Finite Group Databasebeta

← C47×#25383 #26065081

Subgroups — C47×#25383 #26065081

Order 12032.

1048 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×#496C211yesmaximal, characteristic
2C2×C47×#464C211yesmaximal, characteristic, complemented
3C2×C47×#464C211yesmaximal, characteristic, complemented
4C2×C47×#463C211yesmaximal, characteristic, complemented
5C47×#2548C211yesmaximal, characteristic, complemented
6C47×#2367C211yesmaximal, characteristic, complemented
7C47×#2055C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2015C211yesmaximal, characteristic, complemented
10C47×#2012C211yesmaximal, characteristic, complemented
11C47×#1982C211yesmaximal, characteristic, complemented
12C47×#1940C211yesmaximal, characteristic, complemented
13C47×#1880C211yesmaximal, characteristic, complemented
14C47×#1879C211yesmaximal, characteristic, complemented
15C47×#1763C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C22×D8×C47C2211yescharacteristic
22C2×#127×C47C2211yescharacteristic
23C2×#124×C47C2211yescharacteristic
24C2×#124×C47C2211yescharacteristic
25C2×#124×C47C2211yescharacteristic
26C2×C4×Q8×C47C2211yescharacteristic
27C2×C4×Q8×C47C2211yescharacteristic
28C2×C4×D4×C47C2211yescharacteristic
29C47×#496—24no—
30C47×#464—24no—
31C47×#464—24no—
32C47×#463—24no—
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C2×C4⋊C8×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#97×C47C2211yescharacteristic
45C47×#394—21no—
46C47×#394—21no—
47C47×#391C2211yescharacteristic
48C47×#390—21no—
49C47×#390—21no—
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#388—21no—
54C47×#388—21no—
55C47×#385—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47—21no—
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C23×C4×C47—21no—
71C2×Q16×C47—22no—
72C2×Q16×C47—22no—
73C2×Q16×C47—41no—
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C2×SD16×C47—22no—
77C2×SD16×C47—22no—
78C2×SD16×C47—22no—
79C2×SD16×C47—22no—
80C2×SD16×C47—41no—
81C2×SD16×C47—41no—
82C2×SD16×C47—41no—
83C2×D8×C47—22no—
84C2×D8×C47—22no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—41no—
88C2×D8×C47—41no—
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93#127×C47—22no—
94#127×C47—22no—
95#124×C47—22no—
96#124×C47—22no—
97#124×C47—22no—
98#124×C47—41no—
99#124×C47—41no—
100#124×C47D414yes—
101C4×Q8×C47—22no—
102C4×Q8×C47—22no—
103C4×Q8×C47—22no—
104C4×Q8×C47—41no—
105C4×D4×C47—22no—
106C4×D4×C47—41no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47D411yescharacteristic
110C2×C4⋊C4×C47D411yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C42×C47—21no—
128C2×C42×C47—21no—
129C2×C42×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C2×C42×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C4⋊C8×C47—22no—
134C4⋊C8×C47—22no—
135C4⋊C8×C47—22no—
136#103×C47—22no—
137#103×C47—22no—
138#103×C47D414yescomplemented
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—41no—
143#102×C47—41no—
144#97×C47—22no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47D411yescharacteristic
149#95×C47D411yescharacteristic
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47C2×D412yes—
164C2×Q8×C47C2×D412yes—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—81no—
187C2×D4×C47—81no—
188C2×D4×C47C2×D412yes—
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—42no—
196C22×C4×C47—81no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204Q16×C47—44no—
205SD16×C47—44no—
206SD16×C47—44no—
207SD16×C47—44no—
208D8×C47—44no—
209D8×C47—44no—
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—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47C2×D412yes—
221C2×C8×C47#4112yes—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—41no—
228C4⋊C4×C47—41no—
229C4⋊C4×C47—42no—
230C4⋊C4×C47—42no—
231C4⋊C4×C47C2×D412yes—
232C22⋊C4×C47—24no—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—81no—
241C22⋊C4×C47—81no—
242C22⋊C4×C47—81no—
243C22⋊C4×C47—81no—
244C22⋊C4×C47—81no—
245C42×C47—21no—
246C42×C47—21no—
247C42×C47—21no—
248C42×C47—21no—
249C42×C47—42no—
250C42×C47—42no—
251C42×C47—81no—
252C42×C47C2×D412yes—
253C42×C47#4112yes—
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×C47C22×D411yescharacteristic
276Q8×C47—22no—
277Q8×C47—22no—
278Q8×C47—22no—
279Q8×C47—22no—
280Q8×C47—41no—
281Q8×C47—41no—
282Q8×C47—41no—
283Q8×C47—41no—
284D4×C47—22no—
285D4×C47—22no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—41no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—84no—
297D4×C47—84no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
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—41no—
328C2×C4×C47—41no—
329C2×C4×C47—84no—
330C2×C4×C47#12112yes—
331C2×C4×C47#12112yes—
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C2×#4111yescharacteristic
335C2×C4×C47C2×#4111yescharacteristic
336C2×C4×C47H(5,𝔽2)11yescharacteristic
337C2×C4×C47H(5,𝔽2)11yescharacteristic
338C8×C47—22no—
339C8×C47—22no—
340C8×C47—41no—
341C8×C47—41no—
342#25383C4711yesmaximal, characteristic, direct product factor, Sylow
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
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×C47—81no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47C2×#12111yescharacteristic
365C22×C47D4211yescharacteristic
366C22×C47#55011yescharacteristic
367C22×C47#57511yescharacteristic
368C22×C47#57511yescharacteristic
369C22×C47#57611yescharacteristic
370C22×C47#57711yescharacteristic
371C4×C47—22no—
372C4×C47—22no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—42no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—81no—
381C4×C47—81no—
382C4×C47#53211yescharacteristic
383C4×C47#54011yescharacteristic
384C4×C47D4211yescharacteristic
385C4×C47#54611yescharacteristic
386C2×#496C2×C4711yescharacteristic
387C2×#464C2×C4711yescharacteristic, complemented
388C2×#464C2×C4711yescharacteristic, complemented
389C2×#463C2×C4711yescharacteristic, complemented
390#2548C2×C4711yescharacteristic, complemented
391#2367C2×C4711yescharacteristic, complemented
392#2055C2×C4711yescharacteristic, complemented
393#2054C2×C4711yescharacteristic, complemented
394#2015C2×C4711yescharacteristic, complemented
395#2012C2×C4711yescharacteristic, complemented
396#1982C2×C4711yescharacteristic, complemented
397#1940C2×C4711yescharacteristic, complemented
398#1880C2×C4711yescharacteristic, complemented
399#1879C2×C4711yescharacteristic, complemented
400#1763C2×C4711yescharacteristic, complemented
401C2×C47—82no—
402C2×C47—161no—
403C2×C47—161no—
404C2×C47#242811yescharacteristic
405C2×C47#304011yescharacteristic
406C2×C47#304511yescharacteristic
407C2×C47#326811yescharacteristic
408C2×C47#327111yescharacteristic
409C2×C47#340111yescharacteristic
410C2×C47#340311yescharacteristic
411C22×Q16C22×C4711yescharacteristic
412C22×SD16C22×C4711yescharacteristic
413C22×SD16C22×C4711yescharacteristic
414C22×SD16C22×C4711yescharacteristic
415C22×D8C22×C4711yescharacteristic
416C22×D8C22×C4711yescharacteristic
417C2×#127C22×C4711yescharacteristic
418C2×#124C22×C4711yescharacteristic
419C2×#124C22×C4711yescharacteristic
420C2×#124C22×C4711yescharacteristic
421C2×C4×Q8C22×C4711yescharacteristic
422C2×C4×Q8C22×C4711yescharacteristic
423C2×C4×D4C22×C4711yescharacteristic
424#496—24no—
425#464—24no—
426#464—24no—
427#463—24no—
428C2×C4⋊C8C22×C4711yescharacteristic
429C2×C4⋊C8C22×C4711yescharacteristic
430C2×C4⋊C8C22×C4711yescharacteristic
431C2×#103C22×C4711yescharacteristic
432C2×#103C22×C4711yescharacteristic
433C2×#103C22×C4711yescharacteristic
434C2×#102C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436C2×#102C22×C4711yescharacteristic
437C2×#102C22×C4711yescharacteristic
438C2×#102C22×C4711yescharacteristic
439C2×#97C22×C4711yescharacteristic
440#394—21no—
441#394—21no—
442#391C22×C4711yescharacteristic
443#390—21no—
444#390—21no—
445#390C22×C4711yescharacteristic
446#390C22×C4711yescharacteristic
447#390C22×C4711yescharacteristic
448#388—21no—
449#388—21no—
450#385—21no—
451C4×C4⋊C4C22×C4711yescharacteristic
452C4×C4⋊C4C22×C4711yescharacteristic
453C4×C22⋊C4—21no—
454#340C22×C4711yescharacteristic
455#340C22×C4711yescharacteristic
456#336C22×C4711yescharacteristic
457#336C22×C4711yescharacteristic
458C47#2538311yescharacteristic, direct product factor, Sylow
459C22×Q8C23×C4711yescharacteristic
460C22×Q8C23×C4711yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C4711yescharacteristic
464C22×D4C23×C4711yescharacteristic
465C22×D4C23×C4711yescharacteristic
466C23×C4—21no—
467C2×Q16—22no—
468C2×Q16—22no—
469C2×Q16—41no—
470C2×SD16—22no—
471C2×SD16—22no—
472C2×SD16—22no—
473C2×SD16—22no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—41no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×D8—22no—
480C2×D8—22no—
481C2×D8—22no—
482C2×D8—22no—
483C2×D8—41no—
484C2×D8—41no—
485C22×C8C23×C4711yescharacteristic
486C22×C8C23×C4711yescharacteristic
487C22×C8C23×C4711yescharacteristic
488C22×C8C23×C4711yescharacteristic
489#127—22no—
490#127—22no—
491#124—22no—
492#124—22no—
493#124—22no—
494#124—41no—
495#124—41no—
496#124D4×C4714yes—
497C4×Q8—22no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—41no—
501C4×D4—22no—
502C4×D4—41no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4D4×C4711yescharacteristic
506C2×C4⋊C4D4×C4711yescharacteristic
507C2×C4⋊C4C23×C4711yescharacteristic
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C4⋊C4C23×C4711yescharacteristic
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⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42C23×C4711yescharacteristic
527C2×C42C23×C4711yescharacteristic
528C2×C42C23×C4711yescharacteristic
529C4⋊C8—22no—
530C4⋊C8—22no—
531C4⋊C8—22no—
532#103—22no—
533#103—22no—
534#103D4×C4714yescomplemented
535#102—22no—
536#102—22no—
537#102—22no—
538#102—41no—
539#102—41no—
540#97—22no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95D4×C4711yescharacteristic
545#95D4×C4711yescharacteristic
546C24—21no—
547C24—21no—
548C24—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8C2×D4×C4712yes—
560C2×Q8C2×D4×C4712yes—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4C2×D4×C4712yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
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×C4711yescharacteristic
599C22×C4C24×C4711yescharacteristic
600Q16—44no—
601SD16—44no—
602SD16—44no—
603SD16—44no—
604D8—44no—
605D8—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×C8C2×D4×C4712yes—
617C2×C8#41×C4712yes—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4C2×D4×C4712yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—42no—
647C42—81no—
648C42C2×D4×C4712yes—
649C42#41×C4712yes—
650C23—22no—
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—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C4711yescharacteristic
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—22no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—22no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—84no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
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×C4C22×D4×C4711yescharacteristic
729C2×C4C22×D4×C4711yescharacteristic
730C2×C4C2×#41×C4711yescharacteristic
731C2×C4C2×#41×C4711yescharacteristic
732C2×C4H(5,𝔽2)×C4711yescharacteristic
733C2×C4H(5,𝔽2)×C4711yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—81no—
742C22—81no—
743C22—81no—
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—
759C22C2×#121×C4711yescharacteristic
760C22D42×C4711yescharacteristic
761C22C47×#55011yescharacteristic
762C22C47×#57511yescharacteristic
763C22C47×#57511yescharacteristic
764C22C47×#57611yescharacteristic
765C22C47×#57711yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—42no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4C47×#53211yescharacteristic
778C4C47×#54011yescharacteristic
779C4D42×C4711yescharacteristic
780C4C47×#54611yescharacteristic
781C2—82no—
782C2—161no—
783C2—161no—
784C2C47×#242811yescharacteristic
785C2C47×#304011yescharacteristic
786C2C47×#304511yescharacteristic
787C2C47×#326811yescharacteristic
788C2C47×#327111yescharacteristic
789C2C47×#340111yescharacteristic
790C2C47×#340311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#496C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#464C2semidirect
3. C2×C47×#464C2semidirect
4. C2×C47×#463C2semidirect
5. C47×#2548C2semidirect
6. C47×#2367C2semidirect
7. C47×#2055C2semidirect
8. C47×#2054C2semidirect
9. C47×#2015C2semidirect
10. C47×#2012C2semidirect
11. C47×#1982C2semidirect
12. C47×#1940C2semidirect
13. C47×#1880C2semidirect
14. C47×#1879C2semidirect
15. C47×#1763C2semidirect
138. #103×C47D4semidirect
342. #25383C47direct (N × H)
387. C2×#464C2×C47semidirect
388. C2×#464C2×C47semidirect
389. C2×#463C2×C47semidirect
390. #2548C2×C47semidirect
391. #2367C2×C47semidirect
392. #2055C2×C47semidirect
393. #2054C2×C47semidirect
394. #2015C2×C47semidirect
395. #2012C2×C47semidirect
396. #1982C2×C47semidirect
397. #1940C2×C47semidirect
398. #1880C2×C47semidirect
399. #1879C2×C47semidirect
400. #1763C2×C47semidirect
458. C47#25383direct (N × H)
534. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4962
C2×C47×#4642
C2×C47×#4632
C47×#25482
C47×#23672
C47×#20552
C47×#20542
C47×#20152
C47×#20122
C47×#19822
C47×#19402
C47×#18802
C47×#18792
C47×#17632
#2538347