Finite Group Databasebeta

← C47×#14004 #26053702

Subgroups — C47×#14004 #26053702

Order 12032.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#389C211yesmaximal, characteristic, complemented
2C2×C47×#385C211yesmaximal, characteristic
3C2×C47×#385C211yesmaximal, characteristic
4C2×C47×#385C211yesmaximal, characteristic
5C2×C47×#380C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
7C22×#95×C47C211yesmaximal, characteristic
8C47×#1444C211yesmaximal, characteristic, complemented
9C47×#1442C211yesmaximal, characteristic, complemented
10C47×#1441C211yesmaximal, characteristic, complemented
11C47×#1441C211yesmaximal, characteristic, complemented
12C47×#1436C211yesmaximal, characteristic, complemented
13C47×#1436C211yesmaximal, characteristic, complemented
14C47×C4⋊#95C211yesmaximal, characteristic, complemented
15C47×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C47C2211yescharacteristic
17C24×C4×C47C2211yescharacteristic
18C24×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×C4⋊C4×C47C2211yescharacteristic
26C22×C4⋊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×#385—24no—
35C47×#385—24no—
36C47×#385C418yescomplemented
37C47×#380—24no—
38C4×C22⋊C4×C47—24no—
39C2×#95×C47—24no—
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
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C25×C47C2311yescharacteristic
59C23×C4×C47—22no—
60C23×C4×C47—22no—
61C23×C4×C47—22no—
62C23×C4×C47—22no—
63C23×C4×C47—22no—
64C23×C4×C47—22no—
65C23×C4×C47—22no—
66C23×C4×C47—22no—
67C23×C4×C47—22no—
68C23×C4×C47—22no—
69C23×C4×C47—22no—
70C23×C4×C47—22no—
71C23×C4×C47—22no—
72C23×C4×C47—41no—
73C23×C4×C47—41no—
74C23×C4×C47—41no—
75C23×C4×C47—41no—
76C23×C4×C47—41no—
77C23×C4×C47—41no—
78C23×C4×C47C2×C414yes—
79C23×C4×C47Q814yes—
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—41no—
109C2×C4⋊C4×C47—41no—
110C2×C4⋊C4×C47—41no—
111C2×C4⋊C4×C47—41no—
112C2×C4⋊C4×C47—41no—
113C2×C4⋊C4×C47—41no—
114C2×C4⋊C4×C47—41no—
115C2×C4⋊C4×C47—41no—
116C2×C4⋊C4×C47C2×C414yescomplemented
117C2×C4⋊C4×C47C2×C414yescomplemented
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—22no—
120C2×C22⋊C4×C47—22no—
121C2×C22⋊C4×C47—22no—
122C2×C22⋊C4×C47—22no—
123C2×C22⋊C4×C47—22no—
124C2×C22⋊C4×C47—22no—
125C2×C22⋊C4×C47C2×C414yes—
126C2×C22⋊C4×C47C2×C414yes—
127C2×C22⋊C4×C47D414yes—
128C2×C22⋊C4×C47D414yes—
129C2×C22⋊C4×C47Q814yes—
130C2×C42×C47—22no—
131C2×C42×C47—22no—
132C2×C42×C47—22no—
133C2×C42×C47—22no—
134C2×C42×C47—41no—
135C2×C42×C47—41no—
136#95×C47—22no—
137#95×C47—22no—
138#95×C47—22no—
139#95×C47—22no—
140#95×C47—22no—
141#95×C47—22no—
142#95×C47—22no—
143#95×C47—22no—
144#95×C47—22no—
145#95×C47—22no—
146#95×C47—22no—
147#95×C47—22no—
148#95×C47—22no—
149#95×C47—41no—
150#95×C47—41no—
151#95×C47C2×C414yescomplemented
152#95×C47C2×C414yescomplemented
153#95×C47D414yes—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47C22×C412yes—
163C24×C47C2×D412yes—
164C24×C47C2×D412yes—
165C24×C47C2×Q812yes—
166C24×C47C2×Q812yes—
167C24×C47#4112yes—
168C24×C47#4112yes—
169C24×C47C2411yescharacteristic
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—28no—
187C22×C4×C47—28no—
188C22×C4×C47—28no—
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—28no—
238C22×C4×C47—28no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—44no—
254C22×C4×C47—44no—
255C22×C4×C47—44no—
256C22×C4×C47—44no—
257C22×C4×C47—44no—
258C22×C4×C47—44no—
259C22×C4×C47—44no—
260C22×C4×C47—44no—
261C22×C4×C47—44no—
262C22×C4×C47—44no—
263C22×C4×C47—44no—
264C22×C4×C47—44no—
265C22×C4×C47—44no—
266C22×C4×C47—44no—
267C22×C4×C47—44no—
268C22×C4×C47—44no—
269C22×C4×C47C22×C412yes—
270C22×C4×C47C22×C412yes—
271C22×C4×C47C22×C412yes—
272C22×C4×C47C22×C412yes—
273C22×C4×C47C22×C412yes—
274C22×C4×C47C22×C412yes—
275C22×C4×C47C2×D412yes—
276C22×C4×C47C2×D412yes—
277C22×C4×C47C2×D412yes—
278C22×C4×C47C2×D412yes—
279C22×C4×C47C2×D412yes—
280C22×C4×C47C2×D412yes—
281C22×C4×C47C2×D412yes—
282C22×C4×C47C2×Q812yes—
283C22×C4×C47C2×Q812yes—
284C22×C4×C47C2×Q812yes—
285C22×C4×C47C2×Q812yes—
286C22×C4×C47#4112yes—
287C22×C4×C47#4112yes—
288C22×C4×C47#4112yes—
289C4⋊C4×C47—28no—
290C4⋊C4×C47—44no—
291C4⋊C4×C47—44no—
292C4⋊C4×C47—44no—
293C4⋊C4×C47—44no—
294C4⋊C4×C47—44no—
295C4⋊C4×C47—44no—
296C4⋊C4×C47—44no—
297C22⋊C4×C47—28no—
298C22⋊C4×C47—28no—
299C22⋊C4×C47—44no—
300C22⋊C4×C47C4⋊C4116yescomplemented
301C42×C47—44no—
302C42×C47—44no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—22no—
320C23×C47—22no—
321C23×C47—22no—
322C23×C47—22no—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47C2×C4⋊C414yes—
332C23×C47C4×D414yes—
333C23×C47C4×Q814yes—
334C23×C47#12114yes—
335C23×C47C22⋊Q814yes—
336C23×C47#12514yes—
337C23×C47C4⋊Q814yes—
338C23×C47C23×C411yescharacteristic
339C23×C47C22×D411yescharacteristic
340C23×C47C22×D411yescharacteristic
341C23×C47C22×D411yescharacteristic
342C23×C47C22×Q811yescharacteristic
343C23×C47C22×Q811yescharacteristic
344C23×C47C2×#4111yescharacteristic
345C23×C47C2×#4111yescharacteristic
346C23×C47C2×#4111yescharacteristic
347C23×C47C2×#4111yescharacteristic
348C23×C47C2×#4111yescharacteristic
349C23×C47H(5,𝔽2)11yescharacteristic
350C23×C47H(5,𝔽2)11yescharacteristic
351C23×C47H(5,𝔽2)11yescharacteristic
352C23×C472−1+411yescharacteristic
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—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—22no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—22no—
394C2×C4×C47—22no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—22no—
400C2×C4×C47—22no—
401C2×C4×C47—416no—
402C2×C4×C47—416no—
403C2×C4×C47—416no—
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×C47—41no—
428C2×C4×C47—41no—
429C2×C4×C47—41no—
430C2×C4×C47—41no—
431C2×C4×C47—41no—
432C2×C4×C47—41no—
433C2×C4×C47—41no—
434C2×C4×C47—41no—
435C2×C4×C47—41no—
436C2×C4×C47—41no—
437C2×C4×C47—41no—
438C2×C4×C47—41no—
439C2×C4×C47—41no—
440C2×C4×C47—41no—
441C2×C4×C47—41no—
442C2×C4×C47—41no—
443C2×C4×C47—41no—
444C2×C4×C47—41no—
445C2×C4×C47—41no—
446C2×C4×C47—41no—
447C2×C4×C47—41no—
448C2×C4×C47—41no—
449C2×C4×C47—41no—
450C2×C4×C47C2×C4⋊C414yes—
451C2×C4×C47C2×C4⋊C414yes—
452C2×C4×C47C4×D414yes—
453C2×C4×C47C22⋊Q814yes—
454#14004C4711yesmaximal, characteristic, direct product factor, Sylow
455C22×C47—24no—
456C22×C47—24no—
457C22×C47—24no—
458C22×C47—24no—
459C22×C47—24no—
460C22×C47—24no—
461C22×C47—24no—
462C22×C47—24no—
463C22×C47—24no—
464C22×C47—24no—
465C22×C47—24no—
466C22×C47—24no—
467C22×C47—24no—
468C22×C47—24no—
469C22×C47#38918yescomplemented
470C22×C47C22×C4⋊C411yescharacteristic
471C22×C47C2×C4×D411yescharacteristic
472C22×C47C2×C4×D411yescharacteristic
473C22×C47C2×C4×Q811yescharacteristic
474C22×C47C4×#4111yescharacteristic
475C22×C47#51811yescharacteristic
476C22×C47#52011yescharacteristic
477C22×C47C2×#12111yescharacteristic
478C22×C47C2×C22⋊Q811yescharacteristic
479C22×C47C2×C22⋊Q811yescharacteristic
480C22×C47#52511yescharacteristic
481C22×C47C2×#12511yescharacteristic
482C22×C47#52911yescharacteristic
483C22×C47C2×C4⋊Q811yescharacteristic
484C22×C47#53311yescharacteristic
485C22×C47#53811yescharacteristic
486C22×C47#53911yescharacteristic
487C22×C47#54311yescharacteristic
488C22×C47#54411yescharacteristic
489C22×C47D4211yescharacteristic
490C22×C47D4211yescharacteristic
491C22×C47#54611yescharacteristic
492C22×C47#54611yescharacteristic
493C22×C47#54611yescharacteristic
494C22×C47#54611yescharacteristic
495C22×C47#54611yescharacteristic
496C22×C47#54711yescharacteristic
497C22×C47#54711yescharacteristic
498C22×C47D4×Q811yescharacteristic
499C22×C47#55111yescharacteristic
500C22×C47#55111yescharacteristic
501C22×C47#55211yescharacteristic
502C22×C47#55411yescharacteristic
503C22×C47#55411yescharacteristic
504C22×C47#55411yescharacteristic
505C4×C47—24no—
506C4×C47—24no—
507C4×C47—24no—
508C4×C47—24no—
509C4×C47—42no—
510C4×C47—42no—
511C4×C47—42no—
512C4×C47—42no—
513C4×C47—42no—
514C4×C47—42no—
515C4×C47—42no—
516C4×C47—42no—
517C4×C47—81no—
518C4×C47—81no—
519C2×#389C2×C4711yescharacteristic, complemented
520C2×#385C2×C4711yescharacteristic
521C2×#385C2×C4711yescharacteristic
522C2×#385C2×C4711yescharacteristic
523C2×#380C2×C4711yescharacteristic
524C2×C4×C22⋊C4C2×C4711yescharacteristic
525C22×#95C2×C4711yescharacteristic
526#1444C2×C4711yescharacteristic, complemented
527#1442C2×C4711yescharacteristic, complemented
528#1441C2×C4711yescharacteristic, complemented
529#1441C2×C4711yescharacteristic, complemented
530#1436C2×C4711yescharacteristic, complemented
531#1436C2×C4711yescharacteristic, complemented
532C4⋊#95C2×C4711yescharacteristic, complemented
533C22⋊#95C2×C4711yescharacteristic
534C2×C47—28no—
535C2×C47C2×#38911yescharacteristic
536C2×C47C4×C22⋊Q811yescharacteristic
537C2×C47#232911yescharacteristic
538C2×C47D4×C4⋊C411yescharacteristic
539C2×C47#234911yescharacteristic
540C2×C47#235811yescharacteristic
541C2×C47#235911yescharacteristic
542C2×C47#242411yescharacteristic
543C2×C47#242511yescharacteristic
544C2×C47#243711yescharacteristic
545C2×C47#243811yescharacteristic
546C2×C47#244011yescharacteristic
547C2×C47#247311yescharacteristic
548C2×C47#250511yescharacteristic
549C2×C47#254911yescharacteristic
550C24×C4C22×C4711yescharacteristic
551C24×C4C22×C4711yescharacteristic
552C24×C4C22×C4711yescharacteristic
553C22×C4⋊C4C22×C4711yescharacteristic
554C22×C4⋊C4C22×C4711yescharacteristic
555C22×C4⋊C4C22×C4711yescharacteristic
556C22×C4⋊C4C22×C4711yescharacteristic
557C22×C4⋊C4C22×C4711yescharacteristic
558C22×C4⋊C4C22×C4711yescharacteristic
559C22×C4⋊C4C22×C4711yescharacteristic
560C22×C4⋊C4C22×C4711yescharacteristic
561C22×C22⋊C4C22×C4711yescharacteristic
562C22×C22⋊C4C22×C4711yescharacteristic
563C22×C22⋊C4C22×C4711yescharacteristic
564C22×C22⋊C4C22×C4711yescharacteristic
565C22×C42C22×C4711yescharacteristic
566C22×C42C22×C4711yescharacteristic
567#389—24no—
568#385—24no—
569#385—24no—
570#385C4×C4718yescomplemented
571#380—24no—
572C4×C22⋊C4—24no—
573C2×#95—24no—
574C2×#95C22×C4711yescharacteristic
575C2×#95C22×C4711yescharacteristic
576C2×#95C22×C4711yescharacteristic
577C2×#95C22×C4711yescharacteristic
578C2×#95C22×C4711yescharacteristic
579C2×#95C22×C4711yescharacteristic
580C2×#95C22×C4711yescharacteristic
581C2×#95C22×C4711yescharacteristic
582C2×#95C22×C4711yescharacteristic
583C2×#95C22×C4711yescharacteristic
584C2×#95C22×C4711yescharacteristic
585C2×#95C22×C4711yescharacteristic
586C2×#95C22×C4711yescharacteristic
587C2×#95C22×C4711yescharacteristic
588C2×#95C22×C4711yescharacteristic
589C2×#95C22×C4711yescharacteristic
590C2×#95C22×C4711yescharacteristic
591C2×#95C22×C4711yescharacteristic
592C47#1400411yescharacteristic, direct product factor, Sylow
593C25C23×C4711yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4C2×C4×C4714yes—
614C23×C4Q8×C4714yes—
615C23×C4C23×C4711yescharacteristic
616C23×C4C23×C4711yescharacteristic
617C23×C4C23×C4711yescharacteristic
618C23×C4C23×C4711yescharacteristic
619C23×C4C23×C4711yescharacteristic
620C23×C4C23×C4711yescharacteristic
621C23×C4C23×C4711yescharacteristic
622C23×C4C23×C4711yescharacteristic
623C23×C4C23×C4711yescharacteristic
624C23×C4C23×C4711yescharacteristic
625C23×C4C23×C4711yescharacteristic
626C23×C4C23×C4711yescharacteristic
627C23×C4C23×C4711yescharacteristic
628C23×C4C23×C4711yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4C2×C4×C4714yescomplemented
652C2×C4⋊C4C2×C4×C4714yescomplemented
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4C2×C4×C4714yes—
661C2×C22⋊C4C2×C4×C4714yes—
662C2×C22⋊C4D4×C4714yes—
663C2×C22⋊C4D4×C4714yes—
664C2×C22⋊C4Q8×C4714yes—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—22no—
669C2×C42—41no—
670C2×C42—41no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—41no—
685#95—41no—
686#95C2×C4×C4714yescomplemented
687#95C2×C4×C4714yescomplemented
688#95D4×C4714yes—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C22×C4×C4712yes—
698C24C2×D4×C4712yes—
699C24C2×D4×C4712yes—
700C24C2×Q8×C4712yes—
701C24C2×Q8×C4712yes—
702C24#41×C4712yes—
703C24#41×C4712yes—
704C24C24×C4711yescharacteristic
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—28no—
722C22×C4—28no—
723C22×C4—28no—
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—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—28no—
773C22×C4—28no—
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—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4C22×C4×C4712yes—
805C22×C4C22×C4×C4712yes—
806C22×C4C22×C4×C4712yes—
807C22×C4C22×C4×C4712yes—
808C22×C4C22×C4×C4712yes—
809C22×C4C22×C4×C4712yes—
810C22×C4C2×D4×C4712yes—
811C22×C4C2×D4×C4712yes—
812C22×C4C2×D4×C4712yes—
813C22×C4C2×D4×C4712yes—
814C22×C4C2×D4×C4712yes—
815C22×C4C2×D4×C4712yes—
816C22×C4C2×D4×C4712yes—
817C22×C4C2×Q8×C4712yes—
818C22×C4C2×Q8×C4712yes—
819C22×C4C2×Q8×C4712yes—
820C22×C4C2×Q8×C4712yes—
821C22×C4#41×C4712yes—
822C22×C4#41×C4712yes—
823C22×C4#41×C4712yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—44no—
835C22⋊C4C4⋊C4×C47116yescomplemented
836C42—44no—
837C42—44no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊C4×C4714yes—
867C23C4×D4×C4714yes—
868C23C4×Q8×C4714yes—
869C23#121×C4714yes—
870C23C22⋊Q8×C4714yes—
871C23#125×C4714yes—
872C23C4⋊Q8×C4714yes—
873C23C23×C4×C4711yescharacteristic
874C23C22×D4×C4711yescharacteristic
875C23C22×D4×C4711yescharacteristic
876C23C22×D4×C4711yescharacteristic
877C23C22×Q8×C4711yescharacteristic
878C23C22×Q8×C4711yescharacteristic
879C23C2×#41×C4711yescharacteristic
880C23C2×#41×C4711yescharacteristic
881C23C2×#41×C4711yescharacteristic
882C23C2×#41×C4711yescharacteristic
883C23C2×#41×C4711yescharacteristic
884C23H(5,𝔽2)×C4711yescharacteristic
885C23H(5,𝔽2)×C4711yescharacteristic
886C23H(5,𝔽2)×C4711yescharacteristic
887C232−1+4×C4711yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—416no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
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×C4C2×C4⋊C4×C4714yes—
986C2×C4C2×C4⋊C4×C4714yes—
987C2×C4C4×D4×C4714yes—
988C2×C4C22⋊Q8×C4714yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C47×#38918yescomplemented
1004C22C22×C4⋊C4×C4711yescharacteristic
1005C22C2×C4×D4×C4711yescharacteristic
1006C22C2×C4×D4×C4711yescharacteristic
1007C22C2×C4×Q8×C4711yescharacteristic
1008C22C4×#41×C4711yescharacteristic
1009C22C47×#51811yescharacteristic
1010C22C47×#52011yescharacteristic
1011C22C2×#121×C4711yescharacteristic
1012C22C2×C22⋊Q8×C4711yescharacteristic
1013C22C2×C22⋊Q8×C4711yescharacteristic
1014C22C47×#52511yescharacteristic
1015C22C2×#125×C4711yescharacteristic
1016C22C47×#52911yescharacteristic
1017C22C2×C4⋊Q8×C4711yescharacteristic
1018C22C47×#53311yescharacteristic
1019C22C47×#53811yescharacteristic
1020C22C47×#53911yescharacteristic
1021C22C47×#54311yescharacteristic
1022C22C47×#54411yescharacteristic
1023C22D42×C4711yescharacteristic
1024C22D42×C4711yescharacteristic
1025C22C47×#54611yescharacteristic
1026C22C47×#54611yescharacteristic
1027C22C47×#54611yescharacteristic
1028C22C47×#54611yescharacteristic
1029C22C47×#54611yescharacteristic
1030C22C47×#54711yescharacteristic
1031C22C47×#54711yescharacteristic
1032C22D4×Q8×C4711yescharacteristic
1033C22C47×#55111yescharacteristic
1034C22C47×#55111yescharacteristic
1035C22C47×#55211yescharacteristic
1036C22C47×#55411yescharacteristic
1037C22C47×#55411yescharacteristic
1038C22C47×#55411yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—81no—
1052C4—81no—
1053C2—28no—
1054C2C2×C47×#38911yescharacteristic
1055C2C4×C22⋊Q8×C4711yescharacteristic
1056C2C47×#232911yescharacteristic
1057C2D4×C4⋊C4×C4711yescharacteristic
1058C2C47×#234911yescharacteristic
1059C2C47×#235811yescharacteristic
1060C2C47×#235911yescharacteristic
1061C2C47×#242411yescharacteristic
1062C2C47×#242511yescharacteristic
1063C2C47×#243711yescharacteristic
1064C2C47×#243811yescharacteristic
1065C2C47×#244011yescharacteristic
1066C2C47×#247311yescharacteristic
1067C2C47×#250511yescharacteristic
1068C2C47×#254911yescharacteristic
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
8. C47×#1444C2semidirect
9. C47×#1442C2semidirect
10. C47×#1441C2semidirect
11. C47×#1441C2semidirect
12. C47×#1436C2semidirect
13. C47×#1436C2semidirect
14. C47×C4⋊#95C2semidirect
36. C47×#385C4semidirect
116. C2×C4⋊C4×C47C2×C4semidirect
117. C2×C4⋊C4×C47C2×C4semidirect
151. #95×C47C2×C4semidirect
152. #95×C47C2×C4semidirect
300. C22⋊C4×C47C4⋊C4semidirect
454. #14004C47direct (N × H)
469. C22×C47#389semidirect
519. C2×#389C2×C47semidirect
526. #1444C2×C47semidirect
527. #1442C2×C47semidirect
528. #1441C2×C47semidirect
529. #1441C2×C47semidirect
530. #1436C2×C47semidirect
531. #1436C2×C47semidirect
532. C4⋊#95C2×C47semidirect
570. #385C4×C47semidirect
592. C47#14004direct (N × H)
651. C2×C4⋊C4C2×C4×C47semidirect
652. C2×C4⋊C4C2×C4×C47semidirect
686. #95C2×C4×C47semidirect
687. #95C2×C4×C47semidirect
835. C22⋊C4C4⋊C4×C47semidirect
1003. C22C47×#389semidirect

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×#3852
C2×C47×#3802
C2×C4×C22⋊C4×C472
C22×#95×C472
C47×#14442
C47×#14422
C47×#14412
C47×#14362
C47×C4⋊#952
C47×C22⋊#952
#1400447