Finite Group Databasebeta

← D43×#3486 #26004758

Subgroups — D43×#3486 #26004758

Order 11008.

11254 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D43C211yesmaximal, characteristic, complemented
2C23×Q8×D43C211yesmaximal, characteristic, complemented
3#19148247C211yesmaximal, characteristic, complemented
4#19148246C211yesmaximal, characteristic, complemented
5#19148245C218yesmaximal, complemented
6#19148244C216yesmaximal, complemented
7#19148243C211yesmaximal, characteristic, complemented
8#19148242C216yesmaximal, complemented
9#19148241C218yesmaximal, complemented
10D4×Q8×D43C218yesmaximal, complemented
11#548×D43C218yesmaximal, complemented
12#536×D43C216yesmaximal, complemented
13#525×D43C216yesmaximal, complemented
14#519×D43C211yesmaximal, characteristic, complemented
15C43×#3486C211yesmaximal, characteristic, complemented
16C2×#13063373C2211yescharacteristic, complemented
17C2×#13063373C2214yescomplemented
18C2×#13063372C2216yescomplemented
19C2×#13063372C2214yescomplemented
202−1+4×D43—216no—
21C2×#41×D43C2216yes—
22C2×#41×D43C2214yescomplemented
23C23×Dic86C2213yescomplemented
24C22×Q8×D43—216no—
25C22×Q8×D43C2218yes—
26C22×Q8×D43C2213yes—
27C22×Q8×D43C2211yescharacteristic
28C22×Q8×D43C2218yescomplemented
29C22×Q8×D43C2211yescharacteristic, complemented
30C22×Q8×D43C2213yescomplemented
31C22×Q8×D43C2214yescomplemented
32C23×C4×D43C2213yes—
33Q8×D172C2218yescomplemented
34D4×Dic86C22124yescomplemented
35#14583564C22124yescomplemented
36Q8×C22⋊D43C2218yescomplemented
37Q8×C22⋊D43C2218yescomplemented
38#14583562C22124yescomplemented
39#14583562C22124yescomplemented
40#14583561C2218yescomplemented
41#14583560C2218yescomplemented
42#14583559C22124yescomplemented
43#14583558C22124yescomplemented
44#14583557C22124yescomplemented
45#14583556C2218yescomplemented
46#14583555C22124yescomplemented
47#14583475C2216yescomplemented
48#14583474C22112yescomplemented
49#14583473C2216yescomplemented
50#14583472C22124yescomplemented
51#14583471C22124yescomplemented
52#14583470C2216yescomplemented
53#14583469C22112yescomplemented
54C4⋊Q8×D43C22112yescomplemented
55#124×D43C22112yescomplemented
56#14583412C22112yescomplemented
57#14583411C2216yescomplemented
58#14583410C2216yescomplemented
59#14583409C22112yescomplemented
60#14583408C22124yescomplemented
61#14583407C22112yescomplemented
62#14583406C2216yescomplemented
63#14583405C22112yescomplemented
64#123×D43C22112yes—
65C22⋊Q8×D43C22112yes—
66C22⋊Q8×D43C22124yescomplemented
67#121×D43C22112yes—
68#120×D43C2214yes—
69#14583377C2211yescharacteristic, complemented
70#14583376C2216yescomplemented
71#14583375C2218yescomplemented
72C4×Q8×D43C2218yescomplemented
73C4×D4×D43C22124yes—
74#117×D43C2216yes—
75C2×2−1+4×C43C2211yescharacteristic, complemented
76C23×Q8×C43C2211yescharacteristic, complemented
77D4×Q8×C43C2218yescomplemented
78C43×#548C2218yescomplemented
79C43×#536C2216yescomplemented
80C43×#525C2216yescomplemented
81C43×#519C2211yescharacteristic, complemented
82C24×D43C2311yescharacteristic
83#13063373—28no—
84#13063373—232no—
85#13063372—232no—
86#13063372—248no—
87C2×#10621902C2316yes—
88C2×#10621902C2314yescomplemented
89C2×#10621898C23112yes—
90C2×#10621898C2316yes—
91C2×#10621898C23112yescomplemented
92C2×#10621900C23112yes—
93C2×#10621900C2316yes—
94C2×#10621900C23112yescomplemented
95#41×D43—232no—
96#41×D43—248no—
97C22×Dic86—224no—
98C22×Dic86C23124yes—
99C22×Dic86C2313yes—
100C22×Dic86C2316yes—
101C22×Dic86C2313yes—
102C22×Dic86C23112yescomplemented
103C2×Q8×D43—28no—
104C2×Q8×D43—264no—
105C2×Q8×D43—232no—
106C2×Q8×D43—264no—
107C2×Q8×D43—224no—
108C2×Q8×D43—224no—
109C2×Q8×D43D4116yescomplemented
110C2×Q8×D43C2318yes—
111C2×Q8×D43C23124yes—
112C2×Q8×D43C2316yes—
113C2×Q8×D43C23112yes—
114C2×Q8×D43C23112yes—
115C2×Q8×D43C2314yes—
116C2×Q8×D43C2314yes—
117C2×Q8×D43C23112yescomplemented
118C2×Q8×D43C2314yescomplemented
119C2×D4×D43C2318yes—
120C2×D4×D43C2314yes—
121C2×D4×D43C2316yes—
122C23×Dic43C2313yes—
123C22×C4×D43—224no—
124C22×C4×D43C23112yes—
125C22×C4×D43C23112yes—
126C22×C4×D43C2313yes—
127C22×C4×D43C2313yes—
128C22×C4×D43C2313yes—
129C22×C4×D43C23112yes—
130C22×C4×D43C2313yes—
131#13063325C23112yescomplemented
132#13063324C23148yescomplemented
133#13063323C23112yescomplemented
134#13063323C23112yescomplemented
135#13063314C23112yescomplemented
136#13063313C23112yescomplemented
137#13063312C23112yescomplemented
138#13063311C23148yescomplemented
139#13063310C23124yes—
140#13063309C23112yes—
141#13063308C23112yes—
142#13063307C23124yes—
143#13063306C23112yes—
144#13063305C23112yes—
145#13063305C23124yescomplemented
146#13063304C23112yes—
147#13063304C23124yescomplemented
148#13063303C23124yes—
149#13063303C23148yescomplemented
150#13063302C23124yes—
151#13063302C23148yescomplemented
152#13063301C23112yes—
153#13063301C23124yescomplemented
154#13063300C23112yes—
155#13063299C23112yes—
156#13063298C23124yes—
157#13063297C23124yes—
158#13063296C23112yes—
159#13063295C2314yes—
160#13063295C2318yes—
161#13063294C2314yes—
162#13063293C2314yes—
163#13063293C2318yes—
164Q8×Dic43C2318yescomplemented
165C4×Dic86C23124yescomplemented
166#13063290C23124yescomplemented
167C4×D172C23124yes—
168D4×Dic43C23124yes—
169#13063287C23124yes—
170C4×C22⋊D43C23124yes—
171C4×C22⋊D43C23124yes—
172(C22⋊D43)⋊C4C23124yes—
173(C22⋊D43)⋊C4C23124yes—
174#13063284C2316yes—
175#13063283C23112yes—
176#13063282C23112yes—
177#13063281C23112yes—
178C4⋊C4×D43C23112yes—
179C4⋊C4×D43C23124yes—
180C22⋊C4×D43C2314yes—
181C22⋊C4×D43C2318yes—
182C22⋊C4×D43C23124yes—
183C42×D43C23112yes—
1842−1+4×C43—28no—
185C2×#41×C43C2316yes—
186C2×#41×C43C2314yescomplemented
187C22×Q8×C43—28no—
188C22×Q8×C43C2318yes—
189C22×Q8×C43C2313yes—
190C22×Q8×C43C2311yescharacteristic
191C22×Q8×C43C2314yescomplemented
192C23×C4×C43C2313yes—
193C4⋊Q8×C43C23112yescomplemented
194#124×C43C23112yescomplemented
195#123×C43C23112yes—
196C22⋊Q8×C43C23112yes—
197C22⋊Q8×C43C23124yescomplemented
198#121×C43C23112yes—
199#120×C43C2314yes—
200C4×Q8×C43C2318yescomplemented
201C4×D4×C43C23124yes—
202#117×C43C2316yes—
203C24×C43C2411yescharacteristic
204C23×D43—24no—
205C23×D43—28no—
206C23×D43C2414yes—
207C23×D43C2411yescharacteristic
208C23×D43C2412yes—
209C23×D43C2411yescharacteristic
210C23×D43C2412yes—
211#41×C43—216no—
212#41×C43—224no—
213C2×Q8×C43—232no—
214C2×Q8×C43—216no—
215C2×Q8×C43—212no—
216C2×Q8×C43C2×D418yescomplemented
217C2×Q8×C43C2416yes—
218C2×Q8×C43C24112yes—
219C2×Q8×C43C2414yes—
220C2×D4×C43C2418yes—
221C2×D4×C43C2414yes—
222C2×D4×C43C2416yes—
223C22×C4×C43—212no—
224C22×C4×C43C24112yes—
225C22×C4×C43C24112yes—
226C22×C4×C43C2413yes—
227C22×C4×C43C2413yes—
228C2×C22⋊D43C2418yes—
229C2×C22⋊D43C2418yes—
230C2×C22⋊D43C2414yes—
231C2×C22⋊D43C2414yes—
232C2×C22⋊D43C24112yes—
233C22×Dic43—212no—
234C22×Dic43C24112yes—
235C22×Dic43C24112yes—
236C22×Dic43C2413yes—
237C22×Dic43C2413yes—
238#10621902—216no—
239#10621902—224no—
240Q8×D43—232no—
241Q8×D43—216no—
242Q8×D43—248no—
243Q8×D43—248no—
244Q8×D43—224no—
245Q8×D43—296no—
246Q8×D43—248no—
247Q8×D43C2×D4132yes—
248Q8×D43C2×D4132yescomplemented
249#10621900—248no—
250#10621900—224no—
251#10621900—248no—
252D4×D43—224no—
253D4×D43—216no—
254D4×D43—232no—
255#10621898—224no—
256#10621898—248no—
257#10621898—248no—
258C2×D172C2418yes—
259C2×D172C2414yes—
260C2×D172C2416yes—
261C2×C4×D43—212no—
262C2×C4×D43—212no—
263C2×C4×D43—248no—
264C2×C4×D43—248no—
265C2×C4×D43—248no—
266C2×C4×D43—212no—
267C2×C4×D43C2×D4124yes—
268C2×C4×D43C2418yes—
269C2×C4×D43C2416yes—
270C2×C4×D43C2414yes—
271C2×C4×D43C24112yes—
272C2×C4×D43C24112yes—
273C2×C4×D43C24112yes—
274C2×C4×D43C24112yes—
275C2×C4×D43C2416yes—
276C2×C4×D43C2416yes—
277C2×C4×D43C2416yes—
278C2×Dic86—212no—
279C2×Dic86—224no—
280C2×Dic86—296no—
281C2×Dic86—248no—
282C2×Dic86C2×D4124yescomplemented
283C2×Dic86C24112yes—
284C2×Dic86C24124yes—
285C2×Dic86C2416yes—
286C2×Dic86C24112yes—
287C2×Dic86C24112yes—
288C4⋊C4×C43C24112yes—
289C4⋊C4×C43C24124yes—
290C22⋊C4×C43C2414yes—
291C22⋊C4×C43C2418yes—
292C22⋊C4×C43C24124yes—
293C42×C43C24112yes—
294C22⋊Dic43C2414yes—
295C22⋊Dic43C2418yes—
296C22⋊Dic43C24124yes—
297(C2×D43)⋊C4C2418yes—
298(C2×D43)⋊C4C2418yes—
299(C2×D43)⋊C4C24124yes—
300(C2×D43)⋊C4C2418yes—
301(C2×D43)⋊C4C24124yes—
302C4⋊Dic43C24112yes—
303C4⋊Dic43C24124yes—
304Dic43⋊C4C24124yes—
305Dic43⋊C4C24124yes—
306Dic43⋊C4C24124yes—
307C4×Dic43C24124yes—
308C4×Dic43C24112yes—
309C23×C43—22no—
310C23×C43—24no—
311C23×C43C2514yes—
312C23×C43C2511yescharacteristic
313C23×C43C2512yes—
314C22×D43—232no—
315C22×D43—22no—
316C22×D43—24no—
317C22×D43—24no—
318C22×D43—24no—
319C22×D43—24no—
320C22×D43—24no—
321C22×D43—24no—
322C22×D43—24no—
323C22×D43—28no—
324C22×D43—216no—
325C22×D43C22×D414yes—
326C22×D432−1+418yescomplemented
327C22×D43C2514yes—
328C22×D43C2511yescharacteristic
329C22×D43C2512yes—
330C22×D43C2511yescharacteristic
331Q8×C43—224no—
332Q8×C43—212no—
333Q8×C43C22×D4116yes—
334D4×C43—28no—
335D4×C43—216no—
336D4×C43—212no—
337C2×C4×C43—26no—
338C2×C4×C43—224no—
339C2×C4×C43—224no—
340C2×C4×C43C22×D4112yes—
341C2×C4×C43C2518yes—
342C2×C4×C43C2514yes—
343C2×C4×C43C2516yes—
344C2×C4×C43C2516yes—
345C22⋊D43—28no—
346C22⋊D43—216no—
347C22⋊D43—28no—
348C22⋊D43—216no—
349C22⋊D43—224no—
350C2×Dic43—26no—
351C2×Dic43—224no—
352C2×Dic43—224no—
353C2×Dic43C22×D4112yes—
354C2×Dic43C2518yes—
355C2×Dic43C2514yes—
356C2×Dic43C2516yes—
357C2×Dic43C2516yes—
358D172—28no—
359D172—216no—
360D172—212no—
361C4×D43—28no—
362C4×D43—212no—
363C4×D43—212no—
364C4×D43—216no—
365C4×D43—224no—
366C4×D43—224no—
367C4×D43—224no—
368C4×D43—224no—
369C4×D43C22×D4124yes—
370C4×D43C22×D4124yes—
371Dic86—224no—
372Dic86—212no—
373Dic86—248no—
374Dic86—224no—
375Dic86C22×D4148yes—
376C2×#3486—431nomaximal, Sylow
377C22×C43—28no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—24no—
382C22×C43—28no—
383C22×C43C23×D412yes—
384C22×C43C2×2−1+414yescomplemented
385C22×C43C2611yescharacteristic
386C2×D43—216no—
387C2×D43—28no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—28no—
392C2×D43—216no—
393C2×D43—24no—
394C2×D43—28no—
395C2×D43—416no—
396C2×D43C23×D412yes—
397C2×D43C23×D412yes—
398C2×D43C2×2−1+414yes—
399C2×D43C2×2−1+414yescomplemented
400C4×C43—26no—
401C4×C43—24no—
402C4×C43—28no—
403C4×C43C23×D4112yes—
404Dic43—26no—
405Dic43—24no—
406Dic43—28no—
407Dic43C23×D4112yes—
408C22×2−1+4—431no—
409C24×Q8—431no—
410#3486—431no—
411#3486—431no—
412#3486—438no—
413#3486—438no—
414#3486—436no—
415#3486—436no—
416#3486—431no—
417#3486D4311yescharacteristic, direct product factor
418C2×D4×Q8—438no—
419C2×#548—438no—
420C2×#536—436no—
421C2×#525—436no—
422C2×#519—431no—
423C2×C43—22no—
424C2×C43—24no—
425C2×C43—44no—
426C2×C43C24×D411yescharacteristic
427C2×C43C22×2−1+412yes—
428D43—22no—
429D43—24no—
430D43—44no—
431D43#348614yesdirect product factor
432C2×2−1+4—436no—
433C2×2−1+4—434no—
434C2×2−1+4—431no—
435C2×2−1+4—434no—
436C2×2−1+4—8616no—
437C2×2−1+4C2×D4311yescharacteristic, complemented
438C22×#41—436no—
439C22×#41—434no—
440C23×Q8—431no—
441C23×Q8—433no—
442C23×Q8—438no—
443C23×Q8—438no—
444C23×Q8—433no—
445C23×Q8—431no—
446C23×Q8—434no—
447C23×Q8—433no—
448C23×Q8—8616no—
449C23×Q8C2×D4311yescharacteristic, complemented
450C24×C4—433no—
451D4×Q8—438no—
452D4×Q8—438no—
453D4×Q8—4324no—
454D4×Q8—4324no—
455D4×Q8—4324no—
456D4×Q8—438no—
457D4×Q8—4324no—
458D4×Q8C2×D4318yescomplemented
459#548—438no—
460#548—438no—
461#548—4324no—
462#548—4324no—
463#548—4324no—
464#548—438no—
465#548—4324no—
466#548C2×D4318yescomplemented
467#536—436no—
468#536—436no—
469#536—4312no—
470#536—4312no—
471#536—4324no—
472#536—4324no—
473#536—436no—
474#536C2×D4316yescomplemented
475C2×C4⋊Q8—4312no—
476C2×#124—4312no—
477#525—436no—
478#525—436no—
479#525—4312no—
480#525—4312no—
481#525—4312no—
482#525—4312no—
483#525—4324no—
484#525—436no—
485#525C2×D4316yescomplemented
486C2×#123—4312no—
487C2×C22⋊Q8—4312no—
488C2×C22⋊Q8—4324no—
489C2×#121—4312no—
490C2×#120—434no—
491#519—431no—
492#519—438no—
493#519—436no—
494#519C2×D4311yescharacteristic, complemented
495C2×C4×Q8—438no—
496C2×C4×D4—4324no—
497C2×#117—436no—
498C43C2×#348611yescharacteristic, complemented, Sylow
499C25—431no—
5002−1+4—28no—
5012−1+4—8632no—
5022−1+4—8632no—
5032−1+4—8648no—
5042−1+4—868no—
505C2×#41—436no—
506C2×#41—434no—
507C2×#41—4312no—
508C2×#41—436no—
509C2×#41—4312no—
510C2×#41—4312no—
511C2×#41—436no—
512C2×#41—4312no—
513C2×#41—8648no—
514C2×#41—8632no—
515C2×#41C22×D4316yes—
516C2×#41C22×D4314yescomplemented
517C22×Q8—28no—
518C22×Q8—4316no—
519C22×Q8—434no—
520C22×Q8—434no—
521C22×Q8—4312no—
522C22×Q8—436no—
523C22×Q8—4312no—
524C22×Q8—4324no—
525C22×Q8—438no—
526C22×Q8—4312no—
527C22×Q8—434no—
528C22×Q8—433no—
529C22×Q8—436no—
530C22×Q8—433no—
531C22×Q8—4324no—
532C22×Q8—4312no—
533C22×Q8—8624no—
534C22×Q8—8624no—
535C22×Q8—8664no—
536C22×Q8—8664no—
537C22×Q8—8624no—
538C22×Q8—8632no—
539C22×Q8—868no—
540C22×Q8C22×D4313yes—
541C22×Q8C22×D4318yes—
542C22×Q8C22×D4311yescharacteristic
543C22×Q8C22×D4314yescomplemented
544C22×D4—438no—
545C22×D4—434no—
546C22×D4—436no—
547C23×C4—433no—
548C23×C4—433no—
549C23×C4—4312no—
550C23×C4—4312no—
551C23×C4—433no—
552C23×C4—433no—
553C23×C4—4312no—
554C23×C4—433no—
555C23×C4—8624no—
556C23×C4C22×D4313yes—
557C4⋊Q8—4312no—
558C4⋊Q8—4312no—
559C4⋊Q8—4348no—
560C4⋊Q8—4312no—
561C4⋊Q8C22×D43112yescomplemented
562#124—4312no—
563#124—4312no—
564#124—4348no—
565#124—4312no—
566#124C22×D43112yescomplemented
567#123—4312no—
568#123—4312no—
569#123—4324no—
570#123—4324no—
571#123—4312no—
572#123C22×D43112yes—
573C22⋊Q8—4312no—
574C22⋊Q8—4324no—
575C22⋊Q8—4312no—
576C22⋊Q8—4324no—
577C22⋊Q8—4324no—
578C22⋊Q8—4312no—
579C22⋊Q8—4348no—
580C22⋊Q8—4324no—
581C22⋊Q8—4324no—
582C22⋊Q8—4348no—
583C22⋊Q8C22×D43112yes—
584C22⋊Q8C22×D43124yescomplemented
585#121—4312no—
586#121—4324no—
587#121—4312no—
588#121—4312no—
589#121—4324no—
590#121C22×D43112yes—
591#120—434no—
592#120—434no—
593#120—438no—
594#120—438no—
595#120—434no—
596#120C22×D4314yes—
597C4×Q8—438no—
598C4×Q8—4324no—
599C4×Q8—4324no—
600C4×Q8C22×D4318yescomplemented
601C4×D4—4324no—
602C4×D4—4324no—
603C4×D4—4324no—
604C4×D4—4324no—
605C4×D4—4324no—
606C4×D4—4324no—
607C4×D4—4324no—
608C4×D4C22×D43124yes—
609#117—436no—
610#117—4312no—
611#117—4312no—
612#117—4312no—
613#117C22×D4316yes—
614C2×C4⋊C4—4312no—
615C2×C4⋊C4—4324no—
616C2×C22⋊C4—434no—
617C2×C22⋊C4—438no—
618C2×C22⋊C4—4324no—
619C2×C42—4312no—
620C24—431no—
621C24—432no—
622C24—434no—
623C24—432no—
624C24—431no—
625C24—864no—
626C24—868no—
627C24C23×D4311yescharacteristic
628#41—216no—
629#41—224no—
630#41—8648no—
631#41—8648no—
632#41—8648no—
633#41—8624no—
634#41—8624no—
635#41—8648no—
636#41—8616no—
637#41—8624no—
638C2×Q8—232no—
639C2×Q8—216no—
640C2×Q8—212no—
641C2×Q8—4332no—
642C2×Q8—4332no—
643C2×Q8—4324no—
644C2×Q8—4312no—
645C2×Q8—4324no—
646C2×Q8—4312no—
647C2×Q8—4312no—
648C2×Q8—436no—
649C2×Q8—8624no—
650C2×Q8—8696no—
651C2×Q8—8648no—
652C2×Q8—8648no—
653C2×Q8—8648no—
654C2×Q8—8624no—
655C2×Q8—8696no—
656C2×Q8—8648no—
657C2×Q8—8632no—
658C2×Q8—8616no—
659C2×Q8—8612no—
660C2×Q8D4×D4318yescomplemented
661C2×Q8C23×D4316yes—
662C2×Q8C23×D43112yes—
663C2×Q8C23×D4314yes—
664C2×D4—438no—
665C2×D4—438no—
666C2×D4—434no—
667C2×D4—434no—
668C2×D4—4312no—
669C2×D4—438no—
670C2×D4—434no—
671C2×D4—436no—
672C2×D4—8624no—
673C2×D4—8616no—
674C2×D4—8632no—
675C2×D4C23×D4318yes—
676C2×D4C23×D4314yes—
677C2×D4C23×D4316yes—
678C22×C4—212no—
679C22×C4—433no—
680C22×C4—4324no—
681C22×C4—436no—
682C22×C4—436no—
683C22×C4—4312no—
684C22×C4—4312no—
685C22×C4—433no—
686C22×C4—438no—
687C22×C4—436no—
688C22×C4—434no—
689C22×C4—4312no—
690C22×C4—4312no—
691C22×C4—4312no—
692C22×C4—4312no—
693C22×C4—436no—
694C22×C4—8612no—
695C22×C4—8648no—
696C22×C4—8648no—
697C22×C4—8648no—
698C22×C4—8612no—
699C22×C4—8612no—
700C22×C4—8612no—
701C22×C4C23×D43112yes—
702C22×C4C23×D43112yes—
703C22×C4C23×D4313yes—
704C22×C4C23×D4313yes—
705C4⋊C4—4324no—
706C4⋊C4—4312no—
707C4⋊C4—4324no—
708C4⋊C4—4324no—
709C4⋊C4—4324no—
710C4⋊C4C23×D43112yes—
711C4⋊C4C23×D43124yes—
712C22⋊C4—434no—
713C22⋊C4—438no—
714C22⋊C4—4324no—
715C22⋊C4—438no—
716C22⋊C4—438no—
717C22⋊C4—438no—
718C22⋊C4—4324no—
719C22⋊C4—4324no—
720C22⋊C4C23×D4314yes—
721C22⋊C4C23×D4318yes—
722C22⋊C4C23×D43124yes—
723C42—4324no—
724C42—4312no—
725C42C23×D43112yes—
726C23—22no—
727C23—24no—
728C23—431no—
729C23—434no—
730C23—438no—
731C23—431no—
732C23—432no—
733C23—434no—
734C23—864no—
735C23—864no—
736C23—864no—
737C23—864no—
738C23—864no—
739C23—864no—
740C23—868no—
741C23—8616no—
742C23—8632no—
743C23—862no—
744C23—864no—
745C23C24×D4314yes—
746C23C24×D4311yescharacteristic
747C23C24×D4312yes—
748Q8—224no—
749Q8—212no—
750Q8—4348no—
751Q8—8648no—
752Q8—8624no—
753Q8—8624no—
754Q8—8612no—
755Q8C2×D4×D43116yes—
756D4—28no—
757D4—216no—
758D4—212no—
759D4—868no—
760D4—8616no—
761D4—8624no—
762D4—868no—
763D4—8616no—
764D4—868no—
765D4—8616no—
766D4—8612no—
767C2×C4—26no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—4312no—
771C2×C4—436no—
772C2×C4—4324no—
773C2×C4—4324no—
774C2×C4—438no—
775C2×C4—436no—
776C2×C4—434no—
777C2×C4—8624no—
778C2×C4—8624no—
779C2×C4—868no—
780C2×C4—8612no—
781C2×C4—8612no—
782C2×C4—8616no—
783C2×C4—8624no—
784C2×C4—8624no—
785C2×C4—866no—
786C2×C4—8624no—
787C2×C4—8624no—
788C2×C4C2×D4×D43112yes—
789C2×C4C24×D4318yes—
790C2×C4C24×D4316yes—
791C2×C4C24×D4314yes—
792C2×C4C24×D4316yes—
793C22—28no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—28no—
799C22—432no—
800C22—434no—
801C22—432no—
802C22—434no—
803C22—868no—
804C22—8616no—
805C22—868no—
806C22—8616no—
807C22—862no—
808C22—862no—
809C22—862no—
810C22—864no—
811C22—868no—
812C22—17216no—
813C22C22×D4×D4312yes—
814C222−1+4×D4314yescomplemented
815C22C25×D4311yescharacteristic
816C4—24no—
817C4—26no—
818C4—28no—
819C4—4312no—
820C4—864no—
821C4—866no—
822C4—868no—
823C4C22×D4×D43112yes—
824C2—22no—
825C2—24no—
826C2—44no—
827C2—434no—
828C2—862no—
829C2—864no—
830C2—1724no—
831C2C23×D4×D4311yescharacteristic
832C2C2×2−1+4×D4312yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3486C2
hypercenter#3486D43
hypocenterC43C2×#3486
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D43C2semidirect
2. C23×Q8×D43C2semidirect
3. #19148247C2semidirect
4. #19148246C2semidirect
5. #19148245C2semidirect
6. #19148244C2semidirect
7. #19148243C2semidirect
8. #19148242C2semidirect
9. #19148241C2semidirect
10. D4×Q8×D43C2semidirect
11. #548×D43C2semidirect
12. #536×D43C2semidirect
13. #525×D43C2semidirect
14. #519×D43C2semidirect
15. C43×#3486C2semidirect
16. C2×#13063373C22semidirect
17. C2×#13063373C22semidirect
18. C2×#13063372C22semidirect
19. C2×#13063372C22semidirect
22. C2×#41×D43C22semidirect
23. C23×Dic86C22semidirect
28. C22×Q8×D43C22semidirect
29. C22×Q8×D43C22semidirect
30. C22×Q8×D43C22semidirect
31. C22×Q8×D43C22semidirect
33. Q8×D172C22semidirect
34. D4×Dic86C22semidirect
35. #14583564C22semidirect
36. Q8×C22⋊D43C22semidirect
37. Q8×C22⋊D43C22semidirect
38. #14583562C22semidirect
39. #14583562C22semidirect
40. #14583561C22semidirect
41. #14583560C22semidirect
42. #14583559C22semidirect
43. #14583558C22semidirect
44. #14583557C22semidirect
45. #14583556C22semidirect
46. #14583555C22semidirect
47. #14583475C22semidirect
48. #14583474C22semidirect
49. #14583473C22semidirect
50. #14583472C22semidirect
51. #14583471C22semidirect
52. #14583470C22semidirect
53. #14583469C22semidirect
54. C4⋊Q8×D43C22semidirect
55. #124×D43C22semidirect
56. #14583412C22semidirect
57. #14583411C22semidirect
58. #14583410C22semidirect
59. #14583409C22semidirect
60. #14583408C22semidirect
61. #14583407C22semidirect
62. #14583406C22semidirect
63. #14583405C22semidirect
66. C22⋊Q8×D43C22semidirect
69. #14583377C22semidirect
70. #14583376C22semidirect
71. #14583375C22semidirect
72. C4×Q8×D43C22semidirect
75. C2×2−1+4×C43C22semidirect
76. C23×Q8×C43C22semidirect
77. D4×Q8×C43C22semidirect
78. C43×#548C22semidirect
79. C43×#536C22semidirect
80. C43×#525C22semidirect
81. C43×#519C22semidirect
88. C2×#10621902C23semidirect
91. C2×#10621898C23semidirect
94. C2×#10621900C23semidirect
102. C22×Dic86C23semidirect
109. C2×Q8×D43D4semidirect
117. C2×Q8×D43C23semidirect
118. C2×Q8×D43C23semidirect
131. #13063325C23semidirect
132. #13063324C23semidirect
133. #13063323C23semidirect
134. #13063323C23semidirect
135. #13063314C23semidirect
136. #13063313C23semidirect
137. #13063312C23semidirect
138. #13063311C23semidirect
145. #13063305C23semidirect
147. #13063304C23semidirect
149. #13063303C23semidirect
151. #13063302C23semidirect
153. #13063301C23semidirect
164. Q8×Dic43C23semidirect
165. C4×Dic86C23semidirect
166. #13063290C23semidirect
186. C2×#41×C43C23semidirect
191. C22×Q8×C43C23semidirect
193. C4⋊Q8×C43C23semidirect
194. #124×C43C23semidirect
197. C22⋊Q8×C43C23semidirect
200. C4×Q8×C43C23semidirect
216. C2×Q8×C43C2×D4semidirect
248. Q8×D43C2×D4semidirect
282. C2×Dic86C2×D4semidirect
326. C22×D432−1+4semidirect
384. C22×C43C2×2−1+4semidirect
399. C2×D43C2×2−1+4semidirect
417. #3486D43direct (N × H)
431. D43#3486direct (N × H)
437. C2×2−1+4C2×D43semidirect
449. C23×Q8C2×D43semidirect
458. D4×Q8C2×D43semidirect
466. #548C2×D43semidirect
474. #536C2×D43semidirect
485. #525C2×D43semidirect
494. #519C2×D43semidirect
498. C43C2×#3486semidirect
516. C2×#41C22×D43semidirect
543. C22×Q8C22×D43semidirect
561. C4⋊Q8C22×D43semidirect
566. #124C22×D43semidirect
584. C22⋊Q8C22×D43semidirect
600. C4×Q8C22×D43semidirect
660. C2×Q8D4×D43semidirect
814. C222−1+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
C23×Q8×D432
#191482472
#191482462
#191482452
#191482442
#191482432
#191482422
#191482412
D4×Q8×D432
#548×D432
#536×D432
#525×D432
#519×D432
C43×#34862
C2×#348643