Finite Group Databasebeta

← C47×#18252 #26057950

Subgroups — C47×#18252 #26057950

Order 12032.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3534C211yesmaximal, characteristic, complemented
2C47×#3006C211yesmaximal, characteristic, complemented
3C47×#3002C211yesmaximal, characteristic, complemented
4C47×#2430C211yesmaximal, characteristic, complemented
5C47×#1606C211yesmaximal, characteristic, complemented
6C47×#1604C211yesmaximal, characteristic, complemented
7C47×#1603C211yesmaximal, characteristic, complemented
8C47×#1601C211yesmaximal, characteristic, complemented
9C47×#1600C211yesmaximal, characteristic, complemented
10C47×#1598C211yesmaximal, characteristic, complemented
11C47×#1597C211yesmaximal, characteristic, complemented
12C47×#1595C211yesmaximal, characteristic, complemented
13C47×#1504C211yesmaximal, characteristic, complemented
14C2×C47×#327C211yesmaximal, characteristic, complemented
15C47×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C47—21no—
18C2×#135×C47—21no—
19C47×#562—21no—
20C47×#560—21no—
21C47×#553—21no—
22C47×#551—21no—
23C47×#546—21no—
24C47×#546—21no—
25C47×#546—21no—
26D42×C47—21no—
27C47×#540—21no—
28C47×#539—21no—
29C47×#539C2211yescharacteristic
30C47×#538—21no—
31C47×#538C2211yescharacteristic
32C47×#537C2211yescharacteristic
33C47×#534—21no—
34C47×#534C2211yescharacteristic
35C47×#525C2211yescharacteristic
36C2×#123×C47C2211yescharacteristic
37C2×#121×C47—21no—
38C2×#121×C47C2211yescharacteristic
39C47×#452—21no—
40C47×#451C2211yescharacteristic, complemented
41C47×#450C2211yescharacteristic, complemented
42C47×#449—21no—
43C47×#449—21no—
44C47×#449—21no—
45C47×#448C2211yescharacteristic
46C47×#448C2211yescharacteristic, complemented
47C47×#448C2211yescharacteristic, complemented
48C47×#447C2211yescharacteristic
49C47×#447C2211yescharacteristic, complemented
50C47×#447C2211yescharacteristic, complemented
51C47×#417—21no—
52C47×#416—21no—
53C47×#407C2211yescharacteristic, complemented
54C2×C22⋊C8×C47C2211yescharacteristic, complemented
55C47×#395C2211yescharacteristic, complemented
56C47×#394C2211yescharacteristic, complemented
57C47×#393C2211yescharacteristic, complemented
58C47×#392C2211yescharacteristic, complemented
59C47×#386—21no—
60C47×#386—21no—
61C47×#385—21no—
62C2×#95×C47C2211yescharacteristic, complemented
63C47×#328C2211yescharacteristic, complemented
64C47×#328C2211yescharacteristic, complemented
65C47×#327C2211yescharacteristic
66C47×#327C2211yescharacteristic
67C47×#327C2211yescharacteristic, complemented
68C47×#327C2211yescharacteristic, complemented
69C47×#327C2211yescharacteristic, complemented
70C47×#327C2211yescharacteristic, complemented
71C47×#324C2211yescharacteristic, complemented
72C47×#324C2211yescharacteristic, complemented
73C47×#323C2211yescharacteristic, complemented
74C47×#323C2211yescharacteristic, complemented
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—44no—
81C2×#41×C47D411yescharacteristic, complemented
82C22×Q8×C47C2311yescharacteristic
83C22×D4×C47—21no—
84C22×D4×C47—21no—
85C22×D4×C47—21no—
86C22×D4×C47—21no—
87C22×D4×C47—21no—
88C22×D4×C47D411yescharacteristic
89C22×D4×C47D411yescharacteristic, complemented
90C22×D4×C47C2311yescharacteristic
91C23×C4×C47—21no—
92C23×C4×C47—21no—
93C23×C4×C47C2311yescharacteristic
94AGL(1,ℤ/8)×C47—44no—
95#135×C47—44no—
96C2×Q16×C47—21no—
97C2×SD16×C47—21no—
98C2×SD16×C47—21no—
99C2×SD16×C47—21no—
100C2×SD16×C47—21no—
101C2×D8×C47—21no—
102C2×D8×C47—21no—
103C2×D8×C47—21no—
104C2×M16×C47—21no—
105C22×C8×C47—21no—
106#127×C47—21no—
107#126×C47—21no—
108#126×C47—21no—
109#126×C47—21no—
110#126×C47—21no—
111#125×C47—21no—
112#125×C47—21no—
113#124×C47—21no—
114#124×C47—21no—
115#124×C47—21no—
116#123×C47—21no—
117#123×C47—21no—
118#123×C47—21no—
119#123×C47—21no—
120#123×C47—21no—
121#123×C47—21no—
122#123×C47—21no—
123#123×C47—21no—
124#123×C47—21no—
125#123×C47—21no—
126#123×C47—21no—
127#123×C47—21no—
128#123×C47—21no—
129#123×C47—21no—
130C22⋊Q8×C47—21no—
131C22⋊Q8×C47—21no—
132C22⋊Q8×C47—21no—
133C22⋊Q8×C47—21no—
134C22⋊Q8×C47—21no—
135C22⋊Q8×C47D411yescharacteristic, complemented
136C22⋊Q8×C47C2311yescharacteristic
137#121×C47—21no—
138#121×C47—21no—
139#121×C47—21no—
140#121×C47—21no—
141#121×C47—21no—
142#121×C47—21no—
143#121×C47—21no—
144#121×C47—21no—
145#121×C47—21no—
146#121×C47—21no—
147#121×C47—21no—
148#121×C47—21no—
149#121×C47—21no—
150#121×C47—21no—
151#121×C47—21no—
152#121×C47—44no—
153#121×C47D411yescharacteristic, complemented
154#121×C47D411yescharacteristic, complemented
155#121×C47D411yescharacteristic, complemented
156#121×C47C2311yescharacteristic
157#121×C47C2311yescharacteristic
158#121×C47C2311yescharacteristic
159#120×C47—21no—
160#120×C47—21no—
161#120×C47—21no—
162#120×C47—21no—
163#120×C47—21no—
164#120×C47—21no—
165#120×C47—21no—
166#120×C47—21no—
167C4×D4×C47—21no—
168C4×D4×C47—21no—
169C4×D4×C47—21no—
170C4×D4×C47—21no—
171C4×D4×C47—21no—
172C4×D4×C47—21no—
173C4×D4×C47—21no—
174C4×D4×C47—21no—
175#117×C47—21no—
176#117×C47D411yescharacteristic, complemented
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47D411yescharacteristic
179C2×C4⋊C4×C47D411yescharacteristic, complemented
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C22⋊C4×C47—21no—
184C2×C22⋊C4×C47—21no—
185C2×C22⋊C4×C47—21no—
186C2×C22⋊C4×C47—21no—
187C2×C22⋊C4×C47—21no—
188C2×C22⋊C4×C47D411yescharacteristic
189C2×C22⋊C4×C47D411yescharacteristic
190C2×C22⋊C4×C47C2311yescharacteristic
191#103×C47—21no—
192#103×C47—21no—
193#103×C47—21no—
194#103×C47—21no—
195#102×C47—21no—
196#102×C47—21no—
197#102×C47—21no—
198#102×C47—21no—
199C22⋊C8×C47—21no—
200C22⋊C8×C47—21no—
201C22⋊C8×C47C2311yescharacteristic
202C22⋊C8×C47C2311yescharacteristic
203C22⋊C8×C47C2311yescharacteristic
204C22⋊C8×C47C2311yescharacteristic
205#95×C47—21no—
206#95×C47—21no—
207#95×C47—21no—
208#95×C47C2311yescharacteristic
209#95×C47C2311yescharacteristic
210C24×C47—21no—
211C24×C47—21no—
212C24×C47—21no—
213C24×C47C2×D411yescharacteristic
214C24×C47C2×D411yescharacteristic
215#41×C47—24no—
216#41×C47—24no—
217#41×C47—42no—
218#41×C47—42no—
219#41×C47—42no—
220#41×C47—42no—
221#41×C47—42no—
222#41×C47—42no—
223#41×C47—42no—
224#41×C47—81no—
225#41×C47—81no—
226C2×Q8×C47—21no—
227C2×Q8×C47—21no—
228C2×Q8×C47—21no—
229C2×Q8×C47—42no—
230C2×Q8×C47C2×D411yescharacteristic
231C2×D4×C47—24no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—21no—
235C2×D4×C47—21no—
236C2×D4×C47—21no—
237C2×D4×C47—21no—
238C2×D4×C47—21no—
239C2×D4×C47—21no—
240C2×D4×C47—21no—
241C2×D4×C47—21no—
242C2×D4×C47—21no—
243C2×D4×C47—21no—
244C2×D4×C47—21no—
245C2×D4×C47—21no—
246C2×D4×C47—21no—
247C2×D4×C47—21no—
248C2×D4×C47—21no—
249C2×D4×C47—21no—
250C2×D4×C47—21no—
251C2×D4×C47—42no—
252C2×D4×C47—42no—
253C2×D4×C47—42no—
254C2×D4×C47—42no—
255C2×D4×C47—41no—
256C2×D4×C47—41no—
257C2×D4×C47—42no—
258C2×D4×C47—42no—
259C2×D4×C47—81no—
260C2×D4×C47—81no—
261C2×D4×C47—81no—
262C2×D4×C47—81no—
263C2×D4×C47—81no—
264C2×D4×C47—82no—
265C2×D4×C47C2×D411yescharacteristic
266C2×D4×C47C2×D411yescharacteristic
267C2×D4×C47C2×D411yescharacteristic
268C22×C4×C47—21no—
269C22×C4×C47—21no—
270C22×C4×C47—21no—
271C22×C4×C47—21no—
272C22×C4×C47—21no—
273C22×C4×C47—21no—
274C22×C4×C47—21no—
275C22×C4×C47—21no—
276C22×C4×C47—21no—
277C22×C4×C47—21no—
278C22×C4×C47—42no—
279C22×C4×C47—42no—
280C22×C4×C47—42no—
281C22×C4×C47—42no—
282C22×C4×C47—41no—
283C22×C4×C47—41no—
284C22×C4×C47—42no—
285C22×C4×C47—81no—
286C22×C4×C47C2×D411yescharacteristic
287C22×C4×C47C2×D411yescharacteristic
288C22×C4×C47C2×D411yescharacteristic
289C22×C4×C47C2×D411yescharacteristic
290C22×C4×C47C2×D411yescharacteristic
291C22×C4×C47C2×D411yescharacteristic
292C22×C4×C47C2×D411yescharacteristic
293C22×C4×C47C2×D411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295Q16×C47—42no—
296SD16×C47—42no—
297SD16×C47—42no—
298SD16×C47—42no—
299SD16×C47—42no—
300D8×C47—42no—
301D8×C47—42no—
302D8×C47—42no—
303M16×C47—42no—
304C2×C8×C47—21no—
305C2×C8×C47—21no—
306C2×C8×C47—21no—
307C2×C8×C47—21no—
308C2×C8×C47—42no—
309C4⋊C4×C47—21no—
310C4⋊C4×C47—21no—
311C4⋊C4×C47—21no—
312C4⋊C4×C47—21no—
313C4⋊C4×C47—21no—
314C4⋊C4×C47—21no—
315C4⋊C4×C47—21no—
316C4⋊C4×C47—21no—
317C4⋊C4×C47—21no—
318C4⋊C4×C47—21no—
319C4⋊C4×C47—21no—
320C4⋊C4×C47—21no—
321C4⋊C4×C47—21no—
322C4⋊C4×C47—42no—
323C4⋊C4×C47C2×D411yescharacteristic
324C4⋊C4×C47C2×D411yescharacteristic
325C4⋊C4×C47C2×D411yescharacteristic
326C4⋊C4×C47C2×D411yescharacteristic
327C22⋊C4×C47—21no—
328C22⋊C4×C47—21no—
329C22⋊C4×C47—21no—
330C22⋊C4×C47—21no—
331C22⋊C4×C47—21no—
332C22⋊C4×C47—21no—
333C22⋊C4×C47—21no—
334C22⋊C4×C47—21no—
335C22⋊C4×C47—21no—
336C22⋊C4×C47—21no—
337C22⋊C4×C47—21no—
338C22⋊C4×C47—21no—
339C22⋊C4×C47—21no—
340C22⋊C4×C47—21no—
341C22⋊C4×C47—21no—
342C22⋊C4×C47—21no—
343C22⋊C4×C47—21no—
344C22⋊C4×C47—21no—
345C22⋊C4×C47—21no—
346C22⋊C4×C47—21no—
347C22⋊C4×C47—21no—
348C22⋊C4×C47—21no—
349C22⋊C4×C47—21no—
350C22⋊C4×C47—21no—
351C22⋊C4×C47—21no—
352C22⋊C4×C47—42no—
353C22⋊C4×C47—42no—
354C22⋊C4×C47—42no—
355C22⋊C4×C47—81no—
356C42×C47—21no—
357C42×C47—21no—
358C42×C47—21no—
359C23×C47—21no—
360C23×C47—21no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—21no—
364C23×C47—21no—
365C23×C47—21no—
366C23×C47—21no—
367C23×C47—21no—
368C23×C47—21no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—41no—
376C23×C47—41no—
377C23×C47—41no—
378C23×C47—42no—
379C23×C47—81no—
380C23×C47—81no—
381C23×C47—81no—
382C23×C47—81no—
383C23×C47—81no—
384C23×C47#12011yescharacteristic
385C23×C47#12011yescharacteristic
386C23×C47C22×D411yescharacteristic
387Q8×C47—22no—
388Q8×C47—22no—
389Q8×C47—41no—
390Q8×C47—41no—
391Q8×C47—41no—
392Q8×C47—81no—
393D4×C47—22no—
394D4×C47—22no—
395D4×C47—41no—
396D4×C47—41no—
397D4×C47—41no—
398D4×C47—41no—
399D4×C47—41no—
400D4×C47—44no—
401D4×C47—41no—
402D4×C47—41no—
403D4×C47—41no—
404D4×C47—41no—
405D4×C47—41no—
406D4×C47—41no—
407D4×C47—44no—
408D4×C47—42no—
409D4×C47—42no—
410D4×C47—81no—
411D4×C47—81no—
412D4×C47—81no—
413D4×C47—81no—
414D4×C47—81no—
415D4×C47—81no—
416D4×C47—81no—
417D4×C47—81no—
418D4×C47—81no—
419D4×C47—81no—
420D4×C47—81no—
421D4×C47—81no—
422D4×C47—84no—
423C2×C4×C47—22no—
424C2×C4×C47—22no—
425C2×C4×C47—22no—
426C2×C4×C47—22no—
427C2×C4×C47—21no—
428C2×C4×C47—21no—
429C2×C4×C47—21no—
430C2×C4×C47—21no—
431C2×C4×C47—21no—
432C2×C4×C47—21no—
433C2×C4×C47—21no—
434C2×C4×C47—21no—
435C2×C4×C47—21no—
436C2×C4×C47—21no—
437C2×C4×C47—41no—
438C2×C4×C47—41no—
439C2×C4×C47—41no—
440C2×C4×C47—41no—
441C2×C4×C47—44no—
442C2×C4×C47—44no—
443C2×C4×C47—41no—
444C2×C4×C47—41no—
445C2×C4×C47—41no—
446C2×C4×C47—41no—
447C2×C4×C47—41no—
448C2×C4×C47—41no—
449C2×C4×C47—41no—
450C2×C4×C47—41no—
451C2×C4×C47—41no—
452C2×C4×C47—81no—
453C2×C4×C47—81no—
454C2×C4×C47—81no—
455C2×C4×C47—81no—
456C2×C4×C47—81no—
457C2×C4×C47—81no—
458C2×C4×C47—81no—
459C2×C4×C47—84no—
460C2×C4×C47#12011yescharacteristic
461C2×C4×C47#12011yescharacteristic
462C2×C4×C47C22×D411yescharacteristic
463C2×C4×C47C22×D411yescharacteristic
464C8×C47—41no—
465C8×C47—41no—
466C8×C47—41no—
467C8×C47—41no—
468#18252C4711yesmaximal, characteristic, direct product factor, Sylow
469C22×C47—21no—
470C22×C47—21no—
471C22×C47—21no—
472C22×C47—21no—
473C22×C47—21no—
474C22×C47—21no—
475C22×C47—21no—
476C22×C47—42no—
477C22×C47—42no—
478C22×C47—42no—
479C22×C47—42no—
480C22×C47—41no—
481C22×C47—41no—
482C22×C47—41no—
483C22×C47—41no—
484C22×C47—41no—
485C22×C47—41no—
486C22×C47—41no—
487C22×C47—41no—
488C22×C47—42no—
489C22×C47—41no—
490C22×C47—41no—
491C22×C47—41no—
492C22×C47—41no—
493C22×C47—81no—
494C22×C47—81no—
495C22×C47—81no—
496C22×C47—81no—
497C22×C47—81no—
498C22×C47—81no—
499C22×C47—162no—
500C22×C47—162no—
501C22×C47B(4,𝔽2)12yes—
502C22×C47C2×#12011yescharacteristic
503C22×C47#57611yescharacteristic
504C22×C47#57711yescharacteristic
505C4×C47—21no—
506C4×C47—21no—
507C4×C47—21no—
508C4×C47—21no—
509C4×C47—42no—
510C4×C47—41no—
511C4×C47—41no—
512C4×C47—41no—
513C4×C47—41no—
514C4×C47—41no—
515C4×C47—41no—
516C4×C47—42no—
517C4×C47—41no—
518C4×C47—41no—
519C4×C47—81no—
520#3534C2×C4711yescharacteristic, complemented
521#3006C2×C4711yescharacteristic, complemented
522#3002C2×C4711yescharacteristic, complemented
523#2430C2×C4711yescharacteristic, complemented
524#1606C2×C4711yescharacteristic, complemented
525#1604C2×C4711yescharacteristic, complemented
526#1603C2×C4711yescharacteristic, complemented
527#1601C2×C4711yescharacteristic, complemented
528#1600C2×C4711yescharacteristic, complemented
529#1598C2×C4711yescharacteristic, complemented
530#1597C2×C4711yescharacteristic, complemented
531#1595C2×C4711yescharacteristic, complemented
532#1504C2×C4711yescharacteristic, complemented
533C2×#327C2×C4711yescharacteristic, complemented
534#1468C2×C4711yescharacteristic, complemented
535C2×C47—21no—
536C2×C47—21no—
537C2×C47—22no—
538C2×C47—41no—
539C2×C47—82no—
540C2×C47—81no—
541C2×C47—81no—
542C2×C47—81no—
543C2×C47—81no—
544C2×C47#301211yescharacteristic
545C2×C47#301811yescharacteristic
546C2×C47C2×B(4,𝔽2)11yescharacteristic
547C22×#41C22×C4711yescharacteristic, complemented
548C2×AGL(1,ℤ/8)—21no—
549C2×#135—21no—
550#562—21no—
551#560—21no—
552#553—21no—
553#551—21no—
554#546—21no—
555#546—21no—
556#546—21no—
557D42—21no—
558#540—21no—
559#539—21no—
560#539C22×C4711yescharacteristic
561#538—21no—
562#538C22×C4711yescharacteristic
563#537C22×C4711yescharacteristic
564#534—21no—
565#534C22×C4711yescharacteristic
566#525C22×C4711yescharacteristic
567C2×#123C22×C4711yescharacteristic
568C2×#121—21no—
569C2×#121C22×C4711yescharacteristic
570#452—21no—
571#451C22×C4711yescharacteristic, complemented
572#450C22×C4711yescharacteristic, complemented
573#449—21no—
574#449—21no—
575#449—21no—
576#448C22×C4711yescharacteristic
577#448C22×C4711yescharacteristic, complemented
578#448C22×C4711yescharacteristic, complemented
579#447C22×C4711yescharacteristic
580#447C22×C4711yescharacteristic, complemented
581#447C22×C4711yescharacteristic, complemented
582#417—21no—
583#416—21no—
584#407C22×C4711yescharacteristic, complemented
585C2×C22⋊C8C22×C4711yescharacteristic, complemented
586#395C22×C4711yescharacteristic, complemented
587#394C22×C4711yescharacteristic, complemented
588#393C22×C4711yescharacteristic, complemented
589#392C22×C4711yescharacteristic, complemented
590#386—21no—
591#386—21no—
592#385—21no—
593C2×#95C22×C4711yescharacteristic, complemented
594#328C22×C4711yescharacteristic, complemented
595#328C22×C4711yescharacteristic, complemented
596#327C22×C4711yescharacteristic
597#327C22×C4711yescharacteristic
598#327C22×C4711yescharacteristic, complemented
599#327C22×C4711yescharacteristic, complemented
600#327C22×C4711yescharacteristic, complemented
601#327C22×C4711yescharacteristic, complemented
602#324C22×C4711yescharacteristic, complemented
603#324C22×C4711yescharacteristic, complemented
604#323C22×C4711yescharacteristic, complemented
605#323C22×C4711yescharacteristic, complemented
606C47#1825211yescharacteristic, direct product factor, Sylow
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C4711yescharacteristic, complemented
614C22×Q8C23×C4711yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C4711yescharacteristic
621C22×D4D4×C4711yescharacteristic, complemented
622C22×D4C23×C4711yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C4711yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C4711yescharacteristic, complemented
668C22⋊Q8C23×C4711yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C4711yescharacteristic, complemented
686#121D4×C4711yescharacteristic, complemented
687#121D4×C4711yescharacteristic, complemented
688#121C23×C4711yescharacteristic
689#121C23×C4711yescharacteristic
690#121C23×C4711yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C4711yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C4711yescharacteristic
711C2×C4⋊C4D4×C4711yescharacteristic, complemented
712C2×C4⋊C4C23×C4711yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C4711yescharacteristic
721C2×C22⋊C4D4×C4711yescharacteristic
722C2×C22⋊C4C23×C4711yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C4711yescharacteristic
734C22⋊C8C23×C4711yescharacteristic
735C22⋊C8C23×C4711yescharacteristic
736C22⋊C8C23×C4711yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C4711yescharacteristic
741#95C23×C4711yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C4711yescharacteristic
746C24C2×D4×C4711yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C4711yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C4711yescharacteristic
798C2×D4C2×D4×C4711yescharacteristic
799C2×D4C2×D4×C4711yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C4711yescharacteristic
819C22×C4C2×D4×C4711yescharacteristic
820C22×C4C2×D4×C4711yescharacteristic
821C22×C4C2×D4×C4711yescharacteristic
822C22×C4C2×D4×C4711yescharacteristic
823C22×C4C2×D4×C4711yescharacteristic
824C22×C4C2×D4×C4711yescharacteristic
825C22×C4C2×D4×C4711yescharacteristic
826C22×C4C24×C4711yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C4711yescharacteristic
856C4⋊C4C2×D4×C4711yescharacteristic
857C4⋊C4C2×D4×C4711yescharacteristic
858C4⋊C4C2×D4×C4711yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C4711yescharacteristic
917C23#120×C4711yescharacteristic
918C23C22×D4×C4711yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C4711yescharacteristic
993C2×C4#120×C4711yescharacteristic
994C2×C4C22×D4×C4711yescharacteristic
995C2×C4C22×D4×C4711yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C47×B(4,𝔽2)12yes—
1033C22C2×#120×C4711yescharacteristic
1034C22C47×#57611yescharacteristic
1035C22C47×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C47×#301211yescharacteristic
1061C2C47×#301811yescharacteristic
1062C2C2×C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3534C2semidirect
2. C47×#3006C2semidirect
3. C47×#3002C2semidirect
4. C47×#2430C2semidirect
5. C47×#1606C2semidirect
6. C47×#1604C2semidirect
7. C47×#1603C2semidirect
8. C47×#1601C2semidirect
9. C47×#1600C2semidirect
10. C47×#1598C2semidirect
11. C47×#1597C2semidirect
12. C47×#1595C2semidirect
13. C47×#1504C2semidirect
14. C2×C47×#327C2semidirect
15. C47×#1468C2semidirect
16. C22×#41×C47C22semidirect
40. C47×#451C22semidirect
41. C47×#450C22semidirect
46. C47×#448C22semidirect
47. C47×#448C22semidirect
49. C47×#447C22semidirect
50. C47×#447C22semidirect
53. C47×#407C22semidirect
54. C2×C22⋊C8×C47C22semidirect
55. C47×#395C22semidirect
56. C47×#394C22semidirect
57. C47×#393C22semidirect
58. C47×#392C22semidirect
62. C2×#95×C47C22semidirect
63. C47×#328C22semidirect
64. C47×#328C22semidirect
67. C47×#327C22semidirect
68. C47×#327C22semidirect
69. C47×#327C22semidirect
70. C47×#327C22semidirect
71. C47×#324C22semidirect
72. C47×#324C22semidirect
73. C47×#323C22semidirect
74. C47×#323C22semidirect
81. C2×#41×C47D4semidirect
89. C22×D4×C47D4semidirect
135. C22⋊Q8×C47D4semidirect
153. #121×C47D4semidirect
154. #121×C47D4semidirect
155. #121×C47D4semidirect
176. #117×C47D4semidirect
179. C2×C4⋊C4×C47D4semidirect
468. #18252C47direct (N × H)
520. #3534C2×C47semidirect
521. #3006C2×C47semidirect
522. #3002C2×C47semidirect
523. #2430C2×C47semidirect
524. #1606C2×C47semidirect
525. #1604C2×C47semidirect
526. #1603C2×C47semidirect
527. #1601C2×C47semidirect
528. #1600C2×C47semidirect
529. #1598C2×C47semidirect
530. #1597C2×C47semidirect
531. #1595C2×C47semidirect
532. #1504C2×C47semidirect
533. C2×#327C2×C47semidirect
534. #1468C2×C47semidirect
547. C22×#41C22×C47semidirect
571. #451C22×C47semidirect
572. #450C22×C47semidirect
577. #448C22×C47semidirect
578. #448C22×C47semidirect
580. #447C22×C47semidirect
581. #447C22×C47semidirect
584. #407C22×C47semidirect
585. C2×C22⋊C8C22×C47semidirect
586. #395C22×C47semidirect
587. #394C22×C47semidirect
588. #393C22×C47semidirect
589. #392C22×C47semidirect
593. C2×#95C22×C47semidirect
594. #328C22×C47semidirect
595. #328C22×C47semidirect
598. #327C22×C47semidirect
599. #327C22×C47semidirect
600. #327C22×C47semidirect
601. #327C22×C47semidirect
602. #324C22×C47semidirect
603. #324C22×C47semidirect
604. #323C22×C47semidirect
605. #323C22×C47semidirect
606. C47#18252direct (N × H)
613. C2×#41D4×C47semidirect
621. C22×D4D4×C47semidirect
667. C22⋊Q8D4×C47semidirect
685. #121D4×C47semidirect
686. #121D4×C47semidirect
687. #121D4×C47semidirect
708. #117D4×C47semidirect
711. C2×C4⋊C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35342
C47×#30062
C47×#30022
C47×#24302
C47×#16062
C47×#16042
C47×#16032
C47×#16012
C47×#16002
C47×#15982
C47×#15972
C47×#15952
C47×#15042
C2×C47×#3272
C47×#14682
#1825247