Finite Group Databasebeta

← C47×#24471 #26064169

Subgroups — C47×#24471 #26064169

Order 12032.

1444 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×#3488C211yesmaximal, characteristic
2C47×#3056C211yesmaximal, characteristic, complemented
3C2×C47×#455C211yesmaximal, characteristic, complemented
4C47×#3007C211yesmaximal, characteristic, complemented
5C2×C47×#421C211yesmaximal, characteristic, complemented
6C47×#2620C211yesmaximal, characteristic, complemented
7C47×#2039C211yesmaximal, characteristic, complemented
8C47×#2037C211yesmaximal, characteristic, complemented
9C47×#2007C211yesmaximal, characteristic, complemented
10C47×#2004C211yesmaximal, characteristic, complemented
11C47×#1900C211yesmaximal, characteristic, complemented
12C47×#1897C211yesmaximal, characteristic, complemented
13C47×#1882C211yesmaximal, characteristic, complemented
14C47×#1859C211yesmaximal, 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
39C2×#117×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
50C47×#421—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×#396—22no—
65C47×#394—22no—
66C47×#391C2211yescharacteristic, complemented
67C47×#390C2211yescharacteristic, complemented
68C47×#384C2211yescharacteristic, 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×C47C2311yescharacteristic
102#137×C47—22no—
103#137×C47—22no—
104#137×C47—22no—
105#137×C47—41no—
106#137×C47—41no—
107#137×C47—41no—
108C2×Q16×C47—21no—
109C2×Q16×C47—21no—
110C2×Q16×C47—21no—
111C2×SD16×C47—21no—
112C2×SD16×C47—21no—
113C2×SD16×C47—21no—
114C2×M16×C47—21no—
115C2×M16×C47—22no—
116C2×M16×C47—41no—
117C2×M16×C47C2311yescharacteristic
118C2×M16×C47C2311yescharacteristic
119C2×M16×C47C2311yescharacteristic
120C2×M16×C47C2311yescharacteristic
121C22×C8×C47—21no—
122#127×C47—22no—
123#127×C47—21no—
124#124×C47—22no—
125#124×C47—21no—
126#124×C47—22no—
127#124×C47—41no—
128#123×C47—22no—
129#123×C47—21no—
130C22⋊Q8×C47—22no—
131C22⋊Q8×C47—21no—
132C22⋊Q8×C47—21no—
133C22⋊Q8×C47—21no—
134C22⋊Q8×C47—21no—
135C22⋊Q8×C47—21no—
136C22⋊Q8×C47—21no—
137C22⋊Q8×C47D411yescharacteristic
138C22⋊Q8×C47D411yescharacteristic
139#121×C47—22no—
140#121×C47—22no—
141#121×C47—22no—
142#121×C47—22no—
143#121×C47—22no—
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—22no—
151#121×C47—21no—
152#121×C47—21no—
153#121×C47D411yescharacteristic
154#121×C47D411yescharacteristic
155#120×C47—22no—
156#120×C47—22no—
157#120×C47—22no—
158#120×C47—21no—
159#120×C47—22no—
160C4×Q8×C47—21no—
161C4×D4×C47—22no—
162C4×D4×C47—22no—
163C4×D4×C47—21no—
164C4×D4×C47—22no—
165C4×D4×C47—21no—
166C4×D4×C47—21no—
167#117×C47—21no—
168#117×C47—22no—
169#117×C47—41no—
170#117×C47C2311yescharacteristic
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—22no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—22no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—22no—
181C2×C22⋊C4×C47—22no—
182C2×C22⋊C4×C47D412yes—
183C2×C42×C47C2311yescharacteristic
184C2×C42×C47C2311yescharacteristic
185#107×C47—21no—
186#106×C47—21no—
187#104×C47—22no—
188#104×C47—22no—
189#104×C47—22no—
190#104×C47—22no—
191#104×C47—41no—
192#104×C47D414yescomplemented
193#103×C47—21no—
194#103×C47—21no—
195#103×C47—21no—
196#103×C47—21no—
197#103×C47—21no—
198#102×C47—21no—
199#102×C47—21no—
200#102×C47—21no—
201#100×C47—22no—
202#100×C47—41no—
203C22⋊C8×C47—21no—
204C22⋊C8×C47—21no—
205#95×C47—22no—
206C24×C47—22no—
207C24×C47—21no—
208C24×C47C2×D412yes—
209C24×C47C2×D411yescharacteristic
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—82no—
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—22no—
291C22×C4×C47—21no—
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×C47C2×D411yescharacteristic
301C22×C4×C47C2×D411yescharacteristic
302C22×C4×C47C2×D411yescharacteristic
303C22×C4×C47C2×D411yescharacteristic
304C22×C4×C47C2×D411yescharacteristic
305C22×C4×C47C2×D412yes—
306C22×C4×C47C2411yescharacteristic
307Q16×C47—42no—
308Q16×C47—42no—
309Q16×C47—42no—
310SD16×C47—42no—
311SD16×C47—42no—
312SD16×C47—42no—
313M16×C47—21no—
314M16×C47—21no—
315M16×C47—21no—
316M16×C47—21no—
317M16×C47—21no—
318M16×C47—21no—
319M16×C47—21no—
320M16×C47—42no—
321M16×C47C2×D412yescomplemented
322C2×C8×C47—21no—
323C2×C8×C47—21no—
324C2×C8×C47—21no—
325C2×C8×C47—21no—
326C2×C8×C47—42no—
327C4⋊C4×C47—22no—
328C4⋊C4×C47—22no—
329C4⋊C4×C47—21no—
330C4⋊C4×C47—21no—
331C4⋊C4×C47—21no—
332C4⋊C4×C47—21no—
333C4⋊C4×C47—21no—
334C4⋊C4×C47—21no—
335C4⋊C4×C47—42no—
336C4⋊C4×C47—41no—
337C4⋊C4×C47—41no—
338C4⋊C4×C47—82no—
339C4⋊C4×C47C2×D411yescharacteristic
340C4⋊C4×C47C2×D411yescharacteristic
341C22⋊C4×C47—22no—
342C22⋊C4×C47—22no—
343C22⋊C4×C47—22no—
344C22⋊C4×C47—22no—
345C22⋊C4×C47—22no—
346C22⋊C4×C47—21no—
347C22⋊C4×C47—21no—
348C22⋊C4×C47—21no—
349C22⋊C4×C47—21no—
350C22⋊C4×C47—22no—
351C22⋊C4×C47—22no—
352C22⋊C4×C47—21no—
353C22⋊C4×C47—42no—
354C22⋊C4×C47—44no—
355C22⋊C4×C47—41no—
356C22⋊C4×C47—41no—
357C22⋊C4×C47—82no—
358C42×C47—22no—
359C42×C47—21no—
360C42×C47—21no—
361C42×C47—21no—
362C42×C47—21no—
363C42×C47C2×D412yescomplemented
364C23×C47—21no—
365C23×C47—21no—
366C23×C47—21no—
367C23×C47—22no—
368C23×C47—21no—
369C23×C47—21no—
370C23×C47—22no—
371C23×C47—22no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—42no—
375C23×C47—42no—
376C23×C47—44no—
377C23×C47—42no—
378C23×C47—42no—
379C23×C47—81no—
380C23×C47—82no—
381C23×C47—82no—
382C23×C47#12011yescharacteristic
383C23×C47#12011yescharacteristic
384C23×C47C22×D411yescharacteristic
385Q8×C47—21no—
386Q8×C47—21no—
387Q8×C47—21no—
388Q8×C47—21no—
389Q8×C47—21no—
390Q8×C47—42no—
391Q8×C47—41no—
392Q8×C47—41no—
393Q8×C47—41no—
394Q8×C47—41no—
395Q8×C47#12112yes—
396D4×C47—22no—
397D4×C47—22no—
398D4×C47—21no—
399D4×C47—21no—
400D4×C47—21no—
401D4×C47—21no—
402D4×C47—21no—
403D4×C47—42no—
404D4×C47—42no—
405D4×C47—44no—
406D4×C47—42no—
407D4×C47—44no—
408D4×C47—44no—
409D4×C47—42no—
410D4×C47—41no—
411D4×C47—41no—
412D4×C47—41no—
413D4×C47—41no—
414D4×C47—41no—
415D4×C47—41no—
416D4×C47—41no—
417D4×C47—41no—
418D4×C47—81no—
419D4×C47—82no—
420D4×C47—82no—
421D4×C47—82no—
422D4×C47—82no—
423D4×C47#12112yes—
424C2×C4×C47—21no—
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—22no—
434C2×C4×C47—21no—
435C2×C4×C47—21no—
436C2×C4×C47—22no—
437C2×C4×C47—21no—
438C2×C4×C47—22no—
439C2×C4×C47—21no—
440C2×C4×C47—21no—
441C2×C4×C47—21no—
442C2×C4×C47—22no—
443C2×C4×C47—42no—
444C2×C4×C47—42no—
445C2×C4×C47—42no—
446C2×C4×C47—44no—
447C2×C4×C47—41no—
448C2×C4×C47—41no—
449C2×C4×C47—41no—
450C2×C4×C47—41no—
451C2×C4×C47—41no—
452C2×C4×C47—41no—
453C2×C4×C47—42no—
454C2×C4×C47—41no—
455C2×C4×C47—42no—
456C2×C4×C47—41no—
457C2×C4×C47—41no—
458C2×C4×C47—41no—
459C2×C4×C47—41no—
460C2×C4×C47—41no—
461C2×C4×C47—41no—
462C2×C4×C47—82no—
463C2×C4×C47#12011yescharacteristic
464C2×C4×C47#12011yescharacteristic
465C2×C4×C47C22×D411yescharacteristic
466C2×C4×C47C22×D411yescharacteristic
467C2×C4×C47C22×D411yescharacteristic
468C2×C4×C47C2×#4111yescharacteristic
469C2×C4×C47H(5,𝔽2)11yescharacteristic
470C2×C4×C47H(5,𝔽2)11yescharacteristic
471C8×C47—22no—
472C8×C47—41no—
473C8×C47—41no—
474C8×C47—41no—
475#24471C4711yesmaximal, characteristic, direct product factor, Sylow
476C22×C47—21no—
477C22×C47—21no—
478C22×C47—21no—
479C22×C47—21no—
480C22×C47—22no—
481C22×C47—21no—
482C22×C47—21no—
483C22×C47—21no—
484C22×C47—21no—
485C22×C47—41no—
486C22×C47—41no—
487C22×C47—41no—
488C22×C47—41no—
489C22×C47—42no—
490C22×C47—42no—
491C22×C47—41no—
492C22×C47—41no—
493C22×C47—41no—
494C22×C47—42no—
495C22×C47—41no—
496C22×C47—81no—
497C22×C47—81no—
498C22×C47—82no—
499C22×C47—82no—
500C22×C47—84no—
501C22×C47—164no—
502C22×C47C2×#12011yescharacteristic
503C22×C47D4211yescharacteristic
504C22×C47#54611yescharacteristic
505C4×C47—21no—
506C4×C47—21no—
507C4×C47—22no—
508C4×C47—42no—
509C4×C47—41no—
510C4×C47—41no—
511C4×C47—42no—
512C4×C47—41no—
513C4×C47—41no—
514C4×C47—81no—
515C4×C47—81no—
516C4×C47—81no—
517C4×C47C2×#12111yescharacteristic
518C4×C47#53411yescharacteristic
519C4×C47D4211yescharacteristic
520C4×C47#54611yescharacteristic
521#3488C2×C4711yescharacteristic
522#3056C2×C4711yescharacteristic, complemented
523C2×#455C2×C4711yescharacteristic, complemented
524#3007C2×C4711yescharacteristic, complemented
525C2×#421C2×C4711yescharacteristic, complemented
526#2620C2×C4711yescharacteristic, complemented
527#2039C2×C4711yescharacteristic, complemented
528#2037C2×C4711yescharacteristic, complemented
529#2007C2×C4711yescharacteristic, complemented
530#2004C2×C4711yescharacteristic, complemented
531#1900C2×C4711yescharacteristic, complemented
532#1897C2×C4711yescharacteristic, complemented
533#1882C2×C4711yescharacteristic, complemented
534#1859C2×C4711yescharacteristic, complemented
535#1792C2×C4711yescharacteristic, complemented
536C2×C47—21no—
537C2×C47—21no—
538C2×C47—41no—
539C2×C47—41no—
540C2×C47—42no—
541C2×C47—81no—
542C2×C47—82no—
543C2×C47—81no—
544C2×C47#241011yescharacteristic
545C2×C47#301911yescharacteristic
546C2×C47#302211yescharacteristic
547C2×H(5,𝔽2)C22×C4711yescharacteristic
548C22×#41C22×C4711yescharacteristic
549C2×#137C22×C4711yescharacteristic
550C2×#137C22×C4711yescharacteristic, complemented
551C2×#137C22×C4711yescharacteristic, complemented
552C22×M16C22×C4711yescharacteristic, complemented
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C22×C4711yescharacteristic
561#535—21no—
562#535C22×C4711yescharacteristic
563C2×#124C22×C4711yescharacteristic, complemented
564#525—21no—
565#525C22×C4711yescharacteristic
566C2×C22⋊Q8C22×C4711yescharacteristic, complemented
567C2×#121—21no—
568C2×#121C22×C4711yescharacteristic
569#520C22×C4711yescharacteristic
570C2×#117C22×C4711yescharacteristic, complemented
571#470—21no—
572#468—21no—
573#467—21no—
574#465—21no—
575#455—24no—
576#452—21no—
577#452—21no—
578#451—21no—
579#450—21no—
580#428C22×C4711yescharacteristic, complemented
581#421—24no—
582C2×#104C22×C4711yescharacteristic
583C2×#104C22×C4711yescharacteristic
584C2×#104C22×C4711yescharacteristic, complemented
585C2×#104C22×C4711yescharacteristic, complemented
586C2×#104C22×C4711yescharacteristic, complemented
587C2×#104C22×C4711yescharacteristic, complemented
588#419C22×C4711yescharacteristic, complemented
589#417C22×C4711yescharacteristic
590#417C22×C4711yescharacteristic, complemented
591#417C22×C4711yescharacteristic, complemented
592C2×#100C22×C4711yescharacteristic, complemented
593C2×#100C22×C4711yescharacteristic, complemented
594#407C22×C4711yescharacteristic, complemented
595#396—22no—
596#394—22no—
597#391C22×C4711yescharacteristic, complemented
598#390C22×C4711yescharacteristic, complemented
599#384C22×C4711yescharacteristic, complemented
600#343C22×C4711yescharacteristic, complemented
601#343C22×C4711yescharacteristic, complemented
602#339C22×C4711yescharacteristic, complemented
603#339C22×C4711yescharacteristic, complemented
604C47#2447111yescharacteristic, direct product factor, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C4711yescharacteristic
618C2×#41D4×C4711yescharacteristic
619C2×#41C23×C4711yescharacteristic
620C2×#41C23×C4711yescharacteristic
621C2×#41C23×C4711yescharacteristic
622C22×Q8D4×C4711yescharacteristic
623C22×Q8C23×C4711yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C4711yescharacteristic
630C22×D4D4×C4712yes—
631C22×D4C23×C4711yescharacteristic
632C23×C4—21no—
633C23×C4C23×C4711yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C4711yescharacteristic
650C2×M16C23×C4711yescharacteristic
651C2×M16C23×C4711yescharacteristic
652C2×M16C23×C4711yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C4711yescharacteristic
670C22⋊Q8D4×C4711yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C4711yescharacteristic
686#121D4×C4711yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C4711yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C4711yescharacteristic
708C2×C4⋊C4C23×C4711yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C4712yes—
715C2×C42C23×C4711yescharacteristic
716C2×C42C23×C4711yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C4714yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C4712yes—
741C24C2×D4×C4711yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C4712yes—
765#41#41×C4712yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C4711yescharacteristic
776C2×Q8C2×D4×C4711yescharacteristic
777C2×Q8C2×D4×C4711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C4711yescharacteristic
812C2×D4C2×D4×C4711yescharacteristic
813C2×D4C2×D4×C4711yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C4711yescharacteristic
833C22×C4C2×D4×C4711yescharacteristic
834C22×C4C2×D4×C4711yescharacteristic
835C22×C4C2×D4×C4711yescharacteristic
836C22×C4C2×D4×C4711yescharacteristic
837C22×C4C2×D4×C4712yes—
838C22×C4C24×C4711yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C4712yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C4711yescharacteristic
872C4⋊C4C2×D4×C4711yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C4712yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C4711yescharacteristic
915C23#120×C4711yescharacteristic
916C23C22×D4×C4711yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C4712yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—81no—
951D4—82no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C4712yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C4711yescharacteristic
996C2×C4#120×C4711yescharacteristic
997C2×C4C22×D4×C4711yescharacteristic
998C2×C4C22×D4×C4711yescharacteristic
999C2×C4C22×D4×C4711yescharacteristic
1000C2×C4C2×#41×C4711yescharacteristic
1001C2×C4H(5,𝔽2)×C4711yescharacteristic
1002C2×C4H(5,𝔽2)×C4711yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C4711yescharacteristic
1034C22D42×C4711yescharacteristic
1035C22C47×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C4711yescharacteristic
1049C4C47×#53411yescharacteristic
1050C4D42×C4711yescharacteristic
1051C4C47×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C47×#241011yescharacteristic
1061C2C47×#301911yescharacteristic
1062C2C47×#302211yescharacteristic
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. C2×C47×#421C2semidirect
6. C47×#2620C2semidirect
7. C47×#2039C2semidirect
8. C47×#2037C2semidirect
9. C47×#2007C2semidirect
10. C47×#2004C2semidirect
11. C47×#1900C2semidirect
12. C47×#1897C2semidirect
13. C47×#1882C2semidirect
14. C47×#1859C2semidirect
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. C2×#117×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
66. C47×#391C22semidirect
67. C47×#390C22semidirect
68. C47×#384C22semidirect
69. C47×#343C22semidirect
70. C47×#343C22semidirect
71. C47×#339C22semidirect
72. C47×#339C22semidirect
192. #104×C47D4semidirect
321. M16×C47C2×D4semidirect
363. C42×C47C2×D4semidirect
475. #24471C47direct (N × H)
522. #3056C2×C47semidirect
523. C2×#455C2×C47semidirect
524. #3007C2×C47semidirect
525. C2×#421C2×C47semidirect
526. #2620C2×C47semidirect
527. #2039C2×C47semidirect
528. #2037C2×C47semidirect
529. #2007C2×C47semidirect
530. #2004C2×C47semidirect
531. #1900C2×C47semidirect
532. #1897C2×C47semidirect
533. #1882C2×C47semidirect
534. #1859C2×C47semidirect
535. #1792C2×C47semidirect
550. C2×#137C22×C47semidirect
551. C2×#137C22×C47semidirect
552. C22×M16C22×C47semidirect
563. C2×#124C22×C47semidirect
566. C2×C22⋊Q8C22×C47semidirect
570. C2×#117C22×C47semidirect
580. #428C22×C47semidirect
584. C2×#104C22×C47semidirect
585. C2×#104C22×C47semidirect
586. C2×#104C22×C47semidirect
587. C2×#104C22×C47semidirect
588. #419C22×C47semidirect
590. #417C22×C47semidirect
591. #417C22×C47semidirect
592. C2×#100C22×C47semidirect
593. C2×#100C22×C47semidirect
594. #407C22×C47semidirect
597. #391C22×C47semidirect
598. #390C22×C47semidirect
599. #384C22×C47semidirect
600. #343C22×C47semidirect
601. #343C22×C47semidirect
602. #339C22×C47semidirect
603. #339C22×C47semidirect
604. C47#24471direct (N × H)
724. #104D4×C47semidirect
853. M16C2×D4×C47semidirect
895. C42C2×D4×C47semidirect

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
C2×C47×#4212
C47×#26202
C47×#20392
C47×#20372
C47×#20072
C47×#20042
C47×#19002
C47×#18972
C47×#18822
C47×#18592
C47×#17922
#2447147