Finite Group Databasebeta

← D47×#1925 #26218636

Subgroups — D47×#1925 #26218636

Order 12032.

1454 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D47C211yesmaximal, characteristic, complemented
2C2×#102×D47C211yesmaximal, characteristic
3C2×#102×D47C211yesmaximal, characteristic
4#390×D47C211yesmaximal, characteristic
5C4×C4⋊C4×D47C211yesmaximal, characteristic, complemented
6#20244011C211yesmaximal, characteristic, complemented
7#20244010C211yesmaximal, characteristic, complemented
8#20244009C211yesmaximal, characteristic, complemented
9#20244008C211yesmaximal, characteristic, complemented
10#20244007C211yesmaximal, characteristic, complemented
11#20244006C211yesmaximal, characteristic, complemented
12#20244005C211yesmaximal, characteristic, complemented
13#340×D47C211yesmaximal, characteristic, complemented
14#336×D47C211yesmaximal, characteristic, complemented
15C47×#1925C211yesmaximal, characteristic, complemented
16C22×D4×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19C2×C4⋊C4×D47C2211yescharacteristic
20C2×C4⋊C4×D47C2211yescharacteristic
21C2×C4⋊C4×D47C2211yescharacteristic
22C2×C22⋊C4×D47—21no—
23C2×C22⋊C4×D47—21no—
24C2×C42×D47—21no—
25C2×C42×D47C2211yescharacteristic
26C2×#13093958C2211yescharacteristic, complemented
27C2×#13093957C2211yescharacteristic, complemented
28C2×#13093957C2211yescharacteristic, complemented
29#107×D47—24no—
30C2×#13093946C2211yescharacteristic
31C2×#13093946C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36#102×D47—24no—
37#102×D47C418yescomplemented
38#15689026C2211yescharacteristic
39#15689025C2211yescharacteristic
40#15689024C2211yescharacteristic
41#15689023—21no—
42#15689023—21no—
43C4⋊C4×Dic47C2211yescharacteristic, complemented
44C4⋊C4×Dic47C2211yescharacteristic, complemented
45C4×Dic47⋊C4—21no—
46C4×C4⋊Dic47C2211yescharacteristic, complemented
47#15688974—21no—
48#95×D47—21no—
49#15688886C2211yescharacteristic, complemented
50#15688885C2211yescharacteristic, complemented
51#15688885C2211yescharacteristic, complemented
52#15688878C2211yescharacteristic, complemented
53#15688877C2211yescharacteristic, complemented
54#15688877C2211yescharacteristic, complemented
55C2×#107×C47C2211yescharacteristic, complemented
56C2×#102×C47C2211yescharacteristic
57C2×#102×C47C2211yescharacteristic
58C47×#390C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C24×D47—21no—
63C22×D188C2311yescharacteristic
64C22×C22⋊D47—21no—
65C2×D4×D47—22no—
66C2×D4×D47—22no—
67C2×D4×D47—22no—
68C2×D4×D47—22no—
69C2×D4×D47—22no—
70C2×D4×D47C2×C414yes—
71C22×C4×D47—21no—
72C22×C4×D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47D411yescharacteristic
75C22×C4×D47D411yescharacteristic
76C22×C4×D47C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C2×C8×D47—22no—
80C2×C8×D47—22no—
81C2×C8×D47—22no—
82C2×C8×D47—22no—
83C2×C8×D47—22no—
84C2×C8×D47C2×C414yes—
85C2×C4⋊Dic47C2311yescharacteristic
86C2×C4⋊Dic47C2311yescharacteristic
87C2×C4⋊Dic47C2311yescharacteristic
88C2×Dic47⋊C4—21no—
89C2×Dic47⋊C4—21no—
90C2×Dic47⋊C4—21no—
91C4⋊C4×D47—22no—
92C4⋊C4×D47—22no—
93C4⋊C4×D47—22no—
94C4⋊C4×D47—22no—
95C4⋊C4×D47C2×C414yes—
96C4⋊C4×D47D414yes—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×(C2×D47)⋊C4—21no—
103C22⋊C4×D47—44no—
104C22⋊C4×D47—44no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47D411yescharacteristic
109C2×C4×Dic47D411yescharacteristic
110C2×C4×Dic47C2311yescharacteristic
111C42×D47—22no—
112C42×D47—22no—
113C42×D47—44no—
114#13093958—22no—
115#13093957—22no—
116#13093957—22no—
117#13093946—22no—
118#13093946C2×C414yescomplemented
119#13093945—22no—
120#13093945C2×C414yescomplemented
121#13093944—22no—
122#13093944C2×C414yescomplemented
123C47⋊#95—21no—
124C47⋊#95—21no—
125C47⋊#95—21no—
126C22×D4×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136#107×C47—22no—
137#102×C47—22no—
138#102×C47C2×C414yescomplemented
139#95×C47—21no—
140C24×C47—21no—
141C23×D47—21no—
142C23×D47—24no—
143C23×D47—42no—
144C23×D47—42no—
145C23×D47—42no—
146C23×D47—42no—
147C23×D47—42no—
148C23×D47—42no—
149C23×D47C2×D411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47C22×C412yes—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2411yescharacteristic
162C2×C22⋊D47—24no—
163C2×C22⋊D47—42no—
164C2×C22⋊D47—42no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47C2×D411yescharacteristic
169C22×Dic47C2×D411yescharacteristic
170C22×Dic47C2×D411yescharacteristic
171D4×D47—28no—
172D4×D47—28no—
173D4×D47—44no—
174D4×D47—44no—
175C2×D188—21no—
176C2×D188—21no—
177C2×D188—21no—
178C2×D188—21no—
179C2×D188—21no—
180C2×D188C22×C412yes—
181C2×C4×D47—22no—
182C2×C4×D47—22no—
183C2×C4×D47—24no—
184C2×C4×D47—24no—
185C2×C4×D47—22no—
186C2×C4×D47—22no—
187C2×C4×D47—22no—
188C2×C4×D47—42no—
189C2×C4×D47—42no—
190C2×C4×D47—42no—
191C2×C4×D47—42no—
192C2×C4×D47—42no—
193C2×C4×D47—42no—
194C2×C4×D47—42no—
195C2×C4×D47D814yes—
196C2×C4×D47C22×C412yes—
197C2×C4×D47C2×D412yes—
198C2×C4×D47#4112yes—
199C2×C4×D47#4112yes—
200C2×C4×D47#4112yes—
201C2×C4×D47#4112yes—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47C22×C412yes—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47C22×C412yes—
213C4⋊C4×C47C2×D412yes—
214C22⋊C4×C47—42no—
215C22⋊C4×C47—42no—
216C42×C47—21no—
217C42×C47—21no—
218C42×C47—42no—
219C22⋊Dic47—42no—
220C22⋊Dic47—42no—
221(C2×D47)⋊C4—42no—
222(C2×D47)⋊C4—42no—
223(C2×D47)⋊C4—42no—
224(C2×D47)⋊C4—42no—
225C4⋊Dic47—21no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47—21no—
229C4⋊Dic47C22×C412yes—
230C4⋊Dic47C2×D412yes—
231Dic47⋊C4—24no—
232Dic47⋊C4—24no—
233Dic47⋊C4—42no—
234C4×Dic47—21no—
235C4×Dic47—21no—
236C4×Dic47—22no—
237C4×Dic47—22no—
238C4×Dic47—42no—
239C4×Dic47—42no—
240C4×Dic47—42no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8C22×C412yes—
247C8×D47—28no—
248C8×D47—44no—
249C23×C47—22no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47C22×D411yescharacteristic
257C22×D47—22no—
258C22×D47—41no—
259C22×D47—41no—
260C22×D47—41no—
261C22×D47—41no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—48no—
265C22×D47—48no—
266C22×D47—48no—
267C22×D47—84no—
268C22×D47—84no—
269C22×D47—84no—
270C22×D47—84no—
271C22×D47C4×D412yes—
272C22×D47#12112yes—
273C22×D47#12312yes—
274C22×D47C2×D812yes—
275C22×D47#13512yes—
276C22×D47AGL(1,ℤ/8)12yes—
277C22×D47#13712yes—
278D4×C47—22no—
279D4×C47—22no—
280D4×C47—41no—
281D4×C47—41no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47C2×D812yes—
297C2×C4×C47C23×C411yescharacteristic
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C2×#4111yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47C2×#4111yescharacteristic
303C22⋊D47—48no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318C2×Dic47C4×D412yes—
319C2×Dic47#12112yes—
320C2×Dic47#12312yes—
321C2×Dic47C2×D812yes—
322D188—22no—
323D188—22no—
324D188—41no—
325D188—41no—
326C4×D47—28no—
327C4×D47—48no—
328C4×D47—48no—
329C4×D47—44no—
330C4×D47—84no—
331C4×D47#11714yes—
332C4×D47C4×D414yes—
333C4×D47#12414yes—
334C4×D47#12614yes—
335C8×C47—22no—
336C8×C47—41no—
337C47⋊C8—22no—
338C47⋊C8—41no—
339C2×#1925—471nomaximal, Sylow
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—81no—
344C22×C47—81no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47C2×C4×D411yescharacteristic
348C22×C47C2×#12111yescharacteristic
349C22×C47C2×#12311yescharacteristic
350C22×C47C22×D811yescharacteristic
351C22×C47C2×#13511yescharacteristic
352C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C47C2×#13711yescharacteristic
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—81no—
358C2×D47—81no—
359C2×D47—81no—
360C2×D47—81no—
361C2×D47—816no—
362C2×D47#38814yes—
363C2×D47C4×D814yes—
364C2×D47#44014yes—
365C2×D47#45914yes—
366C2×D47#46414yes—
367C2×D47#48014yes—
368C2×D47#48214yes—
369C4×C47—22no—
370C4×C47—41no—
371C4×C47—42no—
372C4×C47—42no—
373C4×C47—81no—
374C4×C47C2×#11711yescharacteristic
375C4×C47C2×C4×D411yescharacteristic
376C4×C47C2×#12411yescharacteristic
377C4×C47C2×#12611yescharacteristic
378Dic47—22no—
379Dic47—41no—
380Dic47—42no—
381Dic47—42no—
382Dic47—81no—
383Dic47#38814yes—
384C22×#107—471no—
385C22×#102—471no—
386C22×#102—471no—
387C2×#390—471no—
388C2×C4×C4⋊C4—471no—
389#1925—471no—
390#1925—471no—
391#1925—471no—
392#1925—471no—
393#1925—471no—
394#1925—471no—
395#1925—471no—
396#1925D4711yescharacteristic, direct product factor
397C2×#340—471no—
398C2×#336—471no—
399C2×C47—82no—
400C2×C47C2×#38811yescharacteristic
401C2×C47C2×C4×D811yescharacteristic
402C2×C47C2×#44011yescharacteristic
403C2×C47C2×#45911yescharacteristic
404C2×C47C2×#46411yescharacteristic
405C2×C47C2×#48011yescharacteristic
406C2×C47C2×#48211yescharacteristic
407D47—82no—
408D47#192518yesdirect product factor
409C23×D4—471no—
410C23×C8—471no—
411C23×C8—471no—
412C22×C4⋊C4—471no—
413C22×C4⋊C4—471no—
414C22×C4⋊C4—471no—
415C22×C22⋊C4—941no—
416C22×C22⋊C4—941no—
417C22×C42—471no—
418C22×C42—941no—
419C2×#107—471no—
420C2×#107—471no—
421C2×#107—471no—
422C2×#107—944no—
423C2×#107C2×D4711yescharacteristic, complemented
424C2×#102—471no—
425C2×#102—471no—
426C2×#102—471no—
427C2×#102—478no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—944no—
432C2×#102C2×D4711yescharacteristic
433C2×#102C2×D4711yescharacteristic
434#390—471no—
435#390—471no—
436#390—471no—
437#390—941no—
438#390—941no—
439#390C2×D4711yescharacteristic
440C4×C4⋊C4—471no—
441C4×C4⋊C4—471no—
442C4×C4⋊C4—471no—
443C4×C4⋊C4—941no—
444C4×C4⋊C4—941no—
445C4×C4⋊C4C2×D4711yescharacteristic, complemented
446C2×#95—941no—
447#340—471no—
448#340—471no—
449#340—471no—
450#340C2×D4711yescharacteristic, complemented
451#336—471no—
452#336—471no—
453#336—471no—
454#336C2×D4711yescharacteristic, complemented
455C47C2×#192511yescharacteristic, complemented, Sylow
456C25—941no—
457C22×D4—474no—
458C22×D4—471no—
459C22×D4—942no—
460C22×D4—942no—
461C22×D4—942no—
462C22×D4—942no—
463C22×D4—942no—
464C22×D4—941no—
465C22×D4C22×D4711yescharacteristic
466C23×C4—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—941no—
470C23×C4—941no—
471C23×C4—941no—
472C22×C8—471no—
473C22×C8—474no—
474C22×C8—471no—
475C22×C8—942no—
476C22×C8—942no—
477C22×C8—942no—
478C22×C8—942no—
479C22×C8—942no—
480C22×C8C22×D4711yescharacteristic
481C22×C8C22×D4711yescharacteristic
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—474no—
485C2×C4⋊C4—474no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—942no—
488C2×C4⋊C4—942no—
489C2×C4⋊C4—942no—
490C2×C4⋊C4—942no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4C22×D4711yescharacteristic
495C2×C4⋊C4C22×D4711yescharacteristic
496C2×C4⋊C4C22×D4711yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—941no—
500C2×C22⋊C4—941no—
501C2×C22⋊C4—941no—
502C2×C22⋊C4—941no—
503C2×C22⋊C4—941no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—1884no—
506C2×C22⋊C4—1884no—
507C2×C42—21no—
508C2×C42—471no—
509C2×C42—471no—
510C2×C42—471no—
511C2×C42—942no—
512C2×C42—942no—
513C2×C42—941no—
514C2×C42—941no—
515C2×C42—941no—
516C2×C42—1884no—
517C2×C42C22×D4711yescharacteristic
518#107—22no—
519#107—942no—
520#107—942no—
521#107—942no—
522#102—22no—
523#102—474no—
524#102—474no—
525#102—474no—
526#102—942no—
527#102—942no—
528#102—942no—
529#102C4×D4714yescomplemented
530#95—21no—
531#95—941no—
532#95—941no—
533#95—941no—
534C24—21no—
535C24—471no—
536C24—944no—
537C24—941no—
538C24—1882no—
539C24—1882no—
540C24—1882no—
541C24—1882no—
542C24—1882no—
543C24—1882no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—472no—
550C2×D4—948no—
551C2×D4—948no—
552C2×D4—944no—
553C2×D4—941no—
554C2×D4—941no—
555C2×D4—941no—
556C2×D4—941no—
557C2×D4—941no—
558C2×D4—1884no—
559C2×D4—1884no—
560C2×D4—1882no—
561C2×D4—1882no—
562C2×D4C2×C4×D4712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—471no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—472no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—471no—
574C22×C4—474no—
575C22×C4—471no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—944no—
581C22×C4—944no—
582C22×C4—942no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—1882no—
587C22×C4—1882no—
588C22×C4—1882no—
589C22×C4—1882no—
590C22×C4—1882no—
591C22×C4—1882no—
592C22×C4—1882no—
593C22×C4D4×D4711yescharacteristic
594C22×C4D4×D4711yescharacteristic
595C22×C4C23×D4711yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—472no—
602C2×C8—948no—
603C2×C8—941no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—1884no—
609C2×C8C2×C4×D4712yes—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—472no—
615C4⋊C4—472no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—941no—
621C4⋊C4—941no—
622C4⋊C4—1882no—
623C4⋊C4C2×C4×D4712yes—
624C4⋊C4D4×D4712yes—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—1882no—
628C22⋊C4—1882no—
629C22⋊C4—1882no—
630C22⋊C4—1882no—
631C22⋊C4—1882no—
632C22⋊C4—1882no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—942no—
637C42—942no—
638C42—941no—
639C42—941no—
640C42—1882no—
641C42—1882no—
642C42—1882no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—472no—
651C23—472no—
652C23—472no—
653C23—472no—
654C23—472no—
655C23—472no—
656C23—472no—
657C23—942no—
658C23—3764no—
659C23—3764no—
660C23—3764no—
661C23—3764no—
662C23—1888no—
663C23—1888no—
664C23—1888no—
665C23—1881no—
666C23—1881no—
667C23—1881no—
668C23—1881no—
669C23—1881no—
670C23—1881no—
671C23C2×D4×D4711yescharacteristic
672D4—22no—
673D4—22no—
674D4—41no—
675D4—41no—
676D4—942no—
677D4—942no—
678D4—1888no—
679D4—1881no—
680D4—1881no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—472no—
696C2×C4—472no—
697C2×C4—472no—
698C2×C4—474no—
699C2×C4—474no—
700C2×C4—474no—
701C2×C4—474no—
702C2×C4—472no—
703C2×C4—948no—
704C2×C4—941no—
705C2×C4—941no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—3764no—
712C2×C4—1884no—
713C2×C4—1888no—
714C2×C4—1888no—
715C2×C4—1881no—
716C2×C4—1881no—
717C2×C4—1881no—
718C2×C4—1881no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1881no—
722C2×C4D8×D4712yes—
723C2×C4C22×C4×D4711yescharacteristic
724C2×C4C2×D4×D4711yescharacteristic
725C2×C4#41×D4711yescharacteristic
726C2×C4#41×D4711yescharacteristic
727C2×C4#41×D4711yescharacteristic
728C2×C4#41×D4711yescharacteristic
729C8—22no—
730C8—41no—
731C8—942no—
732C8—1881no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—474no—
741C22—474no—
742C22—474no—
743C22—474no—
744C22—474no—
745C22—474no—
746C22—474no—
747C22—37616no—
748C22—3761no—
749C22—3761no—
750C22—3761no—
751C22—3761no—
752C22—1882no—
753C22—1882no—
754C22—1882no—
755C22C4×D4×D4711yescharacteristic
756C22#121×D4711yescharacteristic
757C22#123×D4711yescharacteristic
758C22C2×D8×D4711yescharacteristic
759C22#135×D4711yescharacteristic
760C22AGL(1,ℤ/8)×D4711yescharacteristic
761C22#137×D4711yescharacteristic
762C4—22no—
763C4—41no—
764C4—42no—
765C4—42no—
766C4—81no—
767C4—474no—
768C4—942no—
769C4—3761no—
770C4—1881no—
771C4—1882no—
772C4—1882no—
773C4#117×D4711yescharacteristic
774C4C4×D4×D4711yescharacteristic
775C4#124×D4711yescharacteristic
776C4#126×D4711yescharacteristic
777C2—82no—
778C2—478no—
779C2—3762no—
780C2#388×D4711yescharacteristic
781C2C4×D8×D4711yescharacteristic
782C2#440×D4711yescharacteristic
783C2#459×D4711yescharacteristic
784C2#464×D4711yescharacteristic
785C2#480×D4711yescharacteristic
786C2#482×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1925C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
cosocleC22×C4×C47C24
hypercenter#1925D47
hypocenterC47C2×#1925
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
1. C2×#107×D47C2semidirect
5. C4×C4⋊C4×D47C2semidirect
6. #20244011C2semidirect
7. #20244010C2semidirect
8. #20244009C2semidirect
9. #20244008C2semidirect
10. #20244007C2semidirect
11. #20244006C2semidirect
12. #20244005C2semidirect
13. #340×D47C2semidirect
14. #336×D47C2semidirect
15. C47×#1925C2semidirect
26. C2×#13093958C22semidirect
27. C2×#13093957C22semidirect
28. C2×#13093957C22semidirect
37. #102×D47C4semidirect
43. C4⋊C4×Dic47C22semidirect
44. C4⋊C4×Dic47C22semidirect
46. C4×C4⋊Dic47C22semidirect
49. #15688886C22semidirect
50. #15688885C22semidirect
51. #15688885C22semidirect
52. #15688878C22semidirect
53. #15688877C22semidirect
54. #15688877C22semidirect
55. C2×#107×C47C22semidirect
59. C4×C4⋊C4×C47C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
118. #13093946C2×C4semidirect
120. #13093945C2×C4semidirect
122. #13093944C2×C4semidirect
138. #102×C47C2×C4semidirect
396. #1925D47direct (N × H)
408. D47#1925direct (N × H)
423. C2×#107C2×D47semidirect
445. C4×C4⋊C4C2×D47semidirect
450. #340C2×D47semidirect
454. #336C2×D47semidirect
455. C47C2×#1925semidirect
529. #102C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
C2×#102×D472
#390×D472
C4×C4⋊C4×D472
#202440112
#202440102
#202440092
#202440082
#202440072
#202440062
#202440052
#340×D472
#336×D472
C47×#19252
C2×#192547