Finite Group Databasebeta

← C31×#32709 #21489468

Subgroups — C31×#32709 #21489468

Order 7936.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2848C211yesmaximal, characteristic, complemented
2C31×#2847C211yesmaximal, characteristic
3C31×#2077C211yesmaximal, characteristic, complemented
4C31×#2076C211yesmaximal, characteristic, complemented
5C31×#2075C211yesmaximal, characteristic, complemented
6C31×#2036C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#2034C211yesmaximal, characteristic, complemented
10C31×#2033C211yesmaximal, characteristic, complemented
11C31×#2033C211yesmaximal, characteristic, complemented
12C31×#2000C211yesmaximal, characteristic, complemented
13C31×#2000C211yesmaximal, characteristic, complemented
14C31×#2000C211yesmaximal, characteristic, complemented
15C31×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic, complemented
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C31×#121C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#120—21no—
25C2×C31×#107C2211yescharacteristic, complemented
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×#103C2211yescharacteristic, complemented
29C2×C31×#103C2211yescharacteristic, complemented
30C2×C31×#103C2211yescharacteristic, complemented
31C2×C31×#102C2211yescharacteristic, complemented
32C2×C31×#102C2211yescharacteristic, complemented
33C2×C31×#102C2211yescharacteristic, complemented
34C2×C31×C22⋊C8C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C31×#386—21no—
41C31×#386—21no—
42C31×#386—21no—
43C31×#385—21no—
44C31×#385—21no—
45C31×#385—21no—
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C31×#380C2211yescharacteristic
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#379—21no—
53C31×#340C2211yescharacteristic, complemented
54C31×#340C2211yescharacteristic, complemented
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C25×C31D411yescharacteristic
60C22×Q8×C31C2311yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—41no—
66C23×C4×C31—41no—
67C23×C4×C31—41no—
68C23×C4×C31—41no—
69C23×C4×C31—41no—
70C23×C4×C31—41no—
71C23×C4×C31D411yescharacteristic
72C23×C4×C31D411yescharacteristic
73C23×C4×C31D411yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C2×SD16×C31—41no—
78C2×SD16×C31—41no—
79C2×SD16×C31—41no—
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C31×C22⋊Q8—41no—
85C31×C22⋊Q8—41no—
86C31×C22⋊Q8—41no—
87C31×C22⋊Q8—41no—
88C31×C22⋊Q8—41no—
89C31×C22⋊Q8—41no—
90C31×#121—41no—
91C31×#121—41no—
92C31×#121—41no—
93C31×#121—41no—
94C31×#121—41no—
95C31×#121—41no—
96C31×#120—44no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C31×#107—41no—
119C31×#107—41no—
120C31×#106—41no—
121C31×#103—41no—
122C31×#103—41no—
123C31×#103—41no—
124C31×#102—41no—
125C31×#102—41no—
126C31×#102—41no—
127C31×C22⋊C8—41no—
128C31×C22⋊C8—41no—
129C31×C22⋊C8—41no—
130C31×C22⋊C8—41no—
131C31×C22⋊C8—41no—
132C31×C22⋊C8—41no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—21no—
143C24×C31—41no—
144C24×C31—41no—
145C24×C31—41no—
146C24×C31—41no—
147C24×C31C2×D411yescharacteristic
148C24×C31C2×D411yescharacteristic
149C24×C31C2×D411yescharacteristic
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
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—41no—
197C22×C4×C31—41no—
198C22×C4×C31—41no—
199C22×C4×C31—41no—
200C22×C4×C31—41no—
201C22×C4×C31—41no—
202C22×C4×C31—41no—
203C22×C4×C31—41no—
204C22×C4×C31—41no—
205C22×C4×C31—44no—
206C22×C4×C31—44no—
207C22×C4×C31—44no—
208C22×C4×C31—44no—
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2411yescharacteristic
213SD16×C31—44no—
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—21no—
225C2×C8×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
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—42no—
240C4⋊C4×C31—42no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253#32709C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—44no—
273C23×C31—44no—
274C23×C31—44no—
275C23×C31—44no—
276C23×C31—44no—
277C23×C31—44no—
278C23×C31—44no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31#13512yes—
287C23×C31AGL(1,ℤ/8)12yes—
288C23×C31#13712yes—
289C23×C31C22×D411yescharacteristic
290Q8×C31—41no—
291Q8×C31—41no—
292Q8×C31—41no—
293Q8×C31—41no—
294D4×C31—41no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—41no—
298D4×C31—84no—
299D4×C31—84no—
300D4×C31—84no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—44no—
311C2×C4×C31—44no—
312C2×C4×C31—44no—
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—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31H(5,𝔽2)11yescharacteristic
347C2×C4×C31H(5,𝔽2)11yescharacteristic
348C2×C4×C31H(5,𝔽2)11yescharacteristic
349C2×C4×C31H(5,𝔽2)11yescharacteristic
350C2×C4×C31H(5,𝔽2)11yescharacteristic
351C2×C4×C31H(5,𝔽2)11yescharacteristic
352C8×C31—41no—
353C8×C31—41no—
354C8×C31—41no—
355C8×C31—41no—
356#2848C2×C3111yescharacteristic, complemented
357#2847C2×C3111yescharacteristic
358#2077C2×C3111yescharacteristic, complemented
359#2076C2×C3111yescharacteristic, complemented
360#2075C2×C3111yescharacteristic, complemented
361#2036C2×C3111yescharacteristic, complemented
362#2036C2×C3111yescharacteristic, complemented
363#2035C2×C3111yescharacteristic, complemented
364#2034C2×C3111yescharacteristic, complemented
365#2033C2×C3111yescharacteristic, complemented
366#2033C2×C3111yescharacteristic, complemented
367#2000C2×C3111yescharacteristic, complemented
368#2000C2×C3111yescharacteristic, complemented
369#2000C2×C3111yescharacteristic, complemented
370#1779C2×C3111yescharacteristic, complemented
371C22×C31—22no—
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—22no—
378C22×C31—22no—
379C22×C31—22no—
380C22×C31—416no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31#53411yescharacteristic
401C22×C31#53411yescharacteristic
402C22×C31#53411yescharacteristic
403C22×C31C2×#13511yescharacteristic
404C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C31C2×#13711yescharacteristic
406C22×C31#57511yescharacteristic
407C4×C31—41no—
408C4×C31—41no—
409C4×C31—41no—
410C4×C31—81no—
411C4×C31—81no—
412C4×C31—81no—
413C4×C31—81no—
414C4×C31—81no—
415C4×C31—81no—
416C4×C31—81no—
417C4×C31#56011yescharacteristic
418C4×C31#56011yescharacteristic
419C4×C31#56011yescharacteristic
420C4×C31H(3,𝔽4)11yescharacteristic
421C24×C4C22×C3111yescharacteristic
422C22×SD16C22×C3111yescharacteristic, complemented
423C2×C22⋊Q8C22×C3111yescharacteristic
424C2×C22⋊Q8C22×C3111yescharacteristic
425C2×C22⋊Q8C22×C3111yescharacteristic
426C2×#121C22×C3111yescharacteristic
427C2×#121C22×C3111yescharacteristic
428C2×#121C22×C3111yescharacteristic
429C2×#120—21no—
430C2×#107C22×C3111yescharacteristic, complemented
431C2×#107C22×C3111yescharacteristic, complemented
432C2×#106C22×C3111yescharacteristic, complemented
433C2×#103C22×C3111yescharacteristic, complemented
434C2×#103C22×C3111yescharacteristic, complemented
435C2×#103C22×C3111yescharacteristic, complemented
436C2×#102C22×C3111yescharacteristic, complemented
437C2×#102C22×C3111yescharacteristic, complemented
438C2×#102C22×C3111yescharacteristic, complemented
439C2×C22⋊C8C22×C3111yescharacteristic
440C2×C22⋊C8C22×C3111yescharacteristic
441C2×C22⋊C8C22×C3111yescharacteristic
442C2×C22⋊C8C22×C3111yescharacteristic
443C2×C22⋊C8C22×C3111yescharacteristic
444C2×C22⋊C8C22×C3111yescharacteristic
445#386—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#380C22×C3111yescharacteristic
452#380C22×C3111yescharacteristic
453#380C22×C3111yescharacteristic
454#380C22×C3111yescharacteristic
455#380C22×C3111yescharacteristic
456#380C22×C3111yescharacteristic
457#379—21no—
458#340C22×C3111yescharacteristic, complemented
459#340C22×C3111yescharacteristic, complemented
460#340C22×C3111yescharacteristic, complemented
461#340C22×C3111yescharacteristic, complemented
462#340C22×C3111yescharacteristic, complemented
463#340C22×C3111yescharacteristic, complemented
464C2×C31—42no—
465C2×C31—42no—
466C2×C31—42no—
467C2×C31—161no—
468C2×C31#281211yescharacteristic
469C2×C31#318811yescharacteristic
470C2×C31#319011yescharacteristic
471C2×C31#319111yescharacteristic
472C2×C31#319311yescharacteristic
473C2×C31#319411yescharacteristic
474C2×C31#319611yescharacteristic
475C25D4×C3111yescharacteristic
476C22×Q8C23×C3111yescharacteristic
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4C23×C3111yescharacteristic
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4D4×C3111yescharacteristic
488C23×C4D4×C3111yescharacteristic
489C23×C4D4×C3111yescharacteristic
490C23×C4C23×C3111yescharacteristic
491C23×C4C23×C3111yescharacteristic
492C23×C4C23×C3111yescharacteristic
493C2×SD16—41no—
494C2×SD16—41no—
495C2×SD16—41no—
496C22×C8C23×C3111yescharacteristic
497C22×C8C23×C3111yescharacteristic
498C22×C8C23×C3111yescharacteristic
499C22×C8C23×C3111yescharacteristic
500C22⋊Q8—41no—
501C22⋊Q8—41no—
502C22⋊Q8—41no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506#121—41no—
507#121—41no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#120—44no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C3111yescharacteristic
517C2×C4⋊C4C23×C3111yescharacteristic
518C2×C4⋊C4C23×C3111yescharacteristic
519C2×C4⋊C4C23×C3111yescharacteristic
520C2×C4⋊C4C23×C3111yescharacteristic
521C2×C4⋊C4C23×C3111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534#107—41no—
535#107—41no—
536#106—41no—
537#103—41no—
538#103—41no—
539#103—41no—
540#102—41no—
541#102—41no—
542#102—41no—
543C22⋊C8—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555C31#3270911yescharacteristic, direct product factor, Sylow
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24C2×D4×C3111yescharacteristic
565C24C2×D4×C3111yescharacteristic
566C24C2×D4×C3111yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
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—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×D4×C3111yescharacteristic
627C22×C4C2×D4×C3111yescharacteristic
628C22×C4C2×D4×C3111yescharacteristic
629C22×C4C24×C3111yescharacteristic
630SD16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
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⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23C31×#13512yes—
703C23C31×AGL(1,ℤ/8)12yes—
704C23C31×#13712yes—
705C23C22×D4×C3111yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
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—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4C31×H(5,𝔽2)11yescharacteristic
763C2×C4C31×H(5,𝔽2)11yescharacteristic
764C2×C4C31×H(5,𝔽2)11yescharacteristic
765C2×C4C31×H(5,𝔽2)11yescharacteristic
766C2×C4C31×H(5,𝔽2)11yescharacteristic
767C2×C4C31×H(5,𝔽2)11yescharacteristic
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C31×#53411yescharacteristic
802C22C31×#53411yescharacteristic
803C22C31×#53411yescharacteristic
804C22C2×C31×#13511yescharacteristic
805C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
806C22C2×C31×#13711yescharacteristic
807C22C31×#57511yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C31×#56011yescharacteristic
819C4C31×#56011yescharacteristic
820C4C31×#56011yescharacteristic
821C4C31×H(3,𝔽4)11yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2C31×#281211yescharacteristic
827C2C31×#318811yescharacteristic
828C2C31×#319011yescharacteristic
829C2C31×#319111yescharacteristic
830C2C31×#319311yescharacteristic
831C2C31×#319411yescharacteristic
832C2C31×#319611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2848C2semidirect
3. C31×#2077C2semidirect
4. C31×#2076C2semidirect
5. C31×#2075C2semidirect
6. C31×#2036C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
9. C31×#2034C2semidirect
10. C31×#2033C2semidirect
11. C31×#2033C2semidirect
12. C31×#2000C2semidirect
13. C31×#2000C2semidirect
14. C31×#2000C2semidirect
15. C31×#1779C2semidirect
17. C22×SD16×C31C22semidirect
25. C2×C31×#107C22semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×#103C22semidirect
29. C2×C31×#103C22semidirect
30. C2×C31×#103C22semidirect
31. C2×C31×#102C22semidirect
32. C2×C31×#102C22semidirect
33. C2×C31×#102C22semidirect
53. C31×#340C22semidirect
54. C31×#340C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
253. #32709C31direct (N × H)
356. #2848C2×C31semidirect
358. #2077C2×C31semidirect
359. #2076C2×C31semidirect
360. #2075C2×C31semidirect
361. #2036C2×C31semidirect
362. #2036C2×C31semidirect
363. #2035C2×C31semidirect
364. #2034C2×C31semidirect
365. #2033C2×C31semidirect
366. #2033C2×C31semidirect
367. #2000C2×C31semidirect
368. #2000C2×C31semidirect
369. #2000C2×C31semidirect
370. #1779C2×C31semidirect
422. C22×SD16C22×C31semidirect
430. C2×#107C22×C31semidirect
431. C2×#107C22×C31semidirect
432. C2×#106C22×C31semidirect
433. C2×#103C22×C31semidirect
434. C2×#103C22×C31semidirect
435. C2×#103C22×C31semidirect
436. C2×#102C22×C31semidirect
437. C2×#102C22×C31semidirect
438. C2×#102C22×C31semidirect
458. #340C22×C31semidirect
459. #340C22×C31semidirect
460. #340C22×C31semidirect
461. #340C22×C31semidirect
462. #340C22×C31semidirect
463. #340C22×C31semidirect
555. C31#32709direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28482
C31×#28472
C31×#20772
C31×#20762
C31×#20752
C31×#20362
C31×#20352
C31×#20342
C31×#20332
C31×#20002
C31×#17792
#3270931