Finite Group Databasebeta

← C47×#22180 #26061878

Subgroups — C47×#22180 #26061878

Order 12032.

978 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#465C211yesmaximal, characteristic
2C4×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
3C4×#121×C47C211yesmaximal, characteristic
4C47×#1927C211yesmaximal, characteristic, complemented
5C47×#1926C211yesmaximal, characteristic, complemented
6C47×#1920C211yesmaximal, characteristic, complemented
7C47×#1919C211yesmaximal, characteristic, complemented
8C47×#1893C211yesmaximal, characteristic
9C47×#1892C211yesmaximal, characteristic, complemented
10C47×#1880C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1865C211yesmaximal, characteristic, complemented
13C47×#1864C211yesmaximal, characteristic, complemented
14C47×#1807C211yesmaximal, characteristic, complemented
15C2×C47×#336C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×#121×C47C2211yescharacteristic
21C2×C4×Q8×C47C2211yescharacteristic
22C2×C4×D4×C47—21no—
23C2×C4×D4×C47C2211yescharacteristic
24C22×C42×C47C2211yescharacteristic
25C47×#465C418yescomplemented
26C2×#106×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C2×#106×C47C2211yescharacteristic
29C2×#103×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C47×#391C2211yescharacteristic
36C47×#390C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#389C2211yescharacteristic
39C47×#388—21no—
40C47×#387—21no—
41C47×#386—21no—
42C47×#385—21no—
43C47×#380C2211yescharacteristic
44C47×#380C2211yescharacteristic
45C4×C4⋊C4×C47—21no—
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C22⋊C4×C47—21no—
49C4×C22⋊C4×C47—21no—
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×Q8×C47C2311yescharacteristic
61C22×D4×C47—21no—
62C22×D4×C47C2311yescharacteristic
63C23×C4×C47—21no—
64C23×C4×C47D411yescharacteristic
65C23×C4×C47D411yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C2×SD16×C47—41no—
68C2×SD16×C47—41no—
69C2×SD16×C47C2×C414yescomplemented
70C22×C8×C47—22no—
71C22×C8×C47—41no—
72C22×C8×C47—41no—
73C22×C8×C47—41no—
74C22×C8×C47—41no—
75C22×C8×C47C2×C414yescomplemented
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22⋊Q8×C47—22no—
81C22⋊Q8×C47C2×C414yescomplemented
82#121×C47—22no—
83#121×C47C2×C414yes—
84C4×Q8×C47—41no—
85C4×Q8×C47—41no—
86C4×D4×C47—41no—
87C4×D4×C47—41no—
88C4×D4×C47—44no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C42×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47—41no—
110C2×C42×C47—41no—
111C2×C42×C47D411yescharacteristic
112C2×C42×C47D411yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115#106×C47—41no—
116#106×C47—41no—
117#106×C47C2×C414yescomplemented
118#103×C47—41no—
119#103×C47—41no—
120#103×C47C2×C414yescomplemented
121#102×C47—41no—
122#102×C47—41no—
123#102×C47C2×C414yescomplemented
124#95×C47—21no—
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132C24×C47—21no—
133C24×C47C2×D411yescharacteristic
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47C22×C412yes—
140C2×D4×C47—24no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—42no—
147C2×D4×C47—42no—
148C2×D4×C47C22×C412yes—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—22no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—41no—
162C22×C4×C47—41no—
163C22×C4×C47—41no—
164C22×C4×C47—41no—
165C22×C4×C47—42no—
166C22×C4×C47—42no—
167C22×C4×C47—42no—
168C22×C4×C47SD1614yescomplemented
169C22×C4×C47C22×C412yes—
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47#4112yes—
176C22×C4×C47C2411yescharacteristic
177SD16×C47—44no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—44no—
189C2×C8×C47—44no—
190C2×C8×C47C22×C412yes—
191C2×C8×C47C22×C412yes—
192C4⋊C4×C47—24no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—42no—
204C4⋊C4×C47—42no—
205C4⋊C4×C47—42no—
206C4⋊C4×C47C22×C412yes—
207C4⋊C4×C47C22×C412yes—
208C22⋊C4×C47—24no—
209C22⋊C4×C47—24no—
210C22⋊C4×C47—42no—
211C22⋊C4×C47—42no—
212C22⋊C4×C47—42no—
213C22⋊C4×C47—42no—
214C22⋊C4×C47—42no—
215C42×C47—21no—
216C42×C47—21no—
217C42×C47—21no—
218C42×C47—21no—
219C42×C47—41no—
220C42×C47—41no—
221C42×C47—42no—
222C42×C47—42no—
223C42×C47—42no—
224C23×C47—21no—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—22no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47C4×D412yes—
236C23×C47C2×SD1612yes—
237C23×C47#13512yes—
238C23×C47C22×D411yescharacteristic
239Q8×C47—22no—
240Q8×C47—22no—
241Q8×C47—41no—
242Q8×C47—41no—
243D4×C47—22no—
244D4×C47—22no—
245D4×C47—48no—
246D4×C47—41no—
247D4×C47—41no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—44no—
268C2×C4×C47—44no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—84no—
288C2×C4×C47C4×D412yes—
289C2×C4×C47C2×SD1612yes—
290C2×C4×C47C2×SD1612yes—
291C2×C4×C47C23×C411yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×C4×C47H(5,𝔽2)11yescharacteristic
295C2×C4×C47H(5,𝔽2)11yescharacteristic
296C2×C4×C472−1+411yescharacteristic
297C8×C47—22no—
298C8×C47—22no—
299C8×C47—41no—
300C8×C47—41no—
301#22180C4711yesmaximal, characteristic, direct product factor, Sylow
302C22×C47—22no—
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—22no—
307C22×C47—22no—
308C22×C47—42no—
309C22×C47—42no—
310C22×C47—42no—
311C22×C47—81no—
312C22×C47—81no—
313C22×C47—81no—
314C22×C47—81no—
315C22×C47C4×SD1614yes—
316C22×C47C2×C4×D411yescharacteristic
317C22×C47#53411yescharacteristic
318C22×C47#53711yescharacteristic
319C22×C47C22×SD1611yescharacteristic
320C22×C47C2×#13511yescharacteristic
321C22×C47#57511yescharacteristic
322C22×C47#57511yescharacteristic
323C4×C47—22no—
324C4×C47—22no—
325C4×C47—22no—
326C4×C47—42no—
327C4×C47—41no—
328C4×C47—41no—
329C4×C47—42no—
330C4×C47—42no—
331C4×C47—81no—
332C4×C47—81no—
333C4×C47—81no—
334C4×C47—81no—
335C4×C47#51811yescharacteristic
336C4×C47#52011yescharacteristic
337C4×C47#53811yescharacteristic
338C4×C47#53911yescharacteristic
339C2×#465C2×C4711yescharacteristic
340C4×C22⋊Q8C2×C4711yescharacteristic, complemented
341C4×#121C2×C4711yescharacteristic
342#1927C2×C4711yescharacteristic, complemented
343#1926C2×C4711yescharacteristic, complemented
344#1920C2×C4711yescharacteristic, complemented
345#1919C2×C4711yescharacteristic, complemented
346#1893C2×C4711yescharacteristic
347#1892C2×C4711yescharacteristic, complemented
348#1880C2×C4711yescharacteristic, complemented
349#1877C2×C4711yescharacteristic, complemented
350#1865C2×C4711yescharacteristic, complemented
351#1864C2×C4711yescharacteristic, complemented
352#1807C2×C4711yescharacteristic, complemented
353C2×#336C2×C4711yescharacteristic, complemented
354C2×C47—24no—
355C2×C47—82no—
356C2×C47#232511yescharacteristic
357C2×C47C2×C4×SD1611yescharacteristic
358C2×C47#294311yescharacteristic
359C2×C47#318711yescharacteristic
360C2×C47#319111yescharacteristic
361C2×C47#324611yescharacteristic
362C2×C47#325011yescharacteristic
363C22×SD16C22×C4711yescharacteristic
364C23×C8C22×C4711yescharacteristic
365C23×C8C22×C4711yescharacteristic
366C2×C22⋊Q8C22×C4711yescharacteristic
367C2×#121C22×C4711yescharacteristic
368C2×C4×Q8C22×C4711yescharacteristic
369C2×C4×D4—21no—
370C2×C4×D4C22×C4711yescharacteristic
371C22×C42C22×C4711yescharacteristic
372#465C4×C4718yescomplemented
373C2×#106C22×C4711yescharacteristic
374C2×#106C22×C4711yescharacteristic
375C2×#106C22×C4711yescharacteristic
376C2×#103C22×C4711yescharacteristic
377C2×#103C22×C4711yescharacteristic
378C2×#103C22×C4711yescharacteristic
379C2×#102C22×C4711yescharacteristic
380C2×#102C22×C4711yescharacteristic
381C2×#102C22×C4711yescharacteristic
382#391C22×C4711yescharacteristic
383#390C22×C4711yescharacteristic
384#389C22×C4711yescharacteristic
385#389C22×C4711yescharacteristic
386#388—21no—
387#387—21no—
388#386—21no—
389#385—21no—
390#380C22×C4711yescharacteristic
391#380C22×C4711yescharacteristic
392C4×C4⋊C4—21no—
393C4×C4⋊C4C22×C4711yescharacteristic
394C4×C4⋊C4C22×C4711yescharacteristic
395C4×C22⋊C4—21no—
396C4×C22⋊C4—21no—
397#340C22×C4711yescharacteristic
398#340C22×C4711yescharacteristic
399#340C22×C4711yescharacteristic
400#340C22×C4711yescharacteristic
401#340C22×C4711yescharacteristic
402#340C22×C4711yescharacteristic
403#336C22×C4711yescharacteristic
404#336C22×C4711yescharacteristic
405#336C22×C4711yescharacteristic
406#336C22×C4711yescharacteristic
407C47#2218011yescharacteristic, direct product factor, Sylow
408C22×Q8C23×C4711yescharacteristic
409C22×D4—21no—
410C22×D4C23×C4711yescharacteristic
411C23×C4—21no—
412C23×C4D4×C4711yescharacteristic
413C23×C4D4×C4711yescharacteristic
414C23×C4C23×C4711yescharacteristic
415C2×SD16—41no—
416C2×SD16—41no—
417C2×SD16C2×C4×C4714yescomplemented
418C22×C8—22no—
419C22×C8—41no—
420C22×C8—41no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8C2×C4×C4714yescomplemented
424C22×C8C23×C4711yescharacteristic
425C22×C8C23×C4711yescharacteristic
426C22×C8C23×C4711yescharacteristic
427C22×C8C23×C4711yescharacteristic
428C22⋊Q8—22no—
429C22⋊Q8C2×C4×C4714yescomplemented
430#121—22no—
431#121C2×C4×C4714yes—
432C4×Q8—41no—
433C4×Q8—41no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—44no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4C23×C4711yescharacteristic
442C2×C4⋊C4C23×C4711yescharacteristic
443C2×C4⋊C4C23×C4711yescharacteristic
444C2×C4⋊C4C23×C4711yescharacteristic
445C2×C4⋊C4C23×C4711yescharacteristic
446C2×C4⋊C4C23×C4711yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—41no—
458C2×C42—41no—
459C2×C42D4×C4711yescharacteristic
460C2×C42D4×C4711yescharacteristic
461C2×C42C23×C4711yescharacteristic
462C2×C42C23×C4711yescharacteristic
463#106—41no—
464#106—41no—
465#106C2×C4×C4714yescomplemented
466#103—41no—
467#103—41no—
468#103C2×C4×C4714yescomplemented
469#102—41no—
470#102—41no—
471#102C2×C4×C4714yescomplemented
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480C24—21no—
481C24C2×D4×C4711yescharacteristic
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8C22×C4×C4712yes—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4C22×C4×C4712yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4SD16×C4714yescomplemented
517C22×C4C22×C4×C4712yes—
518C22×C4C2×D4×C4711yescharacteristic
519C22×C4C2×D4×C4711yescharacteristic
520C22×C4C2×D4×C4711yescharacteristic
521C22×C4C2×D4×C4711yescharacteristic
522C22×C4C2×D4×C4711yescharacteristic
523C22×C4#41×C4712yes—
524C22×C4C24×C4711yescharacteristic
525SD16—44no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—44no—
537C2×C8—44no—
538C2×C8C22×C4×C4712yes—
539C2×C8C22×C4×C4712yes—
540C4⋊C4—24no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4C22×C4×C4712yes—
555C4⋊C4C22×C4×C4712yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—41no—
568C42—41no—
569C42—42no—
570C42—42no—
571C42—42no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C4×D4×C4712yes—
584C23C2×SD16×C4712yes—
585C23#135×C4712yes—
586C23C22×D4×C4711yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4—41no—
595D4—41no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4C4×D4×C4712yes—
637C2×C4C2×SD16×C4712yes—
638C2×C4C2×SD16×C4712yes—
639C2×C4C23×C4×C4711yescharacteristic
640C2×C4C2×#41×C4711yescharacteristic
641C2×C4H(5,𝔽2)×C4711yescharacteristic
642C2×C4H(5,𝔽2)×C4711yescharacteristic
643C2×C4H(5,𝔽2)×C4711yescharacteristic
644C2×C42−1+4×C4711yescharacteristic
645C8—22no—
646C8—22no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22C4×SD16×C4714yes—
663C22C2×C4×D4×C4711yescharacteristic
664C22C47×#53411yescharacteristic
665C22C47×#53711yescharacteristic
666C22C22×SD16×C4711yescharacteristic
667C22C2×#135×C4711yescharacteristic
668C22C47×#57511yescharacteristic
669C22C47×#57511yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—41no—
675C4—41no—
676C4—42no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C47×#51811yescharacteristic
683C4C47×#52011yescharacteristic
684C4C47×#53811yescharacteristic
685C4C47×#53911yescharacteristic
686C2—24no—
687C2—82no—
688C2C47×#232511yescharacteristic
689C2C2×C4×SD16×C4711yescharacteristic
690C2C47×#294311yescharacteristic
691C2C47×#318711yescharacteristic
692C2C47×#319111yescharacteristic
693C2C47×#324611yescharacteristic
694C2C47×#325011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Q8×C47C2semidirect
4. C47×#1927C2semidirect
5. C47×#1926C2semidirect
6. C47×#1920C2semidirect
7. C47×#1919C2semidirect
9. C47×#1892C2semidirect
10. C47×#1880C2semidirect
11. C47×#1877C2semidirect
12. C47×#1865C2semidirect
13. C47×#1864C2semidirect
14. C47×#1807C2semidirect
15. C2×C47×#336C2semidirect
25. C47×#465C4semidirect
69. C2×SD16×C47C2×C4semidirect
75. C22×C8×C47C2×C4semidirect
81. C22⋊Q8×C47C2×C4semidirect
117. #106×C47C2×C4semidirect
120. #103×C47C2×C4semidirect
123. #102×C47C2×C4semidirect
168. C22×C4×C47SD16semidirect
301. #22180C47direct (N × H)
340. C4×C22⋊Q8C2×C47semidirect
342. #1927C2×C47semidirect
343. #1926C2×C47semidirect
344. #1920C2×C47semidirect
345. #1919C2×C47semidirect
347. #1892C2×C47semidirect
348. #1880C2×C47semidirect
349. #1877C2×C47semidirect
350. #1865C2×C47semidirect
351. #1864C2×C47semidirect
352. #1807C2×C47semidirect
353. C2×#336C2×C47semidirect
372. #465C4×C47semidirect
407. C47#22180direct (N × H)
417. C2×SD16C2×C4×C47semidirect
423. C22×C8C2×C4×C47semidirect
429. C22⋊Q8C2×C4×C47semidirect
465. #106C2×C4×C47semidirect
468. #103C2×C4×C47semidirect
471. #102C2×C4×C47semidirect
516. C22×C4SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4652
C4×C22⋊Q8×C472
C4×#121×C472
C47×#19272
C47×#19262
C47×#19202
C47×#19192
C47×#18932
C47×#18922
C47×#18802
C47×#18772
C47×#18652
C47×#18642
C47×#18072
C2×C47×#3362
#2218047