Finite Group Databasebeta

← #26005143

Subgroups — #26005143

Order 11008.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583736C212yesmaximal, complemented
2#19148389C212yesmaximal, complemented
3#19148384C216yesmaximal, complemented
4#19148378C213yesmaximal, complemented
5#19148373C211yesmaximal, characteristic, complemented
6#19148368C213yesmaximal, complemented
7#19148365C214yesmaximal, complemented
8#19148353C2112yesmaximal, complemented
9D4×#10621902C214yesmaximal, complemented
10#19148082C2112yesmaximal, complemented
11#19147927C216yesmaximal, complemented
12C2×#14583450C213yesmaximal, complemented
13#532×D43C213yesmaximal, complemented
14C4×#41×D43C211yesmaximal, characteristic, complemented
15C43×#3499C211yesmaximal, characteristic, complemented
16#14583736—232no—
17C2×#13063373C2214yescomplemented
18C2×#13063373C2216yescomplemented
19C2×#13063371C22112yescomplemented
20C2×#13063371C2216yescomplemented
21C2×#13063371C2212yescomplemented
22C22×#10621902C2214yescomplemented
23C22×#10621902C2216yescomplemented
24C2×#41×D43C2211yescharacteristic
25C2×#41×D43C22112yescomplemented
26C2×#41×D43C2216yescomplemented
27#14583571C2214yescomplemented
28#14583570C22112yescomplemented
29#14583564C22112yescomplemented
30#14583560C2218yescomplemented
31#14583559C22124yescomplemented
32#14583552C22112yescomplemented
33#14583550C22124yescomplemented
34#14583541C22148yescomplemented
35#14583540C22124yescomplemented
36#14583537C22124yescomplemented
37D4×D172C22112yescomplemented
38D4×D172C22112yescomplemented
39#14583533C22124yescomplemented
40#14583479C22124yescomplemented
41#14583474C22112yescomplemented
42#14583473C2216yescomplemented
43#14583468C2216yescomplemented
44#14583467C22112yescomplemented
45#14583463C2216yescomplemented
46#14583460C22124yescomplemented
47#14583450C22112yescomplemented
48#14583450C22112yescomplemented
49#14583450C2216yescomplemented
50#14583450C2213yescomplemented
51#14583450C2216yescomplemented
52#14583450C2216yescomplemented
53#14583449C2213yescomplemented
54#14583448C2216yescomplemented
55#14583447C2211yescharacteristic, complemented
56#14583446C22112yescomplemented
57#14583445C2216yescomplemented
58#14583444C22112yescomplemented
59C4⋊Q8×D43C2213yescomplemented
60C2×#13063322C2213yescomplemented
61#127×D43C2213yescomplemented
62C2×#13063314C2216yescomplemented
63#124×D43C2216yescomplemented
64#14583412C22124yescomplemented
65#14583407C22124yescomplemented
66C2×#13063300C22112yescomplemented
67#121×D43C22112yescomplemented
68#41×Dic43C2211yescharacteristic, complemented
69C4×#10621902C2212yescomplemented
70C4×#10621898C2213yescomplemented
71#14583367C2213yescomplemented
72C4×#10621900C2216yescomplemented
73C4×Q8×D43C2212yescomplemented
74C2×#13063287C22112yescomplemented
75C4×D4×D43C22112yescomplemented
76C4×D4×D43C2216yescomplemented
77#117×D43C2213yescomplemented
78C2×C42×D43C2213yescomplemented
79C2×2−1+4×C43C2212yescomplemented
80D4×Q8×C43C2214yescomplemented
81C43×#547C22112yescomplemented
82C43×#536C2216yescomplemented
83C43×#532C2213yescomplemented
84C2×C4⋊Q8×C43C2213yescomplemented
85C4×#41×C43C2211yescharacteristic, complemented
86#13063373—232no—
87#13063373—248no—
88#13063371—216no—
89#13063371—296no—
90#13063371—248no—
91C2×#10621902—232no—
92C2×#10621902—248no—
93C2×#10621902C23112yes—
94C2×#10621902C2314yes—
95C2×#10621902C23112yes—
96C2×#10621902C2316yes—
97C2×#10621902C23112yes—
98C2×#10621902C23112yes—
99C2×#10621902C2311yescharacteristic
100C2×#10621898C23112yes—
101C2×#10621898C2316yes—
102C2×#10621898C23112yes—
103C2×#10621898C23124yes—
104C2×#10621898C2313yes—
105C2×#10621900C23112yes—
106C2×#10621900C2312yes—
107C2×#10621900C2313yes—
108#41×D43—296no—
109#41×D43—248no—
110#41×D43D4116yescomplemented
111C2×Q8×D43C23112yes—
112C2×Q8×D43C2316yes—
113C2×Q8×D43C2311yescharacteristic
114C22×D172C23112yes—
115C22×D172C2316yes—
116C22×D172C23112yes—
117C22×D172C23112yes—
118C2×D4×D43C23112yes—
119C2×D4×D43C2316yes—
120C2×D4×D43C23124yes—
121C2×D4×D43C23112yes—
122C2×D4×D43C23112yes—
123C2×D4×D43C2313yes—
124C22×C4×D43C23112yes—
125C22×C4×D43C23112yes—
126C22×C4×D43C2316yes—
127C22×C4×D43C2313yes—
128#13063325C2311yescharacteristic
129#13063324C23112yes—
130#13063323C2316yes—
131#13063322C23112yes—
132#13063322C2313yes—
133#13063322C2316yes—
134#13063321C23112yes—
135#13063321C2316yes—
136#13063314C23124yes—
137#13063314C2316yes—
138#13063314C23112yes—
139#13063313C2316yes—
140#13063312C2312yes—
141#13063311C23124yes—
142#13063310C23148yes—
143#13063308C23124yes—
144#13063303C23148yes—
145#13063301C23124yes—
146#13063300C23124yes—
147#13063300C23124yes—
148#13063300C23112yes—
149#13063300C23124yes—
150#13063300C23124yes—
151#13063299C23124yes—
152#13063299C23112yes—
153#13063298C23148yes—
154#13063298C23124yes—
155#13063297C23124yes—
156#13063296C2314yes—
157#13063295C23124yes—
158#13063295C23148yes—
159#13063293C23124yes—
160Q8×Dic43C2312yes—
161C4×Dic86C2316yes—
162#13063290C2316yes—
163C4×D172C2316yes—
164C4×D172C23112yes—
165D4×Dic43C2314yes—
166D4×Dic43C2316yes—
167#13063287C23124yes—
168#13063287C23124yes—
169#13063287C23112yes—
170#13063287C2316yes—
171#13063287C23124yes—
172C4×C22⋊D43C23124yes—
173C4×C22⋊D43C23112yes—
174(C22⋊D43)⋊C4C23112yes—
175(C22⋊D43)⋊C4C23124yes—
176#13063284C2313yes—
177#13063283C2316yes—
178#13063282C2316yes—
179#13063281C2316yes—
180C4⋊C4×D43C23112yes—
181C4⋊C4×D43C2316yes—
182C2×(C2×D43)⋊C4C23124yes—
183C22⋊C4×D43C2316yes—
184C22⋊C4×D43C23124yes—
185C2×C4×Dic43C2316yes—
186C2×C4×Dic43C2313yes—
187C42×D43C2311yescharacteristic
188C42×D43C2313yes—
189C42×D43C2316yes—
190C42×D43C2316yes—
191C42×D43C2313yes—
192C42×D43C2313yes—
1932−1+4×C43—216no—
194C2×#41×C43C2316yes—
195C2×#41×C43C23112yes—
196C2×#41×C43C2311yescharacteristic
197C22×Q8×C43C2314yes—
198C22×Q8×C43C2316yes—
199C4⋊Q8×C43C23112yes—
200C4⋊Q8×C43C2313yes—
201C4⋊Q8×C43C2316yes—
202#127×C43C2311yescharacteristic
203#124×C43C2316yes—
204#123×C43C23124yes—
205C22⋊Q8×C43C23124yes—
206#121×C43C23112yes—
207C4×Q8×C43C2312yes—
208C4×D4×C43C23112yes—
209C4×D4×C43C2316yes—
210#117×C43C2313yes—
211C2×C4⋊C4×C43C23112yes—
212C2×C42×C43C2313yes—
213C23×D43C24112yes—
214C23×D43C24112yes—
215C23×D43C2413yes—
216#41×C43—248no—
217#41×C43—224no—
218#41×C43C2×D418yescomplemented
219C2×Q8×C43—216no—
220C2×Q8×C43—224no—
221C2×Q8×C43C24112yes—
222C2×Q8×C43C2416yes—
223C2×Q8×C43C2411yescharacteristic
224C2×D4×C43C2414yes—
225C2×D4×C43C24112yes—
226C2×D4×C43C2412yes—
227C2×D4×C43C2413yes—
228C22×C4×C43C2416yes—
229C22×C4×C43C24112yes—
230C22×C4×C43C24112yes—
231C22×C4×C43C2413yes—
232C2×C22⋊D43C24112yes—
233C2×C22⋊D43C2414yes—
234C2×C22⋊D43C24112yes—
235C2×C22⋊D43C24124yes—
236C2×C22⋊D43C2416yes—
237C22×Dic43C2414yes—
238C22×Dic43C2416yes—
239C22×Dic43C2413yes—
240#10621902—216no—
241#10621902—248no—
242#10621902—248no—
243#10621902—224no—
244#10621902—248no—
245#10621902—248no—
246#10621902C2×D418yescomplemented
247Q8×D43—224no—
248Q8×D43—248no—
249Q8×D43C2×D418yescomplemented
250#10621900—248no—
251#10621900—28no—
252#10621900C2×D4124yescomplemented
253D4×D43—248no—
254D4×D43—296no—
255D4×D43—224no—
256D4×D43—248no—
257D4×D43—424no—
258D4×D43C2×D4124yescomplemented
259#10621898—224no—
260#10621898—296no—
261#10621898—248no—
262#10621898—248no—
263#10621898C2×D4124yescomplemented
264C2×D172—224no—
265C2×D172—248no—
266C2×D172—248no—
267C2×D172—424no—
268C2×D172C24112yes—
269C2×D172C24124yes—
270C2×D172C24112yes—
271C2×D172C24112yes—
272C2×D172C2416yes—
273C2×D172C24124yes—
274C2×D172C2413yes—
275C2×C4×D43—248no—
276C2×C4×D43—248no—
277C2×C4×D43—412no—
278C2×C4×D43C2×D4124yescomplemented
279C2×C4×D43C2412yes—
280C2×C4×D43C2416yes—
281C2×C4×D43C24112yes—
282C2×C4×D43C24112yes—
283C2×C4×D43C24112yes—
284C2×C4×D43C24124yes—
285C2×C4×D43C2416yes—
286C2×C4×D43C2416yes—
287C2×C4×D43C2411yescharacteristic
288C2×C4×D43C2413yes—
289C2×C4×D43C2413yes—
290C2×C4×D43C2413yes—
291C2×Dic86C24112yes—
292C2×Dic86C2412yes—
293C2×Dic86C2413yes—
294C4⋊C4×C43C24112yes—
295C4⋊C4×C43C24124yes—
296C4⋊C4×C43C2416yes—
297C22⋊C4×C43C2416yes—
298C22⋊C4×C43C24124yes—
299C42×C43C2411yescharacteristic
300C42×C43C2413yes—
301C42×C43C2416yes—
302C22⋊Dic43C2418yes—
303C22⋊Dic43C2416yes—
304(C2×D43)⋊C4C24124yes—
305(C2×D43)⋊C4C24112yes—
306(C2×D43)⋊C4C24124yes—
307(C2×D43)⋊C4C24148yes—
308C4⋊Dic43C2414yes—
309C4⋊Dic43C2416yes—
310Dic43⋊C4C24112yes—
311Dic43⋊C4C24124yes—
312C4×Dic43C2412yes—
313C4×Dic43C2411yescharacteristic
314C4×Dic43C2416yes—
315C4×Dic43C2413yes—
316C4×Dic43C2416yes—
317C4×Dic43C2416yes—
318C4×Dic43C2416yes—
319C23×C43C2514yes—
320C23×C43C2513yes—
321C22×D43—224no—
322C22×D43—224no—
323C22×D43—46no—
324C22×D43—424no—
325C22×D43—424no—
326C22×D43C22×D4112yes—
327C22×D43C25112yes—
328C22×D43C2513yes—
329C22×D43C2511yescharacteristic
330Q8×C43—212no—
331Q8×C43—224no—
332Q8×C43C22×D414yes—
333D4×C43—224no—
334D4×C43—24no—
335D4×C43—28no—
336D4×C43C22×D4112yes—
337C2×C4×C43—224no—
338C2×C4×C43—224no—
339C2×C4×C43—212no—
340C2×C4×C43C22×D4112yes—
341C2×C4×C43C2516yes—
342C2×C4×C43C25112yes—
343C2×C4×C43C2511yescharacteristic
344C2×C4×C43C2513yes—
345C2×C4×C43C2512yes—
346C22⋊D43—224no—
347C22⋊D43—28no—
348C22⋊D43—224no—
349C22⋊D43—424no—
350C22⋊D43C22×D4124yes—
351C2×Dic43—28no—
352C2×Dic43—46no—
353C2×Dic43C22×D4112yes—
354C2×Dic43C2512yes—
355C2×Dic43C2516yes—
356C2×Dic43C2514yes—
357C2×Dic43C2511yescharacteristic
358C2×Dic43C2513yes—
359D172—248no—
360D172—224no—
361D172—212no—
362D172—224no—
363D172—224no—
364D172—424no—
365D172C22×D4112yes—
366C4×D43—224no—
367C4×D43—224no—
368C4×D43—24no—
369C4×D43—212no—
370C4×D43—224no—
371C4×D43—248no—
372C4×D43—46no—
373C4×D43—46no—
374C4×D43C22×D4112yes—
375C4×D43C22×D414yes—
376C4×D43C22×D4112yes—
377C4×D43C22×D4112yes—
378Dic86—24no—
379Dic86—224no—
380Dic86C22×D4112yes—
381#62812—431nomaximal, Sylow
382C22×C43—26no—
383C22×C43—24no—
384C22×C43—28no—
385C22×C43C23×D416yes—
386C22×C43C2611yescharacteristic
387C2×D43—26no—
388C2×D43—22no—
389C2×D43—212no—
390C2×D43—224no—
391C2×D43—412no—
392C2×D43—824no—
393C2×D43—824no—
394C2×D43C23×D416yes—
395C2×D43C23×D412yes—
396C4×C43—212no—
397C4×C43—26no—
398C4×C43C23×D412yes—
399C4×C43C23×D416yes—
400C4×C43#58514yescomplemented
401Dic43—24no—
402Dic43—22no—
403Dic43—26no—
404Dic43C23×D416yes—
405Dic43C23×D412yes—
406C2×#585—432no—
407#3500—432no—
408#3500—436no—
409#3499—433no—
410#3499D4311yescharacteristic, complemented
411#3498—433no—
412#3498—431no—
413#3497—434no—
414#3496—4312no—
415D4×#41—434no—
416D4×#41—4312no—
417#3449—436no—
418C2×#532—433no—
419C2×#532—433no—
420C2×C4×#41—431no—
421C2×C43—26no—
422C2×C43—44no—
423C2×C43C24×D411yescharacteristic
424C2×C43C2×#58512yes—
425D43—22no—
426D43—26no—
427D43—412no—
428#585—8632no—
429C2×2−1+4—434no—
430C2×2−1+4—436no—
431C2×2−1+4C2×D4312yescomplemented
432C2×H(5,𝔽2)—4312no—
433C2×H(5,𝔽2)—436no—
434C2×H(5,𝔽2)—432no—
435C22×#41—431no—
436C22×#41—436no—
437C22×#41—4312no—
438C22×#41—436no—
439C22×#41—434no—
440#550—434no—
441#550—4312no—
442D4×Q8—4312no—
443D4×Q8C2×D4314yescomplemented
444#548—438no—
445#548—4324no—
446#547—4312no—
447#547—4324no—
448#547C2×D43112yescomplemented
449#546—4324no—
450#546—4348no—
451#546—4324no—
452D42—4324no—
453D42—4312no—
454D42—4312no—
455#537—4324no—
456#536—436no—
457#536—4312no—
458#536C2×D4316yescomplemented
459#535—436no—
460#535—4312no—
461#535—436no—
462#534—4324no—
463#532—436no—
464#532—433no—
465#532—436no—
466#532—4312no—
467#532—4312no—
468#532—436no—
469#532—436no—
470#532—431no—
471#532—436no—
472#532—4312no—
473#532—4312no—
474#532—433no—
475#532C2×D4313yescomplemented
476C2×C4⋊Q8—433no—
477C2×C4⋊Q8C2×D4313yescomplemented
478C2×#127—433no—
479C2×#127—433no—
480C2×#124—436no—
481C2×#124—436no—
482#525—4324no—
483#525—4324no—
484C2×#121—4312no—
485C2×#121—4312no—
486C4×#41—431no—
487C4×#41—432no—
488C4×#41—436no—
489C4×#41—433no—
490C4×#41—433no—
491C4×#41C2×D4311yescharacteristic, complemented
492C2×C4×Q8—432no—
493C2×C4×D4—436no—
494C2×C4×D4—4312no—
495C2×C4×D4—4312no—
496C2×#117—433no—
497C22×C42—433no—
498C43#6281211yescharacteristic, complemented, Sylow
4992−1+4—216no—
5002−1+4—8632no—
5012−1+4—8648no—
502H(5,𝔽2)—8696no—
503H(5,𝔽2)—8648no—
504H(5,𝔽2)—8616no—
505C2×#41—4316no—
506C2×#41—431no—
507C2×#41—4312no—
508C2×#41—436no—
509C2×#41—4312no—
510C2×#41—4312no—
511C2×#41—4312no—
512C2×#41—434no—
513C2×#41—433no—
514C2×#41—4312no—
515C2×#41—432no—
516C2×#41—433no—
517C2×#41—436no—
518C2×#41—4312no—
519C2×#41—4324no—
520C2×#41—4312no—
521C2×#41—8648no—
522C2×#41—8648no—
523C2×#41—8632no—
524C2×#41—8696no—
525C2×#41C22×D4316yes—
526C2×#41C22×D43112yes—
527C2×#41C22×D4311yescharacteristic
528C22×Q8—431no—
529C22×Q8—436no—
530C22×Q8—4312no—
531C22×Q8C22×D4316yes—
532C22×Q8C22×D4314yes—
533C22×D4—433no—
534C22×D4—4312no—
535C22×D4—436no—
536C22×D4—4324no—
537C22×D4—4312no—
538C22×D4—4312no—
539C22×D4—4312no—
540C22×D4—436no—
541C22×D4—4312no—
542C22×D4—4312no—
543C23×C4—433no—
544C23×C4—4312no—
545C23×C4—4312no—
546C23×C4—436no—
547C4⋊Q8—436no—
548C4⋊Q8—4312no—
549C4⋊Q8—431no—
550C4⋊Q8C22×D4313yes—
551C4⋊Q8C22×D4316yes—
552C4⋊Q8C22×D43112yes—
553#127—436no—
554#127—4312no—
555#127—433no—
556#127—436no—
557#127—4312no—
558#127C22×D4311yescharacteristic
559#124—436no—
560#124—4312no—
561#124—4324no—
562#124—432no—
563#124—4324no—
564#124—436no—
565#124C22×D4316yes—
566#123—4324no—
567#123—4348no—
568#123C22×D43124yes—
569C22⋊Q8—4324no—
570C22⋊Q8—4348no—
571C22⋊Q8C22×D43124yes—
572#121—434no—
573#121—4324no—
574#121—4312no—
575#121—4324no—
576#121—4312no—
577#121—4324no—
578#121—4324no—
579#121—4324no—
580#121—4324no—
581#121—4324no—
582#121—4348no—
583#121C22×D43112yes—
584#120—4324no—
585#120—4348no—
586#120—4324no—
587C4×Q8—432no—
588C4×Q8—436no—
589C4×Q8—436no—
590C4×Q8C22×D4312yes—
591C4×D4—434no—
592C4×D4—436no—
593C4×D4—4312no—
594C4×D4—4324no—
595C4×D4—4312no—
596C4×D4—436no—
597C4×D4—4324no—
598C4×D4—4324no—
599C4×D4—4324no—
600C4×D4—4312no—
601C4×D4—4324no—
602C4×D4—436no—
603C4×D4—4312no—
604C4×D4C22×D4316yes—
605C4×D4C22×D43112yes—
606#117—433no—
607#117—436no—
608#117—436no—
609#117—436no—
610#117C22×D4313yes—
611C2×C4⋊C4—436no—
612C2×C4⋊C4—4312no—
613C2×C4⋊C4C22×D43112yes—
614C2×C22⋊C4—4324no—
615C2×C22⋊C4—436no—
616C2×C22⋊C4—4324no—
617C2×C42—436no—
618C2×C42—433no—
619C2×C42—433no—
620C2×C42—436no—
621C2×C42—436no—
622C2×C42—433no—
623C2×C42—433no—
624C2×C42—431no—
625C2×C42C22×D4313yes—
626C24—433no—
627C24—4312no—
628C24—4312no—
629#41—248no—
630#41—224no—
631#41—438no—
632#41—4324no—
633#41—4324no—
634#41—8648no—
635#41—8696no—
636#41—8648no—
637#41—8648no—
638#41—868no—
639#41—8624no—
640#41—8648no—
641#41—8648no—
642#41—8648no—
643#41—8648no—
644#41—8616no—
645#41—8624no—
646#41D4×D4318yescomplemented
647C2×Q8—216no—
648C2×Q8—224no—
649C2×Q8—438no—
650C2×Q8—433no—
651C2×Q8—4312no—
652C2×Q8—432no—
653C2×Q8—8624no—
654C2×Q8—8648no—
655C2×Q8C23×D43112yes—
656C2×Q8C23×D4316yes—
657C2×Q8C23×D4311yescharacteristic
658C2×D4—436no—
659C2×D4—4324no—
660C2×D4—4312no—
661C2×D4—434no—
662C2×D4—4312no—
663C2×D4—4324no—
664C2×D4—433no—
665C2×D4—4312no—
666C2×D4—4324no—
667C2×D4—4312no—
668C2×D4—4312no—
669C2×D4—436no—
670C2×D4—4324no—
671C2×D4—8648no—
672C2×D4—8648no—
673C2×D4—8624no—
674C2×D4—8696no—
675C2×D4—8648no—
676C2×D4—8648no—
677C2×D4—8624no—
678C2×D4—17224no—
679C2×D4—17224no—
680C2×D4C23×D4314yes—
681C2×D4C23×D43112yes—
682C2×D4C23×D4312yes—
683C2×D4C23×D4313yes—
684C22×C4—433no—
685C22×C4—4324no—
686C22×C4—431no—
687C22×C4—433no—
688C22×C4—433no—
689C22×C4—433no—
690C22×C4—434no—
691C22×C4—436no—
692C22×C4—432no—
693C22×C4—436no—
694C22×C4—4312no—
695C22×C4—4312no—
696C22×C4—4324no—
697C22×C4—4312no—
698C22×C4—436no—
699C22×C4—436no—
700C22×C4—8648no—
701C22×C4—8648no—
702C22×C4—17212no—
703C22×C4C23×D4316yes—
704C22×C4C23×D43112yes—
705C22×C4C23×D43112yes—
706C22×C4C23×D4313yes—
707C4⋊C4—434no—
708C4⋊C4—4312no—
709C4⋊C4—436no—
710C4⋊C4—4324no—
711C4⋊C4C23×D43112yes—
712C4⋊C4C23×D4316yes—
713C4⋊C4C23×D43124yes—
714C22⋊C4—438no—
715C22⋊C4—436no—
716C22⋊C4—4324no—
717C22⋊C4—4312no—
718C22⋊C4—4348no—
719C22⋊C4—4324no—
720C22⋊C4C23×D4316yes—
721C22⋊C4C23×D43124yes—
722C42—432no—
723C42—431no—
724C42—436no—
725C42—433no—
726C42—436no—
727C42—436no—
728C42—436no—
729C42C23×D4311yescharacteristic
730C42C23×D4313yes—
731C42C23×D4316yes—
732C23—433no—
733C23—431no—
734C23—4312no—
735C23—4312no—
736C23—8624no—
737C23—8624no—
738C23—17224no—
739C23—17224no—
740C23—1726no—
741C23C24×D4314yes—
742C23C24×D4313yes—
743Q8—224no—
744Q8—212no—
745Q8—4312no—
746Q8—8624no—
747Q8—864no—
748Q8C2×D4×D4314yes—
749D4—224no—
750D4—24no—
751D4—28no—
752D4—4324no—
753D4—4312no—
754D4—8624no—
755D4—8648no—
756D4—8624no—
757D4—868no—
758D4—8624no—
759D4—8624no—
760D4—8612no—
761D4—8624no—
762D4—17224no—
763D4—17224no—
764D4C2×D4×D43112yes—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—212no—
768C2×C4—4312no—
769C2×C4—431no—
770C2×C4—433no—
771C2×C4—434no—
772C2×C4—4312no—
773C2×C4—4312no—
774C2×C4—4312no—
775C2×C4—432no—
776C2×C4—436no—
777C2×C4—434no—
778C2×C4—8624no—
779C2×C4—8648no—
780C2×C4—8624no—
781C2×C4—868no—
782C2×C4—8624no—
783C2×C4—864no—
784C2×C4—8612no—
785C2×C4—1726no—
786C2×C4—1726no—
787C2×C4—1726no—
788C2×C4C2×D4×D43112yes—
789C2×C4C24×D4316yes—
790C2×C4C24×D43112yes—
791C2×C4C24×D4311yescharacteristic
792C2×C4C24×D4313yes—
793C2×C4C24×D4312yes—
794C22—26no—
795C22—24no—
796C22—28no—
797C22—432no—
798C22—436no—
799C22—862no—
800C22—866no—
801C22—8612no—
802C22—8624no—
803C22—34424no—
804C22—34424no—
805C22—17212no—
806C22C22×D4×D4316yes—
807C22C25×D4311yescharacteristic
808C4—212no—
809C4—26no—
810C4—432no—
811C4—436no—
812C4—864no—
813C4—862no—
814C4—866no—
815C4C22×D4×D4316yes—
816C4C22×D4×D4312yes—
817C4#1458373614yescomplemented
818C2—26no—
819C2—44no—
820C2—866no—
821C2—862no—
822C2—17212no—
823C2C23×D4×D4311yescharacteristic
824C2C2×#1458373612yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3499C2
hypercenter#3499D43
hypocenterC43#62812
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#14583736C2semidirect
2. #19148389C2semidirect
3. #19148384C2semidirect
4. #19148378C2semidirect
5. #19148373C2semidirect
6. #19148368C2semidirect
7. #19148365C2semidirect
8. #19148353C2semidirect
9. D4×#10621902C2semidirect
10. #19148082C2semidirect
11. #19147927C2semidirect
12. C2×#14583450C2semidirect
13. #532×D43C2semidirect
14. C4×#41×D43C2semidirect
15. C43×#3499C2semidirect
17. C2×#13063373C22semidirect
18. C2×#13063373C22semidirect
19. C2×#13063371C22semidirect
20. C2×#13063371C22semidirect
21. C2×#13063371C22semidirect
22. C22×#10621902C22semidirect
23. C22×#10621902C22semidirect
25. C2×#41×D43C22semidirect
26. C2×#41×D43C22semidirect
27. #14583571C22semidirect
28. #14583570C22semidirect
29. #14583564C22semidirect
30. #14583560C22semidirect
31. #14583559C22semidirect
32. #14583552C22semidirect
33. #14583550C22semidirect
34. #14583541C22semidirect
35. #14583540C22semidirect
36. #14583537C22semidirect
37. D4×D172C22semidirect
38. D4×D172C22semidirect
39. #14583533C22semidirect
40. #14583479C22semidirect
41. #14583474C22semidirect
42. #14583473C22semidirect
43. #14583468C22semidirect
44. #14583467C22semidirect
45. #14583463C22semidirect
46. #14583460C22semidirect
47. #14583450C22semidirect
48. #14583450C22semidirect
49. #14583450C22semidirect
50. #14583450C22semidirect
51. #14583450C22semidirect
52. #14583450C22semidirect
53. #14583449C22semidirect
54. #14583448C22semidirect
55. #14583447C22semidirect
56. #14583446C22semidirect
57. #14583445C22semidirect
58. #14583444C22semidirect
59. C4⋊Q8×D43C22semidirect
60. C2×#13063322C22semidirect
61. #127×D43C22semidirect
62. C2×#13063314C22semidirect
63. #124×D43C22semidirect
64. #14583412C22semidirect
65. #14583407C22semidirect
66. C2×#13063300C22semidirect
67. #121×D43C22semidirect
68. #41×Dic43C22semidirect
69. C4×#10621902C22semidirect
70. C4×#10621898C22semidirect
71. #14583367C22semidirect
72. C4×#10621900C22semidirect
73. C4×Q8×D43C22semidirect
74. C2×#13063287C22semidirect
75. C4×D4×D43C22semidirect
76. C4×D4×D43C22semidirect
77. #117×D43C22semidirect
78. C2×C42×D43C22semidirect
79. C2×2−1+4×C43C22semidirect
80. D4×Q8×C43C22semidirect
81. C43×#547C22semidirect
82. C43×#536C22semidirect
83. C43×#532C22semidirect
84. C2×C4⋊Q8×C43C22semidirect
85. C4×#41×C43C22semidirect
110. #41×D43D4semidirect
218. #41×C43C2×D4semidirect
246. #10621902C2×D4semidirect
249. Q8×D43C2×D4semidirect
252. #10621900C2×D4semidirect
258. D4×D43C2×D4semidirect
263. #10621898C2×D4semidirect
278. C2×C4×D43C2×D4semidirect
400. C4×C43#585semidirect
410. #3499D43semidirect
431. C2×2−1+4C2×D43semidirect
443. D4×Q8C2×D43semidirect
448. #547C2×D43semidirect
458. #536C2×D43semidirect
475. #532C2×D43semidirect
477. C2×C4⋊Q8C2×D43semidirect
491. C4×#41C2×D43semidirect
498. C43#62812semidirect
646. #41D4×D43semidirect
817. C4#14583736semidirect

Maximal subgroups

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

subgroupindex
C2×#145837362
#191483892
#191483842
#191483782
#191483732
#191483682
#191483652
#191483532
D4×#106219022
#191480822
#191479272
C2×#145834502
#532×D432
C4×#41×D432
C43×#34992
#6281243