Finite Group Databasebeta

← D43×#3330 #25973498

Subgroups — D43×#3330 #25973498

Order 11008.

2374 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#547×D43C211yesmaximal, characteristic, complemented
2#547×D43C211yesmaximal, characteristic, complemented
3#19146903C211yesmaximal, characteristic, complemented
4#19146902C211yesmaximal, characteristic, complemented
5#19146901C211yesmaximal, characteristic, complemented
6#19146900C211yesmaximal, characteristic, complemented
7#19146899C211yesmaximal, characteristic, complemented
8#19146898C212yesmaximal, complemented
9#19146897C211yesmaximal, characteristic, complemented
10#19146896C212yesmaximal, complemented
11#19146895C212yesmaximal, complemented
12#19146894C211yesmaximal, characteristic, complemented
13#19146893C212yesmaximal, complemented
14#487×D43C211yesmaximal, characteristic, complemented
15#484×D43C212yesmaximal, complemented
16#474×D43C211yesmaximal, characteristic, complemented
17#468×D43C212yesmaximal, complemented
18#461×D43C211yesmaximal, characteristic, complemented
19#449×D43C212yesmaximal, complemented
20C4×D8×D43C211yesmaximal, characteristic, complemented
21#436×D43C211yesmaximal, characteristic, complemented
22#417×D43C212yesmaximal, complemented
23C43×#3330C211yesmaximal, characteristic, complemented
24C2×#41×D43—21no—
25C2×#41×D43C2212yes—
26C2×SD16×D43C2212yes—
27C2×D8×D43C2211yescharacteristic
28C2×M16×D43C2212yes—
29#14583554C2211yescharacteristic, complemented
30#14583554C2211yescharacteristic, complemented
31#14583553C2211yescharacteristic, complemented
32#14583553C2211yescharacteristic, complemented
33#14583552C2211yescharacteristic, complemented
34#14583552C2211yescharacteristic, complemented
35#14583551—21no—
36#14583551C2212yescomplemented
37#14583550—21no—
38#14583550C2212yescomplemented
39#14583549—21no—
40#14583549C2212yescomplemented
41#14583548—21no—
42#14583548C2212yescomplemented
43#14583547—22no—
44#14583547—22no—
45C4⋊Q8×D43C2211yescharacteristic
46C4⋊Q8×D43C2211yescharacteristic
47#123×D43—22no—
48#123×D43—22no—
49C22⋊Q8×D43—21no—
50C22⋊Q8×D43C2212yes—
51#121×D43—21no—
52#121×D43C2212yes—
53C4×D4×D43C2211yescharacteristic
54C4×D4×D43C2211yescharacteristic
55C4×D4×D43C2211yescharacteristic
56C2×C4⋊C4×D43—21no—
57C2×C4⋊C4×D43C2212yes—
58#14583251C2211yescharacteristic, complemented
59#14583250C2211yescharacteristic, complemented
60#14583249C2211yescharacteristic, complemented
61#14583248C2212yescomplemented
62#14583248C2212yescomplemented
63#14583236C2212yescomplemented
64#14583236C2212yescomplemented
65#14583235C2212yescomplemented
66#14583234C2212yescomplemented
67#14583233C2212yescomplemented
68#14583233C2212yescomplemented
69#14583232C2212yescomplemented
70#14583180C2211yescharacteristic, complemented
71#14583179C2211yescharacteristic, complemented
72#14583178C2212yescomplemented
73#14583177C2212yescomplemented
74#14583176C2211yescharacteristic, complemented
75#14583148C2212yescomplemented
76#14583147C2212yescomplemented
77#14583146C2212yescomplemented
78#14583145C2212yescomplemented
79#14583144C2212yescomplemented
80#14583143C2212yescomplemented
81#14583142C2212yescomplemented
82#14583105C2211yescharacteristic, complemented
83#14583104C2211yescharacteristic, complemented
84#14583103C2212yescomplemented
85#14583102C2212yescomplemented
86#14583101C2211yescharacteristic, complemented
87#14583047C2212yescomplemented
88#14583046C2212yescomplemented
89#14583045C2212yescomplemented
90#14583044C2212yescomplemented
91#14583043C2212yescomplemented
92#14583042C2212yescomplemented
93#14583041C2212yescomplemented
94C4×D344C2211yescharacteristic, complemented
95D8×Dic43C2211yescharacteristic, complemented
96#14582981C2211yescharacteristic, complemented
97C4×#10621882C2211yescharacteristic, complemented
98C4×#10621882C2211yescharacteristic, complemented
99#14582979C2211yescharacteristic, complemented
100#14582979C2211yescharacteristic, complemented
101#14582978C2211yescharacteristic, complemented
102#14582977C2211yescharacteristic, complemented
103#14582976C2211yescharacteristic, complemented
104#14582975C2212yescomplemented
105#14582974C2212yescomplemented
106#107×D43C2211yescharacteristic
107#107×D43C2212yes—
108C4⋊C8×D43C2211yescharacteristic
109#14582901C2212yescomplemented
110#14582900C2212yescomplemented
111#14582899C2212yescomplemented
112#14582899C2212yescomplemented
113#14582898C2212yescomplemented
114#14582897C2212yescomplemented
115#14582897C2212yescomplemented
116#103×D43C2212yes—
117#103×D43C2212yes—
118#103×D43C2212yes—
119#102×D43C2212yes—
120#102×D43C2211yescharacteristic
121#102×D43C2211yescharacteristic
122C22⋊C8×D43C2212yes—
123C4×C8×D43C2211yescharacteristic
124C43×#547C2211yescharacteristic, complemented
125C43×#547C2211yescharacteristic, complemented
126C43×#487C2211yescharacteristic, complemented
127C43×#484C2212yescomplemented
128C43×#474C2211yescharacteristic, complemented
129C43×#468C2212yescomplemented
130C43×#461C2211yescharacteristic, complemented
131C43×#449C2212yescomplemented
132C4×D8×C43C2211yescharacteristic, complemented
133C43×#436C2211yescharacteristic, complemented
134C43×#417C2212yescomplemented
135C2×#10621902—21no—
136C2×#10621902C2312yes—
137C2×#10621898—22no—
138C2×#10621898—21no—
139C2×#10621898—22no—
140C2×#10621898C2312yes—
141C2×#10621900—21no—
142C2×#10621900—22no—
143C2×#10621900—22no—
144C2×#10621900C2312yes—
145#41×D43—28no—
146#41×D43—44no—
147#41×D43—48no—
148C2×Q8×D43—21no—
149C2×Q8×D43C2312yes—
150C2×D4×D43—22no—
151C2×D4×D43—22no—
152C2×D4×D43D411yescharacteristic
153C2×D4×D43C2311yescharacteristic
154C2×D4×D43C2311yescharacteristic
155C22×C4×D43—22no—
156C22×C4×D43—21no—
157C22×C4×D43—22no—
158C22×C4×D43—21no—
159C22×C4×D43C2312yes—
160C2×#10621873C2312yes—
161C2×#10621883C2312yes—
162C2×#10621884C2312yes—
163SD16×D43—44no—
164C2×D344C2311yescharacteristic
165C2×#10621882C2311yescharacteristic
166C2×#10621882C2311yescharacteristic
167D8×D43—24no—
168C2×#10621877C2312yes—
169C2×#10621872C2312yes—
170C2×#10621872C2312yes—
171M16×D43—44no—
172C2×C8×D43C2311yescharacteristic
173C2×C8×D43C2311yescharacteristic
174C2×C8×D43C2312yes—
175#13063325C2311yescharacteristic
176#13063325C2311yescharacteristic
177#13063324—21no—
178#13063324—21no—
179#13063324—21no—
180#13063324C2312yes—
181#13063323—21no—
182#13063323C2312yes—
183#13063310—22no—
184#13063310—22no—
185#13063310—22no—
186#13063310—22no—
187#13063309—22no—
188#13063309—22no—
189#13063308—22no—
190#13063308—22no—
191#13063307—22no—
192#13063307—22no—
193#13063307—22no—
194#13063307—22no—
195#13063306—22no—
196#13063306—22no—
197#13063305—21no—
198#13063305C2312yes—
199#13063304—21no—
200#13063304C2312yes—
201#13063303—22no—
202#13063303—22no—
203#13063302—22no—
204#13063302—22no—
205#13063301—21no—
206#13063301C2312yes—
207#13063300—21no—
208#13063300C2312yes—
209#13063299—21no—
210#13063299C2312yes—
211#13063298—22no—
212#13063298—22no—
213#13063297—22no—
214#13063297—22no—
215#13063296—21no—
216#13063296C2312yes—
217C4×D172C2311yescharacteristic
218C4×D172C2311yescharacteristic
219C4×D172C2311yescharacteristic
220D4×Dic43D411yescharacteristic
221D4×Dic43C2311yescharacteristic
222D4×Dic43C2311yescharacteristic
223#13063287D411yescharacteristic
224#13063287C2311yescharacteristic
225#13063287C2311yescharacteristic
226C4×C22⋊D43—21no—
227C4×C22⋊D43—21no—
228C4×C22⋊D43C2312yes—
229(C22⋊D43)⋊C4—21no—
230(C22⋊D43)⋊C4—21no—
231(C22⋊D43)⋊C4D412yes—
232C2×C4⋊Dic43—21no—
233C2×C4⋊Dic43C2312yes—
234C2×Dic43⋊C4—22no—
235C2×Dic43⋊C4—22no—
236C4⋊C4×D43—21no—
237C4⋊C4×D43—22no—
238C4⋊C4×D43—22no—
239C4⋊C4×D43—22no—
240C4⋊C4×D43—21no—
241C4⋊C4×D43—21no—
242C4⋊C4×D43—21no—
243C4⋊C4×D43—21no—
244C4⋊C4×D43—22no—
245C4⋊C4×D43D411yescharacteristic
246C4⋊C4×D43C2312yes—
247C4⋊C4×D43C2312yes—
248C4⋊C4×D43C2311yescharacteristic
249C4⋊C4×D43C2312yes—
250C4⋊C4×D43C2311yescharacteristic
251C22⋊C4×D43—22no—
252C22⋊C4×D43—21no—
253C22⋊C4×D43—21no—
254C22⋊C4×D43—22no—
255C22⋊C4×D43D412yes—
256C42×D43C2311yescharacteristic
257#13063259C2312yes—
258#13063259C2311yescharacteristic
259#13063258C2312yes—
260#13063258C2312yes—
261#13063258C2311yescharacteristic
262#13063258C2311yescharacteristic
263C4⋊(C43⋊C8)C2311yescharacteristic
264Dic43⋊C8C2312yes—
265#13063250C2312yes—
266#13063250C2312yes—
267#13063250C2312yes—
268#13063249C2312yes—
269#13063249C2312yes—
270#13063249C2312yes—
271#13063248C2312yes—
272#13063248C2312yes—
273#13063248C2312yes—
274#13063247C2312yes—
275#13063247C2311yescharacteristic
276#13063247C2311yescharacteristic
277#13063246C2312yes—
278#13063246C2311yescharacteristic
279#13063246C2311yescharacteristic
280#13063245C2312yes—
281#13063245C2311yescharacteristic
282#13063245C2311yescharacteristic
283C22⋊(C43⋊C8)C2312yes—
284(C2×D43)⋊C8C2312yes—
285(C2×D43)⋊C8C2312yes—
286C4×C43⋊C8C2311yescharacteristic
287C8×Dic43C2311yescharacteristic
288C8×Dic43C2311yescharacteristic
289C2×#41×C43—21no—
290C2×#41×C43C2312yes—
291C2×SD16×C43C2312yes—
292C2×D8×C43C2311yescharacteristic
293C2×M16×C43C2312yes—
294C4⋊Q8×C43C2311yescharacteristic
295C4⋊Q8×C43C2311yescharacteristic
296#123×C43—22no—
297#123×C43—22no—
298C22⋊Q8×C43—21no—
299C22⋊Q8×C43C2312yes—
300#121×C43—21no—
301#121×C43C2312yes—
302C4×D4×C43C2311yescharacteristic
303C4×D4×C43C2311yescharacteristic
304C4×D4×C43C2311yescharacteristic
305C2×C4⋊C4×C43—21no—
306C2×C4⋊C4×C43C2312yes—
307#107×C43C2312yes—
308#107×C43C2311yescharacteristic
309C4⋊C8×C43C2311yescharacteristic
310#103×C43C2312yes—
311#103×C43C2312yes—
312#103×C43C2312yes—
313#102×C43C2312yes—
314#102×C43C2311yescharacteristic
315#102×C43C2311yescharacteristic
316C22⋊C8×C43C2312yes—
317C4×C8×C43C2311yescharacteristic
318C23×D43—21no—
319C23×D43—21no—
320C23×D43C2×D412yes—
321#41×C43—24no—
322#41×C43—42no—
323#41×C43—44no—
324C2×Q8×C43—21no—
325C2×Q8×C43C2412yes—
326C2×D4×C43—22no—
327C2×D4×C43—22no—
328C2×D4×C43C2×D411yescharacteristic
329C2×D4×C43C2411yescharacteristic
330C2×D4×C43C2411yescharacteristic
331C22×C4×C43—21no—
332C22×C4×C43—22no—
333C22×C4×C43—21no—
334C22×C4×C43—22no—
335C22×C4×C43C2412yes—
336C2×C22⋊D43—21no—
337C2×C22⋊D43—21no—
338C2×C22⋊D43—22no—
339C2×C22⋊D43—22no—
340C2×C22⋊D43—22no—
341C2×C22⋊D43—22no—
342C2×C22⋊D43C2×D412yes—
343C22×Dic43—21no—
344C22×Dic43—22no—
345C22×Dic43—21no—
346C22×Dic43—22no—
347C22×Dic43C2×D412yes—
348#10621902—24no—
349#10621902—42no—
350#10621902—44no—
351Q8×D43—24no—
352Q8×D43—24no—
353Q8×D43—44no—
354#10621900—24no—
355#10621900—42no—
356#10621900—48no—
357#10621900—48no—
358#10621900—44no—
359D4×D43—24no—
360D4×D43—22no—
361D4×D43—22no—
362D4×D43—22no—
363D4×D43—48no—
364D4×D43—48no—
365D4×D43#4114yescomplemented
366#10621898—24no—
367#10621898—42no—
368#10621898—48no—
369#10621898—44no—
370#10621898—48no—
371C2×D172—22no—
372C2×D172—22no—
373C2×D172C2×D411yescharacteristic
374C2×D172C2411yescharacteristic
375C2×D172C2411yescharacteristic
376C2×C4×D43—24no—
377C2×C4×D43—24no—
378C2×C4×D43—21no—
379C2×C4×D43—22no—
380C2×C4×D43—21no—
381C2×C4×D43—21no—
382C2×C4×D43—22no—
383C2×C4×D43—21no—
384C2×C4×D43—21no—
385C2×C4×D43—22no—
386C2×C4×D43—21no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—22no—
390C2×C4×D43—48no—
391C2×C4×D43—48no—
392C2×C4×D43—44no—
393C2×C4×D43—44no—
394C2×C4×D43C2×D411yescharacteristic
395C2×C4×D43C2×D412yes—
396C2×C4×D43C2×D412yes—
397C2×C4×D43C2×D411yescharacteristic
398C2×C4×D43C2412yes—
399C2×C4×D43C2411yescharacteristic
400C2×Dic86—21no—
401C2×Dic86—22no—
402C2×Dic86—22no—
403C2×Dic86C2412yes—
404SD16×C43—42no—
405D8×C43—22no—
406M16×C43—42no—
407C2×C8×C43C2411yescharacteristic
408C2×C8×C43C2411yescharacteristic
409C2×C8×C43C2412yes—
410C4⋊C4×C43—21no—
411C4⋊C4×C43—22no—
412C4⋊C4×C43—22no—
413C4⋊C4×C43—21no—
414C4⋊C4×C43—21no—
415C4⋊C4×C43C2×D411yescharacteristic
416C4⋊C4×C43C2411yescharacteristic
417C4⋊C4×C43C2412yes—
418C4⋊C4×C43C2411yescharacteristic
419C22⋊C4×C43—21no—
420C22⋊C4×C43—21no—
421C22⋊C4×C43—22no—
422C22⋊C4×C43—22no—
423C22⋊C4×C43C2×D412yes—
424C42×C43C2411yescharacteristic
425C22⋊Dic43—21no—
426C22⋊Dic43—21no—
427C22⋊Dic43—22no—
428C22⋊Dic43—22no—
429C22⋊Dic43C2×D412yes—
430#10621884—42no—
431#10621883—42no—
432#10621882—22no—
433#10621882—22no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4C2×D412yes—
443(C2×D43)⋊C4C2×D412yes—
444C4⋊Dic43—21no—
445C4⋊Dic43—22no—
446C4⋊Dic43—21no—
447C4⋊Dic43—21no—
448C4⋊Dic43—22no—
449C4⋊Dic43C2×D411yescharacteristic
450C4⋊Dic43C2411yescharacteristic
451C4⋊Dic43C2412yes—
452C4⋊Dic43C2411yescharacteristic
453Dic43⋊C4—22no—
454Dic43⋊C4—21no—
455Dic43⋊C4—22no—
456Dic43⋊C4—22no—
457Dic43⋊C4—22no—
458Dic43⋊C4—22no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—21no—
463Dic43⋊C4C2×D412yes—
464C4×Dic43C2×D411yescharacteristic
465C4×Dic43C2×D411yescharacteristic
466C4×Dic43C2411yescharacteristic
467#10621877—42no—
468C2×C43⋊C8C2411yescharacteristic
469C2×C43⋊C8C2411yescharacteristic
470C2×C43⋊C8C2412yes—
471D344—22no—
472#10621873—42no—
473#10621872—42no—
474#10621872—42no—
475C8×D43—22no—
476C8×D43—22no—
477C8×D43—24no—
478C23×C43—21no—
479C23×C43—21no—
480C23×C43C22×D412yes—
481C22×D43—21no—
482C22×D43—24no—
483C22×D43—24no—
484C22×D43—24no—
485C22×D43—24no—
486C22×D43—21no—
487C22×D43—42no—
488C22×D43—42no—
489C22×D43—42no—
490C22×D43—42no—
491C22×D43—42no—
492C22×D43C22×D412yes—
493C22×D43C22×D411yescharacteristic
494Q8×C43—22no—
495Q8×C43—22no—
496Q8×C43—42no—
497D4×C43—22no—
498D4×C43—21no—
499D4×C43—21no—
500D4×C43—21no—
501D4×C43—44no—
502D4×C43—44no—
503D4×C43C2×#4112yescomplemented
504C2×C4×C43—22no—
505C2×C4×C43—22no—
506C2×C4×C43—22no—
507C2×C4×C43—22no—
508C2×C4×C43—21no—
509C2×C4×C43—21no—
510C2×C4×C43—44no—
511C2×C4×C43—44no—
512C2×C4×C43—42no—
513C2×C4×C43—42no—
514C2×C4×C43C22×D411yescharacteristic
515C2×C4×C43C22×D412yes—
516C2×C4×C43C22×D411yescharacteristic
517C2×C4×C43C2511yescharacteristic
518C22⋊D43—24no—
519C22⋊D43—24no—
520C22⋊D43—44no—
521C22⋊D43—44no—
522C22⋊D43—44no—
523C22⋊D43—44no—
524C22⋊D43—42no—
525C2×Dic43—24no—
526C2×Dic43—21no—
527C2×Dic43—22no—
528C2×Dic43—22no—
529C2×Dic43—21no—
530C2×Dic43—44no—
531C2×Dic43—44no—
532C2×Dic43—42no—
533C2×Dic43—42no—
534C2×Dic43C22×D411yescharacteristic
535C2×Dic43C22×D412yes—
536C2×Dic43C22×D411yescharacteristic
537C2×Dic43C22×D411yescharacteristic
538D172—22no—
539D172—21no—
540D172—21no—
541D172—21no—
542D172—44no—
543D172—44no—
544D172C2×#4112yescomplemented
545C4×D43—24no—
546C4×D43—22no—
547C4×D43—22no—
548C4×D43—22no—
549C4×D43—24no—
550C4×D43—44no—
551C4×D43—44no—
552C4×D43—44no—
553C4×D43—44no—
554C4×D43—44no—
555C4×D43—42no—
556C4×D43—42no—
557C4×D43—44no—
558C4×D43—42no—
559C4×D43—42no—
560C4×D43—42no—
561C4×D43—42no—
562C4×D43AGL(1,ℤ/8)14yes—
563C4×D43C2×#4112yes—
564C4×D43H(5,𝔽2)12yes—
565Dic86—22no—
566Dic86—22no—
567Dic86—42no—
568Dic86—44no—
569Dic86—44no—
570C8×C43—21no—
571C8×C43—21no—
572C8×C43—22no—
573C43⋊C8—21no—
574C43⋊C8—21no—
575C43⋊C8—22no—
576C2×#3330—431nomaximal, Sylow
577C22×C43—22no—
578C22×C43—22no—
579C22×C43—22no—
580C22×C43—22no—
581C22×C43—41no—
582C22×C43—41no—
583C22×C43—41no—
584C22×C43—41no—
585C22×C43—41no—
586C22×C43C23×D411yescharacteristic
587C2×D43—22no—
588C2×D43—22no—
589C2×D43—22no—
590C2×D43—22no—
591C2×D43—41no—
592C2×D43—41no—
593C2×D43—48no—
594C2×D43—48no—
595C2×D43—41no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—84no—
599C2×D43#54612yes—
600C2×D43C2×AGL(1,ℤ/8)12yes—
601C2×D43#57812yes—
602C4×C43—22no—
603C4×C43—21no—
604C4×C43—42no—
605C4×C43—42no—
606C4×C43—41no—
607C4×C43—41no—
608C4×C43C2×AGL(1,ℤ/8)12yes—
609C4×C43C22×#4111yescharacteristic
610C4×C43C2×H(5,𝔽2)11yescharacteristic
611Dic43—22no—
612Dic43—21no—
613Dic43—42no—
614Dic43—42no—
615Dic43—41no—
616Dic43—41no—
617Dic43#54612yes—
618Dic43C2×AGL(1,ℤ/8)12yes—
619C2×#547—431no—
620C2×#547—431no—
621#3330—431no—
622#3330—432no—
623#3330—431no—
624#3330—432no—
625#3330—431no—
626#3330—432no—
627#3330—431no—
628#3330—431no—
629#3330—432no—
630#3330—431no—
631#3330—431no—
632#3330D4311yescharacteristic, direct product factor
633C2×#487—431no—
634C2×#484—432no—
635C2×#474—431no—
636C2×#468—432no—
637C2×#461—431no—
638C2×#449—432no—
639C2×C4×D8—431no—
640C2×#436—431no—
641C2×#417—432no—
642C2×C43—42no—
643C2×C43—42no—
644C2×C43—81no—
645C2×C43C2×#54611yescharacteristic
646C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
647C2×C43C2×#57811yescharacteristic
648D43—42no—
649D43—42no—
650D43—81no—
651D43#333014yesdirect product factor
652C22×#41—432no—
653C22×#41—861no—
654C22×SD16—432no—
655C22×D8—431no—
656C22×M16—432no—
657#547—431no—
658#547—432no—
659#547—431no—
660#547—431no—
661#547—432no—
662#547—432no—
663#547—431no—
664#547—432no—
665#547—431no—
666#547—431no—
667#547—861no—
668#547—861no—
669#547—861no—
670#547—862no—
671#547—862no—
672#547—861no—
673#547C2×D4311yescharacteristic, complemented
674#547C2×D4311yescharacteristic, complemented
675C2×C4⋊Q8—431no—
676C2×C4⋊Q8—431no—
677C2×#123—862no—
678C2×#123—862no—
679C2×C22⋊Q8—432no—
680C2×C22⋊Q8—861no—
681C2×#121—432no—
682C2×#121—861no—
683C2×C4×D4—431no—
684C2×C4×D4—431no—
685C2×C4×D4—431no—
686C22×C4⋊C4—432no—
687C22×C4⋊C4—861no—
688#487—431no—
689#487—431no—
690#487—432no—
691#487—432no—
692#487—431no—
693#487C2×D4311yescharacteristic, complemented
694#484—432no—
695#484—432no—
696#484—432no—
697#484—432no—
698#484—432no—
699#484—432no—
700#484—432no—
701#484C2×D4312yescomplemented
702#474—431no—
703#474—431no—
704#474—432no—
705#474—431no—
706#474—432no—
707#474C2×D4311yescharacteristic, complemented
708#468—432no—
709#468—432no—
710#468—432no—
711#468—432no—
712#468—432no—
713#468—432no—
714#468—432no—
715#468C2×D4312yescomplemented
716#461—432no—
717#461—431no—
718#461—431no—
719#461—431no—
720#461—432no—
721#461C2×D4311yescharacteristic, complemented
722#449—432no—
723#449—432no—
724#449—432no—
725#449—432no—
726#449—432no—
727#449—432no—
728#449—432no—
729#449C2×D4312yescomplemented
730C4×D8—431no—
731C4×D8—431no—
732C4×D8—431no—
733C4×D8—431no—
734C4×D8—431no—
735C4×D8—431no—
736C4×D8—431no—
737C4×D8C2×D4311yescharacteristic, complemented
738#436—432no—
739#436—431no—
740#436—431no—
741#436—432no—
742#436—431no—
743#436C2×D4311yescharacteristic, complemented
744C2×#107—431no—
745C2×#107—432no—
746C2×C4⋊C8—431no—
747#417—432no—
748#417—432no—
749#417—432no—
750#417—432no—
751#417—432no—
752#417—432no—
753#417—432no—
754#417C2×D4312yescomplemented
755C2×#103—432no—
756C2×#103—432no—
757C2×#103—432no—
758C2×#102—431no—
759C2×#102—432no—
760C2×#102—431no—
761C2×C22⋊C8—432no—
762C2×C4×C8—431no—
763C43C2×#333011yescharacteristic, complemented, Sylow
764C2×#41—21no—
765C2×#41—432no—
766C2×#41—432no—
767C2×#41—432no—
768C2×#41—862no—
769C2×#41—862no—
770C2×#41—861no—
771C2×#41—862no—
772C2×#41—862no—
773C2×#41—861no—
774C2×#41—861no—
775C2×#41—868no—
776C2×#41—1724no—
777C2×#41—1728no—
778C2×#41C22×D4312yes—
779C22×Q8—432no—
780C22×Q8—861no—
781C22×D4—431no—
782C22×D4—431no—
783C22×D4—431no—
784C22×D4—862no—
785C22×D4—862no—
786C23×C4—432no—
787C23×C4—861no—
788C23×C4—862no—
789C23×C4—861no—
790C23×C4—862no—
791C2×SD16—432no—
792C2×SD16—432no—
793C2×SD16—432no—
794C2×SD16—1724no—
795C2×SD16C22×D4312yes—
796C2×D8—431no—
797C2×D8—431no—
798C2×D8—431no—
799C2×D8—864no—
800C2×D8C22×D4311yescharacteristic
801C2×M16—432no—
802C2×M16—432no—
803C2×M16—432no—
804C2×M16—1724no—
805C2×M16C22×D4312yes—
806C22×C8—431no—
807C22×C8—432no—
808C22×C8—431no—
809C4⋊Q8—432no—
810C4⋊Q8—432no—
811C4⋊Q8—431no—
812C4⋊Q8—431no—
813C4⋊Q8—861no—
814C4⋊Q8—861no—
815C4⋊Q8—861no—
816C4⋊Q8—861no—
817C4⋊Q8C22×D4311yescharacteristic
818C4⋊Q8C22×D4311yescharacteristic
819#123—22no—
820#123—22no—
821#123—862no—
822#123—862no—
823#123—862no—
824#123—862no—
825#123—862no—
826#123—862no—
827#123—862no—
828#123—862no—
829#123—862no—
830#123—862no—
831#123—862no—
832#123—862no—
833#123—862no—
834#123—862no—
835C22⋊Q8—21no—
836C22⋊Q8—432no—
837C22⋊Q8—432no—
838C22⋊Q8—432no—
839C22⋊Q8—862no—
840C22⋊Q8—862no—
841C22⋊Q8—862no—
842C22⋊Q8—862no—
843C22⋊Q8—861no—
844C22⋊Q8—861no—
845C22⋊Q8—861no—
846C22⋊Q8C22×D4312yes—
847#121—21no—
848#121—432no—
849#121—432no—
850#121—432no—
851#121—862no—
852#121—862no—
853#121—861no—
854#121—861no—
855#121—862no—
856#121—862no—
857#121—861no—
858#121C22×D4312yes—
859C4×D4—431no—
860C4×D4—432no—
861C4×D4—431no—
862C4×D4—432no—
863C4×D4—431no—
864C4×D4—431no—
865C4×D4—431no—
866C4×D4—431no—
867C4×D4—431no—
868C4×D4—431no—
869C4×D4—431no—
870C4×D4—861no—
871C4×D4—861no—
872C4×D4—861no—
873C4×D4—861no—
874C4×D4C22×D4311yescharacteristic
875C4×D4C22×D4311yescharacteristic
876C4×D4C22×D4311yescharacteristic
877C2×C4⋊C4—21no—
878C2×C4⋊C4—431no—
879C2×C4⋊C4—432no—
880C2×C4⋊C4—431no—
881C2×C4⋊C4—432no—
882C2×C4⋊C4—432no—
883C2×C4⋊C4—432no—
884C2×C4⋊C4—431no—
885C2×C4⋊C4—861no—
886C2×C4⋊C4—862no—
887C2×C4⋊C4—862no—
888C2×C4⋊C4—862no—
889C2×C4⋊C4—861no—
890C2×C4⋊C4—862no—
891C2×C4⋊C4—861no—
892C2×C4⋊C4—861no—
893C2×C4⋊C4—862no—
894C2×C4⋊C4—861no—
895C2×C4⋊C4—862no—
896C2×C4⋊C4—861no—
897C2×C4⋊C4C22×D4312yes—
898C2×C22⋊C4—432no—
899C2×C22⋊C4—861no—
900C2×C22⋊C4—861no—
901C2×C22⋊C4—862no—
902C2×C22⋊C4—862no—
903C2×C42—431no—
904#107—431no—
905#107—432no—
906#107—431no—
907#107—431no—
908#107—432no—
909#107—432no—
910#107C22×D4311yescharacteristic
911#107C22×D4312yes—
912C4⋊C8—432no—
913C4⋊C8—431no—
914C4⋊C8C22×D4311yescharacteristic
915#103—432no—
916#103—432no—
917#103—432no—
918#103—432no—
919#103—432no—
920#103—432no—
921#103—432no—
922#103—432no—
923#103—432no—
924#103C22×D4312yes—
925#103C22×D4312yes—
926#103C22×D4312yes—
927#102—431no—
928#102—432no—
929#102—431no—
930#102—431no—
931#102—432no—
932#102—431no—
933#102—431no—
934#102—432no—
935#102—431no—
936#102C22×D4311yescharacteristic
937#102C22×D4312yes—
938#102C22×D4311yescharacteristic
939C22⋊C8—432no—
940C22⋊C8—432no—
941C22⋊C8—432no—
942C22⋊C8C22×D4312yes—
943C4×C8—431no—
944C4×C8—431no—
945C4×C8—431no—
946C4×C8C22×D4311yescharacteristic
947C24—432no—
948C24—861no—
949C24—861no—
950#41—24no—
951#41—42no—
952#41—44no—
953#41—864no—
954#41—864no—
955#41—864no—
956#41—1722no—
957#41—1728no—
958#41—1728no—
959#41—1724no—
960#41—1722no—
961#41—1728no—
962#41—1722no—
963#41—1724no—
964#41—1728no—
965#41—1724no—
966C2×Q8—21no—
967C2×Q8—432no—
968C2×Q8—862no—
969C2×Q8—862no—
970C2×Q8—864no—
971C2×Q8—864no—
972C2×Q8—861no—
973C2×Q8—1724no—
974C2×Q8C23×D4312yes—
975C2×D4—22no—
976C2×D4—22no—
977C2×D4—434no—
978C2×D4—432no—
979C2×D4—431no—
980C2×D4—431no—
981C2×D4—431no—
982C2×D4—862no—
983C2×D4—862no—
984C2×D4—864no—
985C2×D4—862no—
986C2×D4—862no—
987C2×D4—862no—
988C2×D4—861no—
989C2×D4—861no—
990C2×D4—862no—
991C2×D4—862no—
992C2×D4—862no—
993C2×D4—862no—
994C2×D4—1728no—
995C2×D4—1728no—
996C2×D4D4×D4311yescharacteristic
997C2×D4C23×D4311yescharacteristic
998C2×D4C23×D4311yescharacteristic
999C22×C4—22no—
1000C22×C4—21no—
1001C22×C4—22no—
1002C22×C4—21no—
1003C22×C4—431no—
1004C22×C4—431no—
1005C22×C4—432no—
1006C22×C4—431no—
1007C22×C4—432no—
1008C22×C4—432no—
1009C22×C4—432no—
1010C22×C4—864no—
1011C22×C4—864no—
1012C22×C4—861no—
1013C22×C4—862no—
1014C22×C4—861no—
1015C22×C4—861no—
1016C22×C4—861no—
1017C22×C4—862no—
1018C22×C4—862no—
1019C22×C4—862no—
1020C22×C4—862no—
1021C22×C4—861no—
1022C22×C4—862no—
1023C22×C4—861no—
1024C22×C4—862no—
1025C22×C4—861no—
1026C22×C4—862no—
1027C22×C4—861no—
1028C22×C4—1724no—
1029C22×C4—1724no—
1030C22×C4—1728no—
1031C22×C4—1728no—
1032C22×C4C23×D4312yes—
1033SD16—42no—
1034SD16—1722no—
1035SD16—1722no—
1036SD16—1722no—
1037D8—22no—
1038D8—862no—
1039D8—862no—
1040D8—862no—
1041M16—42no—
1042M16—1722no—
1043M16—1722no—
1044M16—1722no—
1045C2×C8—431no—
1046C2×C8—431no—
1047C2×C8—432no—
1048C2×C8—862no—
1049C2×C8—864no—
1050C2×C8—862no—
1051C2×C8C23×D4311yescharacteristic
1052C2×C8C23×D4311yescharacteristic
1053C2×C8C23×D4312yes—
1054C4⋊C4—21no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—432no—
1060C4⋊C4—431no—
1061C4⋊C4—431no—
1062C4⋊C4—432no—
1063C4⋊C4—431no—
1064C4⋊C4—861no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—862no—
1068C4⋊C4—861no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—862no—
1072C4⋊C4—862no—
1073C4⋊C4—862no—
1074C4⋊C4—862no—
1075C4⋊C4—861no—
1076C4⋊C4—862no—
1077C4⋊C4—861no—
1078C4⋊C4—861no—
1079C4⋊C4D4×D4311yescharacteristic
1080C4⋊C4C23×D4311yescharacteristic
1081C4⋊C4C23×D4312yes—
1082C4⋊C4C23×D4311yescharacteristic
1083C22⋊C4—22no—
1084C22⋊C4—21no—
1085C22⋊C4—21no—
1086C22⋊C4—22no—
1087C22⋊C4—432no—
1088C22⋊C4—432no—
1089C22⋊C4—432no—
1090C22⋊C4—861no—
1091C22⋊C4—861no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—862no—
1095C22⋊C4—861no—
1096C22⋊C4—861no—
1097C22⋊C4—862no—
1098C22⋊C4—862no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—862no—
1102C22⋊C4D4×D4312yes—
1103C42—431no—
1104C42—431no—
1105C42—431no—
1106C42C23×D4311yescharacteristic
1107C23—21no—
1108C23—21no—
1109C23—431no—
1110C23—432no—
1111C23—864no—
1112C23—864no—
1113C23—864no—
1114C23—864no—
1115C23—861no—
1116C23—861no—
1117C23—1722no—
1118C23—1722no—
1119C23—1722no—
1120C23—1722no—
1121C23—1722no—
1122C23C2×D4×D4312yes—
1123Q8—22no—
1124Q8—22no—
1125Q8—42no—
1126Q8—862no—
1127Q8—862no—
1128Q8—1724no—
1129Q8—1724no—
1130Q8—1722no—
1131D4—22no—
1132D4—21no—
1133D4—21no—
1134D4—21no—
1135D4—44no—
1136D4—44no—
1137D4—432no—
1138D4—864no—
1139D4—864no—
1140D4—862no—
1141D4—861no—
1142D4—861no—
1143D4—861no—
1144D4—1724no—
1145D4—1724no—
1146D4—1722no—
1147D4—1724no—
1148D4—1724no—
1149D4—1724no—
1150D4—1724no—
1151D4#41×D4312yescomplemented
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—44no—
1159C2×C4—44no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—431no—
1163C2×C4—431no—
1164C2×C4—434no—
1165C2×C4—432no—
1166C2×C4—432no—
1167C2×C4—431no—
1168C2×C4—432no—
1169C2×C4—864no—
1170C2×C4—864no—
1171C2×C4—862no—
1172C2×C4—864no—
1173C2×C4—862no—
1174C2×C4—862no—
1175C2×C4—861no—
1176C2×C4—861no—
1177C2×C4—862no—
1178C2×C4—862no—
1179C2×C4—1724no—
1180C2×C4—1722no—
1181C2×C4—1722no—
1182C2×C4—1724no—
1183C2×C4—1722no—
1184C2×C4—1724no—
1185C2×C4—1724no—
1186C2×C4—1722no—
1187C2×C4—1724no—
1188C2×C4—1724no—
1189C2×C4—1722no—
1190C2×C4—1722no—
1191C2×C4—1724no—
1192C2×C4—1724no—
1193C2×C4—1722no—
1194C2×C4—1722no—
1195C2×C4C2×D4×D4311yescharacteristic
1196C2×C4C2×D4×D4312yes—
1197C2×C4C2×D4×D4311yescharacteristic
1198C2×C4C24×D4311yescharacteristic
1199C8—21no—
1200C8—21no—
1201C8—22no—
1202C8—861no—
1203C8—861no—
1204C8—862no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—432no—
1215C22—432no—
1216C22—432no—
1217C22—862no—
1218C22—862no—
1219C22—862no—
1220C22—862no—
1221C22—3444no—
1222C22—1728no—
1223C22—1728no—
1224C22—1721no—
1225C22—1721no—
1226C22—1721no—
1227C22—1721no—
1228C22—1721no—
1229C22C22×D4×D4311yescharacteristic
1230C4—22no—
1231C4—21no—
1232C4—42no—
1233C4—41no—
1234C4—42no—
1235C4—41no—
1236C4—432no—
1237C4—432no—
1238C4—862no—
1239C4—861no—
1240C4—1722no—
1241C4—1721no—
1242C4—1722no—
1243C4—1721no—
1244C4AGL(1,ℤ/8)×D4312yes—
1245C4C2×#41×D4311yescharacteristic
1246C4H(5,𝔽2)×D4311yescharacteristic
1247C2—42no—
1248C2—42no—
1249C2—81no—
1250C2—434no—
1251C2—3441no—
1252C2—1722no—
1253C2—1722no—
1254C2#546×D4311yescharacteristic
1255C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1256C2#578×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3330C2
socleC22×C43C23×D4
hypercenter#3330D43
hypocenterC43C2×#3330
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #547×D43C2semidirect
2. #547×D43C2semidirect
3. #19146903C2semidirect
4. #19146902C2semidirect
5. #19146901C2semidirect
6. #19146900C2semidirect
7. #19146899C2semidirect
8. #19146898C2semidirect
9. #19146897C2semidirect
10. #19146896C2semidirect
11. #19146895C2semidirect
12. #19146894C2semidirect
13. #19146893C2semidirect
14. #487×D43C2semidirect
15. #484×D43C2semidirect
16. #474×D43C2semidirect
17. #468×D43C2semidirect
18. #461×D43C2semidirect
19. #449×D43C2semidirect
20. C4×D8×D43C2semidirect
21. #436×D43C2semidirect
22. #417×D43C2semidirect
23. C43×#3330C2semidirect
29. #14583554C22semidirect
30. #14583554C22semidirect
31. #14583553C22semidirect
32. #14583553C22semidirect
33. #14583552C22semidirect
34. #14583552C22semidirect
36. #14583551C22semidirect
38. #14583550C22semidirect
40. #14583549C22semidirect
42. #14583548C22semidirect
58. #14583251C22semidirect
59. #14583250C22semidirect
60. #14583249C22semidirect
61. #14583248C22semidirect
62. #14583248C22semidirect
63. #14583236C22semidirect
64. #14583236C22semidirect
65. #14583235C22semidirect
66. #14583234C22semidirect
67. #14583233C22semidirect
68. #14583233C22semidirect
69. #14583232C22semidirect
70. #14583180C22semidirect
71. #14583179C22semidirect
72. #14583178C22semidirect
73. #14583177C22semidirect
74. #14583176C22semidirect
75. #14583148C22semidirect
76. #14583147C22semidirect
77. #14583146C22semidirect
78. #14583145C22semidirect
79. #14583144C22semidirect
80. #14583143C22semidirect
81. #14583142C22semidirect
82. #14583105C22semidirect
83. #14583104C22semidirect
84. #14583103C22semidirect
85. #14583102C22semidirect
86. #14583101C22semidirect
87. #14583047C22semidirect
88. #14583046C22semidirect
89. #14583045C22semidirect
90. #14583044C22semidirect
91. #14583043C22semidirect
92. #14583042C22semidirect
93. #14583041C22semidirect
94. C4×D344C22semidirect
95. D8×Dic43C22semidirect
96. #14582981C22semidirect
97. C4×#10621882C22semidirect
98. C4×#10621882C22semidirect
99. #14582979C22semidirect
100. #14582979C22semidirect
101. #14582978C22semidirect
102. #14582977C22semidirect
103. #14582976C22semidirect
104. #14582975C22semidirect
105. #14582974C22semidirect
109. #14582901C22semidirect
110. #14582900C22semidirect
111. #14582899C22semidirect
112. #14582899C22semidirect
113. #14582898C22semidirect
114. #14582897C22semidirect
115. #14582897C22semidirect
124. C43×#547C22semidirect
125. C43×#547C22semidirect
126. C43×#487C22semidirect
127. C43×#484C22semidirect
128. C43×#474C22semidirect
129. C43×#468C22semidirect
130. C43×#461C22semidirect
131. C43×#449C22semidirect
132. C4×D8×C43C22semidirect
133. C43×#436C22semidirect
134. C43×#417C22semidirect
365. D4×D43#41semidirect
503. D4×C43C2×#41semidirect
544. D172C2×#41semidirect
632. #3330D43direct (N × H)
651. D43#3330direct (N × H)
673. #547C2×D43semidirect
674. #547C2×D43semidirect
693. #487C2×D43semidirect
701. #484C2×D43semidirect
707. #474C2×D43semidirect
715. #468C2×D43semidirect
721. #461C2×D43semidirect
729. #449C2×D43semidirect
737. C4×D8C2×D43semidirect
743. #436C2×D43semidirect
754. #417C2×D43semidirect
763. C43C2×#3330semidirect
1151. D4#41×D43semidirect

Maximal subgroups

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

subgroupindex
#547×D432
#191469032
#191469022
#191469012
#191469002
#191468992
#191468982
#191468972
#191468962
#191468952
#191468942
#191468932
#487×D432
#484×D432
#474×D432
#468×D432
#461×D432
#449×D432
C4×D8×D432
#436×D432
#417×D432
C43×#33302
C2×#333043