Finite Group Databasebeta

← C47×#24662 #26064360

Subgroups — C47×#24662 #26064360

Order 12032.

970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#459C211yesmaximal, characteristic, complemented
2C2×C47×#433C211yesmaximal, characteristic, complemented
3C47×#2619C211yesmaximal, characteristic, complemented
4C47×#2324C211yesmaximal, characteristic, complemented
5C47×#2034C211yesmaximal, characteristic, complemented
6C47×#2033C211yesmaximal, characteristic, complemented
7C47×#1999C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1982C211yesmaximal, characteristic, complemented
10C47×#1972C211yesmaximal, characteristic, complemented
11C47×#1970C211yesmaximal, characteristic, complemented
12C47×#1949C211yesmaximal, characteristic, complemented
13C47×#1936C211yesmaximal, characteristic, complemented
14C47×#1934C211yesmaximal, characteristic, complemented
15C47×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C2×#127×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×#121×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×#117×C47C2211yescharacteristic
24C47×#459—24no—
25C47×#433—24no—
26C2×#107×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4⋊C8×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×#97×C47C2211yescharacteristic
41C2×C4×C8×C47C2211yescharacteristic
42C47×#394—21no—
43C47×#394—21no—
44C47×#392—21no—
45C47×#392—21no—
46C47×#390—21no—
47C47×#390C2211yescharacteristic
48C47×#390C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#388—21no—
52C47×#386—21no—
53C47×#385—21no—
54C47×#382C2211yescharacteristic
55C47×#380C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
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×C47C2311yescharacteristic
71C2×D8×C47—22no—
72C2×D8×C47—22no—
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—41no—
76C2×D8×C47—41no—
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81#127×C47—22no—
82#127×C47—22no—
83#121×C47—22no—
84#121×C47—22no—
85#121×C47—41no—
86#121×C47—41no—
87#121×C47—41no—
88#121×C47—41no—
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91#117×C47—22no—
92#117×C47—22no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47D411yescharacteristic
95C2×C4⋊C4×C47D411yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
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×C47D411yescharacteristic
113C2×C22⋊C4×C47D411yescharacteristic
114C2×C42×C47—21no—
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117#107×C47—41no—
118#106×C47—41no—
119C4⋊C8×C47—22no—
120C4⋊C8×C47D414yescomplemented
121#102×C47—22no—
122#102×C47—22no—
123#102×C47—22no—
124#102×C47—22no—
125#102×C47—41no—
126#102×C47—41no—
127#102×C47—41no—
128#102×C47—41no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—22no—
131#97×C47—22no—
132C4×C8×C47—22no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47C2×D411yescharacteristic
142C2×D4×C47—24no—
143C2×D4×C47—21no—
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—81no—
165C2×D4×C47—81no—
166C2×D4×C47—81no—
167C2×D4×C47—81no—
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×C47#4112yes—
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—42no—
187C22×C4×C47—81no—
188C22×C4×C47—81no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195D8×C47—44no—
196D8×C47—44no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
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×C47C2×D412yes—
208C2×C8×C47C2×D412yes—
209C4⋊C4×C47—22no—
210C4⋊C4×C47—22no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
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—81no—
221C4⋊C4×C47#4112yes—
222C22⋊C4×C47—24no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—42no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—81no—
229C22⋊C4×C47—81no—
230C22⋊C4×C47—81no—
231C22⋊C4×C47—81no—
232C22⋊C4×C47—81no—
233C22⋊C4×C47—81no—
234C22⋊C4×C47—81no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—81no—
238C42×C47C2×D412yes—
239C42×C47#4112yes—
240C23×C47—21no—
241C23×C47—22no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
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×C47C22×D411yescharacteristic
269D4×C47—22no—
270D4×C47—22no—
271D4×C47—41no—
272D4×C47—41no—
273D4×C47—41no—
274D4×C47—41no—
275D4×C47—41no—
276D4×C47—41no—
277D4×C47—41no—
278D4×C47—41no—
279D4×C47—41no—
280D4×C47—41no—
281D4×C47—84no—
282D4×C47—84no—
283D4×C47—84no—
284D4×C47—84no—
285D4×C47—84no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—22no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
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—84no—
319C2×C4×C47#12112yes—
320C2×C4×C47#12112yes—
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C2×#4111yescharacteristic
323C2×C4×C47C2×#4111yescharacteristic
324C2×C4×C47C2×#4111yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C47H(5,𝔽2)11yescharacteristic
327C8×C47—22no—
328C8×C47—22no—
329C8×C47—41no—
330C8×C47—41no—
331#24662C4711yesmaximal, characteristic, direct product factor, Sylow
332C22×C47—41no—
333C22×C47—42no—
334C22×C47—41no—
335C22×C47—42no—
336C22×C47—41no—
337C22×C47—42no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—81no—
343C22×C47—81no—
344C22×C47—81no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
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×C47C2×#12111yescharacteristic
361C22×C47#52511yescharacteristic
362C22×C47#53511yescharacteristic
363C22×C47#57611yescharacteristic
364C22×C47#57611yescharacteristic
365C22×C47#57611yescharacteristic
366C22×C47#57711yescharacteristic
367C4×C47—22no—
368C4×C47—22no—
369C4×C47—42no—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47—81no—
374C4×C47—81no—
375C4×C47—81no—
376C4×C47—81no—
377C4×C47#54611yescharacteristic
378C4×C47#55011yescharacteristic
379C4×C47#55311yescharacteristic
380C4×C47#55511yescharacteristic
381C2×#459C2×C4711yescharacteristic, complemented
382C2×#433C2×C4711yescharacteristic, complemented
383#2619C2×C4711yescharacteristic, complemented
384#2324C2×C4711yescharacteristic, complemented
385#2034C2×C4711yescharacteristic, complemented
386#2033C2×C4711yescharacteristic, complemented
387#1999C2×C4711yescharacteristic, complemented
388#1999C2×C4711yescharacteristic, complemented
389#1982C2×C4711yescharacteristic, complemented
390#1972C2×C4711yescharacteristic, complemented
391#1970C2×C4711yescharacteristic, complemented
392#1949C2×C4711yescharacteristic, complemented
393#1936C2×C4711yescharacteristic, complemented
394#1934C2×C4711yescharacteristic, complemented
395#1804C2×C4711yescharacteristic, complemented
396C2×C47—81no—
397C2×C47—82no—
398C2×C47—161no—
399C2×C47—161no—
400C2×C47#241411yescharacteristic
401C2×C47#305811yescharacteristic
402C2×C47#306211yescharacteristic
403C2×C47#311911yescharacteristic
404C2×C47#312211yescharacteristic
405C2×C47#322011yescharacteristic
406C2×C47#322411yescharacteristic
407C22×D8C22×C4711yescharacteristic
408C22×D8C22×C4711yescharacteristic
409C2×#127C22×C4711yescharacteristic
410C2×#121C22×C4711yescharacteristic
411C2×#121C22×C4711yescharacteristic
412C2×#121C22×C4711yescharacteristic
413C2×C4×D4C22×C4711yescharacteristic
414C2×#117C22×C4711yescharacteristic
415#459—24no—
416#433—24no—
417C2×#107C22×C4711yescharacteristic
418C2×#106C22×C4711yescharacteristic
419C2×C4⋊C8C22×C4711yescharacteristic
420C2×C4⋊C8C22×C4711yescharacteristic
421C2×#102C22×C4711yescharacteristic
422C2×#102C22×C4711yescharacteristic
423C2×#102C22×C4711yescharacteristic
424C2×#102C22×C4711yescharacteristic
425C2×#102C22×C4711yescharacteristic
426C2×#102C22×C4711yescharacteristic
427C2×#102C22×C4711yescharacteristic
428C2×#102C22×C4711yescharacteristic
429C2×C22⋊C8C22×C4711yescharacteristic
430C2×C22⋊C8C22×C4711yescharacteristic
431C2×#97C22×C4711yescharacteristic
432C2×C4×C8C22×C4711yescharacteristic
433#394—21no—
434#394—21no—
435#392—21no—
436#392—21no—
437#390—21no—
438#390C22×C4711yescharacteristic
439#390C22×C4711yescharacteristic
440#390C22×C4711yescharacteristic
441#389C22×C4711yescharacteristic
442#388—21no—
443#386—21no—
444#385—21no—
445#382C22×C4711yescharacteristic
446#380C22×C4711yescharacteristic
447C4×C4⋊C4C22×C4711yescharacteristic
448#340C22×C4711yescharacteristic
449#340C22×C4711yescharacteristic
450#340C22×C4711yescharacteristic
451#340C22×C4711yescharacteristic
452C47#2466211yescharacteristic, direct product factor, Sylow
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C23×C4711yescharacteristic
459C22×D4C23×C4711yescharacteristic
460C22×D4C23×C4711yescharacteristic
461C23×C4—21no—
462C23×C4C23×C4711yescharacteristic
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C22×C8C23×C4711yescharacteristic
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473#127—22no—
474#127—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—41no—
479#121—41no—
480#121—41no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C4711yescharacteristic
487C2×C4⋊C4D4×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C4⋊C4C23×C4711yescharacteristic
490C2×C4⋊C4C23×C4711yescharacteristic
491C2×C4⋊C4C23×C4711yescharacteristic
492C2×C4⋊C4C23×C4711yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C4711yescharacteristic
505C2×C22⋊C4D4×C4711yescharacteristic
506C2×C42—21no—
507C2×C42C23×C4711yescharacteristic
508C2×C42C23×C4711yescharacteristic
509#107—41no—
510#106—41no—
511C4⋊C8—22no—
512C4⋊C8D4×C4714yescomplemented
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524C4×C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×D4×C4711yescharacteristic
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
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—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4#41×C4712yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C4711yescharacteristic
582C22×C4C2×D4×C4711yescharacteristic
583C22×C4C2×D4×C4711yescharacteristic
584C22×C4C2×D4×C4711yescharacteristic
585C22×C4C2×D4×C4711yescharacteristic
586C22×C4C24×C4711yescharacteristic
587D8—44no—
588D8—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8C2×D4×C4712yes—
600C2×C8C2×D4×C4712yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4#41×C4712yes—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—81no—
630C42C2×D4×C4712yes—
631C42#41×C4712yes—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C22×D4×C4711yescharacteristic
661D4—22no—
662D4—22no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
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—84no—
711C2×C4#121×C4712yes—
712C2×C4#121×C4712yes—
713C2×C4C22×D4×C4711yescharacteristic
714C2×C4C2×#41×C4711yescharacteristic
715C2×C4C2×#41×C4711yescharacteristic
716C2×C4C2×#41×C4711yescharacteristic
717C2×C4H(5,𝔽2)×C4711yescharacteristic
718C2×C4H(5,𝔽2)×C4711yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#121×C4711yescharacteristic
752C22C47×#52511yescharacteristic
753C22C47×#53511yescharacteristic
754C22C47×#57611yescharacteristic
755C22C47×#57611yescharacteristic
756C22C47×#57611yescharacteristic
757C22C47×#57711yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—41no—
762C4—42no—
763C4—41no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C47×#54611yescharacteristic
769C4C47×#55011yescharacteristic
770C4C47×#55311yescharacteristic
771C4C47×#55511yescharacteristic
772C2—81no—
773C2—82no—
774C2—161no—
775C2—161no—
776C2C47×#241411yescharacteristic
777C2C47×#305811yescharacteristic
778C2C47×#306211yescharacteristic
779C2C47×#311911yescharacteristic
780C2C47×#312211yescharacteristic
781C2C47×#322011yescharacteristic
782C2C47×#322411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#459C2semidirect
2. C2×C47×#433C2semidirect
3. C47×#2619C2semidirect
4. C47×#2324C2semidirect
5. C47×#2034C2semidirect
6. C47×#2033C2semidirect
7. C47×#1999C2semidirect
8. C47×#1999C2semidirect
9. C47×#1982C2semidirect
10. C47×#1972C2semidirect
11. C47×#1970C2semidirect
12. C47×#1949C2semidirect
13. C47×#1936C2semidirect
14. C47×#1934C2semidirect
15. C47×#1804C2semidirect
120. C4⋊C8×C47D4semidirect
331. #24662C47direct (N × H)
381. C2×#459C2×C47semidirect
382. C2×#433C2×C47semidirect
383. #2619C2×C47semidirect
384. #2324C2×C47semidirect
385. #2034C2×C47semidirect
386. #2033C2×C47semidirect
387. #1999C2×C47semidirect
388. #1999C2×C47semidirect
389. #1982C2×C47semidirect
390. #1972C2×C47semidirect
391. #1970C2×C47semidirect
392. #1949C2×C47semidirect
393. #1936C2×C47semidirect
394. #1934C2×C47semidirect
395. #1804C2×C47semidirect
452. C47#24662direct (N × H)
512. C4⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4592
C2×C47×#4332
C47×#26192
C47×#23242
C47×#20342
C47×#20332
C47×#19992
C47×#19822
C47×#19722
C47×#19702
C47×#19492
C47×#19362
C47×#19342
C47×#18042
#2466247