Finite Group Databasebeta

← D43×#3548 #26004386

Subgroups — D43×#3548 #26004386

Order 11008.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148995C211yesmaximal, characteristic, complemented
2#19148994C214yesmaximal, complemented
3#19148993C212yesmaximal, complemented
4#19148992C214yesmaximal, complemented
5#19148991C214yesmaximal, complemented
6#19148990C218yesmaximal, complemented
7#19148989C214yesmaximal, complemented
8#19148988C214yesmaximal, complemented
9#562×D43C214yesmaximal, complemented
10#554×D43C214yesmaximal, complemented
11#550×D43C214yesmaximal, complemented
12#547×D43C214yesmaximal, complemented
13#540×D43C214yesmaximal, complemented
14#537×D43C218yesmaximal, complemented
15#533×D43C211yesmaximal, characteristic, complemented
16#532×D43C212yesmaximal, complemented
17C43×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D43C2218yes—
19C2×#41×D43C2214yes—
20#14583647C2214yescomplemented
21#14583646C22116yescomplemented
22#14583645C22116yescomplemented
23#14583644C22116yescomplemented
24#14583643C2218yescomplemented
25#14583610C2214yescomplemented
26#14583609C2214yescomplemented
27#14583608C2218yescomplemented
28#14583607C2218yescomplemented
29#14583606C2214yescomplemented
30#14583605C2218yescomplemented
31#14583604C2218yescomplemented
32#14583603C22116yescomplemented
33#14583571C2214yescomplemented
34#14583570C2218yescomplemented
35#14583570C2214yescomplemented
36#14583569C2218yescomplemented
37#14583569C2214yescomplemented
38#14583568C2218yescomplemented
39#14583567C22116yescomplemented
40#14583567C2218yescomplemented
41#14583554C2214yescomplemented
42#14583553C2214yescomplemented
43#14583552C2214yescomplemented
44#14583551C2218yescomplemented
45#14583550C2218yescomplemented
46#14583549C2218yescomplemented
47#14583548C2218yescomplemented
48#14583547C22116yescomplemented
49#14583505C2214yescomplemented
50#14583504C2214yescomplemented
51#14583503C2214yescomplemented
52#14583502C2218yescomplemented
53#14583501C22116yescomplemented
54#14583500C2218yescomplemented
55#14583499C22116yescomplemented
56#14583480C2218yescomplemented
57#14583479C2218yescomplemented
58#14583479C22116yescomplemented
59#14583479C2218yescomplemented
60#14583478C2218yescomplemented
61#14583478C22116yescomplemented
62#14583478C2218yescomplemented
63#14583477C2218yescomplemented
64#14583477C2218yescomplemented
65#14583476C22116yescomplemented
66#14583476C22116yescomplemented
67#14583456C2211yescharacteristic, complemented
68#14583455C2212yescomplemented
69#14583454C2212yescomplemented
70#14583453C2214yescomplemented
71#14583452C2212yescomplemented
72#14583451C2214yescomplemented
73#14583450C2212yescomplemented
74#14583449C2212yescomplemented
75#14583448C2214yescomplemented
76#14583447C2212yescomplemented
77#14583446C2214yescomplemented
78#14583446C2214yescomplemented
79#14583445C2214yescomplemented
80#14583444C2214yescomplemented
81#14583444C2214yescomplemented
82C4⋊Q8×D43C2212yes—
83C4⋊Q8×D43C2212yes—
84#127×D43C2212yes—
85#127×D43C2214yes—
86#125×D43C2214yes—
87#125×D43C2212yes—
88#124×D43C2214yes—
89#123×D43C22116yes—
90C22⋊Q8×D43C2218yes—
91C22⋊Q8×D43C22116yes—
92C22⋊Q8×D43C2214yes—
93#121×D43C2218yes—
94#121×D43C22116yes—
95#121×D43C2214yes—
96#121×D43C2214yes—
97#121×D43C22116yes—
98C4×Q8×D43C2214yes—
99C4×D4×D43C2214yes—
100C4×D4×D43C2214yes—
101C4×D4×D43C2218yes—
102#117×D43C2212yes—
103C2×C4⋊C4×D43C2218yes—
104C2×C42×D43C2211yescharacteristic
105C43×#562C2214yescomplemented
106C43×#554C2214yescomplemented
107C43×#550C2214yescomplemented
108C43×#547C2214yescomplemented
109C43×#540C2214yescomplemented
110C43×#537C2218yescomplemented
111C43×#533C2211yescharacteristic, complemented
112C43×#532C2212yescomplemented
113C2×#10621902C2318yes—
114C2×#10621902C2314yes—
115C2×#10621898C2318yes—
116C2×#10621898C23116yes—
117C2×#10621898C2314yes—
118C2×#10621898C2318yes—
119C2×#10621900C2318yes—
120C2×#10621900C23116yes—
121C2×#10621900C2318yes—
122C2×#10621900C2314yes—
123#41×D43—416no—
124#41×D43—432no—
125C2×Q8×D43C2314yes—
126C2×Q8×D43C2314yes—
127C2×D4×D43C2314yes—
128C2×D4×D43C2314yes—
129C2×D4×D43C2318yes—
130C2×D4×D43C23116yes—
131C2×D4×D43C2314yes—
132C22×C4×D43C2311yescharacteristic
133C22×C4×D43C2312yes—
134C22×C4×D43C2318yes—
135C22×C4×D43C23116yes—
136#13063325C2312yes—
137#13063325C2312yes—
138#13063324C2314yes—
139#13063324C2314yes—
140#13063324C2314yes—
141#13063324C2314yes—
142#13063323C2314yes—
143#13063323C2314yes—
144#13063322C2312yes—
145#13063322C2314yes—
146#13063321C2314yes—
147#13063321C23116yes—
148#13063321C2314yes—
149#13063321C2314yes—
150#13063321C2318yes—
151#13063317C2314yes—
152#13063317C2312yes—
153#13063316C2318yes—
154#13063316C2314yes—
155#13063315C23116yes—
156#13063315C2318yes—
157#13063314C2314yes—
158#13063313C2314yes—
159#13063312C2314yes—
160#13063311C2318yes—
161#13063311C2318yes—
162#13063310C23116yes—
163#13063310C23116yes—
164#13063309C23116yes—
165#13063308C23116yes—
166#13063307C23116yes—
167#13063307C23116yes—
168#13063306C23116yes—
169#13063305C2318yes—
170#13063305C23116yes—
171#13063305C2314yes—
172#13063304C2318yes—
173#13063304C23116yes—
174#13063304C2314yes—
175#13063303C23116yes—
176#13063303C23116yes—
177#13063303C23116yes—
178#13063303C2318yes—
179#13063302C23116yes—
180#13063302C23116yes—
181#13063302C23116yes—
182#13063302C2318yes—
183#13063301C2318yes—
184#13063301C23116yes—
185#13063301C2314yes—
186#13063300C2318yes—
187#13063300C23116yes—
188#13063300C2314yes—
189#13063300C2314yes—
190#13063300C23116yes—
191#13063299C2318yes—
192#13063299C23116yes—
193#13063299C2314yes—
194#13063299C2314yes—
195#13063299C23116yes—
196#13063298C23116yes—
197#13063298C23116yes—
198#13063298C23116yes—
199#13063298C2318yes—
200#13063298C2318yes—
201#13063298C23116yes—
202#13063298C23116yes—
203#13063297C23116yes—
204#13063297C23116yes—
205#13063297C23116yes—
206#13063297C2318yes—
207#13063297C2318yes—
208#13063297C23116yes—
209#13063297C23116yes—
210#13063296C2318yes—
211#13063296C23116yes—
212#13063296C2314yes—
213#13063296C2314yes—
214#13063296C23116yes—
215Q8×Dic43C2314yes—
216C4×Dic86C2318yes—
217C4×Dic86C2314yes—
218#13063290C2318yes—
219#13063290C2314yes—
220C4×D172C2314yes—
221C4×D172C2318yes—
222C4×D172C2314yes—
223D4×Dic43C2318yes—
224D4×Dic43C2314yes—
225D4×Dic43C2314yes—
226#13063287C2314yes—
227#13063287C2318yes—
228#13063287C2314yes—
229C4×C22⋊D43C23116yes—
230C4×C22⋊D43C2318yes—
231C4×C22⋊D43C2318yes—
232(C22⋊D43)⋊C4C2318yes—
233(C22⋊D43)⋊C4C23116yes—
234(C22⋊D43)⋊C4C2318yes—
235#13063284C2312yes—
236#13063283C2314yes—
237#13063282C2314yes—
238#13063281C2314yes—
239C2×C4⋊Dic43C2318yes—
240C2×Dic43⋊C4C23116yes—
241C4⋊C4×D43C2318yes—
242C4⋊C4×D43C2318yes—
243C4⋊C4×D43C23116yes—
244C4⋊C4×D43C2314yes—
245C4⋊C4×D43C2314yes—
246C4⋊C4×D43C23116yes—
247C4⋊C4×D43C2314yes—
248C4⋊C4×D43C2314yes—
249C4⋊C4×D43C2318yes—
250C22⋊C4×D43C2314yes—
251C22⋊C4×D43C23116yes—
252C22⋊C4×D43C2318yes—
253C22⋊C4×D43C2318yes—
254C2×C4×Dic43C2311yescharacteristic
255C2×C4×Dic43C2312yes—
256C42×D43C2311yescharacteristic
257C42×D43C2312yes—
258C42×D43C2311yescharacteristic
259C42×D43C2311yescharacteristic
260C42×D43C2312yes—
261C42×D43C2311yescharacteristic
262C42×D43C2314yes—
263C2×#41×C43C2318yes—
264C2×#41×C43C2314yes—
265C4⋊Q8×C43C2312yes—
266C4⋊Q8×C43C2312yes—
267#127×C43C2312yes—
268#127×C43C2314yes—
269#125×C43C2312yes—
270#125×C43C2314yes—
271#124×C43C2314yes—
272#123×C43C23116yes—
273C22⋊Q8×C43C2314yes—
274C22⋊Q8×C43C2318yes—
275C22⋊Q8×C43C23116yes—
276#121×C43C2318yes—
277#121×C43C23116yes—
278#121×C43C2314yes—
279#121×C43C2314yes—
280#121×C43C23116yes—
281C4×Q8×C43C2314yes—
282C4×D4×C43C2314yes—
283C4×D4×C43C2314yes—
284C4×D4×C43C2318yes—
285#117×C43C2312yes—
286C2×C4⋊C4×C43C2318yes—
287C2×C42×C43C2311yescharacteristic
288C23×D43C2411yescharacteristic
289C23×D43C2418yes—
290#41×C43—48no—
291#41×C43—416no—
292C2×Q8×C43C2414yes—
293C2×Q8×C43C2414yes—
294C2×D4×C43C2414yes—
295C2×D4×C43C2414yes—
296C2×D4×C43C2418yes—
297C2×D4×C43C24116yes—
298C2×D4×C43C2414yes—
299C22×C4×C43C2411yescharacteristic
300C22×C4×C43C2412yes—
301C22×C4×C43C2418yes—
302C22×C4×C43C24116yes—
303C2×C22⋊D43C2418yes—
304C2×C22⋊D43C2418yes—
305C2×C22⋊D43C2418yes—
306C2×C22⋊D43C2418yes—
307C2×C22⋊D43C24116yes—
308C2×C22⋊D43C2418yes—
309C2×C22⋊D43C24116yes—
310C22×Dic43C2411yescharacteristic
311C22×Dic43C2412yes—
312C22×Dic43C2418yes—
313C22×Dic43C24116yes—
314#10621902—48no—
315#10621902—416no—
316Q8×D43—216no—
317Q8×D43—48no—
318#10621900—416no—
319#10621900—432no—
320#10621900—416no—
321#10621900—48no—
322D4×D43—216no—
323D4×D43—216no—
324D4×D43—416no—
325D4×D43—48no—
326D4×D43—432no—
327#10621898—432no—
328#10621898—416no—
329#10621898—416no—
330#10621898—48no—
331C2×D172C2414yes—
332C2×D172C2414yes—
333C2×D172C2418yes—
334C2×D172C2414yes—
335C2×D172C24116yes—
336C2×C4×D43—232no—
337C2×C4×D43—28no—
338C2×C4×D43—24no—
339C2×C4×D43—432no—
340C2×C4×D43C2411yescharacteristic
341C2×C4×D43C2412yes—
342C2×C4×D43C2411yescharacteristic
343C2×C4×D43C2411yescharacteristic
344C2×C4×D43C2412yes—
345C2×C4×D43C2412yes—
346C2×C4×D43C2418yes—
347C2×C4×D43C2418yes—
348C2×C4×D43C2418yes—
349C2×C4×D43C2418yes—
350C2×C4×D43C24116yes—
351C2×C4×D43C24116yes—
352C2×C4×D43C2412yes—
353C2×C4×D43C2411yescharacteristic
354C2×Dic86C2418yes—
355C2×Dic86C2414yes—
356C2×Dic86C2414yes—
357C2×Dic86C2418yes—
358C4⋊C4×C43C2414yes—
359C4⋊C4×C43C2414yes—
360C4⋊C4×C43C24116yes—
361C4⋊C4×C43C2414yes—
362C4⋊C4×C43C2414yes—
363C4⋊C4×C43C2418yes—
364C22⋊C4×C43C2414yes—
365C22⋊C4×C43C24116yes—
366C22⋊C4×C43C2418yes—
367C22⋊C4×C43C2418yes—
368C42×C43C2411yescharacteristic
369C42×C43C2412yes—
370C42×C43C2411yescharacteristic
371C42×C43C2414yes—
372C22⋊Dic43C2414yes—
373C22⋊Dic43C24116yes—
374C22⋊Dic43C2418yes—
375C22⋊Dic43C2418yes—
376(C2×D43)⋊C4C2418yes—
377(C2×D43)⋊C4C2418yes—
378(C2×D43)⋊C4C24116yes—
379(C2×D43)⋊C4C2418yes—
380(C2×D43)⋊C4C24116yes—
381(C2×D43)⋊C4C2418yes—
382(C2×D43)⋊C4C2418yes—
383C4⋊Dic43C2414yes—
384C4⋊Dic43C2414yes—
385C4⋊Dic43C24116yes—
386C4⋊Dic43C2414yes—
387C4⋊Dic43C2414yes—
388C4⋊Dic43C2418yes—
389Dic43⋊C4C2418yes—
390Dic43⋊C4C2418yes—
391Dic43⋊C4C24116yes—
392Dic43⋊C4C24116yes—
393Dic43⋊C4C2418yes—
394Dic43⋊C4C2418yes—
395Dic43⋊C4C2418yes—
396Dic43⋊C4C2418yes—
397C4×Dic43C2411yescharacteristic
398C4×Dic43C2412yes—
399C4×Dic43C2412yes—
400C4×Dic43C2412yes—
401C4×Dic43C2412yes—
402C4×Dic43C2411yescharacteristic
403C4×Dic43C2412yes—
404C4×Dic43C2418yes—
405C4×Dic43C2414yes—
406C23×C43C2511yescharacteristic
407C23×C43C2518yes—
408C22×D43—24no—
409C22×D43—216no—
410C22×D43—216no—
411C22×D43—22no—
412C22×D43—216no—
413C22×D43C2511yescharacteristic
414C22×D43C2518yes—
415C22×D43C2511yescharacteristic
416Q8×C43—28no—
417Q8×C43—44no—
418D4×C43—28no—
419D4×C43—28no—
420D4×C43—416no—
421D4×C43—44no—
422D4×C43—48no—
423C2×C4×C43—24no—
424C2×C4×C43—216no—
425C2×C4×C43—22no—
426C2×C4×C43—416no—
427C2×C4×C43C2512yes—
428C2×C4×C43C2511yescharacteristic
429C2×C4×C43C2518yes—
430C2×C4×C43C2518yes—
431C2×C4×C43C2512yes—
432C2×C4×C43C2511yescharacteristic
433C22⋊D43—216no—
434C22⋊D43—216no—
435C22⋊D43—416no—
436C22⋊D43—416no—
437C22⋊D43—48no—
438C22⋊D43—48no—
439C22⋊D43—48no—
440C2×Dic43—24no—
441C2×Dic43—216no—
442C2×Dic43—22no—
443C2×Dic43—416no—
444C2×Dic43C2511yescharacteristic
445C2×Dic43C2512yes—
446C2×Dic43C2518yes—
447C2×Dic43C2518yes—
448C2×Dic43C2512yes—
449C2×Dic43C2511yescharacteristic
450D172—28no—
451D172—28no—
452D172—416no—
453D172—44no—
454D172—48no—
455C4×D43—216no—
456C4×D43—24no—
457C4×D43—216no—
458C4×D43—22no—
459C4×D43—24no—
460C4×D43—216no—
461C4×D43—22no—
462C4×D43—216no—
463C4×D43—24no—
464C4×D43—22no—
465C4×D43—416no—
466C4×D43—416no—
467C4×D43H(5,𝔽2)18yes—
468C4×D432−1+414yes—
469Dic86—28no—
470Dic86—216no—
471Dic86—48no—
472Dic86—44no—
473C2×#3548—431nomaximal, Sylow
474C22×C43—22no—
475C22×C43—28no—
476C22×C43—28no—
477C22×C43—21no—
478C22×C43—28no—
479C22×C43C2611yescharacteristic
480C2×D43—22no—
481C2×D43—28no—
482C2×D43—28no—
483C2×D43—21no—
484C2×D43—28no—
485C2×D43—44no—
486C2×D43—432no—
487C2×D43C2×H(5,𝔽2)14yes—
488C2×D43C2×2−1+412yes—
489C4×C43—28no—
490C4×C43—22no—
491C4×C43—28no—
492C4×C43—21no—
493C4×C43C2×H(5,𝔽2)14yes—
494C4×C43C2×2−1+412yes—
495Dic43—28no—
496Dic43—22no—
497Dic43—28no—
498Dic43—21no—
499Dic43C2×H(5,𝔽2)14yes—
500Dic43C2×2−1+412yes—
501#3548—434no—
502#3548—434no—
503#3548—434no—
504#3548—434no—
505#3548—434no—
506#3548—438no—
507#3548—431no—
508#3548—432no—
509#3548D4311yescharacteristic, direct product factor
510C2×#562—434no—
511C2×#554—434no—
512C2×#550—434no—
513C2×#547—434no—
514C2×#540—434no—
515C2×#537—438no—
516C2×#533—431no—
517C2×#532—432no—
518C2×C43—41no—
519C2×C43—48no—
520C2×C43C22×H(5,𝔽2)12yes—
521C2×C43C22×2−1+411yescharacteristic
522D43—41no—
523D43—48no—
524D43#354814yesdirect product factor
525C22×#41—434no—
526C22×#41—438no—
527#562—434no—
528#562—438no—
529#562—4316no—
530#562—4316no—
531#562—4316no—
532#562C2×D4314yescomplemented
533#554—434no—
534#554—438no—
535#554—4316no—
536#554—438no—
537#554—434no—
538#554—434no—
539#554—438no—
540#554—438no—
541#554C2×D4314yescomplemented
542#550—438no—
543#550—438no—
544#550—434no—
545#550—438no—
546#550—4316no—
547#550—434no—
548#550—438no—
549#550—434no—
550#550C2×D4314yescomplemented
551#547—438no—
552#547—434no—
553#547—4316no—
554#547—438no—
555#547—438no—
556#547—434no—
557#547—434no—
558#547—438no—
559#547C2×D4314yescomplemented
560#540—434no—
561#540—434no—
562#540—4316no—
563#540—4316no—
564#540—438no—
565#540—438no—
566#540—434no—
567#540C2×D4314yescomplemented
568#537—438no—
569#537—438no—
570#537—438no—
571#537—4316no—
572#537—438no—
573#537—4316no—
574#537—4316no—
575#537—438no—
576#537—4316no—
577#537—438no—
578#537—438no—
579#537C2×D4318yescomplemented
580#533—432no—
581#533—432no—
582#533—434no—
583#533—434no—
584#533—432no—
585#533—431no—
586#533C2×D4311yescharacteristic, complemented
587#532—434no—
588#532—432no—
589#532—432no—
590#532—434no—
591#532—434no—
592#532—434no—
593#532—434no—
594#532—434no—
595#532—432no—
596#532C2×D4312yescomplemented
597C2×C4⋊Q8—432no—
598C2×C4⋊Q8—432no—
599C2×#127—432no—
600C2×#127—434no—
601C2×#125—432no—
602C2×#125—434no—
603C2×#124—434no—
604C2×#123—4316no—
605C2×C22⋊Q8—434no—
606C2×C22⋊Q8—438no—
607C2×C22⋊Q8—4316no—
608C2×#121—434no—
609C2×#121—434no—
610C2×#121—4316no—
611C2×#121—438no—
612C2×#121—4316no—
613C2×C4×Q8—434no—
614C2×C4×D4—434no—
615C2×C4×D4—434no—
616C2×C4×D4—438no—
617C2×#117—432no—
618C22×C4⋊C4—438no—
619C22×C42—431no—
620C43C2×#354811yescharacteristic, complemented, Sylow
621C2×#41—434no—
622C2×#41—438no—
623C2×#41—438no—
624C2×#41—434no—
625C2×#41—4316no—
626C2×#41—438no—
627C2×#41—438no—
628C2×#41—434no—
629C2×#41—4316no—
630C2×#41—438no—
631C2×#41—17216no—
632C2×#41—17232no—
633C2×#41C22×D4314yes—
634C2×#41C22×D4318yes—
635C22×Q8—434no—
636C22×Q8—434no—
637C22×D4—434no—
638C22×D4—434no—
639C22×D4—438no—
640C22×D4—4316no—
641C22×D4—434no—
642C23×C4—438no—
643C23×C4—431no—
644C23×C4—432no—
645C23×C4—4316no—
646C4⋊Q8—434no—
647C4⋊Q8—434no—
648C4⋊Q8—434no—
649C4⋊Q8—434no—
650C4⋊Q8—434no—
651C4⋊Q8—434no—
652C4⋊Q8—432no—
653C4⋊Q8—432no—
654C4⋊Q8C22×D4312yes—
655C4⋊Q8C22×D4312yes—
656#127—434no—
657#127—434no—
658#127—434no—
659#127—4316no—
660#127—438no—
661#127—432no—
662#127—434no—
663#127C22×D4312yes—
664#127C22×D4314yes—
665#125—438no—
666#125—434no—
667#125—4316no—
668#125—438no—
669#125—432no—
670#125—434no—
671#125C22×D4312yes—
672#125C22×D4314yes—
673#124—434no—
674#124—434no—
675#124—438no—
676#124—438no—
677#124—434no—
678#124C22×D4314yes—
679#123—4316no—
680#123—4316no—
681#123—4316no—
682#123—4316no—
683#123—4316no—
684#123—4316no—
685#123—4316no—
686#123C22×D43116yes—
687C22⋊Q8—434no—
688C22⋊Q8—438no—
689C22⋊Q8—4316no—
690C22⋊Q8—434no—
691C22⋊Q8—438no—
692C22⋊Q8—4316no—
693C22⋊Q8—438no—
694C22⋊Q8—434no—
695C22⋊Q8—4316no—
696C22⋊Q8—438no—
697C22⋊Q8—4316no—
698C22⋊Q8—4316no—
699C22⋊Q8—4316no—
700C22⋊Q8—438no—
701C22⋊Q8—4316no—
702C22⋊Q8—4316no—
703C22⋊Q8—4316no—
704C22⋊Q8C22×D4314yes—
705C22⋊Q8C22×D4318yes—
706C22⋊Q8C22×D43116yes—
707#121—434no—
708#121—438no—
709#121—434no—
710#121—438no—
711#121—4316no—
712#121—4316no—
713#121—4316no—
714#121—438no—
715#121—4316no—
716#121—4316no—
717#121—4316no—
718#121—4316no—
719#121—434no—
720#121—434no—
721#121—4316no—
722#121—438no—
723#121—4316no—
724#121—434no—
725#121—434no—
726#121—4316no—
727#121—438no—
728#121—4316no—
729#121—438no—
730#121—438no—
731#121—4316no—
732#121—4316no—
733#121—4316no—
734#121—4316no—
735#121—4316no—
736#121C22×D4314yes—
737#121C22×D4314yes—
738#121C22×D43116yes—
739#121C22×D4318yes—
740#121C22×D43116yes—
741C4×Q8—434no—
742C4×Q8—438no—
743C4×Q8—434no—
744C4×Q8—438no—
745C4×Q8—434no—
746C4×Q8C22×D4314yes—
747C4×D4—434no—
748C4×D4—434no—
749C4×D4—438no—
750C4×D4—438no—
751C4×D4—438no—
752C4×D4—4316no—
753C4×D4—434no—
754C4×D4—434no—
755C4×D4—438no—
756C4×D4—438no—
757C4×D4—438no—
758C4×D4—4316no—
759C4×D4—434no—
760C4×D4—434no—
761C4×D4—438no—
762C4×D4C22×D4314yes—
763C4×D4C22×D4314yes—
764C4×D4C22×D4318yes—
765#117—432no—
766#117—434no—
767#117—434no—
768#117—434no—
769#117C22×D4312yes—
770C2×C4⋊C4—4316no—
771C2×C4⋊C4—438no—
772C2×C4⋊C4—434no—
773C2×C4⋊C4—434no—
774C2×C4⋊C4—4316no—
775C2×C4⋊C4—4316no—
776C2×C4⋊C4—438no—
777C2×C4⋊C4—438no—
778C2×C4⋊C4—434no—
779C2×C4⋊C4—434no—
780C2×C4⋊C4—438no—
781C2×C4⋊C4C22×D4318yes—
782C2×C22⋊C4—434no—
783C2×C22⋊C4—4316no—
784C2×C22⋊C4—438no—
785C2×C22⋊C4—438no—
786C2×C42—432no—
787C2×C42—431no—
788C2×C42—434no—
789C2×C42—431no—
790C2×C42—432no—
791C2×C42—431no—
792C2×C42—431no—
793C2×C42—432no—
794C2×C42—431no—
795C2×C42C22×D4311yescharacteristic
796C24—431no—
797C24—438no—
798#41—48no—
799#41—416no—
800#41—17216no—
801#41—1728no—
802#41—17216no—
803#41—17232no—
804#41—17216no—
805#41—1728no—
806#41—1728no—
807#41—17216no—
808#41—17232no—
809#41—17216no—
810C2×Q8—438no—
811C2×Q8—434no—
812C2×Q8—438no—
813C2×Q8—434no—
814C2×Q8—8616no—
815C2×Q8—1728no—
816C2×Q8C23×D4314yes—
817C2×Q8C23×D4314yes—
818C2×D4—438no—
819C2×D4—438no—
820C2×D4—438no—
821C2×D4—438no—
822C2×D4—4316no—
823C2×D4—4316no—
824C2×D4—438no—
825C2×D4—434no—
826C2×D4—434no—
827C2×D4—438no—
828C2×D4—4316no—
829C2×D4—434no—
830C2×D4—8616no—
831C2×D4—8616no—
832C2×D4—17216no—
833C2×D4—1728no—
834C2×D4—17232no—
835C2×D4C23×D4314yes—
836C2×D4C23×D4314yes—
837C2×D4C23×D4318yes—
838C2×D4C23×D43116yes—
839C2×D4C23×D4314yes—
840C22×C4—431no—
841C22×C4—432no—
842C22×C4—431no—
843C22×C4—432no—
844C22×C4—438no—
845C22×C4—4316no—
846C22×C4—431no—
847C22×C4—432no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—438no—
853C22×C4—438no—
854C22×C4—438no—
855C22×C4—438no—
856C22×C4—4316no—
857C22×C4—4316no—
858C22×C4—8632no—
859C22×C4—868no—
860C22×C4—864no—
861C22×C4—17232no—
862C22×C4C23×D4311yescharacteristic
863C22×C4C23×D4312yes—
864C22×C4C23×D4318yes—
865C22×C4C23×D43116yes—
866C4⋊C4—438no—
867C4⋊C4—434no—
868C4⋊C4—438no—
869C4⋊C4—434no—
870C4⋊C4—4316no—
871C4⋊C4—4316no—
872C4⋊C4—4316no—
873C4⋊C4—438no—
874C4⋊C4—434no—
875C4⋊C4—438no—
876C4⋊C4—434no—
877C4⋊C4—438no—
878C4⋊C4—438no—
879C4⋊C4—438no—
880C4⋊C4C23×D4314yes—
881C4⋊C4C23×D4314yes—
882C4⋊C4C23×D43116yes—
883C4⋊C4C23×D4314yes—
884C4⋊C4C23×D4314yes—
885C4⋊C4C23×D4318yes—
886C22⋊C4—434no—
887C22⋊C4—4316no—
888C22⋊C4—438no—
889C22⋊C4—438no—
890C22⋊C4—438no—
891C22⋊C4—4316no—
892C22⋊C4—4316no—
893C22⋊C4—438no—
894C22⋊C4—438no—
895C22⋊C4—438no—
896C22⋊C4—438no—
897C22⋊C4C23×D4314yes—
898C22⋊C4C23×D43116yes—
899C22⋊C4C23×D4318yes—
900C22⋊C4C23×D4318yes—
901C42—431no—
902C42—432no—
903C42—432no—
904C42—432no—
905C42—432no—
906C42—432no—
907C42—431no—
908C42—438no—
909C42—434no—
910C42C23×D4311yescharacteristic
911C42C23×D4312yes—
912C42C23×D4311yescharacteristic
913C42C23×D4314yes—
914C23—431no—
915C23—431no—
916C23—438no—
917C23—864no—
918C23—8616no—
919C23—862no—
920C23—8616no—
921C23—8616no—
922C23C24×D4311yescharacteristic
923C23C24×D4318yes—
924Q8—28no—
925Q8—44no—
926Q8—8616no—
927Q8—868no—
928Q8—1728no—
929Q8—1724no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—8616no—
936D4—8616no—
937D4—868no—
938D4—868no—
939D4—1728no—
940D4—1724no—
941D4—17216no—
942D4—1728no—
943D4—1728no—
944D4—1728no—
945D4—17216no—
946D4—17216no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—431no—
952C2×C4—432no—
953C2×C4—438no—
954C2×C4—434no—
955C2×C4—431no—
956C2×C4—432no—
957C2×C4—438no—
958C2×C4—438no—
959C2×C4—8616no—
960C2×C4—864no—
961C2×C4—862no—
962C2×C4—8616no—
963C2×C4—864no—
964C2×C4—862no—
965C2×C4—8616no—
966C2×C4—8616no—
967C2×C4—864no—
968C2×C4—862no—
969C2×C4—8616no—
970C2×C4—864no—
971C2×C4—862no—
972C2×C4—17216no—
973C2×C4—17216no—
974C2×C4—17216no—
975C2×C4C24×D4311yescharacteristic
976C2×C4C24×D4312yes—
977C2×C4C24×D4318yes—
978C2×C4C24×D4318yes—
979C2×C4C24×D4312yes—
980C2×C4C24×D4311yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—434no—
987C22—432no—
988C22—862no—
989C22—868no—
990C22—868no—
991C22—861no—
992C22—868no—
993C22—1724no—
994C22—17232no—
995C22C25×D4311yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—434no—
1001C4—432no—
1002C4—868no—
1003C4—862no—
1004C4—868no—
1005C4—861no—
1006C4H(5,𝔽2)×D4314yes—
1007C42−1+4×D4312yes—
1008C2—41no—
1009C2—48no—
1010C2—434no—
1011C2—1721no—
1012C2—1728no—
1013C2C2×H(5,𝔽2)×D4312yes—
1014C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3548C2
hypercenter#3548D43
hypocenterC43C2×#3548
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #19148995C2semidirect
2. #19148994C2semidirect
3. #19148993C2semidirect
4. #19148992C2semidirect
5. #19148991C2semidirect
6. #19148990C2semidirect
7. #19148989C2semidirect
8. #19148988C2semidirect
9. #562×D43C2semidirect
10. #554×D43C2semidirect
11. #550×D43C2semidirect
12. #547×D43C2semidirect
13. #540×D43C2semidirect
14. #537×D43C2semidirect
15. #533×D43C2semidirect
16. #532×D43C2semidirect
17. C43×#3548C2semidirect
20. #14583647C22semidirect
21. #14583646C22semidirect
22. #14583645C22semidirect
23. #14583644C22semidirect
24. #14583643C22semidirect
25. #14583610C22semidirect
26. #14583609C22semidirect
27. #14583608C22semidirect
28. #14583607C22semidirect
29. #14583606C22semidirect
30. #14583605C22semidirect
31. #14583604C22semidirect
32. #14583603C22semidirect
33. #14583571C22semidirect
34. #14583570C22semidirect
35. #14583570C22semidirect
36. #14583569C22semidirect
37. #14583569C22semidirect
38. #14583568C22semidirect
39. #14583567C22semidirect
40. #14583567C22semidirect
41. #14583554C22semidirect
42. #14583553C22semidirect
43. #14583552C22semidirect
44. #14583551C22semidirect
45. #14583550C22semidirect
46. #14583549C22semidirect
47. #14583548C22semidirect
48. #14583547C22semidirect
49. #14583505C22semidirect
50. #14583504C22semidirect
51. #14583503C22semidirect
52. #14583502C22semidirect
53. #14583501C22semidirect
54. #14583500C22semidirect
55. #14583499C22semidirect
56. #14583480C22semidirect
57. #14583479C22semidirect
58. #14583479C22semidirect
59. #14583479C22semidirect
60. #14583478C22semidirect
61. #14583478C22semidirect
62. #14583478C22semidirect
63. #14583477C22semidirect
64. #14583477C22semidirect
65. #14583476C22semidirect
66. #14583476C22semidirect
67. #14583456C22semidirect
68. #14583455C22semidirect
69. #14583454C22semidirect
70. #14583453C22semidirect
71. #14583452C22semidirect
72. #14583451C22semidirect
73. #14583450C22semidirect
74. #14583449C22semidirect
75. #14583448C22semidirect
76. #14583447C22semidirect
77. #14583446C22semidirect
78. #14583446C22semidirect
79. #14583445C22semidirect
80. #14583444C22semidirect
81. #14583444C22semidirect
105. C43×#562C22semidirect
106. C43×#554C22semidirect
107. C43×#550C22semidirect
108. C43×#547C22semidirect
109. C43×#540C22semidirect
110. C43×#537C22semidirect
111. C43×#533C22semidirect
112. C43×#532C22semidirect
509. #3548D43direct (N × H)
524. D43#3548direct (N × H)
532. #562C2×D43semidirect
541. #554C2×D43semidirect
550. #550C2×D43semidirect
559. #547C2×D43semidirect
567. #540C2×D43semidirect
579. #537C2×D43semidirect
586. #533C2×D43semidirect
596. #532C2×D43semidirect
620. C43C2×#3548semidirect

Maximal subgroups

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

subgroupindex
#191489952
#191489942
#191489932
#191489922
#191489912
#191489902
#191489892
#191489882
#562×D432
#554×D432
#550×D432
#547×D432
#540×D432
#537×D432
#533×D432
#532×D432
C43×#35482
C2×#354843