Finite Group Databasebeta

← D47×#1802 #26215721

Subgroups — D47×#1802 #26215721

Order 12032.

2030 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
3C2×#102×D47C212yesmaximal
4#384×D47C211yesmaximal, characteristic, complemented
5#20243389C211yesmaximal, characteristic, complemented
6#20243388C211yesmaximal, characteristic, complemented
7#20243387C212yesmaximal, complemented
8#20243386C212yesmaximal, complemented
9#20243385C211yesmaximal, characteristic, complemented
10#340×D47C212yesmaximal, complemented
11C47×#1802C211yesmaximal, characteristic, complemented
12C22×D4×D47C2211yescharacteristic
13C23×C4×D47—21no—
14C22×C8×D47C2212yes—
15C2×C4×D188C2211yescharacteristic
16C2×D4×Dic47C2211yescharacteristic
17C2×#13093986C2211yescharacteristic
18C2×C4×C22⋊D47—21no—
19C2×(C22⋊D47)⋊C4—21no—
20C4×D4×D47—24no—
21C4×D4×D47C418yescomplemented
22C2×C4⋊C4×D47—21no—
23C2×C4⋊C4×D47—21no—
24C2×C4⋊C4×D47C2212yes—
25C2×C4⋊C4×D47C2211yescharacteristic
26C2×C22⋊C4×D47—21no—
27C2×C42×D47C2211yescharacteristic
28C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
29C2×Dic47⋊C8C2212yescomplemented
30C4⋊C8×D47—24no—
31C2×#13093946C2212yes—
32C2×#13093945C2212yes—
33C2×#13093944C2212yes—
34#102×D47—28no—
35#15688993C2211yescharacteristic, complemented
36#15688992—21no—
37#15688992—21no—
38#15688992C2212yescomplemented
39#15688886C2212yescomplemented
40#15688885C2212yescomplemented
41#15688885C2212yescomplemented
42C2×C4×D4×C47C2211yescharacteristic
43C2×C4⋊C8×C47C2211yescharacteristic, complemented
44C2×#102×C47C2212yes—
45C47×#384C2211yescharacteristic, complemented
46C47×#340C2212yescomplemented
47C24×D47—21no—
48C22×D188C2311yescharacteristic
49C22×C22⋊D47—21no—
50C2×D4×D47—22no—
51C2×D4×D47—22no—
52C2×D4×D47—22no—
53C2×D4×D47C2×C414yes—
54C2×D4×D47D414yes—
55C2×D4×D47Q814yes—
56C23×Dic47—21no—
57C22×C4×D47—21no—
58C22×C4×D47—21no—
59C22×C4×D47—21no—
60C22×C4×D47—28no—
61C22×C4×D47—22no—
62C22×C4×D47—44no—
63C22×C4×D47—44no—
64C22×C4×D47D411yescharacteristic
65C22×C4×D47D411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C47⋊C8C2312yes—
68C2×C8×D47—24no—
69C2×C8×D47—24no—
70C2×C8×D47—24no—
71C4×D188—22no—
72C4×D188C2×C414yescomplemented
73D4×Dic47—22no—
74D4×Dic47C2×C414yescomplemented
75#13093986—22no—
76#13093986C2×C414yescomplemented
77C4×C22⋊D47—28no—
78(C22⋊D47)⋊C4—28no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47C2312yes—
82C2×C4⋊Dic47C2311yescharacteristic
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—22no—
85C2×Dic47⋊C4—22no—
86C2×Dic47⋊C4—22no—
87C4⋊C4×D47—22no—
88C4⋊C4×D47—24no—
89C4⋊C4×D47—24no—
90C4⋊C4×D47—44no—
91C4⋊C4×D47—44no—
92C4⋊C4×D47C2×C414yes—
93C2×C22⋊Dic47—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×(C2×D47)⋊C4—21no—
96C22⋊C4×D47—28no—
97C2×C4×Dic47D411yescharacteristic
98C2×C4×Dic47D411yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C42×D47C2×C414yes—
101C42×D47D414yes—
102C4⋊(C47⋊C8)—22no—
103Dic47⋊C8—24no—
104#13093946—24no—
105#13093945—24no—
106#13093944—24no—
107C22×D4×C47C2311yescharacteristic
108C23×C4×C47—21no—
109C22×C8×C47C2312yes—
110C4×D4×C47—22no—
111C4×D4×C47C2×C414yescomplemented
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47C2312yes—
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C22⋊C4×C47—21no—
117C2×C42×C47C2311yescharacteristic
118C4⋊C8×C47—22no—
119#102×C47—24no—
120C24×C47—21no—
121C23×D47—21no—
122C23×D47—24no—
123C23×D47—24no—
124C23×D47—24no—
125C23×D47—42no—
126C23×D47—42no—
127C23×D47—42no—
128C23×D47—42no—
129C23×D47C2×D411yescharacteristic
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47C22×C412yes—
134C2×D4×C47C2×D412yes—
135C2×D4×C47C2×Q812yes—
136C22×C4×C47—21no—
137C22×C4×C47—24no—
138C22×C4×C47—22no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2411yescharacteristic
144C2×C22⋊D47—24no—
145C2×C22⋊D47—24no—
146C2×C22⋊D47—24no—
147C22×Dic47—21no—
148C22×Dic47—24no—
149C22×Dic47—22no—
150C22×Dic47—42no—
151C22×Dic47—42no—
152C22×Dic47C2×D411yescharacteristic
153C22×Dic47C2×D411yescharacteristic
154C22×Dic47C2×D411yescharacteristic
155D4×D47—28no—
156D4×D47—28no—
157D4×D47—28no—
158D4×D47C4⋊C4116yescomplemented
159C2×D188—21no—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188C22×C412yes—
163C2×D188C2×D412yes—
164C2×D188C2×Q812yes—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—24no—
168C2×C4×D47—24no—
169C2×C4×D47—24no—
170C2×C4×D47—42no—
171C2×C4×D47—42no—
172C2×C4×D47—42no—
173C2×C4×D47—42no—
174C2×C4×D47—42no—
175C2×C4×D47—42no—
176C2×C4×D47—432no—
177C2×C4×D47—44no—
178C2×C4×D47—44no—
179C2×C4×D47—44no—
180C2×C4×D47C22⋊C414yes—
181C2×C4×D47C22⋊C414yes—
182C2×C4×D47D814yes—
183C2×C4×D47SD1614yes—
184C2×C4×D47C22×C412yes—
185C2×C4×D47C2×D412yes—
186C2×C4×D47C2×D412yes—
187C2×C4×D47C2×Q812yes—
188C2×C4×D47#4112yes—
189C2×C4×D47#4112yes—
190C2×C8×C47—22no—
191C2×C8×C47—22no—
192C2×C8×C47—22no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47—22no—
196C4⋊C4×C47—42no—
197C4⋊C4×C47—42no—
198C4⋊C4×C47C22×C412yes—
199C22⋊C4×C47—24no—
200C42×C47C22×C412yes—
201C42×C47C2×D412yes—
202C22⋊Dic47—24no—
203(C2×D47)⋊C4—24no—
204(C2×D47)⋊C4—24no—
205C4⋊Dic47—21no—
206C4⋊Dic47—22no—
207C4⋊Dic47—22no—
208C4⋊Dic47—42no—
209C4⋊Dic47—42no—
210C4⋊Dic47C22×C412yes—
211Dic47⋊C4—24no—
212Dic47⋊C4—44no—
213Dic47⋊C4—44no—
214Dic47⋊C4—44no—
215C4×Dic47C22⋊C414yes—
216C4×Dic47C22⋊C414yes—
217C4×Dic47C22×C412yes—
218C4×Dic47C2×D412yes—
219C2×C47⋊C8—22no—
220C2×C47⋊C8—22no—
221C2×C47⋊C8—22no—
222C8×D47—48no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—41no—
227C23×C47—41no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47C22×D411yescharacteristic
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—22no—
234C22×D47—216no—
235C22×D47—41no—
236C22×D47—41no—
237C22×D47—41no—
238C22×D47—41no—
239C22×D47—48no—
240C22×D47—48no—
241C22×D47—48no—
242C22×D47—48no—
243C22×D47—48no—
244C22×D47—48no—
245C22×D47C2×C22⋊C412yes—
246C22×D47#12112yes—
247C22×D47C22⋊Q812yes—
248C22×D47C2×D812yes—
249C22×D47C2×SD1612yes—
250C22×D47AGL(1,ℤ/8)12yes—
251C22×D47#13712yes—
252D4×C47—22no—
253D4×C47—22no—
254D4×C47—22no—
255D4×C47C2×C4⋊C414yescomplemented
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—22no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—48no—
262C2×C4×C47—42no—
263C2×C4×C47—42no—
264C2×C4×C47—42no—
265C2×C4×C47C2×C22⋊C412yes—
266C2×C4×C47C2×C22⋊C412yes—
267C2×C4×C47C2×D812yes—
268C2×C4×C47C2×SD1612yes—
269C2×C4×C47C23×C411yescharacteristic
270C2×C4×C47C22×D411yescharacteristic
271C2×C4×C47C22×D411yescharacteristic
272C2×C4×C47C22×Q811yescharacteristic
273C2×C4×C47C2×#4111yescharacteristic
274C2×C4×C47C2×#4111yescharacteristic
275C22⋊D47—216no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—22no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—48no—
282C2×Dic47—42no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47C2×C22⋊C412yes—
286C2×Dic47C2×C22⋊C412yes—
287C2×Dic47C2×C22⋊C412yes—
288C2×Dic47#12112yes—
289C2×Dic47C22⋊Q812yes—
290C2×Dic47C2×D812yes—
291C2×Dic47C2×SD1612yes—
292D188—22no—
293D188—22no—
294D188—22no—
295D188C2×C4⋊C414yescomplemented
296C4×D47—28no—
297C4×D47—48no—
298C4×D47—48no—
299C4×D47—48no—
300C4×D47—88no—
301C4×D47#102116yescomplemented
302C4×D47C2×C4⋊C414yes—
303C4×D47#11714yes—
304C4×D47#12114yes—
305C4×D47C22⋊Q814yes—
306C8×C47—42no—
307C47⋊C8—42no—
308C2×#1802—471nomaximal, Sylow
309C22×C47—24no—
310C22×C47—42no—
311C22×C47—42no—
312C22×C47—42no—
313C22×C47—42no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47C22×C22⋊C411yescharacteristic
317C22×C47C2×#12111yescharacteristic
318C22×C47C2×C22⋊Q811yescharacteristic
319C22×C47C22×D811yescharacteristic
320C22×C47C22×SD1611yescharacteristic
321C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C47C2×#13711yescharacteristic
323C2×D47—24no—
324C2×D47—42no—
325C2×D47—42no—
326C2×D47—42no—
327C2×D47—42no—
328C2×D47—42no—
329C2×D47—42no—
330C2×D47—432no—
331C2×D47#38014yes—
332C2×D47C2×#10214yes—
333C2×D47#41714yes—
334C2×D47#45914yes—
335C2×D47#46114yes—
336C2×D47#47414yes—
337C2×D47#47614yes—
338C4×C47—22no—
339C4×C47—42no—
340C4×C47—82no—
341C4×C47C2×#10214yescomplemented
342C4×C47C22×C4⋊C411yescharacteristic
343C4×C47C2×#11711yescharacteristic
344C4×C47C2×#12111yescharacteristic
345C4×C47C2×C22⋊Q811yescharacteristic
346Dic47—22no—
347Dic47—42no—
348Dic47—82no—
349Dic47#38014yes—
350Dic47C2×#10214yescomplemented
351C22×C4×D4—471no—
352C22×C4⋊C8—471no—
353C22×#102—472no—
354C2×#384—471no—
355#1802—471no—
356#1802—472no—
357#1802—471no—
358#1802—472no—
359#1802—471no—
360#1802D4711yescharacteristic, direct product factor
361C2×#340—472no—
362C2×C47—44no—
363C2×C47C2×#38011yescharacteristic
364C2×C47C22×#10211yescharacteristic
365C2×C47C2×#41711yescharacteristic
366C2×C47C2×#45911yescharacteristic
367C2×C47C2×#46111yescharacteristic
368C2×C47C2×#47411yescharacteristic
369C2×C47C2×#47611yescharacteristic
370D47—44no—
371D47#180218yesdirect product factor
372C23×D4—471no—
373C24×C4—941no—
374C23×C8—472no—
375C2×C4×D4—471no—
376C2×C4×D4—478no—
377C2×C4×D4—471no—
378C2×C4×D4—471no—
379C2×C4×D4—941no—
380C2×C4×D4—944no—
381C2×C4×D4—941no—
382C2×C4×D4C2×D4711yescharacteristic
383C22×C4⋊C4—471no—
384C22×C4⋊C4—472no—
385C22×C4⋊C4—941no—
386C22×C4⋊C4—941no—
387C22×C22⋊C4—941no—
388C22×C42—471no—
389C2×C4⋊C8—472no—
390C2×C4⋊C8—471no—
391C2×C4⋊C8—944no—
392C2×C4⋊C8C2×D4711yescharacteristic, complemented
393C2×#102—472no—
394C2×#102—472no—
395C2×#102—472no—
396C2×#102—948no—
397C2×#102C2×D4712yes—
398#384—472no—
399#384—471no—
400#384—941no—
401#384—941no—
402#384C2×D4711yescharacteristic, complemented
403#340—472no—
404#340—472no—
405#340—472no—
406#340C2×D4712yescomplemented
407C47C2×#180211yescharacteristic, complemented, Sylow
408C25—941no—
409C22×D4—474no—
410C22×D4—474no—
411C22×D4—474no—
412C22×D4—471no—
413C22×D4—942no—
414C22×D4—942no—
415C22×D4—942no—
416C22×D4—941no—
417C22×D4C22×D4711yescharacteristic
418C23×C4—21no—
419C23×C4—471no—
420C23×C4—471no—
421C23×C4—471no—
422C23×C4—941no—
423C23×C4—948no—
424C23×C4—941no—
425C23×C4—942no—
426C23×C4—941no—
427C23×C4—941no—
428C23×C4—1884no—
429C23×C4—1884no—
430C22×C8—472no—
431C22×C8—944no—
432C22×C8—944no—
433C22×C8—944no—
434C22×C8C22×D4712yes—
435C4×D4—22no—
436C4×D4—474no—
437C4×D4—474no—
438C4×D4—474no—
439C4×D4—948no—
440C4×D4—942no—
441C4×D4—948no—
442C4×D4—942no—
443C4×D4—942no—
444C4×D4C4×D4714yescomplemented
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—471no—
448C2×C4⋊C4—474no—
449C2×C4⋊C4—472no—
450C2×C4⋊C4—942no—
451C2×C4⋊C4—944no—
452C2×C4⋊C4—944no—
453C2×C4⋊C4—941no—
454C2×C4⋊C4—942no—
455C2×C4⋊C4—942no—
456C2×C4⋊C4—942no—
457C2×C4⋊C4—941no—
458C2×C4⋊C4—941no—
459C2×C4⋊C4—1884no—
460C2×C4⋊C4—1884no—
461C2×C4⋊C4C22×D4712yes—
462C2×C4⋊C4C22×D4711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—948no—
465C2×C22⋊C4—941no—
466C2×C22⋊C4—941no—
467C2×C22⋊C4—941no—
468C2×C42—471no—
469C2×C42—471no—
470C2×C42—471no—
471C2×C42—474no—
472C2×C42—474no—
473C2×C42C22×D4711yescharacteristic
474C4⋊C8—22no—
475C4⋊C8—944no—
476C4⋊C8—942no—
477#102—24no—
478#102—944no—
479#102—944no—
480#102—944no—
481C24—21no—
482C24—471no—
483C24—944no—
484C24—944no—
485C24—944no—
486C24—941no—
487C24—1882no—
488C24—1882no—
489C24—1882no—
490C24—1882no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—4716no—
495C2×D4—472no—
496C2×D4—472no—
497C2×D4—472no—
498C2×D4—948no—
499C2×D4—948no—
500C2×D4—948no—
501C2×D4—944no—
502C2×D4—944no—
503C2×D4—944no—
504C2×D4—941no—
505C2×D4—941no—
506C2×D4—941no—
507C2×D4C2×C4×D4712yes—
508C2×D4D4×D4712yes—
509C2×D4Q8×D4712yes—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—471no—
516C22×C4—471no—
517C22×C4—474no—
518C22×C4—474no—
519C22×C4—474no—
520C22×C4—472no—
521C22×C4—472no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—472no—
525C22×C4—472no—
526C22×C4—471no—
527C22×C4—474no—
528C22×C4—944no—
529C22×C4—942no—
530C22×C4—942no—
531C22×C4—944no—
532C22×C4—944no—
533C22×C4—941no—
534C22×C4—944no—
535C22×C4—942no—
536C22×C4—1882no—
537C22×C4—1882no—
538C22×C4—18832no—
539C22×C4—1884no—
540C22×C4—1884no—
541C22×C4—1884no—
542C22×C4—1882no—
543C22×C4—1882no—
544C22×C4—1882no—
545C22×C4—1882no—
546C22×C4—1882no—
547C22×C4—1882no—
548C22×C4D4×D4711yescharacteristic
549C22×C4D4×D4711yescharacteristic
550C22×C4C23×D4711yescharacteristic
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—942no—
555C2×C8—942no—
556C2×C8—942no—
557C2×C8—1888no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—472no—
564C4⋊C4—944no—
565C4⋊C4—941no—
566C4⋊C4—942no—
567C4⋊C4—942no—
568C4⋊C4—1882no—
569C4⋊C4—1884no—
570C4⋊C4—1884no—
571C4⋊C4—1884no—
572C4⋊C4—1882no—
573C4⋊C4C2×C4×D4712yes—
574C22⋊C4—24no—
575C22⋊C4—944no—
576C22⋊C4—944no—
577C22⋊C4—944no—
578C42—474no—
579C42—474no—
580C42—472no—
581C42—472no—
582C42C2×C4×D4712yes—
583C42D4×D4712yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—472no—
592C23—472no—
593C23—472no—
594C23—472no—
595C23—472no—
596C23—472no—
597C23—472no—
598C23—9416no—
599C23—942no—
600C23—942no—
601C23—942no—
602C23—1888no—
603C23—1888no—
604C23—1888no—
605C23—1888no—
606C23—1888no—
607C23—1888no—
608C23—1881no—
609C23—1881no—
610C23—1881no—
611C23—1881no—
612C23C2×D4×D4711yescharacteristic
613D4—22no—
614D4—22no—
615D4—22no—
616D4—474no—
617D4—9416no—
618D4—942no—
619D4—942no—
620D4—942no—
621D4C4⋊C4×D4714yescomplemented
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—48no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—472no—
632C2×C4—472no—
633C2×C4—472no—
634C2×C4—472no—
635C2×C4—472no—
636C2×C4—472no—
637C2×C4—474no—
638C2×C4—474no—
639C2×C4—474no—
640C2×C4—474no—
641C2×C4—4716no—
642C2×C4—472no—
643C2×C4—948no—
644C2×C4—941no—
645C2×C4—941no—
646C2×C4—942no—
647C2×C4—3768no—
648C2×C4—1888no—
649C2×C4—1888no—
650C2×C4—1888no—
651C2×C4—1882no—
652C2×C4—1882no—
653C2×C4—1882no—
654C2×C4—1881no—
655C2×C4—1881no—
656C2×C4—1888no—
657C2×C4C22⋊C4×D4712yes—
658C2×C4C22⋊C4×D4712yes—
659C2×C4D8×D4712yes—
660C2×C4SD16×D4712yes—
661C2×C4C22×C4×D4711yescharacteristic
662C2×C4C2×D4×D4711yescharacteristic
663C2×C4C2×D4×D4711yescharacteristic
664C2×C4C2×Q8×D4711yescharacteristic
665C2×C4#41×D4711yescharacteristic
666C2×C4#41×D4711yescharacteristic
667C8—42no—
668C8—1882no—
669C22—24no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—474no—
677C22—474no—
678C22—474no—
679C22—474no—
680C22—474no—
681C22—474no—
682C22—474no—
683C22—944no—
684C22—18832no—
685C22—1882no—
686C22—1882no—
687C22—1882no—
688C22—1882no—
689C22—1882no—
690C22—1882no—
691C22C2×C22⋊C4×D4711yescharacteristic
692C22#121×D4711yescharacteristic
693C22C22⋊Q8×D4711yescharacteristic
694C22C2×D8×D4711yescharacteristic
695C22C2×SD16×D4711yescharacteristic
696C22AGL(1,ℤ/8)×D4711yescharacteristic
697C22#137×D4711yescharacteristic
698C4—22no—
699C4—42no—
700C4—82no—
701C4—474no—
702C4—474no—
703C4—942no—
704C4—3762no—
705C4—1882no—
706C4#102×D4714yescomplemented
707C4C2×C4⋊C4×D4711yescharacteristic
708C4#117×D4711yescharacteristic
709C4#121×D4711yescharacteristic
710C4C22⋊Q8×D4711yescharacteristic
711C2—44no—
712C2—478no—
713C2—1884no—
714C2#380×D4711yescharacteristic
715C2C2×#102×D4711yescharacteristic
716C2#417×D4711yescharacteristic
717C2#459×D4711yescharacteristic
718C2#461×D4711yescharacteristic
719C2#474×D4711yescharacteristic
720C2#476×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1802C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
cosocleC22×C4×C47C24
hypercenter#1802D47
hypocenterC47C2×#1802
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D47C2semidirect
4. #384×D47C2semidirect
5. #20243389C2semidirect
6. #20243388C2semidirect
7. #20243387C2semidirect
8. #20243386C2semidirect
9. #20243385C2semidirect
10. #340×D47C2semidirect
11. C47×#1802C2semidirect
21. C4×D4×D47C4semidirect
28. C2×C4⋊(C47⋊C8)C22semidirect
29. C2×Dic47⋊C8C22semidirect
35. #15688993C22semidirect
38. #15688992C22semidirect
39. #15688886C22semidirect
40. #15688885C22semidirect
41. #15688885C22semidirect
43. C2×C4⋊C8×C47C22semidirect
45. C47×#384C22semidirect
46. C47×#340C22semidirect
72. C4×D188C2×C4semidirect
74. D4×Dic47C2×C4semidirect
76. #13093986C2×C4semidirect
111. C4×D4×C47C2×C4semidirect
158. D4×D47C4⋊C4semidirect
255. D4×C47C2×C4⋊C4semidirect
295. D188C2×C4⋊C4semidirect
301. C4×D47#102semidirect
341. C4×C47C2×#102semidirect
350. Dic47C2×#102semidirect
360. #1802D47direct (N × H)
371. D47#1802direct (N × H)
392. C2×C4⋊C8C2×D47semidirect
402. #384C2×D47semidirect
406. #340C2×D47semidirect
407. C47C2×#1802semidirect
444. C4×D4C4×D47semidirect
621. D4C4⋊C4×D47semidirect
706. C4#102×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
C2×C4⋊C8×D472
C2×#102×D472
#384×D472
#202433892
#202433882
#202433872
#202433862
#202433852
#340×D472
C47×#18022
C2×#180247