Finite Group Databasebeta

← C31×#14738 #21471497

Subgroups — C31×#14738 #21471497

Order 7936.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C211yesmaximal, characteristic, complemented
2C2×C31×#385C211yesmaximal, characteristic
3C2×C31×#385C211yesmaximal, characteristic
4C22×C31×#95C211yesmaximal, characteristic
5C31×#1445C211yesmaximal, characteristic, complemented
6C31×#1443C211yesmaximal, characteristic, complemented
7C31×#1443C211yesmaximal, characteristic, complemented
8C31×#1442C211yesmaximal, characteristic, complemented
9C31×#1442C211yesmaximal, characteristic, complemented
10C31×#1442C211yesmaximal, characteristic, complemented
11C31×#1441C211yesmaximal, characteristic, complemented
12C31×C22⋊#95C211yesmaximal, characteristic
13C31×C22⋊#95C211yesmaximal, characteristic
14C31×C22⋊#95C211yesmaximal, characteristic
15C31×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C31×#400—24no—
28C31×#385—24no—
29C31×#385—24no—
30C2×C31×#95—24no—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
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
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C25×C31C2311yescharacteristic
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—22no—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—22no—
71C23×C4×C31—41no—
72C23×C4×C31—41no—
73C23×C4×C31—41no—
74C23×C4×C31—41no—
75C23×C4×C31—41no—
76C23×C4×C31—41no—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—41no—
100C2×C4⋊C4×C31—41no—
101C2×C4⋊C4×C31—41no—
102C2×C4⋊C4×C31—41no—
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—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31D414yes—
114C2×C22⋊C4×C31Q814yes—
115C31×#95—22no—
116C31×#95—22no—
117C31×#95—22no—
118C31×#95—22no—
119C31×#95—22no—
120C31×#95—22no—
121C31×#95—22no—
122C31×#95—22no—
123C31×#95—22no—
124C31×#95—22no—
125C31×#95—22no—
126C31×#95—22no—
127C31×#95—22no—
128C31×#95—22no—
129C31×#95—22no—
130C31×#95—41no—
131C31×#95—41no—
132C31×#95—41no—
133C31×#95—41no—
134C31×#95—41no—
135C31×#95—41no—
136C31×#95—41no—
137C31×#95—41no—
138C31×#95D414yes—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—21no—
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31C2×D412yes—
148C24×C31C2×Q812yes—
149C24×C31#4112yes—
150C24×C31#4112yes—
151C24×C31#4112yes—
152C24×C31#4112yes—
153C24×C31#4112yes—
154C24×C31C2411yescharacteristic
155C22×C4×C31—28no—
156C22×C4×C31—28no—
157C22×C4×C31—28no—
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—21no—
170C22×C4×C31—21no—
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—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—44no—
247C22×C4×C31—44no—
248C22×C4×C31—44no—
249C22×C4×C31—44no—
250C22×C4×C31—44no—
251C22×C4×C31—44no—
252C22×C4×C31—44no—
253C22×C4×C31—44no—
254C22×C4×C31—44no—
255C22×C4×C31—44no—
256C22×C4×C31—44no—
257C22×C4×C31—44no—
258C22×C4×C31—44no—
259C22×C4×C31—44no—
260C22×C4×C31—44no—
261C22×C4×C31—44no—
262C22×C4×C31—44no—
263C22×C4×C31—44no—
264C22×C4×C31C2×D412yes—
265C22×C4×C31C2×D412yes—
266C22×C4×C31C2×D412yes—
267C22×C4×C31C2×D412yes—
268C22×C4×C31C2×D412yes—
269C22×C4×C31C2×Q812yes—
270C22×C4×C31C2×Q812yes—
271C22×C4×C31#4112yes—
272C22×C4×C31#4112yes—
273C22×C4×C31#4112yes—
274C4⋊C4×C31—44no—
275C4⋊C4×C31—44no—
276C4⋊C4×C31—44no—
277C4⋊C4×C31—44no—
278C22⋊C4×C31—28no—
279C22⋊C4×C31—28no—
280C22⋊C4×C31—44no—
281C22⋊C4×C31—44no—
282#14738C3111yesmaximal, characteristic, direct product factor, Sylow
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—22no—
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—22no—
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×C31C22⋊Q814yes—
312C23×C31#12314yes—
313C23×C31#12414yes—
314C23×C31#12514yes—
315C23×C31#12514yes—
316C23×C31#12614yes—
317C23×C31#12614yes—
318C23×C31C22×D411yescharacteristic
319C23×C31C22×D411yescharacteristic
320C23×C31C22×Q811yescharacteristic
321C23×C31C2×#4111yescharacteristic
322C23×C31C2×#4111yescharacteristic
323C23×C31C2×#4111yescharacteristic
324C23×C31C2×#4111yescharacteristic
325C23×C31C2×#4111yescharacteristic
326C23×C31C2×#4111yescharacteristic
327C23×C31C2×#4111yescharacteristic
328C23×C31C2×#4111yescharacteristic
329C23×C31H(5,𝔽2)11yescharacteristic
330C23×C31H(5,𝔽2)11yescharacteristic
331C23×C31H(5,𝔽2)11yescharacteristic
332C23×C312−1+411yescharacteristic
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—416no—
364C2×C4×C31—416no—
365C2×C4×C31—416no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
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×#400C2×C3111yescharacteristic, complemented
435C2×#385C2×C3111yescharacteristic
436C2×#385C2×C3111yescharacteristic
437C22×#95C2×C3111yescharacteristic
438#1445C2×C3111yescharacteristic, complemented
439#1443C2×C3111yescharacteristic, complemented
440#1443C2×C3111yescharacteristic, complemented
441#1442C2×C3111yescharacteristic, complemented
442#1442C2×C3111yescharacteristic, complemented
443#1442C2×C3111yescharacteristic, complemented
444#1441C2×C3111yescharacteristic, complemented
445C22⋊#95C2×C3111yescharacteristic
446C22⋊#95C2×C3111yescharacteristic
447C22⋊#95C2×C3111yescharacteristic
448C22⋊#95C2×C3111yescharacteristic
449C22×C31—24no—
450C22×C31—24no—
451C22×C31—24no—
452C22×C31—24no—
453C22×C31—24no—
454C22×C31—24no—
455C22×C31—24no—
456C22×C31—24no—
457C22×C31—24no—
458C22×C31—24no—
459C22×C31—24no—
460C22×C31—24no—
461C22×C31—24no—
462C22×C31—24no—
463C22×C31#40018yescomplemented
464C22×C31C2×C22⋊Q811yescharacteristic
465C22×C31C2×#12311yescharacteristic
466C22×C31#52511yescharacteristic
467C22×C31#52511yescharacteristic
468C22×C31#52511yescharacteristic
469C22×C31C2×#12411yescharacteristic
470C22×C31C2×#12511yescharacteristic
471C22×C31C2×#12511yescharacteristic
472C22×C31C2×#12611yescharacteristic
473C22×C31C2×#12611yescharacteristic
474C22×C31#52911yescharacteristic
475C22×C31#52911yescharacteristic
476C22×C31#52911yescharacteristic
477C22×C31#53811yescharacteristic
478C22×C31#53811yescharacteristic
479C22×C31#53811yescharacteristic
480C22×C31#53911yescharacteristic
481C22×C31#53911yescharacteristic
482C22×C31#53911yescharacteristic
483C22×C31D4211yescharacteristic
484C22×C31#54611yescharacteristic
485C22×C31#54611yescharacteristic
486C22×C31#54611yescharacteristic
487C22×C31#54611yescharacteristic
488C22×C31#54711yescharacteristic
489C22×C31D4×Q811yescharacteristic
490C22×C31#55111yescharacteristic
491C22×C31#55111yescharacteristic
492C22×C31#55111yescharacteristic
493C22×C31#55111yescharacteristic
494C22×C31#55211yescharacteristic
495C22×C31#55211yescharacteristic
496C22×C31#55411yescharacteristic
497C22×C31#55411yescharacteristic
498C22×C31#55411yescharacteristic
499C4×C31—42no—
500C4×C31—42no—
501C4×C31—42no—
502C4×C31—42no—
503C4×C31—42no—
504C4×C31—42no—
505C4×C31—42no—
506C4×C31—42no—
507C4×C31—42no—
508C4×C31—42no—
509C4×C31—81no—
510C4×C31—81no—
511C4×C31—81no—
512C4×C31—81no—
513C24×C4C22×C3111yescharacteristic
514C24×C4C22×C3111yescharacteristic
515C24×C4C22×C3111yescharacteristic
516C22×C4⋊C4C22×C3111yescharacteristic
517C22×C4⋊C4C22×C3111yescharacteristic
518C22×C4⋊C4C22×C3111yescharacteristic
519C22×C4⋊C4C22×C3111yescharacteristic
520C22×C22⋊C4C22×C3111yescharacteristic
521C22×C22⋊C4C22×C3111yescharacteristic
522C22×C22⋊C4C22×C3111yescharacteristic
523C22×C22⋊C4C22×C3111yescharacteristic
524#400—24no—
525#385—24no—
526#385—24no—
527C2×#95—24no—
528C2×#95C22×C3111yescharacteristic
529C2×#95C22×C3111yescharacteristic
530C2×#95C22×C3111yescharacteristic
531C2×#95C22×C3111yescharacteristic
532C2×#95C22×C3111yescharacteristic
533C2×#95C22×C3111yescharacteristic
534C2×#95C22×C3111yescharacteristic
535C2×#95C22×C3111yescharacteristic
536C2×#95C22×C3111yescharacteristic
537C2×#95C22×C3111yescharacteristic
538C2×#95C22×C3111yescharacteristic
539C2×#95C22×C3111yescharacteristic
540C2×#95C22×C3111yescharacteristic
541C2×#95C22×C3111yescharacteristic
542C2×#95C22×C3111yescharacteristic
543C2×#95C22×C3111yescharacteristic
544C2×#95C22×C3111yescharacteristic
545C2×#95C22×C3111yescharacteristic
546C2×#95C22×C3111yescharacteristic
547C2×#95C22×C3111yescharacteristic
548C2×#95C22×C3111yescharacteristic
549C2×#95C22×C3111yescharacteristic
550C2×#95C22×C3111yescharacteristic
551C2×#95C22×C3111yescharacteristic
552C2×C31—28no—
553C2×C31C2×#40011yescharacteristic
554C2×C31#241811yescharacteristic
555C2×C31#241911yescharacteristic
556C2×C31#244911yescharacteristic
557C2×C31#245011yescharacteristic
558C2×C31#247211yescharacteristic
559C2×C31#247311yescharacteristic
560C2×C31#247311yescharacteristic
561C2×C31#248011yescharacteristic
562C2×C31#248811yescharacteristic
563C2×C31#249311yescharacteristic
564C2×C31#250511yescharacteristic
565C2×C31#250511yescharacteristic
566C2×C31#264311yescharacteristic
567C2×C31#285211yescharacteristic
568C25C23×C3111yescharacteristic
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—22no—
584C23×C4—41no—
585C23×C4—41no—
586C23×C4—41no—
587C23×C4—41no—
588C23×C4—41no—
589C23×C4—41no—
590C23×C4C23×C3111yescharacteristic
591C23×C4C23×C3111yescharacteristic
592C23×C4C23×C3111yescharacteristic
593C23×C4C23×C3111yescharacteristic
594C23×C4C23×C3111yescharacteristic
595C23×C4C23×C3111yescharacteristic
596C23×C4C23×C3111yescharacteristic
597C23×C4C23×C3111yescharacteristic
598C23×C4C23×C3111yescharacteristic
599C23×C4C23×C3111yescharacteristic
600C23×C4C23×C3111yescharacteristic
601C23×C4C23×C3111yescharacteristic
602C23×C4C23×C3111yescharacteristic
603C23×C4C23×C3111yescharacteristic
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4D4×C3114yes—
627C2×C22⋊C4Q8×C3114yes—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95D4×C3114yes—
652C31#1473811yescharacteristic, direct product factor, Sylow
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24C2×D4×C3112yes—
662C24C2×Q8×C3112yes—
663C24#41×C3112yes—
664C24#41×C3112yes—
665C24#41×C3112yes—
666C24#41×C3112yes—
667C24#41×C3112yes—
668C24C24×C3111yescharacteristic
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4C2×D4×C3112yes—
779C22×C4C2×D4×C3112yes—
780C22×C4C2×D4×C3112yes—
781C22×C4C2×D4×C3112yes—
782C22×C4C2×D4×C3112yes—
783C22×C4C2×Q8×C3112yes—
784C22×C4C2×Q8×C3112yes—
785C22×C4#41×C3112yes—
786C22×C4#41×C3112yes—
787C22×C4#41×C3112yes—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23C31×C22⋊Q814yes—
825C23C31×#12314yes—
826C23C31×#12414yes—
827C23C31×#12514yes—
828C23C31×#12514yes—
829C23C31×#12614yes—
830C23C31×#12614yes—
831C23C22×D4×C3111yescharacteristic
832C23C22×D4×C3111yescharacteristic
833C23C22×Q8×C3111yescharacteristic
834C23C2×#41×C3111yescharacteristic
835C23C2×#41×C3111yescharacteristic
836C23C2×#41×C3111yescharacteristic
837C23C2×#41×C3111yescharacteristic
838C23C2×#41×C3111yescharacteristic
839C23C2×#41×C3111yescharacteristic
840C23C2×#41×C3111yescharacteristic
841C23C2×#41×C3111yescharacteristic
842C23C31×H(5,𝔽2)11yescharacteristic
843C23C31×H(5,𝔽2)11yescharacteristic
844C23C31×H(5,𝔽2)11yescharacteristic
845C23C31×2−1+411yescharacteristic
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—416no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22C31×#40018yescomplemented
962C22C2×C31×C22⋊Q811yescharacteristic
963C22C2×C31×#12311yescharacteristic
964C22C31×#52511yescharacteristic
965C22C31×#52511yescharacteristic
966C22C31×#52511yescharacteristic
967C22C2×C31×#12411yescharacteristic
968C22C2×C31×#12511yescharacteristic
969C22C2×C31×#12511yescharacteristic
970C22C2×C31×#12611yescharacteristic
971C22C2×C31×#12611yescharacteristic
972C22C31×#52911yescharacteristic
973C22C31×#52911yescharacteristic
974C22C31×#52911yescharacteristic
975C22C31×#53811yescharacteristic
976C22C31×#53811yescharacteristic
977C22C31×#53811yescharacteristic
978C22C31×#53911yescharacteristic
979C22C31×#53911yescharacteristic
980C22C31×#53911yescharacteristic
981C22D42×C3111yescharacteristic
982C22C31×#54611yescharacteristic
983C22C31×#54611yescharacteristic
984C22C31×#54611yescharacteristic
985C22C31×#54611yescharacteristic
986C22C31×#54711yescharacteristic
987C22D4×Q8×C3111yescharacteristic
988C22C31×#55111yescharacteristic
989C22C31×#55111yescharacteristic
990C22C31×#55111yescharacteristic
991C22C31×#55111yescharacteristic
992C22C31×#55211yescharacteristic
993C22C31×#55211yescharacteristic
994C22C31×#55411yescharacteristic
995C22C31×#55411yescharacteristic
996C22C31×#55411yescharacteristic
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—81no—
1008C4—81no—
1009C4—81no—
1010C4—81no—
1011C2—28no—
1012C2C2×C31×#40011yescharacteristic
1013C2C31×#241811yescharacteristic
1014C2C31×#241911yescharacteristic
1015C2C31×#244911yescharacteristic
1016C2C31×#245011yescharacteristic
1017C2C31×#247211yescharacteristic
1018C2C31×#247311yescharacteristic
1019C2C31×#247311yescharacteristic
1020C2C31×#248011yescharacteristic
1021C2C31×#248811yescharacteristic
1022C2C31×#249311yescharacteristic
1023C2C31×#250511yescharacteristic
1024C2C31×#250511yescharacteristic
1025C2C31×#264311yescharacteristic
1026C2C31×#285211yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#400C2semidirect
5. C31×#1445C2semidirect
6. C31×#1443C2semidirect
7. C31×#1443C2semidirect
8. C31×#1442C2semidirect
9. C31×#1442C2semidirect
10. C31×#1442C2semidirect
11. C31×#1441C2semidirect
282. #14738C31direct (N × H)
434. C2×#400C2×C31semidirect
438. #1445C2×C31semidirect
439. #1443C2×C31semidirect
440. #1443C2×C31semidirect
441. #1442C2×C31semidirect
442. #1442C2×C31semidirect
443. #1442C2×C31semidirect
444. #1441C2×C31semidirect
463. C22×C31#400semidirect
652. C31#14738direct (N × H)
961. C22C31×#400semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4002
C2×C31×#3852
C22×C31×#952
C31×#14452
C31×#14432
C31×#14422
C31×#14412
C31×C22⋊#952
#1473831