Finite Group Databasebeta

← #27080261

Subgroups — #27080261

Order 12032.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689888C211yesmaximal, characteristic, complemented
2C2×#131×D47C211yesmaximal, characteristic, complemented
3#41×D188C211yesmaximal, characteristic
4#20252134C213yesmaximal, complemented
5M16×D188C213yesmaximal, complemented
6#20252116C213yesmaximal, complemented
7#20252116C213yesmaximal, complemented
8#20252107C213yesmaximal, complemented
9#20252093C213yesmaximal, complemented
10#20252084C213yesmaximal, complemented
11C2×#15689196C213yesmaximal, complemented
12#20251956C211yesmaximal, characteristic, complemented
13#20251835C211yesmaximal, characteristic, complemented
14#20251835C211yesmaximal, characteristic, complemented
15C47×#2875C211yesmaximal, characteristic, complemented
16C2×#41×D47C2211yescharacteristic
17C2×#41×D47C2211yescharacteristic
18#15689888—28no—
19C2×#13094032C2213yescomplemented
20C2×#13094032C2213yescomplemented
21C2×#13094031C2211yescharacteristic
22C2×#13094031C2211yescharacteristic
23C2×#13094030C2213yescomplemented
24C2×#13094030C2213yescomplemented
25#131×D47—28no—
26C22×#10625324C2213yescomplemented
27C2×M16×D47C2213yescomplemented
28C2×M16×D47C2213yescomplemented
29C22×C8×D47C2213yescomplemented
30#15689795C411yescharacteristic
31Q8×D188C411yescharacteristic
32#15689785C411yescharacteristic
33#15689785C411yescharacteristic
34#15689777C413yes—
35#15689768C413yes—
36#15689768C413yes—
37D4×D188C413yes—
38#15689673C2213yes—
39#15689635C2213yes—
40#15689635C2213yes—
41C2×C4×D188C2213yes—
42#15689202C2216yescomplemented
43#15689202C2216yescomplemented
44#15689196C2211yescharacteristic
45#15689196C2213yes—
46#15689196C2213yescomplemented
47#15689196C2213yescomplemented
48#15689196C2213yescomplemented
49#15689196C2213yescomplemented
50#15689196C2213yescomplemented
51#15689196C2213yescomplemented
52#15689196C2216yescomplemented
53#15689196C2216yescomplemented
54#15689196C2216yescomplemented
55C8×D188C2216yescomplemented
56C8×D188C2216yescomplemented
57#15689150C2213yescomplemented
58#15689150C2213yescomplemented
59#15689147C2213yescomplemented
60C2×C4⋊(C47⋊C8)C2213yescomplemented
61#15689091C2213yescomplemented
62#15689091C2213yescomplemented
63#15689089C2213yescomplemented
64#15689089C2213yescomplemented
65#15689086C2213yescomplemented
66#15689086C2213yescomplemented
67C2×(C2×D47)⋊C8C2213yescomplemented
68C2×(C2×D47)⋊C8C2213yescomplemented
69C2×#131×C47C2211yescharacteristic
70C2×#131×C47C2211yescharacteristic
71C4×#41×C47C2211yescharacteristic
72C47×#405C2213yescomplemented
73C47×#405C2213yescomplemented
74C4×M16×C47C2213yescomplemented
75C2×#97×C47C2213yescomplemented
76C2×#10625354C2×C411yescharacteristic
77C2×#10625354C2×C411yescharacteristic
78C2×#10625350C2313yes—
79C2×#10625350C2313yes—
80C2×#10625352C2×C413yes—
81C2×#10625352C2×C413yes—
82#41×D47—24no—
83#41×D47—24no—
84#41×D47—24no—
85#41×D47—24no—
86C2×Q8×D47C2×C411yescharacteristic
87C2×Q8×D47C2×C411yescharacteristic
88C22×D188C2×C413yes—
89C2×D4×D47C2×C413yes—
90C2×D4×D47C2×C413yes—
91C22×C4×D47C2313yes—
92C22×C4×D47C2313yes—
93#13094032—212no—
94#13094032—212no—
95#13094031—24no—
96#13094031—24no—
97#13094030—212no—
98#13094030—212no—
99C2×#10625329C2313yes—
100C2×#10625329C2313yes—
101C2×#10625324—212no—
102C2×#10625324C2313yes—
103C2×#10625324C2316yes—
104C2×#10625324C2311yescharacteristic
105C2×#10625324C2313yes—
106C2×#10625324C2313yes—
107M16×D47—212no—
108M16×D47—212no—
109C22×C47⋊C8C2313yes—
110C22×C47⋊C8C2313yes—
111C2×C8×D47—212no—
112C2×C8×D47C2311yescharacteristic
113C2×C8×D47C2313yes—
114C2×C8×D47C2313yes—
115C2×C8×D47C2313yes—
116C2×C8×D47C2316yes—
117#13094024C2×C413yes—
118#13094021C2×C413yes—
119#13094012C2×C413yes—
120#13094012C2×C413yes—
121#13094008C2×C416yes—
122#13094008C2×C416yes—
123#13094004C2×C413yes—
124#13094004C2×C413yes—
125#13094004C2×C413yes—
126#13094004C2×C413yes—
127#13093999C2×C413yes—
128#13093999C2×C413yes—
129#13093999C2×C413yes—
130#13093999C2×C413yes—
131#13093998C2×C416yes—
132#13093998C2×C416yes—
133#13093994C2×C416yes—
134#13093994C2×C416yes—
135C4×D188C2×C413yes—
136C4×D188C2×C413yes—
137C4×D188C2×C413yes—
138C4×D188C2×C413yes—
139C4×D188C2311yescharacteristic
140C4×D188C2313yes—
141C4×D188C2313yes—
142C4×D188C2313yes—
143C4×D188C2316yes—
144C2×C4⋊Dic47C2×C413yes—
145C2×(C2×D47)⋊C4C2×C413yes—
146C2×(C2×D47)⋊C4C2×C413yes—
147C4⋊(C47⋊C8)C2311yescharacteristic
148C4⋊(C47⋊C8)C2313yes—
149C4⋊(C47⋊C8)C2313yes—
150C4⋊(C47⋊C8)C2313yes—
151C4⋊(C47⋊C8)C2316yes—
152(C2×D47)⋊C8C2311yescharacteristic
153(C2×D47)⋊C8C2311yescharacteristic
154(C2×D47)⋊C8C2313yes—
155(C2×D47)⋊C8C2313yes—
156(C2×D47)⋊C8C2313yes—
157(C2×D47)⋊C8C2313yes—
158(C2×D47)⋊C8C2313yes—
159(C2×D47)⋊C8C2313yes—
160(C2×D47)⋊C8C2316yes—
161(C2×D47)⋊C8C2316yes—
162C2×#41×C47C2311yescharacteristic
163#131×C47—24no—
164#131×C47D418yescomplemented
165C2×M16×C47C2313yes—
166C2×M16×C47C2313yes—
167C22×C8×C47C2313yes—
168C22×C8×C47C2313yes—
169C4×Q8×C47C2×C411yescharacteristic
170C4×Q8×C47C2×C411yescharacteristic
171C4×D4×C47C2×C413yes—
172C4×D4×C47C2×C413yes—
173#117×C47C2313yes—
174C2×C42×C47C2313yes—
175#97×C47C2311yescharacteristic
176#97×C47C2313yes—
177#97×C47C2313yes—
178#97×C47C2313yes—
179C4×C8×C47C2316yes—
180C23×D47C22×C413yes—
181C23×D47C22×C413yes—
182#41×C47C2×D414yes—
183#41×C47#4114yes—
184C2×Q8×C47C22×C411yescharacteristic
185C2×D4×C47C22×C413yes—
186C22×C4×C47C22×C413yes—
187C22×C4×C47C22×C413yes—
188C22×C4×C47C2413yes—
189C2×C22⋊D47C22×C416yes—
190C2×C22⋊D47C22×C416yes—
191C22×Dic47C22×C413yes—
192C22×Dic47C22×C413yes—
193#10625354—24no—
194#10625354—24no—
195Q8×D47—24no—
196Q8×D47—24no—
197#10625352—212no—
198#10625352—212no—
199D4×D47—212no—
200D4×D47—212no—
201#10625350—26no—
202#10625350—26no—
203#10625350—26no—
204#10625350—26no—
205C2×D188—46no—
206C2×D188C22×C411yescharacteristic
207C2×D188C22×C413yes—
208C2×D188C22×C413yes—
209C2×D188C22×C413yes—
210C2×D188C22×C413yes—
211C2×D188C22×C413yes—
212C2×D188C22×C416yes—
213C2×C4×D47—26no—
214C2×C4×D47—26no—
215C2×C4×D47—26no—
216C2×C4×D47—26no—
217C2×C4×D47C22×C413yes—
218C2×C4×D47C22×C413yes—
219C2×C4×D47C22×C413yes—
220C2×C4×D47C22×C413yes—
221C2×C4×D47C2411yescharacteristic
222C2×C4×D47C2413yes—
223C2×C4×D47C2413yes—
224C2×C4×D47C2411yescharacteristic
225C2×Dic94C22×C413yes—
226C2×Dic94C22×C413yes—
227M16×C47—26no—
228M16×C47C2×D4112yescomplemented
229C2×C8×C47—26no—
230C2×C8×C47C2×D4112yescomplemented
231C2×C8×C47C2411yescharacteristic
232C2×C8×C47C2413yes—
233C2×C8×C47C2411yescharacteristic
234C2×C8×C47C2413yes—
235C4⋊C4×C47C22×C413yes—
236C4⋊C4×C47C22×C413yes—
237C22⋊C4×C47C22×C416yes—
238C42×C47C22×C413yes—
239C42×C47C22×C413yes—
240C42×C47C2411yescharacteristic
241C42×C47C2413yes—
242(C2×D47)⋊C4C22×C411yescharacteristic
243(C2×D47)⋊C4C22×C411yescharacteristic
244(C2×D47)⋊C4C22×C413yes—
245(C2×D47)⋊C4C22×C413yes—
246(C2×D47)⋊C4C22×C413yes—
247(C2×D47)⋊C4C22×C413yes—
248(C2×D47)⋊C4C22×C413yes—
249(C2×D47)⋊C4C22×C413yes—
250(C2×D47)⋊C4C22×C416yes—
251(C2×D47)⋊C4C22×C416yes—
252C4⋊Dic47C22×C411yescharacteristic
253C4⋊Dic47C22×C413yes—
254C4⋊Dic47C22×C413yes—
255C4⋊Dic47C22×C413yes—
256C4⋊Dic47C22×C416yes—
257#10625329—26no—
258#10625329—26no—
259C2×C47⋊C8—26no—
260C2×C47⋊C8—26no—
261C2×C47⋊C8C2411yescharacteristic
262C2×C47⋊C8C2413yes—
263C2×C47⋊C8C2413yes—
264C2×C47⋊C8C2411yescharacteristic
265#10625324—26no—
266#10625324—212no—
267#10625324—22no—
268#10625324—26no—
269#10625324—26no—
270C8×D47—22no—
271C8×D47—26no—
272C8×D47—26no—
273C8×D47—26no—
274C8×D47—212no—
275C23×C47C23×C413yes—
276C22×D47—26no—
277C22×D47—26no—
278C22×D47—26no—
279C22×D47—43no—
280C22×D47—43no—
281C22×D47—43no—
282C22×D47C23×C411yescharacteristic
283C22×D47C23×C413yes—
284C22×D47C23×C413yes—
285C22×D47C23×C411yescharacteristic
286Q8×C47C4×D414yes—
287D4×C47C4×D4112yes—
288C2×C4×C47—43no—
289C2×C4×C47—43no—
290C2×C4×C47C23×C411yescharacteristic
291C2×C4×C47C23×C413yes—
292C2×C4×C47C23×C413yes—
293C2×C4×C47C23×C411yescharacteristic
294C2×C4×C47C23×C413yes—
295C2×C4×C47C22×D416yes—
296C2×C4×C47C2×#4116yes—
297C2×C4×C47C2511yescharacteristic
298C22⋊D47—212no—
299C22⋊D47—212no—
300C2×Dic47—26no—
301C2×Dic47—26no—
302C2×Dic47C23×C413yes—
303C2×Dic47C23×C413yes—
304C2×Dic47C23×C411yescharacteristic
305C2×Dic47C23×C411yescharacteristic
306D188—22no—
307D188—26no—
308D188—26no—
309D188—26no—
310D188—43no—
311D188—43no—
312D188—46no—
313C4×D47—26no—
314C4×D47—26no—
315C4×D47—26no—
316C4×D47—26no—
317C4×D47—21no—
318C4×D47—23no—
319C4×D47—23no—
320C4×D47—21no—
321C4×D47—21no—
322C4×D47—21no—
323C4×D47—23no—
324C4×D47—23no—
325Dic94—26no—
326Dic94—26no—
327C8×C47—21no—
328C8×C47—23no—
329C8×C47C22×D412yes—
330C8×C47C22×D416yes—
331C47⋊C8—21no—
332C47⋊C8—23no—
333C47⋊C8—23no—
334C47⋊C8—21no—
335#60146—471nomaximal, Sylow
336C22×C47—23no—
337C22×C47—23no—
338C22×C47C2×C4×D416yes—
339C22×C47C24×C411yescharacteristic
340C2×D47—21no—
341C2×D47—21no—
342C2×D47—21no—
343C2×D47—23no—
344C2×D47—23no—
345C2×D47—21no—
346C2×D47—23no—
347C2×D47—23no—
348C2×D47—23no—
349C2×D47—23no—
350C2×D47—21no—
351C2×D47—412no—
352C2×D47—86no—
353C2×D47#56812yescomplemented
354C4×C47—21no—
355C4×C47—23no—
356C4×C47—23no—
357C4×C47—21no—
358C4×C47C2×C4×D416yes—
359C4×C47C23×D411yescharacteristic
360C4×C47C22×#4111yescharacteristic
361Dic47—23no—
362Dic47—23no—
363Dic47—21no—
364Dic47—21no—
365C2×#568—471no—
366C22×#131—471no—
367D4×#41—471no—
368#2935—473no—
369D4×M16—473no—
370#2933—473no—
371#2933—473no—
372#2932—473no—
373#2930—473no—
374#2929—473no—
375C2×#435—473no—
376#2906—471no—
377#2880—471no—
378#2880—471no—
379#2875D4711yescharacteristic, complemented
380C2×C47—26no—
381C2×C47C22×C4×D411yescharacteristic
382C2×C47C2×#56811yescharacteristic
383C2×C47#357311yescharacteristic
384D47—22no—
385D47—43no—
386D47—43no—
387D47—41no—
388C22×#41—471no—
389C22×#41—471no—
390#568—948no—
391C2×#131—471no—
392C2×#131—471no—
393C2×#131—473no—
394C2×#131—473no—
395C2×#131—473no—
396C2×#131—473no—
397C2×#131—948no—
398C2×#131C2×D4711yescharacteristic
399C2×#131C2×D4711yescharacteristic
400C22×M16—473no—
401C22×M16—473no—
402C22×M16—473no—
403C23×C8—473no—
404#550—471no—
405D4×Q8—471no—
406#548—471no—
407#548—471no—
408#547—473no—
409#546—473no—
410#546—473no—
411D42—473no—
412#532—473no—
413#525—473no—
414#525—473no—
415C4×#41C2×D4711yescharacteristic
416C2×C4×D4—473no—
417#436—476no—
418#436—476no—
419#435—471no—
420#435—473no—
421#435—473no—
422#435—473no—
423#435—473no—
424#435—473no—
425#435—473no—
426#435—473no—
427#435—476no—
428#435—476no—
429#435—476no—
430C8×D4—476no—
431C8×D4—476no—
432#424—473no—
433#424—473no—
434#423—473no—
435C2×C4⋊C8—473no—
436#408—473no—
437#408—473no—
438#408—473no—
439#408—473no—
440#407—473no—
441#407—473no—
442C2×C22⋊C8—473no—
443C2×C22⋊C8—473no—
444#405C2×D4713yescomplemented
445#405C2×D4713yescomplemented
446C4×M16C2×D4713yescomplemented
447C2×#97C2×D4713yescomplemented
448C47#6014611yescharacteristic, complemented, Sylow
449C2×#41—471no—
450C2×#41—471no—
451C2×#41—473no—
452C2×#41—473no—
453C2×#41—473no—
454C2×#41—473no—
455C2×#41—944no—
456C2×#41—944no—
457C2×#41—944no—
458C2×#41—944no—
459C2×#41C22×D4711yescharacteristic
460C22×Q8—471no—
461C22×Q8—471no—
462C22×D4—473no—
463C22×D4—473no—
464C22×D4—473no—
465C23×C4—473no—
466C23×C4—473no—
467#131—24no—
468#131—944no—
469#131—944no—
470#131—9412no—
471#131—9412no—
472#131—9412no—
473#131—9412no—
474#131D18818yescomplemented
475C2×M16—473no—
476C2×M16—473no—
477C2×M16—471no—
478C2×M16—473no—
479C2×M16—473no—
480C2×M16—476no—
481C2×M16—473no—
482C2×M16—9412no—
483C2×M16—9412no—
484C2×M16—9412no—
485C2×M16C22×D4713yes—
486C2×M16C22×D4713yes—
487C22×C8—473no—
488C22×C8—473no—
489C22×C8—471no—
490C22×C8—473no—
491C22×C8—473no—
492C22×C8—473no—
493C22×C8—476no—
494C22×C8—9412no—
495C22×C8C22×D4713yes—
496C22×C8C22×D4713yes—
497C4⋊Q8—473no—
498#127—473no—
499#124—473no—
500#124—473no—
501#123—476no—
502#123—476no—
503C22⋊Q8—473no—
504C22⋊Q8—473no—
505C22⋊Q8—473no—
506C22⋊Q8—473no—
507#121—476no—
508#121—476no—
509#121—473no—
510#121—473no—
511#121—473no—
512#121—473no—
513#120—476no—
514#120—476no—
515C4×Q8C4×D4711yescharacteristic
516C4×Q8C4×D4711yescharacteristic
517C4×D4—473no—
518C4×D4—473no—
519C4×D4—473no—
520C4×D4—473no—
521C4×D4—471no—
522C4×D4—473no—
523C4×D4—473no—
524C4×D4—473no—
525C4×D4—476no—
526C4×D4C4×D4713yes—
527C4×D4C4×D4713yes—
528#117C22×D4713yes—
529C2×C4⋊C4—473no—
530C2×C22⋊C4—473no—
531C2×C22⋊C4—473no—
532C2×C42C22×D4713yes—
533C4⋊C8—471no—
534C4⋊C8—473no—
535C4⋊C8—473no—
536C4⋊C8—473no—
537C4⋊C8—476no—
538C22⋊C8—471no—
539C22⋊C8—471no—
540C22⋊C8—473no—
541C22⋊C8—473no—
542C22⋊C8—473no—
543C22⋊C8—473no—
544C22⋊C8—473no—
545C22⋊C8—473no—
546C22⋊C8—476no—
547C22⋊C8—476no—
548#97C22×D4711yescharacteristic
549#97C22×D4713yes—
550#97C22×D4713yes—
551#97C22×D4713yes—
552C4×C8C22×D4716yes—
553C24—473no—
554C24—473no—
555#41—944no—
556#41—944no—
557#41—9412no—
558#41—9412no—
559#41—946no—
560#41—946no—
561#41—946no—
562#41—946no—
563#41C2×D18814yes—
564#41#1062535014yes—
565C2×Q8—473no—
566C2×Q8—473no—
567C2×Q8—944no—
568C2×Q8—944no—
569C2×Q8C2×C4×D4711yescharacteristic
570C2×D4—476no—
571C2×D4—476no—
572C2×D4—471no—
573C2×D4—473no—
574C2×D4—473no—
575C2×D4—473no—
576C2×D4—473no—
577C2×D4—473no—
578C2×D4—476no—
579C2×D4—9412no—
580C2×D4—9412no—
581C2×D4—1886no—
582C2×D4C2×C4×D4713yes—
583C22×C4—473no—
584C22×C4—473no—
585C22×C4—473no—
586C22×C4—473no—
587C22×C4—473no—
588C22×C4—473no—
589C22×C4—471no—
590C22×C4—473no—
591C22×C4—473no—
592C22×C4—471no—
593C22×C4—946no—
594C22×C4—946no—
595C22×C4—946no—
596C22×C4—946no—
597C22×C4C2×C4×D4713yes—
598C22×C4C2×C4×D4713yes—
599C22×C4C23×D4713yes—
600M16—26no—
601M16—946no—
602M16—946no—
603M16—942no—
604M16—946no—
605M16—946no—
606M16—9412no—
607M16—946no—
608M16C2×D188112yescomplemented
609C2×C8—26no—
610C2×C8—471no—
611C2×C8—473no—
612C2×C8—473no—
613C2×C8—471no—
614C2×C8—946no—
615C2×C8—946no—
616C2×C8—942no—
617C2×C8—946no—
618C2×C8—946no—
619C2×C8—946no—
620C2×C8—9412no—
621C2×C8C2×D188112yescomplemented
622C2×C8C23×D4713yes—
623C2×C8C23×D4711yescharacteristic
624C2×C8C23×D4713yes—
625C2×C8C23×D4711yescharacteristic
626C4⋊C4—471no—
627C4⋊C4—473no—
628C4⋊C4—473no—
629C4⋊C4—473no—
630C4⋊C4—476no—
631C4⋊C4C2×C4×D4713yes—
632C4⋊C4C2×C4×D4713yes—
633C22⋊C4—471no—
634C22⋊C4—471no—
635C22⋊C4—473no—
636C22⋊C4—473no—
637C22⋊C4—473no—
638C22⋊C4—473no—
639C22⋊C4—473no—
640C22⋊C4—473no—
641C22⋊C4—476no—
642C22⋊C4—476no—
643C22⋊C4C2×C4×D4716yes—
644C42C2×C4×D4713yes—
645C42C2×C4×D4713yes—
646C42C23×D4713yes—
647C42C23×D4711yescharacteristic
648C23—471no—
649C23—471no—
650C23—473no—
651C23—473no—
652C23—946no—
653C23—946no—
654C23—946no—
655C23—1883no—
656C23—1883no—
657C23—1883no—
658C23C22×C4×D4713yes—
659Q8—946no—
660Q8—946no—
661Q8C4×D18814yes—
662D4—946no—
663D4—942no—
664D4—9412no—
665D4—9412no—
666D4—946no—
667D4—946no—
668D4—1886no—
669D4—1883no—
670D4—1883no—
671D4C4×D188112yes—
672C2×C4—43no—
673C2×C4—43no—
674C2×C4—471no—
675C2×C4—471no—
676C2×C4—473no—
677C2×C4—473no—
678C2×C4—946no—
679C2×C4—946no—
680C2×C4—946no—
681C2×C4—946no—
682C2×C4—946no—
683C2×C4—946no—
684C2×C4—941no—
685C2×C4—943no—
686C2×C4—943no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—943no—
691C2×C4—943no—
692C2×C4C22×C4×D4711yescharacteristic
693C2×C4C22×C4×D4711yescharacteristic
694C2×C4C22×C4×D4713yes—
695C2×C4C22×C4×D4713yes—
696C2×C4C22×C4×D4713yes—
697C2×C4C22×D18816yes—
698C2×C4C2×#1062535016yes—
699C2×C4C24×D4711yescharacteristic
700C8—21no—
701C8—23no—
702C8—941no—
703C8—943no—
704C8—943no—
705C8—941no—
706C8C22×D18812yes—
707C8C22×D18816yes—
708C22—23no—
709C22—23no—
710C22—472no—
711C22—941no—
712C22—941no—
713C22—941no—
714C22—943no—
715C22—943no—
716C22—941no—
717C22—943no—
718C22—943no—
719C22—943no—
720C22—943no—
721C22—941no—
722C22—3766no—
723C22—18812no—
724C22C2×C4×D18816yes—
725C22C23×C4×D4711yescharacteristic
726C4—21no—
727C4—23no—
728C4—21no—
729C4—23no—
730C4—941no—
731C4—941no—
732C4—943no—
733C4—943no—
734C4C2×C4×D18816yes—
735C4C23×D18811yescharacteristic
736C4C22×#1062535011yescharacteristic
737C2—26no—
738C2—942no—
739C2—1881no—
740C2—1883no—
741C2—1883no—
742C2C22×C4×D18811yescharacteristic
743C2#568×D4711yescharacteristic
744C2#2025810111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2875C2
prime radical#41×D188C2
cosocleC2×C4×C47C25
hypercenter#2875D47
hypocenterC47#60146
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2875

Complements

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

NH ≅ G/Ntype
1. C2×#15689888C2semidirect
2. C2×#131×D47C2semidirect
4. #20252134C2semidirect
5. M16×D188C2semidirect
6. #20252116C2semidirect
7. #20252116C2semidirect
8. #20252107C2semidirect
9. #20252093C2semidirect
10. #20252084C2semidirect
11. C2×#15689196C2semidirect
12. #20251956C2semidirect
13. #20251835C2semidirect
14. #20251835C2semidirect
15. C47×#2875C2semidirect
19. C2×#13094032C22semidirect
20. C2×#13094032C22semidirect
23. C2×#13094030C22semidirect
24. C2×#13094030C22semidirect
26. C22×#10625324C22semidirect
27. C2×M16×D47C22semidirect
28. C2×M16×D47C22semidirect
29. C22×C8×D47C22semidirect
42. #15689202C22semidirect
43. #15689202C22semidirect
46. #15689196C22semidirect
47. #15689196C22semidirect
48. #15689196C22semidirect
49. #15689196C22semidirect
50. #15689196C22semidirect
51. #15689196C22semidirect
52. #15689196C22semidirect
53. #15689196C22semidirect
54. #15689196C22semidirect
55. C8×D188C22semidirect
56. C8×D188C22semidirect
57. #15689150C22semidirect
58. #15689150C22semidirect
59. #15689147C22semidirect
60. C2×C4⋊(C47⋊C8)C22semidirect
61. #15689091C22semidirect
62. #15689091C22semidirect
63. #15689089C22semidirect
64. #15689089C22semidirect
65. #15689086C22semidirect
66. #15689086C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
72. C47×#405C22semidirect
73. C47×#405C22semidirect
74. C4×M16×C47C22semidirect
75. C2×#97×C47C22semidirect
164. #131×C47D4semidirect
228. M16×C47C2×D4semidirect
230. C2×C8×C47C2×D4semidirect
353. C2×D47#568semidirect
379. #2875D47semidirect
444. #405C2×D47semidirect
445. #405C2×D47semidirect
446. C4×M16C2×D47semidirect
447. C2×#97C2×D47semidirect
448. C47#60146semidirect
474. #131D188semidirect
608. M16C2×D188semidirect
621. C2×C8C2×D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156898882
C2×#131×D472
#41×D1882
#202521342
M16×D1882
#202521162
#202521072
#202520932
#202520842
C2×#156891962
#202519562
#202518352
C47×#28752
#6014647