Finite Group Databasebeta

← C47×#24762 #26064460

Subgroups — C47×#24762 #26064460

Order 12032.

1060 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×#469C211yesmaximal, characteristic, complemented
2C2×C47×#466C211yesmaximal, characteristic, complemented
3C2×C47×#459C211yesmaximal, characteristic, complemented
4C2×C47×#424C211yesmaximal, characteristic, complemented
5C47×#2619C211yesmaximal, characteristic, complemented
6C47×#2324C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2054C211yesmaximal, characteristic, complemented
10C47×#2054C211yesmaximal, characteristic, complemented
11C47×#1982C211yesmaximal, characteristic, complemented
12C47×#1949C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1893C211yesmaximal, characteristic, complemented
15C47×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#127×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C2×#117×C47C2211yescharacteristic
26C47×#469—24no—
27C47×#466—24no—
28C47×#459—24no—
29C2×#107×C47C2211yescharacteristic
30C2×#106×C47C2211yescharacteristic
31C47×#424—24no—
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C2×C4⋊C8×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C47×#394—21no—
45C47×#394—21no—
46C47×#392—21no—
47C47×#392—21no—
48C47×#390—21no—
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#388—21no—
54C47×#386—21no—
55C47×#385—21no—
56C47×#382C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
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×C47—21no—
68C22×D4×C47C2311yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C22×D4×C47C2311yescharacteristic
71C23×C4×C47—21no—
72C23×C4×C47C2311yescharacteristic
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—22no—
76C2×D8×C47—22no—
77C2×D8×C47—41no—
78C2×D8×C47—41no—
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#127×C47—22no—
90#127×C47—22no—
91#121×C47—22no—
92#121×C47—22no—
93#121×C47—22no—
94#121×C47—22no—
95#121×C47—22no—
96#121×C47D414yescomplemented
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99#117×C47—22no—
100#117×C47—22no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47D411yescharacteristic
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
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×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47D411yescharacteristic
121C2×C22⋊C4×C47D411yescharacteristic
122C2×C42×C47—21no—
123C2×C42×C47C2311yescharacteristic
124C2×C42×C47C2311yescharacteristic
125#107×C47—22no—
126#106×C47—22no—
127C4⋊C8×C47—22no—
128C4⋊C8×C47—22no—
129C4⋊C8×C47—22no—
130C4⋊C8×C47D414yescomplemented
131#102×C47—22no—
132#102×C47—22no—
133#102×C47—22no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—41no—
138#102×C47—41no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47C2×D411yescharacteristic
148C2×D4×C47—24no—
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—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—81no—
171C2×D4×C47—81no—
172C2×D4×C47—81no—
173C2×D4×C47—81no—
174C2×D4×C47—81no—
175C2×D4×C47—81no—
176C2×D4×C47—81no—
177C2×D4×C47—81no—
178C2×D4×C47—81no—
179C2×D4×C47—81no—
180C2×D4×C47C2×D412yes—
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—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×C47C2×D412yes—
199C22×C4×C47#4112yes—
200C22×C4×C47C2411yescharacteristic
201D8×C47—44no—
202D8×C47—44no—
203M16×C47—44no—
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×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—44no—
215C2×C8×C47C2×D412yes—
216C2×C8×C47C2×D412yes—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—22no—
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—81no—
229C4⋊C4×C47C2×D412yes—
230C22⋊C4×C47—24no—
231C22⋊C4×C47—22no—
232C22⋊C4×C47—22no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—81no—
237C22⋊C4×C47—81no—
238C22⋊C4×C47—81no—
239C22⋊C4×C47—81no—
240C22⋊C4×C47—81no—
241C22⋊C4×C47—81no—
242C22⋊C4×C47—81no—
243C42×C47—21no—
244C42×C47—21no—
245C42×C47—81no—
246C42×C47C2×D412yes—
247C42×C47#4112yes—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—22no—
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×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47#12112yes—
276C23×C47C22×D411yescharacteristic
277D4×C47—22no—
278D4×C47—22no—
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—41no—
288D4×C47—41no—
289D4×C47—84no—
290D4×C47—84no—
291D4×C47—84no—
292D4×C47—84no—
293D4×C47—84no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—22no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
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—84no—
326C2×C4×C47#12112yes—
327C2×C4×C47#12112yes—
328C2×C4×C47#12112yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47C2×#4111yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C2×C4×C472−1+411yescharacteristic
335C8×C47—22no—
336C8×C47—22no—
337C8×C47—41no—
338C8×C47—41no—
339#24762C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
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—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47C2×#12111yescharacteristic
369C22×C47C2×#12111yescharacteristic
370C22×C47#53711yescharacteristic
371C22×C47#57611yescharacteristic
372C22×C47#57611yescharacteristic
373C22×C47#57611yescharacteristic
374C22×C47#57711yescharacteristic
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—42no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47—81no—
382C4×C47—81no—
383C4×C47—81no—
384C4×C47—81no—
385C4×C47D4211yescharacteristic
386C4×C47#54711yescharacteristic
387C4×C47#54811yescharacteristic
388C4×C47#55311yescharacteristic
389C2×#469C2×C4711yescharacteristic, complemented
390C2×#466C2×C4711yescharacteristic, complemented
391C2×#459C2×C4711yescharacteristic, complemented
392C2×#424C2×C4711yescharacteristic, complemented
393#2619C2×C4711yescharacteristic, complemented
394#2324C2×C4711yescharacteristic, complemented
395#2067C2×C4711yescharacteristic, complemented
396#2065C2×C4711yescharacteristic, complemented
397#2054C2×C4711yescharacteristic, complemented
398#2054C2×C4711yescharacteristic, complemented
399#1982C2×C4711yescharacteristic, complemented
400#1949C2×C4711yescharacteristic, complemented
401#1895C2×C4711yescharacteristic, complemented
402#1893C2×C4711yescharacteristic, complemented
403#1804C2×C4711yescharacteristic, complemented
404C2×C47—42no—
405C2×C47—82no—
406C2×C47—161no—
407C2×C47—161no—
408C2×C47#241611yescharacteristic
409C2×C47#304111yescharacteristic
410C2×C47#304511yescharacteristic
411C2×C47#305811yescharacteristic
412C2×C47#306211yescharacteristic
413C2×C47#325711yescharacteristic
414C2×C47#325911yescharacteristic
415C22×D8C22×C4711yescharacteristic
416C22×D8C22×C4711yescharacteristic
417C22×M16C22×C4711yescharacteristic
418C23×C8C22×C4711yescharacteristic
419C2×#127C22×C4711yescharacteristic
420C2×#121C22×C4711yescharacteristic
421C2×#121C22×C4711yescharacteristic
422C2×#121C22×C4711yescharacteristic
423C2×C4×D4C22×C4711yescharacteristic
424C2×#117C22×C4711yescharacteristic
425#469—24no—
426#466—24no—
427#459—24no—
428C2×#107C22×C4711yescharacteristic
429C2×#106C22×C4711yescharacteristic
430#424—24no—
431C2×C4⋊C8C22×C4711yescharacteristic
432C2×C4⋊C8C22×C4711yescharacteristic
433C2×C4⋊C8C22×C4711yescharacteristic
434C2×C4⋊C8C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436C2×#102C22×C4711yescharacteristic
437C2×#102C22×C4711yescharacteristic
438C2×#102C22×C4711yescharacteristic
439C2×#102C22×C4711yescharacteristic
440C2×#102C22×C4711yescharacteristic
441C2×#102C22×C4711yescharacteristic
442C2×#102C22×C4711yescharacteristic
443#394—21no—
444#394—21no—
445#392—21no—
446#392—21no—
447#390—21no—
448#390C22×C4711yescharacteristic
449#390C22×C4711yescharacteristic
450#390C22×C4711yescharacteristic
451#389C22×C4711yescharacteristic
452#388—21no—
453#386—21no—
454#385—21no—
455#382C22×C4711yescharacteristic
456#380C22×C4711yescharacteristic
457C4×C4⋊C4C22×C4711yescharacteristic
458#340C22×C4711yescharacteristic
459#340C22×C4711yescharacteristic
460#340C22×C4711yescharacteristic
461#340C22×C4711yescharacteristic
462C47#2476211yescharacteristic, direct product factor, Sylow
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C23×C4711yescharacteristic
469C22×D4C23×C4711yescharacteristic
470C22×D4C23×C4711yescharacteristic
471C23×C4—21no—
472C23×C4C23×C4711yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
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#127—22no—
490#127—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—22no—
496#121D4×C4714yescomplemented
497C4×D4—22no—
498C4×D4—22no—
499#117—22no—
500#117—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4D4×C4711yescharacteristic
503C2×C4⋊C4D4×C4711yescharacteristic
504C2×C4⋊C4C23×C4711yescharacteristic
505C2×C4⋊C4C23×C4711yescharacteristic
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C4⋊C4C23×C4711yescharacteristic
508C2×C4⋊C4C23×C4711yescharacteristic
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×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C4711yescharacteristic
521C2×C22⋊C4D4×C4711yescharacteristic
522C2×C42—21no—
523C2×C42C23×C4711yescharacteristic
524C2×C42C23×C4711yescharacteristic
525#107—22no—
526#106—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8D4×C4714yescomplemented
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24C2×D4×C4711yescharacteristic
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
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—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C4712yes—
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—42no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C4711yescharacteristic
594C22×C4C2×D4×C4711yescharacteristic
595C22×C4C2×D4×C4711yescharacteristic
596C22×C4C2×D4×C4711yescharacteristic
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4712yes—
599C22×C4#41×C4712yes—
600C22×C4C24×C4711yescharacteristic
601D8—44no—
602D8—44no—
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
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—44no—
615C2×C8C2×D4×C4712yes—
616C2×C8C2×D4×C4712yes—
617C4⋊C4—22no—
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—81no—
629C4⋊C4C2×D4×C4712yes—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42C2×D4×C4712yes—
647C42#41×C4712yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
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#121×C4712yes—
676C23C22×D4×C4711yescharacteristic
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—84no—
690D4—84no—
691D4—84no—
692D4—84no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
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—84no—
726C2×C4#121×C4712yes—
727C2×C4#121×C4712yes—
728C2×C4#121×C4712yes—
729C2×C4C22×D4×C4711yescharacteristic
730C2×C4C22×D4×C4711yescharacteristic
731C2×C4C2×#41×C4711yescharacteristic
732C2×C4C2×#41×C4711yescharacteristic
733C2×C4H(5,𝔽2)×C4711yescharacteristic
734C2×C42−1+4×C4711yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C4711yescharacteristic
768C22C2×#121×C4711yescharacteristic
769C22C47×#53711yescharacteristic
770C22C47×#57611yescharacteristic
771C22C47×#57611yescharacteristic
772C22C47×#57611yescharacteristic
773C22C47×#57711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4D42×C4711yescharacteristic
785C4C47×#54711yescharacteristic
786C4C47×#54811yescharacteristic
787C4C47×#55311yescharacteristic
788C2—42no—
789C2—82no—
790C2—161no—
791C2—161no—
792C2C47×#241611yescharacteristic
793C2C47×#304111yescharacteristic
794C2C47×#304511yescharacteristic
795C2C47×#305811yescharacteristic
796C2C47×#306211yescharacteristic
797C2C47×#325711yescharacteristic
798C2C47×#325911yescharacteristic
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×#469C2semidirect
2. C2×C47×#466C2semidirect
3. C2×C47×#459C2semidirect
4. C2×C47×#424C2semidirect
5. C47×#2619C2semidirect
6. C47×#2324C2semidirect
7. C47×#2067C2semidirect
8. C47×#2065C2semidirect
9. C47×#2054C2semidirect
10. C47×#2054C2semidirect
11. C47×#1982C2semidirect
12. C47×#1949C2semidirect
13. C47×#1895C2semidirect
14. C47×#1893C2semidirect
15. C47×#1804C2semidirect
96. #121×C47D4semidirect
130. C4⋊C8×C47D4semidirect
339. #24762C47direct (N × H)
389. C2×#469C2×C47semidirect
390. C2×#466C2×C47semidirect
391. C2×#459C2×C47semidirect
392. C2×#424C2×C47semidirect
393. #2619C2×C47semidirect
394. #2324C2×C47semidirect
395. #2067C2×C47semidirect
396. #2065C2×C47semidirect
397. #2054C2×C47semidirect
398. #2054C2×C47semidirect
399. #1982C2×C47semidirect
400. #1949C2×C47semidirect
401. #1895C2×C47semidirect
402. #1893C2×C47semidirect
403. #1804C2×C47semidirect
462. C47#24762direct (N × H)
496. #121D4×C47semidirect
530. 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×#4692
C2×C47×#4662
C2×C47×#4592
C2×C47×#4242
C47×#26192
C47×#23242
C47×#20672
C47×#20652
C47×#20542
C47×#19822
C47×#19492
C47×#18952
C47×#18932
C47×#18042
#2476247