Finite Group Databasebeta

← C2×#20251542 #26422631

Subgroups — C2×#20251542 #26422631

Order 12032.

1914 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251542C2116yesmaximal, direct product factor
2C2×#15689065C211yesmaximal, characteristic, complemented
3C2×#15689065C211yesmaximal, characteristic, complemented
4C2×#15689064C211yesmaximal, characteristic, complemented
5C2×#15689055C211yesmaximal, characteristic, complemented
6C2×#15689054C211yesmaximal, characteristic, complemented
7C2×#15689052C211yesmaximal, characteristic
8C2×#15689052C211yesmaximal, characteristic
9C2×#15689050C211yesmaximal, characteristic
10C2×#15689045C211yesmaximal, characteristic
11C2×#15689045C211yesmaximal, characteristic
12C2×#15689043C211yesmaximal, characteristic, complemented
13C2×#15689036C211yesmaximal, characteristic
14C2×#15689029C211yesmaximal, characteristic, complemented
15C2×#15689014C211yesmaximal, characteristic
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33#15689065C2218yescomplemented
34#15689065C2218yescomplemented
35#15689064C2218yescomplemented
36#15689055C2218yescomplemented
37#15689054C2218yescomplemented
38#15689052C2218yes—
39#15689052C2218yes—
40#15689050C2218yes—
41#15689045C2218yes—
42#15689045C2218yes—
43#15689043C2218yescomplemented
44#15689036C2218yes—
45#15689029C2218yescomplemented
46#15689014C2218yes—
47C2×C47⋊#95C2211yescharacteristic
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×C42×C47C2211yescharacteristic
62C47×#387C2218yescomplemented
63C2×#95×C47C2211yescharacteristic
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C24×D47C2311yescharacteristic
68C22×Dic94—24no—
69C22×Dic94—42no—
70C22×Dic94—42no—
71C22×Dic94C2314yes—
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C2×C4⋊Dic47—42no—
80C2×C4⋊Dic47—42no—
81C2×C4⋊Dic47—42no—
82C2×C4⋊Dic47C2314yes—
83C2×C4⋊Dic47C2314yes—
84C2×C4⋊Dic47C2314yes—
85C2×Dic47⋊C4—42no—
86C2×Dic47⋊C4—42no—
87C2×Dic47⋊C4—42no—
88C2×Dic47⋊C4—42no—
89C2×Dic47⋊C4—42no—
90C2×Dic47⋊C4C2314yes—
91C2×Dic47⋊C4C2314yes—
92C2×Dic47⋊C4C2314yes—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×(C2×D47)⋊C4—24no—
96C2×(C2×D47)⋊C4—42no—
97C2×(C2×D47)⋊C4—42no—
98C2×(C2×D47)⋊C4—42no—
99C2×(C2×D47)⋊C4—42no—
100C2×(C2×D47)⋊C4—42no—
101C2×(C2×D47)⋊C4—42no—
102C2×(C2×D47)⋊C4C2314yes—
103C2×(C2×D47)⋊C4C2314yes—
104C2×(C2×D47)⋊C4C2314yes—
105C2×(C2×D47)⋊C4C2314yes—
106C2×(C2×D47)⋊C4C2314yes—
107C2×(C2×D47)⋊C4C2314yes—
108C2×(C2×D47)⋊C4C2314yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47—24no—
129C2×C4⋊C4×C47—42no—
130C2×C4⋊C4×C47C2314yes—
131C2×C4⋊C4×C47C2314yes—
132C2×C42×C47—42no—
133C2×C42×C47C2314yes—
134#95×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—22no—
166C22×C4×C47—22no—
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—22no—
195C22×Dic47—22no—
196C22×Dic47C2412yes—
197C22×Dic47C2412yes—
198C22×Dic47C2412yes—
199C22×Dic47C2412yes—
200C22×Dic47C2412yes—
201C22×Dic47C2412yes—
202C22×Dic47C2412yes—
203C2×Dic94—28no—
204C2×Dic94—44no—
205C2×Dic94—44no—
206C2×Dic94—416no—
207C4⋊C4×C47—28no—
208C4⋊C4×C47—44no—
209C42×C47—44no—
210(C2×D47)⋊C4—28no—
211(C2×D47)⋊C4—44no—
212(C2×D47)⋊C4—44no—
213(C2×D47)⋊C4—44no—
214(C2×D47)⋊C4—44no—
215(C2×D47)⋊C4—44no—
216(C2×D47)⋊C4—44no—
217C4⋊Dic47—44no—
218C4⋊Dic47—44no—
219C4⋊Dic47—44no—
220Dic47⋊C4—44no—
221Dic47⋊C4—44no—
222Dic47⋊C4—44no—
223Dic47⋊C4—44no—
224Dic47⋊C4—44no—
225C23×C47C2×#4112yes—
226C23×C47H(5,𝔽2)12yes—
227C23×C47H(5,𝔽2)12yes—
228C23×C47H(5,𝔽2)12yes—
229C23×C472−1+412yes—
230C23×C472−1+412yes—
231C23×C472−1+412yes—
232C23×C47C2511yescharacteristic
233C22×D47—22no—
234C22×D47—22no—
235C22×D47—22no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—44no—
241C22×D47—44no—
242C22×D47—44no—
243C22×D47—44no—
244C22×D47—44no—
245C22×D47—44no—
246C22×D47—44no—
247C2×C4×C47—28no—
248C2×C4×C47—22no—
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—22no—
268C2×C4×C47—44no—
269C2×C4×C47—44no—
270C2×C4×C47—44no—
271C2×C4×C47—44no—
272C2×C4×C47—44no—
273C2×C4×C47—44no—
274C2×C4×C47C2×#4114yes—
275C2×Dic47—22no—
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—22no—
296C2×Dic47—44no—
297C2×Dic47—44no—
298C2×Dic47—44no—
299C2×Dic47—44no—
300C2×Dic47—44no—
301C2×Dic47—44no—
302C2×Dic47—44no—
303Dic94—416no—
304C2×#2831—471nomaximal, Sylow
305C22×C47#53814yes—
306C22×C47#54114yes—
307C22×C47#54214yes—
308C22×C47#56214yes—
309C22×C47#56214yes—
310C22×C47#56314yes—
311C22×C47#56314yes—
312C22×C47C22×#4111yescharacteristic
313C22×C47C2×H(5,𝔽2)11yescharacteristic
314C22×C47C2×H(5,𝔽2)11yescharacteristic
315C22×C47C2×H(5,𝔽2)11yescharacteristic
316C22×C47C2×2−1+411yescharacteristic
317C22×C47C2×2−1+411yescharacteristic
318C22×C47C2×2−1+411yescharacteristic
319C2×D47—42no—
320C2×D47—42no—
321C2×D47—42no—
322C2×D47—42no—
323C2×D47—42no—
324C2×D47—42no—
325C2×D47—42no—
326C2×D47—88no—
327C4×C47—24no—
328C4×C47—42no—
329C4×C47—42no—
330C4×C47—42no—
331C4×C47—42no—
332C4×C47—42no—
333C4×C47—42no—
334Dic47—42no—
335Dic47—42no—
336Dic47—42no—
337Dic47—42no—
338Dic47—42no—
339Dic47—42no—
340Dic47—42no—
341#2831—4716no—
342C2×#400—471no—
343C2×#400—471no—
344C2×#400—471no—
345C2×#398—471no—
346C2×#398—471no—
347C2×#397—471no—
348C2×#397—471no—
349C2×#397—471no—
350C2×#396—471no—
351C2×#396—471no—
352C2×#395—471no—
353C2×#393—471no—
354C2×#391—471no—
355C2×#388—471no—
356C2×#387D4711yescharacteristic, complemented
357C2×C47#283118yescomplemented
358C2×C47C2×#53811yescharacteristic
359C2×C47C2×#54111yescharacteristic
360C2×C47C2×#54211yescharacteristic
361C2×C47C2×#56211yescharacteristic
362C2×C47C2×#56211yescharacteristic
363C2×C47C2×#56311yescharacteristic
364C2×C47C2×#56311yescharacteristic
365D47—82no—
366C23×Q8—471no—
367C22×C4⋊C4—471no—
368C22×C4⋊C4—471no—
369C22×C4⋊C4—471no—
370C22×C4⋊C4—471no—
371C22×C4⋊C4—471no—
372C22×C4⋊C4—471no—
373C22×C4⋊C4—471no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4C2×D4711yescharacteristic
376C22×C4⋊C4C2×D4711yescharacteristic
377C22×C22⋊C4—471no—
378C22×C22⋊C4—471no—
379C22×C22⋊C4—471no—
380C22×C22⋊C4—471no—
381C22×C22⋊C4—471no—
382C22×C22⋊C4—471no—
383C22×C22⋊C4—471no—
384C22×C42C2×D4711yescharacteristic
385#400—478no—
386#400—478no—
387#400—478no—
388#398—478no—
389#398—478no—
390#397—478no—
391#397—478no—
392#397—478no—
393#396—478no—
394#396—478no—
395#395—478no—
396#393—478no—
397#391—478no—
398#388—478no—
399#387C2×D4718yescomplemented
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×#95—471no—
412C2×#95C2×D4711yescharacteristic
413C2×#95C2×D4711yescharacteristic
414C2×#95C2×D4711yescharacteristic
415C2×#95C2×D4711yescharacteristic
416C47C2×#283111yescharacteristic, complemented, Sylow
417C25—471no—
418C22×Q8—474no—
419C22×Q8—944no—
420C22×Q8—1882no—
421C22×Q8—1882no—
422C23×C4—471no—
423C23×C4—471no—
424C23×C4—471no—
425C23×C4—471no—
426C23×C4—471no—
427C23×C4—471no—
428C23×C4—471no—
429C23×C4C22×D4711yescharacteristic
430C23×C4C22×D4711yescharacteristic
431C23×C4C22×D4711yescharacteristic
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4711yescharacteristic
434C23×C4C22×D4711yescharacteristic
435C23×C4C22×D4711yescharacteristic
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—474no—
439C2×C4⋊C4—474no—
440C2×C4⋊C4—474no—
441C2×C4⋊C4—474no—
442C2×C4⋊C4—474no—
443C2×C4⋊C4—474no—
444C2×C4⋊C4—474no—
445C2×C4⋊C4—474no—
446C2×C4⋊C4—1882no—
447C2×C4⋊C4—1882no—
448C2×C4⋊C4—1882no—
449C2×C4⋊C4—1882no—
450C2×C4⋊C4—1882no—
451C2×C4⋊C4—1882no—
452C2×C4⋊C4—1882no—
453C2×C4⋊C4—1882no—
454C2×C4⋊C4C22×D4714yes—
455C2×C4⋊C4C22×D4714yes—
456C2×C22⋊C4—474no—
457C2×C22⋊C4—474no—
458C2×C22⋊C4—474no—
459C2×C22⋊C4—474no—
460C2×C22⋊C4—474no—
461C2×C22⋊C4—474no—
462C2×C22⋊C4—474no—
463C2×C22⋊C4—944no—
464C2×C22⋊C4—1882no—
465C2×C22⋊C4—1882no—
466C2×C22⋊C4—1882no—
467C2×C22⋊C4—1882no—
468C2×C22⋊C4—1882no—
469C2×C22⋊C4—1882no—
470C2×C42—42no—
471C2×C42C22×D4714yes—
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#95—474no—
484#95C22×D4714yes—
485#95C22×D4714yes—
486#95C22×D4714yes—
487#95C22×D4714yes—
488C24—472no—
489C24—942no—
490C24—942no—
491C24—942no—
492C24—942no—
493C24—942no—
494C24—942no—
495C24—942no—
496C24C23×D4711yescharacteristic
497C2×Q8—948no—
498C2×Q8—1884no—
499C2×Q8—1884no—
500C2×Q8—18816no—
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—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—472no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—472no—
525C22×C4—472no—
526C22×C4—472no—
527C22×C4—472no—
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—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4#1062535014yes—
550C22×C4C23×D4712yes—
551C22×C4C23×D4712yes—
552C22×C4C23×D4712yes—
553C22×C4C23×D4712yes—
554C22×C4C23×D4712yes—
555C22×C4C23×D4712yes—
556C22×C4C23×D4712yes—
557C4⋊C4—28no—
558C4⋊C4—44no—
559C4⋊C4—1884no—
560C4⋊C4—1884no—
561C4⋊C4—1884no—
562C4⋊C4—1884no—
563C4⋊C4—1884no—
564C4⋊C4—1884no—
565C4⋊C4—1884no—
566C4⋊C4—1884no—
567C22⋊C4—948no—
568C22⋊C4—1884no—
569C22⋊C4—1884no—
570C22⋊C4—1884no—
571C22⋊C4—1884no—
572C22⋊C4—1884no—
573C22⋊C4—1884no—
574C42—44no—
575C23—942no—
576C23—942no—
577C23—942no—
578C23—942no—
579C23—942no—
580C23—942no—
581C23—942no—
582C23—1884no—
583C23—1884no—
584C23—1884no—
585C23—1884no—
586C23—1884no—
587C23—1884no—
588C23—1884no—
589C23C2×#1062535012yes—
590C23#1309406912yes—
591C23#1309407012yes—
592C23#1309407012yes—
593C23#1309407112yes—
594C23#1309407112yes—
595C23#1309407212yes—
596C23C24×D4711yescharacteristic
597Q8—18816no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
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—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
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—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—1884no—
647C2×C4—1884no—
648C2×C4—1884no—
649C2×C4—1884no—
650C2×C4—1884no—
651C2×C4—1884no—
652C2×C4—1884no—
653C2×C4C2×#1062535014yes—
654C22—3768no—
655C22—1882no—
656C22—1882no—
657C22—1882no—
658C22—1882no—
659C22—1882no—
660C22—1882no—
661C22—1882no—
662C22#1568970614yes—
663C22#1568973114yes—
664C22#1568974414yes—
665C22#1568987014yes—
666C22#1568987114yes—
667C22#1568987414yes—
668C22#1568987514yes—
669C22C22×#1062535011yescharacteristic
670C22C2×#1309406911yescharacteristic
671C22C2×#1309407011yescharacteristic
672C22C2×#1309407011yescharacteristic
673C22C2×#1309407111yescharacteristic
674C22C2×#1309407111yescharacteristic
675C22C2×#1309407211yescharacteristic
676C4—24no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—1882no—
684C4—1882no—
685C4—1882no—
686C4—1882no—
687C4—1882no—
688C4—1882no—
689C4—1882no—
690C2—3762no—
691C2#2025154218yesdirect product factor
692C2C2×#1568970611yescharacteristic
693C2C2×#1568973111yescharacteristic
694C2C2×#1568974411yescharacteristic
695C2C2×#1568987011yescharacteristic
696C2C2×#1568987111yescharacteristic
697C2C2×#1568987411yescharacteristic
698C2C2×#1568987511yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#387D47
hypocenterC47C2×#2831
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #20251542C2direct (N × H)
2. C2×#15689065C2semidirect
3. C2×#15689065C2semidirect
4. C2×#15689064C2semidirect
5. C2×#15689055C2semidirect
6. C2×#15689054C2semidirect
12. C2×#15689043C2semidirect
14. C2×#15689029C2semidirect
16. C2×C47×#387C2semidirect
33. #15689065C22semidirect
34. #15689065C22semidirect
35. #15689064C22semidirect
36. #15689055C22semidirect
37. #15689054C22semidirect
43. #15689043C22semidirect
45. #15689029C22semidirect
62. C47×#387C22semidirect
356. C2×#387D47semidirect
357. C2×C47#2831semidirect
399. #387C2×D47semidirect
416. C47C2×#2831semidirect
691. C2#20251542direct (N × H)

Maximal subgroups

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

subgroupindex
#202515422
C2×#156890652
C2×#156890642
C2×#156890552
C2×#156890542
C2×#156890522
C2×#156890502
C2×#156890452
C2×#156890432
C2×#156890362
C2×#156890292
C2×#156890142
C2×C47×#3872
C2×#283147