Finite Group Databasebeta

← D43×#3499 #26005005

Subgroups — D43×#3499 #26005005

Order 11008.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D43C212yesmaximal, complemented
2#19148380C211yesmaximal, characteristic, complemented
3#19148379C214yesmaximal, complemented
4#19148378C213yesmaximal, complemented
5#19148377C216yesmaximal, complemented
6#19148376C212yesmaximal, complemented
7#19148375C213yesmaximal, complemented
8#19148374C2112yesmaximal, complemented
9D4×Q8×D43C214yesmaximal, complemented
10#547×D43C2112yesmaximal, complemented
11#536×D43C216yesmaximal, complemented
12#532×D43C213yesmaximal, complemented
13C2×C4⋊Q8×D43C213yesmaximal, complemented
14C4×#41×D43C211yesmaximal, characteristic, complemented
15C43×#3499C211yesmaximal, characteristic, complemented
16C2×#13063373C2216yescomplemented
17C2×#13063373C2214yescomplemented
18C2×#13063372C22112yescomplemented
19C2×#13063372C2216yescomplemented
20C2×#13063372C2212yescomplemented
212−1+4×D43—232no—
22C2×#41×D43C22112yes—
23C2×#41×D43C2216yes—
24C2×#41×D43C2211yescharacteristic
25C22×Q8×D43C2214yes—
26C22×Q8×D43C2216yes—
27Q8×D172C2214yescomplemented
28D4×Dic86C22112yescomplemented
29#14583564C22112yescomplemented
30Q8×C22⋊D43C2218yescomplemented
31#14583562C22124yescomplemented
32#14583554C22112yescomplemented
33#14583553C22112yescomplemented
34#14583552C22112yescomplemented
35#14583551C22124yescomplemented
36#14583550C22124yescomplemented
37#14583549C22124yescomplemented
38#14583548C22124yescomplemented
39#14583547C22148yescomplemented
40#14583475C2216yescomplemented
41#14583474C22112yescomplemented
42#14583473C2216yescomplemented
43#14583472C22124yescomplemented
44#14583471C22124yescomplemented
45#14583470C2216yescomplemented
46#14583469C22112yescomplemented
47#14583450C2213yescomplemented
48#14583449C2213yescomplemented
49#14583448C2216yescomplemented
50#14583447C2213yescomplemented
51#14583446C22112yescomplemented
52#14583445C2216yescomplemented
53#14583444C22112yescomplemented
54C2×#13063325C2213yescomplemented
55C2×#13063324C22112yescomplemented
56C2×#13063323C2216yescomplemented
57C4⋊Q8×D43C22112yes—
58C4⋊Q8×D43C2213yes—
59C4⋊Q8×D43C2216yes—
60C4⋊Q8×D43C22112yescomplemented
61C4⋊Q8×D43C2216yescomplemented
62C4⋊Q8×D43C2216yescomplemented
63#127×D43C2211yescharacteristic
64#124×D43C2216yes—
65#123×D43C22124yes—
66C22⋊Q8×D43C22124yes—
67#121×D43C22112yes—
68#41×Dic43C2211yescharacteristic, complemented
69C4×#10621902C2212yescomplemented
70C4×#10621898C2213yescomplemented
71#14583367C2213yescomplemented
72C4×#10621900C2216yescomplemented
73C4×Q8×D43C2212yes—
74C4×D4×D43C2216yes—
75C4×D4×D43C22112yes—
76#117×D43C2213yes—
77C2×C4⋊C4×D43C22112yes—
78C2×C42×D43C2213yes—
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#13063372—216no—
89#13063372—296no—
90#13063372—248no—
91C2×#10621902C23112yes—
92C2×#10621902C2316yes—
93C2×#10621902C2311yescharacteristic
94C2×#10621898C23112yes—
95C2×#10621898C2316yes—
96C2×#10621898C23112yes—
97C2×#10621898C23124yes—
98C2×#10621898C2313yes—
99C2×#10621900C23112yes—
100C2×#10621900C23112yes—
101C2×#10621900C2316yes—
102C2×#10621900C23124yes—
103C2×#10621900C2313yes—
104#41×D43—296no—
105#41×D43—248no—
106#41×D43D4116yescomplemented
107C22×Dic86C23112yes—
108C22×Dic86C2316yes—
109C22×Dic86C23112yes—
110C2×Q8×D43—232no—
111C2×Q8×D43—248no—
112C2×Q8×D43C23112yes—
113C2×Q8×D43C2314yes—
114C2×Q8×D43C23112yes—
115C2×Q8×D43C2316yes—
116C2×Q8×D43C23112yes—
117C2×Q8×D43C23112yes—
118C2×Q8×D43C2311yescharacteristic
119C2×D4×D43C2314yes—
120C2×D4×D43C23112yes—
121C2×D4×D43C2312yes—
122C2×D4×D43C2313yes—
123C22×C4×D43C2316yes—
124C22×C4×D43C23112yes—
125C22×C4×D43C23112yes—
126C22×C4×D43C2313yes—
127#13063325C23112yes—
128#13063325C2313yes—
129#13063325C2316yes—
130#13063324C23124yes—
131#13063324C23124yes—
132#13063324C23112yes—
133#13063324C23124yes—
134#13063323C23124yes—
135#13063323C2316yes—
136#13063323C23112yes—
137#13063322C2311yescharacteristic
138#13063321C2314yes—
139#13063321C2312yes—
140#13063314C2316yes—
141#13063313C2316yes—
142#13063312C2316yes—
143#13063311C23124yes—
144#13063310C23148yes—
145#13063309C23124yes—
146#13063308C23124yes—
147#13063307C23148yes—
148#13063306C23124yes—
149#13063305C23124yes—
150#13063304C23124yes—
151#13063303C23148yes—
152#13063302C23148yes—
153#13063301C23124yes—
154#13063300C23112yes—
155#13063299C23112yes—
156#13063298C23124yes—
157#13063297C23124yes—
158#13063296C23112yes—
159Q8×Dic43C2312yes—
160C4×Dic86C2316yes—
161#13063290C2316yes—
162C4×D172C2316yes—
163C4×D172C23112yes—
164D4×Dic43C23112yes—
165D4×Dic43C2316yes—
166#13063287C23112yes—
167#13063287C2316yes—
168C4×C22⋊D43C23124yes—
169C4×C22⋊D43C23112yes—
170(C22⋊D43)⋊C4C23124yes—
171(C22⋊D43)⋊C4C23112yes—
172#13063284C2313yes—
173#13063283C2316yes—
174#13063282C2316yes—
175#13063281C2316yes—
176C2×C4⋊Dic43C23112yes—
177C2×Dic43⋊C4C23124yes—
178C4⋊C4×D43C23124yes—
179C4⋊C4×D43C23112yes—
180C4⋊C4×D43C23124yes—
181C4⋊C4×D43C23124yes—
182C4⋊C4×D43C2316yes—
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×C43C2316yes—
209C4×D4×C43C23112yes—
210#117×C43C2313yes—
211C2×C4⋊C4×C43C23112yes—
212C2×C42×C43C2313yes—
213C23×D43C2414yes—
214C23×D43C2413yes—
215#41×C43—248no—
216#41×C43—224no—
217#41×C43C2×D418yescomplemented
218C2×Q8×C43—216no—
219C2×Q8×C43—224no—
220C2×Q8×C43C24112yes—
221C2×Q8×C43C2416yes—
222C2×Q8×C43C2411yescharacteristic
223C2×D4×C43C2414yes—
224C2×D4×C43C24112yes—
225C2×D4×C43C2412yes—
226C2×D4×C43C2413yes—
227C22×C4×C43C2416yes—
228C22×C4×C43C24112yes—
229C22×C4×C43C24112yes—
230C22×C4×C43C2413yes—
231C2×C22⋊D43C2418yes—
232C2×C22⋊D43C24112yes—
233C2×C22⋊D43C24112yes—
234C2×C22⋊D43C2414yes—
235C2×C22⋊D43C2416yes—
236C22×Dic43C2416yes—
237C22×Dic43C24112yes—
238C22×Dic43C24112yes—
239C22×Dic43C2413yes—
240#10621902—248no—
241#10621902—224no—
242#10621902C2×D418yescomplemented
243Q8×D43—216no—
244Q8×D43—248no—
245Q8×D43—224no—
246Q8×D43—248no—
247Q8×D43—248no—
248Q8×D43—248no—
249Q8×D43C2×D418yes—
250#10621900—248no—
251#10621900—296no—
252#10621900—248no—
253#10621900—224no—
254#10621900C2×D4124yescomplemented
255D4×D43—28no—
256D4×D43—216no—
257D4×D43—248no—
258D4×D43C2×D4124yes—
259#10621898—224no—
260#10621898—296no—
261#10621898—248no—
262#10621898—248no—
263#10621898C2×D4124yescomplemented
264C2×D172C2414yes—
265C2×D172C24112yes—
266C2×D172C2412yes—
267C2×D172C2413yes—
268C2×C4×D43—248no—
269C2×C4×D43—224no—
270C2×C4×D43—248no—
271C2×C4×D43C2×D4124yes—
272C2×C4×D43C2416yes—
273C2×C4×D43C2416yes—
274C2×C4×D43C2416yes—
275C2×C4×D43C24112yes—
276C2×C4×D43C24124yes—
277C2×C4×D43C24112yes—
278C2×C4×D43C24112yes—
279C2×C4×D43C2411yescharacteristic
280C2×C4×D43C2413yes—
281C2×C4×D43C2413yes—
282C2×C4×D43C2413yes—
283C2×C4×D43C2412yes—
284C2×Dic86—224no—
285C2×Dic86—248no—
286C2×Dic86—248no—
287C2×Dic86C24124yes—
288C2×Dic86C24112yes—
289C2×Dic86C24112yes—
290C2×Dic86C2416yes—
291C2×Dic86C2413yes—
292C4⋊C4×C43C24112yes—
293C4⋊C4×C43C24124yes—
294C4⋊C4×C43C2416yes—
295C22⋊C4×C43C2416yes—
296C22⋊C4×C43C24124yes—
297C42×C43C2411yescharacteristic
298C42×C43C2413yes—
299C42×C43C2416yes—
300C22⋊Dic43C2416yes—
301C22⋊Dic43C24124yes—
302(C2×D43)⋊C4C24112yes—
303(C2×D43)⋊C4C24124yes—
304(C2×D43)⋊C4C24124yes—
305C4⋊Dic43C24112yes—
306C4⋊Dic43C24124yes—
307C4⋊Dic43C2416yes—
308Dic43⋊C4C24124yes—
309Dic43⋊C4C24148yes—
310Dic43⋊C4C24112yes—
311C4×Dic43C2411yescharacteristic
312C4×Dic43C2412yes—
313C4×Dic43C2416yes—
314C4×Dic43C2413yes—
315C4×Dic43C2416yes—
316C4×Dic43C2416yes—
317C4×Dic43C2416yes—
318C23×C43C2514yes—
319C23×C43C2513yes—
320C22×D43—212no—
321C22×D43—28no—
322C22×D43—216no—
323C22×D43C22×D4112yes—
324C22×D43C2514yes—
325C22×D43C2513yes—
326C22×D43C2511yescharacteristic
327Q8×C43—212no—
328Q8×C43—224no—
329Q8×C43C22×D414yes—
330D4×C43—224no—
331D4×C43—24no—
332D4×C43—28no—
333D4×C43C22×D4112yes—
334C2×C4×C43—224no—
335C2×C4×C43—224no—
336C2×C4×C43—212no—
337C2×C4×C43C22×D4112yes—
338C2×C4×C43C2516yes—
339C2×C4×C43C25112yes—
340C2×C4×C43C2511yescharacteristic
341C2×C4×C43C2513yes—
342C2×C4×C43C2512yes—
343C22⋊D43—224no—
344C22⋊D43—224no—
345C22⋊D43—28no—
346C22⋊D43—216no—
347C22⋊D43C22×D4124yes—
348C2×Dic43—224no—
349C2×Dic43—224no—
350C2×Dic43—212no—
351C2×Dic43C22×D4112yes—
352C2×Dic43C2516yes—
353C2×Dic43C25112yes—
354C2×Dic43C2511yescharacteristic
355C2×Dic43C2513yes—
356C2×Dic43C2512yes—
357D172—224no—
358D172—24no—
359D172—28no—
360D172C22×D4112yes—
361C4×D43—224no—
362C4×D43—248no—
363C4×D43—212no—
364C4×D43—224no—
365C4×D43—212no—
366C4×D43—224no—
367C4×D43—212no—
368C4×D43C22×D4112yes—
369C4×D43C22×D414yes—
370C4×D43C22×D4112yes—
371C4×D43C22×D4112yes—
372C4×D432−1+418yescomplemented
373Dic86—212no—
374Dic86—224no—
375Dic86—224no—
376Dic86—248no—
377Dic86C22×D4112yes—
378C2×#3499—431nomaximal, Sylow
379C22×C43—26no—
380C22×C43—24no—
381C22×C43—28no—
382C22×C43C23×D416yes—
383C22×C43C2611yescharacteristic
384C2×D43—26no—
385C2×D43—224no—
386C2×D43—24no—
387C2×D43—28no—
388C2×D43—416no—
389C2×D43C23×D416yes—
390C2×D43C23×D412yes—
391C2×D43C2×2−1+414yes—
392C4×C43—212no—
393C4×C43—26no—
394C4×C43C23×D412yes—
395C4×C43C23×D416yes—
396C4×C43C2×2−1+414yescomplemented
397Dic43—212no—
398Dic43—26no—
399Dic43C23×D412yes—
400Dic43C23×D416yes—
401Dic43C2×2−1+414yescomplemented
402C22×2−1+4—432no—
403#3499—432no—
404#3499—434no—
405#3499—4312no—
406#3499—436no—
407#3499—433no—
408#3499—433no—
409#3499—431no—
410#3499D4311yescharacteristic, direct product factor
411C2×D4×Q8—434no—
412C2×#547—4312no—
413C2×#536—436no—
414C2×#532—433no—
415C22×C4⋊Q8—433no—
416C2×C4×#41—431no—
417C2×C43—26no—
418C2×C43—44no—
419C2×C43C24×D411yescharacteristic
420C2×C43C22×2−1+412yes—
421D43—26no—
422D43—44no—
423D43#349914yesdirect product factor
424C2×2−1+4—436no—
425C2×2−1+4—4312no—
426C2×2−1+4—432no—
427C2×2−1+4—434no—
428C2×2−1+4—436no—
429C2×2−1+4—8632no—
430C2×2−1+4C2×D4312yescomplemented
431C22×#41—431no—
432C22×#41—436no—
433C22×#41—4312no—
434C23×Q8—436no—
435C23×Q8—434no—
436D4×Q8—438no—
437D4×Q8—4312no—
438D4×Q8—4324no—
439D4×Q8—434no—
440D4×Q8—4312no—
441D4×Q8C2×D4314yescomplemented
442#547—4324no—
443#547—4312no—
444#547—4348no—
445#547—4324no—
446#547—4324no—
447#547—4312no—
448#547—4312no—
449#547—4324no—
450#547C2×D43112yescomplemented
451#536—436no—
452#536—436no—
453#536—4312no—
454#536—4312no—
455#536—4324no—
456#536—4324no—
457#536—436no—
458#536C2×D4316yescomplemented
459#532—436no—
460#532—433no—
461#532—433no—
462#532—436no—
463#532—4312no—
464#532—4312no—
465#532—433no—
466#532C2×D4313yescomplemented
467C2×C4⋊Q8—436no—
468C2×C4⋊Q8—433no—
469C2×C4⋊Q8—436no—
470C2×C4⋊Q8—4312no—
471C2×C4⋊Q8—436no—
472C2×C4⋊Q8—436no—
473C2×C4⋊Q8—4312no—
474C2×C4⋊Q8—4312no—
475C2×C4⋊Q8—433no—
476C2×C4⋊Q8C2×D4313yescomplemented
477C2×#127—431no—
478C2×#124—436no—
479C2×#123—4324no—
480C2×C22⋊Q8—4324no—
481C2×#121—4312no—
482C4×#41—431no—
483C4×#41—432no—
484C4×#41—436no—
485C4×#41—433no—
486C4×#41—433no—
487C4×#41C2×D4311yescharacteristic, complemented
488C2×C4×Q8—432no—
489C2×C4×D4—436no—
490C2×C4×D4—4312no—
491C2×#117—433no—
492C22×C4⋊C4—4312no—
493C22×C42—433no—
494C43C2×#349911yescharacteristic, complemented, Sylow
4952−1+4—216no—
4962−1+4—8632no—
4972−1+4—8648no—
4982−1+4—8696no—
4992−1+4—8648no—
5002−1+4—8616no—
501C2×#41—4316no—
502C2×#41—431no—
503C2×#41—436no—
504C2×#41—4312no—
505C2×#41—433no—
506C2×#41—4312no—
507C2×#41—436no—
508C2×#41—4312no—
509C2×#41—4324no—
510C2×#41—433no—
511C2×#41—4312no—
512C2×#41—436no—
513C2×#41—4312no—
514C2×#41—4324no—
515C2×#41—8648no—
516C2×#41—8696no—
517C2×#41C22×D4316yes—
518C2×#41C22×D43112yes—
519C2×#41C22×D4311yescharacteristic
520C22×Q8—431no—
521C22×Q8—4312no—
522C22×Q8—436no—
523C22×Q8—4312no—
524C22×Q8—4312no—
525C22×Q8—4312no—
526C22×Q8—434no—
527C22×Q8—4312no—
528C22×Q8—436no—
529C22×Q8—4312no—
530C22×Q8—8648no—
531C22×Q8—8632no—
532C22×Q8C22×D4316yes—
533C22×Q8C22×D4314yes—
534C22×D4—433no—
535C22×D4—434no—
536C22×D4—4312no—
537C22×D4—432no—
538C23×C4—433no—
539C23×C4—436no—
540C23×C4—4312no—
541C23×C4—4312no—
542C4⋊Q8—436no—
543C4⋊Q8—4312no—
544C4⋊Q8—4324no—
545C4⋊Q8—4312no—
546C4⋊Q8—4324no—
547C4⋊Q8—4324no—
548C4⋊Q8—4324no—
549C4⋊Q8—433no—
550C4⋊Q8—436no—
551C4⋊Q8—4312no—
552C4⋊Q8C22×D4313yes—
553C4⋊Q8C22×D4316yes—
554C4⋊Q8C22×D43112yes—
555#127—432no—
556#127—434no—
557#127—431no—
558#127C22×D4311yescharacteristic
559#124—436no—
560#124—436no—
561#124—4324no—
562#124—436no—
563#124C22×D4316yes—
564#123—4324no—
565#123—4324no—
566#123—4348no—
567#123—4348no—
568#123—4324no—
569#123C22×D43124yes—
570C22⋊Q8—4324no—
571C22⋊Q8—4324no—
572C22⋊Q8—4348no—
573C22⋊Q8—4324no—
574C22⋊Q8—4348no—
575C22⋊Q8C22×D43124yes—
576#121—4312no—
577#121—4324no—
578#121—4312no—
579#121—4312no—
580#121—4324no—
581#121C22×D43112yes—
582C4×Q8—432no—
583C4×Q8—436no—
584C4×Q8—436no—
585C4×Q8C22×D4312yes—
586C4×D4—436no—
587C4×D4—4312no—
588C4×D4—4312no—
589C4×D4—4324no—
590C4×D4—436no—
591C4×D4—4312no—
592C4×D4—4312no—
593C4×D4—4324no—
594C4×D4—436no—
595C4×D4—4312no—
596C4×D4C22×D4316yes—
597C4×D4C22×D43112yes—
598#117—433no—
599#117—436no—
600#117—436no—
601#117—436no—
602#117C22×D4313yes—
603C2×C4⋊C4—4324no—
604C2×C4⋊C4—4312no—
605C2×C4⋊C4—4312no—
606C2×C4⋊C4—4324no—
607C2×C4⋊C4—4324no—
608C2×C4⋊C4—4324no—
609C2×C4⋊C4—436no—
610C2×C4⋊C4C22×D43112yes—
611C2×C22⋊C4—436no—
612C2×C22⋊C4—4324no—
613C2×C42—436no—
614C2×C42—433no—
615C2×C42—433no—
616C2×C42—436no—
617C2×C42—436no—
618C2×C42—433no—
619C2×C42—433no—
620C2×C42—431no—
621C2×C42C22×D4313yes—
622C24—433no—
623C24—434no—
624#41—248no—
625#41—224no—
626#41—438no—
627#41—4324no—
628#41—4324no—
629#41—8648no—
630#41—8696no—
631#41—8648no—
632#41—8648no—
633#41—8624no—
634#41—8624no—
635#41—8696no—
636#41—8648no—
637#41—8648no—
638#41—8624no—
639#41D4×D4318yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—438no—
643C2×Q8—433no—
644C2×Q8—4324no—
645C2×Q8—4312no—
646C2×Q8—4312no—
647C2×Q8—436no—
648C2×Q8—8648no—
649C2×Q8—8648no—
650C2×Q8—8624no—
651C2×Q8—8648no—
652C2×Q8—8648no—
653C2×Q8—8648no—
654C2×Q8—8648no—
655C2×Q8—8616no—
656C2×Q8—8624no—
657C2×Q8C23×D43112yes—
658C2×Q8C23×D4316yes—
659C2×Q8C23×D4311yescharacteristic
660C2×D4—436no—
661C2×D4—4324no—
662C2×D4—438no—
663C2×D4—4312no—
664C2×D4—4312no—
665C2×D4—434no—
666C2×D4—433no—
667C2×D4—434no—
668C2×D4—4312no—
669C2×D4—432no—
670C2×D4—868no—
671C2×D4—8616no—
672C2×D4—8648no—
673C2×D4C23×D4314yes—
674C2×D4C23×D43112yes—
675C2×D4C23×D4312yes—
676C2×D4C23×D4313yes—
677C22×C4—433no—
678C22×C4—4324no—
679C22×C4—432no—
680C22×C4—431no—
681C22×C4—433no—
682C22×C4—433no—
683C22×C4—433no—
684C22×C4—436no—
685C22×C4—4312no—
686C22×C4—4312no—
687C22×C4—436no—
688C22×C4—436no—
689C22×C4—436no—
690C22×C4—4312no—
691C22×C4—4324no—
692C22×C4—4312no—
693C22×C4—4312no—
694C22×C4—8648no—
695C22×C4—8624no—
696C22×C4—8648no—
697C22×C4C23×D4316yes—
698C22×C4C23×D43112yes—
699C22×C4C23×D43112yes—
700C22×C4C23×D4313yes—
701C4⋊C4—4324no—
702C4⋊C4—4312no—
703C4⋊C4—4348no—
704C4⋊C4—4324no—
705C4⋊C4—4312no—
706C4⋊C4—436no—
707C4⋊C4C23×D43112yes—
708C4⋊C4C23×D43124yes—
709C4⋊C4C23×D4316yes—
710C22⋊C4—436no—
711C22⋊C4—4324no—
712C22⋊C4—4312no—
713C22⋊C4—4324no—
714C22⋊C4—4324no—
715C22⋊C4C23×D4316yes—
716C22⋊C4C23×D43124yes—
717C42—431no—
718C42—432no—
719C42—436no—
720C42—433no—
721C42—436no—
722C42—436no—
723C42—436no—
724C42C23×D4311yescharacteristic
725C42C23×D4313yes—
726C42C23×D4316yes—
727C23—431no—
728C23—4312no—
729C23—433no—
730C23—434no—
731C23—8612no—
732C23—868no—
733C23—8616no—
734C23C24×D4314yes—
735C23C24×D4313yes—
736Q8—224no—
737Q8—212no—
738Q8—4312no—
739Q8—8624no—
740Q8—8648no—
741Q8—8624no—
742Q8—8612no—
743Q8C2×D4×D4314yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—4324no—
748D4—4312no—
749D4—8624no—
750D4—868no—
751D4—8616no—
752D4—8624no—
753D4—8624no—
754D4—864no—
755D4—868no—
756D4C2×D4×D43112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—4312no—
761C2×C4—432no—
762C2×C4—431no—
763C2×C4—433no—
764C2×C4—434no—
765C2×C4—4312no—
766C2×C4—4312no—
767C2×C4—4312no—
768C2×C4—438no—
769C2×C4—436no—
770C2×C4—4312no—
771C2×C4—8624no—
772C2×C4—8612no—
773C2×C4—8624no—
774C2×C4—8648no—
775C2×C4—8612no—
776C2×C4—8624no—
777C2×C4—8612no—
778C2×C4—8624no—
779C2×C4—8624no—
780C2×C4—8612no—
781C2×C4C2×D4×D43112yes—
782C2×C4C24×D4316yes—
783C2×C4C24×D43112yes—
784C2×C4C24×D4311yescharacteristic
785C2×C4C24×D4313yes—
786C2×C4C24×D4312yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—432no—
791C22—434no—
792C22—436no—
793C22—8624no—
794C22—866no—
795C22—864no—
796C22—868no—
797C22—17216no—
798C22C22×D4×D4316yes—
799C22C25×D4311yescharacteristic
800C4—212no—
801C4—26no—
802C4—432no—
803C4—436no—
804C4—434no—
805C4—8612no—
806C4—866no—
807C4C22×D4×D4316yes—
808C4C22×D4×D4312yes—
809C42−1+4×D4314yescomplemented
810C2—26no—
811C2—44no—
812C2—434no—
813C2—866no—
814C2—1724no—
815C2C23×D4×D4311yescharacteristic
816C2C2×2−1+4×D4312yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3499C2
hypercenter#3499D43
hypocenterC43C2×#3499
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D43C2semidirect
2. #19148380C2semidirect
3. #19148379C2semidirect
4. #19148378C2semidirect
5. #19148377C2semidirect
6. #19148376C2semidirect
7. #19148375C2semidirect
8. #19148374C2semidirect
9. D4×Q8×D43C2semidirect
10. #547×D43C2semidirect
11. #536×D43C2semidirect
12. #532×D43C2semidirect
13. C2×C4⋊Q8×D43C2semidirect
14. C4×#41×D43C2semidirect
15. C43×#3499C2semidirect
16. C2×#13063373C22semidirect
17. C2×#13063373C22semidirect
18. C2×#13063372C22semidirect
19. C2×#13063372C22semidirect
20. C2×#13063372C22semidirect
27. Q8×D172C22semidirect
28. D4×Dic86C22semidirect
29. #14583564C22semidirect
30. Q8×C22⋊D43C22semidirect
31. #14583562C22semidirect
32. #14583554C22semidirect
33. #14583553C22semidirect
34. #14583552C22semidirect
35. #14583551C22semidirect
36. #14583550C22semidirect
37. #14583549C22semidirect
38. #14583548C22semidirect
39. #14583547C22semidirect
40. #14583475C22semidirect
41. #14583474C22semidirect
42. #14583473C22semidirect
43. #14583472C22semidirect
44. #14583471C22semidirect
45. #14583470C22semidirect
46. #14583469C22semidirect
47. #14583450C22semidirect
48. #14583449C22semidirect
49. #14583448C22semidirect
50. #14583447C22semidirect
51. #14583446C22semidirect
52. #14583445C22semidirect
53. #14583444C22semidirect
54. C2×#13063325C22semidirect
55. C2×#13063324C22semidirect
56. C2×#13063323C22semidirect
60. C4⋊Q8×D43C22semidirect
61. C4⋊Q8×D43C22semidirect
62. C4⋊Q8×D43C22semidirect
68. #41×Dic43C22semidirect
69. C4×#10621902C22semidirect
70. C4×#10621898C22semidirect
71. #14583367C22semidirect
72. C4×#10621900C22semidirect
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
106. #41×D43D4semidirect
217. #41×C43C2×D4semidirect
242. #10621902C2×D4semidirect
254. #10621900C2×D4semidirect
263. #10621898C2×D4semidirect
372. C4×D432−1+4semidirect
396. C4×C43C2×2−1+4semidirect
401. Dic43C2×2−1+4semidirect
410. #3499D43direct (N × H)
423. D43#3499direct (N × H)
430. C2×2−1+4C2×D43semidirect
441. D4×Q8C2×D43semidirect
450. #547C2×D43semidirect
458. #536C2×D43semidirect
466. #532C2×D43semidirect
476. C2×C4⋊Q8C2×D43semidirect
487. C4×#41C2×D43semidirect
494. C43C2×#3499semidirect
639. #41D4×D43semidirect
809. C42−1+4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D432
#191483802
#191483792
#191483782
#191483772
#191483762
#191483752
#191483742
D4×Q8×D432
#547×D432
#536×D432
#532×D432
C2×C4⋊Q8×D432
C4×#41×D432
C43×#34992
C2×#349943