Finite Group Databasebeta

← C47×#14442 #26054140

Subgroups — C47×#14442 #26054140

Order 12032.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#389C211yesmaximal, characteristic, complemented
2C2×C47×#388C211yesmaximal, characteristic
3C2×C47×#388C211yesmaximal, characteristic
4C2×C47×#385C211yesmaximal, characteristic
5C2×C47×#385C211yesmaximal, characteristic
6C47×#1444C211yesmaximal, characteristic, complemented
7C47×#1442C211yesmaximal, characteristic, complemented
8C47×#1442C211yesmaximal, characteristic, complemented
9C47×#1441C211yesmaximal, characteristic, complemented
10C47×#1439C211yesmaximal, characteristic
11C47×#1439C211yesmaximal, characteristic
12C47×#1436C211yesmaximal, characteristic, complemented
13C47×C4⋊#95C211yesmaximal, characteristic, complemented
14C47×C4⋊#95C211yesmaximal, characteristic, complemented
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×C4⋊C4×C47C2211yescharacteristic
24C22×C4⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2211yescharacteristic
28C22×C22⋊C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47C2211yescharacteristic
30C22×C22⋊C4×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C22×C42×C47C2211yescharacteristic
33C47×#389—24no—
34C47×#388—24no—
35C47×#388C418yescomplemented
36C47×#385—24no—
37C47×#385—24no—
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
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C25×C47C2311yescharacteristic
57C23×C4×C47—22no—
58C23×C4×C47—22no—
59C23×C4×C47—22no—
60C23×C4×C47—41no—
61C23×C4×C47—41no—
62C23×C4×C47—41no—
63C23×C4×C47—41no—
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
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
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—22no—
84C2×C4⋊C4×C47—22no—
85C2×C4⋊C4×C47—22no—
86C2×C4⋊C4×C47—22no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—41no—
91C2×C4⋊C4×C47—41no—
92C2×C4⋊C4×C47—41no—
93C2×C4⋊C4×C47—41no—
94C2×C4⋊C4×C47—41no—
95C2×C4⋊C4×C47—41no—
96C2×C4⋊C4×C47—41no—
97C2×C4⋊C4×C47—41no—
98C2×C4⋊C4×C47—41no—
99C2×C4⋊C4×C47—41no—
100C2×C4⋊C4×C47C2×C414yescomplemented
101C2×C4⋊C4×C47D414yes—
102C2×C22⋊C4×C47—22no—
103C2×C22⋊C4×C47—22no—
104C2×C22⋊C4×C47—22no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47—22no—
107C2×C22⋊C4×C47—22no—
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—41no—
110C2×C22⋊C4×C47—41no—
111C2×C22⋊C4×C47—41no—
112C2×C22⋊C4×C47—41no—
113C2×C22⋊C4×C47—41no—
114C2×C22⋊C4×C47—41no—
115C2×C22⋊C4×C47C2×C414yes—
116C2×C22⋊C4×C47C2×C414yes—
117C2×C22⋊C4×C47C2×C414yes—
118C2×C22⋊C4×C47D414yes—
119C2×C22⋊C4×C47Q814yes—
120C2×C42×C47—22no—
121C2×C42×C47—22no—
122C2×C42×C47—41no—
123C2×C42×C47—41no—
124C2×C42×C47—41no—
125C2×C42×C47C2×C414yescomplemented
126#95×C47—22no—
127#95×C47—22no—
128#95×C47—22no—
129#95×C47—22no—
130#95×C47—22no—
131#95×C47—22no—
132#95×C47—22no—
133#95×C47—22no—
134#95×C47—22no—
135#95×C47—41no—
136#95×C47—41no—
137#95×C47—41no—
138#95×C47—41no—
139#95×C47—41no—
140#95×C47—41no—
141#95×C47—41no—
142#95×C47C2×C414yescomplemented
143#95×C47C2×C414yescomplemented
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C22×C412yes—
157C24×C47C2×D412yes—
158C24×C47C2×Q812yes—
159C24×C47C2411yescharacteristic
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—21no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—44no—
243C22×C4×C47—44no—
244C22×C4×C47—44no—
245C22×C4×C47—44no—
246C22×C4×C47—44no—
247C22×C4×C47—44no—
248C22×C4×C47—44no—
249C22×C4×C47C22×C412yes—
250C22×C4×C47C22×C412yes—
251C22×C4×C47C22×C412yes—
252C22×C4×C47C22×C412yes—
253C22×C4×C47C22×C412yes—
254C22×C4×C47C22×C412yes—
255C22×C4×C47C2×D412yes—
256C22×C4×C47C2×D412yes—
257C22×C4×C47C2×D412yes—
258C22×C4×C47C2×D412yes—
259C22×C4×C47C2×D412yes—
260C22×C4×C47C2×Q812yes—
261C22×C4×C47C2×Q812yes—
262C22×C4×C47#4112yes—
263C22×C4×C47#4112yes—
264C22×C4×C47#4112yes—
265C4⋊C4×C47—28no—
266C4⋊C4×C47—44no—
267C4⋊C4×C47—44no—
268C4⋊C4×C47—44no—
269C4⋊C4×C47—44no—
270C4⋊C4×C47—44no—
271C4⋊C4×C47—44no—
272C4⋊C4×C47—44no—
273C22⋊C4×C47—28no—
274C22⋊C4×C47—44no—
275C22⋊C4×C47—44no—
276C22⋊C4×C47—44no—
277C22⋊C4×C47—44no—
278C22⋊C4×C47C4⋊C4116yescomplemented
279C42×C47—44no—
280C42×C47—44no—
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—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
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×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47C2×C4⋊C414yes—
316C23×C47C23×C411yescharacteristic
317C23×C47C22×D411yescharacteristic
318C23×C47C22×D411yescharacteristic
319C23×C47C22×Q811yescharacteristic
320C23×C47C2×#4111yescharacteristic
321C23×C47C2×#4111yescharacteristic
322C23×C47C2×#4111yescharacteristic
323C23×C47H(5,𝔽2)11yescharacteristic
324C23×C47H(5,𝔽2)11yescharacteristic
325C23×C47H(5,𝔽2)11yescharacteristic
326C23×C47H(5,𝔽2)11yescharacteristic
327C23×C47H(5,𝔽2)11yescharacteristic
328C23×C472−1+411yescharacteristic
329C23×C472−1+411yescharacteristic
330C23×C472−1+411yescharacteristic
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—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—416no—
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×C47—41no—
421C2×C4×C47—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47—41no—
427C2×C4×C47C2×C4⋊C414yes—
428C2×C4×C47C2×C4⋊C414yes—
429C2×C4×C47C4×D414yes—
430#14442C4711yesmaximal, characteristic, direct product factor, Sylow
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47—42no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47C22×C4⋊C411yescharacteristic
447C22×C47C2×C4×D411yescharacteristic
448C22×C47C4×#4111yescharacteristic
449C22×C47#51811yescharacteristic
450C22×C47#52011yescharacteristic
451C22×C47#52011yescharacteristic
452C22×C47#52011yescharacteristic
453C22×C47#53411yescharacteristic
454C22×C47#53511yescharacteristic
455C22×C47#53611yescharacteristic
456C22×C47#53711yescharacteristic
457C22×C47#53811yescharacteristic
458C22×C47#53811yescharacteristic
459C22×C47#53911yescharacteristic
460C22×C47#53911yescharacteristic
461C22×C47#54111yescharacteristic
462C22×C47#54211yescharacteristic
463C22×C47#54411yescharacteristic
464C22×C47#54411yescharacteristic
465C22×C47D4211yescharacteristic
466C22×C47#54611yescharacteristic
467C22×C47#54611yescharacteristic
468C22×C47#54611yescharacteristic
469C22×C47#54711yescharacteristic
470C22×C47#54811yescharacteristic
471C22×C47D4×Q811yescharacteristic
472C22×C47#55411yescharacteristic
473C22×C47#55411yescharacteristic
474C22×C47#55411yescharacteristic
475C22×C47#55611yescharacteristic
476C22×C47#55911yescharacteristic
477C22×C47#56011yescharacteristic
478C22×C47#56211yescharacteristic
479C22×C47#56211yescharacteristic
480C22×C47#56311yescharacteristic
481C4×C47—24no—
482C4×C47—24no—
483C4×C47—24no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47—42no—
487C4×C47—42no—
488C4×C47—42no—
489C4×C47—42no—
490C4×C47—42no—
491C4×C47—81no—
492C4×C47—81no—
493C4×C47—81no—
494C4×C47—81no—
495C2×#389C2×C4711yescharacteristic, complemented
496C2×#388C2×C4711yescharacteristic
497C2×#388C2×C4711yescharacteristic
498C2×#385C2×C4711yescharacteristic
499C2×#385C2×C4711yescharacteristic
500#1444C2×C4711yescharacteristic, complemented
501#1442C2×C4711yescharacteristic, complemented
502#1442C2×C4711yescharacteristic, complemented
503#1441C2×C4711yescharacteristic, complemented
504#1439C2×C4711yescharacteristic
505#1439C2×C4711yescharacteristic
506#1436C2×C4711yescharacteristic, complemented
507C4⋊#95C2×C4711yescharacteristic, complemented
508C4⋊#95C2×C4711yescharacteristic, complemented
509C22⋊#95C2×C4711yescharacteristic
510C2×C47—44no—
511C2×C47#231711yescharacteristic
512C2×C47#232511yescharacteristic
513C2×C47#233411yescharacteristic
514C2×C47D4×C4⋊C411yescharacteristic
515C2×C47#234911yescharacteristic
516C2×C47#236711yescharacteristic
517C2×C47#237611yescharacteristic
518C2×C47#267811yescharacteristic
519C2×C47#268111yescharacteristic
520C2×C47#268911yescharacteristic
521C2×C47#270411yescharacteristic
522C2×C47#271011yescharacteristic
523C2×C47#272911yescharacteristic
524C2×C47#278811yescharacteristic
525C2×C47#280711yescharacteristic
526C24×C4C22×C4711yescharacteristic
527C22×C4⋊C4C22×C4711yescharacteristic
528C22×C4⋊C4C22×C4711yescharacteristic
529C22×C4⋊C4C22×C4711yescharacteristic
530C22×C4⋊C4C22×C4711yescharacteristic
531C22×C4⋊C4C22×C4711yescharacteristic
532C22×C4⋊C4C22×C4711yescharacteristic
533C22×C4⋊C4C22×C4711yescharacteristic
534C22×C4⋊C4C22×C4711yescharacteristic
535C22×C22⋊C4C22×C4711yescharacteristic
536C22×C22⋊C4C22×C4711yescharacteristic
537C22×C22⋊C4C22×C4711yescharacteristic
538C22×C22⋊C4C22×C4711yescharacteristic
539C22×C22⋊C4C22×C4711yescharacteristic
540C22×C22⋊C4C22×C4711yescharacteristic
541C22×C42C22×C4711yescharacteristic
542C22×C42C22×C4711yescharacteristic
543#389—24no—
544#388—24no—
545#388C4×C4718yescomplemented
546#385—24no—
547#385—24no—
548C2×#95C22×C4711yescharacteristic
549C2×#95C22×C4711yescharacteristic
550C2×#95C22×C4711yescharacteristic
551C2×#95C22×C4711yescharacteristic
552C2×#95C22×C4711yescharacteristic
553C2×#95C22×C4711yescharacteristic
554C2×#95C22×C4711yescharacteristic
555C2×#95C22×C4711yescharacteristic
556C2×#95C22×C4711yescharacteristic
557C2×#95C22×C4711yescharacteristic
558C2×#95C22×C4711yescharacteristic
559C2×#95C22×C4711yescharacteristic
560C2×#95C22×C4711yescharacteristic
561C2×#95C22×C4711yescharacteristic
562C2×#95C22×C4711yescharacteristic
563C2×#95C22×C4711yescharacteristic
564C2×#95C22×C4711yescharacteristic
565C2×#95C22×C4711yescharacteristic
566C47#1444211yescharacteristic, direct product factor, Sylow
567C25C23×C4711yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C4711yescharacteristic
576C23×C4C23×C4711yescharacteristic
577C23×C4C23×C4711yescharacteristic
578C23×C4C23×C4711yescharacteristic
579C23×C4C23×C4711yescharacteristic
580C23×C4C23×C4711yescharacteristic
581C23×C4C23×C4711yescharacteristic
582C23×C4C23×C4711yescharacteristic
583C23×C4C23×C4711yescharacteristic
584C23×C4C23×C4711yescharacteristic
585C23×C4C23×C4711yescharacteristic
586C23×C4C23×C4711yescharacteristic
587C23×C4C23×C4711yescharacteristic
588C23×C4C23×C4711yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×C4×C4714yescomplemented
612C2×C4⋊C4D4×C4714yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C2×C4×C4714yes—
627C2×C22⋊C4C2×C4×C4714yes—
628C2×C22⋊C4C2×C4×C4714yes—
629C2×C22⋊C4D4×C4714yes—
630C2×C22⋊C4Q8×C4714yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C4714yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C4714yescomplemented
654#95C2×C4×C4714yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C4712yes—
668C24C2×D4×C4712yes—
669C24C2×Q8×C4712yes—
670C24C24×C4711yescharacteristic
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—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—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C4712yes—
761C22×C4C22×C4×C4712yes—
762C22×C4C22×C4×C4712yes—
763C22×C4C22×C4×C4712yes—
764C22×C4C22×C4×C4712yes—
765C22×C4C22×C4×C4712yes—
766C22×C4C2×D4×C4712yes—
767C22×C4C2×D4×C4712yes—
768C22×C4C2×D4×C4712yes—
769C22×C4C2×D4×C4712yes—
770C22×C4C2×D4×C4712yes—
771C22×C4C2×Q8×C4712yes—
772C22×C4C2×Q8×C4712yes—
773C22×C4#41×C4712yes—
774C22×C4#41×C4712yes—
775C22×C4#41×C4712yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C47116yescomplemented
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
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—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C4714yes—
827C23C23×C4×C4711yescharacteristic
828C23C22×D4×C4711yescharacteristic
829C23C22×D4×C4711yescharacteristic
830C23C22×Q8×C4711yescharacteristic
831C23C2×#41×C4711yescharacteristic
832C23C2×#41×C4711yescharacteristic
833C23C2×#41×C4711yescharacteristic
834C23H(5,𝔽2)×C4711yescharacteristic
835C23H(5,𝔽2)×C4711yescharacteristic
836C23H(5,𝔽2)×C4711yescharacteristic
837C23H(5,𝔽2)×C4711yescharacteristic
838C23H(5,𝔽2)×C4711yescharacteristic
839C232−1+4×C4711yescharacteristic
840C232−1+4×C4711yescharacteristic
841C232−1+4×C4711yescharacteristic
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—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—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
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×C4C2×C4⋊C4×C4714yes—
939C2×C4C2×C4⋊C4×C4714yes—
940C2×C4C4×D4×C4714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C4711yescharacteristic
957C22C2×C4×D4×C4711yescharacteristic
958C22C4×#41×C4711yescharacteristic
959C22C47×#51811yescharacteristic
960C22C47×#52011yescharacteristic
961C22C47×#52011yescharacteristic
962C22C47×#52011yescharacteristic
963C22C47×#53411yescharacteristic
964C22C47×#53511yescharacteristic
965C22C47×#53611yescharacteristic
966C22C47×#53711yescharacteristic
967C22C47×#53811yescharacteristic
968C22C47×#53811yescharacteristic
969C22C47×#53911yescharacteristic
970C22C47×#53911yescharacteristic
971C22C47×#54111yescharacteristic
972C22C47×#54211yescharacteristic
973C22C47×#54411yescharacteristic
974C22C47×#54411yescharacteristic
975C22D42×C4711yescharacteristic
976C22C47×#54611yescharacteristic
977C22C47×#54611yescharacteristic
978C22C47×#54611yescharacteristic
979C22C47×#54711yescharacteristic
980C22C47×#54811yescharacteristic
981C22D4×Q8×C4711yescharacteristic
982C22C47×#55411yescharacteristic
983C22C47×#55411yescharacteristic
984C22C47×#55411yescharacteristic
985C22C47×#55611yescharacteristic
986C22C47×#55911yescharacteristic
987C22C47×#56011yescharacteristic
988C22C47×#56211yescharacteristic
989C22C47×#56211yescharacteristic
990C22C47×#56311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C47×#231711yescharacteristic
1007C2C47×#232511yescharacteristic
1008C2C47×#233411yescharacteristic
1009C2D4×C4⋊C4×C4711yescharacteristic
1010C2C47×#234911yescharacteristic
1011C2C47×#236711yescharacteristic
1012C2C47×#237611yescharacteristic
1013C2C47×#267811yescharacteristic
1014C2C47×#268111yescharacteristic
1015C2C47×#268911yescharacteristic
1016C2C47×#270411yescharacteristic
1017C2C47×#271011yescharacteristic
1018C2C47×#272911yescharacteristic
1019C2C47×#278811yescharacteristic
1020C2C47×#280711yescharacteristic
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
1. C2×C47×#389C2semidirect
6. C47×#1444C2semidirect
7. C47×#1442C2semidirect
8. C47×#1442C2semidirect
9. C47×#1441C2semidirect
12. C47×#1436C2semidirect
13. C47×C4⋊#95C2semidirect
14. C47×C4⋊#95C2semidirect
35. C47×#388C4semidirect
100. C2×C4⋊C4×C47C2×C4semidirect
125. C2×C42×C47C2×C4semidirect
142. #95×C47C2×C4semidirect
143. #95×C47C2×C4semidirect
278. C22⋊C4×C47C4⋊C4semidirect
430. #14442C47direct (N × H)
495. C2×#389C2×C47semidirect
500. #1444C2×C47semidirect
501. #1442C2×C47semidirect
502. #1442C2×C47semidirect
503. #1441C2×C47semidirect
506. #1436C2×C47semidirect
507. C4⋊#95C2×C47semidirect
508. C4⋊#95C2×C47semidirect
545. #388C4×C47semidirect
566. C47#14442direct (N × H)
611. C2×C4⋊C4C2×C4×C47semidirect
636. C2×C42C2×C4×C47semidirect
653. #95C2×C4×C47semidirect
654. #95C2×C4×C47semidirect
789. 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×#3892
C2×C47×#3882
C2×C47×#3852
C47×#14442
C47×#14422
C47×#14412
C47×#14392
C47×#14362
C47×C4⋊#952
C47×C22⋊#952
#1444247