Finite Group Databasebeta

← D43×#3335 #25975012

Subgroups — D43×#3335 #25975012

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#554×D43C211yesmaximal, characteristic, complemented
2#547×D43C211yesmaximal, characteristic
3#19146955C211yesmaximal, characteristic, complemented
4#19146954C211yesmaximal, characteristic, complemented
5#19146953C211yesmaximal, characteristic, complemented
6#19146952C211yesmaximal, characteristic, complemented
7#19146951C211yesmaximal, characteristic, complemented
8#19146950C212yesmaximal, complemented
9#19146949C211yesmaximal, characteristic, complemented
10#19146948C212yesmaximal, complemented
11#19146947C212yesmaximal, complemented
12#19146946C211yesmaximal, characteristic, complemented
13#19146945C212yesmaximal, complemented
14#498×D43C211yesmaximal, characteristic, complemented
15#481×D43C212yesmaximal, complemented
16#483×D43C212yesmaximal, complemented
17#475×D43C211yesmaximal, characteristic, complemented
18#476×D43C211yesmaximal, characteristic, complemented
19#465×D43C212yesmaximal, complemented
20C4×SD16×D43C211yesmaximal, characteristic, complemented
21C8×D4×D43C211yesmaximal, characteristic, complemented
22C2×#106×D43C212yesmaximal, complemented
23C43×#3335C211yesmaximal, characteristic, complemented
24C2×#41×D43—21no—
25C2×SD16×D43C2211yescharacteristic
26C22×C8×D43C2212yes—
27#14583610C2211yescharacteristic, complemented
28#14583609C2211yescharacteristic, complemented
29#14583608—21no—
30#14583607C2212yescomplemented
31#14583606C2211yescharacteristic, complemented
32#14583605—21no—
33#14583604C2212yescomplemented
34#14583603—22no—
35#14583554C2211yescharacteristic
36#14583553C2211yescharacteristic
37#14583552C2211yescharacteristic
38#14583551—21no—
39#14583550C2212yes—
40#14583549C2212yes—
41#14583548—21no—
42#14583547—22no—
43C4⋊Q8×D43C2211yescharacteristic
44C4⋊Q8×D43C2211yescharacteristic
45#125×D43—21no—
46#123×D43—22no—
47C22⋊Q8×D43—21no—
48C22⋊Q8×D43—22no—
49C22⋊Q8×D43C2212yes—
50#121×D43C2212yes—
51C4×Q8×D43C2211yescharacteristic
52C4×D4×D43—21no—
53C4×D4×D43C2211yescharacteristic
54C4×D4×D43C2211yescharacteristic
55C2×C4⋊C4×D43C2212yes—
56C2×C4⋊C4×D43C2212yes—
57#14583297C2211yescharacteristic, complemented
58#14583296C2212yescomplemented
59#14583296C2212yescomplemented
60#14583295C2211yescharacteristic, complemented
61#14583295C2211yescharacteristic, complemented
62#14583231C2212yescomplemented
63#14583231C2212yescomplemented
64#14583230C2212yescomplemented
65#14583229C2212yescomplemented
66#14583228C2212yescomplemented
67#14583228C2212yescomplemented
68#14583227C2212yescomplemented
69#14583219C2212yescomplemented
70#14583219C2212yescomplemented
71#14583218C2212yescomplemented
72#14583217C2212yescomplemented
73#14583216C2212yescomplemented
74#14583216C2212yescomplemented
75#14583215C2212yescomplemented
76#14583190C2211yescharacteristic, complemented
77#14583189C2211yescharacteristic, complemented
78#14583188C2212yescomplemented
79#14583187C2212yescomplemented
80#14583186C2211yescharacteristic, complemented
81#14583185C2211yescharacteristic, complemented
82#14583184C2211yescharacteristic, complemented
83#14583183C2212yescomplemented
84#14583182C2212yescomplemented
85#14583181C2211yescharacteristic, complemented
86#14583131C2212yescomplemented
87#14583130C2212yescomplemented
88#14583129C2212yescomplemented
89#14583128C2212yescomplemented
90#14583127C2212yescomplemented
91#14583126C2212yescomplemented
92#14583125C2212yescomplemented
93#14582990C2211yescharacteristic, complemented
94C4×#10621873C2211yescharacteristic, complemented
95SD16×Dic43C2211yescharacteristic, complemented
96C4×#10621884C2211yescharacteristic, complemented
97#14582986C2211yescharacteristic, complemented
98C4×#10621883C2211yescharacteristic, complemented
99#14582984C2211yescharacteristic, complemented
100C8×D172C2211yescharacteristic, complemented
101D4×C43⋊C8C2211yescharacteristic, complemented
102#14582964C2211yescharacteristic, complemented
103C8×C22⋊D43C2212yescomplemented
104(C22⋊D43)⋊C8C2212yescomplemented
105C2×#13063257C2212yescomplemented
106C2×#13063256C2212yescomplemented
107C2×#13063256C2212yescomplemented
108#106×D43C2212yes—
109#106×D43C2212yes—
110#106×D43C2212yes—
111#106×D43C2212yes—
112#106×D43C2211yescharacteristic
113#106×D43C2212yescomplemented
114#106×D43C2212yescomplemented
115#106×D43C2212yescomplemented
116#106×D43C2212yescomplemented
117C4⋊C8×D43C2211yescharacteristic
118#103×D43C2211yescharacteristic
119#103×D43C2212yes—
120#102×D43C2211yescharacteristic
121#102×D43C2212yes—
122C22⋊C8×D43C2212yes—
123C4×C8×D43C2211yescharacteristic
124C43×#554C2211yescharacteristic, complemented
125C43×#547C2211yescharacteristic
126C43×#498C2211yescharacteristic, complemented
127C43×#483C2212yescomplemented
128C43×#481C2212yescomplemented
129C43×#476C2211yescharacteristic, complemented
130C43×#475C2211yescharacteristic, complemented
131C43×#465C2212yescomplemented
132C4×SD16×C43C2211yescharacteristic, complemented
133C8×D4×C43C2211yescharacteristic, complemented
134C2×#106×C43C2212yescomplemented
135C2×#10621902—21no—
136C2×#10621898—22no—
137C2×#10621898—21no—
138C2×#10621900—21no—
139C2×#10621900—22no—
140#41×D43—48no—
141C2×Q8×D43—21no—
142C2×Q8×D43—21no—
143C2×Q8×D43C2311yescharacteristic
144C2×D4×D43—22no—
145C2×D4×D43D411yescharacteristic
146C2×D4×D43C2311yescharacteristic
147C22×C4×D43—22no—
148C22×C4×D43—22no—
149C22×C4×D43—21no—
150C22×C4×D43C2312yes—
151C2×#10621873C2311yescharacteristic
152C2×#10621883C2311yescharacteristic
153C2×#10621884C2311yescharacteristic
154SD16×D43—24no—
155C22×C43⋊C8C2312yes—
156C2×C8×D43—28no—
157C2×C8×D43C2311yescharacteristic
158C2×C8×D43C2312yes—
159C2×C8×D43C2312yes—
160C2×C8×D43C2312yes—
161C2×C8×D43C2311yescharacteristic
162#13063325C2311yescharacteristic
163#13063325C2311yescharacteristic
164#13063324—21no—
165#13063324—21no—
166#13063324C2312yes—
167#13063324C2312yes—
168#13063323—21no—
169#13063323—21no—
170#13063317—21no—
171#13063316—21no—
172#13063316—21no—
173#13063315—22no—
174#13063315—22no—
175#13063310—22no—
176#13063310—22no—
177#13063309—22no—
178#13063308—22no—
179#13063307—22no—
180#13063307—22no—
181#13063306—22no—
182#13063305—21no—
183#13063305—22no—
184#13063305C2312yes—
185#13063304—22no—
186#13063304—21no—
187#13063304C2312yes—
188#13063303—22no—
189#13063303—22no—
190#13063303—22no—
191#13063303—22no—
192#13063302—22no—
193#13063302—22no—
194#13063302—22no—
195#13063302—22no—
196#13063301—22no—
197#13063301—21no—
198#13063301C2312yes—
199#13063300C2312yes—
200#13063299C2312yes—
201#13063298—22no—
202#13063297—22no—
203#13063296C2312yes—
204Q8×Dic43C2311yescharacteristic
205C4×Dic86—21no—
206C4×Dic86C2311yescharacteristic
207#13063290—21no—
208#13063290C2311yescharacteristic
209C4×D172—21no—
210C4×D172C2311yescharacteristic
211C4×D172C2311yescharacteristic
212D4×Dic43—21no—
213D4×Dic43D411yescharacteristic
214D4×Dic43C2311yescharacteristic
215#13063287—21no—
216#13063287D411yescharacteristic
217#13063287C2311yescharacteristic
218C4×C22⋊D43—22no—
219C4×C22⋊D43—21no—
220C4×C22⋊D43C2312yes—
221(C22⋊D43)⋊C4—22no—
222(C22⋊D43)⋊C4—21no—
223(C22⋊D43)⋊C4D412yes—
224C2×C4⋊Dic43C2312yes—
225C2×C4⋊Dic43C2312yes—
226C2×Dic43⋊C4—22no—
227C2×Dic43⋊C4—22no—
228C4⋊C4×D43—22no—
229C4⋊C4×D43—22no—
230C4⋊C4×D43—22no—
231C4⋊C4×D43—22no—
232C4⋊C4×D43—21no—
233C4⋊C4×D43—21no—
234C4⋊C4×D43—22no—
235C4⋊C4×D43—21no—
236C4⋊C4×D43D411yescharacteristic
237C4⋊C4×D43C2312yes—
238C4⋊C4×D43C2312yes—
239C4⋊C4×D43C2311yescharacteristic
240C4⋊C4×D43C2311yescharacteristic
241C4⋊C4×D43C2312yes—
242C4⋊C4×D43C2312yes—
243C4⋊C4×D43C2312yes—
244C4⋊C4×D43C2312yes—
245C22⋊C4×D43—22no—
246C22⋊C4×D43—21no—
247C22⋊C4×D43—22no—
248C22⋊C4×D43D412yes—
249C42×D43—21no—
250C42×D43C2311yescharacteristic
251#13063257C2312yes—
252#13063257C2312yes—
253#13063257C2312yes—
254#13063257C2311yescharacteristic
255#13063257C2312yes—
256#13063256C2312yes—
257#13063256C2312yes—
258#13063256C2312yes—
259#13063256C2312yes—
260#13063256C2312yes—
261#13063256C2312yes—
262#13063256C2311yescharacteristic
263#13063256C2311yescharacteristic
264#13063256C2312yes—
265#13063256C2312yes—
266C4⋊(C43⋊C8)C2311yescharacteristic
267Dic43⋊C8C2312yes—
268#13063250C2312yes—
269#13063250C2311yescharacteristic
270#13063249C2312yes—
271#13063249C2311yescharacteristic
272#13063248C2312yes—
273#13063248C2311yescharacteristic
274#13063247C2312yes—
275#13063247C2311yescharacteristic
276#13063246C2312yes—
277#13063246C2311yescharacteristic
278#13063245C2312yes—
279#13063245C2311yescharacteristic
280C22⋊(C43⋊C8)C2312yes—
281(C2×D43)⋊C8C2312yes—
282(C2×D43)⋊C8C2312yes—
283C4×C43⋊C8C2311yescharacteristic
284C8×Dic43C2311yescharacteristic
285C8×Dic43C2311yescharacteristic
286C2×#41×C43—21no—
287C2×SD16×C43C2311yescharacteristic
288C22×C8×C43C2312yes—
289C4⋊Q8×C43C2311yescharacteristic
290C4⋊Q8×C43C2311yescharacteristic
291#125×C43—21no—
292#123×C43—22no—
293C22⋊Q8×C43—21no—
294C22⋊Q8×C43—22no—
295C22⋊Q8×C43C2312yes—
296#121×C43C2312yes—
297C4×Q8×C43C2311yescharacteristic
298C4×D4×C43—21no—
299C4×D4×C43C2311yescharacteristic
300C4×D4×C43C2311yescharacteristic
301C2×C4⋊C4×C43C2312yes—
302C2×C4⋊C4×C43C2312yes—
303#106×C43C2312yes—
304#106×C43C2312yes—
305#106×C43C2312yes—
306#106×C43C2311yescharacteristic
307#106×C43C2312yes—
308C4⋊C8×C43C2311yescharacteristic
309#103×C43C2312yes—
310#103×C43C2311yescharacteristic
311#102×C43C2312yes—
312#102×C43C2311yescharacteristic
313C22⋊C8×C43C2312yes—
314C4×C8×C43C2311yescharacteristic
315C23×D43—21no—
316C23×D43C2×D412yes—
317#41×C43—44no—
318C2×Q8×C43—21no—
319C2×Q8×C43—21no—
320C2×Q8×C43C2411yescharacteristic
321C2×D4×C43—22no—
322C2×D4×C43C2×D411yescharacteristic
323C2×D4×C43C2411yescharacteristic
324C22×C4×C43—21no—
325C22×C4×C43—22no—
326C22×C4×C43—22no—
327C22×C4×C43C2412yes—
328C2×C22⋊D43—21no—
329C2×C22⋊D43—22no—
330C2×C22⋊D43—22no—
331C2×C22⋊D43C2×D412yes—
332C22×Dic43—21no—
333C22×Dic43—22no—
334C22×Dic43—22no—
335C22×Dic43C2×D412yes—
336#10621902—44no—
337Q8×D43—22no—
338Q8×D43—22no—
339Q8×D43—44no—
340Q8×D43—82no—
341#10621900—44no—
342#10621900—48no—
343D4×D43—22no—
344D4×D43—22no—
345D4×D43—48no—
346D4×D43SD1618yescomplemented
347#10621898—48no—
348#10621898—44no—
349C2×D172—22no—
350C2×D172C2×D411yescharacteristic
351C2×D172C2411yescharacteristic
352C2×C4×D43—24no—
353C2×C4×D43—24no—
354C2×C4×D43—21no—
355C2×C4×D43—21no—
356C2×C4×D43—21no—
357C2×C4×D43—21no—
358C2×C4×D43—22no—
359C2×C4×D43—21no—
360C2×C4×D43—22no—
361C2×C4×D43—22no—
362C2×C4×D43—22no—
363C2×C4×D43—22no—
364C2×C4×D43—22no—
365C2×C4×D43—44no—
366C2×C4×D43—48no—
367C2×C4×D43—84no—
368C2×C4×D43C2×D411yescharacteristic
369C2×C4×D43C2×D412yes—
370C2×C4×D43C2×D412yes—
371C2×C4×D43C2×D411yescharacteristic
372C2×C4×D43C2412yes—
373C2×C4×D43C2411yescharacteristic
374C2×Dic86—21no—
375C2×Dic86—21no—
376C2×Dic86—22no—
377C2×Dic86—21no—
378C2×Dic86—22no—
379C2×Dic86C2411yescharacteristic
380SD16×C43—22no—
381C2×C8×C43—24no—
382C2×C8×C43C2411yescharacteristic
383C2×C8×C43C2412yes—
384C2×C8×C43C2411yescharacteristic
385C4⋊C4×C43—22no—
386C4⋊C4×C43—22no—
387C4⋊C4×C43—21no—
388C4⋊C4×C43—21no—
389C4⋊C4×C43—22no—
390C4⋊C4×C43—21no—
391C4⋊C4×C43C2×D411yescharacteristic
392C4⋊C4×C43C2411yescharacteristic
393C4⋊C4×C43C2412yes—
394C4⋊C4×C43C2411yescharacteristic
395C4⋊C4×C43C2412yes—
396C22⋊C4×C43—21no—
397C22⋊C4×C43—22no—
398C22⋊C4×C43—22no—
399C22⋊C4×C43C2×D412yes—
400C42×C43—21no—
401C42×C43C2411yescharacteristic
402C22⋊Dic43—21no—
403C22⋊Dic43—22no—
404C22⋊Dic43—22no—
405C22⋊Dic43C2×D412yes—
406#10621884—22no—
407#10621883—22no—
408(C2×D43)⋊C4—21no—
409(C2×D43)⋊C4—22no—
410(C2×D43)⋊C4—21no—
411(C2×D43)⋊C4—22no—
412(C2×D43)⋊C4—22no—
413(C2×D43)⋊C4—22no—
414(C2×D43)⋊C4C2×D412yes—
415(C2×D43)⋊C4C2×D412yes—
416C4⋊Dic43—22no—
417C4⋊Dic43—22no—
418C4⋊Dic43—21no—
419C4⋊Dic43—21no—
420C4⋊Dic43—21no—
421C4⋊Dic43—22no—
422C4⋊Dic43C2×D411yescharacteristic
423C4⋊Dic43C2411yescharacteristic
424C4⋊Dic43C2412yes—
425C4⋊Dic43C2411yescharacteristic
426C4⋊Dic43C2412yes—
427Dic43⋊C4—21no—
428Dic43⋊C4—22no—
429Dic43⋊C4—21no—
430Dic43⋊C4—21no—
431Dic43⋊C4—22no—
432Dic43⋊C4—22no—
433Dic43⋊C4—22no—
434Dic43⋊C4—22no—
435Dic43⋊C4—22no—
436Dic43⋊C4—22no—
437Dic43⋊C4—22no—
438Dic43⋊C4—21no—
439Dic43⋊C4—22no—
440Dic43⋊C4—22no—
441Dic43⋊C4C2×D412yes—
442C4×Dic43—21no—
443C4×Dic43—21no—
444C4×Dic43—21no—
445C4×Dic43C2×D411yescharacteristic
446C4×Dic43C2×D411yescharacteristic
447C4×Dic43C2411yescharacteristic
448C2×C43⋊C8—24no—
449C2×C43⋊C8C2411yescharacteristic
450C2×C43⋊C8C2412yes—
451C2×C43⋊C8C2411yescharacteristic
452#10621873—22no—
453C8×D43—24no—
454C8×D43—22no—
455C8×D43—24no—
456C8×D43—24no—
457C8×D43#4114yescomplemented
458C23×C43—21no—
459C23×C43C22×D412yes—
460C22×D43—24no—
461C22×D43—24no—
462C22×D43—21no—
463C22×D43—42no—
464C22×D43—42no—
465C22×D43—42no—
466C22×D43C2×SD1618yes—
467C22×D43C22×D412yes—
468C22×D43C22×D411yescharacteristic
469Q8×C43—21no—
470Q8×C43—21no—
471Q8×C43—42no—
472Q8×C43—81no—
473D4×C43—21no—
474D4×C43—21no—
475D4×C43—44no—
476D4×C43C2×SD1614yescomplemented
477C2×C4×C43—22no—
478C2×C4×C43—22no—
479C2×C4×C43—21no—
480C2×C4×C43—21no—
481C2×C4×C43—22no—
482C2×C4×C43—22no—
483C2×C4×C43—21no—
484C2×C4×C43—44no—
485C2×C4×C43—42no—
486C2×C4×C43—82no—
487C2×C4×C43C22×D411yescharacteristic
488C2×C4×C43C22×D412yes—
489C2×C4×C43C22×D411yescharacteristic
490C2×C4×C43C2511yescharacteristic
491C22⋊D43—44no—
492C22⋊D43—44no—
493C22⋊D43—42no—
494C22⋊D43C2×SD1618yescomplemented
495C2×Dic43—24no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—21no—
501C2×Dic43—44no—
502C2×Dic43—42no—
503C2×Dic43—82no—
504C2×Dic43C22×D411yescharacteristic
505C2×Dic43C22×D412yes—
506C2×Dic43C22×D411yescharacteristic
507C2×Dic43C22×D411yescharacteristic
508D172—21no—
509D172—21no—
510D172—44no—
511D172C2×SD1614yescomplemented
512C4×D43—24no—
513C4×D43—22no—
514C4×D43—22no—
515C4×D43—22no—
516C4×D43—24no—
517C4×D43—42no—
518C4×D43—42no—
519C4×D43—44no—
520C4×D43—44no—
521C4×D43—44no—
522C4×D43—42no—
523C4×D43—44no—
524C4×D43—42no—
525C4×D43—42no—
526C4×D43—82no—
527C4×D43—82no—
528C4×D43C2×SD1614yes—
529C4×D43C2×#4112yes—
530C4×D432−1+412yes—
531Dic86—21no—
532Dic86—21no—
533Dic86—42no—
534Dic86—42no—
535Dic86—44no—
536Dic86—82no—
537Dic86—81no—
538C8×C43—22no—
539C8×C43—21no—
540C8×C43C2×#4112yescomplemented
541C43⋊C8—22no—
542C43⋊C8—21no—
543C43⋊C8C2×#4112yescomplemented
544C2×#3335—431nomaximal, Sylow
545C22×C43—22no—
546C22×C43—22no—
547C22×C43—41no—
548C22×C43—41no—
549C22×C43—41no—
550C22×C43C22×SD1614yes—
551C22×C43C23×D411yescharacteristic
552C2×D43—22no—
553C2×D43—22no—
554C2×D43—216no—
555C2×D43—41no—
556C2×D43—41no—
557C2×D43—41no—
558C2×D43—84no—
559C2×D43#54712yes—
560C2×D43C22×SD1614yes—
561C2×D43C22×SD1612yes—
562C2×D43#57712yes—
563C4×C43—22no—
564C4×C43—21no—
565C4×C43—41no—
566C4×C43—42no—
567C4×C43—41no—
568C4×C43—42no—
569C4×C43—41no—
570C4×C43C22×SD1612yes—
571C4×C43C22×#4111yescharacteristic
572C4×C43C2×2−1+411yescharacteristic
573Dic43—22no—
574Dic43—21no—
575Dic43—41no—
576Dic43—42no—
577Dic43—41no—
578Dic43—42no—
579Dic43—41no—
580Dic43#54712yes—
581Dic43C22×SD1612yes—
582C2×#554—431no—
583C2×#547—431no—
584#3335—431no—
585#3335—432no—
586#3335—432no—
587#3335—431no—
588#3335—431no—
589#3335—432no—
590#3335—431no—
591#3335—431no—
592#3335—432no—
593#3335—431no—
594#3335—431no—
595#3335D4311yescharacteristic, direct product factor
596C2×#498—431no—
597C2×#481—432no—
598C2×#483—432no—
599C2×#475—431no—
600C2×#476—431no—
601C2×#465—432no—
602C2×C4×SD16—431no—
603C2×C8×D4—431no—
604C22×#106—432no—
605C2×C43—24no—
606C2×C43—81no—
607C2×C43C2×#54711yescharacteristic
608C2×C43C23×SD1611yescharacteristic
609C2×C43C2×#57711yescharacteristic
610D43—24no—
611D43—81no—
612D43#333514yesdirect product factor
613C22×#41—861no—
614C22×SD16—431no—
615C23×C8—432no—
616#554—431no—
617#554—432no—
618#554—431no—
619#554—431no—
620#554—432no—
621#554—861no—
622#554—862no—
623#554—861no—
624#554C2×D4311yescharacteristic, complemented
625#547—431no—
626#547—432no—
627#547—431no—
628#547—431no—
629#547—432no—
630#547—861no—
631#547—862no—
632#547—861no—
633#547C2×D4311yescharacteristic
634C2×C4⋊Q8—431no—
635C2×C4⋊Q8—431no—
636C2×#125—861no—
637C2×#123—862no—
638C2×C22⋊Q8—432no—
639C2×C22⋊Q8—862no—
640C2×C22⋊Q8—861no—
641C2×#121—432no—
642C2×C4×Q8—431no—
643C2×C4×D4—431no—
644C2×C4×D4—431no—
645C2×C4×D4—861no—
646C22×C4⋊C4—432no—
647C22×C4⋊C4—432no—
648#498—431no—
649#498—431no—
650#498—432no—
651#498—432no—
652#498—431no—
653#498C2×D4311yescharacteristic, complemented
654#483—432no—
655#483—432no—
656#483—432no—
657#483—432no—
658#483—432no—
659#483—432no—
660#483—432no—
661#483C2×D4312yescomplemented
662#481—432no—
663#481—432no—
664#481—432no—
665#481—432no—
666#481—432no—
667#481—432no—
668#481—432no—
669#481C2×D4312yescomplemented
670#476—431no—
671#476—431no—
672#476—432no—
673#476—431no—
674#476—432no—
675#476C2×D4311yescharacteristic, complemented
676#475—431no—
677#475—431no—
678#475—432no—
679#475—431no—
680#475—432no—
681#475C2×D4311yescharacteristic, complemented
682#465—432no—
683#465—432no—
684#465—432no—
685#465—432no—
686#465—432no—
687#465—432no—
688#465—432no—
689#465C2×D4312yescomplemented
690C4×SD16—431no—
691C4×SD16—431no—
692C4×SD16—431no—
693C4×SD16—431no—
694C4×SD16—431no—
695C4×SD16—431no—
696C4×SD16—431no—
697C4×SD16C2×D4311yescharacteristic, complemented
698C8×D4—432no—
699C8×D4—431no—
700C8×D4—431no—
701C8×D4—432no—
702C8×D4—431no—
703C8×D4C2×D4311yescharacteristic, complemented
704C2×#106—432no—
705C2×#106—432no—
706C2×#106—432no—
707C2×#106—432no—
708C2×#106—432no—
709C2×#106—432no—
710C2×#106—432no—
711C2×#106—432no—
712C2×#106—432no—
713C2×#106—432no—
714C2×#106—432no—
715C2×#106—431no—
716C2×#106C2×D4312yescomplemented
717C2×C4⋊C8—431no—
718C2×#103—432no—
719C2×#103—431no—
720C2×#102—431no—
721C2×#102—432no—
722C2×C22⋊C8—432no—
723C2×C4×C8—431no—
724C43C2×#333511yescharacteristic, complemented, Sylow
725C2×#41—21no—
726C2×#41—862no—
727C2×#41—861no—
728C2×#41—862no—
729C2×#41—861no—
730C2×#41—861no—
731C2×#41—1728no—
732C22×Q8—431no—
733C22×Q8—861no—
734C22×Q8—861no—
735C22×D4—431no—
736C22×D4—431no—
737C22×D4—862no—
738C23×C4—432no—
739C23×C4—861no—
740C23×C4—862no—
741C23×C4—862no—
742C2×SD16—431no—
743C2×SD16—431no—
744C2×SD16—431no—
745C2×SD16—864no—
746C2×SD16C22×D4311yescharacteristic
747C22×C8—431no—
748C22×C8—432no—
749C22×C8—432no—
750C22×C8—432no—
751C22×C8—432no—
752C22×C8—431no—
753C22×C8—868no—
754C22×C8C22×D4312yes—
755C4⋊Q8—432no—
756C4⋊Q8—432no—
757C4⋊Q8—431no—
758C4⋊Q8—431no—
759C4⋊Q8—861no—
760C4⋊Q8—861no—
761C4⋊Q8—861no—
762C4⋊Q8—861no—
763C4⋊Q8C22×D4311yescharacteristic
764C4⋊Q8C22×D4311yescharacteristic
765#125—21no—
766#125—861no—
767#125—862no—
768#125—862no—
769#125—861no—
770#125—861no—
771#123—22no—
772#123—862no—
773#123—862no—
774#123—862no—
775#123—862no—
776#123—862no—
777#123—862no—
778#123—862no—
779C22⋊Q8—21no—
780C22⋊Q8—22no—
781C22⋊Q8—432no—
782C22⋊Q8—432no—
783C22⋊Q8—432no—
784C22⋊Q8—862no—
785C22⋊Q8—862no—
786C22⋊Q8—862no—
787C22⋊Q8—862no—
788C22⋊Q8—862no—
789C22⋊Q8—862no—
790C22⋊Q8—862no—
791C22⋊Q8—862no—
792C22⋊Q8—862no—
793C22⋊Q8—862no—
794C22⋊Q8—861no—
795C22⋊Q8—861no—
796C22⋊Q8—861no—
797C22⋊Q8—862no—
798C22⋊Q8C22×D4312yes—
799#121—432no—
800#121—432no—
801#121—432no—
802#121—862no—
803#121—862no—
804#121C22×D4312yes—
805C4×Q8—431no—
806C4×Q8—431no—
807C4×Q8—431no—
808C4×Q8—861no—
809C4×Q8—861no—
810C4×Q8C22×D4311yescharacteristic
811C4×D4—21no—
812C4×D4—431no—
813C4×D4—432no—
814C4×D4—431no—
815C4×D4—432no—
816C4×D4—431no—
817C4×D4—431no—
818C4×D4—431no—
819C4×D4—431no—
820C4×D4—861no—
821C4×D4—861no—
822C4×D4—861no—
823C4×D4—862no—
824C4×D4—861no—
825C4×D4—862no—
826C4×D4—861no—
827C4×D4C22×D4311yescharacteristic
828C4×D4C22×D4311yescharacteristic
829C2×C4⋊C4—431no—
830C2×C4⋊C4—432no—
831C2×C4⋊C4—432no—
832C2×C4⋊C4—431no—
833C2×C4⋊C4—431no—
834C2×C4⋊C4—432no—
835C2×C4⋊C4—432no—
836C2×C4⋊C4—432no—
837C2×C4⋊C4—432no—
838C2×C4⋊C4—432no—
839C2×C4⋊C4—432no—
840C2×C4⋊C4—862no—
841C2×C4⋊C4—862no—
842C2×C4⋊C4—862no—
843C2×C4⋊C4—862no—
844C2×C4⋊C4—861no—
845C2×C4⋊C4—861no—
846C2×C4⋊C4—862no—
847C2×C4⋊C4—861no—
848C2×C4⋊C4—862no—
849C2×C4⋊C4—862no—
850C2×C4⋊C4C22×D4312yes—
851C2×C4⋊C4C22×D4312yes—
852C2×C22⋊C4—432no—
853C2×C22⋊C4—861no—
854C2×C22⋊C4—862no—
855C2×C22⋊C4—862no—
856C2×C42—431no—
857C2×C42—861no—
858#106—431no—
859#106—432no—
860#106—432no—
861#106—432no—
862#106—432no—
863#106—431no—
864#106—431no—
865#106—432no—
866#106—432no—
867#106—432no—
868#106—432no—
869#106—432no—
870#106—432no—
871#106—432no—
872#106—432no—
873#106C22×D4311yescharacteristic
874#106C22×D4312yes—
875#106C22×D4312yes—
876#106C22×D4312yes—
877#106C22×D4312yes—
878C4⋊C8—432no—
879C4⋊C8—431no—
880C4⋊C8C22×D4311yescharacteristic
881#103—431no—
882#103—432no—
883#103—431no—
884#103—432no—
885#103—431no—
886#103—432no—
887#103C22×D4311yescharacteristic
888#103C22×D4312yes—
889#102—431no—
890#102—432no—
891#102—431no—
892#102—432no—
893#102—431no—
894#102—432no—
895#102C22×D4311yescharacteristic
896#102C22×D4312yes—
897C22⋊C8—432no—
898C22⋊C8—432no—
899C22⋊C8—432no—
900C22⋊C8C22×D4312yes—
901C4×C8—431no—
902C4×C8—431no—
903C4×C8—431no—
904C4×C8C22×D4311yescharacteristic
905C24—432no—
906C24—861no—
907#41—44no—
908#41—1728no—
909#41—1724no—
910#41—1728no—
911#41—1724no—
912#41—1724no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—431no—
916C2×Q8—862no—
917C2×Q8—861no—
918C2×Q8—862no—
919C2×Q8—862no—
920C2×Q8—862no—
921C2×Q8—861no—
922C2×Q8—861no—
923C2×Q8—3442no—
924C2×Q8—1724no—
925C2×Q8C23×D4311yescharacteristic
926C2×D4—22no—
927C2×D4—432no—
928C2×D4—438no—
929C2×D4—431no—
930C2×D4—431no—
931C2×D4—862no—
932C2×D4—862no—
933C2×D4—862no—
934C2×D4—861no—
935C2×D4—862no—
936C2×D4—862no—
937C2×D4—1728no—
938C2×D4D4×D4311yescharacteristic
939C2×D4C23×D4311yescharacteristic
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—21no—
943C22×C4—431no—
944C22×C4—431no—
945C22×C4—432no—
946C22×C4—431no—
947C22×C4—432no—
948C22×C4—432no—
949C22×C4—432no—
950C22×C4—864no—
951C22×C4—864no—
952C22×C4—861no—
953C22×C4—862no—
954C22×C4—862no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—862no—
958C22×C4—861no—
959C22×C4—862no—
960C22×C4—862no—
961C22×C4—862no—
962C22×C4—861no—
963C22×C4—862no—
964C22×C4—862no—
965C22×C4—861no—
966C22×C4—3444no—
967C22×C4—1724no—
968C22×C4—1728no—
969C22×C4C23×D4312yes—
970SD16—22no—
971SD16—862no—
972SD16—862no—
973SD16—862no—
974C2×C8—24no—
975C2×C8—431no—
976C2×C8—434no—
977C2×C8—431no—
978C2×C8—432no—
979C2×C8—864no—
980C2×C8—864no—
981C2×C8—862no—
982C2×C8—864no—
983C2×C8—864no—
984C2×C8C23×D4311yescharacteristic
985C2×C8C23×D4312yes—
986C2×C8C23×D4311yescharacteristic
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—432no—
994C4⋊C4—431no—
995C4⋊C4—431no—
996C4⋊C4—432no—
997C4⋊C4—431no—
998C4⋊C4—432no—
999C4⋊C4—861no—
1000C4⋊C4—861no—
1001C4⋊C4—862no—
1002C4⋊C4—862no—
1003C4⋊C4—862no—
1004C4⋊C4—862no—
1005C4⋊C4—862no—
1006C4⋊C4—862no—
1007C4⋊C4—862no—
1008C4⋊C4—861no—
1009C4⋊C4—861no—
1010C4⋊C4—862no—
1011C4⋊C4—862no—
1012C4⋊C4—862no—
1013C4⋊C4—862no—
1014C4⋊C4—862no—
1015C4⋊C4—861no—
1016C4⋊C4—861no—
1017C4⋊C4—862no—
1018C4⋊C4—861no—
1019C4⋊C4D4×D4311yescharacteristic
1020C4⋊C4C23×D4311yescharacteristic
1021C4⋊C4C23×D4312yes—
1022C4⋊C4C23×D4311yescharacteristic
1023C4⋊C4C23×D4312yes—
1024C22⋊C4—22no—
1025C22⋊C4—21no—
1026C22⋊C4—22no—
1027C22⋊C4—432no—
1028C22⋊C4—432no—
1029C22⋊C4—432no—
1030C22⋊C4—861no—
1031C22⋊C4—862no—
1032C22⋊C4—862no—
1033C22⋊C4—862no—
1034C22⋊C4—861no—
1035C22⋊C4—862no—
1036C22⋊C4—862no—
1037C22⋊C4—861no—
1038C22⋊C4—862no—
1039C22⋊C4D4×D4312yes—
1040C42—21no—
1041C42—431no—
1042C42—431no—
1043C42—431no—
1044C42—861no—
1045C42—861no—
1046C42—861no—
1047C42C23×D4311yescharacteristic
1048C23—21no—
1049C23—431no—
1050C23—438no—
1051C23—432no—
1052C23—864no—
1053C23—864no—
1054C23—861no—
1055C23—1722no—
1056C23—1722no—
1057C23—1722no—
1058C23C2×D4×D4312yes—
1059Q8—21no—
1060Q8—21no—
1061Q8—42no—
1062Q8—81no—
1063Q8—861no—
1064Q8—861no—
1065Q8—3441no—
1066Q8—3442no—
1067Q8—1722no—
1068Q8—1724no—
1069Q8—1722no—
1070D4—21no—
1071D4—21no—
1072D4—44no—
1073D4—438no—
1074D4—434no—
1075D4—861no—
1076D4—861no—
1077D4—1724no—
1078D4—1722no—
1079D4—1724no—
1080D4—1724no—
1081D4SD16×D4314yescomplemented
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—44no—
1090C2×C4—42no—
1091C2×C4—82no—
1092C2×C4—431no—
1093C2×C4—431no—
1094C2×C4—434no—
1095C2×C4—432no—
1096C2×C4—432no—
1097C2×C4—431no—
1098C2×C4—432no—
1099C2×C4—864no—
1100C2×C4—864no—
1101C2×C4—862no—
1102C2×C4—864no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—861no—
1106C2×C4—861no—
1107C2×C4—862no—
1108C2×C4—861no—
1109C2×C4—862no—
1110C2×C4—3442no—
1111C2×C4—3442no—
1112C2×C4—3442no—
1113C2×C4—1722no—
1114C2×C4—1722no—
1115C2×C4—1724no—
1116C2×C4—1722no—
1117C2×C4—1724no—
1118C2×C4—1724no—
1119C2×C4—1724no—
1120C2×C4—1722no—
1121C2×C4—1722no—
1122C2×C4—1724no—
1123C2×C4—1722no—
1124C2×C4C2×D4×D4311yescharacteristic
1125C2×C4C2×D4×D4312yes—
1126C2×C4C2×D4×D4311yescharacteristic
1127C2×C4C24×D4311yescharacteristic
1128C8—22no—
1129C8—21no—
1130C8—432no—
1131C8—862no—
1132C8—861no—
1133C8#41×D4312yescomplemented
1134C22—22no—
1135C22—22no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—432no—
1140C22—432no—
1141C22—432no—
1142C22—434no—
1143C22—8616no—
1144C22—862no—
1145C22—862no—
1146C22—3444no—
1147C22—1721no—
1148C22—1721no—
1149C22—1721no—
1150C22C2×SD16×D4314yes—
1151C22C22×D4×D4311yescharacteristic
1152C4—22no—
1153C4—21no—
1154C4—41no—
1155C4—42no—
1156C4—41no—
1157C4—41no—
1158C4—42no—
1159C4—432no—
1160C4—432no—
1161C4—862no—
1162C4—861no—
1163C4—1721no—
1164C4—1722no—
1165C4—1721no—
1166C4—1721no—
1167C4—1722no—
1168C4C2×SD16×D4312yes—
1169C4C2×#41×D4311yescharacteristic
1170C42−1+4×D4311yescharacteristic
1171C2—24no—
1172C2—81no—
1173C2—434no—
1174C2—864no—
1175C2—3441no—
1176C2#547×D4311yescharacteristic
1177C2C22×SD16×D4311yescharacteristic
1178C2#577×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3335C2
socleC22×C43C23×D4
prime radical#547×D43C2
hypercenter#3335D43
hypocenterC43C2×#3335
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3335

Complements

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

NH ≅ G/Ntype
1. #554×D43C2semidirect
3. #19146955C2semidirect
4. #19146954C2semidirect
5. #19146953C2semidirect
6. #19146952C2semidirect
7. #19146951C2semidirect
8. #19146950C2semidirect
9. #19146949C2semidirect
10. #19146948C2semidirect
11. #19146947C2semidirect
12. #19146946C2semidirect
13. #19146945C2semidirect
14. #498×D43C2semidirect
15. #481×D43C2semidirect
16. #483×D43C2semidirect
17. #475×D43C2semidirect
18. #476×D43C2semidirect
19. #465×D43C2semidirect
20. C4×SD16×D43C2semidirect
21. C8×D4×D43C2semidirect
22. C2×#106×D43C2semidirect
23. C43×#3335C2semidirect
27. #14583610C22semidirect
28. #14583609C22semidirect
30. #14583607C22semidirect
31. #14583606C22semidirect
33. #14583604C22semidirect
57. #14583297C22semidirect
58. #14583296C22semidirect
59. #14583296C22semidirect
60. #14583295C22semidirect
61. #14583295C22semidirect
62. #14583231C22semidirect
63. #14583231C22semidirect
64. #14583230C22semidirect
65. #14583229C22semidirect
66. #14583228C22semidirect
67. #14583228C22semidirect
68. #14583227C22semidirect
69. #14583219C22semidirect
70. #14583219C22semidirect
71. #14583218C22semidirect
72. #14583217C22semidirect
73. #14583216C22semidirect
74. #14583216C22semidirect
75. #14583215C22semidirect
76. #14583190C22semidirect
77. #14583189C22semidirect
78. #14583188C22semidirect
79. #14583187C22semidirect
80. #14583186C22semidirect
81. #14583185C22semidirect
82. #14583184C22semidirect
83. #14583183C22semidirect
84. #14583182C22semidirect
85. #14583181C22semidirect
86. #14583131C22semidirect
87. #14583130C22semidirect
88. #14583129C22semidirect
89. #14583128C22semidirect
90. #14583127C22semidirect
91. #14583126C22semidirect
92. #14583125C22semidirect
93. #14582990C22semidirect
94. C4×#10621873C22semidirect
95. SD16×Dic43C22semidirect
96. C4×#10621884C22semidirect
97. #14582986C22semidirect
98. C4×#10621883C22semidirect
99. #14582984C22semidirect
100. C8×D172C22semidirect
101. D4×C43⋊C8C22semidirect
102. #14582964C22semidirect
103. C8×C22⋊D43C22semidirect
104. (C22⋊D43)⋊C8C22semidirect
105. C2×#13063257C22semidirect
106. C2×#13063256C22semidirect
107. C2×#13063256C22semidirect
113. #106×D43C22semidirect
114. #106×D43C22semidirect
115. #106×D43C22semidirect
116. #106×D43C22semidirect
124. C43×#554C22semidirect
126. C43×#498C22semidirect
127. C43×#483C22semidirect
128. C43×#481C22semidirect
129. C43×#476C22semidirect
130. C43×#475C22semidirect
131. C43×#465C22semidirect
132. C4×SD16×C43C22semidirect
133. C8×D4×C43C22semidirect
134. C2×#106×C43C22semidirect
346. D4×D43SD16semidirect
457. C8×D43#41semidirect
476. D4×C43C2×SD16semidirect
494. C22⋊D43C2×SD16semidirect
511. D172C2×SD16semidirect
540. C8×C43C2×#41semidirect
543. C43⋊C8C2×#41semidirect
595. #3335D43direct (N × H)
612. D43#3335direct (N × H)
624. #554C2×D43semidirect
653. #498C2×D43semidirect
661. #483C2×D43semidirect
669. #481C2×D43semidirect
675. #476C2×D43semidirect
681. #475C2×D43semidirect
689. #465C2×D43semidirect
697. C4×SD16C2×D43semidirect
703. C8×D4C2×D43semidirect
716. C2×#106C2×D43semidirect
724. C43C2×#3335semidirect
1081. D4SD16×D43semidirect
1133. C8#41×D43semidirect

Maximal subgroups

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

subgroupindex
#554×D432
#547×D432
#191469552
#191469542
#191469532
#191469522
#191469512
#191469502
#191469492
#191469482
#191469472
#191469462
#191469452
#498×D432
#481×D432
#483×D432
#475×D432
#476×D432
#465×D432
C4×SD16×D432
C8×D4×D432
C2×#106×D432
C43×#33352
C2×#333543