Finite Group Databasebeta

← #26232501

Subgroups — #26232501

Order 12032.

1162 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689815C211yesmaximal, characteristic
2C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic
3#20246313C211yesmaximal, characteristic
4#20244351C211yesmaximal, characteristic, complemented
5#20244342C211yesmaximal, characteristic, complemented
6#20243812C211yesmaximal, characteristic, complemented
7#20243808C211yesmaximal, characteristic, complemented
8#20243697C211yesmaximal, characteristic, complemented
9#20243482C211yesmaximal, characteristic, complemented
10#20243475C211yesmaximal, characteristic, complemented
11#20243401C211yesmaximal, characteristic, complemented
12#103×Dic47C211yesmaximal, characteristic, complemented
13#20243103C211yesmaximal, characteristic, complemented
14C2×#15688885C211yesmaximal, characteristic, complemented
15C47×#1872C211yesmaximal, characteristic, complemented
16C23×C47⋊C8C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18#15689815—24no—
19#15689815C418yescomplemented
20C2×#13094019—21no—
21C2×#13094015—21no—
22C2×#13094015C2211yescharacteristic
23C2×#13094008—21no—
24C2×#13094000C2211yescharacteristic
25C2×Q8×Dic47C2211yescharacteristic
26C2×C4×C22⋊D47C2211yescharacteristic
27C2×#13093982C2211yescharacteristic
28C2×#13093982C2211yescharacteristic
29C2×#13093980—21no—
30C22×C4⋊Dic47C2211yescharacteristic
31(C22⋊D47)⋊C8—24no—
32C2×Dic47⋊C8C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×C8×Dic47C2211yescharacteristic
37#15689013—21no—
38#15689004—21no—
39#15689002—21no—
40#15688988C2211yescharacteristic
41#15688983C2211yescharacteristic
42#15688980C2211yescharacteristic
43C4⋊C4×Dic47C2211yescharacteristic
44C4×C22⋊Dic47—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C2×C22⋊Q8×C47C2211yescharacteristic
56C22×C4⋊C4×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×C22⋊D47D411yescharacteristic
63C23×Dic47—21no—
64C22×C4×D47C2311yescharacteristic
65C22×C47⋊C8—22no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—41no—
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C2×C8×D47—22no—
71C2×C8×D47—22no—
72C2×C8×D47—41no—
73#13094019—28no—
74#13094015—28no—
75#13094015—22no—
76#13094015C2×C414yescomplemented
77#13094008—28no—
78#13094000—22no—
79#13094000C2×C414yescomplemented
80Q8×Dic47—22no—
81Q8×Dic47C2×C414yescomplemented
82C4×C22⋊D47C2×C414yes—
83C4×C22⋊D47D414yes—
84#13093982—22no—
85#13093982—22no—
86#13093982—41no—
87#13093982C2×C414yescomplemented
88#13093980—28no—
89C2×C4⋊Dic47—22no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47C2×C414yes—
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×C4⋊Dic47C2311yescharacteristic
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4D411yescharacteristic
101C2×C22⋊Dic47—21no—
102C2×C22⋊Dic47D411yescharacteristic
103C2×(C2×D47)⋊C4—21no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4—21no—
106C2×(C2×D47)⋊C4—21no—
107C2×(C2×D47)⋊C4D411yescharacteristic
108C2×C4×Dic47—21no—
109C2×C4×Dic47—21no—
110C2×C4×Dic47—21no—
111C2×C4×Dic47—21no—
112C2×C4×Dic47C2311yescharacteristic
113Dic47⋊C8—22no—
114#13093948—22no—
115#13093948—41no—
116(C2×D47)⋊C8—22no—
117C8×Dic47—22no—
118C47⋊#95—21no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C22×Q8×C47C2311yescharacteristic
124C23×C4×C47—21no—
125C23×C4×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22⋊Q8×C47—22no—
129C22⋊Q8×C47C2×C414yes—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—22no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—41no—
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C22⋊C4×C47—21no—
138#103×C47—22no—
139#103×C47—41no—
140C22⋊C8×C47—22no—
141C24×C47C2×D411yescharacteristic
142C23×D47C2×D411yescharacteristic
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47C22×C412yes—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—42no—
158C22×C4×C47—42no—
159C22×C4×C47—81no—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2411yescharacteristic
164C2×C22⋊D47—22no—
165C2×C22⋊D47—22no—
166C2×C22⋊D47C22⋊C414yes—
167C22×Dic47—24no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—42no—
173C22×Dic47—42no—
174C22×Dic47C2×D411yescharacteristic
175C22×Dic47C2×D411yescharacteristic
176C22×Dic47C2×D411yescharacteristic
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47C22×C412yes—
182C2×C4×D47C2×D412yes—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C4⋊C4×C47—24no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—42no—
195C4⋊C4×C47C22×C412yes—
196C4⋊C4×C47#4112yes—
197C22⋊C4×C47—24no—
198C22⋊Dic47—42no—
199C22⋊Dic47C22⋊C414yes—
200(C2×D47)⋊C4—24no—
201(C2×D47)⋊C4—24no—
202(C2×D47)⋊C4—42no—
203(C2×D47)⋊C4—81no—
204(C2×D47)⋊C4C22⋊C414yes—
205C4⋊Dic47—24no—
206C4⋊Dic47—21no—
207C4⋊Dic47—21no—
208C4⋊Dic47—24no—
209C4⋊Dic47—24no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47C22×C412yes—
215C4⋊Dic47C22×C412yes—
216Dic47⋊C4—24no—
217Dic47⋊C4—24no—
218Dic47⋊C4C22⋊C414yes—
219C4×Dic47—24no—
220C4×Dic47—24no—
221C4×Dic47—42no—
222C4×Dic47—81no—
223C4×Dic47C22×C412yes—
224C4×Dic47C2×D412yes—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—44no—
231C2×C47⋊C8#4112yes—
232C8×D47—44no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47C2×C22⋊C412yes—
238C23×C47#13512yes—
239C23×C47#13512yes—
240C23×C47C22×D411yescharacteristic
241C22×D47—21no—
242C22×D47—21no—
243C22×D47—21no—
244C22×D47—21no—
245C22×D47—21no—
246C22×D47—21no—
247C22×D47C2×C22⋊C412yes—
248Q8×C47—22no—
249Q8×C47—22no—
250Q8×C47—41no—
251Q8×C47—41no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
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—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—84no—
271C2×C4×C47C2×C22⋊C412yes—
272C2×C4×C47C23×C411yescharacteristic
273C2×C4×C47C22×D411yescharacteristic
274C2×C4×C47C2×#4111yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×C4×C47H(5,𝔽2)11yescharacteristic
277C2×C4×C472−1+411yescharacteristic
278C22⋊D47—28no—
279C2×Dic47—21no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47—48no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47C2×C22⋊C412yes—
299C2×Dic47C2×C22⋊C412yes—
300C2×Dic47C2×C22⋊C412yes—
301C4×D47—22no—
302C4×D47—22no—
303C4×D47—22no—
304C4×D47—22no—
305C8×C47—41no—
306C8×C47—41no—
307C47⋊C8—22no—
308C47⋊C8—41no—
309#22486—471nomaximal, Sylow
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47#41614yes—
317C22×C47C22×C22⋊C411yescharacteristic
318C22×C47#54611yescharacteristic
319C22×C47#54711yescharacteristic
320C22×C47C2×#13511yescharacteristic
321C22×C47C2×#13511yescharacteristic
322C22×C47#57711yescharacteristic
323C22×C47#57811yescharacteristic
324C2×D47—22no—
325C2×D47—22no—
326C2×D47—22no—
327C2×D47—41no—
328C2×D47—41no—
329C2×D47—41no—
330C2×D47—41no—
331C4×C47—22no—
332C4×C47—42no—
333C4×C47—42no—
334C4×C47—42no—
335C4×C47—81no—
336C4×C47C4×#4111yescharacteristic
337C4×C47#52011yescharacteristic
338C4×C47#54611yescharacteristic
339C4×C47#54711yescharacteristic
340Dic47—22no—
341Dic47—22no—
342Dic47—22no—
343Dic47—42no—
344Dic47—42no—
345Dic47—81no—
346Dic47—81no—
347C2×#552—471no—
348C2×C8×D4—471no—
349#2352—471no—
350#1991—471no—
351#1989—471no—
352#1892—471no—
353#1892—471no—
354#1873—471no—
355#1872D4711yescharacteristic, complemented
356#1825—471no—
357#1823—471no—
358#1805—471no—
359C4×#103—471no—
360#1735—471no—
361C2×#340—471no—
362C2×C47—24no—
363C2×C47#233911yescharacteristic
364C2×C47C2×#41611yescharacteristic
365C2×C47#289811yescharacteristic
366C2×C47#329611yescharacteristic
367C2×C47#330011yescharacteristic
368C2×C47#333611yescharacteristic
369C2×C47#333711yescharacteristic
370D47—42no—
371C23×C8—471no—
372C23×C8—471no—
373#552—478no—
374#552—944no—
375C2×#126—941no—
376C2×#125—471no—
377C2×#125—941no—
378C2×#123—941no—
379C2×C22⋊Q8—471no—
380C2×C22⋊Q8C2×D4711yescharacteristic
381C2×C4×Q8—471no—
382C2×C4×D4—471no—
383C2×#117—471no—
384C2×#117—471no—
385C2×#117—941no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4C2×D4711yescharacteristic
388C8×D4—944no—
389C2×C4⋊C8—471no—
390C2×#103—471no—
391C2×#103—471no—
392C2×#103C2×D4711yescharacteristic
393C2×#103C2×D4711yescharacteristic
394C2×C22⋊C8—471no—
395C2×C22⋊C8C2×D4711yescharacteristic
396C2×C4×C8—471no—
397#388—941no—
398#387—941no—
399#386—941no—
400#382—471no—
401#380—471no—
402#380—471no—
403C4×C4⋊C4—471no—
404C4×C22⋊C4—941no—
405#340—471no—
406#340—471no—
407#340—471no—
408#340—471no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340C2×D4711yescharacteristic
416#340C2×D4711yescharacteristic
417C47#2248611yescharacteristic, complemented, Sylow
418C22×Q8C22×D4711yescharacteristic
419C22×D4—471no—
420C23×C4—21no—
421C23×C4—471no—
422C23×C4—941no—
423C23×C4C22×D4711yescharacteristic
424C22×C8—471no—
425C22×C8—471no—
426C22×C8—942no—
427C22×C8—942no—
428C22×C8—942no—
429C22×C8—942no—
430C22×C8—1881no—
431C22×C8—1881no—
432C22×C8C22×D4711yescharacteristic
433C22×C8C22×D4711yescharacteristic
434#126—948no—
435#125—474no—
436#125—942no—
437#125—948no—
438#123—948no—
439C22⋊Q8—22no—
440C22⋊Q8—474no—
441C22⋊Q8—942no—
442C22⋊Q8C4×D4714yes—
443C4×Q8—474no—
444C4×Q8—942no—
445C4×D4—474no—
446C4×D4—474no—
447#117—474no—
448#117—948no—
449#117—942no—
450#117—942no—
451#117—1881no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—474no—
458C2×C4⋊C4—471no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—941no—
463C2×C4⋊C4—941no—
464C2×C4⋊C4—941no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4—941no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4C22×D4711yescharacteristic
469C2×C4⋊C4C22×D4711yescharacteristic
470C2×C4⋊C4C22×D4711yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—471no—
473C2×C22⋊C4—471no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4—941no—
478C2×C22⋊C4—941no—
479C2×C42—471no—
480C2×C42—941no—
481C2×C42—941no—
482C2×C42—941no—
483C2×C42—941no—
484C4⋊C8—942no—
485#103—22no—
486#103—41no—
487#103—942no—
488#103—1881no—
489C22⋊C8—22no—
490C22⋊C8—942no—
491C4×C8—942no—
492#95—941no—
493#95—941no—
494#95—941no—
495#95—941no—
496#95—941no—
497C24—471no—
498C24D4×D4711yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C2×C4×D4712yes—
505C2×D4—474no—
506C2×D4—942no—
507C2×D4—942no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—471no—
520C22×C4—471no—
521C22×C4—471no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—941no—
525C22×C4—941no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—944no—
529C22×C4—941no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—1882no—
534C22×C4—1882no—
535C22×C4C2×C4×D4712yes—
536C22×C4D4×D4711yescharacteristic
537C22×C4D4×D4712yes—
538C22×C4C23×D4711yescharacteristic
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—472no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—1884no—
552C2×C8—1884no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—474no—
560C4⋊C4—472no—
561C4⋊C4—472no—
562C4⋊C4—944no—
563C4⋊C4—944no—
564C4⋊C4—944no—
565C4⋊C4—944no—
566C4⋊C4—944no—
567C4⋊C4—941no—
568C4⋊C4—941no—
569C4⋊C4—941no—
570C4⋊C4—941no—
571C4⋊C4—941no—
572C4⋊C4—941no—
573C4⋊C4C2×C4×D4712yes—
574C4⋊C4#1062535212yes—
575C22⋊C4—24no—
576C22⋊C4—474no—
577C22⋊C4—474no—
578C22⋊C4—944no—
579C22⋊C4—944no—
580C22⋊C4—3761no—
581C22⋊C4—1882no—
582C22⋊C4—1882no—
583C42—472no—
584C42—472no—
585C42—944no—
586C42—944no—
587C42—3761no—
588C42—1882no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—472no—
594C23—941no—
595C23—941no—
596C23—941no—
597C23—941no—
598C23—941no—
599C23—941no—
600C23C22⋊C4×D4712yes—
601C23#1309404512yes—
602C23#1309404712yes—
603C23C2×D4×D4711yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—948no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—84no—
628C2×C4—472no—
629C2×C4—472no—
630C2×C4—472no—
631C2×C4—941no—
632C2×C4—941no—
633C2×C4—941no—
634C2×C4—941no—
635C2×C4—941no—
636C2×C4—941no—
637C2×C4—942no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—1881no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1881no—
649C2×C4—1888no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4C22⋊C4×D4712yes—
655C2×C4C22×C4×D4711yescharacteristic
656C2×C4C2×D4×D4711yescharacteristic
657C2×C4#41×D4711yescharacteristic
658C2×C4C2×#1062535211yescharacteristic
659C2×C4#1309406911yescharacteristic
660C2×C4#1309407111yescharacteristic
661C8—41no—
662C8—41no—
663C8—942no—
664C8—1881no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—942no—
672C22—942no—
673C22—942no—
674C22—1881no—
675C22—1881no—
676C22—1881no—
677C22—1881no—
678C22#1568911814yes—
679C22C2×C22⋊C4×D4711yescharacteristic
680C22#1568976011yescharacteristic
681C22#1568977111yescharacteristic
682C22C2×#1309404511yescharacteristic
683C22C2×#1309404711yescharacteristic
684C22#1568993311yescharacteristic
685C22#1568993911yescharacteristic
686C4—22no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—942no—
692C4—942no—
693C4—942no—
694C4—3761no—
695C4—3761no—
696C4—1882no—
697C4—1882no—
698C4C4×#1062535211yescharacteristic
699C4#1568960211yescharacteristic
700C4#1568976211yescharacteristic
701C4#1568977311yescharacteristic
702C2—24no—
703C2—1882no—
704C2#2024621411yescharacteristic
705C2C2×#1568911811yescharacteristic
706C2#2025191911yescharacteristic
707C2#2025522711yescharacteristic
708C2#2025527911yescharacteristic
709C2#2025575411yescharacteristic
710C2#2025576511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1872C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
cosocleC22×C4×C47C24
hypercenter#1872D47
hypocenterC47#22486
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #20244351C2semidirect
5. #20244342C2semidirect
6. #20243812C2semidirect
7. #20243808C2semidirect
8. #20243697C2semidirect
9. #20243482C2semidirect
10. #20243475C2semidirect
11. #20243401C2semidirect
12. #103×Dic47C2semidirect
13. #20243103C2semidirect
14. C2×#15688885C2semidirect
15. C47×#1872C2semidirect
19. #15689815C4semidirect
76. #13094015C2×C4semidirect
79. #13094000C2×C4semidirect
81. Q8×Dic47C2×C4semidirect
87. #13093982C2×C4semidirect
355. #1872D47semidirect
417. C47#22486semidirect

Maximal subgroups

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

subgroupindex
C2×#156898152
C2×(C22⋊D47)⋊C82
#202463132
#202443512
#202443422
#202438122
#202438082
#202436972
#202434822
#202434752
#202434012
#103×Dic472
#202431032
C2×#156888852
C47×#18722
#2248647