Finite Group Databasebeta

← #25966157

Subgroups — #25966157

Order 11008.

3178 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583713C211yesmaximal, characteristic, complemented
2C2×#14583709C212yesmaximal, complemented
3C2×#14583700C211yesmaximal, characteristic, complemented
4#19148387C212yesmaximal, complemented
5#19145089C211yesmaximal, characteristic, complemented
6#19145085C212yesmaximal, complemented
7#19145075C212yesmaximal, complemented
8#19145068C214yesmaximal, complemented
9#19145067C212yesmaximal, complemented
10#19145060C214yesmaximal, complemented
11#19145057C212yesmaximal, complemented
12#19145022C212yesmaximal, complemented
13#19145019C211yesmaximal, characteristic, complemented
14C2×#14583282C211yesmaximal, characteristic, complemented
15#495×D43C212yesmaximal, complemented
16#19143017C211yesmaximal, characteristic, complemented
17C43×#3155C211yesmaximal, characteristic, complemented
18C2×#13063372C2212yes—
19C2×#13063370C2212yes—
20#14583713—28no—
21#14583709—216no—
22#14583700—28no—
23C2×#13063358C2212yescomplemented
24C2×#13063355C2212yescomplemented
25C2×#13063354C2214yescomplemented
26C2×#13063354C2214yescomplemented
27C2×#13063351C2212yes—
28C2×#13063349C2214yes—
29C2×#13063349C2214yescomplemented
30C2×#13063347C2211yescharacteristic
31C2×#13063345C2212yescomplemented
32C2×#13063344C2212yes—
33C2×#13063344C2214yescomplemented
34C2×#13063344C2212yescomplemented
35C22×Dic172C2211yescharacteristic, complemented
36C2×Q16×D43C2212yescomplemented
37C22×#10621883C2212yescomplemented
38C2×SD16×D43C2214yescomplemented
39C2×D8×D43C2212yes—
40C2×#13063333C2211yescharacteristic
41C2×#13063331C2211yescharacteristic
42#14583555—24no—
43#14583546—24no—
44#14583536—28no—
45#14583475C2212yescomplemented
46#14583469C2214yescomplemented
47#14583462C2214yescomplemented
48#14583447C2214yescomplemented
49#14583445C2212yescomplemented
50C2×#13063312C2212yescomplemented
51#124×D43C2214yescomplemented
52#14583367C2211yescharacteristic
53#14583294C2214yescomplemented
54#14583293C2214yescomplemented
55#14583290C2214yescomplemented
56#14583287C2214yescomplemented
57#14583286C2214yescomplemented
58#14583284C2211yescharacteristic, complemented
59#14583283C2212yescomplemented
60#14583282C2212yescomplemented
61#14583282C2212yescomplemented
62#14583282C2212yescomplemented
63#14583282C2212yescomplemented
64#14583282C2211yescharacteristic, complemented
65#14583282C2214yescomplemented
66#14583281C2214yescomplemented
67#14583280C2214yescomplemented
68#14583280C2212yescomplemented
69#14583279C2212yescomplemented
70#14583277C2211yescharacteristic, complemented
71#14583274C2211yescharacteristic, complemented
72#14583271C2214yescomplemented
73#14583270C2212yescomplemented
74#14582856C2212yescomplemented
75#14582855C2211yescharacteristic, complemented
76#14582853C2212yescomplemented
77#14582851C2212yescomplemented
78M16×Dic43C2211yescharacteristic, complemented
79C2×C8×Dic43C2211yescharacteristic, complemented
80C4×C8×D43C2212yescomplemented
81C2×AGL(1,ℤ/8)×C43C2212yescomplemented
82C2×#135×C43C2211yescharacteristic, complemented
83C22×D8×C43C2211yescharacteristic
84C43×#535C2212yescomplemented
85C43×#496C2214yescomplemented
86C43×#495C2212yescomplemented
87C43×#493C2212yescomplemented
88C43×#405C2211yescharacteristic, complemented
89#13063372—28no—
90#13063372—28no—
91#13063370—28no—
92#13063370—28no—
93C2×#10621898—22no—
94C2×#10621898C2311yescharacteristic
95C2×#10621898C2312yes—
96C2×#10621900—24no—
97C2×#10621900—22no—
98C2×#10621900C2314yes—
99C2×#10621900C2314yes—
100C22×Dic86—22no—
101C22×Dic86C2312yes—
102C2×Q8×D43C2314yes—
103C22×C22⋊D43—24no—
104C2×D4×D43—22no—
105C2×D4×D43C2314yes—
106#13063358—28no—
107#13063355—28no—
108#13063354—216no—
109#13063354—216no—
110#13063351—28no—
111#13063349—216no—
112#13063349—216no—
113#13063347—24no—
114#13063345—28no—
115#13063344—28no—
116#13063344—216no—
117#13063344—28no—
118C2×Dic172—24no—
119C2×Dic172C2312yes—
120C2×Dic172C2312yes—
121C2×Dic172C2311yescharacteristic
122C2×Dic172C2314yes—
123C2×#10621885C2314yes—
124C2×#10621885C2312yes—
125Q16×D43—28no—
126C2×#10621873C2314yes—
127C2×#10621873C2312yes—
128C2×#10621883—28no—
129C2×#10621883C2314yes—
130C2×#10621883C2314yes—
131C2×#10621883C2314yes—
132C2×#10621883C2312yes—
133C2×#10621883C2314yes—
134C2×#10621884C2312yes—
135SD16×D43—216no—
136C2×D344C2311yescharacteristic
137C2×#10621882C2314yes—
138C2×#10621882C2312yes—
139D8×D43—28no—
140#13063333D418yescomplemented
141#13063331D418yescomplemented
142C2×#10621877C2311yescharacteristic
143C2×#10621872C2312yes—
144C2×#10621872C2312yes—
145C22×C43⋊C8C2311yescharacteristic
146C2×C8×D43C2312yes—
147C2×C8×D43C2312yes—
148#13063325C2314yes—
149#13063323C2312yes—
150#13063321C2312yes—
151#13063314C2312yes—
152#13063313C2314yes—
153#13063312—24no—
154#13063312C2314yes—
155#13063312C2314yes—
156#13063312C2312yes—
157#13063311—28no—
158#13063309—24no—
159#13063307—28no—
160#13063305—24no—
161#13063302—28no—
162#13063297—24no—
163#13063297—28no—
164#13063296—28no—
165#13063293—28no—
166#13063290D412yes—
167D4×Dic43—28no—
168#13063287D412yes—
169C4×C22⋊D43—24no—
170(C22⋊D43)⋊C4D414yes—
171#13063282C2312yes—
172C2×C22⋊Dic43—24no—
173C22⋊C4×D43—28no—
174C2×C4×Dic43C2311yescharacteristic
175C42×D43C2312yes—
176#13063236C2312yes—
177#13063235C2312yes—
178C4×C43⋊C8C2312yes—
179C8×Dic43C2311yescharacteristic
180C8×Dic43C2312yes—
181C8×Dic43C2311yescharacteristic
182C8×Dic43C2311yescharacteristic
183C8×Dic43C2311yescharacteristic
184C2×#41×C43C2312yes—
185C22×D4×C43C2312yes—
186AGL(1,ℤ/8)×C43—28no—
187#135×C43—24no—
188C2×Q16×C43C2311yescharacteristic
189C2×SD16×C43C2312yes—
190C2×SD16×C43C2314yes—
191C2×D8×C43—24no—
192C2×D8×C43C2312yes—
193C2×D8×C43C2312yes—
194C2×D8×C43C2311yescharacteristic
195C2×D8×C43C2314yes—
196C2×M16×C43C2311yescharacteristic
197C22×C8×C43C2311yescharacteristic
198#127×C43C2314yes—
199#124×C43C2314yes—
200#121×C43—24no—
201#120×C43—24no—
202#117×C43C2311yescharacteristic
203#97×C43C2312yes—
204C4×C8×C43C2312yes—
205C24×C43—22no—
206C23×D43—24no—
207#41×C43—24no—
208#41×C43—24no—
209C2×Q8×C43C2412yes—
210C2×D4×C43—22no—
211C2×D4×C43—28no—
212C2×D4×C43—22no—
213C2×D4×C43—24no—
214C2×D4×C43—24no—
215C2×D4×C43C2414yes—
216C2×D4×C43C2412yes—
217C22×C4×C43—22no—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—22no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—416no—
225C2×C22⋊D43C2×D412yes—
226C22×Dic43—24no—
227C22×Dic43—24no—
228C22×Dic43—22no—
229C22×Dic43C2×D412yes—
230Q8×D43—28no—
231Q8×D43—28no—
232#10621900—28no—
233#10621900—28no—
234#10621900—28no—
235#10621900—28no—
236#10621900—416no—
237#10621900—48no—
238D4×D43—28no—
239D4×D43—28no—
240D4×D43—48no—
241#10621898—24no—
242#10621898—24no—
243#10621898—48no—
244#10621898C2×D414yes—
245#10621898C2×D414yes—
246C2×D172C2×D411yescharacteristic
247C2×D172C2412yes—
248C2×C4×D43—22no—
249C2×C4×D43—24no—
250C2×C4×D43C2×D414yes—
251C2×C4×D43C2412yes—
252C2×Dic86—24no—
253C2×Dic86—24no—
254C2×Dic86—22no—
255C2×Dic86—24no—
256C2×Dic86—48no—
257C2×Dic86C2×D411yescharacteristic
258C2×Dic86C2414yes—
259C2×Dic86C2412yes—
260Q16×C43—22no—
261SD16×C43—24no—
262SD16×C43—28no—
263D8×C43—24no—
264D8×C43—24no—
265D8×C43—22no—
266D8×C43—28no—
267M16×C43C2×D414yes—
268C2×C8×C43C2×D414yes—
269C2×C8×C43C2411yescharacteristic
270C2×C8×C43C2412yes—
271C2×C8×C43C2411yescharacteristic
272C4⋊C4×C43C2×D412yes—
273C22⋊C4×C43—28no—
274C22⋊C4×C43C2×D412yes—
275C42×C43C2412yes—
276C22⋊Dic43—28no—
277C22⋊Dic43—28no—
278C22⋊Dic43—24no—
279#10621885—28no—
280#10621885—24no—
281#10621884—24no—
282#10621883—28no—
283#10621883—28no—
284#10621883—24no—
285#10621883—28no—
286#10621883—28no—
287#10621882—28no—
288#10621882—24no—
289(C2×D43)⋊C4—28no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4C2×D414yes—
292C4⋊Dic43—28no—
293Dic43⋊C4—24no—
294Dic43⋊C4C2×D414yes—
295C4×Dic43C2×D414yes—
296C4×Dic43C2×D412yes—
297C4×Dic43C2411yescharacteristic
298C4×Dic43C2411yescharacteristic
299#10621877C2×D414yes—
300C2×C43⋊C8C2×D414yes—
301C2×C43⋊C8C2411yescharacteristic
302C2×C43⋊C8C2411yescharacteristic
303C2×C43⋊C8C2412yes—
304Dic172—24no—
305Dic172—24no—
306Dic172—22no—
307Dic172—28no—
308D344—22no—
309#10621873—28no—
310#10621873—24no—
311#10621872C2×D418yes—
312#10621872C2×D418yes—
313C8×D43C2×D418yes—
314C8×D43C2×D418yes—
315C23×C43—24no—
316C23×C43—22no—
317C23×C43—44no—
318C23×C43—84no—
319C23×C43C22×D411yescharacteristic
320C22×D43—22no—
321C22×D43—48no—
322C22×D43—88no—
323C22×D43C22×D412yes—
324Q8×C43—22no—
325Q8×C43—22no—
326D4×C43—24no—
327D4×C43—22no—
328D4×C43—24no—
329D4×C43—22no—
330D4×C43—44no—
331D4×C43—44no—
332D4×C43—88no—
333C2×C4×C43—22no—
334C2×C4×C43—44no—
335C2×C4×C43C22×D414yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D412yes—
338C2×C4×C43C22×D412yes—
339C2×C4×C43C2511yescharacteristic
340C22⋊D43—44no—
341C22⋊D43—48no—
342C22⋊D43—48no—
343C22⋊D43—48no—
344C22⋊D43—84no—
345C22⋊D43#12718yes—
346C2×Dic43—22no—
347C2×Dic43—24no—
348C2×Dic43—42no—
349C2×Dic43—44no—
350C2×Dic43—48no—
351C2×Dic43—48no—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355D172—22no—
356D172—22no—
357D172#12714yes—
358C4×D43—44no—
359C4×D43—48no—
360C4×D43—44no—
361C4×D43C22×D414yes—
362C4×D43C22×D414yes—
363Dic86—24no—
364Dic86—22no—
365Dic86—24no—
366Dic86—22no—
367Dic86—44no—
368Dic86—48no—
369Dic86#12714yes—
370C8×C43C22×D412yes—
371C8×C43C22×D414yes—
372C8×C43C22×D412yes—
373C43⋊C8C22×D412yes—
374C43⋊C8C22×D414yes—
375C43⋊C8C22×D412yes—
376#60649—431nomaximal, Sylow
377C22×C43—22no—
378C22×C43—48no—
379C22×C43—44no—
380C22×C43—44no—
381C22×C43—42no—
382C22×C43—164no—
383C22×C43C2×#12712yes—
384C22×C43C23×D411yescharacteristic
385C2×D43—24no—
386C2×D43—44no—
387C2×D43—42no—
388C2×D43—168no—
389C2×D43C2×#12714yes—
390C4×C43—24no—
391C4×C43—42no—
392C4×C43C2×#12712yes—
393C4×C43C23×D411yescharacteristic
394C4×C43C23×D411yescharacteristic
395Dic43—22no—
396Dic43—22no—
397Dic43—44no—
398Dic43—42no—
399Dic43C2×#12714yes—
400C2×#578—431no—
401C2×#577—432no—
402C2×#576—431no—
403#3500—432no—
404#3156—432no—
405#3156—431no—
406#3155—432no—
407#3155D4311yescharacteristic, complemented
408#3154—434no—
409#3154—432no—
410#3153—434no—
411#3153—432no—
412#3147—432no—
413#3147—431no—
414C2×#495—432no—
415C2×#495—431no—
416C4×#131—431no—
417C2×C43—22no—
418C2×C43—84no—
419C2×C43—82no—
420C2×C43C22×#12711yescharacteristic
421C2×C43#358412yes—
422D43—24no—
423D43—82no—
424C2×2−1+4—432no—
425C2×H(5,𝔽2)—432no—
426#578—868no—
427#577—8616no—
428#576—868no—
429C2×#137—432no—
430C2×#137—434no—
431C2×#137—434no—
432C2×#137—432no—
433C2×AGL(1,ℤ/8)—432no—
434C2×AGL(1,ℤ/8)—434no—
435C2×AGL(1,ℤ/8)—434no—
436C2×AGL(1,ℤ/8)C2×D4312yescomplemented
437C2×#135—432no—
438C2×#135—434no—
439C2×#135—432no—
440C2×#135—432no—
441C2×#135—431no—
442C2×#135C2×D4311yescharacteristic, complemented
443C22×Q16—432no—
444C22×Q16—431no—
445C22×SD16—432no—
446C22×SD16—434no—
447C22×D8—432no—
448C22×D8C2×D4311yescharacteristic
449C2×#131—431no—
450C2×#131—431no—
451#548—864no—
452#546—868no—
453#546—864no—
454#536—434no—
455#536—432no—
456#535—434no—
457#535C2×D4312yescomplemented
458#532—432no—
459#532—434no—
460C2×#124—432no—
461C2×#124—434no—
462C4×#41—431no—
463#497—434no—
464#497—434no—
465#497—434no—
466#496—434no—
467#496—434no—
468#496C2×D4314yescomplemented
469#495—431no—
470#495—434no—
471#495—432no—
472#495—432no—
473#495—432no—
474#495—432no—
475#495—432no—
476#495—431no—
477#495—434no—
478#495—434no—
479#495—432no—
480#495C2×D4312yescomplemented
481#494—431no—
482#494—432no—
483#493—431no—
484#493C2×D4312yescomplemented
485#492—432no—
486#492—434no—
487#405—431no—
488#405—432no—
489#405—432no—
490#405C2×D4311yescharacteristic, complemented
491C4×M16—431no—
492C4×M16—432no—
493C2×C4×C8—431no—
494C2×C4×C8—432no—
495C43#6064911yescharacteristic, complemented, Sylow
4962−1+4—868no—
4972−1+4—868no—
498H(5,𝔽2)—868no—
499H(5,𝔽2)—868no—
500C2×#41—431no—
501C2×#41—434no—
502C2×#41—434no—
503C2×#41—432no—
504C2×#41—862no—
505C2×#41—864no—
506C2×#41—862no—
507C2×#41C22×D4312yes—
508C22×Q8—434no—
509C22×Q8—432no—
510C22×Q8—862no—
511C22×D4—434no—
512C22×D4—862no—
513C22×D4—864no—
514C22×D4C22×D4312yes—
515#137—8616no—
516#137—8616no—
517#137—868no—
518#137—868no—
519AGL(1,ℤ/8)—28no—
520AGL(1,ℤ/8)—8616no—
521AGL(1,ℤ/8)—8616no—
522AGL(1,ℤ/8)—868no—
523#135—24no—
524#135—868no—
525#135—8616no—
526#135—868no—
527#135—868no—
528#135—864no—
529C2×Q16—434no—
530C2×Q16—432no—
531C2×Q16—432no—
532C2×Q16—432no—
533C2×Q16—431no—
534C2×Q16—434no—
535C2×Q16—868no—
536C2×Q16—864no—
537C2×Q16C22×D4311yescharacteristic
538C2×SD16—432no—
539C2×SD16—434no—
540C2×SD16—434no—
541C2×SD16—432no—
542C2×SD16—434no—
543C2×SD16—434no—
544C2×SD16—434no—
545C2×SD16—432no—
546C2×SD16—8616no—
547C2×SD16—868no—
548C2×SD16C22×D4314yes—
549C2×SD16C22×D4312yes—
550C2×D8—24no—
551C2×D8—434no—
552C2×D8—432no—
553C2×D8—431no—
554C2×D8—868no—
555C2×D8C22×D4312yes—
556C2×D8C22×D4312yes—
557C2×D8C22×D4311yescharacteristic
558C2×D8C22×D4314yes—
559#131—438no—
560#131—438no—
561C2×M16—431no—
562C2×M16—432no—
563C2×M16—432no—
564C2×M16C22×D4311yescharacteristic
565C22×C8—431no—
566C22×C8—432no—
567C22×C8—432no—
568C22×C8C22×D4311yescharacteristic
569C4⋊Q8—432no—
570C4⋊Q8—434no—
571#127—432no—
572#127C22×D4314yes—
573#124—432no—
574#124—434no—
575#124—434no—
576#124—432no—
577#124—434no—
578#124—868no—
579#124—864no—
580#124C22×D4314yes—
581#123—868no—
582#123—864no—
583C22⋊Q8—868no—
584C22⋊Q8—864no—
585#121—24no—
586#121—868no—
587#121—868no—
588#121—864no—
589#120—24no—
590#120—868no—
591C4×Q8—432no—
592C4×D4—432no—
593C4×D4—434no—
594C4×D4—864no—
595C4×D4—868no—
596#117—432no—
597#117C22×D4311yescharacteristic
598C2×C22⋊C4—868no—
599C2×C22⋊C4—864no—
600C2×C42—431no—
601C2×C42—432no—
602#97—432no—
603#97—432no—
604#97C22×D4312yes—
605C4×C8—431no—
606C4×C8—431no—
607C4×C8—432no—
608C4×C8—431no—
609C4×C8—431no—
610C4×C8—432no—
611C4×C8C22×D4312yes—
612C24—22no—
613C24—864no—
614#41—24no—
615#41—24no—
616#41—434no—
617#41—434no—
618#41—868no—
619#41—868no—
620#41—868no—
621#41—868no—
622#41—864no—
623#41—864no—
624#41—1728no—
625#41—17216no—
626#41—1728no—
627C2×Q8—431no—
628C2×Q8—434no—
629C2×Q8—432no—
630C2×Q8—864no—
631C2×Q8—868no—
632C2×Q8—868no—
633C2×Q8—862no—
634C2×Q8—864no—
635C2×Q8—864no—
636C2×Q8—1728no—
637C2×Q8C23×D4312yes—
638C2×D4—22no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—28no—
643C2×D4—432no—
644C2×D4—431no—
645C2×D4—432no—
646C2×D4—868no—
647C2×D4—868no—
648C2×D4—864no—
649C2×D4—864no—
650C2×D4—864no—
651C2×D4—864no—
652C2×D4—862no—
653C2×D4—1728no—
654C2×D4—17216no—
655C2×D4C23×D4314yes—
656C2×D4C23×D4312yes—
657C22×C4—22no—
658C22×C4—432no—
659C22×C4—432no—
660C22×C4—434no—
661C22×C4—864no—
662C22×C4—864no—
663C22×C4—864no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4C23×D4311yescharacteristic
667Q16—22no—
668Q16—868no—
669Q16—864no—
670Q16—864no—
671Q16—864no—
672Q16—862no—
673Q16—868no—
674SD16—28no—
675SD16—24no—
676SD16—868no—
677SD16—868no—
678SD16—864no—
679SD16—868no—
680SD16—868no—
681SD16—864no—
682SD16—868no—
683SD16—864no—
684D8—24no—
685D8—24no—
686D8—22no—
687D8—28no—
688D8—868no—
689D8—864no—
690D8—862no—
691M16—434no—
692M16—438no—
693M16—438no—
694M16D4×D4314yes—
695C2×C8—434no—
696C2×C8—431no—
697C2×C8—431no—
698C2×C8—432no—
699C2×C8—438no—
700C2×C8—438no—
701C2×C8D4×D4314yes—
702C2×C8C23×D4311yescharacteristic
703C2×C8C23×D4311yescharacteristic
704C2×C8C23×D4312yes—
705C4⋊C4—434no—
706C4⋊C4—864no—
707C4⋊C4—868no—
708C4⋊C4D4×D4312yes—
709C22⋊C4—28no—
710C22⋊C4—434no—
711C22⋊C4—864no—
712C22⋊C4—868no—
713C22⋊C4—868no—
714C22⋊C4—864no—
715C22⋊C4—868no—
716C22⋊C4D4×D4312yes—
717C42—434no—
718C42—432no—
719C42—431no—
720C42—431no—
721C42C23×D4312yes—
722C23—24no—
723C23—22no—
724C23—44no—
725C23—84no—
726C23—432no—
727C23—862no—
728C23—3448no—
729C23—1728no—
730C23C2×D4×D4311yescharacteristic
731Q8—22no—
732Q8—22no—
733Q8—434no—
734Q8—864no—
735Q8—862no—
736Q8—864no—
737Q8—862no—
738Q8—1728no—
739Q8—1724no—
740D4—24no—
741D4—22no—
742D4—24no—
743D4—22no—
744D4—44no—
745D4—44no—
746D4—88no—
747D4—438no—
748D4—434no—
749D4—862no—
750D4—862no—
751D4—3444no—
752D4—1728no—
753D4—1728no—
754D4—1728no—
755D4—1724no—
756C2×C4—22no—
757C2×C4—44no—
758C2×C4—432no—
759C2×C4—434no—
760C2×C4—434no—
761C2×C4—432no—
762C2×C4—432no—
763C2×C4—864no—
764C2×C4—862no—
765C2×C4—1724no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1728no—
769C2×C4—1722no—
770C2×C4—1724no—
771C2×C4—1724no—
772C2×C4C2×D4×D4314yes—
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×D4×D4312yes—
775C2×C4C2×D4×D4312yes—
776C2×C4C24×D4311yescharacteristic
777C8—432no—
778C8—432no—
779C8—434no—
780C8C2×D4×D4312yes—
781C8C2×D4×D4314yes—
782C8C2×D4×D4312yes—
783C22—22no—
784C22—44no—
785C22—48no—
786C22—42no—
787C22—44no—
788C22—164no—
789C22—434no—
790C22—864no—
791C22—1724no—
792C22—1722no—
793C22—6888no—
794C22#127×D4312yes—
795C22C22×D4×D4311yescharacteristic
796C4—24no—
797C4—42no—
798C4—434no—
799C4—862no—
800C4—862no—
801C4—1722no—
802C4—1724no—
803C4#127×D4312yes—
804C4C22×D4×D4311yescharacteristic
805C4C22×D4×D4311yescharacteristic
806C2—22no—
807C2—84no—
808C2—82no—
809C2—864no—
810C2—3442no—
811C2C2×#127×D4311yescharacteristic
812C2#1914936312yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3155C2
socleC22×C43C23×D4
hypercenter#3155D43
hypocenterC43#60649
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. C2×#14583713C2semidirect
2. C2×#14583709C2semidirect
3. C2×#14583700C2semidirect
4. #19148387C2semidirect
5. #19145089C2semidirect
6. #19145085C2semidirect
7. #19145075C2semidirect
8. #19145068C2semidirect
9. #19145067C2semidirect
10. #19145060C2semidirect
11. #19145057C2semidirect
12. #19145022C2semidirect
13. #19145019C2semidirect
14. C2×#14583282C2semidirect
15. #495×D43C2semidirect
16. #19143017C2semidirect
17. C43×#3155C2semidirect
23. C2×#13063358C22semidirect
24. C2×#13063355C22semidirect
25. C2×#13063354C22semidirect
26. C2×#13063354C22semidirect
29. C2×#13063349C22semidirect
31. C2×#13063345C22semidirect
33. C2×#13063344C22semidirect
34. C2×#13063344C22semidirect
35. C22×Dic172C22semidirect
36. C2×Q16×D43C22semidirect
37. C22×#10621883C22semidirect
38. C2×SD16×D43C22semidirect
45. #14583475C22semidirect
46. #14583469C22semidirect
47. #14583462C22semidirect
48. #14583447C22semidirect
49. #14583445C22semidirect
50. C2×#13063312C22semidirect
51. #124×D43C22semidirect
53. #14583294C22semidirect
54. #14583293C22semidirect
55. #14583290C22semidirect
56. #14583287C22semidirect
57. #14583286C22semidirect
58. #14583284C22semidirect
59. #14583283C22semidirect
60. #14583282C22semidirect
61. #14583282C22semidirect
62. #14583282C22semidirect
63. #14583282C22semidirect
64. #14583282C22semidirect
65. #14583282C22semidirect
66. #14583281C22semidirect
67. #14583280C22semidirect
68. #14583280C22semidirect
69. #14583279C22semidirect
70. #14583277C22semidirect
71. #14583274C22semidirect
72. #14583271C22semidirect
73. #14583270C22semidirect
74. #14582856C22semidirect
75. #14582855C22semidirect
76. #14582853C22semidirect
77. #14582851C22semidirect
78. M16×Dic43C22semidirect
79. C2×C8×Dic43C22semidirect
80. C4×C8×D43C22semidirect
81. C2×AGL(1,ℤ/8)×C43C22semidirect
82. C2×#135×C43C22semidirect
84. C43×#535C22semidirect
85. C43×#496C22semidirect
86. C43×#495C22semidirect
87. C43×#493C22semidirect
88. C43×#405C22semidirect
140. #13063333D4semidirect
141. #13063331D4semidirect
407. #3155D43semidirect
436. C2×AGL(1,ℤ/8)C2×D43semidirect
442. C2×#135C2×D43semidirect
457. #535C2×D43semidirect
468. #496C2×D43semidirect
480. #495C2×D43semidirect
484. #493C2×D43semidirect
490. #405C2×D43semidirect
495. C43#60649semidirect

Maximal subgroups

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

subgroupindex
C2×#145837132
C2×#145837092
C2×#145837002
#191483872
#191450892
#191450852
#191450752
#191450682
#191450672
#191450602
#191450572
#191450222
#191450192
C2×#145832822
#495×D432
#191430172
C43×#31552
#6064943