Finite Group Databasebeta

← C47×#26954 #26066652

Subgroups — C47×#26954 #26066652

Order 12032.

1026 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#482C211yesmaximal, characteristic, complemented
2C2×C47×#459C211yesmaximal, characteristic, complemented
3C47×#2428C211yesmaximal, characteristic, complemented
4C47×#2363C211yesmaximal, characteristic, complemented
5C47×#2088C211yesmaximal, characteristic, complemented
6C47×#2041C211yesmaximal, characteristic, complemented
7C47×#1999C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1972C211yesmaximal, characteristic, complemented
10C47×#1925C211yesmaximal, characteristic, complemented
11C47×#1924C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1875C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C47×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C2×#127×C47C2211yescharacteristic
19C2×#121×C47—21no—
20C2×#121×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C2×#117×C47C2211yescharacteristic
26C47×#482—24no—
27C47×#459—24no—
28C2×#107×C47C2211yescharacteristic
29C2×#106×C47C2211yescharacteristic
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×C22⋊C8×C47C2211yescharacteristic
41C2×#97×C47C2211yescharacteristic
42C47×#394—21no—
43C47×#392—21no—
44C47×#390—21no—
45C47×#390C2211yescharacteristic
46C47×#390C2211yescharacteristic
47C47×#389C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#388—21no—
50C47×#386—21no—
51C47×#386—21no—
52C4×C4⋊C4×C47C2211yescharacteristic
53C4×C22⋊C4×C47—21no—
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×D4×C47—21no—
62C22×D4×C47—21no—
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C23×C4×C47—21no—
70C23×C4×C47—21no—
71C23×C4×C47C2311yescharacteristic
72C2×D8×C47—22no—
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—22no—
76C2×D8×C47—41no—
77C2×D8×C47—41no—
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82#127×C47—22no—
83#127×C47—41no—
84#121×C47—22no—
85#121×C47—22no—
86#121×C47—22no—
87#121×C47—22no—
88#121×C47—44no—
89#121×C47—41no—
90#121×C47—41no—
91C4×D4×C47—22no—
92C4×D4×C47—22no—
93C4×D4×C47—41no—
94C4×D4×C47—41no—
95#117×C47—22no—
96#117×C47—41no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47D411yescharacteristic
115C2×C22⋊C4×C47D411yescharacteristic
116C2×C42×C47—21no—
117C2×C42×C47—21no—
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120#107×C47—22no—
121#106×C47—22no—
122C4⋊C8×C47—22no—
123#102×C47—22no—
124#102×C47—22no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128#102×C47—41no—
129#102×C47—41no—
130#102×C47D414yescomplemented
131C22⋊C8×C47—22no—
132C22⋊C8×C47—41no—
133#97×C47—41no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47D411yescharacteristic
138#95×C47D411yescharacteristic
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143C2×D4×C47—24no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
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—42no—
161C2×D4×C47—42no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
168C2×D4×C47—81no—
169C2×D4×C47—81no—
170C2×D4×C47—81no—
171C2×D4×C47—81no—
172C2×D4×C47—81no—
173C2×D4×C47—81no—
174C2×D4×C47C2×D412yes—
175C2×D4×C47#4112yes—
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—42no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47—81no—
192C22×C4×C47—81no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199D8×C47—44no—
200D8×C47—44no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
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×C47C2×D412yes—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—42no—
221C4⋊C4×C47—81no—
222C4⋊C4×C47C2×D412yes—
223C4⋊C4×C47#4112yes—
224C4⋊C4×C47#4112yes—
225C22⋊C4×C47—24no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—41no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—81no—
236C22⋊C4×C47—81no—
237C42×C47—21no—
238C42×C47—21no—
239C42×C47—21no—
240C42×C47—21no—
241C42×C47—42no—
242C42×C47—81no—
243C23×C47—22no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—22no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
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×C47C22×D411yescharacteristic
272D4×C47—22no—
273D4×C47—22no—
274D4×C47—22no—
275D4×C47—22no—
276D4×C47—41no—
277D4×C47—41no—
278D4×C47—41no—
279D4×C47—41no—
280D4×C47—41no—
281D4×C47—41no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—84no—
285D4×C47—84no—
286D4×C47—84no—
287D4×C47—84no—
288D4×C47—84no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—22no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—22no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—41no—
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—84no—
323C2×C4×C47—84no—
324C2×C4×C47AGL(1,ℤ/8)12yes—
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×C4×C47C2×#4111yescharacteristic
328C2×C4×C47C2×#4111yescharacteristic
329C2×C4×C47H(5,𝔽2)11yescharacteristic
330C2×C4×C47H(5,𝔽2)11yescharacteristic
331C8×C47—22no—
332C8×C47—41no—
333C8×C47—41no—
334C8×C47—41no—
335#26954C4711yesmaximal, characteristic, direct product factor, Sylow
336C22×C47—41no—
337C22×C47—42no—
338C22×C47—41no—
339C22×C47—42no—
340C22×C47—41no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—41no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—81no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47—81no—
353C22×C47—81no—
354C22×C47—81no—
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#52511yescharacteristic
365C22×C47D4211yescharacteristic
366C22×C47#54611yescharacteristic
367C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C47#57511yescharacteristic
369C22×C47#57611yescharacteristic
370C22×C47#57611yescharacteristic
371C4×C47—22no—
372C4×C47—42no—
373C4×C47—41no—
374C4×C47—42no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—42no—
379C4×C47—81no—
380C4×C47—81no—
381C4×C47#53211yescharacteristic
382C4×C47#54011yescharacteristic
383C4×C47#54611yescharacteristic
384C4×C47#55311yescharacteristic
385C2×#482C2×C4711yescharacteristic, complemented
386C2×#459C2×C4711yescharacteristic, complemented
387#2428C2×C4711yescharacteristic, complemented
388#2363C2×C4711yescharacteristic, complemented
389#2088C2×C4711yescharacteristic, complemented
390#2041C2×C4711yescharacteristic, complemented
391#1999C2×C4711yescharacteristic, complemented
392#1999C2×C4711yescharacteristic, complemented
393#1972C2×C4711yescharacteristic, complemented
394#1925C2×C4711yescharacteristic, complemented
395#1924C2×C4711yescharacteristic, complemented
396#1879C2×C4711yescharacteristic, complemented
397#1875C2×C4711yescharacteristic, complemented
398#1862C2×C4711yescharacteristic, complemented
399#1762C2×C4711yescharacteristic, complemented
400C2×C47—81no—
401C2×C47—82no—
402C2×C47—82no—
403C2×C47—161no—
404C2×C47#246411yescharacteristic
405C2×C47#311511yescharacteristic
406C2×C47#312211yescharacteristic
407C2×C47#326411yescharacteristic
408C2×C47#326811yescharacteristic
409C2×C47#330911yescharacteristic
410C2×C47#332511yescharacteristic
411C22×D8C22×C4711yescharacteristic
412C22×D8C22×C4711yescharacteristic
413C2×#127C22×C4711yescharacteristic
414C2×#121—21no—
415C2×#121C22×C4711yescharacteristic
416C2×#121C22×C4711yescharacteristic
417C2×#121C22×C4711yescharacteristic
418C2×C4×D4C22×C4711yescharacteristic
419C2×C4×D4C22×C4711yescharacteristic
420C2×#117C22×C4711yescharacteristic
421#482—24no—
422#459—24no—
423C2×#107C22×C4711yescharacteristic
424C2×#106C22×C4711yescharacteristic
425C2×C4⋊C8C22×C4711yescharacteristic
426C2×#102C22×C4711yescharacteristic
427C2×#102C22×C4711yescharacteristic
428C2×#102C22×C4711yescharacteristic
429C2×#102C22×C4711yescharacteristic
430C2×#102C22×C4711yescharacteristic
431C2×#102C22×C4711yescharacteristic
432C2×#102C22×C4711yescharacteristic
433C2×#102C22×C4711yescharacteristic
434C2×C22⋊C8C22×C4711yescharacteristic
435C2×C22⋊C8C22×C4711yescharacteristic
436C2×#97C22×C4711yescharacteristic
437#394—21no—
438#392—21no—
439#390—21no—
440#390C22×C4711yescharacteristic
441#390C22×C4711yescharacteristic
442#389C22×C4711yescharacteristic
443#389C22×C4711yescharacteristic
444#388—21no—
445#386—21no—
446#386—21no—
447C4×C4⋊C4C22×C4711yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4C22×C4711yescharacteristic
450#340C22×C4711yescharacteristic
451#340C22×C4711yescharacteristic
452#340C22×C4711yescharacteristic
453#340C22×C4711yescharacteristic
454#336C22×C4711yescharacteristic
455#336C22×C4711yescharacteristic
456C47#2695411yescharacteristic, direct product factor, Sylow
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C4711yescharacteristic
463C22×D4C23×C4711yescharacteristic
464C22×D4C23×C4711yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C4711yescharacteristic
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C2×D8—41no—
474C22×C8C23×C4711yescharacteristic
475C22×C8C23×C4711yescharacteristic
476C22×C8C23×C4711yescharacteristic
477C22×C8C23×C4711yescharacteristic
478#127—22no—
479#127—41no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—44no—
485#121—41no—
486#121—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C4711yescharacteristic
496C2×C4⋊C4C23×C4711yescharacteristic
497C2×C4⋊C4C23×C4711yescharacteristic
498C2×C4⋊C4C23×C4711yescharacteristic
499C2×C4⋊C4C23×C4711yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C4711yescharacteristic
511C2×C22⋊C4D4×C4711yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C23×C4711yescharacteristic
515C2×C42C23×C4711yescharacteristic
516#107—22no—
517#106—22no—
518C4⋊C8—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—41no—
525#102—41no—
526#102D4×C4714yescomplemented
527C22⋊C8—22no—
528C22⋊C8—41no—
529#97—41no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C4711yescharacteristic
534#95D4×C4711yescharacteristic
535C24—21no—
536C24—21no—
537C24—21no—
538C24C2×D4×C4711yescharacteristic
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4C2×D4×C4712yes—
571C2×D4#41×C4712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C2×D4×C4711yescharacteristic
590C22×C4C2×D4×C4711yescharacteristic
591C22×C4C2×D4×C4711yescharacteristic
592C22×C4C2×D4×C4711yescharacteristic
593C22×C4C2×D4×C4711yescharacteristic
594C22×C4C24×C4711yescharacteristic
595D8—44no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8C2×D4×C4712yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C4712yes—
619C4⋊C4#41×C4712yes—
620C4⋊C4#41×C4712yes—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C22×D4×C4711yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—84no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
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—84no—
719C2×C4—84no—
720C2×C4AGL(1,ℤ/8)×C4712yes—
721C2×C4C22×D4×C4711yescharacteristic
722C2×C4C2×#41×C4711yescharacteristic
723C2×C4C2×#41×C4711yescharacteristic
724C2×C4C2×#41×C4711yescharacteristic
725C2×C4H(5,𝔽2)×C4711yescharacteristic
726C2×C4H(5,𝔽2)×C4711yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C47×#52511yescharacteristic
760C22D42×C4711yescharacteristic
761C22C47×#54611yescharacteristic
762C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
763C22C47×#57511yescharacteristic
764C22C47×#57611yescharacteristic
765C22C47×#57611yescharacteristic
766C4—22no—
767C4—41no—
768C4—41no—
769C4—42no—
770C4—42no—
771C4—41no—
772C4—42no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4C47×#53211yescharacteristic
777C4C47×#54011yescharacteristic
778C4C47×#54611yescharacteristic
779C4C47×#55311yescharacteristic
780C2—81no—
781C2—82no—
782C2—82no—
783C2—161no—
784C2C47×#246411yescharacteristic
785C2C47×#311511yescharacteristic
786C2C47×#312211yescharacteristic
787C2C47×#326411yescharacteristic
788C2C47×#326811yescharacteristic
789C2C47×#330911yescharacteristic
790C2C47×#332511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#482C2semidirect
2. C2×C47×#459C2semidirect
3. C47×#2428C2semidirect
4. C47×#2363C2semidirect
5. C47×#2088C2semidirect
6. C47×#2041C2semidirect
7. C47×#1999C2semidirect
8. C47×#1999C2semidirect
9. C47×#1972C2semidirect
10. C47×#1925C2semidirect
11. C47×#1924C2semidirect
12. C47×#1879C2semidirect
13. C47×#1875C2semidirect
14. C47×#1862C2semidirect
15. C47×#1762C2semidirect
130. #102×C47D4semidirect
335. #26954C47direct (N × H)
385. C2×#482C2×C47semidirect
386. C2×#459C2×C47semidirect
387. #2428C2×C47semidirect
388. #2363C2×C47semidirect
389. #2088C2×C47semidirect
390. #2041C2×C47semidirect
391. #1999C2×C47semidirect
392. #1999C2×C47semidirect
393. #1972C2×C47semidirect
394. #1925C2×C47semidirect
395. #1924C2×C47semidirect
396. #1879C2×C47semidirect
397. #1875C2×C47semidirect
398. #1862C2×C47semidirect
399. #1762C2×C47semidirect
456. C47#26954direct (N × H)
526. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4822
C2×C47×#4592
C47×#24282
C47×#23632
C47×#20882
C47×#20412
C47×#19992
C47×#19722
C47×#19252
C47×#19242
C47×#18792
C47×#18752
C47×#18622
C47×#17622
#2695447