Finite Group Databasebeta

← C31×#16893 #21473652

Subgroups — C31×#16893 #21473652

Order 7936.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#386C211yesmaximal, characteristic
2C2×C31×#385C211yesmaximal, characteristic, complemented
3C31×#1445C211yesmaximal, characteristic, complemented
4C31×#1443C211yesmaximal, characteristic, complemented
5C31×#1442C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1439C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic
14C31×#1438C211yesmaximal, characteristic
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C31×#386—24no—
34C31×#385—24no—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C25×C31C2311yescharacteristic
54C25×C31C2311yescharacteristic
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—41no—
58C22×D4×C31—41no—
59C22×D4×C31—41no—
60C22×D4×C31—41no—
61C22×D4×C31Q814yes—
62C23×C4×C31—41no—
63C23×C4×C31—41no—
64C23×C4×C31—41no—
65C23×C4×C31—41no—
66C23×C4×C31—41no—
67C23×C4×C31—41no—
68C23×C4×C31D414yes—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—41no—
87C2×C4⋊C4×C31—41no—
88C2×C4⋊C4×C31—41no—
89C2×C4⋊C4×C31—41no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31—41no—
92C2×C4⋊C4×C31—41no—
93C2×C4⋊C4×C31—41no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—41no—
110C2×C22⋊C4×C31—41no—
111C2×C22⋊C4×C31—41no—
112C2×C22⋊C4×C31—41no—
113C2×C22⋊C4×C31—41no—
114C2×C22⋊C4×C31—41no—
115C2×C22⋊C4×C31—41no—
116C2×C22⋊C4×C31—41no—
117C2×C22⋊C4×C31—41no—
118C2×C22⋊C4×C31—41no—
119C2×C22⋊C4×C31—41no—
120C2×C22⋊C4×C31—41no—
121C2×C22⋊C4×C31—41no—
122C2×C22⋊C4×C31—41no—
123C2×C22⋊C4×C31—41no—
124C2×C22⋊C4×C31—41no—
125C2×C22⋊C4×C31—41no—
126C2×C22⋊C4×C31—41no—
127C31×#95—22no—
128C31×#95—22no—
129C31×#95—22no—
130C31×#95—22no—
131C31×#95—22no—
132C31×#95—22no—
133C31×#95—41no—
134C31×#95—41no—
135C31×#95—41no—
136C31×#95—41no—
137C31×#95—41no—
138C31×#95—41no—
139C31×#95—41no—
140C31×#95—41no—
141C31×#95—41no—
142C31×#95—41no—
143C31×#95—41no—
144C31×#95—41no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31C2×D412yes—
172C24×C31C2×Q812yes—
173C24×C31C2×Q812yes—
174C24×C31#4112yes—
175C24×C31C2411yescharacteristic
176C2×D4×C31—28no—
177C2×D4×C31—44no—
178C2×D4×C31—44no—
179C2×D4×C31—44no—
180C2×D4×C31—44no—
181C2×D4×C31—44no—
182C2×D4×C31—44no—
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—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
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—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—44no—
268C22×C4×C31—44no—
269C22×C4×C31—44no—
270C22×C4×C31—44no—
271C22×C4×C31—44no—
272C22×C4×C31—44no—
273C22×C4×C31—44no—
274C22×C4×C31C2×D412yes—
275C22×C4×C31C2×D412yes—
276C22×C4×C31C2×Q812yes—
277C22×C4×C31#4112yes—
278C22×C4×C31#4112yes—
279C22×C4×C31#4112yes—
280C22×C4×C31#4112yes—
281C4⋊C4×C31—44no—
282C4⋊C4×C31—44no—
283C4⋊C4×C31—44no—
284C4⋊C4×C31—44no—
285C22⋊C4×C31—28no—
286C22⋊C4×C31—44no—
287C22⋊C4×C31—44no—
288C22⋊C4×C31—44no—
289C22⋊C4×C31—44no—
290C22⋊C4×C31—44no—
291C22⋊C4×C31—44no—
292C22⋊C4×C31—44no—
293C22⋊C4×C31—44no—
294C22⋊C4×C31—44no—
295C22⋊C4×C31—44no—
296#16893C3111yesmaximal, characteristic, direct product factor, Sylow
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—22no—
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31—41no—
360C23×C31—41no—
361C23×C31—41no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—41no—
366C23×C31C22⋊Q814yes—
367C23×C31C22×D411yescharacteristic
368C23×C31C22×Q811yescharacteristic
369C23×C31C2×#4111yescharacteristic
370C23×C31C2×#4111yescharacteristic
371C23×C31C2×#4111yescharacteristic
372C23×C31C2×#4111yescharacteristic
373C23×C31C2×#4111yescharacteristic
374C23×C31H(5,𝔽2)11yescharacteristic
375C23×C31H(5,𝔽2)11yescharacteristic
376C23×C31H(5,𝔽2)11yescharacteristic
377C23×C31H(5,𝔽2)11yescharacteristic
378C23×C31H(5,𝔽2)11yescharacteristic
379C23×C31H(5,𝔽2)11yescharacteristic
380C23×C31H(5,𝔽2)11yescharacteristic
381C23×C31H(5,𝔽2)11yescharacteristic
382D4×C31—416no—
383C2×C4×C31—22no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—416no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—41no—
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—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—41no—
472C2×C4×C31—41no—
473C2×C4×C31—41no—
474C2×C4×C31—41no—
475C2×#386C2×C3111yescharacteristic
476C2×#385C2×C3111yescharacteristic, complemented
477#1445C2×C3111yescharacteristic, complemented
478#1443C2×C3111yescharacteristic, complemented
479#1442C2×C3111yescharacteristic, complemented
480#1441C2×C3111yescharacteristic, complemented
481#1439C2×C3111yescharacteristic, complemented
482#1439C2×C3111yescharacteristic, complemented
483#1439C2×C3111yescharacteristic, complemented
484#1439C2×C3111yescharacteristic, complemented
485#1439C2×C3111yescharacteristic, complemented
486#1439C2×C3111yescharacteristic, complemented
487#1438C2×C3111yescharacteristic
488#1438C2×C3111yescharacteristic
489C22⋊#95C2×C3111yescharacteristic, complemented
490C22×C31—24no—
491C22×C31—24no—
492C22×C31—24no—
493C22×C31—42no—
494C22×C31—42no—
495C22×C31—42no—
496C22×C31—42no—
497C22×C31—42no—
498C22×C31—42no—
499C22×C31—42no—
500C22×C31—42no—
501C22×C31—42no—
502C22×C31—42no—
503C22×C31—42no—
504C22×C31—42no—
505C22×C31—42no—
506C22×C31—42no—
507C22×C31—42no—
508C22×C31—42no—
509C22×C31—42no—
510C22×C31—42no—
511C22×C31—42no—
512C22×C31—81no—
513C22×C31—81no—
514C22×C31—81no—
515C22×C31—81no—
516C22×C31—81no—
517C22×C31—81no—
518C22×C31—81no—
519C22×C31—81no—
520C22×C31C2×C22⋊Q811yescharacteristic
521C22×C31#52511yescharacteristic
522C22×C31#53211yescharacteristic
523C22×C31#53411yescharacteristic
524C22×C31#53411yescharacteristic
525C22×C31#53411yescharacteristic
526C22×C31#53511yescharacteristic
527C22×C31#53811yescharacteristic
528C22×C31#53811yescharacteristic
529C22×C31#53811yescharacteristic
530C22×C31#53811yescharacteristic
531C22×C31#53811yescharacteristic
532C22×C31#53811yescharacteristic
533C22×C31#54011yescharacteristic
534C22×C31#54011yescharacteristic
535C22×C31#54011yescharacteristic
536C22×C31#54011yescharacteristic
537C22×C31#54311yescharacteristic
538C22×C31#54311yescharacteristic
539C22×C31#55111yescharacteristic
540C22×C31#55111yescharacteristic
541C22×C31#55111yescharacteristic
542C22×C31#55311yescharacteristic
543C22×C31#55311yescharacteristic
544C22×C31#55311yescharacteristic
545C22×C31#55311yescharacteristic
546C22×C31#55411yescharacteristic
547C22×C31#55411yescharacteristic
548C22×C31#55411yescharacteristic
549C22×C31#55411yescharacteristic
550C22×C31#55911yescharacteristic
551C22×C31#56011yescharacteristic
552C22×C31#56011yescharacteristic
553C22×C31#56011yescharacteristic
554C22×C31H(3,𝔽4)11yescharacteristic
555C4×C31—42no—
556C4×C31—42no—
557C4×C31—42no—
558C4×C31—42no—
559C4×C31—42no—
560C4×C31—42no—
561C4×C31—42no—
562C4×C31—81no—
563C4×C31—81no—
564C4×C31—81no—
565C4×C31—81no—
566C4×C31—81no—
567C4×C31—81no—
568C23×D4C22×C3111yescharacteristic
569C24×C4C22×C3111yescharacteristic
570C22×C4⋊C4C22×C3111yescharacteristic
571C22×C4⋊C4C22×C3111yescharacteristic
572C22×C4⋊C4C22×C3111yescharacteristic
573C22×C4⋊C4C22×C3111yescharacteristic
574C22×C22⋊C4C22×C3111yescharacteristic
575C22×C22⋊C4C22×C3111yescharacteristic
576C22×C22⋊C4C22×C3111yescharacteristic
577C22×C22⋊C4C22×C3111yescharacteristic
578C22×C22⋊C4C22×C3111yescharacteristic
579C22×C22⋊C4C22×C3111yescharacteristic
580C22×C22⋊C4C22×C3111yescharacteristic
581C22×C22⋊C4C22×C3111yescharacteristic
582C22×C22⋊C4C22×C3111yescharacteristic
583C22×C22⋊C4C22×C3111yescharacteristic
584C22×C22⋊C4C22×C3111yescharacteristic
585#386—24no—
586#385—24no—
587C2×#95C22×C3111yescharacteristic
588C2×#95C22×C3111yescharacteristic
589C2×#95C22×C3111yescharacteristic
590C2×#95C22×C3111yescharacteristic
591C2×#95C22×C3111yescharacteristic
592C2×#95C22×C3111yescharacteristic
593C2×#95C22×C3111yescharacteristic
594C2×#95C22×C3111yescharacteristic
595C2×#95C22×C3111yescharacteristic
596C2×#95C22×C3111yescharacteristic
597C2×#95C22×C3111yescharacteristic
598C2×#95C22×C3111yescharacteristic
599C2×#95C22×C3111yescharacteristic
600C2×#95C22×C3111yescharacteristic
601C2×#95C22×C3111yescharacteristic
602C2×#95C22×C3111yescharacteristic
603C2×#95C22×C3111yescharacteristic
604C2×#95C22×C3111yescharacteristic
605C2×C31—44no—
606C2×C31—82no—
607C2×C31#256411yescharacteristic
608C2×C31#257911yescharacteristic
609C2×C31#260211yescharacteristic
610C2×C31#262611yescharacteristic
611C2×C31#263511yescharacteristic
612C2×C31#266111yescharacteristic
613C2×C31#274811yescharacteristic
614C2×C31#274911yescharacteristic
615C2×C31#275311yescharacteristic
616C2×C31#277811yescharacteristic
617C2×C31#278011yescharacteristic
618C2×C31#278011yescharacteristic
619C2×C31#279711yescharacteristic
620C2×C31#280411yescharacteristic
621C2×C31#281211yescharacteristic
622C25C23×C3111yescharacteristic
623C25C23×C3111yescharacteristic
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4Q8×C3114yes—
631C23×C4—41no—
632C23×C4—41no—
633C23×C4—41no—
634C23×C4—41no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4D4×C3114yes—
638C23×C4C23×C3111yescharacteristic
639C23×C4C23×C3111yescharacteristic
640C23×C4C23×C3111yescharacteristic
641C23×C4C23×C3111yescharacteristic
642C23×C4C23×C3111yescharacteristic
643C23×C4C23×C3111yescharacteristic
644C23×C4C23×C3111yescharacteristic
645C23×C4C23×C3111yescharacteristic
646C23×C4C23×C3111yescharacteristic
647C23×C4C23×C3111yescharacteristic
648C23×C4C23×C3111yescharacteristic
649C23×C4C23×C3111yescharacteristic
650C23×C4C23×C3111yescharacteristic
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714C31#1689311yescharacteristic, direct product factor, Sylow
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24C2×D4×C3112yes—
742C24C2×Q8×C3112yes—
743C24C2×Q8×C3112yes—
744C24#41×C3112yes—
745C24C24×C3111yescharacteristic
746C2×D4—28no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4C2×D4×C3112yes—
845C22×C4C2×D4×C3112yes—
846C22×C4C2×Q8×C3112yes—
847C22×C4#41×C3112yes—
848C22×C4#41×C3112yes—
849C22×C4#41×C3112yes—
850C22×C4#41×C3112yes—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C22⋊C4—28no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23C31×C22⋊Q814yes—
936C23C22×D4×C3111yescharacteristic
937C23C22×Q8×C3111yescharacteristic
938C23C2×#41×C3111yescharacteristic
939C23C2×#41×C3111yescharacteristic
940C23C2×#41×C3111yescharacteristic
941C23C2×#41×C3111yescharacteristic
942C23C2×#41×C3111yescharacteristic
943C23C31×H(5,𝔽2)11yescharacteristic
944C23C31×H(5,𝔽2)11yescharacteristic
945C23C31×H(5,𝔽2)11yescharacteristic
946C23C31×H(5,𝔽2)11yescharacteristic
947C23C31×H(5,𝔽2)11yescharacteristic
948C23C31×H(5,𝔽2)11yescharacteristic
949C23C31×H(5,𝔽2)11yescharacteristic
950C23C31×H(5,𝔽2)11yescharacteristic
951D4—416no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—416no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22C2×C31×C22⋊Q811yescharacteristic
1075C22C31×#52511yescharacteristic
1076C22C31×#53211yescharacteristic
1077C22C31×#53411yescharacteristic
1078C22C31×#53411yescharacteristic
1079C22C31×#53411yescharacteristic
1080C22C31×#53511yescharacteristic
1081C22C31×#53811yescharacteristic
1082C22C31×#53811yescharacteristic
1083C22C31×#53811yescharacteristic
1084C22C31×#53811yescharacteristic
1085C22C31×#53811yescharacteristic
1086C22C31×#53811yescharacteristic
1087C22C31×#54011yescharacteristic
1088C22C31×#54011yescharacteristic
1089C22C31×#54011yescharacteristic
1090C22C31×#54011yescharacteristic
1091C22C31×#54311yescharacteristic
1092C22C31×#54311yescharacteristic
1093C22C31×#55111yescharacteristic
1094C22C31×#55111yescharacteristic
1095C22C31×#55111yescharacteristic
1096C22C31×#55311yescharacteristic
1097C22C31×#55311yescharacteristic
1098C22C31×#55311yescharacteristic
1099C22C31×#55311yescharacteristic
1100C22C31×#55411yescharacteristic
1101C22C31×#55411yescharacteristic
1102C22C31×#55411yescharacteristic
1103C22C31×#55411yescharacteristic
1104C22C31×#55911yescharacteristic
1105C22C31×#56011yescharacteristic
1106C22C31×#56011yescharacteristic
1107C22C31×#56011yescharacteristic
1108C22C31×H(3,𝔽4)11yescharacteristic
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C2—44no—
1123C2—82no—
1124C2C31×#256411yescharacteristic
1125C2C31×#257911yescharacteristic
1126C2C31×#260211yescharacteristic
1127C2C31×#262611yescharacteristic
1128C2C31×#263511yescharacteristic
1129C2C31×#266111yescharacteristic
1130C2C31×#274811yescharacteristic
1131C2C31×#274911yescharacteristic
1132C2C31×#275311yescharacteristic
1133C2C31×#277811yescharacteristic
1134C2C31×#278011yescharacteristic
1135C2C31×#278011yescharacteristic
1136C2C31×#279711yescharacteristic
1137C2C31×#280411yescharacteristic
1138C2C31×#281211yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#385C2semidirect
3. C31×#1445C2semidirect
4. C31×#1443C2semidirect
5. C31×#1442C2semidirect
6. C31×#1441C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
15. C31×C22⋊#95C2semidirect
296. #16893C31direct (N × H)
476. C2×#385C2×C31semidirect
477. #1445C2×C31semidirect
478. #1443C2×C31semidirect
479. #1442C2×C31semidirect
480. #1441C2×C31semidirect
481. #1439C2×C31semidirect
482. #1439C2×C31semidirect
483. #1439C2×C31semidirect
484. #1439C2×C31semidirect
485. #1439C2×C31semidirect
486. #1439C2×C31semidirect
489. C22⋊#95C2×C31semidirect
714. C31#16893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3862
C2×C31×#3852
C31×#14452
C31×#14432
C31×#14422
C31×#14412
C31×#14392
C31×#14382
C31×C22⋊#952
#1689331