Finite Group Databasebeta

← C2×#20248200 #26385891

Subgroups — C2×#20248200 #26385891

Order 12032.

2074 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
1#20248200C2116yesmaximal, direct product factor
2C2×#15689062C211yesmaximal, characteristic, complemented
3C2×#15689050C211yesmaximal, characteristic
4C2×#15689045C211yesmaximal, characteristic
5C2×#15689022C211yesmaximal, characteristic, complemented
6C2×#15689015C211yesmaximal, characteristic
7C2×#15689015C211yesmaximal, characteristic
8C2×#15689013C211yesmaximal, characteristic
9C2×#15689013C211yesmaximal, characteristic
10C2×#15689013C211yesmaximal, characteristic
11C2×#15689010C211yesmaximal, characteristic, complemented
12C2×#15689008C211yesmaximal, characteristic, complemented
13C2×#15688988C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×#15688968C211yesmaximal, characteristic, complemented
16C2×C47×#398C211yesmaximal, characteristic, complemented
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34#15689062C2218yescomplemented
35#15689050C2218yes—
36#15689045C2218yes—
37#15689022C2218yescomplemented
38#15689015C2218yes—
39#15689015C2218yes—
40#15689013C2218yes—
41#15689013C2218yes—
42#15689013C2218yes—
43#15689010C2218yescomplemented
44#15689008C2218yescomplemented
45#15688988C2218yescomplemented
46C4⋊C4×Dic47C2218yescomplemented
47#15688968C2218yescomplemented
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C22×C4⋊C4×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C47×#398C2218yescomplemented
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C24×D47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C2×C4⋊Dic47—24no—
76C2×C4⋊Dic47—24no—
77C2×C4⋊Dic47—42no—
78C2×C4⋊Dic47—42no—
79C2×C4⋊Dic47C2314yes—
80C2×C4⋊Dic47C2314yes—
81C2×C4⋊Dic47C2314yes—
82C2×C4⋊Dic47C2314yes—
83C2×Dic47⋊C4—24no—
84C2×Dic47⋊C4C2314yes—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—24no—
89C2×(C2×D47)⋊C4—24no—
90C2×(C2×D47)⋊C4—42no—
91C2×(C2×D47)⋊C4—42no—
92C2×(C2×D47)⋊C4C2314yes—
93C2×(C2×D47)⋊C4C2314yes—
94C2×(C2×D47)⋊C4C2314yes—
95C2×(C2×D47)⋊C4C2314yes—
96C2×(C2×D47)⋊C4C2314yes—
97C2×(C2×D47)⋊C4C2314yes—
98C2×(C2×D47)⋊C4C2314yes—
99C2×C4×Dic47—24no—
100C2×C4×Dic47—24no—
101C2×C4×Dic47—24no—
102C2×C4×Dic47—24no—
103C2×C4×Dic47—24no—
104C2×C4×Dic47C2314yes—
105C2×C4×Dic47C2314yes—
106C2×C4×Dic47C2314yes—
107C2×C4×Dic47C2314yes—
108C2×C4×Dic47C2314yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C23×C4×C47C2311yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47—24no—
128C2×C4⋊C4×C47—24no—
129C2×C4⋊C4×C47—42no—
130C2×C4⋊C4×C47—42no—
131C2×C4⋊C4×C47C2314yes—
132C2×C4⋊C4×C47C2314yes—
133C2×C4⋊C4×C47C2314yes—
134C2×C4⋊C4×C47C2314yes—
135#95×C47C2314yes—
136#95×C47C2314yes—
137#95×C47C2314yes—
138C24×C47C2411yescharacteristic
139C23×D47—22no—
140C23×D47—22no—
141C23×D47—22no—
142C23×D47—22no—
143C23×D47—22no—
144C23×D47—22no—
145C23×D47—22no—
146C23×D47C2412yes—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47#4114yes—
166C22×C4×C47#4114yes—
167C22×C4×C47#4114yes—
168C22×C4×C47C2412yes—
169C22×C4×C47C2412yes—
170C22×C4×C47C2412yes—
171C22×C4×C47C2412yes—
172C22×C4×C47C2412yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47#4114yes—
195C22×Dic47#4114yes—
196C22×Dic47C2412yes—
197C22×Dic47C2412yes—
198C22×Dic47C2412yes—
199C22×Dic47C2412yes—
200C22×Dic47C2412yes—
201C22×Dic47C2412yes—
202C22×Dic47C2412yes—
203C4⋊C4×C47—28no—
204C4⋊C4×C47—28no—
205C4⋊C4×C47—44no—
206C4⋊C4×C47—44no—
207(C2×D47)⋊C4—28no—
208(C2×D47)⋊C4—28no—
209(C2×D47)⋊C4—28no—
210(C2×D47)⋊C4—28no—
211(C2×D47)⋊C4—28no—
212(C2×D47)⋊C4—44no—
213(C2×D47)⋊C4—44no—
214C4⋊Dic47—28no—
215C4⋊Dic47—28no—
216C4⋊Dic47—44no—
217C4⋊Dic47—44no—
218Dic47⋊C4—28no—
219C4×Dic47—28no—
220C4×Dic47—28no—
221C4×Dic47—28no—
222C4×Dic47—28no—
223C4×Dic47—28no—
224C23×C47C2×#4112yes—
225C23×C47C2×#4112yes—
226C23×C47C2×#4112yes—
227C23×C47C2×#4112yes—
228C23×C47C2×#4112yes—
229C23×C47H(5,𝔽2)12yes—
230C23×C472−1+412yes—
231C23×C47C2511yescharacteristic
232C22×D47—22no—
233C22×D47—22no—
234C22×D47—22no—
235C22×D47—22no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47—22no—
239C22×D47—44no—
240C22×D47—44no—
241C22×D47—44no—
242C22×D47—44no—
243C22×D47—44no—
244C22×D47—44no—
245C22×D47—44no—
246C2×C4×C47—28no—
247C2×C4×C47—28no—
248C2×C4×C47—28no—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
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—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—44no—
268C2×C4×C47—44no—
269C2×C4×C47—44no—
270C2×C4×C47—44no—
271C2×C4×C47C2×#4114yes—
272C2×C4×C47C2×#4114yes—
273C2×C4×C47C2×#4114yes—
274C2×Dic47—28no—
275C2×Dic47—28no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—44no—
296C2×Dic47—44no—
297C2×Dic47—44no—
298C2×Dic47—44no—
299C2×Dic47—44no—
300C2×Dic47C2×#4114yes—
301C2×Dic47C2×#4114yes—
302C2×#2529—471nomaximal, Sylow
303C22×C47#52914yes—
304C22×C47#52914yes—
305C22×C47#54214yes—
306C22×C47#55214yes—
307C22×C47#55214yes—
308C22×C47#55314yes—
309C22×C47#55514yes—
310C22×C47C22×#4111yescharacteristic
311C22×C47C22×#4111yescharacteristic
312C22×C47C22×#4111yescharacteristic
313C22×C47C22×#4111yescharacteristic
314C22×C47C22×#4111yescharacteristic
315C22×C47C2×H(5,𝔽2)11yescharacteristic
316C22×C47C2×2−1+411yescharacteristic
317C2×D47—42no—
318C2×D47—42no—
319C2×D47—42no—
320C2×D47—42no—
321C2×D47—42no—
322C2×D47—42no—
323C2×D47—42no—
324C2×D47—88no—
325C4×C47—24no—
326C4×C47—24no—
327C4×C47—24no—
328C4×C47—42no—
329C4×C47—42no—
330C4×C47—42no—
331C4×C47—42no—
332Dic47—24no—
333Dic47—24no—
334Dic47—42no—
335Dic47—42no—
336Dic47—42no—
337Dic47—42no—
338Dic47—42no—
339#2529—4716no—
340C2×#400—471no—
341C2×#398D4711yescharacteristic, complemented
342C2×#397—471no—
343C2×#396—471no—
344C2×#389—471no—
345C2×#388—471no—
346C2×#388—471no—
347C2×#388—471no—
348C2×#388—471no—
349C2×#388—471no—
350C2×#387—471no—
351C2×#387—471no—
352C2×#382—471no—
353C2×C4×C4⋊C4—471no—
354C2×#376—471no—
355C2×C47#252918yescomplemented
356C2×C47C2×#52911yescharacteristic
357C2×C47C2×#52911yescharacteristic
358C2×C47C2×#54211yescharacteristic
359C2×C47C2×#55211yescharacteristic
360C2×C47C2×#55211yescharacteristic
361C2×C47C2×#55311yescharacteristic
362C2×C47C2×#55511yescharacteristic
363D47—82no—
364C22×C4⋊C4—471no—
365C22×C4⋊C4—471no—
366C22×C4⋊C4—471no—
367C22×C4⋊C4—471no—
368C22×C4⋊C4—471no—
369C22×C4⋊C4C2×D4711yescharacteristic
370C22×C4⋊C4C2×D4711yescharacteristic
371C22×C4⋊C4C2×D4711yescharacteristic
372C22×C4⋊C4C2×D4711yescharacteristic
373C22×C22⋊C4—471no—
374C22×C22⋊C4—471no—
375C22×C22⋊C4—471no—
376C22×C22⋊C4—471no—
377C22×C22⋊C4—471no—
378C22×C22⋊C4—471no—
379C22×C22⋊C4—471no—
380C22×C42—471no—
381C22×C42—471no—
382C22×C42—471no—
383C22×C42—471no—
384C22×C42—471no—
385#400—478no—
386#398C2×D4718yescomplemented
387#397—478no—
388#396—478no—
389#389—478no—
390#388—478no—
391#388—478no—
392#388—478no—
393#388—478no—
394#388—478no—
395#387—478no—
396#387—478no—
397#382—478no—
398C4×C4⋊C4—478no—
399#376—478no—
400C2×#95—471no—
401C2×#95—471no—
402C2×#95—471no—
403C2×#95—471no—
404C2×#95—471no—
405C2×#95—471no—
406C2×#95—471no—
407C2×#95—471no—
408C2×#95—471no—
409C2×#95—471no—
410C2×#95—471no—
411C2×#95C2×D4711yescharacteristic
412C2×#95C2×D4711yescharacteristic
413C2×#95C2×D4711yescharacteristic
414C47C2×#252911yescharacteristic, complemented, Sylow
415C25—471no—
416C23×C4—471no—
417C23×C4—471no—
418C23×C4—471no—
419C23×C4—471no—
420C23×C4—471no—
421C23×C4—471no—
422C23×C4—471no—
423C23×C4C22×D4711yescharacteristic
424C23×C4C22×D4711yescharacteristic
425C23×C4C22×D4711yescharacteristic
426C23×C4C22×D4711yescharacteristic
427C23×C4C22×D4711yescharacteristic
428C23×C4C22×D4711yescharacteristic
429C23×C4C22×D4711yescharacteristic
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—474no—
435C2×C4⋊C4—474no—
436C2×C4⋊C4—474no—
437C2×C4⋊C4—474no—
438C2×C4⋊C4—474no—
439C2×C4⋊C4—944no—
440C2×C4⋊C4—944no—
441C2×C4⋊C4—944no—
442C2×C4⋊C4—1882no—
443C2×C4⋊C4—1882no—
444C2×C4⋊C4C22×D4714yes—
445C2×C4⋊C4C22×D4714yes—
446C2×C4⋊C4C22×D4714yes—
447C2×C4⋊C4C22×D4714yes—
448C2×C22⋊C4—474no—
449C2×C22⋊C4—474no—
450C2×C22⋊C4—474no—
451C2×C22⋊C4—474no—
452C2×C22⋊C4—474no—
453C2×C22⋊C4—474no—
454C2×C22⋊C4—474no—
455C2×C22⋊C4—944no—
456C2×C22⋊C4—944no—
457C2×C22⋊C4—944no—
458C2×C22⋊C4—944no—
459C2×C22⋊C4—944no—
460C2×C22⋊C4—1882no—
461C2×C22⋊C4—1882no—
462C2×C42—474no—
463C2×C42—474no—
464C2×C42—474no—
465C2×C42—474no—
466C2×C42—474no—
467C2×C42—944no—
468C2×C42—944no—
469C2×C42—944no—
470C2×C42—944no—
471C2×C42—944no—
472#95—474no—
473#95—474no—
474#95—474no—
475#95—474no—
476#95—474no—
477#95—474no—
478#95—474no—
479#95—474no—
480#95—474no—
481#95—474no—
482#95—474no—
483#95C22×D4714yes—
484#95C22×D4714yes—
485#95C22×D4714yes—
486C24—472no—
487C24—942no—
488C24—942no—
489C24—942no—
490C24—942no—
491C24—942no—
492C24—942no—
493C24—942no—
494C24C23×D4711yescharacteristic
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—474no—
514C22×C4—474no—
515C22×C4—472no—
516C22×C4—472no—
517C22×C4—472no—
518C22×C4—472no—
519C22×C4—472no—
520C22×C4—472no—
521C22×C4—472no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4—942no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4#1062535214yes—
542C22×C4#1062535414yes—
543C22×C4#1062535414yes—
544C22×C4C23×D4712yes—
545C22×C4C23×D4712yes—
546C22×C4C23×D4712yes—
547C22×C4C23×D4712yes—
548C22×C4C23×D4712yes—
549C22×C4C23×D4712yes—
550C22×C4C23×D4712yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—948no—
556C4⋊C4—948no—
557C4⋊C4—948no—
558C4⋊C4—1884no—
559C4⋊C4—1884no—
560C22⋊C4—948no—
561C22⋊C4—948no—
562C22⋊C4—948no—
563C22⋊C4—948no—
564C22⋊C4—948no—
565C22⋊C4—1884no—
566C22⋊C4—1884no—
567C42—948no—
568C42—948no—
569C42—948no—
570C42—948no—
571C42—948no—
572C23—942no—
573C23—942no—
574C23—942no—
575C23—942no—
576C23—942no—
577C23—942no—
578C23—942no—
579C23—1884no—
580C23—1884no—
581C23—1884no—
582C23—1884no—
583C23—1884no—
584C23—1884no—
585C23—1884no—
586C23#41×D4712yes—
587C23#41×D4712yes—
588C23C2×#1062535212yes—
589C23C2×#1062535412yes—
590C23C2×#1062535412yes—
591C23#1309406912yes—
592C23#1309407112yes—
593C23C24×D4711yescharacteristic
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—28no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—474no—
620C2×C4—474no—
621C2×C4—948no—
622C2×C4—948no—
623C2×C4—942no—
624C2×C4—942no—
625C2×C4—942no—
626C2×C4—942no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—942no—
630C2×C4—942no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—942no—
635C2×C4—942no—
636C2×C4—942no—
637C2×C4—942no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—1884no—
643C2×C4—1884no—
644C2×C4—1884no—
645C2×C4—1884no—
646C2×C4—1884no—
647C2×C4C2×#1062535214yes—
648C2×C4C2×#1062535414yes—
649C2×C4C2×#1062535414yes—
650C22—3768no—
651C22—1882no—
652C22—1882no—
653C22—1882no—
654C22—1882no—
655C22—1882no—
656C22—1882no—
657C22—1882no—
658C22#1568965814yes—
659C22#1568965914yes—
660C22#1568974114yes—
661C22#1568981114yes—
662C22#1568981514yes—
663C22#1568981614yes—
664C22#1568983914yes—
665C22C2×#41×D4711yescharacteristic
666C22C2×#41×D4711yescharacteristic
667C22C22×#1062535211yescharacteristic
668C22C22×#1062535411yescharacteristic
669C22C22×#1062535411yescharacteristic
670C22C2×#1309406911yescharacteristic
671C22C2×#1309407111yescharacteristic
672C4—24no—
673C4—24no—
674C4—24no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—944no—
680C4—944no—
681C4—1882no—
682C4—1882no—
683C4—1882no—
684C4—1882no—
685C4—1882no—
686C2—3762no—
687C2#2024820018yesdirect product factor
688C2C2×#1568965811yescharacteristic
689C2C2×#1568965911yescharacteristic
690C2C2×#1568974111yescharacteristic
691C2C2×#1568981111yescharacteristic
692C2C2×#1568981511yescharacteristic
693C2C2×#1568981611yescharacteristic
694C2C2×#1568983911yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#398C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#398D47
hypocenterC47C2×#2529
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #20248200C2direct (N × H)
2. C2×#15689062C2semidirect
5. C2×#15689022C2semidirect
11. C2×#15689010C2semidirect
12. C2×#15689008C2semidirect
13. C2×#15688988C2semidirect
14. C2×C4⋊C4×Dic47C2semidirect
15. C2×#15688968C2semidirect
16. C2×C47×#398C2semidirect
34. #15689062C22semidirect
37. #15689022C22semidirect
43. #15689010C22semidirect
44. #15689008C22semidirect
45. #15688988C22semidirect
46. C4⋊C4×Dic47C22semidirect
47. #15688968C22semidirect
63. C47×#398C22semidirect
341. C2×#398D47semidirect
355. C2×C47#2529semidirect
386. #398C2×D47semidirect
414. C47C2×#2529semidirect
687. C2#20248200direct (N × H)

Maximal subgroups

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

subgroupindex
#202482002
C2×#156890622
C2×#156890502
C2×#156890452
C2×#156890222
C2×#156890152
C2×#156890132
C2×#156890102
C2×#156890082
C2×#156889882
C2×C4⋊C4×Dic472
C2×#156889682
C2×C47×#3982
C2×#252947