Finite Group Databasebeta

← C2×C47×#3308 #26100827

Subgroups — C2×C47×#3308 #26100827

Order 12032.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#548C211yesmaximal, characteristic, complemented
2C2×C47×#547C211yesmaximal, characteristic, complemented
3C47×#3308C2116yesmaximal, direct product factor
4C2×C47×#489C211yesmaximal, characteristic, complemented
5C2×C47×#484C211yesmaximal, characteristic, complemented
6C2×C47×#480C211yesmaximal, characteristic, complemented
7C2×C47×#477C211yesmaximal, characteristic, complemented
8C2×C47×#468C211yesmaximal, characteristic, complemented
9C2×C47×#466C211yesmaximal, characteristic, complemented
10C2×C47×#463C211yesmaximal, characteristic, complemented
11C2×C47×#449C211yesmaximal, characteristic, complemented
12C2×C47×#448C211yesmaximal, characteristic, complemented
13C2×C47×#440C211yesmaximal, characteristic, complemented
14C2×C47×#435C211yesmaximal, characteristic, complemented
15C2×C47×#417C211yesmaximal, characteristic, complemented
16C22×#103×C47C211yesmaximal, characteristic, complemented
17C22×#41×C47—21no—
18C22×#41×C47C2211yescharacteristic
19C23×Q8×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C22×SD16×C47C2211yescharacteristic
22C22×D8×C47C2211yescharacteristic
23C22×M16×C47C2211yescharacteristic
24C23×C8×C47C2211yescharacteristic
25C47×#548—24no—
26C47×#548C2218yescomplemented
27C47×#547—24no—
28C47×#547C2218yescomplemented
29C2×C4⋊Q8×C47C2211yescharacteristic
30C2×#124×C47—21no—
31C2×#124×C47C2211yescharacteristic
32C2×#123×C47—21no—
33C2×#123×C47—21no—
34C2×C22⋊Q8×C47—21no—
35C2×C22⋊Q8×C47—21no—
36C2×C22⋊Q8×C47C2211yescharacteristic
37C2×#121×C47—21no—
38C2×#121×C47C2211yescharacteristic
39C2×#121×C47C2211yescharacteristic
40C2×#121×C47C2211yescharacteristic
41C2×C4×Q8×C47C2211yescharacteristic
42C2×C4×D4×C47—21no—
43C2×C4×D4×C47C2211yescharacteristic
44C2×C4×D4×C47C2211yescharacteristic
45C22×C4⋊C4×C47C2211yescharacteristic
46C22×C4⋊C4×C47C2211yescharacteristic
47C47×#489C2218yescomplemented
48C47×#484C2218yescomplemented
49C47×#480C2218yescomplemented
50C47×#477C2218yescomplemented
51C47×#468C2218yescomplemented
52C47×#466C2218yescomplemented
53C47×#463C2218yescomplemented
54C47×#449C2218yescomplemented
55C47×#448C2218yescomplemented
56C47×#440C2218yescomplemented
57C47×#435C2218yescomplemented
58C2×#107×C47C2211yescharacteristic
59C2×#107×C47C2211yescharacteristic
60C2×#107×C47C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C47×#417C2218yescomplemented
63C2×#103×C47C2211yescharacteristic
64C2×#103×C47C2211yescharacteristic
65C2×#103×C47C2211yescharacteristic
66C2×#103×C47C2211yescharacteristic
67C2×#103×C47C2211yescharacteristic
68C2×#103×C47C2211yescharacteristic
69C2×#103×C47C2218yescomplemented
70C2×#102×C47C2211yescharacteristic
71C2×#102×C47C2211yescharacteristic
72C2×#102×C47C2211yescharacteristic
73C2×#102×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C2×#41×C47—28no—
78C2×#41×C47—22no—
79C2×#41×C47—24no—
80C2×#41×C47—42no—
81C2×#41×C47—48no—
82C2×#41×C47C2314yes—
83C22×Q8×C47—21no—
84C22×Q8×C47—21no—
85C22×Q8×C47—22no—
86C22×Q8×C47—24no—
87C22×Q8×C47—42no—
88C22×Q8×C47C2311yescharacteristic
89C22×Q8×C47C2314yes—
90C22×Q8×C47C2311yescharacteristic
91C22×D4×C47—21no—
92C22×D4×C47—21no—
93C22×D4×C47—21no—
94C22×D4×C47—21no—
95C22×D4×C47D411yescharacteristic
96C22×D4×C47C2311yescharacteristic
97C22×D4×C47C2311yescharacteristic
98C23×C4×C47—21no—
99C23×C4×C47—21no—
100C23×C4×C47—21no—
101C23×C4×C47—21no—
102C23×C4×C47—21no—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C2×SD16×C47—24no—
106C2×SD16×C47—42no—
107C2×SD16×C47C2314yes—
108C2×SD16×C47C2314yes—
109C2×D8×C47—42no—
110C2×D8×C47C2314yes—
111C2×M16×C47—42no—
112C2×M16×C47C2314yes—
113C22×C8×C47—42no—
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118C22×C8×C47C2314yes—
119C4⋊Q8×C47—22no—
120C4⋊Q8×C47C2314yes—
121#124×C47—28no—
122#124×C47—22no—
123#124×C47C2314yes—
124#123×C47—28no—
125#123×C47—28no—
126C22⋊Q8×C47—22no—
127C22⋊Q8×C47—28no—
128C22⋊Q8×C47—28no—
129C22⋊Q8×C47C2314yes—
130#121×C47—28no—
131#121×C47—22no—
132#121×C47—22no—
133#121×C47—22no—
134#121×C47C2314yes—
135#121×C47C2314yes—
136#121×C47C2314yes—
137C4×Q8×C47—22no—
138C4×Q8×C47C2314yes—
139C4×D4×C47—28no—
140C4×D4×C47—22no—
141C4×D4×C47D414yes—
142C4×D4×C47C2314yes—
143C4×D4×C47C2314yes—
144C2×C4⋊C4×C47—21no—
145C2×C4⋊C4×C47—21no—
146C2×C4⋊C4×C47—22no—
147C2×C4⋊C4×C47—22no—
148C2×C4⋊C4×C47—21no—
149C2×C4⋊C4×C47—21no—
150C2×C4⋊C4×C47—21no—
151C2×C4⋊C4×C47D411yescharacteristic
152C2×C4⋊C4×C47C2314yes—
153C2×C4⋊C4×C47C2314yes—
154C2×C4⋊C4×C47C2311yescharacteristic
155C2×C4⋊C4×C47C2311yescharacteristic
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C4⋊C4×C47C2311yescharacteristic
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×C47C2314yes—
170#107×C47C2314yes—
171#107×C47C2314yes—
172C4⋊C8×C47C2314yes—
173#103×C47C2314yes—
174#103×C47C2314yes—
175#103×C47C2314yes—
176#103×C47C2314yes—
177#103×C47C2314yes—
178#103×C47C2314yes—
179#102×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182#102×C47C2314yes—
183C22⋊C8×C47C2314yes—
184C22⋊C8×C47C2314yes—
185#97×C47C2314yes—
186C24×C47—21no—
187C24×C47—21no—
188C24×C47C2×D411yescharacteristic
189C24×C47C2×D411yescharacteristic
190#41×C47—28no—
191#41×C47—44no—
192#41×C47—48no—
193#41×C47—432no—
194C2×Q8×C47—21no—
195C2×Q8×C47—24no—
196C2×Q8×C47—21no—
197C2×Q8×C47—24no—
198C2×Q8×C47—22no—
199C2×Q8×C47—28no—
200C2×Q8×C47—22no—
201C2×Q8×C47—22no—
202C2×Q8×C47—44no—
203C2×Q8×C47—44no—
204C2×Q8×C47—48no—
205C2×Q8×C47—44no—
206C2×Q8×C47#4114yescomplemented
207C2×Q8×C47C2412yes—
208C2×Q8×C47C2412yes—
209C2×D4×C47—24no—
210C2×D4×C47—24no—
211C2×D4×C47—24no—
212C2×D4×C47—24no—
213C2×D4×C47—24no—
214C2×D4×C47—21no—
215C2×D4×C47—21no—
216C2×D4×C47—22no—
217C2×D4×C47—22no—
218C2×D4×C47—22no—
219C2×D4×C47—22no—
220C2×D4×C47—44no—
221C2×D4×C47—44no—
222C2×D4×C47—44no—
223C2×D4×C47—44no—
224C2×D4×C47C2×D414yes—
225C2×D4×C47C2412yes—
226C2×D4×C47C2412yes—
227C22×C4×C47—21no—
228C22×C4×C47—22no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—24no—
233C22×C4×C47—24no—
234C22×C4×C47—24no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—24no—
241C22×C4×C47—24no—
242C22×C4×C47—44no—
243C22×C4×C47—44no—
244C22×C4×C47—44no—
245C22×C4×C47—44no—
246C22×C4×C47—44no—
247C22×C4×C47C2×D412yes—
248C22×C4×C47C2×D412yes—
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2412yes—
254C22×C4×C47C2412yes—
255C22×C4×C47C2411yescharacteristic
256SD16×C47—28no—
257SD16×C47—44no—
258D8×C47—44no—
259M16×C47—44no—
260C2×C8×C47—22no—
261C2×C8×C47—22no—
262C2×C8×C47—22no—
263C2×C8×C47—22no—
264C2×C8×C47—44no—
265C2×C8×C47C2412yes—
266C2×C8×C47C2412yes—
267C2×C8×C47C2412yes—
268C2×C8×C47C2412yes—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—24no—
273C4⋊C4×C47—24no—
274C4⋊C4×C47—24no—
275C4⋊C4×C47—24no—
276C4⋊C4×C47—24no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47C2×D414yes—
279C4⋊C4×C47C2412yes—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C4⋊C4×C47C2412yes—
283C22⋊C4×C47—24no—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—24no—
288C22⋊C4×C47—24no—
289C22⋊C4×C47—24no—
290C22⋊C4×C47C2×D414yes—
291C22⋊C4×C47C2×D414yes—
292C42×C47—24no—
293C42×C47C2×D412yes—
294C42×C47C2412yes—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—42no—
303C23×C47—42no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47AGL(1,ℤ/8)14yes—
309C23×C47C22×D412yes—
310C23×C47C22×D412yes—
311C23×C47C22×D411yescharacteristic
312Q8×C47—24no—
313Q8×C47—22no—
314Q8×C47—22no—
315Q8×C47—22no—
316Q8×C47—48no—
317Q8×C47—48no—
318Q8×C47—42no—
319Q8×C47C2×#4114yescomplemented
320D4×C47—28no—
321D4×C47—22no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—48no—
326D4×C47—48no—
327D4×C47—48no—
328D4×C47—48no—
329D4×C47—42no—
330D4×C47—42no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—24no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—24no—
338C2×C4×C47—24no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—48no—
349C2×C4×C47—48no—
350C2×C4×C47—48no—
351C2×C4×C47—48no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47—42no—
355C2×C4×C47—42no—
356C2×C4×C47—48no—
357C2×C4×C47—42no—
358C2×C4×C47C22×D412yes—
359C2×C4×C47C22×D412yes—
360C2×C4×C47C22×D412yes—
361C2×C4×C47C22×D412yes—
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C2×#4112yes—
364C2×C4×C47H(5,𝔽2)12yes—
365C2×C4×C47C2511yescharacteristic
366C8×C47—22no—
367C8×C47—22no—
368C8×C47—22no—
369C8×C47—22no—
370C2×#3308C4711yesmaximal, characteristic, direct product factor, Sylow
371C22×C47—22no—
372C22×C47—28no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—44no—
378C22×C47—42no—
379C22×C47—42no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—84no—
385C22×C47—84no—
386C22×C47#54612yes—
387C22×C47C2×AGL(1,ℤ/8)14yes—
388C22×C47C2×AGL(1,ℤ/8)12yes—
389C22×C47#57812yes—
390C22×C47C23×D411yescharacteristic
391C4×C47—22no—
392C4×C47—22no—
393C4×C47—24no—
394C4×C47—22no—
395C4×C47—22no—
396C4×C47—42no—
397C4×C47—42no—
398C4×C47—42no—
399C4×C47—42no—
400C4×C47—42no—
401C4×C47#54612yes—
402C4×C47C22×#4111yescharacteristic
403C4×C47C2×H(5,𝔽2)11yescharacteristic
404C2×#548C2×C4711yescharacteristic, complemented
405C2×#547C2×C4711yescharacteristic, complemented
406#3308C2×C47116yesdirect product factor
407C2×#489C2×C4711yescharacteristic, complemented
408C2×#484C2×C4711yescharacteristic, complemented
409C2×#480C2×C4711yescharacteristic, complemented
410C2×#477C2×C4711yescharacteristic, complemented
411C2×#468C2×C4711yescharacteristic, complemented
412C2×#466C2×C4711yescharacteristic, complemented
413C2×#463C2×C4711yescharacteristic, complemented
414C2×#449C2×C4711yescharacteristic, complemented
415C2×#448C2×C4711yescharacteristic, complemented
416C2×#440C2×C4711yescharacteristic, complemented
417C2×#435C2×C4711yescharacteristic, complemented
418C2×#417C2×C4711yescharacteristic, complemented
419C22×#103C2×C4711yescharacteristic, complemented
420C2×C47—24no—
421C2×C47—42no—
422C2×C47—82no—
423C2×C47—82no—
424C2×C47#330814yesdirect product factor
425C2×C47C2×#54611yescharacteristic
426C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
427C2×C47C2×#57811yescharacteristic
428C22×#41—21no—
429C22×#41C22×C4711yescharacteristic
430C23×Q8C22×C4711yescharacteristic
431C22×SD16C22×C4711yescharacteristic
432C22×SD16C22×C4711yescharacteristic
433C22×D8C22×C4711yescharacteristic
434C22×M16C22×C4711yescharacteristic
435C23×C8C22×C4711yescharacteristic
436#548—24no—
437#548C22×C4718yescomplemented
438#547—24no—
439#547C22×C4718yescomplemented
440C2×C4⋊Q8C22×C4711yescharacteristic
441C2×#124—21no—
442C2×#124C22×C4711yescharacteristic
443C2×#123—21no—
444C2×#123—21no—
445C2×C22⋊Q8—21no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8C22×C4711yescharacteristic
448C2×#121—21no—
449C2×#121C22×C4711yescharacteristic
450C2×#121C22×C4711yescharacteristic
451C2×#121C22×C4711yescharacteristic
452C2×C4×Q8C22×C4711yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C22×C4711yescharacteristic
455C2×C4×D4C22×C4711yescharacteristic
456C22×C4⋊C4C22×C4711yescharacteristic
457C22×C4⋊C4C22×C4711yescharacteristic
458#489C22×C4718yescomplemented
459#484C22×C4718yescomplemented
460#480C22×C4718yescomplemented
461#477C22×C4718yescomplemented
462#468C22×C4718yescomplemented
463#466C22×C4718yescomplemented
464#463C22×C4718yescomplemented
465#449C22×C4718yescomplemented
466#448C22×C4718yescomplemented
467#440C22×C4718yescomplemented
468#435C22×C4718yescomplemented
469C2×#107C22×C4711yescharacteristic
470C2×#107C22×C4711yescharacteristic
471C2×#107C22×C4711yescharacteristic
472C2×C4⋊C8C22×C4711yescharacteristic
473#417C22×C4718yescomplemented
474C2×#103C22×C4711yescharacteristic
475C2×#103C22×C4711yescharacteristic
476C2×#103C22×C4711yescharacteristic
477C2×#103C22×C4711yescharacteristic
478C2×#103C22×C4711yescharacteristic
479C2×#103C22×C4711yescharacteristic
480C2×#103C22×C4718yescomplemented
481C2×#102C22×C4711yescharacteristic
482C2×#102C22×C4711yescharacteristic
483C2×#102C22×C4711yescharacteristic
484C2×#102C22×C4711yescharacteristic
485C2×C22⋊C8C22×C4711yescharacteristic
486C2×C22⋊C8C22×C4711yescharacteristic
487C2×#97C22×C4711yescharacteristic
488C47C2×#330811yescharacteristic, direct product factor, Sylow
489C2×#41—28no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41—48no—
494C2×#41C23×C4714yes—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—22no—
498C22×Q8—24no—
499C22×Q8—42no—
500C22×Q8C23×C4711yescharacteristic
501C22×Q8C23×C4714yes—
502C22×Q8C23×C4711yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4D4×C4711yescharacteristic
508C22×D4C23×C4711yescharacteristic
509C22×D4C23×C4711yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C23×C4711yescharacteristic
516C23×C4C23×C4711yescharacteristic
517C2×SD16—24no—
518C2×SD16—42no—
519C2×SD16C23×C4714yes—
520C2×SD16C23×C4714yes—
521C2×D8—42no—
522C2×D8C23×C4714yes—
523C2×M16—42no—
524C2×M16C23×C4714yes—
525C22×C8—42no—
526C22×C8C23×C4711yescharacteristic
527C22×C8C23×C4711yescharacteristic
528C22×C8C23×C4711yescharacteristic
529C22×C8C23×C4711yescharacteristic
530C22×C8C23×C4714yes—
531C4⋊Q8—22no—
532C4⋊Q8C23×C4714yes—
533#124—28no—
534#124—22no—
535#124C23×C4714yes—
536#123—28no—
537#123—28no—
538C22⋊Q8—22no—
539C22⋊Q8—28no—
540C22⋊Q8—28no—
541C22⋊Q8C23×C4714yes—
542#121—28no—
543#121—22no—
544#121—22no—
545#121—22no—
546#121C23×C4714yes—
547#121C23×C4714yes—
548#121C23×C4714yes—
549C4×Q8—22no—
550C4×Q8C23×C4714yes—
551C4×D4—28no—
552C4×D4—22no—
553C4×D4D4×C4714yes—
554C4×D4C23×C4714yes—
555C4×D4C23×C4714yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C4711yescharacteristic
564C2×C4⋊C4C23×C4711yescharacteristic
565C2×C4⋊C4C23×C4711yescharacteristic
566C2×C4⋊C4C23×C4711yescharacteristic
567C2×C4⋊C4C23×C4714yes—
568C2×C4⋊C4C23×C4714yes—
569C2×C4⋊C4C23×C4711yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C4711yescharacteristic
578C2×C22⋊C4D4×C4711yescharacteristic
579C2×C42—21no—
580C2×C42C23×C4711yescharacteristic
581#107C23×C4714yes—
582#107C23×C4714yes—
583#107C23×C4714yes—
584C4⋊C8C23×C4714yes—
585#103C23×C4714yes—
586#103C23×C4714yes—
587#103C23×C4714yes—
588#103C23×C4714yes—
589#103C23×C4714yes—
590#103C23×C4714yes—
591#102C23×C4714yes—
592#102C23×C4714yes—
593#102C23×C4714yes—
594#102C23×C4714yes—
595C22⋊C8C23×C4714yes—
596C22⋊C8C23×C4714yes—
597#97C23×C4714yes—
598C24—21no—
599C24—21no—
600C24C2×D4×C4711yescharacteristic
601C24C2×D4×C4711yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—432no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—24no—
610C2×Q8—22no—
611C2×Q8—28no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—48no—
617C2×Q8—44no—
618C2×Q8#41×C4714yescomplemented
619C2×Q8C24×C4712yes—
620C2×Q8C24×C4712yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4C2×D4×C4714yes—
637C2×D4C24×C4712yes—
638C2×D4C24×C4712yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4C2×D4×C4711yescharacteristic
660C22×C4C2×D4×C4711yescharacteristic
661C22×C4C2×D4×C4711yescharacteristic
662C22×C4C2×D4×C4711yescharacteristic
663C22×C4C2×D4×C4712yes—
664C22×C4C2×D4×C4712yes—
665C22×C4C24×C4712yes—
666C22×C4C24×C4712yes—
667C22×C4C24×C4711yescharacteristic
668SD16—28no—
669SD16—44no—
670D8—44no—
671M16—44no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8C24×C4712yes—
678C2×C8C24×C4712yes—
679C2×C8C24×C4712yes—
680C2×C8C24×C4712yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4C2×D4×C4714yes—
691C4⋊C4C24×C4712yes—
692C4⋊C4C24×C4712yes—
693C4⋊C4C24×C4712yes—
694C4⋊C4C24×C4712yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4C2×D4×C4714yes—
703C22⋊C4C2×D4×C4714yes—
704C42—24no—
705C42C2×D4×C4712yes—
706C42C24×C4712yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23AGL(1,ℤ/8)×C4714yes—
721C23C22×D4×C4712yes—
722C23C22×D4×C4712yes—
723C23C22×D4×C4711yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—48no—
730Q8—42no—
731Q8C2×#41×C4714yescomplemented
732D4—28no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—48no—
738D4—48no—
739D4—48no—
740D4—48no—
741D4—42no—
742D4—42no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—48no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—48no—
769C2×C4—42no—
770C2×C4C22×D4×C4712yes—
771C2×C4C22×D4×C4712yes—
772C2×C4C22×D4×C4712yes—
773C2×C4C22×D4×C4712yes—
774C2×C4C22×D4×C4711yescharacteristic
775C2×C4C2×#41×C4712yes—
776C2×C4H(5,𝔽2)×C4712yes—
777C2×C4C25×C4711yescharacteristic
778C8—22no—
779C8—22no—
780C8—22no—
781C8—22no—
782C22—28no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—84no—
796C22—84no—
797C22C47×#54612yes—
798C22C2×AGL(1,ℤ/8)×C4714yes—
799C22C2×AGL(1,ℤ/8)×C4712yes—
800C22C47×#57812yes—
801C22C23×D4×C4711yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4C47×#54612yes—
813C4C22×#41×C4711yescharacteristic
814C4C2×H(5,𝔽2)×C4711yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—82no—
819C2C47×#330814yesdirect product factor
820C2C2×C47×#54611yescharacteristic
821C2C22×AGL(1,ℤ/8)×C4711yescharacteristic
822C2C2×C47×#57811yescharacteristic
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×#548C2semidirect
2. C2×C47×#547C2semidirect
3. C47×#3308C2direct (N × H)
4. C2×C47×#489C2semidirect
5. C2×C47×#484C2semidirect
6. C2×C47×#480C2semidirect
7. C2×C47×#477C2semidirect
8. C2×C47×#468C2semidirect
9. C2×C47×#466C2semidirect
10. C2×C47×#463C2semidirect
11. C2×C47×#449C2semidirect
12. C2×C47×#448C2semidirect
13. C2×C47×#440C2semidirect
14. C2×C47×#435C2semidirect
15. C2×C47×#417C2semidirect
16. C22×#103×C47C2semidirect
26. C47×#548C22semidirect
28. C47×#547C22semidirect
47. C47×#489C22semidirect
48. C47×#484C22semidirect
49. C47×#480C22semidirect
50. C47×#477C22semidirect
51. C47×#468C22semidirect
52. C47×#466C22semidirect
53. C47×#463C22semidirect
54. C47×#449C22semidirect
55. C47×#448C22semidirect
56. C47×#440C22semidirect
57. C47×#435C22semidirect
62. C47×#417C22semidirect
69. C2×#103×C47C22semidirect
206. C2×Q8×C47#41semidirect
319. Q8×C47C2×#41semidirect
370. C2×#3308C47direct (N × H)
404. C2×#548C2×C47semidirect
405. C2×#547C2×C47semidirect
406. #3308C2×C47direct (N × H)
407. C2×#489C2×C47semidirect
408. C2×#484C2×C47semidirect
409. C2×#480C2×C47semidirect
410. C2×#477C2×C47semidirect
411. C2×#468C2×C47semidirect
412. C2×#466C2×C47semidirect
413. C2×#463C2×C47semidirect
414. C2×#449C2×C47semidirect
415. C2×#448C2×C47semidirect
416. C2×#440C2×C47semidirect
417. C2×#435C2×C47semidirect
418. C2×#417C2×C47semidirect
419. C22×#103C2×C47semidirect
424. C2×C47#3308direct (N × H)
437. #548C22×C47semidirect
439. #547C22×C47semidirect
458. #489C22×C47semidirect
459. #484C22×C47semidirect
460. #480C22×C47semidirect
461. #477C22×C47semidirect
462. #468C22×C47semidirect
463. #466C22×C47semidirect
464. #463C22×C47semidirect
465. #449C22×C47semidirect
466. #448C22×C47semidirect
467. #440C22×C47semidirect
468. #435C22×C47semidirect
473. #417C22×C47semidirect
480. C2×#103C22×C47semidirect
488. C47C2×#3308direct (N × H)
618. C2×Q8#41×C47semidirect
731. Q8C2×#41×C47semidirect
819. C2C47×#3308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5482
C2×C47×#5472
C47×#33082
C2×C47×#4892
C2×C47×#4842
C2×C47×#4802
C2×C47×#4772
C2×C47×#4682
C2×C47×#4662
C2×C47×#4632
C2×C47×#4492
C2×C47×#4482
C2×C47×#4402
C2×C47×#4352
C2×C47×#4172
C22×#103×C472
C2×#330847