Finite Group Databasebeta

← C47×#24567 #26064265

Subgroups — C47×#24567 #26064265

Order 12032.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#482C211yesmaximal, characteristic, complemented
2C2×C47×#408C211yesmaximal, characteristic, complemented
3C47×#2615C211yesmaximal, characteristic
4C47×#2311C211yesmaximal, characteristic, complemented
5C47×#2077C211yesmaximal, characteristic, complemented
6C47×#2075C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic, complemented
10C47×#1893C211yesmaximal, characteristic, complemented
11C47×#1874C211yesmaximal, characteristic, complemented
12C47×#1853C211yesmaximal, characteristic, complemented
13C47×#1825C211yesmaximal, characteristic, complemented
14C47×#1809C211yesmaximal, characteristic, complemented
15C47×#1807C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×#121×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#117×C47C2211yescharacteristic
23C22×C4⋊C4×C47C2211yescharacteristic
24C47×#482—24no—
25C2×#107×C47C2211yescharacteristic
26C2×#106×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C2×#106×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C47×#408—24no—
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C47×#393—21no—
39C47×#392—21no—
40C47×#392—21no—
41C47×#392—21no—
42C47×#391—21no—
43C47×#390—21no—
44C47×#386—21no—
45C47×#386—21no—
46C47×#380C2211yescharacteristic
47C47×#380C2211yescharacteristic
48C47×#380C2211yescharacteristic
49C47×#380C2211yescharacteristic
50C47×#380C2211yescharacteristic
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C2×#41×C47—22no—
62C2×#41×C47—22no—
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—41no—
66C2×#41×C47—41no—
67C22×Q8×C47D411yescharacteristic
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47D411yescharacteristic
72C22×D4×C47D411yescharacteristic
73C22×D4×C47D411yescharacteristic
74C22×D4×C47C2311yescharacteristic
75C23×C4×C47—21no—
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C2×M16×C47—22no—
80C2×M16×C47—22no—
81C2×M16×C47—41no—
82C22×C8×C47—22no—
83C22×C8×C47—22no—
84C22×C8×C47—41no—
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89#121×C47—22no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—22no—
93#121×C47—41no—
94#121×C47—41no—
95#117×C47—22no—
96#117×C47—22no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—41no—
99C2×C4⋊C4×C47—41no—
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C42×C47—21no—
119#107×C47—22no—
120#106×C47—22no—
121#106×C47—41no—
122#106×C47—41no—
123#102×C47—22no—
124#102×C47—22no—
125#102×C47—41no—
126#102×C47—41no—
127C22⋊C8×C47—22no—
128C22⋊C8×C47—22no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47D414yescomplemented
131#95×C47—21no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138C24×C47—21no—
139C24×C47C2×D411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142#41×C47—44no—
143#41×C47—44no—
144#41×C47—44no—
145#41×C47—44no—
146C2×Q8×C47—22no—
147C2×Q8×C47—22no—
148C2×Q8×C47—41no—
149C2×D4×C47—22no—
150C2×D4×C47—22no—
151C2×D4×C47—22no—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47—22no—
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—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—42no—
167C2×D4×C47—81no—
168C2×D4×C47—81no—
169C2×D4×C47—81no—
170C2×D4×C47—81no—
171C2×D4×C47—81no—
172C2×D4×C47—81no—
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—42no—
195C22×C4×C47—81no—
196C22×C4×C47—81no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47#4112yes—
202C22×C4×C47#4112yes—
203C22×C4×C47#4112yes—
204C22×C4×C47C2411yescharacteristic
205M16×C47—44no—
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×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—44no—
217C2×C8×C47C2×D412yes—
218C2×C8×C47C2×D412yes—
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—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—81no—
239C22⋊C4×C47—81no—
240C22⋊C4×C47—81no—
241C22⋊C4×C47—81no—
242C22⋊C4×C47—81no—
243C22⋊C4×C47—81no—
244C22⋊C4×C47—81no—
245C42×C47—42no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
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—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47#12112yes—
273C23×C47#12312yes—
274C23×C47C22×D411yescharacteristic
275Q8×C47—44no—
276D4×C47—44no—
277D4×C47—44no—
278D4×C47—44no—
279D4×C47—41no—
280D4×C47—41no—
281D4×C47—41no—
282D4×C47—41no—
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—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
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—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—84no—
327C2×C4×C47#12112yes—
328C2×C4×C47#12312yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47C2×#4111yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C8×C47—22no—
336C8×C47—22no—
337C8×C47—41no—
338C8×C47—41no—
339#24567C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
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—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47C2×#12111yescharacteristic
369C22×C47C2×#12311yescharacteristic
370C22×C47#53411yescharacteristic
371C22×C47#57611yescharacteristic
372C22×C47#57711yescharacteristic
373C22×C47#57711yescharacteristic
374C22×C47#57711yescharacteristic
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—41no—
378C4×C47—81no—
379C4×C47—81no—
380C4×C47—81no—
381C4×C47—81no—
382C4×C47—81no—
383C4×C47—81no—
384C4×C47—81no—
385C4×C47#54611yescharacteristic
386C4×C47#54611yescharacteristic
387C4×C47#55111yescharacteristic
388C4×C47#55111yescharacteristic
389C2×#482C2×C4711yescharacteristic, complemented
390C2×#408C2×C4711yescharacteristic, complemented
391#2615C2×C4711yescharacteristic
392#2311C2×C4711yescharacteristic, complemented
393#2077C2×C4711yescharacteristic, complemented
394#2075C2×C4711yescharacteristic, complemented
395#2034C2×C4711yescharacteristic, complemented
396#2034C2×C4711yescharacteristic, complemented
397#1895C2×C4711yescharacteristic, complemented
398#1893C2×C4711yescharacteristic, complemented
399#1874C2×C4711yescharacteristic, complemented
400#1853C2×C4711yescharacteristic, complemented
401#1825C2×C4711yescharacteristic, complemented
402#1809C2×C4711yescharacteristic, complemented
403#1807C2×C4711yescharacteristic, complemented
404C2×C47—42no—
405C2×C47—42no—
406C2×C47—81no—
407C2×C47—161no—
408C2×C47#241211yescharacteristic
409C2×C47#306011yescharacteristic
410C2×C47#306211yescharacteristic
411C2×C47#309611yescharacteristic
412C2×C47#309911yescharacteristic
413C2×C47#319811yescharacteristic
414C2×C47#320011yescharacteristic
415C22×#41C22×C4711yescharacteristic
416C22×M16C22×C4711yescharacteristic
417C23×C8C22×C4711yescharacteristic
418C2×#121C22×C4711yescharacteristic
419C2×#121C22×C4711yescharacteristic
420C2×#121C22×C4711yescharacteristic
421C2×#117C22×C4711yescharacteristic
422C22×C4⋊C4C22×C4711yescharacteristic
423#482—24no—
424C2×#107C22×C4711yescharacteristic
425C2×#106C22×C4711yescharacteristic
426C2×#106C22×C4711yescharacteristic
427C2×#106C22×C4711yescharacteristic
428C2×#102C22×C4711yescharacteristic
429C2×#102C22×C4711yescharacteristic
430C2×#102C22×C4711yescharacteristic
431C2×#102C22×C4711yescharacteristic
432#408—24no—
433C2×C22⋊C8C22×C4711yescharacteristic
434C2×C22⋊C8C22×C4711yescharacteristic
435C2×C22⋊C8C22×C4711yescharacteristic
436C2×C22⋊C8C22×C4711yescharacteristic
437#393—21no—
438#392—21no—
439#392—21no—
440#392—21no—
441#391—21no—
442#390—21no—
443#386—21no—
444#386—21no—
445#380C22×C4711yescharacteristic
446#380C22×C4711yescharacteristic
447#380C22×C4711yescharacteristic
448#380C22×C4711yescharacteristic
449#380C22×C4711yescharacteristic
450#380C22×C4711yescharacteristic
451#380C22×C4711yescharacteristic
452#340C22×C4711yescharacteristic
453#340C22×C4711yescharacteristic
454#340C22×C4711yescharacteristic
455#340C22×C4711yescharacteristic
456#340C22×C4711yescharacteristic
457#340C22×C4711yescharacteristic
458#340C22×C4711yescharacteristic
459#340C22×C4711yescharacteristic
460C47#2456711yescharacteristic, direct product factor, Sylow
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C22×Q8D4×C4711yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C4711yescharacteristic
472C22×D4D4×C4711yescharacteristic
473C22×D4D4×C4711yescharacteristic
474C22×D4C23×C4711yescharacteristic
475C23×C4—21no—
476C23×C4C23×C4711yescharacteristic
477C23×C4C23×C4711yescharacteristic
478C23×C4C23×C4711yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C4711yescharacteristic
486C22×C8C23×C4711yescharacteristic
487C22×C8C23×C4711yescharacteristic
488C22×C8C23×C4711yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#117—22no—
496#117—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4C23×C4711yescharacteristic
501C2×C4⋊C4C23×C4711yescharacteristic
502C2×C4⋊C4C23×C4711yescharacteristic
503C2×C4⋊C4C23×C4711yescharacteristic
504C2×C4⋊C4C23×C4711yescharacteristic
505C2×C4⋊C4C23×C4711yescharacteristic
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
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×C42—21no—
519#107—22no—
520#106—22no—
521#106—41no—
522#106—41no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8D4×C4714yescomplemented
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×D4×C4711yescharacteristic
540C24C2×D4×C4711yescharacteristic
541C24C2×D4×C4711yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
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—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—21no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4711yescharacteristic
599C22×C4C2×D4×C4712yes—
600C22×C4C2×D4×C4711yescharacteristic
601C22×C4#41×C4712yes—
602C22×C4#41×C4712yes—
603C22×C4#41×C4712yes—
604C22×C4C24×C4711yescharacteristic
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×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8C2×D4×C4712yes—
618C2×C8C2×D4×C4712yes—
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—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
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—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23#121×C4712yes—
673C23#123×C4712yes—
674C23C22×D4×C4711yescharacteristic
675Q8—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
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—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—84no—
727C2×C4#121×C4712yes—
728C2×C4#123×C4712yes—
729C2×C4C22×D4×C4711yescharacteristic
730C2×C4C2×#41×C4711yescharacteristic
731C2×C4C2×#41×C4711yescharacteristic
732C2×C4C2×#41×C4711yescharacteristic
733C2×C4H(5,𝔽2)×C4711yescharacteristic
734C2×C4H(5,𝔽2)×C4711yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C4711yescharacteristic
768C22C2×#123×C4711yescharacteristic
769C22C47×#53411yescharacteristic
770C22C47×#57611yescharacteristic
771C22C47×#57711yescharacteristic
772C22C47×#57711yescharacteristic
773C22C47×#57711yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C47×#54611yescharacteristic
785C4C47×#54611yescharacteristic
786C4C47×#55111yescharacteristic
787C4C47×#55111yescharacteristic
788C2—42no—
789C2—42no—
790C2—81no—
791C2—161no—
792C2C47×#241211yescharacteristic
793C2C47×#306011yescharacteristic
794C2C47×#306211yescharacteristic
795C2C47×#309611yescharacteristic
796C2C47×#309911yescharacteristic
797C2C47×#319811yescharacteristic
798C2C47×#320011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#482C2semidirect
2. C2×C47×#408C2semidirect
4. C47×#2311C2semidirect
5. C47×#2077C2semidirect
6. C47×#2075C2semidirect
7. C47×#2034C2semidirect
8. C47×#2034C2semidirect
9. C47×#1895C2semidirect
10. C47×#1893C2semidirect
11. C47×#1874C2semidirect
12. C47×#1853C2semidirect
13. C47×#1825C2semidirect
14. C47×#1809C2semidirect
15. C47×#1807C2semidirect
130. C22⋊C8×C47D4semidirect
339. #24567C47direct (N × H)
389. C2×#482C2×C47semidirect
390. C2×#408C2×C47semidirect
392. #2311C2×C47semidirect
393. #2077C2×C47semidirect
394. #2075C2×C47semidirect
395. #2034C2×C47semidirect
396. #2034C2×C47semidirect
397. #1895C2×C47semidirect
398. #1893C2×C47semidirect
399. #1874C2×C47semidirect
400. #1853C2×C47semidirect
401. #1825C2×C47semidirect
402. #1809C2×C47semidirect
403. #1807C2×C47semidirect
460. C47#24567direct (N × H)
530. C22⋊C8D4×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×#4082
C47×#26152
C47×#23112
C47×#20772
C47×#20752
C47×#20342
C47×#18952
C47×#18932
C47×#18742
C47×#18532
C47×#18252
C47×#18092
C47×#18072
#2456747