Finite Group Databasebeta

← #27079857

Subgroups — #27079857

Order 12032.

4902 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689958C211yesmaximal, characteristic
2C2×#15689888C211yesmaximal, characteristic, complemented
3#520×D47C211yesmaximal, characteristic, complemented
4#20251922C211yesmaximal, characteristic, complemented
5#20251919C213yesmaximal, complemented
6#20251918C211yesmaximal, characteristic, complemented
7#20251917C213yesmaximal, complemented
8#20251914C211yesmaximal, characteristic, complemented
9#20251913C213yesmaximal, complemented
10#20251909C213yesmaximal, complemented
11#20251903C213yesmaximal, complemented
12#20251902C213yesmaximal, complemented
13C2×#15689121C213yesmaximal, complemented
14#417×D47C213yesmaximal, complemented
15C47×#2897C211yesmaximal, characteristic, complemented
16#15689958—28no—
17#15689958C4116yescomplemented
18C2×#13094071—21no—
19C2×#13094071C2211yescharacteristic
20C2×#13094071C2213yes—
21C2×#13094069—23no—
22C2×#13094069C2213yes—
23C22×#10625352—23no—
24C22×#10625352C2213yes—
25C2×#41×D47—21no—
26C2×#41×D47C2213yes—
27C2×#41×D47C2211yescharacteristic
28#15689888—28no—
29C2×#13094032C2213yescomplemented
30C2×#13094031C2211yescharacteristic, complemented
31C2×#13094030C2213yescomplemented
32C22×#10625324C2213yescomplemented
33C2×M16×D47C2213yescomplemented
34#15689606C2211yescharacteristic, complemented
35#15689605—21no—
36#15689604C2213yescomplemented
37#15689603C2213yescomplemented
38#15689602—23no—
39C4×Q8×D47—21no—
40C4×D4×D47—23no—
41#117×D47C2213yescomplemented
42C2×C4⋊C4×D47C2213yescomplemented
43#15689133C2213yescomplemented
44#15689131C2213yescomplemented
45#15689130C2213yescomplemented
46#15689130C2213yescomplemented
47#15689128C2213yescomplemented
48#15689126C2213yescomplemented
49#15689126C2213yescomplemented
50#15689125C2213yescomplemented
51#15689124C2213yescomplemented
52#15689123C2213yescomplemented
53#15689123C2211yescharacteristic, complemented
54#15689122C2213yescomplemented
55#15689121C2216yescomplemented
56#15689121C2216yescomplemented
57#15689121C2216yescomplemented
58#15689121C2213yescomplemented
59#15689121C2213yescomplemented
60#15689120C2213yescomplemented
61#15689119C2213yescomplemented
62#15689117C2213yescomplemented
63#15689116C2216yescomplemented
64#15689116C2216yescomplemented
65C2×#13093949C2213yescomplemented
66C2×#13093947C2213yescomplemented
67#103×D47C2216yescomplemented
68C2×#13093945C2213yescomplemented
69#102×D47C2216yescomplemented
70C2×H(5,𝔽2)×C47C2211yescharacteristic
71C2×#131×C47C2211yescharacteristic, complemented
72C47×#520C2211yescharacteristic, complemented
73C47×#418C2213yescomplemented
74C47×#417C2213yescomplemented
75C47×#416C2213yescomplemented
76C2×#102×C47C2213yescomplemented
77#13094071—24no—
78#13094071—216no—
79#13094071—212no—
80#13094071C2×C4124yescomplemented
81#13094071C2×C418yescomplemented
82#13094069—248no—
83#13094069—212no—
84#13094069C2×C4124yescomplemented
85C2×#10625354D411yescharacteristic
86C2×#10625354C2311yescharacteristic
87C2×#10625350—23no—
88C2×#10625350—23no—
89C2×#10625350C2313yes—
90C2×#10625350C2313yes—
91C2×#10625352—23no—
92C2×#10625352—26no—
93C2×#10625352—23no—
94C2×#10625352—248no—
95C2×#10625352—23no—
96C2×#10625352—23no—
97C2×#10625352—212no—
98C2×#10625352—23no—
99C2×#10625352C2×C4124yescomplemented
100C2×#10625352D413yes—
101C2×#10625352C2313yes—
102C2×#10625352C2316yes—
103#41×D47—216no—
104#41×D47—212no—
105#41×D47C2×C418yes—
106#41×D47C2×C4124yescomplemented
107#41×D47D418yes—
108C22×Dic94—23no—
109C22×Dic94C2313yes—
110C2×Q8×D47—21no—
111C2×Q8×D47D411yescharacteristic
112C2×Q8×D47C2313yes—
113C22×C22⋊D47—23no—
114C22×C22⋊D47—26no—
115C2×D4×D47—23no—
116C2×D4×D47—23no—
117C2×D4×D47D413yes—
118C2×D4×D47C2313yes—
119C23×Dic47—23no—
120C22×C4×D47—23no—
121C22×C4×D47—23no—
122C22×C4×D47C2313yes—
123#13094032—212no—
124#13094031—24no—
125#13094030—212no—
126C2×#10625329C2313yes—
127C2×#10625324—212no—
128C2×#10625324C2313yes—
129C2×#10625324C2311yescharacteristic
130C2×#10625324C2313yes—
131C2×#10625324C2313yes—
132M16×D47—212no—
133C22×C47⋊C8C2313yes—
134C2×C8×D47C2316yes—
135Q8×Dic47—21no—
136C4×Dic94—23no—
137#13093989—23no—
138C4×D188—23no—
139D4×Dic47—23no—
140#13093986—23no—
141C4×C22⋊D47—26no—
142(C22⋊D47)⋊C4—26no—
143#13093983C2313yes—
144#13093982C2313yes—
145#13093982C2313yes—
146#13093981—23no—
147#13093980—23no—
148C2×C4⋊Dic47C2313yes—
149C2×Dic47⋊C4—23no—
150C4⋊C4×D47—23no—
151C4⋊C4×D47—23no—
152C4⋊C4×D47C2313yes—
153C4⋊C4×D47C2316yes—
154C4⋊C4×D47C2311yescharacteristic
155C22⋊C4×D47—23no—
156C42×D47—23no—
157#13093949C2316yes—
158#13093949C2313yes—
159#13093949C2313yes—
160#13093948C2313yes—
161#13093948C2311yescharacteristic
162#13093947C2316yes—
163#13093947C2313yes—
164#13093947C2313yes—
165#13093946C2313yes—
166#13093946C2311yescharacteristic
167#13093945C2316yes—
168#13093945C2313yes—
169#13093945C2313yes—
170#13093944C2313yes—
171#13093944C2311yescharacteristic
172H(5,𝔽2)×C47—24no—
173H(5,𝔽2)×C47C2×C418yescomplemented
174C2×#41×C47—21no—
175C2×#41×C47C2313yes—
176C2×#41×C47C2311yescharacteristic
177C22×D4×C47—23no—
178C22×D4×C47C2313yes—
179#131×C47—24no—
180C2×M16×C47C2313yes—
181C22×C8×C47C2313yes—
182C4×Q8×C47—21no—
183C4×D4×C47—23no—
184#117×C47C2313yes—
185C2×C4⋊C4×C47C2313yes—
186#103×C47C2313yes—
187#103×C47C2311yescharacteristic
188#102×C47C2316yes—
189#102×C47C2313yes—
190#102×C47C2313yes—
191C24×C47—23no—
192C23×D47—23no—
193C23×D47C2×D413yes—
194#41×C47—28no—
195#41×C47—26no—
196#41×C47C22×C414yes—
197#41×C47C22×C4112yescomplemented
198#41×C47C2×D414yes—
199C2×Q8×C47C2×D411yescharacteristic
200C2×Q8×C47C2411yescharacteristic
201C2×D4×C47—23no—
202C2×D4×C47—224no—
203C2×D4×C47—23no—
204C2×D4×C47—26no—
205C2×D4×C47C22×C4112yescomplemented
206C2×D4×C47C2×D413yes—
207C2×D4×C47C2413yes—
208C22×C4×C47—23no—
209C22×C4×C47—23no—
210C22×C4×C47C2413yes—
211C2×C22⋊D47—23no—
212C2×C22⋊D47—224no—
213C2×C22⋊D47—23no—
214C2×C22⋊D47—26no—
215C2×C22⋊D47—248no—
216C2×C22⋊D47—23no—
217C2×C22⋊D47C2×D416yes—
218C22×Dic47—23no—
219C22×Dic47—224no—
220C22×Dic47—23no—
221C22×Dic47—26no—
222C22×Dic47—23no—
223C22×Dic47C2×D413yes—
224#10625354—22no—
225#10625354C22⋊C418yes—
226#10625354C22×C414yes—
227Q8×D47—28no—
228Q8×D47—26no—
229Q8×D47C22⋊C418yes—
230Q8×D47C22×C4112yescomplemented
231#10625352—224no—
232#10625352—248no—
233#10625352—224no—
234#10625352—224no—
235#10625352—224no—
236#10625352—26no—
237#10625352—212no—
238#10625352—224no—
239#10625352C22⋊C4124yes—
240#10625352C22×C4112yes—
241#10625352C22×C4124yescomplemented
242D4×D47—224no—
243D4×D47—224no—
244D4×D47—26no—
245D4×D47C22⋊C4124yes—
246D4×D47C22×C4112yescomplemented
247#10625350—26no—
248#10625350—224no—
249#10625350—224no—
250#10625350C22×C4112yes—
251#10625350C22×C4112yescomplemented
252#10625350C2×D4112yes—
253C2×D188—21no—
254C2×D188C2×D413yes—
255C2×D188C2411yescharacteristic
256C2×C4×D47—23no—
257C2×C4×D47—23no—
258C2×C4×D47—21no—
259C2×C4×D47—224no—
260C2×C4×D47—21no—
261C2×C4×D47—23no—
262C2×C4×D47—26no—
263C2×C4×D47—86no—
264C2×C4×D47C22×C4112yes—
265C2×C4×D47C2×D413yes—
266C2×C4×D47C2×D413yes—
267C2×C4×D47C2×D4112yes—
268C2×C4×D47C2411yescharacteristic
269C2×C4×D47C2413yes—
270C2×Dic94—23no—
271C2×Dic94—26no—
272C2×Dic94—23no—
273C2×Dic94—224no—
274C2×Dic94C22×C4112yescomplemented
275C2×Dic94C2×D413yes—
276C2×Dic94C2413yes—
277M16×C47—26no—
278C2×C8×C47—26no—
279C2×C8×C47C2411yescharacteristic
280C2×C8×C47C2413yes—
281C4⋊C4×C47—23no—
282C4⋊C4×C47C2413yes—
283C4⋊C4×C47C2411yescharacteristic
284C22⋊C4×C47—23no—
285C42×C47—23no—
286C22⋊Dic47—23no—
287(C2×D47)⋊C4—23no—
288(C2×D47)⋊C4—23no—
289C4⋊Dic47—23no—
290C4⋊Dic47C2413yes—
291C4⋊Dic47C2411yescharacteristic
292Dic47⋊C4—23no—
293Dic47⋊C4—26no—
294Dic47⋊C4—21no—
295C4×Dic47—23no—
296C4×Dic47—23no—
297C4×Dic47—23no—
298#10625329—26no—
299C2×C47⋊C8—26no—
300C2×C47⋊C8C2413yes—
301C2×C47⋊C8C2411yescharacteristic
302#10625324—26no—
303#10625324—22no—
304#10625324—26no—
305#10625324—26no—
306C8×D47—212no—
307C23×C47—23no—
308C23×C47—212no—
309C23×C47—83no—
310C23×C47—83no—
311C23×C47C22×D413yes—
312C22×D47—21no—
313C22×D47—212no—
314C22×D47—43no—
315C22×D47—43no—
316C22×D47—83no—
317C22×D47—83no—
318C22×D47C2×C22⋊C4112yes—
319C22×D47C22×D413yes—
320C22×D47C22×D411yescharacteristic
321Q8×C47—21no—
322Q8×C47C2×C22⋊C414yes—
323Q8×C47C23×C412yes—
324D4×C47—212no—
325D4×C47—212no—
326D4×C47—23no—
327D4×C47C2×C22⋊C4112yes—
328D4×C47C23×C416yes—
329C2×C4×C47—21no—
330C2×C4×C47—212no—
331C2×C4×C47—21no—
332C2×C4×C47—23no—
333C2×C4×C47—83no—
334C2×C4×C47C23×C416yes—
335C2×C4×C47C22×D413yes—
336C2×C4×C47C22×D416yes—
337C2×C4×C47C2511yescharacteristic
338C22⋊D47—212no—
339C22⋊D47—212no—
340C22⋊D47—224no—
341C22⋊D47—212no—
342C22⋊D47C2×C22⋊C4124yes—
343C2×Dic47—212no—
344C2×Dic47—23no—
345C2×Dic47—224no—
346C2×Dic47—212no—
347C2×Dic47—21no—
348C2×Dic47—23no—
349C2×Dic47—83no—
350C2×Dic47C2×C22⋊C4112yes—
351C2×Dic47C22×D413yes—
352C2×Dic47C22×D411yescharacteristic
353D188—24no—
354D188—21no—
355D188C2×C22⋊C4112yes—
356D188C23×C412yes—
357C4×D47—212no—
358C4×D47—212no—
359C4×D47—24no—
360C4×D47—42no—
361C4×D47—46no—
362C4×D47—86no—
363C4×D47C2×C22⋊C4112yes—
364C4×D47C2×C22⋊C4112yes—
365C4×D47C23×C412yes—
366C4×D47C23×C416yes—
367C4×D47C22×D416yes—
368C4×D47C22×D412yes—
369Dic94—212no—
370Dic94—23no—
371Dic94—212no—
372Dic94C2×C22⋊C4112yes—
373Dic94C23×C416yes—
374C8×C47—23no—
375C8×C47—21no—
376C47⋊C8—23no—
377C47⋊C8—21no—
378#60089—471nomaximal, Sylow
379C22×C47—23no—
380C22×C47—23no—
381C22×C47—26no—
382C22×C47—43no—
383C22×C47—43no—
384C22×C47—812no—
385C22×C47C22×C22⋊C416yes—
386C22×C47C23×D411yescharacteristic
387C2×D47—21no—
388C2×D47—23no—
389C2×D47—21no—
390C2×D47—23no—
391C2×D47—22no—
392C2×D47—412no—
393C2×D47—41no—
394C2×D47—41no—
395C2×D47—812no—
396C2×D47C22×C22⋊C416yes—
397C2×D47C22×C22⋊C412yes—
398C4×C47—22no—
399C4×C47—43no—
400C4×C47—41no—
401C4×C47C22×C22⋊C416yes—
402C4×C47C24×C411yescharacteristic
403C4×C47C23×D411yescharacteristic
404Dic47—26no—
405Dic47—43no—
406Dic47—41no—
407Dic47C22×C22⋊C416yes—
408Dic47C22×C22⋊C412yes—
409C2×#585—471no—
410C2×#568—471no—
411C2×#520—471no—
412#2898—473no—
413#2898—473no—
414#2898—471no—
415#2898—471no—
416#2897—473no—
417#2897—473no—
418#2897—471no—
419#2897D4711yescharacteristic, complemented
420#2896—473no—
421#2896—473no—
422C2×#417—473no—
423C2×#417—473no—
424C2×C47—26no—
425C2×C47—46no—
426C2×C47C23×C22⋊C411yescharacteristic
427C2×C47#358511yescharacteristic
428C2×C47#358611yescharacteristic
429D47—22no—
430D47—26no—
431D47—42no—
432#585—4716no—
433#585—948no—
434C2×2−1+4—473no—
435C2×2−1+4—471no—
436C2×2−1+4—941no—
437C2×H(5,𝔽2)—473no—
438C2×H(5,𝔽2)—943no—
439C2×H(5,𝔽2)C2×D4711yescharacteristic
440C22×#41—471no—
441C22×#41—473no—
442C22×#41—473no—
443C22×#41—943no—
444C22×#41—941no—
445#568—948no—
446C2×#131—471no—
447C2×#131—473no—
448C2×#131—473no—
449C2×#131C2×D4711yescharacteristic, complemented
450C22×M16—473no—
451C22×M16—473no—
452#520—471no—
453#520—473no—
454#520—473no—
455#520—943no—
456#520—941no—
457#520C2×D4711yescharacteristic, complemented
458C2×C4×Q8—941no—
459C2×C4×D4—943no—
460C2×#117—473no—
461C22×C4⋊C4—473no—
462#419—473no—
463#419—473no—
464#419—473no—
465#419—473no—
466#418—473no—
467#418—473no—
468#418—473no—
469#418C2×D4713yescomplemented
470#417—473no—
471#417—473no—
472#417—473no—
473#417—473no—
474#417—471no—
475#417—476no—
476#417—473no—
477#417—476no—
478#417—476no—
479#417—473no—
480#417C2×D4713yescomplemented
481#416—473no—
482#416—473no—
483#416—473no—
484#416—476no—
485#416—476no—
486#416C2×D4713yescomplemented
487C2×#103—473no—
488C2×#103—473no—
489C2×#103—476no—
490C2×#102—473no—
491C2×#102—476no—
492C2×#102C2×D4713yescomplemented
493C47#6008911yescharacteristic, complemented, Sylow
4942−1+4—478no—
4952−1+4—4724no—
4962−1+4—9416no—
4972−1+4—9412no—
4982−1+4—944no—
499H(5,𝔽2)—24no—
500H(5,𝔽2)—4724no—
501H(5,𝔽2)—9448no—
502H(5,𝔽2)—9412no—
503H(5,𝔽2)C4×D4718yescomplemented
504C2×#41—21no—
505C2×#41—478no—
506C2×#41—478no—
507C2×#41—471no—
508C2×#41—473no—
509C2×#41—473no—
510C2×#41—4724no—
511C2×#41—471no—
512C2×#41—4724no—
513C2×#41—473no—
514C2×#41—476no—
515C2×#41—473no—
516C2×#41—943no—
517C2×#41—943no—
518C2×#41—943no—
519C2×#41—943no—
520C2×#41—943no—
521C2×#41—9412no—
522C2×#41—9412no—
523C2×#41—946no—
524C2×#41—943no—
525C2×#41—9448no—
526C2×#41—9416no—
527C2×#41—943no—
528C2×#41C22×D4713yes—
529C2×#41C22×D4711yescharacteristic
530C22×Q8—471no—
531C22×Q8—473no—
532C22×Q8—473no—
533C22×Q8—943no—
534C22×Q8—941no—
535C22×D4—23no—
536C22×D4—473no—
537C22×D4—473no—
538C22×D4—943no—
539C22×D4—943no—
540C22×D4—946no—
541C22×D4—943no—
542C22×D4C22×D4713yes—
543C23×C4—473no—
544C23×C4—943no—
545C23×C4—943no—
546C23×C4—943no—
547#131—24no—
548#131—9412no—
549#131—9412no—
550#131—944no—
551C2×M16—473no—
552C2×M16—473no—
553C2×M16—471no—
554C2×M16—473no—
555C2×M16—473no—
556C2×M16—9412no—
557C2×M16—9412no—
558C2×M16C22×D4713yes—
559C22×C8—473no—
560C22×C8—476no—
561C22×C8C22×D4713yes—
562C4×Q8—21no—
563C4×Q8—943no—
564C4×Q8—943no—
565C4×Q8—941no—
566C4×D4—23no—
567C4×D4—943no—
568C4×D4—946no—
569C4×D4—943no—
570C4×D4—946no—
571C4×D4—943no—
572#117—473no—
573#117—473no—
574#117—473no—
575#117—943no—
576#117—943no—
577#117C22×D4713yes—
578C2×C4⋊C4—473no—
579C2×C4⋊C4—473no—
580C2×C4⋊C4—476no—
581C2×C4⋊C4—471no—
582C2×C4⋊C4—943no—
583C2×C4⋊C4—943no—
584C2×C4⋊C4—943no—
585C2×C4⋊C4C22×D4713yes—
586C2×C22⋊C4—943no—
587C2×C42—943no—
588#103—473no—
589#103—471no—
590#103—476no—
591#103—473no—
592#103—473no—
593#103—476no—
594#103—473no—
595#103—473no—
596#103C22×D4713yes—
597#103C22×D4711yescharacteristic
598#102—476no—
599#102—473no—
600#102—473no—
601#102—473no—
602#102—471no—
603#102—473no—
604#102—471no—
605#102C22×D4716yes—
606#102C22×D4713yes—
607#102C22×D4713yes—
608C24—23no—
609C24—473no—
610C24—943no—
611#41—28no—
612#41—26no—
613#41—478no—
614#41—4724no—
615#41—4712no—
616#41—4712no—
617#41—474no—
618#41—4712no—
619#41—4724no—
620#41—4712no—
621#41—9424no—
622#41—9424no—
623#41—9424no—
624#41—9424no—
625#41—946no—
626#41—9424no—
627#41—9412no—
628#41—942no—
629#41—9448no—
630#41—9424no—
631#41—9424no—
632#41—946no—
633#41C2×C4×D4714yes—
634#41C2×C4×D47112yescomplemented
635#41D4×D4714yes—
636C2×Q8—478no—
637C2×Q8—473no—
638C2×Q8—4712no—
639C2×Q8—4712no—
640C2×Q8—473no—
641C2×Q8—943no—
642C2×Q8—9424no—
643C2×Q8—946no—
644C2×Q8—948no—
645C2×Q8—943no—
646C2×Q8—946no—
647C2×Q8D4×D4711yescharacteristic
648C2×Q8C23×D4711yescharacteristic
649C2×D4—23no—
650C2×D4—224no—
651C2×D4—23no—
652C2×D4—26no—
653C2×D4—476no—
654C2×D4—4724no—
655C2×D4—4712no—
656C2×D4—473no—
657C2×D4—471no—
658C2×D4—941no—
659C2×D4—946no—
660C2×D4—943no—
661C2×D4—9424no—
662C2×D4—9424no—
663C2×D4—9448no—
664C2×D4—946no—
665C2×D4—943no—
666C2×D4—9424no—
667C2×D4—943no—
668C2×D4C2×C4×D47112yescomplemented
669C2×D4D4×D4713yes—
670C2×D4C23×D4713yes—
671C22×C4—23no—
672C22×C4—23no—
673C22×C4—473no—
674C22×C4—4712no—
675C22×C4—473no—
676C22×C4—473no—
677C22×C4—4712no—
678C22×C4—471no—
679C22×C4—473no—
680C22×C4—941no—
681C22×C4—9424no—
682C22×C4—943no—
683C22×C4—946no—
684C22×C4—941no—
685C22×C4—943no—
686C22×C4—943no—
687C22×C4—946no—
688C22×C4—9424no—
689C22×C4—943no—
690C22×C4—943no—
691C22×C4—943no—
692C22×C4—3766no—
693C22×C4C23×D4713yes—
694M16—26no—
695M16—942no—
696M16—946no—
697M16—946no—
698M16—946no—
699M16—946no—
700C2×C8—26no—
701C2×C8—473no—
702C2×C8—471no—
703C2×C8—9412no—
704C2×C8—946no—
705C2×C8C23×D4713yes—
706C2×C8C23×D4711yescharacteristic
707C4⋊C4—23no—
708C4⋊C4—473no—
709C4⋊C4—471no—
710C4⋊C4—943no—
711C4⋊C4—946no—
712C4⋊C4—941no—
713C4⋊C4—943no—
714C4⋊C4C23×D4713yes—
715C4⋊C4C23×D4711yescharacteristic
716C22⋊C4—23no—
717C22⋊C4—943no—
718C22⋊C4—943no—
719C22⋊C4—943no—
720C42—23no—
721C42—943no—
722C42—943no—
723C42—943no—
724C23—23no—
725C23—212no—
726C23—83no—
727C23—83no—
728C23—473no—
729C23—471no—
730C23—4712no—
731C23—9412no—
732C23—941no—
733C23—3763no—
734C23—3763no—
735C23—1883no—
736C23—1883no—
737C23C2×D4×D4713yes—
738Q8—21no—
739Q8—4712no—
740Q8—476no—
741Q8—9412no—
742Q8—9412no—
743Q8—943no—
744Q8C22⋊C4×D4714yes—
745Q8C22×C4×D4712yes—
746D4—212no—
747D4—212no—
748D4—23no—
749D4—4724no—
750D4—4712no—
751D4—472no—
752D4—944no—
753D4—9412no—
754D4—9412no—
755D4—9424no—
756D4—9412no—
757D4—941no—
758D4C22⋊C4×D47112yes—
759D4C22×C4×D4716yes—
760C2×C4—21no—
761C2×C4—212no—
762C2×C4—21no—
763C2×C4—23no—
764C2×C4—83no—
765C2×C4—4712no—
766C2×C4—473no—
767C2×C4—471no—
768C2×C4—4712no—
769C2×C4—4712no—
770C2×C4—472no—
771C2×C4—476no—
772C2×C4—476no—
773C2×C4—472no—
774C2×C4—944no—
775C2×C4—9412no—
776C2×C4—9412no—
777C2×C4—9424no—
778C2×C4—9412no—
779C2×C4—943no—
780C2×C4—9412no—
781C2×C4—941no—
782C2×C4—943no—
783C2×C4—3766no—
784C2×C4—3763no—
785C2×C4—1882no—
786C2×C4—1886no—
787C2×C4C22×C4×D4716yes—
788C2×C4C2×D4×D4713yes—
789C2×C4C2×D4×D4716yes—
790C2×C4C24×D4711yescharacteristic
791C8—21no—
792C8—23no—
793C8—943no—
794C8—941no—
795C22—23no—
796C22—23no—
797C22—26no—
798C22—43no—
799C22—43no—
800C22—812no—
801C22—472no—
802C22—476no—
803C22—943no—
804C22—941no—
805C22—941no—
806C22—943no—
807C22—942no—
808C22—37612no—
809C22—18812no—
810C22—1881no—
811C22—1881no—
812C22C2×C22⋊C4×D4716yes—
813C22C22×D4×D4711yescharacteristic
814C4—22no—
815C4—43no—
816C4—41no—
817C4—472no—
818C4—476no—
819C4—946no—
820C4—1883no—
821C4—1881no—
822C4C2×C22⋊C4×D4716yes—
823C4C23×C4×D4711yescharacteristic
824C4C22×D4×D4711yescharacteristic
825C2—26no—
826C2—46no—
827C2—946no—
828C2—942no—
829C2—1882no—
830C2C22×C22⋊C4×D4711yescharacteristic
831C2#2025816311yescharacteristic
832C2#2025817011yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC47×#2897C2
socleC22×C47C23×D4
prime radicalC2×#15689958C2
cosocleC2×C4×C47C25
hypercenter#2897D47
hypocenterC47#60089
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. C2×#15689888C2semidirect
3. #520×D47C2semidirect
4. #20251922C2semidirect
5. #20251919C2semidirect
6. #20251918C2semidirect
7. #20251917C2semidirect
8. #20251914C2semidirect
9. #20251913C2semidirect
10. #20251909C2semidirect
11. #20251903C2semidirect
12. #20251902C2semidirect
13. C2×#15689121C2semidirect
14. #417×D47C2semidirect
15. C47×#2897C2semidirect
17. #15689958C4semidirect
29. C2×#13094032C22semidirect
30. C2×#13094031C22semidirect
31. C2×#13094030C22semidirect
32. C22×#10625324C22semidirect
33. C2×M16×D47C22semidirect
34. #15689606C22semidirect
36. #15689604C22semidirect
37. #15689603C22semidirect
41. #117×D47C22semidirect
42. C2×C4⋊C4×D47C22semidirect
43. #15689133C22semidirect
44. #15689131C22semidirect
45. #15689130C22semidirect
46. #15689130C22semidirect
47. #15689128C22semidirect
48. #15689126C22semidirect
49. #15689126C22semidirect
50. #15689125C22semidirect
51. #15689124C22semidirect
52. #15689123C22semidirect
53. #15689123C22semidirect
54. #15689122C22semidirect
55. #15689121C22semidirect
56. #15689121C22semidirect
57. #15689121C22semidirect
58. #15689121C22semidirect
59. #15689121C22semidirect
60. #15689120C22semidirect
61. #15689119C22semidirect
62. #15689117C22semidirect
63. #15689116C22semidirect
64. #15689116C22semidirect
65. C2×#13093949C22semidirect
66. C2×#13093947C22semidirect
67. #103×D47C22semidirect
68. C2×#13093945C22semidirect
69. #102×D47C22semidirect
71. C2×#131×C47C22semidirect
72. C47×#520C22semidirect
73. C47×#418C22semidirect
74. C47×#417C22semidirect
75. C47×#416C22semidirect
76. C2×#102×C47C22semidirect
80. #13094071C2×C4semidirect
81. #13094071C2×C4semidirect
84. #13094069C2×C4semidirect
99. C2×#10625352C2×C4semidirect
106. #41×D47C2×C4semidirect
173. H(5,𝔽2)×C47C2×C4semidirect
197. #41×C47C22×C4semidirect
205. C2×D4×C47C22×C4semidirect
230. Q8×D47C22×C4semidirect
241. #10625352C22×C4semidirect
246. D4×D47C22×C4semidirect
251. #10625350C22×C4semidirect
274. C2×Dic94C22×C4semidirect
419. #2897D47semidirect
449. C2×#131C2×D47semidirect
457. #520C2×D47semidirect
469. #418C2×D47semidirect
480. #417C2×D47semidirect
486. #416C2×D47semidirect
492. C2×#102C2×D47semidirect
493. C47#60089semidirect
503. H(5,𝔽2)C4×D47semidirect
634. #41C2×C4×D47semidirect
668. C2×D4C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899582
C2×#156898882
#520×D472
#202519222
#202519192
#202519182
#202519172
#202519142
#202519132
#202519092
#202519032
#202519022
C2×#156891212
#417×D472
C47×#28972
#6008947