Finite Group Databasebeta

← C47×#24792 #26064490

Subgroups — C47×#24792 #26064490

Order 12032.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#469C211yesmaximal, characteristic, complemented
2C2×C47×#469C211yesmaximal, characteristic, complemented
3C2×C47×#436C211yesmaximal, characteristic, complemented
4C2×C47×#428C211yesmaximal, characteristic, complemented
5C47×#2416C211yesmaximal, characteristic, complemented
6C47×#2414C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2034C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#1970C211yesmaximal, characteristic, complemented
12C47×#1941C211yesmaximal, characteristic, complemented
13C47×#1875C211yesmaximal, characteristic, complemented
14C47×#1874C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C2×#121×C47—21no—
20C2×#121×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C2×#117×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C47×#469—24no—
28C47×#469—24no—
29C47×#436—24no—
30C47×#428—24no—
31C2×#107×C47C2211yescharacteristic
32C2×#107×C47C2211yescharacteristic
33C2×#106×C47C2211yescharacteristic
34C2×#106×C47C2211yescharacteristic
35C2×#106×C47C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C4×C8×C47C2211yescharacteristic
46C47×#396—21no—
47C47×#394—21no—
48C47×#394—21no—
49C47×#392—21no—
50C47×#390—21no—
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#389C2211yescharacteristic
55C47×#388—21no—
56C47×#386—21no—
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47D411yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C23×C4×C47—21no—
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2311yescharacteristic
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—22no—
76C2×M16×C47—22no—
77C2×M16×C47—22no—
78C2×M16×C47—22no—
79C2×M16×C47—22no—
80C2×M16×C47—22no—
81C2×M16×C47D414yescomplemented
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86#121×C47—22no—
87#121×C47—22no—
88#121×C47—22no—
89#121×C47—22no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—41no—
93#121×C47—41no—
94#121×C47—44no—
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97#117×C47—22no—
98#117×C47—41no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—41no—
104C2×C4⋊C4×C47D411yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47D411yescharacteristic
123C2×C22⋊C4×C47D411yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47C2311yescharacteristic
126#107×C47—22no—
127#107×C47—22no—
128#106×C47—22no—
129#106×C47—22no—
130#106×C47D414yescomplemented
131C4⋊C8×C47—22no—
132#102×C47—22no—
133#102×C47—22no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—41no—
137#102×C47—41no—
138C22⋊C8×C47—22no—
139C22⋊C8×C47—22no—
140C4×C8×C47—22no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144#95×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47C2×D411yescharacteristic
148C24×C47C2×D411yescharacteristic
149C2×D4×C47—22no—
150C2×D4×C47—22no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—41no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—81no—
173C2×D4×C47—81no—
174C2×D4×C47—81no—
175C2×D4×C47—81no—
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—42no—
193C22×C4×C47—42no—
194C22×C4×C47—81no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47#4112yes—
201C22×C4×C47C2411yescharacteristic
202D8×C47—44no—
203M16×C47—28no—
204M16×C47—44no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47C2×D412yes—
214C2×C8×C47C2×D412yes—
215C2×C8×C47C2×D412yes—
216C2×C8×C47#4112yes—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—42no—
229C4⋊C4×C47—42no—
230C4⋊C4×C47—81no—
231C4⋊C4×C47C2×D412yes—
232C4⋊C4×C47C2×D412yes—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—81no—
244C22⋊C4×C47—81no—
245C22⋊C4×C47—81no—
246C42×C47—21no—
247C42×C47—21no—
248C42×C47—42no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47#12112yes—
277C23×C47C22×D411yescharacteristic
278D4×C47—44no—
279D4×C47—41no—
280D4×C47—41no—
281D4×C47—41no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—41no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—84no—
288D4×C47—84no—
289D4×C47—84no—
290D4×C47—84no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—22no—
302C2×C4×C47—21no—
303C2×C4×C47—22no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—84no—
328C2×C4×C47#12112yes—
329C2×C4×C47AGL(1,ℤ/8)12yes—
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C2×#4111yescharacteristic
333C2×C4×C47C2×#4111yescharacteristic
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C2×C4×C472−1+411yescharacteristic
336C8×C47—22no—
337C8×C47—41no—
338C8×C47—41no—
339C8×C47#12114yescomplemented
340#24792C4711yesmaximal, characteristic, direct product factor, Sylow
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—81no—
359C22×C47—81no—
360C22×C47—81no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—81no—
369C22×C47C2×#12111yescharacteristic
370C22×C47D4211yescharacteristic
371C22×C47#54711yescharacteristic
372C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C47#57511yescharacteristic
374C22×C47#57611yescharacteristic
375C22×C47#57711yescharacteristic
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—41no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—41no—
382C4×C47—81no—
383C4×C47—81no—
384C4×C47—81no—
385C4×C47—81no—
386C4×C47C2×#12111yescharacteristic
387C4×C47#53711yescharacteristic
388C4×C47#54811yescharacteristic
389C4×C47#55311yescharacteristic
390C2×#469C2×C4711yescharacteristic, complemented
391C2×#469C2×C4711yescharacteristic, complemented
392C2×#436C2×C4711yescharacteristic, complemented
393C2×#428C2×C4711yescharacteristic, complemented
394#2416C2×C4711yescharacteristic, complemented
395#2414C2×C4711yescharacteristic, complemented
396#2067C2×C4711yescharacteristic, complemented
397#2065C2×C4711yescharacteristic, complemented
398#2034C2×C4711yescharacteristic, complemented
399#2033C2×C4711yescharacteristic, complemented
400#1970C2×C4711yescharacteristic, complemented
401#1941C2×C4711yescharacteristic, complemented
402#1875C2×C4711yescharacteristic, complemented
403#1874C2×C4711yescharacteristic, complemented
404#1809C2×C4711yescharacteristic, complemented
405C2×C47—42no—
406C2×C47—81no—
407C2×C47—161no—
408C2×C47—161no—
409C2×C47#241611yescharacteristic
410C2×C47#305511yescharacteristic
411C2×C47#306211yescharacteristic
412C2×C47#327411yescharacteristic
413C2×C47#327511yescharacteristic
414C2×C47#335411yescharacteristic
415C2×C47#335511yescharacteristic
416C22×D8C22×C4711yescharacteristic
417C22×M16C22×C4711yescharacteristic
418C22×M16C22×C4711yescharacteristic
419C2×#121—21no—
420C2×#121C22×C4711yescharacteristic
421C2×#121C22×C4711yescharacteristic
422C2×#121C22×C4711yescharacteristic
423C2×#121C22×C4711yescharacteristic
424C2×C4×D4C22×C4711yescharacteristic
425C2×#117C22×C4711yescharacteristic
426C22×C4⋊C4C22×C4711yescharacteristic
427#469—24no—
428#469—24no—
429#436—24no—
430#428—24no—
431C2×#107C22×C4711yescharacteristic
432C2×#107C22×C4711yescharacteristic
433C2×#106C22×C4711yescharacteristic
434C2×#106C22×C4711yescharacteristic
435C2×#106C22×C4711yescharacteristic
436C2×C4⋊C8C22×C4711yescharacteristic
437C2×#102C22×C4711yescharacteristic
438C2×#102C22×C4711yescharacteristic
439C2×#102C22×C4711yescharacteristic
440C2×#102C22×C4711yescharacteristic
441C2×#102C22×C4711yescharacteristic
442C2×#102C22×C4711yescharacteristic
443C2×C22⋊C8C22×C4711yescharacteristic
444C2×C22⋊C8C22×C4711yescharacteristic
445C2×C4×C8C22×C4711yescharacteristic
446#396—21no—
447#394—21no—
448#394—21no—
449#392—21no—
450#390—21no—
451#390C22×C4711yescharacteristic
452#390C22×C4711yescharacteristic
453#389C22×C4711yescharacteristic
454#389C22×C4711yescharacteristic
455#388—21no—
456#386—21no—
457#380C22×C4711yescharacteristic
458#380C22×C4711yescharacteristic
459#340C22×C4711yescharacteristic
460#340C22×C4711yescharacteristic
461#340C22×C4711yescharacteristic
462#340C22×C4711yescharacteristic
463C47#2479211yescharacteristic, direct product factor, Sylow
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4D4×C4711yescharacteristic
469C22×D4C23×C4711yescharacteristic
470C22×D4C23×C4711yescharacteristic
471C23×C4—21no—
472C23×C4C23×C4711yescharacteristic
473C23×C4C23×C4711yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16D4×C4714yescomplemented
483C22×C8C23×C4711yescharacteristic
484C22×C8C23×C4711yescharacteristic
485C22×C8C23×C4711yescharacteristic
486C22×C8C23×C4711yescharacteristic
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#121—44no—
496C4×D4—22no—
497C4×D4—22no—
498#117—22no—
499#117—41no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4D4×C4711yescharacteristic
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C4⋊C4C23×C4711yescharacteristic
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C4⋊C4C23×C4711yescharacteristic
510C2×C4⋊C4C23×C4711yescharacteristic
511C2×C4⋊C4C23×C4711yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4D4×C4711yescharacteristic
524C2×C22⋊C4D4×C4711yescharacteristic
525C2×C42—21no—
526C2×C42C23×C4711yescharacteristic
527#107—22no—
528#107—22no—
529#106—22no—
530#106—22no—
531#106D4×C4714yescomplemented
532C4⋊C8—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C4×C8—22no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546C24—21no—
547C24—21no—
548C24C2×D4×C4711yescharacteristic
549C24C2×D4×C4711yescharacteristic
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—41no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4C2×D4×C4711yescharacteristic
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4711yescharacteristic
599C22×C4C2×D4×C4712yes—
600C22×C4C2×D4×C4711yescharacteristic
601C22×C4#41×C4712yes—
602C22×C4C24×C4711yescharacteristic
603D8—44no—
604M16—28no—
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8C2×D4×C4712yes—
615C2×C8C2×D4×C4712yes—
616C2×C8C2×D4×C4712yes—
617C2×C8#41×C4712yes—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—81no—
632C4⋊C4C2×D4×C4712yes—
633C4⋊C4C2×D4×C4712yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23#121×C4712yes—
678C23C22×D4×C4711yescharacteristic
679D4—44no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—84no—
729C2×C4#121×C4712yes—
730C2×C4AGL(1,ℤ/8)×C4712yes—
731C2×C4C22×D4×C4711yescharacteristic
732C2×C4C22×D4×C4711yescharacteristic
733C2×C4C2×#41×C4711yescharacteristic
734C2×C4C2×#41×C4711yescharacteristic
735C2×C4H(5,𝔽2)×C4711yescharacteristic
736C2×C42−1+4×C4711yescharacteristic
737C8—22no—
738C8—41no—
739C8—41no—
740C8#121×C4714yescomplemented
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×#121×C4711yescharacteristic
770C22D42×C4711yescharacteristic
771C22C47×#54711yescharacteristic
772C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
773C22C47×#57511yescharacteristic
774C22C47×#57611yescharacteristic
775C22C47×#57711yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C2×#121×C4711yescharacteristic
787C4C47×#53711yescharacteristic
788C4C47×#54811yescharacteristic
789C4C47×#55311yescharacteristic
790C2—42no—
791C2—81no—
792C2—161no—
793C2—161no—
794C2C47×#241611yescharacteristic
795C2C47×#305511yescharacteristic
796C2C47×#306211yescharacteristic
797C2C47×#327411yescharacteristic
798C2C47×#327511yescharacteristic
799C2C47×#335411yescharacteristic
800C2C47×#335511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#469C2semidirect
2. C2×C47×#469C2semidirect
3. C2×C47×#436C2semidirect
4. C2×C47×#428C2semidirect
5. C47×#2416C2semidirect
6. C47×#2414C2semidirect
7. C47×#2067C2semidirect
8. C47×#2065C2semidirect
9. C47×#2034C2semidirect
10. C47×#2033C2semidirect
11. C47×#1970C2semidirect
12. C47×#1941C2semidirect
13. C47×#1875C2semidirect
14. C47×#1874C2semidirect
15. C47×#1809C2semidirect
81. C2×M16×C47D4semidirect
130. #106×C47D4semidirect
339. C8×C47#121semidirect
340. #24792C47direct (N × H)
390. C2×#469C2×C47semidirect
391. C2×#469C2×C47semidirect
392. C2×#436C2×C47semidirect
393. C2×#428C2×C47semidirect
394. #2416C2×C47semidirect
395. #2414C2×C47semidirect
396. #2067C2×C47semidirect
397. #2065C2×C47semidirect
398. #2034C2×C47semidirect
399. #2033C2×C47semidirect
400. #1970C2×C47semidirect
401. #1941C2×C47semidirect
402. #1875C2×C47semidirect
403. #1874C2×C47semidirect
404. #1809C2×C47semidirect
463. C47#24792direct (N × H)
482. C2×M16D4×C47semidirect
531. #106D4×C47semidirect
740. C8#121×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4692
C2×C47×#4362
C2×C47×#4282
C47×#24162
C47×#24142
C47×#20672
C47×#20652
C47×#20342
C47×#20332
C47×#19702
C47×#19412
C47×#18752
C47×#18742
C47×#18092
#2479247