Finite Group Databasebeta

← C2×#20251604 #26422506

Subgroups — C2×#20251604 #26422506

Order 12032.

2110 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251604C2116yesmaximal, direct product factor
2C2×#15689063C211yesmaximal, characteristic, complemented
3C2×#15689059C211yesmaximal, characteristic, complemented
4C2×#15689059C211yesmaximal, characteristic, complemented
5C2×#15689057C211yesmaximal, characteristic, complemented
6C2×#15689056C211yesmaximal, characteristic, complemented
7C2×#15689048C211yesmaximal, characteristic, complemented
8C2×#15689048C211yesmaximal, characteristic, complemented
9C2×#15689046C211yesmaximal, characteristic, complemented
10C2×#15689046C211yesmaximal, characteristic, complemented
11C2×#15689037C211yesmaximal, characteristic
12C2×#15689037C211yesmaximal, characteristic
13C2×#15689019C211yesmaximal, characteristic, complemented
14C2×#15689016C211yesmaximal, characteristic, complemented
15C2×#15689016C211yesmaximal, characteristic, complemented
16C2×C47×#394C211yesmaximal, characteristic
17C22×C4⋊Dic47C2211yescharacteristic
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×Dic47⋊C4C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36#15689063C2218yescomplemented
37#15689059C2218yescomplemented
38#15689059C2218yescomplemented
39#15689057C2218yescomplemented
40#15689056C2218yescomplemented
41#15689048C2218yescomplemented
42#15689048C2218yescomplemented
43#15689046C2218yescomplemented
44#15689046C2218yescomplemented
45#15689037C2218yes—
46#15689037C2218yes—
47#15689019C2218yescomplemented
48#15689016C2218yescomplemented
49#15689016C2218yescomplemented
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
59C23×D4×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#394C2218yes—
66C2×#95×C47C2211yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C2×C4⋊Dic47—24no—
76C2×C4⋊Dic47—42no—
77C2×C4⋊Dic47—42no—
78C2×C4⋊Dic47—42no—
79C2×C4⋊Dic47C2314yes—
80C2×C4⋊Dic47C2314yes—
81C2×C4⋊Dic47C2314yes—
82C2×C4⋊Dic47C2314yes—
83C2×Dic47⋊C4—42no—
84C2×Dic47⋊C4—42no—
85C2×Dic47⋊C4—42no—
86C2×Dic47⋊C4—42no—
87C2×Dic47⋊C4—42no—
88C2×Dic47⋊C4—42no—
89C2×Dic47⋊C4C2314yes—
90C2×Dic47⋊C4C2314yes—
91C2×Dic47⋊C4C2314yes—
92C2×Dic47⋊C4C2314yes—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×C22⋊Dic47—42no—
96C2×C22⋊Dic47—42no—
97C2×C22⋊Dic47—42no—
98C2×C22⋊Dic47—42no—
99C2×C22⋊Dic47—42no—
100C2×C22⋊Dic47—42no—
101C2×C22⋊Dic47—42no—
102C2×C22⋊Dic47—42no—
103C2×C22⋊Dic47C2314yes—
104C2×C22⋊Dic47C2314yes—
105C2×C22⋊Dic47C2314yes—
106C2×C22⋊Dic47C2314yes—
107C2×C22⋊Dic47C2314yes—
108C2×C22⋊Dic47C2314yes—
109C2×C22⋊Dic47C2314yes—
110C2×C22⋊Dic47C2314yes—
111C2×C4×Dic47—42no—
112C2×C4×Dic47C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C25×C47C2311yescharacteristic
123C25×C47C2311yescharacteristic
124C22×D4×C47—42no—
125C22×D4×C47—42no—
126C22×D4×C47—42no—
127C22×D4×C47C2314yes—
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47—42no—
134C2×C4⋊C4×C47C2314yes—
135C2×C22⋊C4×C47—24no—
136C2×C22⋊C4×C47—24no—
137C2×C22⋊C4×C47—42no—
138C2×C22⋊C4×C47—42no—
139C2×C22⋊C4×C47C2314yes—
140C2×C22⋊C4×C47C2314yes—
141C2×C22⋊C4×C47C2314yes—
142C2×C22⋊C4×C47C2314yes—
143#95×C47C2314yes—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47C2412yes—
159C24×C47C2412yes—
160C24×C47C2411yescharacteristic
161C2×D4×C47—44no—
162C2×D4×C47—44no—
163C2×D4×C47—44no—
164C2×D4×C47—416no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47#4114yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2412yes—
182C22×C4×C47C2412yes—
183C22×C4×C47C2412yes—
184C22×C4×C47C2412yes—
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×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C22×Dic47C2412yes—
216C22×Dic47C2412yes—
217C4⋊C4×C47—44no—
218C22⋊C4×C47—28no—
219C22⋊C4×C47—28no—
220C22⋊C4×C47—44no—
221C22⋊C4×C47—44no—
222C22⋊Dic47—44no—
223C22⋊Dic47—44no—
224C22⋊Dic47—44no—
225C22⋊Dic47—44no—
226C22⋊Dic47—44no—
227C22⋊Dic47—44no—
228C22⋊Dic47—44no—
229C22⋊Dic47—44no—
230C4⋊Dic47—28no—
231C4⋊Dic47—44no—
232C4⋊Dic47—44no—
233C4⋊Dic47—44no—
234Dic47⋊C4—44no—
235Dic47⋊C4—44no—
236Dic47⋊C4—44no—
237Dic47⋊C4—44no—
238Dic47⋊C4—44no—
239Dic47⋊C4—44no—
240C4×Dic47—44no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—44no—
256C23×C47—44no—
257C23×C47—44no—
258C23×C47—44no—
259C23×C47—44no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—44no—
267C23×C47—44no—
268C23×C47—44no—
269C23×C47C2×#4112yes—
270C23×C47H(5,𝔽2)12yes—
271C23×C47H(5,𝔽2)12yes—
272C23×C47H(5,𝔽2)12yes—
273C23×C47H(5,𝔽2)12yes—
274C23×C472−1+412yes—
275C23×C472−1+412yes—
276C23×C47C2511yescharacteristic
277D4×C47—416no—
278C2×C4×C47—28no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—44no—
294C2×C4×C47—44no—
295C2×C4×C47—44no—
296C2×C4×C47—44no—
297C2×C4×C47C2×#4114yes—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—44no—
323C2×Dic47—44no—
324C2×Dic47—44no—
325C2×Dic47—44no—
326C2×Dic47—44no—
327C2×Dic47—44no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C2×#2837—471nomaximal, Sylow
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—88no—
346C22×C47—88no—
347C22×C47#53914yes—
348C22×C47#54014yes—
349C22×C47#54214yes—
350C22×C47#56014yes—
351C22×C47#56214yes—
352C22×C47#56214yes—
353C22×C47#56314yes—
354C22×C47C22×#4111yescharacteristic
355C22×C47C2×H(5,𝔽2)11yescharacteristic
356C22×C47C2×H(5,𝔽2)11yescharacteristic
357C22×C47C2×H(5,𝔽2)11yescharacteristic
358C22×C47C2×H(5,𝔽2)11yescharacteristic
359C22×C47C2×2−1+411yescharacteristic
360C22×C47C2×2−1+411yescharacteristic
361C4×C47—24no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47—42no—
366Dic47—42no—
367Dic47—42no—
368Dic47—42no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372Dic47—42no—
373Dic47—42no—
374#2837—4716no—
375C2×#400—471no—
376C2×#399—471no—
377C2×#399—471no—
378C2×#398—471no—
379C2×#398—471no—
380C2×#397—471no—
381C2×#397—471no—
382C2×#396—471no—
383C2×#396—471no—
384C2×#394—471no—
385C2×#394—471no—
386C2×#394D4711yescharacteristic
387C2×#389—471no—
388C2×#388—471no—
389C2×#388—471no—
390C2×C47—82no—
391C2×C47—82no—
392C2×C47#283718yescomplemented
393C2×C47C2×#53911yescharacteristic
394C2×C47C2×#54011yescharacteristic
395C2×C47C2×#54211yescharacteristic
396C2×C47C2×#56011yescharacteristic
397C2×C47C2×#56211yescharacteristic
398C2×C47C2×#56211yescharacteristic
399C2×C47C2×#56311yescharacteristic
400C23×D4C2×D4711yescharacteristic
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—471no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4—471no—
407C22×C4⋊C4—471no—
408C22×C4⋊C4—471no—
409C22×C4⋊C4—471no—
410C22×C4⋊C4—471no—
411C22×C4⋊C4C2×D4711yescharacteristic
412C22×C22⋊C4—471no—
413C22×C22⋊C4—471no—
414C22×C22⋊C4—471no—
415C22×C22⋊C4—471no—
416C22×C22⋊C4—471no—
417C22×C22⋊C4—471no—
418C22×C22⋊C4—471no—
419C22×C22⋊C4—471no—
420C22×C22⋊C4C2×D4711yescharacteristic
421C22×C22⋊C4C2×D4711yescharacteristic
422C22×C22⋊C4C2×D4711yescharacteristic
423C22×C22⋊C4C2×D4711yescharacteristic
424C22×C42—471no—
425#400—478no—
426#399—478no—
427#399—478no—
428#398—478no—
429#398—478no—
430#397—478no—
431#397—478no—
432#396—478no—
433#396—478no—
434#394—478no—
435#394—478no—
436#394C2×D4718yes—
437#389—478no—
438#388—478no—
439#388—478no—
440C2×#95—471no—
441C2×#95—471no—
442C2×#95—471no—
443C2×#95—471no—
444C2×#95—471no—
445C2×#95—471no—
446C2×#95—471no—
447C2×#95—471no—
448C2×#95—471no—
449C2×#95C2×D4711yescharacteristic
450C47C2×#283711yescharacteristic, complemented, Sylow
451C25C22×D4711yescharacteristic
452C25C22×D4711yescharacteristic
453C22×D4—42no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4C22×D4714yes—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4C22×D4711yescharacteristic
466C23×C4C22×D4711yescharacteristic
467C23×C4C22×D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C2×C4⋊C4—42no—
471C2×C4⋊C4—474no—
472C2×C4⋊C4—474no—
473C2×C4⋊C4—474no—
474C2×C4⋊C4—474no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—474no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—474no—
479C2×C4⋊C4—474no—
480C2×C4⋊C4—474no—
481C2×C4⋊C4—944no—
482C2×C4⋊C4—1882no—
483C2×C4⋊C4—1882no—
484C2×C4⋊C4—1882no—
485C2×C4⋊C4—1882no—
486C2×C4⋊C4—1882no—
487C2×C4⋊C4—1882no—
488C2×C4⋊C4—1882no—
489C2×C4⋊C4—1882no—
490C2×C4⋊C4—1882no—
491C2×C4⋊C4C22×D4714yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—474no—
497C2×C22⋊C4—474no—
498C2×C22⋊C4—474no—
499C2×C22⋊C4—474no—
500C2×C22⋊C4—474no—
501C2×C22⋊C4—474no—
502C2×C22⋊C4—474no—
503C2×C22⋊C4—474no—
504C2×C22⋊C4—1882no—
505C2×C22⋊C4—1882no—
506C2×C22⋊C4—1882no—
507C2×C22⋊C4—1882no—
508C2×C22⋊C4—1882no—
509C2×C22⋊C4—1882no—
510C2×C22⋊C4—1882no—
511C2×C22⋊C4—1882no—
512C2×C22⋊C4C22×D4714yes—
513C2×C22⋊C4C22×D4714yes—
514C2×C22⋊C4C22×D4714yes—
515C2×C22⋊C4C22×D4714yes—
516C2×C42—474no—
517C2×C42—1882no—
518#95—474no—
519#95—474no—
520#95—474no—
521#95—474no—
522#95—474no—
523#95—474no—
524#95—474no—
525#95—474no—
526#95—474no—
527#95C22×D4714yes—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C23×D4712yes—
543C24C23×D4712yes—
544C24C23×D4711yescharacteristic
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—416no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—472no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—942no—
595C22×C4#1062535214yes—
596C22×C4C23×D4712yes—
597C22×C4C23×D4712yes—
598C22×C4C23×D4712yes—
599C22×C4C23×D4712yes—
600C22×C4C23×D4712yes—
601C4⋊C4—44no—
602C4⋊C4—948no—
603C4⋊C4—1884no—
604C4⋊C4—1884no—
605C4⋊C4—1884no—
606C4⋊C4—1884no—
607C4⋊C4—1884no—
608C4⋊C4—1884no—
609C4⋊C4—1884no—
610C4⋊C4—1884no—
611C4⋊C4—1884no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—1884no—
617C22⋊C4—1884no—
618C22⋊C4—1884no—
619C22⋊C4—1884no—
620C22⋊C4—1884no—
621C22⋊C4—1884no—
622C22⋊C4—1884no—
623C22⋊C4—1884no—
624C42—1884no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23C2×#1062535212yes—
654C23#1309406912yes—
655C23#1309406912yes—
656C23#1309406912yes—
657C23#1309407012yes—
658C23#1309407112yes—
659C23#1309407112yes—
660C23C24×D4711yescharacteristic
661D4—416no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—1884no—
706C2×C4—1884no—
707C2×C4—1884no—
708C2×C4—1884no—
709C2×C4—1884no—
710C2×C4—1884no—
711C2×C4—1884no—
712C2×C4—1884no—
713C2×C4C2×#1062535214yes—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—88no—
730C22#1568971814yes—
731C22#1568972614yes—
732C22#1568974014yes—
733C22#1568986214yes—
734C22#1568986714yes—
735C22#1568987014yes—
736C22#1568987614yes—
737C22C22×#1062535211yescharacteristic
738C22C2×#1309406911yescharacteristic
739C22C2×#1309406911yescharacteristic
740C22C2×#1309406911yescharacteristic
741C22C2×#1309407011yescharacteristic
742C22C2×#1309407111yescharacteristic
743C22C2×#1309407111yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—1882no—
750C4—1882no—
751C4—1882no—
752C4—1882no—
753C4—1882no—
754C4—1882no—
755C4—1882no—
756C4—1882no—
757C2—82no—
758C2—82no—
759C2#2025160418yesdirect product factor
760C2C2×#1568971811yescharacteristic
761C2C2×#1568972611yescharacteristic
762C2C2×#1568974011yescharacteristic
763C2C2×#1568986211yescharacteristic
764C2C2×#1568986711yescharacteristic
765C2C2×#1568987011yescharacteristic
766C2C2×#1568987611yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#394C2
socleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#394D47
hypocenterC47C2×#2837
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #20251604C2direct (N × H)
2. C2×#15689063C2semidirect
3. C2×#15689059C2semidirect
4. C2×#15689059C2semidirect
5. C2×#15689057C2semidirect
6. C2×#15689056C2semidirect
7. C2×#15689048C2semidirect
8. C2×#15689048C2semidirect
9. C2×#15689046C2semidirect
10. C2×#15689046C2semidirect
13. C2×#15689019C2semidirect
14. C2×#15689016C2semidirect
15. C2×#15689016C2semidirect
36. #15689063C22semidirect
37. #15689059C22semidirect
38. #15689059C22semidirect
39. #15689057C22semidirect
40. #15689056C22semidirect
41. #15689048C22semidirect
42. #15689048C22semidirect
43. #15689046C22semidirect
44. #15689046C22semidirect
47. #15689019C22semidirect
48. #15689016C22semidirect
49. #15689016C22semidirect
392. C2×C47#2837semidirect
450. C47C2×#2837semidirect
759. C2#20251604direct (N × H)

Maximal subgroups

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

subgroupindex
#202516042
C2×#156890632
C2×#156890592
C2×#156890572
C2×#156890562
C2×#156890482
C2×#156890462
C2×#156890372
C2×#156890192
C2×#156890162
C2×C47×#3942
C2×#283747