristic
731C2C31×#326511yescharacteristic
732C2D4×SD16×C3111yescharacteristic
733C2C31×#333511yescharacteristic
734C2C31×#334511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2416C2
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×#481C2semidirect
2. C22×C31×#106C2semidirect
4. D4×C4⋊C4×C31C2semidirect
5. C31×#2094C2semidirect
6. C31×#2084C2semidirect
7. C31×#2077C2semidirect
8. C31×#2034C2semidirect
9. C31×#1926C2semidirect
10. C31×#1919C2semidirect
11. C31×#1893C2semidirect
12. C31×#1874C2semidirect
13. C31×#1869C2semidirect
14. C31×#1853C2semidirect
15. C31×#1853C2semidirect
121. C31×#106D4semidirect
231. #26130C31direct (N × H)
315. C2×#481C2×C31semidirect
316. C22×#106C2×C31semidirect
318. D4×C4⋊C4C2×C31semidirect
319. #2094C2×C31semidirect
320. #2084C2×C31semidirect
321. #2077C2×C31semidirect
322. #2034C2×C31semidirect
323. #1926C2×C31semidirect
324. #1919C2×C31semidirect
325. #1893C2×C31semidirect
326. #1874C2×C31semidirect
327. #1869C2×C31semidirect
328. #1853C2×C31semidirect
329. #1853C2×C31semidirect
350. C22×C31#481semidirect
488. #106D4×C31semidirect
501. C31#26130direct (N × H)
702. C22C31×#481semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4812
C22×C31×#1062
C31×#24162
D4×C4⋊C4×C312
C31×#20942
C31×#20842
C31×#20772
C31×#20342
C31×#19262
C31×#19192
C31×#18932
C31×#18742
C31×#18692
C31×#18532
#2613031