Finite Group Databasebeta

← #26005141

Subgroups — #26005141

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×#14583734C212yesmaximal, complemented
2#19148387C216yesmaximal, complemented
3#19148383C212yesmaximal, complemented
4#19148380C211yesmaximal, characteristic, complemented
5#19148375C213yesmaximal, complemented
6#19148371C213yesmaximal, complemented
7#19148360C214yesmaximal, complemented
8#19148351C2112yesmaximal, complemented
9#19148085C214yesmaximal, complemented
10D4×#10621900C2112yesmaximal, complemented
11#19147926C216yesmaximal, complemented
12C2×#14583447C213yesmaximal, complemented
13#532×D43C213yesmaximal, complemented
14C4×#41×D43C211yesmaximal, characteristic, complemented
15C43×#3498C211yesmaximal, characteristic, complemented
16#14583734—232no—
17C2×#13063372C2214yescomplemented
18C2×#13063372C2216yescomplemented
19C2×#13063372C2212yescomplemented
20C2×#13063370C22112yescomplemented
21C2×#13063370C2216yescomplemented
22C22×#10621900C22112yescomplemented
23C22×#10621900C2216yescomplemented
24C2×#41×D43C2211yescharacteristic
25C2×#41×D43C2214yescomplemented
26C2×#41×D43C2216yescomplemented
27#14583569C22112yescomplemented
28Q8×D172C2214yescomplemented
29D4×Dic86C22112yescomplemented
30#14583556C2218yescomplemented
31#14583555C22124yescomplemented
32#14583554C22112yescomplemented
33#14583553C22112yescomplemented
34#14583549C22124yescomplemented
35#14583546C22124yescomplemented
36#14583543C22124yescomplemented
37#14583536C22148yescomplemented
38#14583534C22112yescomplemented
39D4×C22⋊D43C22124yescomplemented
40#14583478C22124yescomplemented
41#14583475C2216yescomplemented
42#14583470C2216yescomplemented
43#14583469C22112yescomplemented
44#14583466C2216yescomplemented
45#14583462C22112yescomplemented
46#14583459C22124yescomplemented
47#14583450C2211yescharacteristic, complemented
48#14583449C2213yescomplemented
49#14583448C2216yescomplemented
50#14583447C22112yescomplemented
51#14583447C22112yescomplemented
52#14583447C2216yescomplemented
53#14583447C2213yescomplemented
54#14583447C2216yescomplemented
55#14583447C2216yescomplemented
56#14583446C22112yescomplemented
57#14583445C2216yescomplemented
58#14583444C22112yescomplemented
59C2×#13063325C2213yescomplemented
60C4⋊Q8×D43C2213yescomplemented
61#127×D43C2213yescomplemented
62C2×#13063312C2216yescomplemented
63#124×D43C2216yescomplemented
64#14583409C22124yescomplemented
65#14583405C22124yescomplemented
66C2×#13063296C22112yescomplemented
67#121×D43C22112yescomplemented
68#41×Dic43C2211yescharacteristic, complemented
69C4×#10621902C2212yescomplemented
70C4×#10621898C2213yescomplemented
71#14583367C2213yescomplemented
72C4×#10621900C2216yescomplemented
73C4×Q8×D43C2212yescomplemented
74C2×D4×Dic43C22112yescomplemented
75C4×D4×D43C22112yescomplemented
76C4×D4×D43C2216yescomplemented
77#117×D43C2213yescomplemented
78C2×C42×D43C2213yescomplemented
79C2×H(5,𝔽2)×C43C2212yescomplemented
80C43×#550C2214yescomplemented
81D42×C43C22112yescomplemented
82C43×#535C2216yescomplemented
83C43×#532C2213yescomplemented
84C2×#127×C43C2213yescomplemented
85C4×#41×C43C2211yescharacteristic, complemented
86#13063372—216no—
87#13063372—232no—
88#13063372—248no—
89#13063370—296no—
90#13063370—248no—
91C2×#10621902C2312yes—
92C2×#10621902C2311yescharacteristic
93C2×#10621898C23112yes—
94C2×#10621898C2316yes—
95C2×#10621898C23112yes—
96C2×#10621898C2313yes—
97C2×#10621900—296no—
98C2×#10621900—248no—
99C2×#10621900C23112yes—
100C2×#10621900C23112yes—
101C2×#10621900C23112yes—
102C2×#10621900C23112yes—
103C2×#10621900C2316yes—
104C2×#10621900C23112yes—
105C2×#10621900C23112yes—
106C2×#10621900C23124yes—
107C2×#10621900C2313yes—
108#41×D43—232no—
109#41×D43—248no—
110#41×D43D4116yescomplemented
111C22×Dic86C23112yes—
112C22×Dic86C2316yes—
113C2×Q8×D43C2314yes—
114C2×Q8×D43C2316yes—
115C2×Q8×D43C2311yescharacteristic
116C22×C22⋊D43C23112yes—
117C22×C22⋊D43C23124yes—
118C2×D4×D43C23112yes—
119C2×D4×D43C2316yes—
120C2×D4×D43C23112yes—
121C2×D4×D43C23112yes—
122C2×D4×D43C2313yes—
123C23×Dic43C23112yes—
124C22×C4×D43C23112yes—
125C22×C4×D43C2316yes—
126C22×C4×D43C2313yes—
127#13063325C23112yes—
128#13063325C2313yes—
129#13063325C2316yes—
130#13063324C23112yes—
131#13063323C2316yes—
132#13063322C2311yescharacteristic
133#13063321C23112yes—
134#13063321C2316yes—
135#13063314C2312yes—
136#13063313C2316yes—
137#13063312C23124yes—
138#13063312C2316yes—
139#13063312C23112yes—
140#13063311C23124yes—
141#13063309C23124yes—
142#13063307C23148yes—
143#13063306C23124yes—
144#13063305C23124yes—
145#13063304C23124yes—
146#13063302C23148yes—
147#13063300C2314yes—
148#13063299C23112yes—
149#13063298C23124yes—
150#13063297C23148yes—
151#13063297C23124yes—
152#13063296C23124yes—
153#13063296C23124yes—
154#13063296C23112yes—
155#13063296C23124yes—
156#13063296C23124yes—
157#13063294C23124yes—
158#13063293C23148yes—
159Q8×Dic43C2312yes—
160C4×Dic86C2316yes—
161#13063290C2316yes—
162C4×D172C23112yes—
163C4×D172C2316yes—
164D4×Dic43C23124yes—
165D4×Dic43C23124yes—
166D4×Dic43C23112yes—
167D4×Dic43C2316yes—
168D4×Dic43C23124yes—
169#13063287C2314yes—
170#13063287C2316yes—
171C4×C22⋊D43C23124yes—
172C4×C22⋊D43C23112yes—
173(C22⋊D43)⋊C4C23112yes—
174(C22⋊D43)⋊C4C23124yes—
175#13063284C2313yes—
176#13063283C2316yes—
177#13063282C2316yes—
178#13063281C2316yes—
179C2×C4⋊Dic43C23112yes—
180C4⋊C4×D43C23112yes—
181C4⋊C4×D43C2316yes—
182C2×C22⋊Dic43C23124yes—
183C22⋊C4×D43C2316yes—
184C22⋊C4×D43C23124yes—
185C2×C4×Dic43C2316yes—
186C2×C4×Dic43C2313yes—
187C42×D43C2311yescharacteristic
188C42×D43C2313yes—
189C42×D43C2316yes—
190C42×D43C2316yes—
191C42×D43C2313yes—
192C42×D43C2313yes—
193H(5,𝔽2)×C43—216no—
194C2×#41×C43C2314yes—
195C2×#41×C43C2316yes—
196C2×#41×C43C2311yescharacteristic
197C22×D4×C43C2316yes—
198C22×D4×C43C23112yes—
199C22×D4×C43C23112yes—
200C4⋊Q8×C43C2311yescharacteristic
201#127×C43C23112yes—
202#127×C43C2313yes—
203#127×C43C2316yes—
204#124×C43C2316yes—
205#121×C43C23124yes—
206#121×C43C23112yes—
207#120×C43C23124yes—
208C4×Q8×C43C2312yes—
209C4×D4×C43C2316yes—
210C4×D4×C43C23112yes—
211#117×C43C2313yes—
212C2×C42×C43C2313yes—
213C24×C43C24112yes—
214C23×D43C24112yes—
215C23×D43C2413yes—
216#41×C43—216no—
217#41×C43—224no—
218#41×C43C2×D418yescomplemented
219C2×Q8×C43C2412yes—
220C2×Q8×C43C2411yescharacteristic
221C2×D4×C43—248no—
222C2×D4×C43—224no—
223C2×D4×C43—424no—
224C2×D4×C43C24112yes—
225C2×D4×C43C24112yes—
226C2×D4×C43C24112yes—
227C2×D4×C43C2416yes—
228C2×D4×C43C24124yes—
229C2×D4×C43C2413yes—
230C22×C4×C43C2416yes—
231C22×C4×C43C24112yes—
232C22×C4×C43C2413yes—
233C2×C22⋊D43—296no—
234C2×C22⋊D43—248no—
235C2×C22⋊D43C24124yes—
236C2×C22⋊D43C24112yes—
237C2×C22⋊D43C24112yes—
238C2×C22⋊D43C24112yes—
239C2×C22⋊D43C24124yes—
240C2×C22⋊D43C2416yes—
241C22×Dic43—248no—
242C22×Dic43C24112yes—
243C22×Dic43C24112yes—
244C22×Dic43C24124yes—
245C22×Dic43C2416yes—
246C22×Dic43C2413yes—
247#10621902—28no—
248#10621902C2×D418yescomplemented
249Q8×D43—216no—
250Q8×D43—224no—
251Q8×D43C2×D418yescomplemented
252#10621900—248no—
253#10621900—296no—
254#10621900—248no—
255#10621900—248no—
256#10621900—224no—
257#10621900—248no—
258#10621900—248no—
259#10621900—248no—
260#10621900C2×D4124yescomplemented
261D4×D43—248no—
262D4×D43—224no—
263D4×D43—248no—
264D4×D43—424no—
265D4×D43C2×D4124yescomplemented
266#10621898—224no—
267#10621898—248no—
268#10621898—248no—
269#10621898C2×D4124yescomplemented
270C2×D172C2414yes—
271C2×D172C2414yes—
272C2×D172C2412yes—
273C2×D172C2413yes—
274C2×C4×D43—248no—
275C2×C4×D43—412no—
276C2×C4×D43C2×D4124yescomplemented
277C2×C4×D43C2412yes—
278C2×C4×D43C2416yes—
279C2×C4×D43C24112yes—
280C2×C4×D43C2414yes—
281C2×C4×D43C24112yes—
282C2×C4×D43C2416yes—
283C2×C4×D43C2416yes—
284C2×C4×D43C2411yescharacteristic
285C2×C4×D43C2413yes—
286C2×C4×D43C2413yes—
287C2×C4×D43C2413yes—
288C2×Dic86—224no—
289C2×Dic86—248no—
290C2×Dic86C24112yes—
291C2×Dic86C24112yes—
292C2×Dic86C2416yes—
293C2×Dic86C2413yes—
294C4⋊C4×C43C2416yes—
295C4⋊C4×C43C2414yes—
296C22⋊C4×C43C2416yes—
297C22⋊C4×C43C24124yes—
298C42×C43C2411yescharacteristic
299C42×C43C2413yes—
300C42×C43C2416yes—
301C22⋊Dic43C24124yes—
302C22⋊Dic43C2416yes—
303C22⋊Dic43C24148yes—
304(C2×D43)⋊C4C2418yes—
305(C2×D43)⋊C4C24112yes—
306(C2×D43)⋊C4C24124yes—
307C4⋊Dic43C24112yes—
308C4⋊Dic43C2416yes—
309C4⋊Dic43C24124yes—
310Dic43⋊C4C24112yes—
311Dic43⋊C4C24124yes—
312C4×Dic43C2412yes—
313C4×Dic43C2411yescharacteristic
314C4×Dic43C2416yes—
315C4×Dic43C2413yes—
316C4×Dic43C2416yes—
317C4×Dic43C2416yes—
318C4×Dic43C2416yes—
319C23×C43—224no—
320C23×C43—424no—
321C23×C43C25112yes—
322C23×C43C2513yes—
323C22×D43—224no—
324C22×D43—46no—
325C22×D43—424no—
326C22×D43C22×D4112yes—
327C22×D43C2514yes—
328C22×D43C2513yes—
329C22×D43C2511yescharacteristic
330Q8×C43—24no—
331Q8×C43C22×D414yes—
332D4×C43—224no—
333D4×C43—212no—
334D4×C43—224no—
335D4×C43—224no—
336D4×C43—424no—
337D4×C43C22×D4112yes—
338C2×C4×C43—224no—
339C2×C4×C43—212no—
340C2×C4×C43C22×D4112yes—
341C2×C4×C43C2516yes—
342C2×C4×C43C2514yes—
343C2×C4×C43C2511yescharacteristic
344C2×C4×C43C2513yes—
345C2×C4×C43C2512yes—
346C22⋊D43—224no—
347C22⋊D43—248no—
348C22⋊D43—224no—
349C22⋊D43—224no—
350C22⋊D43—424no—
351C22⋊D43C22×D4124yes—
352C2×Dic43—224no—
353C2×Dic43—248no—
354C2×Dic43—224no—
355C2×Dic43—46no—
356C2×Dic43C22×D4112yes—
357C2×Dic43C2512yes—
358C2×Dic43C2516yes—
359C2×Dic43C25112yes—
360C2×Dic43C2511yescharacteristic
361C2×Dic43C2513yes—
362D172—28no—
363D172—24no—
364D172—28no—
365D172C22×D4112yes—
366C4×D43—224no—
367C4×D43—224no—
368C4×D43—24no—
369C4×D43—212no—
370C4×D43—28no—
371C4×D43—46no—
372C4×D43—46no—
373C4×D43C22×D4112yes—
374C4×D43C22×D414yes—
375C4×D43C22×D4112yes—
376C4×D43C22×D4112yes—
377Dic86—212no—
378Dic86—224no—
379Dic86—224no—
380Dic86C22×D4112yes—
381#62812—431nomaximal, Sylow
382C22×C43—26no—
383C22×C43—212no—
384C22×C43—224no—
385C22×C43—824no—
386C22×C43C23×D416yes—
387C22×C43C2611yescharacteristic
388C2×D43—26no—
389C2×D43—22no—
390C2×D43—24no—
391C2×D43—28no—
392C2×D43—412no—
393C2×D43—824no—
394C2×D43C23×D416yes—
395C2×D43C23×D412yes—
396C4×C43—24no—
397C4×C43—26no—
398C4×C43C23×D412yes—
399C4×C43C23×D416yes—
400C4×C43#58514yescomplemented
401Dic43—212no—
402Dic43—22no—
403Dic43—26no—
404Dic43C23×D416yes—
405Dic43C23×D412yes—
406C2×#585—432no—
407#3500—432no—
408#3500—436no—
409#3499—433no—
410#3499—431no—
411#3498—433no—
412#3498D4311yescharacteristic, complemented
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—412no—
423C2×C43C24×D411yescharacteristic
424C2×C43C2×#58512yes—
425D43—22no—
426D43—26no—
427D43—44no—
428#585—8632no—
429C2×2−1+4—434no—
430C2×2−1+4—436no—
431C2×2−1+4—432no—
432C2×H(5,𝔽2)—4312no—
433C2×H(5,𝔽2)—436no—
434C2×H(5,𝔽2)C2×D4312yescomplemented
435C22×#41—431no—
436C22×#41—436no—
437C22×#41—434no—
438C22×#41—436no—
439C22×#41—4312no—
440#550—4312no—
441#550C2×D4314yescomplemented
442D4×Q8—434no—
443D4×Q8—4312no—
444#548—438no—
445#548—4324no—
446#547—4324no—
447#547—4312no—
448#547—4312no—
449#546—4324no—
450#546—4324no—
451#546—4348no—
452D42—4324no—
453D42—4312no—
454D42C2×D43112yescomplemented
455#537—4324no—
456#536—436no—
457#536—4312no—
458#536—436no—
459#535—436no—
460#535—4312no—
461#535C2×D4316yescomplemented
462#534—4324no—
463#532—436no—
464#532—431no—
465#532—433no—
466#532—436no—
467#532—4312no—
468#532—4312no—
469#532—436no—
470#532—436no—
471#532—436no—
472#532—4312no—
473#532—4312no—
474#532—433no—
475#532C2×D4313yescomplemented
476C2×C4⋊Q8—433no—
477C2×C4⋊Q8—433no—
478C2×#127—433no—
479C2×#127C2×D4313yescomplemented
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—4312no—
494C2×C4×D4—436no—
495C2×C4×D4—4312no—
496C2×#117—433no—
497C22×C42—433no—
498C43#6281211yescharacteristic, complemented, Sylow
4992−1+4—8632no—
5002−1+4—8648no—
5012−1+4—8616no—
502H(5,𝔽2)—216no—
503H(5,𝔽2)—8696no—
504H(5,𝔽2)—8648no—
505C2×#41—4316no—
506C2×#41—431no—
507C2×#41—432no—
508C2×#41—433no—
509C2×#41—4312no—
510C2×#41—4312no—
511C2×#41—436no—
512C2×#41—4312no—
513C2×#41—4312no—
514C2×#41—4312no—
515C2×#41—4324no—
516C2×#41—4312no—
517C2×#41—433no—
518C2×#41—436no—
519C2×#41—4312no—
520C2×#41—4312no—
521C2×#41—8648no—
522C2×#41—8648no—
523C2×#41—8696no—
524C2×#41—8632no—
525C2×#41C22×D4316yes—
526C2×#41C22×D4314yes—
527C2×#41C22×D4311yescharacteristic
528C22×Q8—431no—
529C22×Q8—436no—
530C22×Q8—434no—
531C22×Q8—436no—
532C22×Q8—4312no—
533C22×D4—433no—
534C22×D4—4312no—
535C22×D4—4324no—
536C22×D4—4312no—
537C22×D4—436no—
538C22×D4—4312no—
539C22×D4—4312no—
540C22×D4C22×D4316yes—
541C22×D4C22×D43112yes—
542C22×D4C22×D43112yes—
543C23×C4—433no—
544C23×C4—4312no—
545C23×C4—4312no—
546C23×C4—436no—
547C4⋊Q8—436no—
548C4⋊Q8—4312no—
549C4⋊Q8—433no—
550C4⋊Q8—436no—
551C4⋊Q8—4312no—
552C4⋊Q8C22×D4311yescharacteristic
553#127—436no—
554#127—4312no—
555#127—431no—
556#127C22×D4313yes—
557#127C22×D4316yes—
558#127C22×D43112yes—
559#124—432no—
560#124—436no—
561#124—4312no—
562#124—4324no—
563#124—4324no—
564#124—436no—
565#124C22×D4316yes—
566#123—4324no—
567#123—4348no—
568#123—4324no—
569C22⋊Q8—4324no—
570C22⋊Q8—4324no—
571C22⋊Q8—4348no—
572#121—4312no—
573#121—4324no—
574#121—4324no—
575#121—4324no—
576#121—4324no—
577#121—4324no—
578#121—4348no—
579#121—4312no—
580#121—434no—
581#121—4324no—
582#121C22×D43112yes—
583#121C22×D43124yes—
584#120—4324no—
585#120—4348no—
586#120C22×D43124yes—
587C4×Q8—432no—
588C4×Q8—436no—
589C4×Q8—436no—
590C4×Q8C22×D4312yes—
591C4×D4—4312no—
592C4×D4—436no—
593C4×D4—4324no—
594C4×D4—4324no—
595C4×D4—4324no—
596C4×D4—4312no—
597C4×D4—4324no—
598C4×D4—434no—
599C4×D4—436no—
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—4312no—
612C2×C4⋊C4—436no—
613C2×C4⋊C4—4312no—
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—
628C24C23×D43112yes—
629#41—216no—
630#41—224no—
631#41—438no—
632#41—4324no—
633#41—4324no—
634#41—8648no—
635#41—8648no—
636#41—8648no—
637#41—8624no—
638#41—8648no—
639#41—8648no—
640#41—8648no—
641#41—868no—
642#41—8696no—
643#41—8648no—
644#41—8648no—
645#41—8624no—
646#41D4×D4318yescomplemented
647C2×Q8—438no—
648C2×Q8—433no—
649C2×Q8—4312no—
650C2×Q8—4312no—
651C2×Q8—436no—
652C2×Q8—8648no—
653C2×Q8—8624no—
654C2×Q8—8616no—
655C2×Q8—8624no—
656C2×Q8C23×D4312yes—
657C2×Q8C23×D4311yescharacteristic
658C2×D4—248no—
659C2×D4—224no—
660C2×D4—424no—
661C2×D4—436no—
662C2×D4—4324no—
663C2×D4—4324no—
664C2×D4—4312no—
665C2×D4—4312no—
666C2×D4—4312no—
667C2×D4—4324no—
668C2×D4—433no—
669C2×D4—434no—
670C2×D4—434no—
671C2×D4—432no—
672C2×D4—8624no—
673C2×D4—8648no—
674C2×D4—8648no—
675C2×D4—8696no—
676C2×D4—8648no—
677C2×D4—17224no—
678C2×D4C23×D43112yes—
679C2×D4C23×D43112yes—
680C2×D4C23×D43112yes—
681C2×D4C23×D4316yes—
682C2×D4C23×D43124yes—
683C2×D4C23×D4313yes—
684C22×C4—433no—
685C22×C4—4324no—
686C22×C4—431no—
687C22×C4—433no—
688C22×C4—433no—
689C22×C4—433no—
690C22×C4—4312no—
691C22×C4—4312no—
692C22×C4—4324no—
693C22×C4—436no—
694C22×C4—432no—
695C22×C4—436no—
696C22×C4—4312no—
697C22×C4—434no—
698C22×C4—4312no—
699C22×C4—436no—
700C22×C4—436no—
701C22×C4—8648no—
702C22×C4—8648no—
703C22×C4—17212no—
704C22×C4C23×D4316yes—
705C22×C4C23×D43112yes—
706C22×C4C23×D4313yes—
707C4⋊C4—4312no—
708C4⋊C4—4312no—
709C4⋊C4—436no—
710C4⋊C4—4324no—
711C4⋊C4—4324no—
712C4⋊C4C23×D4314yes—
713C4⋊C4C23×D4316yes—
714C22⋊C4—4324no—
715C22⋊C4—436no—
716C22⋊C4—4348no—
717C22⋊C4—438no—
718C22⋊C4—4312no—
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—224no—
733C23—424no—
734C23—433no—
735C23—431no—
736C23—4312no—
737C23—434no—
738C23—8624no—
739C23—17224no—
740C23—1726no—
741C23C24×D43112yes—
742C23C24×D4313yes—
743Q8—24no—
744Q8—4312no—
745Q8—8624no—
746Q8—8624no—
747Q8—8612no—
748Q8C2×D4×D4314yes—
749D4—224no—
750D4—224no—
751D4—212no—
752D4—224no—
753D4—424no—
754D4—4324no—
755D4—4312no—
756D4—868no—
757D4—8624no—
758D4—8624no—
759D4—8648no—
760D4—8624no—
761D4—864no—
762D4—868no—
763D4—17224no—
764D4C2×D4×D43112yes—
765C2×C4—224no—
766C2×C4—212no—
767C2×C4—4312no—
768C2×C4—431no—
769C2×C4—433no—
770C2×C4—434no—
771C2×C4—4312no—
772C2×C4—4312no—
773C2×C4—4312no—
774C2×C4—432no—
775C2×C4—436no—
776C2×C4—4312no—
777C2×C4—868no—
778C2×C4—8624no—
779C2×C4—8624no—
780C2×C4—8648no—
781C2×C4—8624no—
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×D4314yes—
791C2×C4C24×D4311yescharacteristic
792C2×C4C24×D4313yes—
793C2×C4C24×D4312yes—
794C22—26no—
795C22—212no—
796C22—224no—
797C22—824no—
798C22—432no—
799C22—436no—
800C22—862no—
801C22—866no—
802C22—864no—
803C22—868no—
804C22—34424no—
805C22—17212no—
806C22C22×D4×D4316yes—
807C22C25×D4311yescharacteristic
808C4—24no—
809C4—26no—
810C4—432no—
811C4—436no—
812C4—8612no—
813C4—862no—
814C4—866no—
815C4C22×D4×D4316yes—
816C4C22×D4×D4312yes—
817C4#1458373414yescomplemented
818C2—26no—
819C2—412no—
820C2—866no—
821C2—862no—
822C2—1724no—
823C2C23×D4×D4311yescharacteristic
824C2C2×#1458373412yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3498C2
hypercenter#3498D43
hypocenterC43#62812
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C2×#14583734C2semidirect
2. #19148387C2semidirect
3. #19148383C2semidirect
4. #19148380C2semidirect
5. #19148375C2semidirect
6. #19148371C2semidirect
7. #19148360C2semidirect
8. #19148351C2semidirect
9. #19148085C2semidirect
10. D4×#10621900C2semidirect
11. #19147926C2semidirect
12. C2×#14583447C2semidirect
13. #532×D43C2semidirect
14. C4×#41×D43C2semidirect
15. C43×#3498C2semidirect
17. C2×#13063372C22semidirect
18. C2×#13063372C22semidirect
19. C2×#13063372C22semidirect
20. C2×#13063370C22semidirect
21. C2×#13063370C22semidirect
22. C22×#10621900C22semidirect
23. C22×#10621900C22semidirect
25. C2×#41×D43C22semidirect
26. C2×#41×D43C22semidirect
27. #14583569C22semidirect
28. Q8×D172C22semidirect
29. D4×Dic86C22semidirect
30. #14583556C22semidirect
31. #14583555C22semidirect
32. #14583554C22semidirect
33. #14583553C22semidirect
34. #14583549C22semidirect
35. #14583546C22semidirect
36. #14583543C22semidirect
37. #14583536C22semidirect
38. #14583534C22semidirect
39. D4×C22⋊D43C22semidirect
40. #14583478C22semidirect
41. #14583475C22semidirect
42. #14583470C22semidirect
43. #14583469C22semidirect
44. #14583466C22semidirect
45. #14583462C22semidirect
46. #14583459C22semidirect
47. #14583450C22semidirect
48. #14583449C22semidirect
49. #14583448C22semidirect
50. #14583447C22semidirect
51. #14583447C22semidirect
52. #14583447C22semidirect
53. #14583447C22semidirect
54. #14583447C22semidirect
55. #14583447C22semidirect
56. #14583446C22semidirect
57. #14583445C22semidirect
58. #14583444C22semidirect
59. C2×#13063325C22semidirect
60. C4⋊Q8×D43C22semidirect
61. #127×D43C22semidirect
62. C2×#13063312C22semidirect
63. #124×D43C22semidirect
64. #14583409C22semidirect
65. #14583405C22semidirect
66. C2×#13063296C22semidirect
67. #121×D43C22semidirect
68. #41×Dic43C22semidirect
69. C4×#10621902C22semidirect
70. C4×#10621898C22semidirect
71. #14583367C22semidirect
72. C4×#10621900C22semidirect
73. C4×Q8×D43C22semidirect
74. C2×D4×Dic43C22semidirect
75. C4×D4×D43C22semidirect
76. C4×D4×D43C22semidirect
77. #117×D43C22semidirect
78. C2×C42×D43C22semidirect
79. C2×H(5,𝔽2)×C43C22semidirect
80. C43×#550C22semidirect
81. D42×C43C22semidirect
82. C43×#535C22semidirect
83. C43×#532C22semidirect
84. C2×#127×C43C22semidirect
85. C4×#41×C43C22semidirect
110. #41×D43D4semidirect
218. #41×C43C2×D4semidirect
248. #10621902C2×D4semidirect
251. Q8×D43C2×D4semidirect
260. #10621900C2×D4semidirect
265. D4×D43C2×D4semidirect
269. #10621898C2×D4semidirect
276. C2×C4×D43C2×D4semidirect
400. C4×C43#585semidirect
412. #3498D43semidirect
434. C2×H(5,𝔽2)C2×D43semidirect
441. #550C2×D43semidirect
454. D42C2×D43semidirect
461. #535C2×D43semidirect
475. #532C2×D43semidirect
479. C2×#127C2×D43semidirect
491. C4×#41C2×D43semidirect
498. C43#62812semidirect
646. #41D4×D43semidirect
817. C4#14583734semidirect

Maximal subgroups

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

subgroupindex
C2×#145837342
#191483872
#191483832
#191483802
#191483752
#191483712
#191483602
#191483512
#191480852
D4×#106219002
#191479262
C2×#145834472
#532×D432
C4×#41×D432
C43×#34982
#6281243