Finite Group Databasebeta

← C2×C47×#3318 #26100826

Subgroups — C2×C47×#3318 #26100826

Order 12032.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#553C211yesmaximal, characteristic, complemented
2C2×D42×C47C211yesmaximal, characteristic, complemented
3C47×#3318C2116yesmaximal, direct product factor
4C2×C47×#490C211yesmaximal, characteristic, complemented
5C2×C47×#481C211yesmaximal, characteristic, complemented
6C2×C47×#482C211yesmaximal, characteristic, complemented
7C2×C47×#478C211yesmaximal, characteristic, complemented
8C2×C47×#469C211yesmaximal, characteristic, complemented
9C2×C47×#466C211yesmaximal, characteristic, complemented
10C2×C47×#459C211yesmaximal, characteristic, complemented
11C2×C47×#447C211yesmaximal, characteristic, complemented
12C2×C47×#447C211yesmaximal, characteristic, complemented
13C2×C47×#442C211yesmaximal, characteristic, complemented
14C2×C47×#435C211yesmaximal, characteristic, complemented
15C2×C47×#418C211yesmaximal, characteristic, complemented
16C22×#102×C47C211yesmaximal, characteristic, complemented
17C23×D4×C47—21no—
18C23×D4×C47C2211yescharacteristic
19C23×D4×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C22×D8×C47C2211yescharacteristic, complemented
22C22×D8×C47C2211yescharacteristic, complemented
23C22×M16×C47C2211yescharacteristic, complemented
24C23×C8×C47C2211yescharacteristic, complemented
25C47×#553—24no—
26C47×#553C2218yescomplemented
27D42×C47—24no—
28D42×C47C2218yescomplemented
29C2×#127×C47C2211yescharacteristic
30C2×#126×C47—21no—
31C2×#125×C47C2211yescharacteristic, complemented
32C2×#123×C47—21no—
33C2×#121×C47—21no—
34C2×#121×C47—21no—
35C2×#121×C47C2211yescharacteristic
36C2×#121×C47C2211yescharacteristic
37C2×#121×C47C2211yescharacteristic, complemented
38C2×#121×C47C2211yescharacteristic, complemented
39C2×#120×C47—21no—
40C2×#120×C47—21no—
41C2×C4×D4×C47—21no—
42C2×C4×D4×C47C2211yescharacteristic
43C2×C4×D4×C47C2211yescharacteristic
44C2×C4×D4×C47C2211yescharacteristic, complemented
45C2×#117×C47C2211yescharacteristic, complemented
46C22×C4⋊C4×C47C2211yescharacteristic, complemented
47C47×#490C2218yescomplemented
48C47×#482C2218yescomplemented
49C47×#481C2218yescomplemented
50C47×#478C2218yescomplemented
51C47×#469C2218yescomplemented
52C47×#466C2218yescomplemented
53C47×#459C2218yescomplemented
54C47×#447C2218yescomplemented
55C47×#447C2218yescomplemented
56C47×#442C2218yescomplemented
57C47×#435C2218yescomplemented
58C2×#107×C47C2211yescharacteristic, complemented
59C2×#106×C47C2211yescharacteristic, complemented
60C2×#106×C47C2211yescharacteristic, complemented
61C2×C4⋊C8×C47C2211yescharacteristic, complemented
62C47×#418C2218yescomplemented
63C2×#102×C47C2211yescharacteristic
64C2×#102×C47C2211yescharacteristic
65C2×#102×C47C2211yescharacteristic
66C2×#102×C47C2211yescharacteristic, complemented
67C2×#102×C47C2211yescharacteristic, complemented
68C2×#102×C47C2211yescharacteristic, complemented
69C2×#102×C47C2211yescharacteristic, complemented
70C2×#102×C47C2211yescharacteristic, complemented
71C2×#102×C47C2211yescharacteristic, complemented
72C2×#102×C47C2211yescharacteristic, complemented
73C2×#102×C47C2218yescomplemented
74C2×C22⋊C8×C47C2211yescharacteristic, complemented
75C2×C22⋊C8×C47C2211yescharacteristic, complemented
76C2×#97×C47C2211yescharacteristic, complemented
77C25×C47—21no—
78C25×C47—21no—
79C22×D4×C47—24no—
80C22×D4×C47—24no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47—21no—
85C22×D4×C47—28no—
86C22×D4×C47—21no—
87C22×D4×C47—21no—
88C22×D4×C47—21no—
89C22×D4×C47—22no—
90C22×D4×C47—22no—
91C22×D4×C47—21no—
92C22×D4×C47—42no—
93C22×D4×C47—42no—
94C22×D4×C47—48no—
95C22×D4×C47D411yescharacteristic
96C22×D4×C47C2311yescharacteristic
97C22×D4×C47C2311yescharacteristic
98C22×D4×C47C2311yescharacteristic
99C22×D4×C47C2314yes—
100C22×D4×C47C2314yes—
101C22×D4×C47C2311yescharacteristic
102C23×C4×C47—21no—
103C23×C4×C47—21no—
104C23×C4×C47—21no—
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C2×D8×C47—24no—
108C2×D8×C47—42no—
109C2×D8×C47—42no—
110C2×D8×C47C2314yes—
111C2×D8×C47C2314yescomplemented
112C2×D8×C47C2314yescomplemented
113C2×M16×C47—42no—
114C2×M16×C47C2314yescomplemented
115C22×C8×C47—42no—
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118C22×C8×C47C2311yescharacteristic
119C22×C8×C47C2311yescharacteristic
120C22×C8×C47C2314yescomplemented
121#127×C47—22no—
122#127×C47C2314yes—
123#126×C47—28no—
124#125×C47—22no—
125#125×C47C2314yescomplemented
126#123×C47—28no—
127#121×C47—28no—
128#121×C47—22no—
129#121×C47—22no—
130#121×C47—22no—
131#121×C47—22no—
132#121×C47—28no—
133#121×C47C2314yes—
134#121×C47C2314yes—
135#121×C47C2314yescomplemented
136#121×C47C2314yescomplemented
137#120×C47—28no—
138#120×C47—28no—
139C4×D4×C47—28no—
140C4×D4×C47—22no—
141C4×D4×C47—22no—
142C4×D4×C47D414yes—
143C4×D4×C47C2314yes—
144C4×D4×C47C2314yes—
145C4×D4×C47C2314yescomplemented
146#117×C47—22no—
147#117×C47C2314yescomplemented
148C2×C4⋊C4×C47—21no—
149C2×C4⋊C4×C47—22no—
150C2×C4⋊C4×C47—21no—
151C2×C4⋊C4×C47—21no—
152C2×C4⋊C4×C47D411yescharacteristic
153C2×C4⋊C4×C47C2311yescharacteristic
154C2×C4⋊C4×C47C2311yescharacteristic
155C2×C4⋊C4×C47C2311yescharacteristic
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C4⋊C4×C47C2314yescomplemented
158C2×C22⋊C4×C47—21no—
159C2×C22⋊C4×C47—21no—
160C2×C22⋊C4×C47—21no—
161C2×C22⋊C4×C47—21no—
162C2×C22⋊C4×C47—21no—
163C2×C22⋊C4×C47—21no—
164C2×C22⋊C4×C47—21no—
165C2×C22⋊C4×C47D411yescharacteristic
166C2×C22⋊C4×C47D411yescharacteristic
167C2×C42×C47—21no—
168C2×C42×C47C2311yescharacteristic
169#107×C47C2314yescomplemented
170#106×C47C2314yescomplemented
171#106×C47C2314yescomplemented
172C4⋊C8×C47C2314yescomplemented
173#102×C47C2314yes—
174#102×C47C2314yes—
175#102×C47C2314yes—
176#102×C47C2314yescomplemented
177#102×C47C2314yescomplemented
178#102×C47C2314yescomplemented
179#102×C47C2314yescomplemented
180#102×C47C2314yescomplemented
181#102×C47C2314yescomplemented
182#102×C47C2314yescomplemented
183C22⋊C8×C47C2314yescomplemented
184C22⋊C8×C47C2314yescomplemented
185#97×C47C2314yescomplemented
186C24×C47—21no—
187C24×C47—21no—
188C24×C47—21no—
189C24×C47—21no—
190C24×C47—24no—
191C24×C47—24no—
192C24×C47—44no—
193C24×C47—44no—
194C24×C47—44no—
195C24×C47—44no—
196C24×C47—82no—
197C24×C47—82no—
198C24×C47C2×D411yescharacteristic
199C24×C47C2×D411yescharacteristic
200C2×D4×C47—24no—
201C2×D4×C47—28no—
202C2×D4×C47—28no—
203C2×D4×C47—24no—
204C2×D4×C47—24no—
205C2×D4×C47—24no—
206C2×D4×C47—24no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—24no—
210C2×D4×C47—24no—
211C2×D4×C47—21no—
212C2×D4×C47—21no—
213C2×D4×C47—24no—
214C2×D4×C47—24no—
215C2×D4×C47—22no—
216C2×D4×C47—22no—
217C2×D4×C47—22no—
218C2×D4×C47—22no—
219C2×D4×C47—22no—
220C2×D4×C47—22no—
221C2×D4×C47—22no—
222C2×D4×C47—44no—
223C2×D4×C47—44no—
224C2×D4×C47—48no—
225C2×D4×C47—48no—
226C2×D4×C47—44no—
227C2×D4×C47—44no—
228C2×D4×C47—44no—
229C2×D4×C47—432no—
230C2×D4×C47—44no—
231C2×D4×C47—44no—
232C2×D4×C47—44no—
233C2×D4×C47—82no—
234C2×D4×C47—82no—
235C2×D4×C47C2×D414yes—
236C2×D4×C47#4114yes—
237C2×D4×C47C2412yes—
238C2×D4×C47C2412yes—
239C2×D4×C47C2412yes—
240C2×D4×C47C2412yes—
241C22×C4×C47—22no—
242C22×C4×C47—22no—
243C22×C4×C47—22no—
244C22×C4×C47—22no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—24no—
250C22×C4×C47—24no—
251C22×C4×C47—24no—
252C22×C4×C47—44no—
253C22×C4×C47—82no—
254C22×C4×C47—82no—
255C22×C4×C47C2×D412yes—
256C22×C4×C47C2×D412yes—
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2×D411yescharacteristic
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2412yes—
262C22×C4×C47C2412yes—
263C22×C4×C47C2411yescharacteristic
264D8×C47—28no—
265D8×C47—44no—
266D8×C47—44no—
267M16×C47—44no—
268C2×C8×C47—22no—
269C2×C8×C47—22no—
270C2×C8×C47—22no—
271C2×C8×C47—22no—
272C2×C8×C47—44no—
273C2×C8×C47C2412yes—
274C2×C8×C47C2412yes—
275C2×C8×C47C2412yes—
276C2×C8×C47C2412yes—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—24no—
280C4⋊C4×C47—24no—
281C4⋊C4×C47—24no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47C2×D414yes—
285C4⋊C4×C47C2412yes—
286C4⋊C4×C47C2412yes—
287C4⋊C4×C47C2412yes—
288C4⋊C4×C47C2412yes—
289C22⋊C4×C47—24no—
290C22⋊C4×C47—24no—
291C22⋊C4×C47—24no—
292C22⋊C4×C47—24no—
293C22⋊C4×C47—24no—
294C22⋊C4×C47—24no—
295C22⋊C4×C47—24no—
296C22⋊C4×C47C2×D414yes—
297C22⋊C4×C47C2×D414yes—
298C42×C47—24no—
299C42×C47C2×D412yes—
300C42×C47C2412yes—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—24no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—48no—
312C23×C47—48no—
313C23×C47—48no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—48no—
320C23×C47—42no—
321C23×C47—42no—
322C23×C47—42no—
323C23×C47—42no—
324C23×C47—42no—
325C23×C47—42no—
326C23×C47—84no—
327C23×C47—84no—
328C23×C47—816no—
329C23×C47—816no—
330C23×C47AGL(1,ℤ/8)14yes—
331C23×C47C22×D412yes—
332C23×C47C22×D412yes—
333C23×C47C22×D411yescharacteristic
334D4×C47—28no—
335D4×C47—24no—
336D4×C47—22no—
337D4×C47—22no—
338D4×C47—22no—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—22no—
343D4×C47—48no—
344D4×C47—48no—
345D4×C47—48no—
346D4×C47—48no—
347D4×C47—48no—
348D4×C47—48no—
349D4×C47—42no—
350D4×C47—42no—
351D4×C47—42no—
352D4×C47—84no—
353D4×C47—84no—
354D4×C47C2×#4114yes—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—24no—
360C2×C4×C47—24no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—48no—
370C2×C4×C47—42no—
371C2×C4×C47—42no—
372C2×C4×C47—42no—
373C2×C4×C47—42no—
374C2×C4×C47—84no—
375C2×C4×C47—84no—
376C2×C4×C47C22×D412yes—
377C2×C4×C47C22×D412yes—
378C2×C4×C47C22×D412yes—
379C2×C4×C47C22×D412yes—
380C2×C4×C47C22×D411yescharacteristic
381C2×C4×C47C2×#4112yes—
382C2×C4×C47H(5,𝔽2)12yes—
383C2×C4×C47C2511yescharacteristic
384C8×C47—22no—
385C8×C47—22no—
386C8×C47—22no—
387C8×C47—22no—
388C2×#3318C4711yesmaximal, characteristic, direct product factor, Sylow
389C22×C47—22no—
390C22×C47—28no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—24no—
394C22×C47—22no—
395C22×C47—22no—
396C22×C47—44no—
397C22×C47—48no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—42no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—816no—
410C22×C47—816no—
411C22×C47—84no—
412C22×C47—84no—
413C22×C47—84no—
414C22×C47#54612yes—
415C22×C47C2×AGL(1,ℤ/8)14yes—
416C22×C47C2×AGL(1,ℤ/8)12yes—
417C22×C47#57612yes—
418C22×C47C23×D411yescharacteristic
419C4×C47—22no—
420C4×C47—22no—
421C4×C47—22no—
422C4×C47—22no—
423C4×C47—42no—
424C4×C47—42no—
425C4×C47—42no—
426C4×C47—42no—
427C4×C47#54612yes—
428C4×C47C22×#4111yescharacteristic
429C4×C47C2×H(5,𝔽2)11yescharacteristic
430C2×#553C2×C4711yescharacteristic, complemented
431C2×D42C2×C4711yescharacteristic, complemented
432#3318C2×C47116yesdirect product factor
433C2×#490C2×C4711yescharacteristic, complemented
434C2×#481C2×C4711yescharacteristic, complemented
435C2×#482C2×C4711yescharacteristic, complemented
436C2×#478C2×C4711yescharacteristic, complemented
437C2×#469C2×C4711yescharacteristic, complemented
438C2×#466C2×C4711yescharacteristic, complemented
439C2×#459C2×C4711yescharacteristic, complemented
440C2×#447C2×C4711yescharacteristic, complemented
441C2×#447C2×C4711yescharacteristic, complemented
442C2×#442C2×C4711yescharacteristic, complemented
443C2×#435C2×C4711yescharacteristic, complemented
444C2×#418C2×C4711yescharacteristic, complemented
445C22×#102C2×C4711yescharacteristic, complemented
446C2×C47—24no—
447C2×C47—42no—
448C2×C47—44no—
449C2×C47—82no—
450C2×C47—82no—
451C2×C47—82no—
452C2×C47#331814yesdirect product factor
453C2×C47C2×#54611yescharacteristic
454C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
455C2×C47C2×#57611yescharacteristic
456C23×D4—21no—
457C23×D4C22×C4711yescharacteristic
458C23×D4C22×C4711yescharacteristic
459C22×D8C22×C4711yescharacteristic
460C22×D8C22×C4711yescharacteristic, complemented
461C22×D8C22×C4711yescharacteristic, complemented
462C22×M16C22×C4711yescharacteristic, complemented
463C23×C8C22×C4711yescharacteristic, complemented
464#553—24no—
465#553C22×C4718yescomplemented
466D42—24no—
467D42C22×C4718yescomplemented
468C2×#127C22×C4711yescharacteristic
469C2×#126—21no—
470C2×#125C22×C4711yescharacteristic, complemented
471C2×#123—21no—
472C2×#121—21no—
473C2×#121—21no—
474C2×#121C22×C4711yescharacteristic
475C2×#121C22×C4711yescharacteristic
476C2×#121C22×C4711yescharacteristic, complemented
477C2×#121C22×C4711yescharacteristic, complemented
478C2×#120—21no—
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C4711yescharacteristic
482C2×C4×D4C22×C4711yescharacteristic
483C2×C4×D4C22×C4711yescharacteristic, complemented
484C2×#117C22×C4711yescharacteristic, complemented
485C22×C4⋊C4C22×C4711yescharacteristic, complemented
486#490C22×C4718yescomplemented
487#482C22×C4718yescomplemented
488#481C22×C4718yescomplemented
489#478C22×C4718yescomplemented
490#469C22×C4718yescomplemented
491#466C22×C4718yescomplemented
492#459C22×C4718yescomplemented
493#447C22×C4718yescomplemented
494#447C22×C4718yescomplemented
495#442C22×C4718yescomplemented
496#435C22×C4718yescomplemented
497C2×#107C22×C4711yescharacteristic, complemented
498C2×#106C22×C4711yescharacteristic, complemented
499C2×#106C22×C4711yescharacteristic, complemented
500C2×C4⋊C8C22×C4711yescharacteristic, complemented
501#418C22×C4718yescomplemented
502C2×#102C22×C4711yescharacteristic
503C2×#102C22×C4711yescharacteristic
504C2×#102C22×C4711yescharacteristic
505C2×#102C22×C4718yescomplemented
506C2×#102C22×C4711yescharacteristic, complemented
507C2×#102C22×C4711yescharacteristic, complemented
508C2×#102C22×C4711yescharacteristic, complemented
509C2×#102C22×C4711yescharacteristic, complemented
510C2×#102C22×C4711yescharacteristic, complemented
511C2×#102C22×C4711yescharacteristic, complemented
512C2×#102C22×C4711yescharacteristic, complemented
513C2×C22⋊C8C22×C4711yescharacteristic, complemented
514C2×C22⋊C8C22×C4711yescharacteristic, complemented
515C2×#97C22×C4711yescharacteristic, complemented
516C47C2×#331811yescharacteristic, direct product factor, Sylow
517C25—21no—
518C25—21no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—28no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—21no—
532C22×D4—42no—
533C22×D4—42no—
534C22×D4—48no—
535C22×D4D4×C4711yescharacteristic
536C22×D4C23×C4711yescharacteristic
537C22×D4C23×C4711yescharacteristic
538C22×D4C23×C4711yescharacteristic
539C22×D4C23×C4714yes—
540C22×D4C23×C4714yes—
541C22×D4C23×C4711yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C23×C4711yescharacteristic
546C23×C4C23×C4711yescharacteristic
547C2×D8—24no—
548C2×D8—42no—
549C2×D8—42no—
550C2×D8C23×C4714yes—
551C2×D8C23×C4714yescomplemented
552C2×D8C23×C4714yescomplemented
553C2×M16—42no—
554C2×M16C23×C4714yescomplemented
555C22×C8—42no—
556C22×C8C23×C4711yescharacteristic
557C22×C8C23×C4711yescharacteristic
558C22×C8C23×C4711yescharacteristic
559C22×C8C23×C4711yescharacteristic
560C22×C8C23×C4714yescomplemented
561#127—22no—
562#127C23×C4714yes—
563#126—28no—
564#125—22no—
565#125C23×C4714yescomplemented
566#123—28no—
567#121—28no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—28no—
573#121C23×C4714yes—
574#121C23×C4714yes—
575#121C23×C4714yescomplemented
576#121C23×C4714yescomplemented
577#120—28no—
578#120—28no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4D4×C4714yes—
583C4×D4C23×C4714yes—
584C4×D4C23×C4714yes—
585C4×D4C23×C4714yescomplemented
586#117—22no—
587#117C23×C4714yescomplemented
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4D4×C4711yescharacteristic
593C2×C4⋊C4C23×C4711yescharacteristic
594C2×C4⋊C4C23×C4711yescharacteristic
595C2×C4⋊C4C23×C4711yescharacteristic
596C2×C4⋊C4C23×C4711yescharacteristic
597C2×C4⋊C4C23×C4714yescomplemented
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C4711yescharacteristic
606C2×C22⋊C4D4×C4711yescharacteristic
607C2×C42—21no—
608C2×C42C23×C4711yescharacteristic
609#107C23×C4714yescomplemented
610#106C23×C4714yescomplemented
611#106C23×C4714yescomplemented
612C4⋊C8C23×C4714yescomplemented
613#102C23×C4714yes—
614#102C23×C4714yes—
615#102C23×C4714yes—
616#102C23×C4714yescomplemented
617#102C23×C4714yescomplemented
618#102C23×C4714yescomplemented
619#102C23×C4714yescomplemented
620#102C23×C4714yescomplemented
621#102C23×C4714yescomplemented
622#102C23×C4714yescomplemented
623C22⋊C8C23×C4714yescomplemented
624C22⋊C8C23×C4714yescomplemented
625#97C23×C4714yescomplemented
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—24no—
631C24—24no—
632C24—44no—
633C24—44no—
634C24—44no—
635C24—44no—
636C24—82no—
637C24—82no—
638C24C2×D4×C4711yescharacteristic
639C24C2×D4×C4711yescharacteristic
640C2×D4—24no—
641C2×D4—28no—
642C2×D4—28no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—432no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—82no—
674C2×D4—82no—
675C2×D4C2×D4×C4714yes—
676C2×D4#41×C4714yes—
677C2×D4C24×C4712yes—
678C2×D4C24×C4712yes—
679C2×D4C24×C4712yes—
680C2×D4C24×C4712yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—44no—
693C22×C4—82no—
694C22×C4—82no—
695C22×C4C2×D4×C4711yescharacteristic
696C22×C4C2×D4×C4711yescharacteristic
697C22×C4C2×D4×C4711yescharacteristic
698C22×C4C2×D4×C4711yescharacteristic
699C22×C4C2×D4×C4712yes—
700C22×C4C2×D4×C4712yes—
701C22×C4C24×C4712yes—
702C22×C4C24×C4712yes—
703C22×C4C24×C4711yescharacteristic
704D8—28no—
705D8—44no—
706D8—44no—
707M16—44no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—44no—
713C2×C8C24×C4712yes—
714C2×C8C24×C4712yes—
715C2×C8C24×C4712yes—
716C2×C8C24×C4712yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4C2×D4×C4714yes—
725C4⋊C4C24×C4712yes—
726C4⋊C4C24×C4712yes—
727C4⋊C4C24×C4712yes—
728C4⋊C4C24×C4712yes—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4C2×D4×C4714yes—
737C22⋊C4C2×D4×C4714yes—
738C42—24no—
739C42C2×D4×C4712yes—
740C42C24×C4712yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—48no—
752C23—48no—
753C23—48no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—48no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—84no—
767C23—84no—
768C23—816no—
769C23—816no—
770C23AGL(1,ℤ/8)×C4714yes—
771C23C22×D4×C4712yes—
772C23C22×D4×C4712yes—
773C23C22×D4×C4711yescharacteristic
774D4—28no—
775D4—24no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—48no—
786D4—48no—
787D4—48no—
788D4—48no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4C2×#41×C4714yes—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C22×D4×C4712yes—
817C2×C4C22×D4×C4712yes—
818C2×C4C22×D4×C4712yes—
819C2×C4C22×D4×C4712yes—
820C2×C4C22×D4×C4711yescharacteristic
821C2×C4C2×#41×C4712yes—
822C2×C4H(5,𝔽2)×C4712yes—
823C2×C4C25×C4711yescharacteristic
824C8—22no—
825C8—22no—
826C8—22no—
827C8—22no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—44no—
836C22—48no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—816no—
849C22—816no—
850C22—84no—
851C22—84no—
852C22—84no—
853C22C47×#54612yes—
854C22C2×AGL(1,ℤ/8)×C4714yes—
855C22C2×AGL(1,ℤ/8)×C4712yes—
856C22C47×#57612yes—
857C22C23×D4×C4711yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4C47×#54612yes—
867C4C22×#41×C4711yescharacteristic
868C4C2×H(5,𝔽2)×C4711yescharacteristic
869C2—24no—
870C2—42no—
871C2—44no—
872C2—82no—
873C2—82no—
874C2—82no—
875C2C47×#331814yesdirect product factor
876C2C2×C47×#54611yescharacteristic
877C2C22×AGL(1,ℤ/8)×C4711yescharacteristic
878C2C2×C47×#57611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC2×C4C25×C47
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#553C2semidirect
2. C2×D42×C47C2semidirect
3. C47×#3318C2direct (N × H)
4. C2×C47×#490C2semidirect
5. C2×C47×#481C2semidirect
6. C2×C47×#482C2semidirect
7. C2×C47×#478C2semidirect
8. C2×C47×#469C2semidirect
9. C2×C47×#466C2semidirect
10. C2×C47×#459C2semidirect
11. C2×C47×#447C2semidirect
12. C2×C47×#447C2semidirect
13. C2×C47×#442C2semidirect
14. C2×C47×#435C2semidirect
15. C2×C47×#418C2semidirect
16. C22×#102×C47C2semidirect
21. C22×D8×C47C22semidirect
22. C22×D8×C47C22semidirect
23. C22×M16×C47C22semidirect
24. C23×C8×C47C22semidirect
26. C47×#553C22semidirect
28. D42×C47C22semidirect
31. C2×#125×C47C22semidirect
37. C2×#121×C47C22semidirect
38. C2×#121×C47C22semidirect
44. C2×C4×D4×C47C22semidirect
45. C2×#117×C47C22semidirect
46. C22×C4⋊C4×C47C22semidirect
47. C47×#490C22semidirect
48. C47×#482C22semidirect
49. C47×#481C22semidirect
50. C47×#478C22semidirect
51. C47×#469C22semidirect
52. C47×#466C22semidirect
53. C47×#459C22semidirect
54. C47×#447C22semidirect
55. C47×#447C22semidirect
56. C47×#442C22semidirect
57. C47×#435C22semidirect
58. C2×#107×C47C22semidirect
59. C2×#106×C47C22semidirect
60. C2×#106×C47C22semidirect
61. C2×C4⋊C8×C47C22semidirect
62. C47×#418C22semidirect
66. C2×#102×C47C22semidirect
67. C2×#102×C47C22semidirect
68. C2×#102×C47C22semidirect
69. C2×#102×C47C22semidirect
70. C2×#102×C47C22semidirect
71. C2×#102×C47C22semidirect
72. C2×#102×C47C22semidirect
73. C2×#102×C47C22semidirect
74. C2×C22⋊C8×C47C22semidirect
75. C2×C22⋊C8×C47C22semidirect
76. C2×#97×C47C22semidirect
111. C2×D8×C47C23semidirect
112. C2×D8×C47C23semidirect
114. C2×M16×C47C23semidirect
120. C22×C8×C47C23semidirect
125. #125×C47C23semidirect
135. #121×C47C23semidirect
136. #121×C47C23semidirect
145. C4×D4×C47C23semidirect
147. #117×C47C23semidirect
157. C2×C4⋊C4×C47C23semidirect
169. #107×C47C23semidirect
170. #106×C47C23semidirect
171. #106×C47C23semidirect
172. C4⋊C8×C47C23semidirect
176. #102×C47C23semidirect
177. #102×C47C23semidirect
178. #102×C47C23semidirect
179. #102×C47C23semidirect
180. #102×C47C23semidirect
181. #102×C47C23semidirect
182. #102×C47C23semidirect
183. C22⋊C8×C47C23semidirect
184. C22⋊C8×C47C23semidirect
185. #97×C47C23semidirect
388. C2×#3318C47direct (N × H)
430. C2×#553C2×C47semidirect
431. C2×D42C2×C47semidirect
432. #3318C2×C47direct (N × H)
433. C2×#490C2×C47semidirect
434. C2×#481C2×C47semidirect
435. C2×#482C2×C47semidirect
436. C2×#478C2×C47semidirect
437. C2×#469C2×C47semidirect
438. C2×#466C2×C47semidirect
439. C2×#459C2×C47semidirect
440. C2×#447C2×C47semidirect
441. C2×#447C2×C47semidirect
442. C2×#442C2×C47semidirect
443. C2×#435C2×C47semidirect
444. C2×#418C2×C47semidirect
445. C22×#102C2×C47semidirect
452. C2×C47#3318direct (N × H)
460. C22×D8C22×C47semidirect
461. C22×D8C22×C47semidirect
462. C22×M16C22×C47semidirect
463. C23×C8C22×C47semidirect
465. #553C22×C47semidirect
467. D42C22×C47semidirect
470. C2×#125C22×C47semidirect
476. C2×#121C22×C47semidirect
477. C2×#121C22×C47semidirect
483. C2×C4×D4C22×C47semidirect
484. C2×#117C22×C47semidirect
485. C22×C4⋊C4C22×C47semidirect
486. #490C22×C47semidirect
487. #482C22×C47semidirect
488. #481C22×C47semidirect
489. #478C22×C47semidirect
490. #469C22×C47semidirect
491. #466C22×C47semidirect
492. #459C22×C47semidirect
493. #447C22×C47semidirect
494. #447C22×C47semidirect
495. #442C22×C47semidirect
496. #435C22×C47semidirect
497. C2×#107C22×C47semidirect
498. C2×#106C22×C47semidirect
499. C2×#106C22×C47semidirect
500. C2×C4⋊C8C22×C47semidirect
501. #418C22×C47semidirect
505. C2×#102C22×C47semidirect
506. C2×#102C22×C47semidirect
507. C2×#102C22×C47semidirect
508. C2×#102C22×C47semidirect
509. C2×#102C22×C47semidirect
510. C2×#102C22×C47semidirect
511. C2×#102C22×C47semidirect
512. C2×#102C22×C47semidirect
513. C2×C22⋊C8C22×C47semidirect
514. C2×C22⋊C8C22×C47semidirect
515. C2×#97C22×C47semidirect
516. C47C2×#3318direct (N × H)
551. C2×D8C23×C47semidirect
552. C2×D8C23×C47semidirect
554. C2×M16C23×C47semidirect
560. C22×C8C23×C47semidirect
565. #125C23×C47semidirect
575. #121C23×C47semidirect
576. #121C23×C47semidirect
585. C4×D4C23×C47semidirect
587. #117C23×C47semidirect
597. C2×C4⋊C4C23×C47semidirect
609. #107C23×C47semidirect
610. #106C23×C47semidirect
611. #106C23×C47semidirect
612. C4⋊C8C23×C47semidirect
616. #102C23×C47semidirect
617. #102C23×C47semidirect
618. #102C23×C47semidirect
619. #102C23×C47semidirect
620. #102C23×C47semidirect
621. #102C23×C47semidirect
622. #102C23×C47semidirect
623. C22⋊C8C23×C47semidirect
624. C22⋊C8C23×C47semidirect
625. #97C23×C47semidirect
875. C2C47×#3318direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5532
C2×D42×C472
C47×#33182
C2×C47×#4902
C2×C47×#4812
C2×C47×#4822
C2×C47×#4782
C2×C47×#4692
C2×C47×#4662
C2×C47×#4592
C2×C47×#4472
C2×C47×#4422
C2×C47×#4352
C2×C47×#4182
C22×#102×C472
C2×#331847