Finite Group Databasebeta

← C47×#60146 #26099844

Subgroups — C47×#60146 #26099844

Order 12032.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#568C211yesmaximal, characteristic, complemented
2C22×#131×C47C211yesmaximal, characteristic, complemented
3D4×#41×C47C211yesmaximal, characteristic
4C47×#2935C213yesmaximal, complemented
5D4×M16×C47C213yesmaximal, complemented
6C47×#2933C213yesmaximal, complemented
7C47×#2933C213yesmaximal, complemented
8C47×#2932C213yesmaximal, complemented
9C47×#2930C213yesmaximal, complemented
10C47×#2929C213yesmaximal, complemented
11C2×C47×#435C213yesmaximal, complemented
12C47×#2906C211yesmaximal, characteristic, complemented
13C47×#2880C211yesmaximal, characteristic, complemented
14C47×#2880C211yesmaximal, characteristic, complemented
15C47×#2875C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C47×#568—28no—
19C2×#131×C47—28no—
20C2×#131×C47C2211yescharacteristic
21C2×#131×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic
23C2×#131×C47C2211yescharacteristic
24C2×#131×C47C2213yescomplemented
25C2×#131×C47C2213yescomplemented
26C2×#131×C47C2213yescomplemented
27C2×#131×C47C2213yescomplemented
28C22×M16×C47C2213yescomplemented
29C22×M16×C47C2213yescomplemented
30C22×M16×C47C2213yescomplemented
31C23×C8×C47C2213yescomplemented
32C47×#550C411yescharacteristic
33D4×Q8×C47C411yescharacteristic
34C47×#548C411yescharacteristic
35C47×#548C411yescharacteristic
36C47×#547C413yes—
37C47×#546C413yes—
38C47×#546C413yes—
39D42×C47C413yes—
40C47×#532C2213yes—
41C47×#525C2213yes—
42C47×#525C2213yes—
43C4×#41×C47C2211yescharacteristic
44C2×C4×D4×C47C2213yes—
45C47×#436C2216yescomplemented
46C47×#436C2216yescomplemented
47C47×#435C2211yescharacteristic
48C47×#435C2213yes—
49C47×#435C2213yescomplemented
50C47×#435C2213yescomplemented
51C47×#435C2213yescomplemented
52C47×#435C2213yescomplemented
53C47×#435C2213yescomplemented
54C47×#435C2213yescomplemented
55C47×#435C2216yescomplemented
56C47×#435C2216yescomplemented
57C47×#435C2216yescomplemented
58C8×D4×C47C2216yescomplemented
59C8×D4×C47C2216yescomplemented
60C47×#424C2213yescomplemented
61C47×#424C2213yescomplemented
62C47×#423C2213yescomplemented
63C2×C4⋊C8×C47C2213yescomplemented
64C47×#408C2213yescomplemented
65C47×#408C2213yescomplemented
66C47×#408C2213yescomplemented
67C47×#408C2213yescomplemented
68C47×#407C2213yescomplemented
69C47×#407C2213yescomplemented
70C2×C22⋊C8×C47C2213yescomplemented
71C2×C22⋊C8×C47C2213yescomplemented
72C47×#405C2213yescomplemented
73C47×#405C2213yescomplemented
74C4×M16×C47C2213yescomplemented
75C2×#97×C47C2213yescomplemented
76C2×#41×C47—24no—
77C2×#41×C47—24no—
78C2×#41×C47—24no—
79C2×#41×C47—24no—
80C2×#41×C47C2×C413yes—
81C2×#41×C47C2×C413yes—
82C2×#41×C47C2×C411yescharacteristic
83C2×#41×C47C2×C411yescharacteristic
84C2×#41×C47C2313yes—
85C2×#41×C47C2313yes—
86C2×#41×C47C2311yescharacteristic
87C22×Q8×C47C2×C411yescharacteristic
88C22×Q8×C47C2×C411yescharacteristic
89C22×D4×C47C2×C413yes—
90C22×D4×C47C2×C413yes—
91C22×D4×C47C2×C413yes—
92C23×C4×C47C2313yes—
93C23×C4×C47C2313yes—
94#131×C47—24no—
95#131×C47—24no—
96#131×C47—24no—
97#131×C47—212no—
98#131×C47—212no—
99#131×C47—212no—
100#131×C47—212no—
101#131×C47D418yescomplemented
102C2×M16×C47—212no—
103C2×M16×C47—212no—
104C2×M16×C47—212no—
105C2×M16×C47C2311yescharacteristic
106C2×M16×C47C2313yes—
107C2×M16×C47C2313yes—
108C2×M16×C47C2313yes—
109C2×M16×C47C2313yes—
110C2×M16×C47C2316yes—
111C2×M16×C47C2313yes—
112C2×M16×C47C2313yes—
113C2×M16×C47C2313yes—
114C22×C8×C47—212no—
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2313yes—
117C22×C8×C47C2313yes—
118C22×C8×C47C2313yes—
119C22×C8×C47C2313yes—
120C22×C8×C47C2313yes—
121C22×C8×C47C2316yes—
122C22×C8×C47C2313yes—
123C22×C8×C47C2313yes—
124C4⋊Q8×C47C2×C413yes—
125#127×C47C2×C413yes—
126#124×C47C2×C413yes—
127#124×C47C2×C413yes—
128#123×C47C2×C416yes—
129#123×C47C2×C416yes—
130C22⋊Q8×C47C2×C413yes—
131C22⋊Q8×C47C2×C413yes—
132C22⋊Q8×C47C2×C413yes—
133C22⋊Q8×C47C2×C413yes—
134#121×C47C2×C413yes—
135#121×C47C2×C413yes—
136#121×C47C2×C413yes—
137#121×C47C2×C413yes—
138#121×C47C2×C416yes—
139#121×C47C2×C416yes—
140#120×C47C2×C416yes—
141#120×C47C2×C416yes—
142C4×Q8×C47C2×C411yescharacteristic
143C4×Q8×C47C2×C411yescharacteristic
144C4×D4×C47C2×C413yes—
145C4×D4×C47C2×C413yes—
146C4×D4×C47C2×C413yes—
147C4×D4×C47C2×C413yes—
148C4×D4×C47C2×C413yes—
149C4×D4×C47C2×C413yes—
150C4×D4×C47C2311yescharacteristic
151C4×D4×C47C2313yes—
152C4×D4×C47C2313yes—
153C4×D4×C47C2313yes—
154C4×D4×C47C2316yes—
155#117×C47C2313yes—
156C2×C4⋊C4×C47C2×C413yes—
157C2×C22⋊C4×C47C2×C413yes—
158C2×C22⋊C4×C47C2×C413yes—
159C2×C42×C47C2313yes—
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2313yes—
162C4⋊C8×C47C2313yes—
163C4⋊C8×C47C2313yes—
164C4⋊C8×C47C2316yes—
165C22⋊C8×C47C2311yescharacteristic
166C22⋊C8×C47C2311yescharacteristic
167C22⋊C8×C47C2313yes—
168C22⋊C8×C47C2313yes—
169C22⋊C8×C47C2313yes—
170C22⋊C8×C47C2313yes—
171C22⋊C8×C47C2313yes—
172C22⋊C8×C47C2313yes—
173C22⋊C8×C47C2316yes—
174C22⋊C8×C47C2316yes—
175#97×C47C2311yescharacteristic
176#97×C47C2313yes—
177#97×C47C2313yes—
178#97×C47C2313yes—
179C4×C8×C47C2316yes—
180C24×C47C22×C413yes—
181C24×C47C22×C413yes—
182#41×C47—24no—
183#41×C47—24no—
184#41×C47—212no—
185#41×C47—212no—
186#41×C47—26no—
187#41×C47—26no—
188#41×C47—26no—
189#41×C47—26no—
190#41×C47C2×D414yes—
191#41×C47#4114yes—
192C2×Q8×C47—24no—
193C2×Q8×C47—24no—
194C2×Q8×C47C22×C413yes—
195C2×Q8×C47C22×C413yes—
196C2×Q8×C47C22×C411yescharacteristic
197C2×D4×C47—212no—
198C2×D4×C47—212no—
199C2×D4×C47—46no—
200C2×D4×C47C22×C411yescharacteristic
201C2×D4×C47C22×C413yes—
202C2×D4×C47C22×C416yes—
203C2×D4×C47C22×C416yes—
204C2×D4×C47C22×C413yes—
205C2×D4×C47C22×C413yes—
206C2×D4×C47C22×C413yes—
207C2×D4×C47C22×C413yes—
208C2×D4×C47C22×C416yes—
209C2×D4×C47C22×C413yes—
210C22×C4×C47—26no—
211C22×C4×C47—26no—
212C22×C4×C47—26no—
213C22×C4×C47—26no—
214C22×C4×C47C22×C413yes—
215C22×C4×C47C22×C413yes—
216C22×C4×C47C22×C413yes—
217C22×C4×C47C22×C413yes—
218C22×C4×C47C22×C413yes—
219C22×C4×C47C22×C413yes—
220C22×C4×C47C22×C413yes—
221C22×C4×C47C22×C413yes—
222C22×C4×C47C2411yescharacteristic
223C22×C4×C47C2413yes—
224C22×C4×C47C2413yes—
225C22×C4×C47C2411yescharacteristic
226C22×C4×C47C2413yes—
227M16×C47—26no—
228M16×C47—26no—
229M16×C47—26no—
230M16×C47—22no—
231M16×C47—26no—
232M16×C47—26no—
233M16×C47—212no—
234M16×C47—26no—
235M16×C47C2×D4112yescomplemented
236C2×C8×C47—26no—
237C2×C8×C47—26no—
238C2×C8×C47—26no—
239C2×C8×C47—22no—
240C2×C8×C47—26no—
241C2×C8×C47—26no—
242C2×C8×C47—26no—
243C2×C8×C47—212no—
244C2×C8×C47C2×D4112yescomplemented
245C2×C8×C47C2411yescharacteristic
246C2×C8×C47C2411yescharacteristic
247C2×C8×C47C2413yes—
248C2×C8×C47C2413yes—
249C2×C8×C47C2411yescharacteristic
250C2×C8×C47C2413yes—
251C2×C8×C47C2411yescharacteristic
252C2×C8×C47C2413yes—
253C4⋊C4×C47C22×C411yescharacteristic
254C4⋊C4×C47C22×C413yes—
255C4⋊C4×C47C22×C413yes—
256C4⋊C4×C47C22×C413yes—
257C4⋊C4×C47C22×C413yes—
258C4⋊C4×C47C22×C413yes—
259C4⋊C4×C47C22×C416yes—
260C22⋊C4×C47C22×C411yescharacteristic
261C22⋊C4×C47C22×C411yescharacteristic
262C22⋊C4×C47C22×C413yes—
263C22⋊C4×C47C22×C413yes—
264C22⋊C4×C47C22×C413yes—
265C22⋊C4×C47C22×C413yes—
266C22⋊C4×C47C22×C413yes—
267C22⋊C4×C47C22×C413yes—
268C22⋊C4×C47C22×C416yes—
269C22⋊C4×C47C22×C416yes—
270C22⋊C4×C47C22×C416yes—
271C42×C47C22×C413yes—
272C42×C47C22×C413yes—
273C42×C47C2411yescharacteristic
274C42×C47C2413yes—
275C23×C47—26no—
276C23×C47—26no—
277C23×C47—26no—
278C23×C47—43no—
279C23×C47—43no—
280C23×C47—43no—
281C23×C47C23×C411yescharacteristic
282C23×C47C23×C413yes—
283C23×C47C23×C413yes—
284C23×C47C23×C413yes—
285C23×C47C23×C411yescharacteristic
286Q8×C47—26no—
287Q8×C47—26no—
288Q8×C47C4×D414yes—
289D4×C47—212no—
290D4×C47—212no—
291D4×C47—22no—
292D4×C47—26no—
293D4×C47—26no—
294D4×C47—26no—
295D4×C47—43no—
296D4×C47—43no—
297D4×C47—46no—
298D4×C47C4×D4112yes—
299C2×C4×C47—26no—
300C2×C4×C47—26no—
301C2×C4×C47—26no—
302C2×C4×C47—26no—
303C2×C4×C47—26no—
304C2×C4×C47—26no—
305C2×C4×C47—21no—
306C2×C4×C47—23no—
307C2×C4×C47—23no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—23no—
312C2×C4×C47—23no—
313C2×C4×C47—43no—
314C2×C4×C47—43no—
315C2×C4×C47C23×C411yescharacteristic
316C2×C4×C47C23×C411yescharacteristic
317C2×C4×C47C23×C413yes—
318C2×C4×C47C23×C413yes—
319C2×C4×C47C23×C411yescharacteristic
320C2×C4×C47C23×C411yescharacteristic
321C2×C4×C47C23×C413yes—
322C2×C4×C47C23×C413yes—
323C2×C4×C47C23×C413yes—
324C2×C4×C47C22×D416yes—
325C2×C4×C47C2×#4116yes—
326C2×C4×C47C2511yescharacteristic
327C8×C47—21no—
328C8×C47—23no—
329C8×C47—21no—
330C8×C47—23no—
331C8×C47—21no—
332C8×C47—23no—
333C8×C47C22×D412yes—
334C8×C47C22×D416yes—
335#60146C4711yesmaximal, characteristic, direct product factor, Sylow
336C22×C47—21no—
337C22×C47—23no—
338C22×C47—23no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—23no—
342C22×C47—23no—
343C22×C47—21no—
344C22×C47—23no—
345C22×C47—23no—
346C22×C47—23no—
347C22×C47—23no—
348C22×C47—21no—
349C22×C47—412no—
350C22×C47—86no—
351C22×C47C2×C4×D416yes—
352C22×C47#56812yescomplemented
353C22×C47C24×C411yescharacteristic
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—23no—
357C4×C47—23no—
358C4×C47—21no—
359C4×C47—23no—
360C4×C47—21no—
361C4×C47—23no—
362C4×C47C2×C4×D416yes—
363C4×C47C23×D411yescharacteristic
364C4×C47C22×#4111yescharacteristic
365C2×#568C2×C4711yescharacteristic, complemented
366C22×#131C2×C4711yescharacteristic, complemented
367D4×#41C2×C4711yescharacteristic
368#2935C2×C4713yescomplemented
369D4×M16C2×C4713yescomplemented
370#2933C2×C4713yescomplemented
371#2933C2×C4713yescomplemented
372#2932C2×C4713yescomplemented
373#2930C2×C4713yescomplemented
374#2929C2×C4713yescomplemented
375C2×#435C2×C4713yescomplemented
376#2906C2×C4711yescharacteristic, complemented
377#2880C2×C4711yescharacteristic, complemented
378#2880C2×C4711yescharacteristic, complemented
379#2875C2×C4711yescharacteristic, complemented
380C2×C47—22no—
381C2×C47—26no—
382C2×C47—43no—
383C2×C47—43no—
384C2×C47—41no—
385C2×C47C22×C4×D411yescharacteristic
386C2×C47C2×#56811yescharacteristic
387C2×C47#357311yescharacteristic
388C22×#41C22×C4711yescharacteristic
389C22×#41C22×C4711yescharacteristic
390#568—28no—
391C2×#131—28no—
392C2×#131C22×C4711yescharacteristic
393C2×#131C22×C4711yescharacteristic
394C2×#131C22×C4711yescharacteristic
395C2×#131C22×C4711yescharacteristic
396C2×#131C22×C4713yescomplemented
397C2×#131C22×C4713yescomplemented
398C2×#131C22×C4713yescomplemented
399C2×#131C22×C4713yescomplemented
400C22×M16C22×C4713yescomplemented
401C22×M16C22×C4713yescomplemented
402C22×M16C22×C4713yescomplemented
403C23×C8C22×C4713yescomplemented
404#550C4×C4711yescharacteristic
405D4×Q8C4×C4711yescharacteristic
406#548C4×C4711yescharacteristic
407#548C4×C4711yescharacteristic
408#547C4×C4713yes—
409#546C4×C4713yes—
410#546C4×C4713yes—
411D42C4×C4713yes—
412#532C22×C4713yes—
413#525C22×C4713yes—
414#525C22×C4713yes—
415C4×#41C22×C4711yescharacteristic
416C2×C4×D4C22×C4713yes—
417#436C22×C4716yescomplemented
418#436C22×C4716yescomplemented
419#435C22×C4711yescharacteristic
420#435C22×C4713yes—
421#435C22×C4713yescomplemented
422#435C22×C4713yescomplemented
423#435C22×C4713yescomplemented
424#435C22×C4713yescomplemented
425#435C22×C4713yescomplemented
426#435C22×C4713yescomplemented
427#435C22×C4716yescomplemented
428#435C22×C4716yescomplemented
429#435C22×C4716yescomplemented
430C8×D4C22×C4716yescomplemented
431C8×D4C22×C4716yescomplemented
432#424C22×C4713yescomplemented
433#424C22×C4713yescomplemented
434#423C22×C4713yescomplemented
435C2×C4⋊C8C22×C4713yescomplemented
436#408C22×C4713yescomplemented
437#408C22×C4713yescomplemented
438#408C22×C4713yescomplemented
439#408C22×C4713yescomplemented
440#407C22×C4713yescomplemented
441#407C22×C4713yescomplemented
442C2×C22⋊C8C22×C4713yescomplemented
443C2×C22⋊C8C22×C4713yescomplemented
444#405C22×C4713yescomplemented
445#405C22×C4713yescomplemented
446C4×M16C22×C4713yescomplemented
447C2×#97C22×C4713yescomplemented
448C47#6014611yescharacteristic, direct product factor, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×C4×C4713yes—
454C2×#41C2×C4×C4713yes—
455C2×#41C2×C4×C4711yescharacteristic
456C2×#41C2×C4×C4711yescharacteristic
457C2×#41C23×C4713yes—
458C2×#41C23×C4713yes—
459C2×#41C23×C4711yescharacteristic
460C22×Q8C2×C4×C4711yescharacteristic
461C22×Q8C2×C4×C4711yescharacteristic
462C22×D4C2×C4×C4713yes—
463C22×D4C2×C4×C4713yes—
464C22×D4C2×C4×C4713yes—
465C23×C4C23×C4713yes—
466C23×C4C23×C4713yes—
467#131—24no—
468#131—24no—
469#131—24no—
470#131—212no—
471#131—212no—
472#131—212no—
473#131—212no—
474#131D4×C4718yescomplemented
475C2×M16—212no—
476C2×M16—212no—
477C2×M16—212no—
478C2×M16C23×C4711yescharacteristic
479C2×M16C23×C4713yes—
480C2×M16C23×C4713yes—
481C2×M16C23×C4713yes—
482C2×M16C23×C4713yes—
483C2×M16C23×C4713yes—
484C2×M16C23×C4716yes—
485C2×M16C23×C4713yes—
486C2×M16C23×C4713yes—
487C22×C8—212no—
488C22×C8C23×C4711yescharacteristic
489C22×C8C23×C4713yes—
490C22×C8C23×C4713yes—
491C22×C8C23×C4713yes—
492C22×C8C23×C4713yes—
493C22×C8C23×C4713yes—
494C22×C8C23×C4716yes—
495C22×C8C23×C4713yes—
496C22×C8C23×C4713yes—
497C4⋊Q8C2×C4×C4713yes—
498#127C2×C4×C4713yes—
499#124C2×C4×C4713yes—
500#124C2×C4×C4713yes—
501#123C2×C4×C4716yes—
502#123C2×C4×C4716yes—
503C22⋊Q8C2×C4×C4713yes—
504C22⋊Q8C2×C4×C4713yes—
505C22⋊Q8C2×C4×C4713yes—
506C22⋊Q8C2×C4×C4713yes—
507#121C2×C4×C4713yes—
508#121C2×C4×C4713yes—
509#121C2×C4×C4713yes—
510#121C2×C4×C4713yes—
511#121C2×C4×C4716yes—
512#121C2×C4×C4716yes—
513#120C2×C4×C4716yes—
514#120C2×C4×C4716yes—
515C4×Q8C2×C4×C4711yescharacteristic
516C4×Q8C2×C4×C4711yescharacteristic
517C4×D4C2×C4×C4713yes—
518C4×D4C2×C4×C4713yes—
519C4×D4C2×C4×C4713yes—
520C4×D4C2×C4×C4713yes—
521C4×D4C2×C4×C4713yes—
522C4×D4C2×C4×C4713yes—
523C4×D4C23×C4711yescharacteristic
524C4×D4C23×C4713yes—
525C4×D4C23×C4713yes—
526C4×D4C23×C4713yes—
527C4×D4C23×C4716yes—
528#117C23×C4713yes—
529C2×C4⋊C4C2×C4×C4713yes—
530C2×C22⋊C4C2×C4×C4713yes—
531C2×C22⋊C4C2×C4×C4713yes—
532C2×C42C23×C4713yes—
533C4⋊C8C23×C4711yescharacteristic
534C4⋊C8C23×C4713yes—
535C4⋊C8C23×C4713yes—
536C4⋊C8C23×C4713yes—
537C4⋊C8C23×C4716yes—
538C22⋊C8C23×C4711yescharacteristic
539C22⋊C8C23×C4711yescharacteristic
540C22⋊C8C23×C4713yes—
541C22⋊C8C23×C4713yes—
542C22⋊C8C23×C4713yes—
543C22⋊C8C23×C4713yes—
544C22⋊C8C23×C4713yes—
545C22⋊C8C23×C4713yes—
546C22⋊C8C23×C4716yes—
547C22⋊C8C23×C4716yes—
548#97C23×C4711yescharacteristic
549#97C23×C4713yes—
550#97C23×C4713yes—
551#97C23×C4713yes—
552C4×C8C23×C4716yes—
553C24C22×C4×C4713yes—
554C24C22×C4×C4713yes—
555#41—24no—
556#41—24no—
557#41—212no—
558#41—212no—
559#41—26no—
560#41—26no—
561#41—26no—
562#41—26no—
563#41C2×D4×C4714yes—
564#41#41×C4714yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×C4×C4713yes—
568C2×Q8C22×C4×C4713yes—
569C2×Q8C22×C4×C4711yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×C4×C4711yescharacteristic
574C2×D4C22×C4×C4713yes—
575C2×D4C22×C4×C4716yes—
576C2×D4C22×C4×C4716yes—
577C2×D4C22×C4×C4713yes—
578C2×D4C22×C4×C4713yes—
579C2×D4C22×C4×C4713yes—
580C2×D4C22×C4×C4713yes—
581C2×D4C22×C4×C4716yes—
582C2×D4C22×C4×C4713yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×C4×C4713yes—
588C22×C4C22×C4×C4713yes—
589C22×C4C22×C4×C4713yes—
590C22×C4C22×C4×C4713yes—
591C22×C4C22×C4×C4713yes—
592C22×C4C22×C4×C4713yes—
593C22×C4C22×C4×C4713yes—
594C22×C4C22×C4×C4713yes—
595C22×C4C24×C4711yescharacteristic
596C22×C4C24×C4713yes—
597C22×C4C24×C4713yes—
598C22×C4C24×C4711yescharacteristic
599C22×C4C24×C4713yes—
600M16—26no—
601M16—26no—
602M16—26no—
603M16—22no—
604M16—26no—
605M16—26no—
606M16—212no—
607M16—26no—
608M16C2×D4×C47112yescomplemented
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—26no—
612C2×C8—22no—
613C2×C8—26no—
614C2×C8—26no—
615C2×C8—26no—
616C2×C8—212no—
617C2×C8C2×D4×C47112yescomplemented
618C2×C8C24×C4713yes—
619C2×C8C24×C4711yescharacteristic
620C2×C8C24×C4711yescharacteristic
621C2×C8C24×C4711yescharacteristic
622C2×C8C24×C4713yes—
623C2×C8C24×C4713yes—
624C2×C8C24×C4713yes—
625C2×C8C24×C4711yescharacteristic
626C4⋊C4C22×C4×C4711yescharacteristic
627C4⋊C4C22×C4×C4713yes—
628C4⋊C4C22×C4×C4713yes—
629C4⋊C4C22×C4×C4713yes—
630C4⋊C4C22×C4×C4713yes—
631C4⋊C4C22×C4×C4713yes—
632C4⋊C4C22×C4×C4716yes—
633C22⋊C4C22×C4×C4711yescharacteristic
634C22⋊C4C22×C4×C4711yescharacteristic
635C22⋊C4C22×C4×C4713yes—
636C22⋊C4C22×C4×C4713yes—
637C22⋊C4C22×C4×C4713yes—
638C22⋊C4C22×C4×C4713yes—
639C22⋊C4C22×C4×C4713yes—
640C22⋊C4C22×C4×C4713yes—
641C22⋊C4C22×C4×C4716yes—
642C22⋊C4C22×C4×C4716yes—
643C22⋊C4C22×C4×C4716yes—
644C42C22×C4×C4713yes—
645C42C22×C4×C4713yes—
646C42C24×C4713yes—
647C42C24×C4711yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×C4×C4711yescharacteristic
655C23C23×C4×C4713yes—
656C23C23×C4×C4713yes—
657C23C23×C4×C4713yes—
658C23C23×C4×C4711yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8C4×D4×C4714yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4C4×D4×C47112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—26no—
678C2×C4—21no—
679C2×C4—23no—
680C2×C4—23no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—43no—
687C2×C4—43no—
688C2×C4C23×C4×C4711yescharacteristic
689C2×C4C23×C4×C4711yescharacteristic
690C2×C4C23×C4×C4713yes—
691C2×C4C23×C4×C4713yes—
692C2×C4C23×C4×C4711yescharacteristic
693C2×C4C23×C4×C4711yescharacteristic
694C2×C4C23×C4×C4713yes—
695C2×C4C23×C4×C4713yes—
696C2×C4C23×C4×C4713yes—
697C2×C4C22×D4×C4716yes—
698C2×C4C2×#41×C4716yes—
699C2×C4C25×C4711yescharacteristic
700C8—21no—
701C8—23no—
702C8—21no—
703C8—23no—
704C8—21no—
705C8—23no—
706C8C22×D4×C4712yes—
707C8C22×D4×C4716yes—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—23no—
716C22—23no—
717C22—21no—
718C22—21no—
719C22—23no—
720C22—23no—
721C22—412no—
722C22—86no—
723C22C2×C4×D4×C4716yes—
724C22C47×#56812yescomplemented
725C22C24×C4×C4711yescharacteristic
726C4—21no—
727C4—23no—
728C4—21no—
729C4—23no—
730C4—21no—
731C4—21no—
732C4—23no—
733C4—23no—
734C4C2×C4×D4×C4716yes—
735C4C23×D4×C4711yescharacteristic
736C4C22×#41×C4711yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×C4×D4×C4711yescharacteristic
743C2C2×C47×#56811yescharacteristic
744C2C47×#357311yescharacteristic
subgroupG/H
centerC2×C4×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC22×C47C24×C4
prime radicalD4×#41×C47C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#568C2semidirect
2. C22×#131×C47C2semidirect
4. C47×#2935C2semidirect
5. D4×M16×C47C2semidirect
6. C47×#2933C2semidirect
7. C47×#2933C2semidirect
8. C47×#2932C2semidirect
9. C47×#2930C2semidirect
10. C47×#2929C2semidirect
11. C2×C47×#435C2semidirect
12. C47×#2906C2semidirect
13. C47×#2880C2semidirect
14. C47×#2880C2semidirect
15. C47×#2875C2semidirect
24. C2×#131×C47C22semidirect
25. C2×#131×C47C22semidirect
26. C2×#131×C47C22semidirect
27. C2×#131×C47C22semidirect
28. C22×M16×C47C22semidirect
29. C22×M16×C47C22semidirect
30. C22×M16×C47C22semidirect
31. C23×C8×C47C22semidirect
45. C47×#436C22semidirect
46. C47×#436C22semidirect
49. C47×#435C22semidirect
50. C47×#435C22semidirect
51. C47×#435C22semidirect
52. C47×#435C22semidirect
53. C47×#435C22semidirect
54. C47×#435C22semidirect
55. C47×#435C22semidirect
56. C47×#435C22semidirect
57. C47×#435C22semidirect
58. C8×D4×C47C22semidirect
59. C8×D4×C47C22semidirect
60. C47×#424C22semidirect
61. C47×#424C22semidirect
62. C47×#423C22semidirect
63. C2×C4⋊C8×C47C22semidirect
64. C47×#408C22semidirect
65. C47×#408C22semidirect
66. C47×#408C22semidirect
67. C47×#408C22semidirect
68. C47×#407C22semidirect
69. C47×#407C22semidirect
70. C2×C22⋊C8×C47C22semidirect
71. C2×C22⋊C8×C47C22semidirect
72. C47×#405C22semidirect
73. C47×#405C22semidirect
74. C4×M16×C47C22semidirect
75. C2×#97×C47C22semidirect
101. #131×C47D4semidirect
235. M16×C47C2×D4semidirect
244. C2×C8×C47C2×D4semidirect
335. #60146C47direct (N × H)
352. C22×C47#568semidirect
365. C2×#568C2×C47semidirect
366. C22×#131C2×C47semidirect
368. #2935C2×C47semidirect
369. D4×M16C2×C47semidirect
370. #2933C2×C47semidirect
371. #2933C2×C47semidirect
372. #2932C2×C47semidirect
373. #2930C2×C47semidirect
374. #2929C2×C47semidirect
375. C2×#435C2×C47semidirect
376. #2906C2×C47semidirect
377. #2880C2×C47semidirect
378. #2880C2×C47semidirect
379. #2875C2×C47semidirect
396. C2×#131C22×C47semidirect
397. C2×#131C22×C47semidirect
398. C2×#131C22×C47semidirect
399. C2×#131C22×C47semidirect
400. C22×M16C22×C47semidirect
401. C22×M16C22×C47semidirect
402. C22×M16C22×C47semidirect
403. C23×C8C22×C47semidirect
417. #436C22×C47semidirect
418. #436C22×C47semidirect
421. #435C22×C47semidirect
422. #435C22×C47semidirect
423. #435C22×C47semidirect
424. #435C22×C47semidirect
425. #435C22×C47semidirect
426. #435C22×C47semidirect
427. #435C22×C47semidirect
428. #435C22×C47semidirect
429. #435C22×C47semidirect
430. C8×D4C22×C47semidirect
431. C8×D4C22×C47semidirect
432. #424C22×C47semidirect
433. #424C22×C47semidirect
434. #423C22×C47semidirect
435. C2×C4⋊C8C22×C47semidirect
436. #408C22×C47semidirect
437. #408C22×C47semidirect
438. #408C22×C47semidirect
439. #408C22×C47semidirect
440. #407C22×C47semidirect
441. #407C22×C47semidirect
442. C2×C22⋊C8C22×C47semidirect
443. C2×C22⋊C8C22×C47semidirect
444. #405C22×C47semidirect
445. #405C22×C47semidirect
446. C4×M16C22×C47semidirect
447. C2×#97C22×C47semidirect
448. C47#60146direct (N × H)
474. #131D4×C47semidirect
608. M16C2×D4×C47semidirect
617. C2×C8C2×D4×C47semidirect
724. C22C47×#568semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5682
C22×#131×C472
D4×#41×C472
C47×#29352
D4×M16×C472
C47×#29332
C47×#29322
C47×#29302
C47×#29292
C2×C47×#4352
C47×#29062
C47×#28802
C47×#28752
#6014647