Finite Group Databasebeta

← #26138303

Subgroups — #26138303

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689010C212yesmaximal
2C2×#15688993C211yesmaximal, characteristic
3C2×C4⋊C4×Dic47C211yesmaximal, characteristic
4C2×C4×Dic47⋊C4C211yesmaximal, characteristic
5#20241644C212yesmaximal
6#20241642C212yesmaximal
7#20241622C212yesmaximal
8#20241617C211yesmaximal, characteristic
9#20241617C211yesmaximal, characteristic
10#20241617C211yesmaximal, characteristic
11C47×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2212yes—
15C22×C4⋊Dic47C2211yescharacteristic
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21#15689010—28no—
22#15688993—24no—
23C4⋊C4×Dic47—24no—
24C4×Dic47⋊C4C418yescomplemented
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C2×#95×C47C2212yes—
38C2×#95×C47C2212yes—
39C23×Dic47C2312yes—
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—24no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—24no—
54C2×C4⋊Dic47—42no—
55C2×C4⋊Dic47—42no—
56C2×C4⋊Dic47D414yes—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4C2×C414yes—
60C2×Dic47⋊C4C2×C414yes—
61C2×Dic47⋊C4D414yes—
62C2×Dic47⋊C4Q814yes—
63C2×C4×Dic47—22no—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—24no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—42no—
70C2×C4×Dic47C2×C414yes—
71C2×C4×Dic47C2×C414yes—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C47⋊#95—42no—
77C47⋊#95—42no—
78C47⋊#95—42no—
79C47⋊#95C2×C414yes—
80C47⋊#95C2×C414yes—
81C23×C4×C47C2312yes—
82C23×C4×C47C2312yes—
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47—22no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47Q814yes—
92C2×C42×C47—22no—
93C2×C42×C47—22no—
94C2×C42×C47C2×C414yes—
95#95×C47—24no—
96#95×C47—24no—
97C24×C47C2411yescharacteristic
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47C22×C412yes—
120C22×C4×C47C22×C412yes—
121C22×C4×C47C22×C412yes—
122C22×C4×C47C2×D412yes—
123C22×C4×C47C2×D412yes—
124C22×C4×C47C2×Q814yes—
125C22×C4×C47C2×Q812yes—
126C22×C4×C47C2×Q812yes—
127C22×C4×C47#4112yes—
128C22×C4×C47#4112yes—
129C22×C4×C47#4112yes—
130C22×C4×C47#4112yes—
131C22×C4×C47#4112yes—
132C22×C4×C47#4112yes—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47C22×C412yes—
167C22×Dic47C22×C412yes—
168C22×Dic47C22×C412yes—
169C22×Dic47C22×C412yes—
170C22×Dic47C2×D414yes—
171C22×Dic47C2×D412yes—
172C22×Dic47C2×D412yes—
173C22×Dic47C2×Q812yes—
174C22×Dic47C2×Q812yes—
175C4⋊C4×C47—28no—
176C4⋊C4×C47—44no—
177C42×C47—28no—
178C4⋊Dic47—28no—
179C4⋊Dic47—48no—
180C4⋊Dic47—48no—
181C4⋊Dic47—44no—
182Dic47⋊C4—28no—
183Dic47⋊C4C4⋊C4116yescomplemented
184C4×Dic47—28no—
185C4×Dic47—28no—
186C4×Dic47—48no—
187C23×C47C23×C411yescharacteristic
188C23×C47C22×D411yescharacteristic
189C23×C47C22×D411yescharacteristic
190C23×C47C22×Q811yescharacteristic
191C23×C47C22×Q811yescharacteristic
192C23×C47C2×#4111yescharacteristic
193C23×C47C2×#4111yescharacteristic
194C23×C47C2×#4111yescharacteristic
195C23×C47C2×#4111yescharacteristic
196C23×C47C2×#4111yescharacteristic
197C23×C47C2×#4111yescharacteristic
198C23×C47H(5,𝔽2)11yescharacteristic
199C23×C47H(5,𝔽2)11yescharacteristic
200C23×C472−1+411yescharacteristic
201C23×C472−1+411yescharacteristic
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47C2×C4⋊C414yes—
229C2×C4×C47#11714yes—
230C2×C4×C47#11714yes—
231C2×C4×C47C4×D414yes—
232C2×C4×C47C4×Q814yes—
233C2×C4×C47C22⋊Q814yes—
234C2×C4×C47#12314yes—
235C2×C4×C47#12514yes—
236C2×C4×C47#12614yes—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—24no—
256C2×Dic47—24no—
257C2×Dic47—24no—
258C2×Dic47—42no—
259C2×Dic47—41no—
260C2×Dic47—42no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—42no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277C2×Dic47C2×C4⋊C414yes—
278C2×Dic47C2×C4⋊C414yes—
279#13884—471nomaximal, Sylow
280C22×C47C22×C4⋊C411yescharacteristic
281C22×C47C2×#11711yescharacteristic
282C22×C47C2×#11711yescharacteristic
283C22×C47C2×C4×D411yescharacteristic
284C22×C47C2×C4×Q811yescharacteristic
285C22×C47#52011yescharacteristic
286C22×C47#52011yescharacteristic
287C22×C47C2×C22⋊Q811yescharacteristic
288C22×C47C2×#12311yescharacteristic
289C22×C47C2×#12511yescharacteristic
290C22×C47C2×#12611yescharacteristic
291C22×C47#53211yescharacteristic
292C22×C47#53211yescharacteristic
293C22×C47#53311yescharacteristic
294C22×C47#53311yescharacteristic
295C22×C47#54011yescharacteristic
296C22×C47#54111yescharacteristic
297C22×C47#54211yescharacteristic
298C22×C47#54211yescharacteristic
299C22×C47D4211yescharacteristic
300C22×C47#54611yescharacteristic
301C22×C47#54711yescharacteristic
302C22×C47#54811yescharacteristic
303C22×C47D4×Q811yescharacteristic
304C22×C47D4×Q811yescharacteristic
305C22×C47#55011yescharacteristic
306C22×C47#55211yescharacteristic
307C22×C47#55311yescharacteristic
308C22×C47#55411yescharacteristic
309C22×C47#55411yescharacteristic
310C22×C47#55611yescharacteristic
311C22×C47#55711yescharacteristic
312C22×C47#55711yescharacteristic
313C22×C47Q8211yescharacteristic
314C22×C47#55911yescharacteristic
315C4×C47—24no—
316C4×C47—24no—
317C4×C47—44no—
318C4×C47—82no—
319C4×C47#38718yescomplemented
320Dic47—24no—
321Dic47—24no—
322Dic47—42no—
323Dic47—42no—
324Dic47—44no—
325Dic47—82no—
326C2×#387—472no—
327C2×#384—471no—
328C2×C4×C4⋊C4—471no—
329C2×C4×C4⋊C4—471no—
330#1442—472no—
331#1441—472no—
332#1436—472no—
333C4⋊#95—471no—
334C4⋊#95—471no—
335C4⋊#95—471no—
336C4⋊#95D4711yescharacteristic
337C2×C47#228511yescharacteristic
338C2×C47C2×#38711yescharacteristic
339C2×C47#231411yescharacteristic
340C2×C47D4×C4⋊C411yescharacteristic
341C2×C47Q8×C4⋊C411yescharacteristic
342C2×C47#235211yescharacteristic
343C2×C47#235511yescharacteristic
344C2×C47#244511yescharacteristic
345C2×C47#244611yescharacteristic
346C2×C47#245111yescharacteristic
347C2×C47#245211yescharacteristic
348C2×C47#250611yescharacteristic
349C2×C47#250711yescharacteristic
350C2×C47#251111yescharacteristic
351C2×C47#251211yescharacteristic
352C22×C4⋊C4—471no—
353C22×C4⋊C4—471no—
354C22×C4⋊C4—471no—
355C22×C4⋊C4—471no—
356C22×C4⋊C4—472no—
357C22×C4⋊C4—472no—
358C22×C4⋊C4C2×D4711yescharacteristic
359C22×C4⋊C4C2×D4711yescharacteristic
360C22×C42—471no—
361C22×C42—471no—
362C22×C42—472no—
363C22×C42C2×D4711yescharacteristic
364#387—948no—
365#384—944no—
366C4×C4⋊C4—478no—
367C4×C4⋊C4—944no—
368C2×#95—471no—
369C2×#95—471no—
370C2×#95—472no—
371C2×#95—472no—
372C2×#95—472no—
373C2×#95—472no—
374C2×#95—472no—
375C2×#95—472no—
376C2×#95—472no—
377C2×#95C2×D4712yes—
378C2×#95C2×D4712yes—
379C47#1388411yescharacteristic, complemented, Sylow
380C23×C4—471no—
381C23×C4—471no—
382C23×C4—472no—
383C23×C4—471no—
384C23×C4—471no—
385C23×C4—472no—
386C23×C4C22×D4712yes—
387C23×C4C22×D4712yes—
388C23×C4C22×D4711yescharacteristic
389C23×C4C22×D4711yescharacteristic
390C23×C4C22×D4711yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—474no—
397C2×C4⋊C4—474no—
398C2×C4⋊C4—474no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—474no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—944no—
406C2×C4⋊C4—944no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—942no—
409C2×C4⋊C4—944no—
410C2×C4⋊C4—944no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—1882no—
413C2×C4⋊C4—1882no—
414C2×C4⋊C4Dic9414yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—474no—
418C2×C42—474no—
419C2×C42—942no—
420C2×C42—942no—
421C2×C42—942no—
422C2×C42—942no—
423C2×C42—944no—
424C2×C42—944no—
425C2×C42—1882no—
426C2×C42C4×D4714yes—
427#95—24no—
428#95—24no—
429#95—474no—
430#95—474no—
431#95—944no—
432#95—944no—
433#95—944no—
434#95—944no—
435#95—1882no—
436#95—1882no—
437#95—1882no—
438C24C23×D4711yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—472no—
461C22×C4—472no—
462C22×C4—472no—
463C22×C4—472no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—472no—
468C22×C4—474no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—941no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—942no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—942no—
483C22×C4—941no—
484C22×C4—942no—
485C22×C4—941no—
486C22×C4—942no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—941no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4C2×Dic9414yes—
503C22×C4C2×Dic9412yes—
504C22×C4C2×C4×D4712yes—
505C22×C4C2×C4×D4712yes—
506C22×C4C2×C4×D4712yes—
507C22×C4#1062535012yes—
508C22×C4D4×D4712yes—
509C22×C4D4×D4712yes—
510C22×C4#1062535212yes—
511C22×C4#1062535212yes—
512C22×C4#1062535212yes—
513C22×C4Q8×D4712yes—
514C22×C4#1062535412yes—
515C22×C4#1062535412yes—
516C4⋊C4—28no—
517C4⋊C4—44no—
518C4⋊C4—4716no—
519C4⋊C4—948no—
520C4⋊C4—948no—
521C4⋊C4—1888no—
522C4⋊C4—1888no—
523C4⋊C4—1884no—
524C42—28no—
525C42—948no—
526C42—948no—
527C42—1888no—
528C23C22×C4×D4711yescharacteristic
529C23C2×D4×D4711yescharacteristic
530C23C2×D4×D4711yescharacteristic
531C23C2×Q8×D4711yescharacteristic
532C23C22×Dic9411yescharacteristic
533C23C2×#1062535211yescharacteristic
534C23C2×#1062535211yescharacteristic
535C23C2×#1062535211yescharacteristic
536C23C2×#1062535011yescharacteristic
537C23C2×#1062535411yescharacteristic
538C23C2×#1062535411yescharacteristic
539C23#1309407011yescharacteristic
540C23#1309407011yescharacteristic
541C23#1309407111yescharacteristic
542C23#1309407111yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—474no—
570C2×C4—474no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—944no—
584C2×C4—944no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—942no—
588C2×C4—942no—
589C2×C4—942no—
590C2×C4—942no—
591C2×C4—944no—
592C2×C4—1882no—
593C2×C4—1882no—
594C2×C4—1882no—
595C2×C4—1882no—
596C2×C4—1882no—
597C2×C4—1882no—
598C2×C4—1882no—
599C2×C4—1882no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4—1881no—
604C2×C4—1881no—
605C2×C4—1881no—
606C2×C4—1882no—
607C2×C4—1881no—
608C2×C4—1881no—
609C2×C4—1882no—
610C2×C4—1882no—
611C2×C4C4⋊C4×D4714yes—
612C2×C4#1309398214yes—
613C2×C4#1309398214yes—
614C2×C4(C22⋊D47)⋊C414yes—
615C2×C4C4×Dic9414yes—
616C2×C4#1309400114yes—
617C2×C4#1309400914yes—
618C2×C4#1309401514yes—
619C2×C4#1309401714yes—
620C22C2×C4⋊C4×D4711yescharacteristic
621C22C2×#1309398211yescharacteristic
622C22C2×#1309398211yescharacteristic
623C22C2×(C22⋊D47)⋊C411yescharacteristic
624C22C2×C4×Dic9411yescharacteristic
625C22#1568960311yescharacteristic
626C22#1568960311yescharacteristic
627C22C2×#1309400111yescharacteristic
628C22C2×#1309400911yescharacteristic
629C22C2×#1309401511yescharacteristic
630C22C2×#1309401711yescharacteristic
631C22#1568967111yescharacteristic
632C22#1568967411yescharacteristic
633C22#1568967811yescharacteristic
634C22#1568967811yescharacteristic
635C22#1568972911yescharacteristic
636C22#1568973611yescharacteristic
637C22#1568974211yescharacteristic
638C22#1568974211yescharacteristic
639C22#1568975711yescharacteristic
640C22#1568976411yescharacteristic
641C22#1568977311yescharacteristic
642C22#1568977911yescharacteristic
643C22#1568978611yescharacteristic
644C22D4×Dic9411yescharacteristic
645C22#1568979411yescharacteristic
646C22#1568981511yescharacteristic
647C22#1568982511yescharacteristic
648C22#1568983011yescharacteristic
649C22#1568983111yescharacteristic
650C22#1568984311yescharacteristic
651C22#1568985111yescharacteristic
652C22#1568985211yescharacteristic
653C22Q8×Dic9411yescharacteristic
654C22#1568985811yescharacteristic
655C4—24no—
656C4—24no—
657C4—44no—
658C4—82no—
659C4—944no—
660C4—944no—
661C4—3762no—
662C4—1882no—
663C4—1884no—
664C4—1882no—
665C4#1568901018yescomplemented
666C2#2024579311yescharacteristic
667C2C2×#1568901011yescharacteristic
668C2#2024599811yescharacteristic
669C2#2024628411yescharacteristic
670C2C4⋊C4×Dic9411yescharacteristic
671C2#2024631911yescharacteristic
672C2#2024634311yescharacteristic
673C2#2024715511yescharacteristic
674C2#2024716611yescharacteristic
675C2#2024722911yescharacteristic
676C2#2024724011yescharacteristic
677C2#2024790611yescharacteristic
678C2#2024791711yescharacteristic
679C2#2024796511yescharacteristic
680C2#2024797611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C4⋊#95C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4⋊#95D47
hypocenterC47#13884
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
24. C4×Dic47⋊C4C4semidirect
183. Dic47⋊C4C4⋊C4semidirect
319. C4×C47#387semidirect
379. C47#13884semidirect
665. C4#15689010semidirect

Maximal subgroups

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

subgroupindex
C2×#156890102
C2×#156889932
C2×C4⋊C4×Dic472
C2×C4×Dic47⋊C42
#202416442
#202416422
#202416222
#202416172
C47×C4⋊#952
#1388447