Finite Group Databasebeta

← D47×#1929 #26218773

Subgroups — D47×#1929 #26218773

Order 12032.

1082 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D47C211yesmaximal, characteristic, complemented
2C2×#104×D47C211yesmaximal, characteristic
3#416×D47C211yesmaximal, characteristic
4#408×D47C211yesmaximal, characteristic
5#405×D47C211yesmaximal, characteristic, complemented
6#20244039C211yesmaximal, characteristic, complemented
7#20244038C211yesmaximal, characteristic, complemented
8#20244037C211yesmaximal, characteristic, complemented
9#20244036C211yesmaximal, characteristic, complemented
10#20244035C211yesmaximal, characteristic, complemented
11#20244034C211yesmaximal, characteristic, complemented
12#20244033C211yesmaximal, characteristic, complemented
13#339×D47C211yesmaximal, characteristic, complemented
14#336×D47C211yesmaximal, characteristic, complemented
15C47×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D47C2211yescharacteristic
17C2×M16×D47C2211yescharacteristic
18C2×M16×D47C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#117×D47C2211yescharacteristic
22C2×C42×D47C2211yescharacteristic
23C2×#13093960C2211yescharacteristic, complemented
24C2×#13093959C2211yescharacteristic, complemented
25C2×#13093959C2211yescharacteristic, complemented
26#108×D47—24no—
27C2×#13093952C2211yescharacteristic
28C2×#13093951C2211yescharacteristic
29C2×#13093950C2211yescharacteristic
30#104×D47—24no—
31#15689120C2211yescharacteristic
32#15689119C2211yescharacteristic
33#15689118C411yescharacteristic, complemented
34#15689118C411yescharacteristic, complemented
35#15689117C2211yescharacteristic
36#15689116C411yescharacteristic, complemented
37#15689116C411yescharacteristic, complemented
38#103×D47C411yescharacteristic, complemented
39#103×D47C411yescharacteristic, complemented
40#102×D47C411yescharacteristic, complemented
41#102×D47C411yescharacteristic, complemented
42#15689091C2211yescharacteristic
43#15689090C2211yescharacteristic
44#15689089C2211yescharacteristic
45#15689088—21no—
46#15689088—21no—
47C22⋊C8×D47—21no—
48C22⋊C8×D47—21no—
49#15689081C2211yescharacteristic, complemented
50#15689080—21no—
51#15689079C2211yescharacteristic, complemented
52#15689078C2211yescharacteristic, complemented
53#15689077—21no—
54#97×D47—21no—
55C4×C8×D47—21no—
56#15688884C2211yescharacteristic, complemented
57#15688883C2211yescharacteristic, complemented
58#15688882C2211yescharacteristic, complemented
59#15688878C2211yescharacteristic, complemented
60#15688877C2211yescharacteristic, complemented
61#15688877C2211yescharacteristic, complemented
62C2×#108×C47C2211yescharacteristic, complemented
63C2×#104×C47C2211yescharacteristic
64C47×#416C2211yescharacteristic
65C47×#408C2211yescharacteristic
66C47×#405C2211yescharacteristic, complemented
67C47×#339C2211yescharacteristic, complemented
68C47×#336C2211yescharacteristic, complemented
69C2×#10625354C2×C411yescharacteristic
70C2×#10625350—21no—
71C2×#10625350C2311yescharacteristic
72C2×#10625352—21no—
73C2×#10625352C2×C411yescharacteristic
74#41×D47—22no—
75#41×D47—22no—
76#41×D47—22no—
77#41×D47—22no—
78C2×Q8×D47C2×C411yescharacteristic
79C2×D4×D47—21no—
80C2×D4×D47C2×C411yescharacteristic
81C22×C4×D47—21no—
82C22×C4×D47—21no—
83C22×C4×D47C2311yescharacteristic
84C2×#10625329C2311yescharacteristic
85C2×#10625329C2311yescharacteristic
86C2×#10625324—21no—
87C2×#10625324—21no—
88M16×D47—22no—
89M16×D47—22no—
90M16×D47—22no—
91M16×D47D414yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C2×C8×D47—21no—
95C2×C8×D47—22no—
96C2×C8×D47—22no—
97C2×C8×D47—22no—
98C2×C8×D47—22no—
99C2×C8×D47—21no—
100C2×C8×D47C2×C411yescharacteristic
101C2×C8×D47C2×C411yescharacteristic
102C2×C8×D47C2×C411yescharacteristic
103C2×C8×D47C2×C411yescharacteristic
104C2×C8×D47D411yescharacteristic
105C2×C8×D47D411yescharacteristic
106C2×C8×D47D411yescharacteristic
107C2×C8×D47D411yescharacteristic
108#13093983C2311yescharacteristic
109#13093982C2×C411yescharacteristic
110#13093982C2×C411yescharacteristic
111#13093981—21no—
112#13093980—21no—
113C4⋊C4×D47C2×C411yescharacteristic
114C4⋊C4×D47C2×C411yescharacteristic
115C22⋊C4×D47—21no—
116C2×C4×Dic47—21no—
117C2×C4×Dic47C2311yescharacteristic
118C42×D47—21no—
119C42×D47—22no—
120C42×D47—22no—
121#13093960—22no—
122#13093959—22no—
123#13093959—22no—
124#13093952—22no—
125#13093951—22no—
126#13093950—22no—
127#13093949C2×C411yescharacteristic, complemented
128#13093949C2×C411yescharacteristic, complemented
129#13093948C2×C411yescharacteristic, complemented
130#13093948C2×C411yescharacteristic, complemented
131#13093947C2×C411yescharacteristic, complemented
132#13093947C2×C411yescharacteristic, complemented
133#13093946C2×C411yescharacteristic, complemented
134#13093946C2×C411yescharacteristic, complemented
135#13093945C2×C411yescharacteristic, complemented
136#13093945C2×C411yescharacteristic, complemented
137#13093944C2×C411yescharacteristic, complemented
138#13093944C2×C411yescharacteristic, complemented
139C22⋊(C47⋊C8)—21no—
140C22⋊(C47⋊C8)—21no—
141(C2×D47)⋊C8—21no—
142(C2×D47)⋊C8—21no—
143(C2×D47)⋊C8—21no—
144(C2×D47)⋊C8—21no—
145#13093935—21no—
146#13093934—21no—
147#13093934—21no—
148C4×C47⋊C8—21no—
149C8×Dic47—21no—
150C8×Dic47—21no—
151C2×#41×C47C2311yescharacteristic
152C2×M16×C47C2311yescharacteristic
153C2×M16×C47C2311yescharacteristic
154C22×C8×C47C2311yescharacteristic
155C22×C8×C47C2311yescharacteristic
156#117×C47C2311yescharacteristic
157C2×C42×C47C2311yescharacteristic
158#108×C47—22no—
159#104×C47—22no—
160#103×C47C2×C411yescharacteristic, complemented
161#103×C47C2×C411yescharacteristic, complemented
162#102×C47C2×C411yescharacteristic, complemented
163#102×C47C2×C411yescharacteristic, complemented
164C22⋊C8×C47—21no—
165C22⋊C8×C47—21no—
166#97×C47—21no—
167C4×C8×C47—21no—
168C23×D47—21no—
169C23×D47#4111yescharacteristic
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
174C2×Q8×C47C22×C411yescharacteristic
175C2×D4×C47—21no—
176C2×D4×C47C22×C411yescharacteristic
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47C2411yescharacteristic
180C2×C22⋊D47—21no—
181C2×C22⋊D47—21no—
182C2×C22⋊D47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47#4111yescharacteristic
186#10625354—22no—
187#10625354—22no—
188Q8×D47—22no—
189Q8×D47—22no—
190#10625352—22no—
191#10625352—22no—
192#10625352—42no—
193#10625352—42no—
194D4×D47—22no—
195D4×D47—22no—
196D4×D47—42no—
197D4×D47—42no—
198#10625350—21no—
199#10625350—21no—
200#10625350—21no—
201#10625350—21no—
202#10625350—42no—
203#10625350—42no—
204C2×D188—21no—
205C2×D188C22×C411yescharacteristic
206C2×C4×D47—24no—
207C2×C4×D47—21no—
208C2×C4×D47—21no—
209C2×C4×D47—21no—
210C2×C4×D47—21no—
211C2×C4×D47—21no—
212C2×C4×D47—42no—
213C2×C4×D47—42no—
214C2×C4×D47—42no—
215C2×C4×D47—42no—
216C2×C4×D47C22×C411yescharacteristic
217C2×C4×D47C22×C411yescharacteristic
218C2×C4×D47C2×D412yes—
219C2×C4×D47C2×D411yescharacteristic
220C2×C4×D47C2×D411yescharacteristic
221C2×C4×D47#4112yes—
222C2×C4×D47#4112yes—
223C2×C4×D47#4112yes—
224C2×Dic94—21no—
225C2×Dic94C22×C411yescharacteristic
226M16×C47—21no—
227M16×C47—21no—
228M16×C47—21no—
229M16×C47C2×D412yes—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47C22×C411yescharacteristic
237C2×C8×C47C22×C411yescharacteristic
238C2×C8×C47C2×D411yescharacteristic
239C2×C8×C47C2×D411yescharacteristic
240C4⋊C4×C47C22×C411yescharacteristic
241C4⋊C4×C47C22×C411yescharacteristic
242C22⋊C4×C47—21no—
243C42×C47—21no—
244C42×C47—21no—
245C42×C47—21no—
246C22⋊Dic47—21no—
247(C2×D47)⋊C4—21no—
248(C2×D47)⋊C4—21no—
249C4⋊Dic47C22×C411yescharacteristic
250C4⋊Dic47C22×C411yescharacteristic
251Dic47⋊C4—21no—
252Dic47⋊C4—21no—
253C4×Dic47—21no—
254C4×Dic47—21no—
255C4×Dic47—21no—
256C4×Dic47—21no—
257C4×Dic47—21no—
258C4×Dic47—42no—
259#10625329—21no—
260#10625329—21no—
261#10625329—21no—
262#10625329C2×D412yes—
263C2×C47⋊C8—21no—
264C2×C47⋊C8—21no—
265C2×C47⋊C8—21no—
266C2×C47⋊C8—21no—
267C2×C47⋊C8—21no—
268C2×C47⋊C8—21no—
269C2×C47⋊C8C22×C411yescharacteristic
270C2×C47⋊C8C22×C411yescharacteristic
271C2×C47⋊C8C2×D411yescharacteristic
272C2×C47⋊C8C2×D411yescharacteristic
273#10625324—24no—
274#10625324—42no—
275C8×D47—22no—
276C8×D47—22no—
277C8×D47—22no—
278C8×D47—22no—
279C8×D47—24no—
280C8×D47—22no—
281C8×D47—22no—
282C8×D47—22no—
283C8×D47—22no—
284C8×D47—42no—
285C23×C47—21no—
286C23×C47C2×#4111yescharacteristic
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—21no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47C4×D411yescharacteristic
294C22×D47C4×D411yescharacteristic
295C22×D47#12412yes—
296C22×D47#12612yes—
297Q8×C47—21no—
298Q8×C47—21no—
299D4×C47—21no—
300D4×C47—21no—
301D4×C47—41no—
302D4×C47—41no—
303C2×C4×C47—22no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47C23×C411yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C2×#4111yescharacteristic
315C2×C4×C47C2×#4111yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C22⋊D47—41no—
318C22⋊D47—41no—
319C22⋊D47—42no—
320C22⋊D47—42no—
321C2×Dic47—22no—
322C2×Dic47—21no—
323C2×Dic47—21no—
324C2×Dic47—21no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—42no—
328C2×Dic47C4×D411yescharacteristic
329C2×Dic47C4×D411yescharacteristic
330C2×Dic47#12412yes—
331C2×Dic47#12612yes—
332D188—21no—
333D188—21no—
334D188—42no—
335C4×D47—48no—
336C4×D47—42no—
337C4×D47—42no—
338C4×D47—42no—
339C4×D47—41no—
340C4×D47—41no—
341C4×D47—42no—
342C4×D47#11712yes—
343C4×D47#11712yes—
344C4×D47C4×D412yes—
345C4×D47C4×D412yes—
346C4×D47#12112yes—
347C4×D47#12112yes—
348C4×D47#12312yes—
349C4×D47#12312yes—
350Dic94—21no—
351Dic94—21no—
352Dic94—42no—
353C8×C47—21no—
354C8×C47—21no—
355C8×C47—22no—
356C8×C47—21no—
357C8×C47—21no—
358C8×C47—41no—
359C47⋊C8—21no—
360C47⋊C8—21no—
361C47⋊C8—22no—
362C47⋊C8—21no—
363C47⋊C8—21no—
364C47⋊C8—41no—
365C2×#1929—471nomaximal, Sylow
366C22×C47—21no—
367C22×C47—21no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47C2×C4×D411yescharacteristic
372C22×C47C2×#12411yescharacteristic
373C22×C47C2×#12611yescharacteristic
374C2×D47—21no—
375C2×D47—21no—
376C2×D47—24no—
377C2×D47—24no—
378C2×D47—41no—
379C2×D47—41no—
380C2×D47—41no—
381C2×D47—84no—
382C2×D47#38812yes—
383C2×D47#38812yes—
384C2×D47#44312yes—
385C2×D47#44412yes—
386C4×C47—42no—
387C4×C47—41no—
388C4×C47—41no—
389C4×C47—41no—
390C4×C47C2×#11711yescharacteristic
391C4×C47C2×C4×D411yescharacteristic
392C4×C47C2×#12111yescharacteristic
393C4×C47C2×#12311yescharacteristic
394Dic47—42no—
395Dic47—41no—
396Dic47—41no—
397Dic47—41no—
398Dic47#38812yes—
399Dic47#38812yes—
400C22×#108—471no—
401C22×#104—471no—
402C2×#416—471no—
403C2×#408—471no—
404C2×#405—471no—
405#1929—471no—
406#1929—471no—
407#1929—471no—
408#1929—471no—
409#1929—471no—
410#1929—471no—
411#1929—471no—
412#1929D4711yescharacteristic, direct product factor
413C2×#339—471no—
414C2×#336—471no—
415C2×C47—21no—
416C2×C47—21no—
417C2×C47—81no—
418C2×C47C2×#38811yescharacteristic
419C2×C47C2×#44311yescharacteristic
420C2×C47C2×#44411yescharacteristic
421D47—22no—
422D47—81no—
423D47#192914yesdirect product factor
424C22×#41—471no—
425C22×M16—471no—
426C22×M16—471no—
427C23×C8—471no—
428C23×C8—471no—
429C2×#117—471no—
430C22×C42—471no—
431C2×#108—471no—
432C2×#108—471no—
433C2×#108—471no—
434C2×#108—944no—
435C2×#108C2×D4711yescharacteristic, complemented
436C2×#104—471no—
437C2×#104—471no—
438C2×#104—471no—
439C2×#104—944no—
440C2×#104C2×D4711yescharacteristic
441#416—471no—
442#416—471no—
443#416—471no—
444#416—471no—
445#416—471no—
446#416—471no—
447#416—471no—
448#416C2×D4711yescharacteristic
449C2×#103—471no—
450C2×#103—471no—
451C2×#102—471no—
452C2×#102—471no—
453#408—471no—
454#408—471no—
455#408—471no—
456#408—941no—
457#408—941no—
458#408C2×D4711yescharacteristic
459C2×C22⋊C8—941no—
460C2×C22⋊C8—941no—
461#405—471no—
462#405—471no—
463#405—471no—
464#405—941no—
465#405—941no—
466#405C2×D4711yescharacteristic, complemented
467C2×#97—941no—
468C2×C4×C8—941no—
469#339—471no—
470#339—471no—
471#339—471no—
472#339C2×D4711yescharacteristic, complemented
473#336—471no—
474#336—471no—
475#336—471no—
476#336C2×D4711yescharacteristic, complemented
477C47C2×#192911yescharacteristic, complemented, Sylow
478C2×#41—471no—
479C2×#41—471no—
480C2×#41—471no—
481C2×#41—941no—
482C2×#41—941no—
483C2×#41—942no—
484C2×#41—942no—
485C2×#41—942no—
486C2×#41—942no—
487C2×#41C22×D4711yescharacteristic
488C22×Q8—471no—
489C22×D4—471no—
490C22×D4—941no—
491C23×C4—471no—
492C23×C4—941no—
493C23×C4—941no—
494C2×M16—471no—
495C2×M16—474no—
496C2×M16—471no—
497C2×M16—941no—
498C2×M16—941no—
499C2×M16—942no—
500C2×M16—942no—
501C2×M16—942no—
502C2×M16C22×D4711yescharacteristic
503C2×M16C22×D4711yescharacteristic
504C22×C8—471no—
505C22×C8—471no—
506C22×C8—471no—
507C22×C8—471no—
508C22×C8—471no—
509C22×C8—471no—
510C22×C8—471no—
511C22×C8—471no—
512C22×C8—471no—
513C22×C8—471no—
514C22×C8—942no—
515C22×C8—942no—
516C22×C8—942no—
517C22×C8—942no—
518C22×C8—941no—
519C22×C8—941no—
520C22×C8C22×D4711yescharacteristic
521C22×C8C22×D4711yescharacteristic
522#117—471no—
523#117—471no—
524#117—471no—
525#117—941no—
526#117—941no—
527#117C22×D4711yescharacteristic
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C22⋊C4—941no—
531C2×C42—471no—
532C2×C42—941no—
533C2×C42—942no—
534C2×C42—942no—
535C2×C42—941no—
536C2×C42C22×D4711yescharacteristic
537#108—22no—
538#108—942no—
539#108—942no—
540#108—942no—
541#104—22no—
542#104—942no—
543#104—942no—
544#104—942no—
545#103—471no—
546#103—471no—
547#103—471no—
548#103—471no—
549#103—471no—
550#103—471no—
551#103C4×D4711yescharacteristic, complemented
552#103C4×D4711yescharacteristic, complemented
553#102—471no—
554#102—471no—
555#102—471no—
556#102—471no—
557#102—471no—
558#102—471no—
559#102C4×D4711yescharacteristic, complemented
560#102C4×D4711yescharacteristic, complemented
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—941no—
564C22⋊C8—941no—
565C22⋊C8—941no—
566C22⋊C8—941no—
567C22⋊C8—941no—
568C22⋊C8—941no—
569#97—21no—
570#97—941no—
571#97—941no—
572#97—941no—
573C4×C8—21no—
574C4×C8—941no—
575C4×C8—941no—
576C4×C8—941no—
577C24—471no—
578C24—941no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—942no—
584#41—942no—
585#41—942no—
586#41—942no—
587#41—941no—
588#41—941no—
589#41—941no—
590#41—941no—
591#41—1882no—
592#41—1882no—
593#41—1882no—
594#41—1882no—
595C2×Q8—471no—
596C2×Q8—941no—
597C2×Q8—942no—
598C2×Q8—942no—
599C2×Q8C2×C4×D4711yescharacteristic
600C2×D4—21no—
601C2×D4—471no—
602C2×D4—941no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—941no—
606C2×D4—941no—
607C2×D4—941no—
608C2×D4—1882no—
609C2×D4—1882no—
610C2×D4C2×C4×D4711yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—471no—
614C22×C4—471no—
615C22×C4—471no—
616C22×C4—472no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—941no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—944no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—1882no—
631C22×C4—1882no—
632C22×C4—1882no—
633C22×C4—1882no—
634C22×C4C23×D4711yescharacteristic
635M16—21no—
636M16—21no—
637M16—21no—
638M16—472no—
639M16—944no—
640M16—941no—
641M16—941no—
642M16—941no—
643M16—1882no—
644M16D4×D4712yes—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—471no—
652C2×C8—471no—
653C2×C8—471no—
654C2×C8—471no—
655C2×C8—942no—
656C2×C8—942no—
657C2×C8—942no—
658C2×C8—942no—
659C2×C8—942no—
660C2×C8—942no—
661C2×C8—942no—
662C2×C8—942no—
663C2×C8—944no—
664C2×C8—941no—
665C2×C8—941no—
666C2×C8—941no—
667C2×C8—941no—
668C2×C8—941no—
669C2×C8—941no—
670C2×C8—1882no—
671C2×C8C2×C4×D4711yescharacteristic
672C2×C8C2×C4×D4711yescharacteristic
673C2×C8D4×D4711yescharacteristic
674C2×C8D4×D4711yescharacteristic
675C4⋊C4—471no—
676C4⋊C4—471no—
677C4⋊C4—941no—
678C4⋊C4—941no—
679C4⋊C4C2×C4×D4711yescharacteristic
680C4⋊C4C2×C4×D4711yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—941no—
683C22⋊C4—941no—
684C22⋊C4—941no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—941no—
689C42—941no—
690C42—941no—
691C42—941no—
692C42—941no—
693C42—1882no—
694C23—21no—
695C23—471no—
696C23—471no—
697C23—472no—
698C23—472no—
699C23—942no—
700C23—942no—
701C23—941no—
702C23—1882no—
703C23—1882no—
704C23—1882no—
705C23#41×D4711yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—941no—
709Q8—941no—
710Q8—1882no—
711D4—21no—
712D4—21no—
713D4—41no—
714D4—41no—
715D4—941no—
716D4—941no—
717D4—1882no—
718D4—1882no—
719D4—1882no—
720D4—1881no—
721D4—1881no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—471no—
731C2×C4—471no—
732C2×C4—472no—
733C2×C4—472no—
734C2×C4—472no—
735C2×C4—472no—
736C2×C4—472no—
737C2×C4—472no—
738C2×C4—472no—
739C2×C4—472no—
740C2×C4—472no—
741C2×C4—472no—
742C2×C4—942no—
743C2×C4—941no—
744C2×C4—941no—
745C2×C4—941no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4—1888no—
751C2×C4—1882no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1881no—
756C2×C4C22×C4×D4711yescharacteristic
757C2×C4C2×D4×D4711yescharacteristic
758C2×C4C2×D4×D4711yescharacteristic
759C2×C4#41×D4711yescharacteristic
760C2×C4#41×D4711yescharacteristic
761C2×C4#41×D4711yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—21no—
766C8—21no—
767C8—41no—
768C8—941no—
769C8—941no—
770C8—942no—
771C8—941no—
772C8—941no—
773C8—1881no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—472no—
780C22—472no—
781C22—472no—
782C22—472no—
783C22—944no—
784C22—944no—
785C22—941no—
786C22—941no—
787C22—3764no—
788C22—1881no—
789C22—1881no—
790C22—1881no—
791C22C4×D4×D4711yescharacteristic
792C22#124×D4711yescharacteristic
793C22#126×D4711yescharacteristic
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—472no—
799C4—472no—
800C4—1882no—
801C4—1881no—
802C4—1881no—
803C4—1881no—
804C4#117×D4711yescharacteristic
805C4C4×D4×D4711yescharacteristic
806C4#121×D4711yescharacteristic
807C4#123×D4711yescharacteristic
808C2—21no—
809C2—21no—
810C2—81no—
811C2—474no—
812C2—942no—
813C2—3761no—
814C2#388×D4711yescharacteristic
815C2#443×D4711yescharacteristic
816C2#444×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1929C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×D47C22
cosocleC22×C4×C47C24
hypercenter#1929D47
hypocenterC47C2×#1929
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#108×D47C2semidirect
5. #405×D47C2semidirect
6. #20244039C2semidirect
7. #20244038C2semidirect
8. #20244037C2semidirect
9. #20244036C2semidirect
10. #20244035C2semidirect
11. #20244034C2semidirect
12. #20244033C2semidirect
13. #339×D47C2semidirect
14. #336×D47C2semidirect
15. C47×#1929C2semidirect
23. C2×#13093960C22semidirect
24. C2×#13093959C22semidirect
25. C2×#13093959C22semidirect
33. #15689118C4semidirect
34. #15689118C4semidirect
36. #15689116C4semidirect
37. #15689116C4semidirect
38. #103×D47C4semidirect
39. #103×D47C4semidirect
40. #102×D47C4semidirect
41. #102×D47C4semidirect
49. #15689081C22semidirect
51. #15689079C22semidirect
52. #15689078C22semidirect
56. #15688884C22semidirect
57. #15688883C22semidirect
58. #15688882C22semidirect
59. #15688878C22semidirect
60. #15688877C22semidirect
61. #15688877C22semidirect
62. C2×#108×C47C22semidirect
66. C47×#405C22semidirect
67. C47×#339C22semidirect
68. C47×#336C22semidirect
127. #13093949C2×C4semidirect
128. #13093949C2×C4semidirect
129. #13093948C2×C4semidirect
130. #13093948C2×C4semidirect
131. #13093947C2×C4semidirect
132. #13093947C2×C4semidirect
133. #13093946C2×C4semidirect
134. #13093946C2×C4semidirect
135. #13093945C2×C4semidirect
136. #13093945C2×C4semidirect
137. #13093944C2×C4semidirect
138. #13093944C2×C4semidirect
160. #103×C47C2×C4semidirect
161. #103×C47C2×C4semidirect
162. #102×C47C2×C4semidirect
163. #102×C47C2×C4semidirect
412. #1929D47direct (N × H)
423. D47#1929direct (N × H)
435. C2×#108C2×D47semidirect
466. #405C2×D47semidirect
472. #339C2×D47semidirect
476. #336C2×D47semidirect
477. C47C2×#1929semidirect
551. #103C4×D47semidirect
552. #103C4×D47semidirect
559. #102C4×D47semidirect
560. #102C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D472
C2×#104×D472
#416×D472
#408×D472
#405×D472
#202440392
#202440382
#202440372
#202440362
#202440352
#202440342
#202440332
#339×D472
#336×D472
C47×#19292
C2×#192947