Finite Group Databasebeta

← C47×#14488 #26054186

Subgroups — C47×#14488 #26054186

Order 12032.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#388C211yesmaximal, characteristic
2C2×C47×#388C211yesmaximal, characteristic
3C2×C47×#385C211yesmaximal, characteristic
4C47×#1444C211yesmaximal, characteristic, complemented
5C47×#1442C211yesmaximal, characteristic, complemented
6C47×#1442C211yesmaximal, characteristic, complemented
7C47×#1441C211yesmaximal, characteristic, complemented
8C47×#1439C211yesmaximal, characteristic
9C47×#1439C211yesmaximal, characteristic
10C47×#1436C211yesmaximal, characteristic, complemented
11C47×C4⋊#95C211yesmaximal, characteristic, complemented
12C47×C4⋊#95C211yesmaximal, characteristic, complemented
13C47×#1434C211yesmaximal, characteristic, complemented
14C47×C22⋊#95C211yesmaximal, characteristic
15C47×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C47C2211yescharacteristic
17C22×C4⋊C4×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C4⋊C4×C47C2211yescharacteristic
22C22×C4⋊C4×C47C2211yescharacteristic
23C22×C22⋊C4×C47C2211yescharacteristic
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2211yescharacteristic
28C22×C22⋊C4×C47C2211yescharacteristic
29C22×C42×C47C2211yescharacteristic
30C22×C42×C47C2211yescharacteristic
31C47×#388—24no—
32C47×#388C418yescomplemented
33C47×#385—24no—
34C2×#95×C47C2211yescharacteristic
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2211yescharacteristic
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C2×#95×C47C2211yescharacteristic
42C2×#95×C47C2211yescharacteristic
43C2×#95×C47C2211yescharacteristic
44C2×#95×C47C2211yescharacteristic
45C2×#95×C47C2211yescharacteristic
46C2×#95×C47C2211yescharacteristic
47C2×#95×C47C2211yescharacteristic
48C2×#95×C47C2211yescharacteristic
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C25×C47C2311yescharacteristic
55C23×C4×C47—22no—
56C23×C4×C47—22no—
57C23×C4×C47—22no—
58C23×C4×C47—41no—
59C23×C4×C47—41no—
60C23×C4×C47—41no—
61C23×C4×C47—41no—
62C23×C4×C47C2311yescharacteristic
63C23×C4×C47C2311yescharacteristic
64C23×C4×C47C2311yescharacteristic
65C23×C4×C47C2311yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C23×C4×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C2×C4⋊C4×C47—22no—
77C2×C4⋊C4×C47—22no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—22no—
80C2×C4⋊C4×C47—22no—
81C2×C4⋊C4×C47—22no—
82C2×C4⋊C4×C47—22no—
83C2×C4⋊C4×C47—41no—
84C2×C4⋊C4×C47—41no—
85C2×C4⋊C4×C47—41no—
86C2×C4⋊C4×C47—41no—
87C2×C4⋊C4×C47—41no—
88C2×C4⋊C4×C47—41no—
89C2×C4⋊C4×C47—41no—
90C2×C4⋊C4×C47—41no—
91C2×C4⋊C4×C47—41no—
92C2×C4⋊C4×C47—41no—
93C2×C4⋊C4×C47C2×C414yescomplemented
94C2×C22⋊C4×C47—22no—
95C2×C22⋊C4×C47—22no—
96C2×C22⋊C4×C47—22no—
97C2×C22⋊C4×C47—22no—
98C2×C22⋊C4×C47—22no—
99C2×C22⋊C4×C47—41no—
100C2×C22⋊C4×C47—41no—
101C2×C22⋊C4×C47—41no—
102C2×C22⋊C4×C47—41no—
103C2×C22⋊C4×C47—41no—
104C2×C22⋊C4×C47—41no—
105C2×C22⋊C4×C47—41no—
106C2×C22⋊C4×C47—41no—
107C2×C22⋊C4×C47C2×C414yes—
108C2×C22⋊C4×C47C2×C414yes—
109C2×C22⋊C4×C47C2×C414yes—
110C2×C22⋊C4×C47D414yes—
111C2×C22⋊C4×C47Q814yes—
112C2×C42×C47—22no—
113C2×C42×C47—22no—
114C2×C42×C47—41no—
115C2×C42×C47—41no—
116C2×C42×C47—41no—
117C2×C42×C47C2×C414yescomplemented
118#95×C47—22no—
119#95×C47—22no—
120#95×C47—22no—
121#95×C47—22no—
122#95×C47—22no—
123#95×C47—22no—
124#95×C47—22no—
125#95×C47—41no—
126#95×C47—41no—
127#95×C47—41no—
128#95×C47—41no—
129#95×C47—41no—
130#95×C47—41no—
131#95×C47—41no—
132#95×C47—41no—
133#95×C47—41no—
134#95×C47—41no—
135#95×C47—41no—
136#95×C47C2×C414yescomplemented
137#95×C47C2×C414yescomplemented
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—21no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47C22×C412yes—
151C24×C47C2×D412yes—
152C24×C47C2×Q812yes—
153C24×C47C2411yescharacteristic
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—44no—
239C22×C4×C47—44no—
240C22×C4×C47—44no—
241C22×C4×C47—44no—
242C22×C4×C47—44no—
243C22×C4×C47—44no—
244C22×C4×C47—44no—
245C22×C4×C47C22×C412yes—
246C22×C4×C47C22×C412yes—
247C22×C4×C47C22×C412yes—
248C22×C4×C47C22×C412yes—
249C22×C4×C47C22×C412yes—
250C22×C4×C47C22×C412yes—
251C22×C4×C47C2×D412yes—
252C22×C4×C47C2×D412yes—
253C22×C4×C47C2×Q812yes—
254C22×C4×C47C2×Q812yes—
255C22×C4×C47#4112yes—
256C22×C4×C47#4112yes—
257C22×C4×C47#4112yes—
258C22×C4×C47#4112yes—
259C4⋊C4×C47—44no—
260C4⋊C4×C47—44no—
261C4⋊C4×C47—44no—
262C4⋊C4×C47—44no—
263C4⋊C4×C47—44no—
264C4⋊C4×C47—44no—
265C22⋊C4×C47—44no—
266C22⋊C4×C47—44no—
267C22⋊C4×C47—44no—
268C22⋊C4×C47—44no—
269C22⋊C4×C47—44no—
270C22⋊C4×C47C4⋊C4116yescomplemented
271C42×C47—44no—
272C42×C47—44no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47C2×C4⋊C414yes—
308C23×C47C23×C411yescharacteristic
309C23×C47C22×D411yescharacteristic
310C23×C47C22×Q811yescharacteristic
311C23×C47C2×#4111yescharacteristic
312C23×C47C2×#4111yescharacteristic
313C23×C47C2×#4111yescharacteristic
314C23×C47C2×#4111yescharacteristic
315C23×C47H(5,𝔽2)11yescharacteristic
316C23×C47H(5,𝔽2)11yescharacteristic
317C23×C47H(5,𝔽2)11yescharacteristic
318C23×C47H(5,𝔽2)11yescharacteristic
319C23×C47H(5,𝔽2)11yescharacteristic
320C23×C47H(5,𝔽2)11yescharacteristic
321C23×C472−1+411yescharacteristic
322C23×C472−1+411yescharacteristic
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—416no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—41no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47—41no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—41no—
420C2×C4×C47C2×C4⋊C414yes—
421C2×C4×C47C2×C4⋊C414yes—
422#14488C4711yesmaximal, characteristic, direct product factor, Sylow
423C22×C47—24no—
424C22×C47—24no—
425C22×C47—24no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—42no—
431C22×C47—42no—
432C22×C47—42no—
433C22×C47—42no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47C22×C4⋊C411yescharacteristic
439C22×C47C4×#4111yescharacteristic
440C22×C47C4×#4111yescharacteristic
441C22×C47#51811yescharacteristic
442C22×C47#51811yescharacteristic
443C22×C47#52011yescharacteristic
444C22×C47#52011yescharacteristic
445C22×C47#53511yescharacteristic
446C22×C47#53611yescharacteristic
447C22×C47#53811yescharacteristic
448C22×C47#53811yescharacteristic
449C22×C47#53811yescharacteristic
450C22×C47#53911yescharacteristic
451C22×C47#54011yescharacteristic
452C22×C47#54211yescharacteristic
453C22×C47#54211yescharacteristic
454C22×C47#54211yescharacteristic
455C22×C47#54411yescharacteristic
456C22×C47#54411yescharacteristic
457C22×C47#54611yescharacteristic
458C22×C47#54611yescharacteristic
459C22×C47#54611yescharacteristic
460C22×C47#54611yescharacteristic
461C22×C47#55111yescharacteristic
462C22×C47#55211yescharacteristic
463C22×C47#55311yescharacteristic
464C22×C47#55411yescharacteristic
465C22×C47#55411yescharacteristic
466C22×C47#55411yescharacteristic
467C22×C47#55411yescharacteristic
468C22×C47#55611yescharacteristic
469C22×C47#56011yescharacteristic
470C22×C47#56011yescharacteristic
471C22×C47#56211yescharacteristic
472C22×C47#56211yescharacteristic
473C4×C47—24no—
474C4×C47—24no—
475C4×C47—42no—
476C4×C47—42no—
477C4×C47—42no—
478C4×C47—42no—
479C4×C47—42no—
480C4×C47—42no—
481C4×C47—42no—
482C4×C47—42no—
483C4×C47—81no—
484C4×C47—81no—
485C4×C47—81no—
486C4×C47—81no—
487C2×#388C2×C4711yescharacteristic
488C2×#388C2×C4711yescharacteristic
489C2×#385C2×C4711yescharacteristic
490#1444C2×C4711yescharacteristic, complemented
491#1442C2×C4711yescharacteristic, complemented
492#1442C2×C4711yescharacteristic, complemented
493#1441C2×C4711yescharacteristic, complemented
494#1439C2×C4711yescharacteristic
495#1439C2×C4711yescharacteristic
496#1436C2×C4711yescharacteristic, complemented
497C4⋊#95C2×C4711yescharacteristic, complemented
498C4⋊#95C2×C4711yescharacteristic, complemented
499#1434C2×C4711yescharacteristic, complemented
500C22⋊#95C2×C4711yescharacteristic
501C22⋊#95C2×C4711yescharacteristic
502C2×C47—44no—
503C2×C47#231711yescharacteristic
504C2×C47#233511yescharacteristic
505C2×C47#233711yescharacteristic
506C2×C47#234911yescharacteristic
507C2×C47#234911yescharacteristic
508C2×C47#237311yescharacteristic
509C2×C47#237711yescharacteristic
510C2×C47#268511yescharacteristic
511C2×C47#268711yescharacteristic
512C2×C47#270011yescharacteristic
513C2×C47#270311yescharacteristic
514C2×C47#274211yescharacteristic
515C2×C47#276811yescharacteristic
516C2×C47#278811yescharacteristic
517C2×C47#279011yescharacteristic
518C24×C4C22×C4711yescharacteristic
519C22×C4⋊C4C22×C4711yescharacteristic
520C22×C4⋊C4C22×C4711yescharacteristic
521C22×C4⋊C4C22×C4711yescharacteristic
522C22×C4⋊C4C22×C4711yescharacteristic
523C22×C4⋊C4C22×C4711yescharacteristic
524C22×C4⋊C4C22×C4711yescharacteristic
525C22×C22⋊C4C22×C4711yescharacteristic
526C22×C22⋊C4C22×C4711yescharacteristic
527C22×C22⋊C4C22×C4711yescharacteristic
528C22×C22⋊C4C22×C4711yescharacteristic
529C22×C22⋊C4C22×C4711yescharacteristic
530C22×C22⋊C4C22×C4711yescharacteristic
531C22×C42C22×C4711yescharacteristic
532C22×C42C22×C4711yescharacteristic
533#388—24no—
534#388C4×C4718yescomplemented
535#385—24no—
536C2×#95C22×C4711yescharacteristic
537C2×#95C22×C4711yescharacteristic
538C2×#95C22×C4711yescharacteristic
539C2×#95C22×C4711yescharacteristic
540C2×#95C22×C4711yescharacteristic
541C2×#95C22×C4711yescharacteristic
542C2×#95C22×C4711yescharacteristic
543C2×#95C22×C4711yescharacteristic
544C2×#95C22×C4711yescharacteristic
545C2×#95C22×C4711yescharacteristic
546C2×#95C22×C4711yescharacteristic
547C2×#95C22×C4711yescharacteristic
548C2×#95C22×C4711yescharacteristic
549C2×#95C22×C4711yescharacteristic
550C2×#95C22×C4711yescharacteristic
551C2×#95C22×C4711yescharacteristic
552C2×#95C22×C4711yescharacteristic
553C2×#95C22×C4711yescharacteristic
554C2×#95C22×C4711yescharacteristic
555C2×#95C22×C4711yescharacteristic
556C47#1448811yescharacteristic, direct product factor, Sylow
557C25C23×C4711yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C4711yescharacteristic
566C23×C4C23×C4711yescharacteristic
567C23×C4C23×C4711yescharacteristic
568C23×C4C23×C4711yescharacteristic
569C23×C4C23×C4711yescharacteristic
570C23×C4C23×C4711yescharacteristic
571C23×C4C23×C4711yescharacteristic
572C23×C4C23×C4711yescharacteristic
573C23×C4C23×C4711yescharacteristic
574C23×C4C23×C4711yescharacteristic
575C23×C4C23×C4711yescharacteristic
576C23×C4C23×C4711yescharacteristic
577C23×C4C23×C4711yescharacteristic
578C23×C4C23×C4711yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4C2×C4×C4714yescomplemented
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4C2×C4×C4714yes—
611C2×C22⋊C4C2×C4×C4714yes—
612C2×C22⋊C4C2×C4×C4714yes—
613C2×C22⋊C4D4×C4714yes—
614C2×C22⋊C4Q8×C4714yes—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C4714yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C4714yescomplemented
640#95C2×C4×C4714yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C4712yes—
654C24C2×D4×C4712yes—
655C24C2×Q8×C4712yes—
656C24C24×C4711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
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—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4C22×C4×C4712yes—
749C22×C4C22×C4×C4712yes—
750C22×C4C22×C4×C4712yes—
751C22×C4C22×C4×C4712yes—
752C22×C4C22×C4×C4712yes—
753C22×C4C22×C4×C4712yes—
754C22×C4C2×D4×C4712yes—
755C22×C4C2×D4×C4712yes—
756C22×C4C2×Q8×C4712yes—
757C22×C4C2×Q8×C4712yes—
758C22×C4#41×C4712yes—
759C22×C4#41×C4712yes—
760C22×C4#41×C4712yes—
761C22×C4#41×C4712yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4C4⋊C4×C47116yescomplemented
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C4714yes—
811C23C23×C4×C4711yescharacteristic
812C23C22×D4×C4711yescharacteristic
813C23C22×Q8×C4711yescharacteristic
814C23C2×#41×C4711yescharacteristic
815C23C2×#41×C4711yescharacteristic
816C23C2×#41×C4711yescharacteristic
817C23C2×#41×C4711yescharacteristic
818C23H(5,𝔽2)×C4711yescharacteristic
819C23H(5,𝔽2)×C4711yescharacteristic
820C23H(5,𝔽2)×C4711yescharacteristic
821C23H(5,𝔽2)×C4711yescharacteristic
822C23H(5,𝔽2)×C4711yescharacteristic
823C23H(5,𝔽2)×C4711yescharacteristic
824C232−1+4×C4711yescharacteristic
825C232−1+4×C4711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
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—416no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
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×C4C2×C4⋊C4×C4714yes—
924C2×C4C2×C4⋊C4×C4714yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C4711yescharacteristic
941C22C4×#41×C4711yescharacteristic
942C22C4×#41×C4711yescharacteristic
943C22C47×#51811yescharacteristic
944C22C47×#51811yescharacteristic
945C22C47×#52011yescharacteristic
946C22C47×#52011yescharacteristic
947C22C47×#53511yescharacteristic
948C22C47×#53611yescharacteristic
949C22C47×#53811yescharacteristic
950C22C47×#53811yescharacteristic
951C22C47×#53811yescharacteristic
952C22C47×#53911yescharacteristic
953C22C47×#54011yescharacteristic
954C22C47×#54211yescharacteristic
955C22C47×#54211yescharacteristic
956C22C47×#54211yescharacteristic
957C22C47×#54411yescharacteristic
958C22C47×#54411yescharacteristic
959C22C47×#54611yescharacteristic
960C22C47×#54611yescharacteristic
961C22C47×#54611yescharacteristic
962C22C47×#54611yescharacteristic
963C22C47×#55111yescharacteristic
964C22C47×#55211yescharacteristic
965C22C47×#55311yescharacteristic
966C22C47×#55411yescharacteristic
967C22C47×#55411yescharacteristic
968C22C47×#55411yescharacteristic
969C22C47×#55411yescharacteristic
970C22C47×#55611yescharacteristic
971C22C47×#56011yescharacteristic
972C22C47×#56011yescharacteristic
973C22C47×#56211yescharacteristic
974C22C47×#56211yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C47×#231711yescharacteristic
991C2C47×#233511yescharacteristic
992C2C47×#233711yescharacteristic
993C2C47×#234911yescharacteristic
994C2C47×#234911yescharacteristic
995C2C47×#237311yescharacteristic
996C2C47×#237711yescharacteristic
997C2C47×#268511yescharacteristic
998C2C47×#268711yescharacteristic
999C2C47×#270011yescharacteristic
1000C2C47×#270311yescharacteristic
1001C2C47×#274211yescharacteristic
1002C2C47×#276811yescharacteristic
1003C2C47×#278811yescharacteristic
1004C2C47×#279011yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC25×C47C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1444C2semidirect
5. C47×#1442C2semidirect
6. C47×#1442C2semidirect
7. C47×#1441C2semidirect
10. C47×#1436C2semidirect
11. C47×C4⋊#95C2semidirect
12. C47×C4⋊#95C2semidirect
13. C47×#1434C2semidirect
32. C47×#388C4semidirect
93. C2×C4⋊C4×C47C2×C4semidirect
117. C2×C42×C47C2×C4semidirect
136. #95×C47C2×C4semidirect
137. #95×C47C2×C4semidirect
270. C22⋊C4×C47C4⋊C4semidirect
422. #14488C47direct (N × H)
490. #1444C2×C47semidirect
491. #1442C2×C47semidirect
492. #1442C2×C47semidirect
493. #1441C2×C47semidirect
496. #1436C2×C47semidirect
497. C4⋊#95C2×C47semidirect
498. C4⋊#95C2×C47semidirect
499. #1434C2×C47semidirect
534. #388C4×C47semidirect
556. C47#14488direct (N × H)
596. C2×C4⋊C4C2×C4×C47semidirect
620. C2×C42C2×C4×C47semidirect
639. #95C2×C4×C47semidirect
640. #95C2×C4×C47semidirect
773. C22⋊C4C4⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3882
C2×C47×#3852
C47×#14442
C47×#14422
C47×#14412
C47×#14392
C47×#14362
C47×C4⋊#952
C47×#14342
C47×C22⋊#952
#1448847