Finite Group Databasebeta

← C47×#24467 #26064165

Subgroups — C47×#24467 #26064165

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3488C211yesmaximal, characteristic
2C47×#3056C211yesmaximal, characteristic, complemented
3C2×C47×#455C211yesmaximal, characteristic, complemented
4C47×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C47C211yesmaximal, characteristic, complemented
6C47×#2850C211yesmaximal, characteristic, complemented
7C47×#2040C211yesmaximal, characteristic, complemented
8C47×#2037C211yesmaximal, characteristic, complemented
9C47×#2007C211yesmaximal, characteristic, complemented
10C47×#2004C211yesmaximal, characteristic, complemented
11C47×#1900C211yesmaximal, characteristic, complemented
12C47×#1896C211yesmaximal, characteristic, complemented
13C47×#1882C211yesmaximal, characteristic, complemented
14C47×#1860C211yesmaximal, characteristic, complemented
15C47×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C2×#137×C47C2211yescharacteristic
19C2×#137×C47C2211yescharacteristic, complemented
20C2×#137×C47C2211yescharacteristic, complemented
21C22×M16×C47C2211yescharacteristic, complemented
22C47×#550—21no—
23C47×#548—21no—
24C47×#546—21no—
25C47×#546—22no—
26D42×C47—22no—
27D42×C47—21no—
28C47×#537—21no—
29C47×#537C2211yescharacteristic
30C47×#535—21no—
31C47×#535C2211yescharacteristic
32C2×#124×C47C2211yescharacteristic, complemented
33C47×#525—21no—
34C47×#525C2211yescharacteristic
35C2×C22⋊Q8×C47C2211yescharacteristic, complemented
36C2×#121×C47—21no—
37C2×#121×C47C2211yescharacteristic
38C47×#520C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic, complemented
40C47×#470—21no—
41C47×#468—21no—
42C47×#467—21no—
43C47×#465—21no—
44C47×#455—24no—
45C47×#452—21no—
46C47×#452—21no—
47C47×#451—21no—
48C47×#450—21no—
49C47×#428C2211yescharacteristic, complemented
50C2×#104×C47—24no—
51C2×#104×C47C2211yescharacteristic
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic, complemented
54C2×#104×C47C2211yescharacteristic, complemented
55C2×#104×C47C2211yescharacteristic, complemented
56C2×#104×C47C2211yescharacteristic, complemented
57C47×#419C2211yescharacteristic, complemented
58C47×#417C2211yescharacteristic
59C47×#417C2211yescharacteristic, complemented
60C47×#417C2211yescharacteristic, complemented
61C2×#100×C47C2211yescharacteristic, complemented
62C2×#100×C47C2211yescharacteristic, complemented
63C47×#407C2211yescharacteristic, complemented
64C47×#391C2211yescharacteristic, complemented
65C47×#390C2211yescharacteristic, complemented
66C47×#388—22no—
67C47×#386—22no—
68C47×#382C2211yescharacteristic, complemented
69C47×#343C2211yescharacteristic, complemented
70C47×#343C2211yescharacteristic, complemented
71C47×#339C2211yescharacteristic, complemented
72C47×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C47—22no—
74H(5,𝔽2)×C47—22no—
75H(5,𝔽2)×C47—41no—
76H(5,𝔽2)×C47—41no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—22no—
82C2×#41×C47—22no—
83C2×#41×C47—41no—
84C2×#41×C47—41no—
85C2×#41×C47D411yescharacteristic
86C2×#41×C47D411yescharacteristic
87C2×#41×C47C2311yescharacteristic
88C2×#41×C47C2311yescharacteristic
89C2×#41×C47C2311yescharacteristic
90C22×Q8×C47D411yescharacteristic
91C22×Q8×C47C2311yescharacteristic
92C22×D4×C47—21no—
93C22×D4×C47—22no—
94C22×D4×C47—22no—
95C22×D4×C47—21no—
96C22×D4×C47—21no—
97C22×D4×C47D411yescharacteristic
98C22×D4×C47D412yes—
99C22×D4×C47C2311yescharacteristic
100C23×C4×C47—21no—
101C23×C4×C47—21no—
102C23×C4×C47C2311yescharacteristic
103#137×C47—22no—
104#137×C47—22no—
105#137×C47—22no—
106#137×C47—41no—
107#137×C47—41no—
108#137×C47—41no—
109C2×Q16×C47—21no—
110C2×Q16×C47—21no—
111C2×Q16×C47—21no—
112C2×SD16×C47—21no—
113C2×SD16×C47—21no—
114C2×SD16×C47—21no—
115C2×M16×C47—21no—
116C2×M16×C47—22no—
117C2×M16×C47—41no—
118C2×M16×C47C2311yescharacteristic
119C2×M16×C47C2311yescharacteristic
120C2×M16×C47C2311yescharacteristic
121C2×M16×C47C2311yescharacteristic
122C22×C8×C47—21no—
123#127×C47—22no—
124#127×C47—21no—
125#124×C47—22no—
126#124×C47—21no—
127#124×C47—22no—
128#124×C47—41no—
129#123×C47—22no—
130#123×C47—21no—
131C22⋊Q8×C47—22no—
132C22⋊Q8×C47—21no—
133C22⋊Q8×C47—21no—
134C22⋊Q8×C47—21no—
135C22⋊Q8×C47—21no—
136C22⋊Q8×C47—21no—
137C22⋊Q8×C47—21no—
138C22⋊Q8×C47D411yescharacteristic
139C22⋊Q8×C47D411yescharacteristic
140#121×C47—22no—
141#121×C47—22no—
142#121×C47—22no—
143#121×C47—22no—
144#121×C47—22no—
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—22no—
152#121×C47—21no—
153#121×C47—21no—
154#121×C47D411yescharacteristic
155#121×C47D411yescharacteristic
156#120×C47—22no—
157#120×C47—22no—
158#120×C47—22no—
159#120×C47—21no—
160#120×C47—22no—
161C4×Q8×C47—21no—
162C4×D4×C47—22no—
163C4×D4×C47—22no—
164C4×D4×C47—21no—
165C4×D4×C47—22no—
166C4×D4×C47—21no—
167C4×D4×C47—21no—
168#117×C47—21no—
169#117×C47C2311yescharacteristic
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—22no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—22no—
177C2×C22⋊C4×C47—22no—
178C2×C22⋊C4×C47D412yes—
179C2×C42×C47—22no—
180C2×C42×C47—21no—
181C2×C42×C47—41no—
182C2×C42×C47C2311yescharacteristic
183C2×C42×C47C2311yescharacteristic
184#107×C47—21no—
185#106×C47—21no—
186#104×C47—22no—
187#104×C47—22no—
188#104×C47—22no—
189#104×C47—22no—
190#104×C47—41no—
191#104×C47D414yescomplemented
192#103×C47—21no—
193#103×C47—21no—
194#103×C47—21no—
195#103×C47—21no—
196#103×C47—21no—
197#102×C47—21no—
198#102×C47—21no—
199#102×C47—21no—
200#100×C47—22no—
201#100×C47—41no—
202C22⋊C8×C47—21no—
203C22⋊C8×C47—21no—
204#95×C47—22no—
205#95×C47—22no—
206C24×C47—22no—
207C24×C47—21no—
208C24×C47C2×D411yescharacteristic
209C24×C47C2×D412yes—
210#41×C47—21no—
211#41×C47—21no—
212#41×C47—22no—
213#41×C47—22no—
214#41×C47—21no—
215#41×C47—21no—
216#41×C47—21no—
217#41×C47—21no—
218#41×C47—21no—
219#41×C47—21no—
220#41×C47—21no—
221#41×C47—21no—
222#41×C47—42no—
223#41×C47—42no—
224#41×C47—41no—
225#41×C47—41no—
226#41×C47—42no—
227#41×C47—42no—
228#41×C47—42no—
229#41×C47—42no—
230#41×C47—42no—
231#41×C47—42no—
232#41×C47C2×D412yes—
233#41×C47#4112yes—
234C2×Q8×C47—21no—
235C2×Q8×C47—22no—
236C2×Q8×C47—21no—
237C2×Q8×C47—21no—
238C2×Q8×C47—21no—
239C2×Q8×C47—21no—
240C2×Q8×C47—21no—
241C2×Q8×C47—21no—
242C2×Q8×C47—41no—
243C2×Q8×C47C2×D411yescharacteristic
244C2×Q8×C47C2×D411yescharacteristic
245C2×Q8×C47C2×D411yescharacteristic
246C2×D4×C47—21no—
247C2×D4×C47—22no—
248C2×D4×C47—22no—
249C2×D4×C47—22no—
250C2×D4×C47—22no—
251C2×D4×C47—21no—
252C2×D4×C47—21no—
253C2×D4×C47—21no—
254C2×D4×C47—21no—
255C2×D4×C47—21no—
256C2×D4×C47—22no—
257C2×D4×C47—22no—
258C2×D4×C47—22no—
259C2×D4×C47—21no—
260C2×D4×C47—22no—
261C2×D4×C47—21no—
262C2×D4×C47—21no—
263C2×D4×C47—21no—
264C2×D4×C47—21no—
265C2×D4×C47—21no—
266C2×D4×C47—21no—
267C2×D4×C47—21no—
268C2×D4×C47—41no—
269C2×D4×C47—42no—
270C2×D4×C47—42no—
271C2×D4×C47—42no—
272C2×D4×C47—42no—
273C2×D4×C47—44no—
274C2×D4×C47—44no—
275C2×D4×C47—42no—
276C2×D4×C47—42no—
277C2×D4×C47—44no—
278C2×D4×C47—84no—
279C2×D4×C47C2×D411yescharacteristic
280C2×D4×C47C2×D411yescharacteristic
281C2×D4×C47C2×D411yescharacteristic
282C22×C4×C47—21no—
283C22×C4×C47—21no—
284C22×C4×C47—21no—
285C22×C4×C47—21no—
286C22×C4×C47—21no—
287C22×C4×C47—22no—
288C22×C4×C47—21no—
289C22×C4×C47—21no—
290C22×C4×C47—21no—
291C22×C4×C47—22no—
292C22×C4×C47—21no—
293C22×C4×C47—21no—
294C22×C4×C47—21no—
295C22×C4×C47—21no—
296C22×C4×C47—21no—
297C22×C4×C47—21no—
298C22×C4×C47—42no—
299C22×C4×C47—42no—
300C22×C4×C47—42no—
301C22×C4×C47—42no—
302C22×C4×C47—42no—
303C22×C4×C47C2×D411yescharacteristic
304C22×C4×C47C2×D411yescharacteristic
305C22×C4×C47C2×D411yescharacteristic
306C22×C4×C47C2×D411yescharacteristic
307C22×C4×C47C2×D411yescharacteristic
308C22×C4×C47C2×D412yes—
309C22×C4×C47C2411yescharacteristic
310Q16×C47—42no—
311Q16×C47—42no—
312Q16×C47—42no—
313SD16×C47—42no—
314SD16×C47—42no—
315SD16×C47—42no—
316M16×C47—21no—
317M16×C47—21no—
318M16×C47—21no—
319M16×C47—21no—
320M16×C47—21no—
321M16×C47—21no—
322M16×C47—21no—
323M16×C47—42no—
324M16×C47C2×D412yescomplemented
325C2×C8×C47—21no—
326C2×C8×C47—21no—
327C2×C8×C47—21no—
328C2×C8×C47—21no—
329C2×C8×C47—42no—
330C4⋊C4×C47—22no—
331C4⋊C4×C47—22no—
332C4⋊C4×C47—21no—
333C4⋊C4×C47—21no—
334C4⋊C4×C47—21no—
335C4⋊C4×C47—21no—
336C4⋊C4×C47—21no—
337C4⋊C4×C47—21no—
338C4⋊C4×C47—41no—
339C4⋊C4×C47—41no—
340C4⋊C4×C47C2×D411yescharacteristic
341C4⋊C4×C47C2×D411yescharacteristic
342C22⋊C4×C47—22no—
343C22⋊C4×C47—22no—
344C22⋊C4×C47—22no—
345C22⋊C4×C47—22no—
346C22⋊C4×C47—22no—
347C22⋊C4×C47—21no—
348C22⋊C4×C47—21no—
349C22⋊C4×C47—21no—
350C22⋊C4×C47—21no—
351C22⋊C4×C47—22no—
352C22⋊C4×C47—22no—
353C22⋊C4×C47—21no—
354C22⋊C4×C47—44no—
355C22⋊C4×C47—44no—
356C22⋊C4×C47—41no—
357C22⋊C4×C47—41no—
358C42×C47—22no—
359C42×C47—21no—
360C42×C47—21no—
361C42×C47—21no—
362C42×C47—21no—
363C42×C47—42no—
364C42×C47C2×D412yescomplemented
365C23×C47—21no—
366C23×C47—21no—
367C23×C47—21no—
368C23×C47—22no—
369C23×C47—22no—
370C23×C47—21no—
371C23×C47—21no—
372C23×C47—22no—
373C23×C47—22no—
374C23×C47—41no—
375C23×C47—42no—
376C23×C47—44no—
377C23×C47—42no—
378C23×C47—42no—
379C23×C47—42no—
380C23×C47—81no—
381C23×C47—82no—
382C23×C47—82no—
383C23×C47#12011yescharacteristic
384C23×C47#12011yescharacteristic
385C23×C47C22×D411yescharacteristic
386Q8×C47—21no—
387Q8×C47—21no—
388Q8×C47—21no—
389Q8×C47—21no—
390Q8×C47—21no—
391Q8×C47—42no—
392Q8×C47—41no—
393Q8×C47—41no—
394Q8×C47—41no—
395Q8×C47—41no—
396Q8×C47#12112yes—
397D4×C47—22no—
398D4×C47—22no—
399D4×C47—21no—
400D4×C47—21no—
401D4×C47—21no—
402D4×C47—21no—
403D4×C47—21no—
404D4×C47—42no—
405D4×C47—42no—
406D4×C47—44no—
407D4×C47—42no—
408D4×C47—44no—
409D4×C47—41no—
410D4×C47—41no—
411D4×C47—41no—
412D4×C47—41no—
413D4×C47—44no—
414D4×C47—42no—
415D4×C47—41no—
416D4×C47—41no—
417D4×C47—41no—
418D4×C47—41no—
419D4×C47—81no—
420D4×C47—82no—
421D4×C47—82no—
422D4×C47—82no—
423D4×C47—82no—
424D4×C47#12112yes—
425C2×C4×C47—21no—
426C2×C4×C47—21no—
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—22no—
435C2×C4×C47—21no—
436C2×C4×C47—21no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—21no—
440C2×C4×C47—22no—
441C2×C4×C47—21no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—22no—
445C2×C4×C47—42no—
446C2×C4×C47—42no—
447C2×C4×C47—42no—
448C2×C4×C47—44no—
449C2×C4×C47—41no—
450C2×C4×C47—41no—
451C2×C4×C47—41no—
452C2×C4×C47—48no—
453C2×C4×C47—41no—
454C2×C4×C47—41no—
455C2×C4×C47—41no—
456C2×C4×C47—41no—
457C2×C4×C47—41no—
458C2×C4×C47—42no—
459C2×C4×C47—42no—
460C2×C4×C47—41no—
461C2×C4×C47—41no—
462C2×C4×C47—41no—
463C2×C4×C47—41no—
464C2×C4×C47—82no—
465C2×C4×C47#12011yescharacteristic
466C2×C4×C47#12011yescharacteristic
467C2×C4×C47C22×D411yescharacteristic
468C2×C4×C47C22×D411yescharacteristic
469C2×C4×C47C22×D411yescharacteristic
470C2×C4×C47C2×#4111yescharacteristic
471C2×C4×C47H(5,𝔽2)11yescharacteristic
472C2×C4×C47H(5,𝔽2)11yescharacteristic
473C8×C47—22no—
474C8×C47—41no—
475C8×C47—41no—
476C8×C47—41no—
477#24467C4711yesmaximal, characteristic, direct product factor, Sylow
478C22×C47—21no—
479C22×C47—21no—
480C22×C47—21no—
481C22×C47—21no—
482C22×C47—21no—
483C22×C47—22no—
484C22×C47—21no—
485C22×C47—21no—
486C22×C47—42no—
487C22×C47—42no—
488C22×C47—41no—
489C22×C47—41no—
490C22×C47—41no—
491C22×C47—41no—
492C22×C47—42no—
493C22×C47—42no—
494C22×C47—41no—
495C22×C47—41no—
496C22×C47—41no—
497C22×C47—42no—
498C22×C47—41no—
499C22×C47—84no—
500C22×C47—82no—
501C22×C47—82no—
502C22×C47—164no—
503C22×C47#45512yescomplemented
504C22×C47C2×#12011yescharacteristic
505C22×C47D4211yescharacteristic
506C22×C47#54611yescharacteristic
507C4×C47—21no—
508C4×C47—21no—
509C4×C47—22no—
510C4×C47—42no—
511C4×C47—42no—
512C4×C47—41no—
513C4×C47—41no—
514C4×C47—42no—
515C4×C47—41no—
516C4×C47—41no—
517C4×C47—81no—
518C4×C47—81no—
519C4×C47C2×#12111yescharacteristic
520C4×C47#53411yescharacteristic
521C4×C47D4211yescharacteristic
522C4×C47#54611yescharacteristic
523#3488C2×C4711yescharacteristic
524#3056C2×C4711yescharacteristic, complemented
525C2×#455C2×C4711yescharacteristic, complemented
526#3007C2×C4711yescharacteristic, complemented
527C22×#104C2×C4711yescharacteristic, complemented
528#2850C2×C4711yescharacteristic, complemented
529#2040C2×C4711yescharacteristic, complemented
530#2037C2×C4711yescharacteristic, complemented
531#2007C2×C4711yescharacteristic, complemented
532#2004C2×C4711yescharacteristic, complemented
533#1900C2×C4711yescharacteristic, complemented
534#1896C2×C4711yescharacteristic, complemented
535#1882C2×C4711yescharacteristic, complemented
536#1860C2×C4711yescharacteristic, complemented
537#1792C2×C4711yescharacteristic, complemented
538C2×C47—21no—
539C2×C47—21no—
540C2×C47—22no—
541C2×C47—41no—
542C2×C47—42no—
543C2×C47—81no—
544C2×C47—82no—
545C2×C47—81no—
546C2×C47#241011yescharacteristic
547C2×C47C2×#45511yescharacteristic
548C2×C47#301811yescharacteristic
549C2×H(5,𝔽2)C22×C4711yescharacteristic
550C22×#41C22×C4711yescharacteristic
551C2×#137C22×C4711yescharacteristic
552C2×#137C22×C4711yescharacteristic, complemented
553C2×#137C22×C4711yescharacteristic, complemented
554C22×M16C22×C4711yescharacteristic, complemented
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C22×C4711yescharacteristic
563#535—21no—
564#535C22×C4711yescharacteristic
565C2×#124C22×C4711yescharacteristic, complemented
566#525—21no—
567#525C22×C4711yescharacteristic
568C2×C22⋊Q8C22×C4711yescharacteristic, complemented
569C2×#121—21no—
570C2×#121C22×C4711yescharacteristic
571#520C22×C4711yescharacteristic
572C22×C42C22×C4711yescharacteristic, complemented
573#470—21no—
574#468—21no—
575#467—21no—
576#465—21no—
577#455—24no—
578#452—21no—
579#452—21no—
580#451—21no—
581#450—21no—
582#428C22×C4711yescharacteristic, complemented
583C2×#104—24no—
584C2×#104C22×C4711yescharacteristic
585C2×#104C22×C4711yescharacteristic
586C2×#104C22×C4711yescharacteristic, complemented
587C2×#104C22×C4711yescharacteristic, complemented
588C2×#104C22×C4711yescharacteristic, complemented
589C2×#104C22×C4711yescharacteristic, complemented
590#419C22×C4711yescharacteristic, complemented
591#417C22×C4711yescharacteristic
592#417C22×C4711yescharacteristic, complemented
593#417C22×C4711yescharacteristic, complemented
594C2×#100C22×C4711yescharacteristic, complemented
595C2×#100C22×C4711yescharacteristic, complemented
596#407C22×C4711yescharacteristic, complemented
597#391C22×C4711yescharacteristic, complemented
598#390C22×C4711yescharacteristic, complemented
599#388—22no—
600#386—22no—
601#382C22×C4711yescharacteristic, complemented
602#343C22×C4711yescharacteristic, complemented
603#343C22×C4711yescharacteristic, complemented
604#339C22×C4711yescharacteristic, complemented
605#339C22×C4711yescharacteristic, complemented
606C47#2446711yescharacteristic, direct product factor, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C4711yescharacteristic
620C2×#41D4×C4711yescharacteristic
621C2×#41C23×C4711yescharacteristic
622C2×#41C23×C4711yescharacteristic
623C2×#41C23×C4711yescharacteristic
624C22×Q8D4×C4711yescharacteristic
625C22×Q8C23×C4711yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C4711yescharacteristic
632C22×D4D4×C4712yes—
633C22×D4C23×C4711yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C4711yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C4711yescharacteristic
653C2×M16C23×C4711yescharacteristic
654C2×M16C23×C4711yescharacteristic
655C2×M16C23×C4711yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C4711yescharacteristic
673C22⋊Q8D4×C4711yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C4711yescharacteristic
689#121D4×C4711yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C4711yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C4711yescharacteristic
707C2×C4⋊C4C23×C4711yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C4712yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C4711yescharacteristic
717C2×C42C23×C4711yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C4714yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C4711yescharacteristic
743C24C2×D4×C4712yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C4712yes—
767#41#41×C4712yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C4711yescharacteristic
778C2×Q8C2×D4×C4711yescharacteristic
779C2×Q8C2×D4×C4711yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C4711yescharacteristic
814C2×D4C2×D4×C4711yescharacteristic
815C2×D4C2×D4×C4711yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C4711yescharacteristic
838C22×C4C2×D4×C4711yescharacteristic
839C22×C4C2×D4×C4711yescharacteristic
840C22×C4C2×D4×C4711yescharacteristic
841C22×C4C2×D4×C4711yescharacteristic
842C22×C4C2×D4×C4712yes—
843C22×C4C24×C4711yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C4712yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C4711yescharacteristic
875C4⋊C4C2×D4×C4711yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C4712yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C4711yescharacteristic
918C23#120×C4711yescharacteristic
919C23C22×D4×C4711yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C4712yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—81no—
954D4—82no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C4712yes—
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—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C4711yescharacteristic
1000C2×C4#120×C4711yescharacteristic
1001C2×C4C22×D4×C4711yescharacteristic
1002C2×C4C22×D4×C4711yescharacteristic
1003C2×C4C22×D4×C4711yescharacteristic
1004C2×C4C2×#41×C4711yescharacteristic
1005C2×C4H(5,𝔽2)×C4711yescharacteristic
1006C2×C4H(5,𝔽2)×C4711yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C47×#45512yescomplemented
1037C22C2×#120×C4711yescharacteristic
1038C22D42×C4711yescharacteristic
1039C22C47×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C4711yescharacteristic
1053C4C47×#53411yescharacteristic
1054C4D42×C4711yescharacteristic
1055C4C47×#54611yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C47×#241011yescharacteristic
1065C2C2×C47×#45511yescharacteristic
1066C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3056C2semidirect
3. C2×C47×#455C2semidirect
4. C47×#3007C2semidirect
5. C22×#104×C47C2semidirect
6. C47×#2850C2semidirect
7. C47×#2040C2semidirect
8. C47×#2037C2semidirect
9. C47×#2007C2semidirect
10. C47×#2004C2semidirect
11. C47×#1900C2semidirect
12. C47×#1896C2semidirect
13. C47×#1882C2semidirect
14. C47×#1860C2semidirect
15. C47×#1792C2semidirect
19. C2×#137×C47C22semidirect
20. C2×#137×C47C22semidirect
21. C22×M16×C47C22semidirect
32. C2×#124×C47C22semidirect
35. C2×C22⋊Q8×C47C22semidirect
39. C22×C42×C47C22semidirect
49. C47×#428C22semidirect
53. C2×#104×C47C22semidirect
54. C2×#104×C47C22semidirect
55. C2×#104×C47C22semidirect
56. C2×#104×C47C22semidirect
57. C47×#419C22semidirect
59. C47×#417C22semidirect
60. C47×#417C22semidirect
61. C2×#100×C47C22semidirect
62. C2×#100×C47C22semidirect
63. C47×#407C22semidirect
64. C47×#391C22semidirect
65. C47×#390C22semidirect
68. C47×#382C22semidirect
69. C47×#343C22semidirect
70. C47×#343C22semidirect
71. C47×#339C22semidirect
72. C47×#339C22semidirect
191. #104×C47D4semidirect
324. M16×C47C2×D4semidirect
364. C42×C47C2×D4semidirect
477. #24467C47direct (N × H)
503. C22×C47#455semidirect
524. #3056C2×C47semidirect
525. C2×#455C2×C47semidirect
526. #3007C2×C47semidirect
527. C22×#104C2×C47semidirect
528. #2850C2×C47semidirect
529. #2040C2×C47semidirect
530. #2037C2×C47semidirect
531. #2007C2×C47semidirect
532. #2004C2×C47semidirect
533. #1900C2×C47semidirect
534. #1896C2×C47semidirect
535. #1882C2×C47semidirect
536. #1860C2×C47semidirect
537. #1792C2×C47semidirect
552. C2×#137C22×C47semidirect
553. C2×#137C22×C47semidirect
554. C22×M16C22×C47semidirect
565. C2×#124C22×C47semidirect
568. C2×C22⋊Q8C22×C47semidirect
572. C22×C42C22×C47semidirect
582. #428C22×C47semidirect
586. C2×#104C22×C47semidirect
587. C2×#104C22×C47semidirect
588. C2×#104C22×C47semidirect
589. C2×#104C22×C47semidirect
590. #419C22×C47semidirect
592. #417C22×C47semidirect
593. #417C22×C47semidirect
594. C2×#100C22×C47semidirect
595. C2×#100C22×C47semidirect
596. #407C22×C47semidirect
597. #391C22×C47semidirect
598. #390C22×C47semidirect
601. #382C22×C47semidirect
602. #343C22×C47semidirect
603. #343C22×C47semidirect
604. #339C22×C47semidirect
605. #339C22×C47semidirect
606. C47#24467direct (N × H)
725. #104D4×C47semidirect
858. M16C2×D4×C47semidirect
898. C42C2×D4×C47semidirect
1036. C22C47×#455semidirect

Maximal subgroups

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

subgroupindex
C47×#34882
C47×#30562
C2×C47×#4552
C47×#30072
C22×#104×C472
C47×#28502
C47×#20402
C47×#20372
C47×#20072
C47×#20042
C47×#19002
C47×#18962
C47×#18822
C47×#18602
C47×#17922
#2446747