Finite Group Databasebeta

← C31×#24136 #21480895

Subgroups — C31×#24136 #21480895

Order 7936.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic, complemented
2C2×C31×#478C211yesmaximal, characteristic, complemented
3C2×C31×#442C211yesmaximal, characteristic, complemented
4C31×#2537C211yesmaximal, characteristic, complemented
5C31×#2034C211yesmaximal, characteristic, complemented
6C31×#2033C211yesmaximal, characteristic, complemented
7C31×#1999C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1992C211yesmaximal, characteristic, complemented
10C31×#1955C211yesmaximal, characteristic, complemented
11C31×#1875C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1853C211yesmaximal, characteristic, complemented
15C31×#1802C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C31×#553—24no—
18C31×#553—24no—
19C2×C31×#126—21no—
20C2×C31×#125C2211yescharacteristic
21C2×C31×#123—21no—
22C2×C31×#121—21no—
23C2×C31×#121—21no—
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C31×#478—24no—
35C31×#442—24no—
36C2×C31×#107C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×#106C2211yescharacteristic
39C2×C31×C4⋊C8C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×#97C2211yescharacteristic
51C31×#394—21no—
52C31×#394—21no—
53C31×#384C2211yescharacteristic
54C31×#380—21no—
55C31×#380C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31D411yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×#126—28no—
83C31×#125—22no—
84C31×#125D414yescomplemented
85C31×#123—28no—
86C31×#121—28no—
87C31×#121—22no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—22no—
93C31×#121—41no—
94C31×#121—41no—
95C31×#121—44no—
96C4×D4×C31—28no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31D414yescomplemented
103C31×#117—22no—
104C31×#117—22no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31D411yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
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
132C31×#107—22no—
133C31×#106—22no—
134C31×#106—22no—
135C31×C4⋊C8—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—41no—
141C31×#102—41no—
142C31×C22⋊C8—22no—
143C31×C22⋊C8—22no—
144C31×C22⋊C8—41no—
145C31×C22⋊C8—41no—
146C31×#97—22no—
147C31×#95—21no—
148C31×#95—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152C24×C31C2×D411yescharacteristic
153C2×D4×C31—24no—
154C2×D4×C31—22no—
155C2×D4×C31—24no—
156C2×D4×C31—22no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—41no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—42no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31—81no—
177C2×D4×C31—81no—
178C2×D4×C31C2×D412yes—
179C2×D4×C31#4112yes—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—24no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—24no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—42no—
201C22×C4×C31—42no—
202C22×C4×C31—42no—
203C22×C4×C31—81no—
204C22×C4×C31—81no—
205C22×C4×C31—81no—
206C22×C4×C31—81no—
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2411yescharacteristic
212D8×C31—28no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31#4112yes—
225C4⋊C4×C31—24no—
226C4⋊C4×C31—24no—
227C4⋊C4×C31—24no—
228C4⋊C4×C31—22no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—42no—
239C4⋊C4×C31—81no—
240C4⋊C4×C31C2×D412yes—
241C4⋊C4×C31C2×D412yes—
242C4⋊C4×C31C2×D412yes—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—24no—
245C22⋊C4×C31—24no—
246C22⋊C4×C31—24no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
254C42×C31—24no—
255C42×C31C2×D412yes—
256C42×C31C2×D412yes—
257#24136C3111yesmaximal, characteristic, direct product factor, Sylow
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—41no—
274C23×C31—41no—
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×C31AGL(1,ℤ/8)12yes—
286C23×C31C22×D411yescharacteristic
287D4×C31—22no—
288D4×C31—22no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—44no—
292D4×C31—48no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—84no—
298D4×C31—84no—
299D4×C31—84no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—21no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—84no—
337C2×C4×C31—84no—
338C2×C4×C31—84no—
339C2×C4×C31#12012yes—
340C2×C4×C31#12012yes—
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C2×#4111yescharacteristic
344C2×C4×C31C2×#4111yescharacteristic
345C2×C4×C31H(5,𝔽2)11yescharacteristic
346C2×C4×C312−1+411yescharacteristic
347C8×C31—22no—
348C8×C31—41no—
349C8×C31—41no—
350C8×C31—41no—
351C2×#553C2×C3111yescharacteristic, complemented
352C2×#478C2×C3111yescharacteristic, complemented
353C2×#442C2×C3111yescharacteristic, complemented
354#2537C2×C3111yescharacteristic, complemented
355#2034C2×C3111yescharacteristic, complemented
356#2033C2×C3111yescharacteristic, complemented
357#1999C2×C3111yescharacteristic, complemented
358#1999C2×C3111yescharacteristic, complemented
359#1992C2×C3111yescharacteristic, complemented
360#1955C2×C3111yescharacteristic, complemented
361#1875C2×C3111yescharacteristic, complemented
362#1874C2×C3111yescharacteristic, complemented
363#1854C2×C3111yescharacteristic, complemented
364#1853C2×C3111yescharacteristic, complemented
365#1802C2×C3111yescharacteristic, complemented
366C22×C31—22no—
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—41no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—41no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—42no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31C2×#12011yescharacteristic
395C22×C31#54611yescharacteristic
396C22×C31#54711yescharacteristic
397C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C31#57511yescharacteristic
399C22×C31#57611yescharacteristic
400C22×C31#57711yescharacteristic
401C4×C31—22no—
402C4×C31—22no—
403C4×C31—41no—
404C4×C31—41no—
405C4×C31—42no—
406C4×C31—42no—
407C4×C31—42no—
408C4×C31—81no—
409C4×C31—81no—
410C4×C31—81no—
411C4×C31#52511yescharacteristic
412C4×C31#53711yescharacteristic
413C4×C31#54811yescharacteristic
414C4×C31#55011yescharacteristic
415C22×D8C22×C3111yescharacteristic
416#553—24no—
417#553—24no—
418C2×#126—21no—
419C2×#125C22×C3111yescharacteristic
420C2×#123—21no—
421C2×#121—21no—
422C2×#121—21no—
423C2×#121C22×C3111yescharacteristic
424C2×#121C22×C3111yescharacteristic
425C2×#121C22×C3111yescharacteristic
426C2×#121C22×C3111yescharacteristic
427C2×C4×D4—21no—
428C2×C4×D4C22×C3111yescharacteristic
429C2×C4×D4C22×C3111yescharacteristic
430C2×C4×D4C22×C3111yescharacteristic
431C2×#117C22×C3111yescharacteristic
432C22×C4⋊C4C22×C3111yescharacteristic
433#478—24no—
434#442—24no—
435C2×#107C22×C3111yescharacteristic
436C2×#106C22×C3111yescharacteristic
437C2×#106C22×C3111yescharacteristic
438C2×C4⋊C8C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×#102C22×C3111yescharacteristic
444C2×#102C22×C3111yescharacteristic
445C2×C22⋊C8C22×C3111yescharacteristic
446C2×C22⋊C8C22×C3111yescharacteristic
447C2×C22⋊C8C22×C3111yescharacteristic
448C2×C22⋊C8C22×C3111yescharacteristic
449C2×#97C22×C3111yescharacteristic
450#394—21no—
451#394—21no—
452#384C22×C3111yescharacteristic
453#380—21no—
454#380C22×C3111yescharacteristic
455#380C22×C3111yescharacteristic
456#340C22×C3111yescharacteristic
457#340C22×C3111yescharacteristic
458#340C22×C3111yescharacteristic
459#340C22×C3111yescharacteristic
460#340C22×C3111yescharacteristic
461#340C22×C3111yescharacteristic
462C2×C31—42no—
463C2×C31—81no—
464C2×C31—82no—
465C2×C31—82no—
466C2×C31#240711yescharacteristic
467C2×C31#300611yescharacteristic
468C2×C31#301211yescharacteristic
469C2×C31#330711yescharacteristic
470C2×C31#331811yescharacteristic
471C2×C31#334511yescharacteristic
472C2×C31#334711yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4D4×C3111yescharacteristic
478C22×D4C23×C3111yescharacteristic
479C22×D4C23×C3111yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4C23×C3111yescharacteristic
484C23×C4C23×C3111yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C22×C8C23×C3111yescharacteristic
489C22×C8C23×C3111yescharacteristic
490C22×C8C23×C3111yescharacteristic
491C22×C8C23×C3111yescharacteristic
492#126—28no—
493#125—22no—
494#125D4×C3114yescomplemented
495#123—28no—
496#121—28no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—41no—
504#121—41no—
505#121—44no—
506C4×D4—28no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4D4×C3114yescomplemented
513#117—22no—
514#117—22no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4D4×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C4⋊C4C23×C3111yescharacteristic
527C2×C4⋊C4C23×C3111yescharacteristic
528C2×C4⋊C4C23×C3111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4D4×C3111yescharacteristic
539C2×C22⋊C4D4×C3111yescharacteristic
540C2×C42—21no—
541C2×C42C23×C3111yescharacteristic
542#107—22no—
543#106—22no—
544#106—22no—
545C4⋊C8—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551#102—41no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—41no—
555C22⋊C8—41no—
556#97—22no—
557#95—21no—
558#95—21no—
559C31#2413611yescharacteristic, direct product factor, Sylow
560C24—21no—
561C24—21no—
562C24C2×D4×C3111yescharacteristic
563C24C2×D4×C3111yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C3112yes—
590C2×D4#41×C3112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C2×D4×C3111yescharacteristic
621C22×C4C2×D4×C3111yescharacteristic
622C22×C4C24×C3111yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8#41×C3112yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C3112yes—
652C4⋊C4C2×D4×C3112yes—
653C4⋊C4C2×D4×C3112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C3112yes—
667C42C2×D4×C3112yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23C31×AGL(1,ℤ/8)12yes—
696C23C22×D4×C3111yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4C31×#12012yes—
750C2×C4C31×#12012yes—
751C2×C4C22×D4×C3111yescharacteristic
752C2×C4C22×D4×C3111yescharacteristic
753C2×C4C2×#41×C3111yescharacteristic
754C2×C4C2×#41×C3111yescharacteristic
755C2×C4C31×H(5,𝔽2)11yescharacteristic
756C2×C4C31×2−1+411yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×C31×#12011yescharacteristic
790C22C31×#54611yescharacteristic
791C22C31×#54711yescharacteristic
792C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
793C22C31×#57511yescharacteristic
794C22C31×#57611yescharacteristic
795C22C31×#57711yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4C31×#52511yescharacteristic
807C4C31×#53711yescharacteristic
808C4C31×#54811yescharacteristic
809C4C31×#55011yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C31×#240711yescharacteristic
815C2C31×#300611yescharacteristic
816C2C31×#301211yescharacteristic
817C2C31×#330711yescharacteristic
818C2C31×#331811yescharacteristic
819C2C31×#334511yescharacteristic
820C2C31×#334711yescharacteristic
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×#553C2semidirect
2. C2×C31×#478C2semidirect
3. C2×C31×#442C2semidirect
4. C31×#2537C2semidirect
5. C31×#2034C2semidirect
6. C31×#2033C2semidirect
7. C31×#1999C2semidirect
8. C31×#1999C2semidirect
9. C31×#1992C2semidirect
10. C31×#1955C2semidirect
11. C31×#1875C2semidirect
12. C31×#1874C2semidirect
13. C31×#1854C2semidirect
14. C31×#1853C2semidirect
15. C31×#1802C2semidirect
84. C31×#125D4semidirect
102. C4×D4×C31D4semidirect
257. #24136C31direct (N × H)
351. C2×#553C2×C31semidirect
352. C2×#478C2×C31semidirect
353. C2×#442C2×C31semidirect
354. #2537C2×C31semidirect
355. #2034C2×C31semidirect
356. #2033C2×C31semidirect
357. #1999C2×C31semidirect
358. #1999C2×C31semidirect
359. #1992C2×C31semidirect
360. #1955C2×C31semidirect
361. #1875C2×C31semidirect
362. #1874C2×C31semidirect
363. #1854C2×C31semidirect
364. #1853C2×C31semidirect
365. #1802C2×C31semidirect
494. #125D4×C31semidirect
512. C4×D4D4×C31semidirect
559. C31#24136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5532
C2×C31×#4782
C2×C31×#4422
C31×#25372
C31×#20342
C31×#20332
C31×#19992
C31×#19922
C31×#19552
C31×#18752
C31×#18742
C31×#18542
C31×#18532
C31×#18022
#2413631