Finite Group Databasebeta

← #27079840

Subgroups — #27079840

Order 12032.

4874 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689960C211yesmaximal, characteristic
2C2×#131×D47C211yesmaximal, characteristic, complemented
3#20256588C211yesmaximal, characteristic, complemented
4#20251921C211yesmaximal, characteristic, complemented
5#20251920C213yesmaximal, complemented
6#20251916C213yesmaximal, complemented
7#20251915C211yesmaximal, characteristic, complemented
8#20251912C213yesmaximal, complemented
9#20251911C211yesmaximal, characteristic, complemented
10#20251910C213yesmaximal, complemented
11#20251906C213yesmaximal, complemented
12#20251904C213yesmaximal, complemented
13C2×#15689118C213yesmaximal, complemented
14#416×D47C213yesmaximal, complemented
15C47×#2898C211yesmaximal, characteristic, complemented
16#15689960—28no—
17#15689960C4116yescomplemented
18C2×#13094072—21no—
19C2×#13094072C2213yes—
20C2×#13094070—23no—
21C2×#13094070C2211yescharacteristic
22C2×#13094070C2213yes—
23C22×#10625354—21no—
24C22×#10625354C2213yes—
25C2×#41×D47—23no—
26C2×#41×D47C2213yes—
27C2×#41×D47C2211yescharacteristic
28C2×#13094032C2213yescomplemented
29C2×#13094031C2211yescharacteristic, complemented
30C2×#13094030C2213yescomplemented
31#131×D47—28no—
32C2×M16×D47C2213yescomplemented
33C22×C8×D47C2213yescomplemented
34#15689606C2211yescharacteristic, complemented
35#15689604C2213yescomplemented
36#15689603C2213yescomplemented
37#15689599—21no—
38#15689595—23no—
39C4×#10625354—21no—
40C4×#10625352—23no—
41C2×#13093982C2213yescomplemented
42#117×D47C2213yescomplemented
43#15689132C2213yescomplemented
44#15689130C2216yescomplemented
45#15689129C2213yescomplemented
46#15689127C2213yescomplemented
47#15689126C2216yescomplemented
48#15689125C2213yescomplemented
49#15689124C2213yescomplemented
50#15689123C2216yescomplemented
51#15689123C2216yescomplemented
52#15689122C2213yescomplemented
53#15689120C2213yescomplemented
54#15689119C2213yescomplemented
55#15689118C2216yescomplemented
56#15689118C2213yescomplemented
57#15689118C2216yescomplemented
58#15689118C2216yescomplemented
59#15689118C2213yescomplemented
60#15689117C2213yescomplemented
61#15689116C2213yescomplemented
62#15689116C2211yescharacteristic, complemented
63C2×#13093948C2213yescomplemented
64#103×D47C2213yescomplemented
65#103×D47C2213yescomplemented
66C2×#13093946C2213yescomplemented
67C2×#13093944C2213yescomplemented
68#102×D47C2213yescomplemented
69#102×D47C2213yescomplemented
70C2×2−1+4×C47C2211yescharacteristic
71C2×#131×C47C2211yescharacteristic, complemented
72C47×#520C2211yescharacteristic, complemented
73C47×#419C2213yescomplemented
74C47×#417C2213yescomplemented
75C47×#416C2213yescomplemented
76C2×#103×C47C2213yescomplemented
77#13094072—216no—
78#13094072—212no—
79#13094072C2×C4124yescomplemented
80#13094070—24no—
81#13094070—248no—
82#13094070—212no—
83#13094070C2×C4124yescomplemented
84#13094070C2×C418yescomplemented
85C2×#10625354—21no—
86C2×#10625354—216no—
87C2×#10625354—23no—
88C2×#10625354—23no—
89C2×#10625354—23no—
90C2×#10625354—212no—
91C2×#10625354C2×C4124yescomplemented
92C2×#10625354D411yescharacteristic
93C2×#10625354C2313yes—
94C2×#10625354C2316yes—
95C2×#10625350—26no—
96C2×#10625350—23no—
97C2×#10625350—23no—
98C2×#10625350C2313yes—
99C2×#10625350C2313yes—
100C2×#10625352—23no—
101C2×#10625352D413yes—
102C2×#10625352C2311yescharacteristic
103#41×D47—248no—
104#41×D47—212no—
105#41×D47C2×C418yes—
106#41×D47C2×C4124yescomplemented
107#41×D47D418yes—
108C2×Q8×D47—23no—
109C2×Q8×D47D411yescharacteristic
110C2×Q8×D47C2313yes—
111C22×D188—23no—
112C22×D188—23no—
113C22×D188C2313yes—
114C2×D4×D47—23no—
115C2×D4×D47—23no—
116C2×D4×D47—26no—
117C2×D4×D47D413yes—
118C2×D4×D47C2313yes—
119C22×C4×D47—23no—
120C22×C4×D47—23no—
121C22×C4×D47C2313yes—
122#13094032—212no—
123#13094031—24no—
124#13094030—212no—
125C2×#10625329C2313yes—
126C2×#10625324C2316yes—
127M16×D47—212no—
128C22×C47⋊C8C2313yes—
129C2×C8×D47—212no—
130C2×C8×D47C2313yes—
131C2×C8×D47C2313yes—
132C2×C8×D47C2311yescharacteristic
133C2×C8×D47C2313yes—
134Q8×Dic47—21no—
135C4×Dic94—23no—
136#13093989—23no—
137C4×D188—23no—
138D4×Dic47—23no—
139#13093986—23no—
140C4×C22⋊D47—26no—
141(C22⋊D47)⋊C4—26no—
142#13093983C2313yes—
143#13093982—23no—
144#13093982—23no—
145#13093982C2311yescharacteristic
146#13093982C2313yes—
147#13093982C2316yes—
148#13093981—23no—
149#13093980—23no—
150C2×C4⋊Dic47C2313yes—
151C4⋊C4×D47C2313yes—
152C4⋊C4×D47C2313yes—
153C2×(C2×D47)⋊C4—23no—
154C22⋊C4×D47—23no—
155C2×C4×Dic47—23no—
156C42×D47—23no—
157#13093949C2311yescharacteristic
158#13093949C2313yes—
159#13093948C2313yes—
160#13093948C2313yes—
161#13093948C2316yes—
162#13093947C2311yescharacteristic
163#13093947C2313yes—
164#13093946C2313yes—
165#13093946C2313yes—
166#13093946C2316yes—
167#13093945C2311yescharacteristic
168#13093945C2313yes—
169#13093944C2313yes—
170#13093944C2313yes—
171#13093944C2316yes—
1722−1+4×C47—24no—
1732−1+4×C47C2×C418yescomplemented
174C2×#41×C47—23no—
175C2×#41×C47C2313yes—
176C2×#41×C47C2311yescharacteristic
177C22×Q8×C47—21no—
178C22×Q8×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×C47C2313yes—
188#103×C47C2316yes—
189#102×C47C2311yescharacteristic
190#102×C47C2313yes—
191C23×D47—23no—
192C23×D47—23no—
193C23×D47C2×D413yes—
194#41×C47—224no—
195#41×C47—26no—
196#41×C47C22×C4112yes—
197#41×C47C22×C414yes—
198#41×C47C2×D414yes—
199C2×Q8×C47—28no—
200C2×Q8×C47—23no—
201C2×Q8×C47—26no—
202C2×Q8×C47C22×C4112yes—
203C2×Q8×C47C2×D411yescharacteristic
204C2×Q8×C47C2413yes—
205C2×D4×C47—23no—
206C2×D4×C47C2×D413yes—
207C2×D4×C47C2411yescharacteristic
208C22×C4×C47—23no—
209C22×C4×C47—23no—
210C22×C4×C47—23no—
211C22×C4×C47C2413yes—
212C2×C22⋊D47—23no—
213C2×C22⋊D47—21no—
214C2×C22⋊D47—23no—
215C2×C22⋊D47C2×D416yes—
216C22×Dic47—21no—
217C22×Dic47—23no—
218C22×Dic47C2×D413yes—
219#10625354—28no—
220#10625354—224no—
221#10625354—224no—
222#10625354—224no—
223#10625354—26no—
224#10625354—212no—
225#10625354C22⋊C418yes—
226#10625354C22×C4112yes—
227#10625354C22×C4124yes—
228Q8×D47—26no—
229Q8×D47—224no—
230Q8×D47C22⋊C418yes—
231Q8×D47C22×C4112yes—
232#10625352—224no—
233#10625352—22no—
234#10625352C22⋊C4124yes—
235#10625352C22×C414yes—
236D4×D47—224no—
237D4×D47—224no—
238D4×D47—248no—
239D4×D47—26no—
240D4×D47C22⋊C4124yes—
241D4×D47C22×C4112yes—
242#10625350—26no—
243#10625350—248no—
244#10625350—224no—
245#10625350—224no—
246#10625350C22×C4112yes—
247#10625350C22×C4112yes—
248#10625350C2×D4112yes—
249C2×D188—224no—
250C2×D188—23no—
251C2×D188—26no—
252C2×D188—23no—
253C2×D188—26no—
254C2×D188—224no—
255C2×D188C22×C4112yes—
256C2×D188C2×D413yes—
257C2×D188C2413yes—
258C2×C4×D47—23no—
259C2×C4×D47—23no—
260C2×C4×D47—224no—
261C2×C4×D47—23no—
262C2×C4×D47—26no—
263C2×C4×D47—224no—
264C2×C4×D47—23no—
265C2×C4×D47—23no—
266C2×C4×D47C22×C4112yes—
267C2×C4×D47C2×D413yes—
268C2×C4×D47C2×D413yes—
269C2×C4×D47C2×D4112yes—
270C2×C4×D47C2413yes—
271C2×C4×D47C2411yescharacteristic
272C2×Dic94—23no—
273C2×Dic94C2×D413yes—
274C2×Dic94C2411yescharacteristic
275M16×C47—26no—
276C2×C8×C47—26no—
277C2×C8×C47C2411yescharacteristic
278C2×C8×C47C2413yes—
279C4⋊C4×C47—23no—
280C4⋊C4×C47C2413yes—
281C4⋊C4×C47C2411yescharacteristic
282C22⋊C4×C47—23no—
283C42×C47—23no—
284C22⋊Dic47—23no—
285(C2×D47)⋊C4—21no—
286(C2×D47)⋊C4—23no—
287(C2×D47)⋊C4—26no—
288C4⋊Dic47—23no—
289C4⋊Dic47C2411yescharacteristic
290C4⋊Dic47C2413yes—
291Dic47⋊C4—23no—
292Dic47⋊C4—23no—
293C4×Dic47—23no—
294C4×Dic47—21no—
295C4×Dic47—23no—
296C4×Dic47—26no—
297#10625329—26no—
298C2×C47⋊C8—26no—
299C2×C47⋊C8C2411yescharacteristic
300C2×C47⋊C8C2413yes—
301#10625324—212no—
302C8×D47—22no—
303C8×D47—26no—
304C8×D47—26no—
305C8×D47—26no—
306C23×C47—21no—
307C23×C47C22×D413yes—
308C22×D47—23no—
309C22×D47—212no—
310C22×D47—212no—
311C22×D47—43no—
312C22×D47—43no—
313C22×D47—83no—
314C22×D47—83no—
315C22×D47—83no—
316C22×D47—83no—
317C22×D47C2×C22⋊C4112yes—
318C22×D47C22×D411yescharacteristic
319C22×D47C22×D413yes—
320Q8×C47—212no—
321Q8×C47—23no—
322Q8×C47C2×C22⋊C414yes—
323Q8×C47C23×C416yes—
324D4×C47—212no—
325D4×C47—21no—
326D4×C47C2×C22⋊C4112yes—
327D4×C47C23×C412yes—
328C2×C4×C47—212no—
329C2×C4×C47—23no—
330C2×C4×C47—212no—
331C2×C4×C47—23no—
332C2×C4×C47—21no—
333C2×C4×C47—83no—
334C2×C4×C47C23×C416yes—
335C2×C4×C47C22×D413yes—
336C2×C4×C47C22×D416yes—
337C2×C4×C47C2511yescharacteristic
338C22⋊D47—212no—
339C22⋊D47—24no—
340C22⋊D47—212no—
341C22⋊D47C2×C22⋊C4124yes—
342C2×Dic47—21no—
343C2×Dic47—24no—
344C2×Dic47—21no—
345C2×Dic47—23no—
346C2×Dic47—83no—
347C2×Dic47C2×C22⋊C4112yes—
348C2×Dic47C22×D411yescharacteristic
349C2×Dic47C22×D413yes—
350D188—224no—
351D188—212no—
352D188—212no—
353D188—23no—
354D188C2×C22⋊C4112yes—
355D188C23×C416yes—
356C4×D47—212no—
357C4×D47—212no—
358C4×D47—212no—
359C4×D47—224no—
360C4×D47—83no—
361C4×D47—83no—
362C4×D47C2×C22⋊C4112yes—
363C4×D47C2×C22⋊C4112yes—
364C4×D47C23×C412yes—
365C4×D47C23×C416yes—
366C4×D47C22×D412yes—
367C4×D47C22×D416yes—
368Dic94—21no—
369Dic94—212no—
370Dic94C2×C22⋊C4112yes—
371Dic94C23×C412yes—
372C8×C47—21no—
373C8×C47—23no—
374C47⋊C8—21no—
375C47⋊C8—23no—
376#60086—471nomaximal, Sylow
377C22×C47—23no—
378C22×C47—23no—
379C22×C47—22no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47C22×C22⋊C416yes—
383C22×C47C23×D411yescharacteristic
384C2×D47—23no—
385C2×D47—23no—
386C2×D47—21no—
387C2×D47—21no—
388C2×D47—26no—
389C2×D47—412no—
390C2×D47—43no—
391C2×D47—43no—
392C2×D47—812no—
393C2×D47—812no—
394C2×D47C22×C22⋊C416yes—
395C2×D47C22×C22⋊C412yes—
396C4×C47—26no—
397C4×C47—41no—
398C4×C47—43no—
399C4×C47C22×C22⋊C416yes—
400C4×C47C24×C411yescharacteristic
401C4×C47C23×D411yescharacteristic
402Dic47—22no—
403Dic47—41no—
404Dic47—43no—
405Dic47C22×C22⋊C416yes—
406Dic47C22×C22⋊C412yes—
407C2×#585—471no—
408C22×#131—471no—
409#3428—471no—
410#2898—473no—
411#2898—473no—
412#2898—471no—
413#2898D4711yescharacteristic, complemented
414#2897—473no—
415#2897—473no—
416#2897—471no—
417#2897—471no—
418#2896—473no—
419#2896—473no—
420C2×#416—473no—
421C2×#416—473no—
422C2×C47—26no—
423C2×C47—42no—
424C2×C47C23×C22⋊C411yescharacteristic
425C2×C47#358411yescharacteristic
426C2×C47#358411yescharacteristic
427D47—22no—
428D47—26no—
429D47—46no—
430#585—4716no—
431#585—948no—
432C2×2−1+4—473no—
433C2×2−1+4—941no—
434C2×2−1+4C2×D4711yescharacteristic
435C2×H(5,𝔽2)—473no—
436C2×H(5,𝔽2)—471no—
437C2×H(5,𝔽2)—943no—
438C22×#41—471no—
439C22×#41—473no—
440C22×#41—473no—
441C22×#41—941no—
442C22×#41—943no—
443C2×#131—471no—
444C2×#131—473no—
445C2×#131—473no—
446C2×#131—948no—
447C2×#131C2×D4711yescharacteristic, complemented
448C22×M16—473no—
449C23×C8—473no—
450#520—471no—
451#520—473no—
452#520—473no—
453#520C2×D4711yescharacteristic, complemented
454#519—941no—
455#518—943no—
456C4×#41—943no—
457C4×#41—941no—
458C2×#117—473no—
459C2×#117—473no—
460#419—473no—
461#419—476no—
462#419C2×D4713yescomplemented
463#418—473no—
464#418—473no—
465#418—476no—
466#417—473no—
467#417—473no—
468#417—473no—
469#417—476no—
470#417—476no—
471#417C2×D4713yescomplemented
472#416—473no—
473#416—473no—
474#416—473no—
475#416—473no—
476#416—473no—
477#416—476no—
478#416—476no—
479#416—476no—
480#416—471no—
481#416—473no—
482#416C2×D4713yescomplemented
483C2×#103—473no—
484C2×#103—473no—
485C2×#103—473no—
486C2×#103C2×D4713yescomplemented
487C2×#102—473no—
488C2×#102—473no—
489C2×#102—473no—
490C2×#102—473no—
491C47#6008611yescharacteristic, complemented, Sylow
4922−1+4—24no—
4932−1+4—4724no—
4942−1+4—9416no—
4952−1+4—9412no—
4962−1+4C4×D4718yescomplemented
497H(5,𝔽2)—4724no—
498H(5,𝔽2)—478no—
499H(5,𝔽2)—9448no—
500H(5,𝔽2)—9412no—
501H(5,𝔽2)—944no—
502C2×#41—23no—
503C2×#41—478no—
504C2×#41—478no—
505C2×#41—471no—
506C2×#41—473no—
507C2×#41—473no—
508C2×#41—4724no—
509C2×#41—4724no—
510C2×#41—473no—
511C2×#41—476no—
512C2×#41—471no—
513C2×#41—473no—
514C2×#41—943no—
515C2×#41—946no—
516C2×#41—943no—
517C2×#41—943no—
518C2×#41—943no—
519C2×#41—943no—
520C2×#41—9412no—
521C2×#41—9412no—
522C2×#41—943no—
523C2×#41—9416no—
524C2×#41—9448no—
525C2×#41—941no—
526C2×#41C22×D4713yes—
527C2×#41C22×D4711yescharacteristic
528C22×Q8—21no—
529C22×Q8—471no—
530C22×Q8—473no—
531C22×Q8—943no—
532C22×Q8C22×D4713yes—
533C22×D4—473no—
534C22×D4—473no—
535C22×D4—473no—
536C22×D4—943no—
537C22×D4—943no—
538C22×D4—946no—
539C22×D4—943no—
540C22×D4—943no—
541C23×C4—473no—
542C23×C4—943no—
543C23×C4—943no—
544#131—24no—
545#131—9412no—
546#131—9412no—
547#131—944no—
548C2×M16—473no—
549C2×M16—476no—
550C2×M16—9412no—
551C2×M16C22×D4713yes—
552C22×C8—473no—
553C22×C8—471no—
554C22×C8—473no—
555C22×C8—473no—
556C22×C8—473no—
557C22×C8—9412no—
558C22×C8C22×D4713yes—
559C4×Q8—21no—
560C4×Q8—943no—
561C4×Q8—943no—
562C4×Q8—941no—
563C4×D4—23no—
564C4×D4—943no—
565C4×D4—946no—
566C4×D4—943no—
567C4×D4—946no—
568C4×D4—943no—
569#117—473no—
570#117—471no—
571#117—473no—
572#117—476no—
573#117—943no—
574#117—943no—
575#117—943no—
576#117—943no—
577#117C22×D4713yes—
578C2×C4⋊C4—473no—
579C2×C4⋊C4—473no—
580C2×C4⋊C4—473no—
581C2×C4⋊C4C22×D4713yes—
582C2×C22⋊C4—943no—
583C2×C22⋊C4—943no—
584C2×C42—943no—
585C2×C42—943no—
586#103—473no—
587#103—473no—
588#103—476no—
589#103—471no—
590#103—473no—
591#103—471no—
592#103—473no—
593#103C22×D4713yes—
594#103C22×D4713yes—
595#103C22×D4716yes—
596#102—471no—
597#102—473no—
598#102—473no—
599#102—473no—
600#102—476no—
601#102—473no—
602#102—473no—
603#102—476no—
604#102C22×D4711yescharacteristic
605#102C22×D4713yes—
606C24—473no—
607C24—943no—
608C24—943no—
609#41—224no—
610#41—26no—
611#41—478no—
612#41—4724no—
613#41—4712no—
614#41—4712no—
615#41—4712no—
616#41—4724no—
617#41—474no—
618#41—4712no—
619#41—9424no—
620#41—9448no—
621#41—9424no—
622#41—9424no—
623#41—942no—
624#41—9424no—
625#41—946no—
626#41—9424no—
627#41—9412no—
628#41—9424no—
629#41—948no—
630#41—946no—
631#41C2×C4×D47112yes—
632#41C2×C4×D4714yes—
633#41D4×D4714yes—
634C2×Q8—28no—
635C2×Q8—23no—
636C2×Q8—26no—
637C2×Q8—478no—
638C2×Q8—473no—
639C2×Q8—4712no—
640C2×Q8—471no—
641C2×Q8—943no—
642C2×Q8—946no—
643C2×Q8—9424no—
644C2×Q8C2×C4×D47112yes—
645C2×Q8D4×D4711yescharacteristic
646C2×Q8C23×D4713yes—
647C2×D4—23no—
648C2×D4—476no—
649C2×D4—4724no—
650C2×D4—4712no—
651C2×D4—4712no—
652C2×D4—473no—
653C2×D4—473no—
654C2×D4—9424no—
655C2×D4—943no—
656C2×D4—946no—
657C2×D4—9424no—
658C2×D4—946no—
659C2×D4—943no—
660C2×D4—9448no—
661C2×D4—9424no—
662C2×D4—941no—
663C2×D4—943no—
664C2×D4—9424no—
665C2×D4—943no—
666C2×D4—946no—
667C2×D4D4×D4713yes—
668C2×D4C23×D4711yescharacteristic
669C22×C4—23no—
670C22×C4—23no—
671C22×C4—23no—
672C22×C4—473no—
673C22×C4—4712no—
674C22×C4—473no—
675C22×C4—473no—
676C22×C4—4712no—
677C22×C4—473no—
678C22×C4—471no—
679C22×C4—943no—
680C22×C4—946no—
681C22×C4—9424no—
682C22×C4—9424no—
683C22×C4—943no—
684C22×C4—943no—
685C22×C4—943no—
686C22×C4—941no—
687C22×C4—943no—
688C22×C4—943no—
689C22×C4C23×D4713yes—
690M16—26no—
691M16—9412no—
692M16—946no—
693C2×C8—26no—
694C2×C8—471no—
695C2×C8—473no—
696C2×C8—942no—
697C2×C8—946no—
698C2×C8—946no—
699C2×C8—946no—
700C2×C8—946no—
701C2×C8C23×D4711yescharacteristic
702C2×C8C23×D4713yes—
703C4⋊C4—23no—
704C4⋊C4—471no—
705C4⋊C4—473no—
706C4⋊C4—943no—
707C4⋊C4—943no—
708C4⋊C4—943no—
709C4⋊C4C23×D4711yescharacteristic
710C4⋊C4C23×D4713yes—
711C22⋊C4—23no—
712C22⋊C4—941no—
713C22⋊C4—943no—
714C22⋊C4—946no—
715C22⋊C4—943no—
716C42—23no—
717C42—941no—
718C42—943no—
719C42—946no—
720C42—943no—
721C23—21no—
722C23—471no—
723C23—473no—
724C23—4712no—
725C23—9412no—
726C23—9412no—
727C23—943no—
728C23—3763no—
729C23—3763no—
730C23—3763no—
731C23—3763no—
732C23—1883no—
733C23—1883no—
734C23C2×D4×D4713yes—
735Q8—212no—
736Q8—23no—
737Q8—4712no—
738Q8—472no—
739Q8—9412no—
740Q8—941no—
741Q8C22⋊C4×D4714yes—
742Q8C22×C4×D4716yes—
743D4—212no—
744D4—21no—
745D4—4724no—
746D4—4712no—
747D4—476no—
748D4—9412no—
749D4—9424no—
750D4—9412no—
751D4—944no—
752D4—9412no—
753D4—9412no—
754D4—943no—
755D4C22⋊C4×D47112yes—
756D4C22×C4×D4712yes—
757C2×C4—212no—
758C2×C4—23no—
759C2×C4—212no—
760C2×C4—21no—
761C2×C4—23no—
762C2×C4—83no—
763C2×C4—4712no—
764C2×C4—471no—
765C2×C4—473no—
766C2×C4—4712no—
767C2×C4—4712no—
768C2×C4—472no—
769C2×C4—476no—
770C2×C4—472no—
771C2×C4—476no—
772C2×C4—9412no—
773C2×C4—9424no—
774C2×C4—9412no—
775C2×C4—944no—
776C2×C4—941no—
777C2×C4—9412no—
778C2×C4—943no—
779C2×C4—941no—
780C2×C4—3763no—
781C2×C4—3763no—
782C2×C4—3763no—
783C2×C4C22×C4×D4716yes—
784C2×C4C2×D4×D4713yes—
785C2×C4C2×D4×D4716yes—
786C2×C4C24×D4711yescharacteristic
787C8—21no—
788C8—23no—
789C8—941no—
790C8—943no—
791C22—23no—
792C22—23no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—472no—
797C22—476no—
798C22—943no—
799C22—941no—
800C22—943no—
801C22—941no—
802C22—946no—
803C22—37612no—
804C22—37612no—
805C22—18812no—
806C22—1883no—
807C22—1883no—
808C22C2×C22⋊C4×D4716yes—
809C22C22×D4×D4711yescharacteristic
810C4—26no—
811C4—41no—
812C4—43no—
813C4—472no—
814C4—476no—
815C4—942no—
816C4—1883no—
817C4—1881no—
818C4C2×C22⋊C4×D4716yes—
819C4C23×C4×D4711yescharacteristic
820C4C22×D4×D4711yescharacteristic
821C2—26no—
822C2—42no—
823C2—946no—
824C2—942no—
825C2—1886no—
826C2C22×C22⋊C4×D4711yescharacteristic
827C2#2025815811yescharacteristic
828C2#2025816011yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC47×#2898C2
socleC22×C47C23×D4
prime radicalC2×#15689960C2
cosocleC2×C4×C47C25
hypercenter#2898D47
hypocenterC47#60086
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#131×D47C2semidirect
3. #20256588C2semidirect
4. #20251921C2semidirect
5. #20251920C2semidirect
6. #20251916C2semidirect
7. #20251915C2semidirect
8. #20251912C2semidirect
9. #20251911C2semidirect
10. #20251910C2semidirect
11. #20251906C2semidirect
12. #20251904C2semidirect
13. C2×#15689118C2semidirect
14. #416×D47C2semidirect
15. C47×#2898C2semidirect
17. #15689960C4semidirect
28. C2×#13094032C22semidirect
29. C2×#13094031C22semidirect
30. C2×#13094030C22semidirect
32. C2×M16×D47C22semidirect
33. C22×C8×D47C22semidirect
34. #15689606C22semidirect
35. #15689604C22semidirect
36. #15689603C22semidirect
41. C2×#13093982C22semidirect
42. #117×D47C22semidirect
43. #15689132C22semidirect
44. #15689130C22semidirect
45. #15689129C22semidirect
46. #15689127C22semidirect
47. #15689126C22semidirect
48. #15689125C22semidirect
49. #15689124C22semidirect
50. #15689123C22semidirect
51. #15689123C22semidirect
52. #15689122C22semidirect
53. #15689120C22semidirect
54. #15689119C22semidirect
55. #15689118C22semidirect
56. #15689118C22semidirect
57. #15689118C22semidirect
58. #15689118C22semidirect
59. #15689118C22semidirect
60. #15689117C22semidirect
61. #15689116C22semidirect
62. #15689116C22semidirect
63. C2×#13093948C22semidirect
64. #103×D47C22semidirect
65. #103×D47C22semidirect
66. C2×#13093946C22semidirect
67. C2×#13093944C22semidirect
68. #102×D47C22semidirect
69. #102×D47C22semidirect
71. C2×#131×C47C22semidirect
72. C47×#520C22semidirect
73. C47×#419C22semidirect
74. C47×#417C22semidirect
75. C47×#416C22semidirect
76. C2×#103×C47C22semidirect
79. #13094072C2×C4semidirect
83. #13094070C2×C4semidirect
84. #13094070C2×C4semidirect
91. C2×#10625354C2×C4semidirect
106. #41×D47C2×C4semidirect
173. 2−1+4×C47C2×C4semidirect
413. #2898D47semidirect
447. C2×#131C2×D47semidirect
453. #520C2×D47semidirect
462. #419C2×D47semidirect
471. #417C2×D47semidirect
482. #416C2×D47semidirect
486. C2×#103C2×D47semidirect
491. C47#60086semidirect
496. 2−1+4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899602
C2×#131×D472
#202565882
#202519212
#202519202
#202519162
#202519152
#202519122
#202519112
#202519102
#202519062
#202519042
C2×#156891182
#416×D472
C47×#28982
#6008647