Finite Group Databasebeta

← D43×#3298 #25972972

Subgroups — D43×#3298 #25972972

Order 11008.

2374 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Q8×D43C211yesmaximal, characteristic, complemented
2#547×D43C211yesmaximal, characteristic
3#19146463C211yesmaximal, characteristic, complemented
4#19146462C211yesmaximal, characteristic, complemented
5#19146461C211yesmaximal, characteristic, complemented
6#19146460C211yesmaximal, characteristic, complemented
7#19146459C211yesmaximal, characteristic, complemented
8#19146458C212yesmaximal, complemented
9#19146457C211yesmaximal, characteristic, complemented
10#19146456C212yesmaximal, complemented
11#19146455C212yesmaximal, complemented
12#19146454C211yesmaximal, characteristic, complemented
13#19146453C212yesmaximal, complemented
14#487×D43C211yesmaximal, characteristic, complemented
15#483×D43C212yesmaximal, complemented
16#475×D43C211yesmaximal, characteristic, complemented
17#465×D43C212yesmaximal, complemented
18#461×D43C211yesmaximal, characteristic, complemented
19#448×D43C212yesmaximal, complemented
20C4×SD16×D43C211yesmaximal, characteristic, complemented
21C8×D4×D43C211yesmaximal, characteristic, complemented
22C2×#103×D43C212yesmaximal, complemented
23C43×#3298C211yesmaximal, characteristic, complemented
24C2×#41×D43—21no—
25C22×Q8×D43C2212yes—
26C2×SD16×D43C2211yescharacteristic
27C2×SD16×D43C2212yes—
28C22×C8×D43C2212yes—
29Q8×D172C2211yescharacteristic, complemented
30D4×Dic86—21no—
31D4×Dic86C2211yescharacteristic, complemented
32#14583564—21no—
33#14583564C2211yescharacteristic, complemented
34Q8×C22⋊D43C2212yescomplemented
35#14583562—22no—
36#14583562C2212yescomplemented
37#14583554C2211yescharacteristic
38#14583553C2211yescharacteristic
39#14583552C2211yescharacteristic
40#14583551—21no—
41#14583550C2212yes—
42#14583549C2212yes—
43#14583548—21no—
44#14583547—22no—
45C4⋊Q8×D43—21no—
46C4⋊Q8×D43C2211yescharacteristic
47C4⋊Q8×D43C2211yescharacteristic
48#123×D43—22no—
49C22⋊Q8×D43—21no—
50C22⋊Q8×D43—22no—
51C22⋊Q8×D43C2212yes—
52#121×D43C2212yes—
53C4×Q8×D43C2211yescharacteristic
54C4×D4×D43—21no—
55C4×D4×D43C2211yescharacteristic
56C4×D4×D43C2211yescharacteristic
57C2×C4⋊C4×D43C2212yes—
58#14583251C2211yescharacteristic, complemented
59#14583250C2211yescharacteristic, complemented
60#14583249C2211yescharacteristic, complemented
61#14583248C2212yescomplemented
62#14583248C2212yescomplemented
63#14583231C2212yescomplemented
64#14583231C2212yescomplemented
65#14583230C2212yescomplemented
66#14583229C2212yescomplemented
67#14583228C2212yescomplemented
68#14583228C2212yescomplemented
69#14583227C2212yescomplemented
70#14583185C2211yescharacteristic, complemented
71#14583184C2211yescharacteristic, complemented
72#14583183C2212yescomplemented
73#14583182C2212yescomplemented
74#14583181C2211yescharacteristic, complemented
75#14583131C2212yescomplemented
76#14583130C2212yescomplemented
77#14583129C2212yescomplemented
78#14583128C2212yescomplemented
79#14583127C2212yescomplemented
80#14583126C2212yescomplemented
81#14583125C2212yescomplemented
82#14583105C2211yescharacteristic, complemented
83#14583104C2211yescharacteristic, complemented
84#14583103C2212yescomplemented
85#14583102C2212yescomplemented
86#14583101C2211yescharacteristic, complemented
87#14583040C2212yescomplemented
88#14583039C2212yescomplemented
89#14583039C2212yescomplemented
90#14583038C2212yescomplemented
91#14583037C2212yescomplemented
92#14583036C2212yescomplemented
93#14583036C2212yescomplemented
94#14582990C2211yescharacteristic, complemented
95C4×#10621873C2211yescharacteristic, complemented
96SD16×Dic43C2211yescharacteristic, complemented
97C4×#10621884C2211yescharacteristic, complemented
98#14582986C2211yescharacteristic, complemented
99C4×#10621883C2211yescharacteristic, complemented
100#14582984C2211yescharacteristic, complemented
101C8×D172C2211yescharacteristic, complemented
102D4×C43⋊C8C2211yescharacteristic, complemented
103#14582964C2211yescharacteristic, complemented
104C8×C22⋊D43C2212yescomplemented
105(C22⋊D43)⋊C8C2212yescomplemented
106#106×D43C2211yescharacteristic
107#106×D43C2212yes—
108C4⋊C8×D43C2211yescharacteristic
109C2×#13063250C2212yescomplemented
110C2×#13063249C2212yescomplemented
111C2×#13063248C2212yescomplemented
112#103×D43C2212yes—
113#103×D43C2212yes—
114#103×D43C2212yes—
115#103×D43C2211yescharacteristic
116#103×D43C2212yes—
117#103×D43C2212yescomplemented
118#103×D43C2212yescomplemented
119#103×D43C2212yescomplemented
120#103×D43C2212yescomplemented
121#102×D43C2211yescharacteristic
122C22⋊C8×D43C2212yes—
123C4×C8×D43C2211yescharacteristic
124D4×Q8×C43C2211yescharacteristic, complemented
125C43×#547C2211yescharacteristic
126C43×#487C2211yescharacteristic, complemented
127C43×#483C2212yescomplemented
128C43×#475C2211yescharacteristic, complemented
129C43×#465C2212yescomplemented
130C43×#461C2211yescharacteristic, complemented
131C43×#448C2212yescomplemented
132C4×SD16×C43C2211yescharacteristic, complemented
133C8×D4×C43C2211yescharacteristic, complemented
134C2×#103×C43C2212yescomplemented
135C2×#10621902—21no—
136C2×#10621898—22no—
137C2×#10621898—21no—
138C2×#10621900—21no—
139C2×#10621900—22no—
140#41×D43—48no—
141C22×Dic86—22no—
142C22×Dic86C2312yes—
143C2×Q8×D43—22no—
144C2×Q8×D43—22no—
145C2×Q8×D43—21no—
146C2×Q8×D43—28no—
147C2×Q8×D43—44no—
148C2×Q8×D43C2312yes—
149C2×Q8×D43C2312yes—
150C2×Q8×D43C2312yes—
151C2×Q8×D43C2311yescharacteristic
152C2×D4×D43—22no—
153C2×D4×D43D411yescharacteristic
154C2×D4×D43C2311yescharacteristic
155C22×C4×D43—22no—
156C22×C4×D43—22no—
157C22×C4×D43—21no—
158C22×C4×D43C2312yes—
159C2×#10621873C2311yescharacteristic
160C2×#10621873C2312yes—
161C2×#10621883C2311yescharacteristic
162C2×#10621883C2312yes—
163C2×#10621884C2311yescharacteristic
164C2×#10621884C2312yes—
165SD16×D43—24no—
166SD16×D43—44no—
167C22×C43⋊C8C2312yes—
168C2×C8×D43—44no—
169C2×C8×D43C2311yescharacteristic
170C2×C8×D43C2311yescharacteristic
171C2×C8×D43C2312yes—
172C2×C8×D43C2312yes—
173C2×C8×D43C2312yes—
174#13063325—21no—
175#13063325C2311yescharacteristic
176#13063325C2311yescharacteristic
177#13063324—21no—
178#13063324—21no—
179#13063324—22no—
180#13063324—21no—
181#13063324—21no—
182#13063324—21no—
183#13063324C2312yes—
184#13063323—22no—
185#13063323—21no—
186#13063323C2312yes—
187#13063310—22no—
188#13063310—22no—
189#13063309—22no—
190#13063308—22no—
191#13063307—22no—
192#13063307—22no—
193#13063306—22no—
194#13063305—21no—
195#13063305—22no—
196#13063305C2312yes—
197#13063304—22no—
198#13063304—21no—
199#13063304C2312yes—
200#13063303—22no—
201#13063303—22no—
202#13063303—22no—
203#13063303—22no—
204#13063302—22no—
205#13063302—22no—
206#13063302—22no—
207#13063302—22no—
208#13063301—22no—
209#13063301—21no—
210#13063301C2312yes—
211#13063300C2312yes—
212#13063299C2312yes—
213#13063298—22no—
214#13063297—22no—
215#13063296C2312yes—
216Q8×Dic43C2311yescharacteristic
217C4×Dic86—21no—
218C4×Dic86C2311yescharacteristic
219#13063290—21no—
220#13063290C2311yescharacteristic
221C4×D172—21no—
222C4×D172C2311yescharacteristic
223C4×D172C2311yescharacteristic
224D4×Dic43—21no—
225D4×Dic43D411yescharacteristic
226D4×Dic43C2311yescharacteristic
227#13063287—21no—
228#13063287D411yescharacteristic
229#13063287C2311yescharacteristic
230C4×C22⋊D43—22no—
231C4×C22⋊D43—21no—
232C4×C22⋊D43C2312yes—
233(C22⋊D43)⋊C4—22no—
234(C22⋊D43)⋊C4—21no—
235(C22⋊D43)⋊C4D412yes—
236C2×C4⋊Dic43C2312yes—
237C2×Dic43⋊C4—22no—
238C4⋊C4×D43—22no—
239C4⋊C4×D43—22no—
240C4⋊C4×D43—21no—
241C4⋊C4×D43—21no—
242C4⋊C4×D43—21no—
243C4⋊C4×D43—22no—
244C4⋊C4×D43—21no—
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—22no—
254C22⋊C4×D43D412yes—
255C42×D43—21no—
256C42×D43C2311yescharacteristic
257#13063257C2312yes—
258#13063257C2311yescharacteristic
259#13063256C2312yes—
260#13063256C2312yes—
261#13063256C2311yescharacteristic
262#13063256C2311yescharacteristic
263C4⋊(C43⋊C8)C2311yescharacteristic
264Dic43⋊C8C2312yes—
265#13063250C2312yes—
266#13063250C2312yes—
267#13063250C2312yes—
268#13063250C2312yes—
269#13063250C2311yescharacteristic
270#13063249C2312yes—
271#13063249C2312yes—
272#13063249C2311yescharacteristic
273#13063249C2312yes—
274#13063249C2312yes—
275#13063248C2312yes—
276#13063248C2312yes—
277#13063248C2311yescharacteristic
278#13063248C2312yes—
279#13063248C2312yes—
280#13063247C2311yescharacteristic
281#13063246C2311yescharacteristic
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—
290C22×Q8×C43C2312yes—
291C2×SD16×C43C2311yescharacteristic
292C2×SD16×C43C2312yes—
293C22×C8×C43C2312yes—
294C4⋊Q8×C43—21no—
295C4⋊Q8×C43C2311yescharacteristic
296C4⋊Q8×C43C2311yescharacteristic
297#123×C43—22no—
298C22⋊Q8×C43—21no—
299C22⋊Q8×C43—22no—
300C22⋊Q8×C43C2312yes—
301#121×C43C2312yes—
302C4×Q8×C43C2311yescharacteristic
303C4×D4×C43—21no—
304C4×D4×C43C2311yescharacteristic
305C4×D4×C43C2311yescharacteristic
306C2×C4⋊C4×C43C2312yes—
307#106×C43C2312yes—
308#106×C43C2311yescharacteristic
309C4⋊C8×C43C2311yescharacteristic
310#103×C43C2312yes—
311#103×C43C2312yes—
312#103×C43C2311yescharacteristic
313#103×C43C2312yes—
314#103×C43C2312yes—
315#102×C43C2311yescharacteristic
316C22⋊C8×C43C2312yes—
317C4×C8×C43C2311yescharacteristic
318C23×D43—21no—
319C23×D43C2×D412yes—
320#41×C43—44no—
321C2×Q8×C43—22no—
322C2×Q8×C43—21no—
323C2×Q8×C43—24no—
324C2×Q8×C43—42no—
325C2×Q8×C43C2412yes—
326C2×Q8×C43C2411yescharacteristic
327C2×D4×C43—22no—
328C2×D4×C43C2×D411yescharacteristic
329C2×D4×C43C2411yescharacteristic
330C22×C4×C43—21no—
331C22×C4×C43—22no—
332C22×C4×C43—22no—
333C22×C4×C43C2412yes—
334C2×C22⋊D43—21no—
335C2×C22⋊D43—22no—
336C2×C22⋊D43—22no—
337C2×C22⋊D43C2×D412yes—
338C22×Dic43—21no—
339C22×Dic43—22no—
340C22×Dic43—22no—
341C22×Dic43C2×D412yes—
342#10621902—44no—
343Q8×D43—22no—
344Q8×D43—24no—
345Q8×D43—24no—
346Q8×D43—24no—
347Q8×D43—24no—
348Q8×D43—42no—
349Q8×D43—42no—
350Q8×D43—48no—
351Q8×D43—48no—
352Q8×D43—44no—
353Q8×D43#4114yescomplemented
354#10621900—44no—
355#10621900—48no—
356D4×D43—22no—
357D4×D43—22no—
358D4×D43—48no—
359D4×D43SD1618yescomplemented
360#10621898—48no—
361#10621898—44no—
362C2×D172—22no—
363C2×D172C2×D411yescharacteristic
364C2×D172C2411yescharacteristic
365C2×C4×D43—24no—
366C2×C4×D43—24no—
367C2×C4×D43—21no—
368C2×C4×D43—21no—
369C2×C4×D43—21no—
370C2×C4×D43—21no—
371C2×C4×D43—22no—
372C2×C4×D43—21no—
373C2×C4×D43—22no—
374C2×C4×D43—22no—
375C2×C4×D43—22no—
376C2×C4×D43—22no—
377C2×C4×D43—22no—
378C2×C4×D43—48no—
379C2×C4×D43—44no—
380C2×C4×D43—48no—
381C2×C4×D43C2×D411yescharacteristic
382C2×C4×D43C2×D412yes—
383C2×C4×D43C2×D412yes—
384C2×C4×D43C2×D411yescharacteristic
385C2×C4×D43C2412yes—
386C2×C4×D43C2411yescharacteristic
387C2×Dic86—21no—
388C2×Dic86—24no—
389C2×Dic86—22no—
390C2×Dic86—21no—
391C2×Dic86—22no—
392C2×Dic86—22no—
393C2×Dic86—22no—
394C2×Dic86—22no—
395C2×Dic86—42no—
396C2×Dic86—48no—
397C2×Dic86C2412yes—
398C2×Dic86C2411yescharacteristic
399SD16×C43—22no—
400SD16×C43—42no—
401C2×C8×C43—42no—
402C2×C8×C43C2411yescharacteristic
403C2×C8×C43C2411yescharacteristic
404C2×C8×C43C2412yes—
405C4⋊C4×C43—22no—
406C4⋊C4×C43—21no—
407C4⋊C4×C43—21no—
408C4⋊C4×C43—21no—
409C4⋊C4×C43—22no—
410C4⋊C4×C43—21no—
411C4⋊C4×C43C2×D411yescharacteristic
412C4⋊C4×C43C2411yescharacteristic
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2412yes—
415C22⋊C4×C43—21no—
416C22⋊C4×C43—22no—
417C22⋊C4×C43—22no—
418C22⋊C4×C43C2×D412yes—
419C42×C43—21no—
420C42×C43C2411yescharacteristic
421C22⋊Dic43—21no—
422C22⋊Dic43—22no—
423C22⋊Dic43—22no—
424C22⋊Dic43C2×D412yes—
425#10621884—22no—
426#10621884—42no—
427#10621883—22no—
428#10621883—42no—
429(C2×D43)⋊C4—21no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—21no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—22no—
434(C2×D43)⋊C4—22no—
435(C2×D43)⋊C4C2×D412yes—
436(C2×D43)⋊C4C2×D412yes—
437C4⋊Dic43—22no—
438C4⋊Dic43—21no—
439C4⋊Dic43—21no—
440C4⋊Dic43—21no—
441C4⋊Dic43—21no—
442C4⋊Dic43—22no—
443C4⋊Dic43C2×D411yescharacteristic
444C4⋊Dic43C2411yescharacteristic
445C4⋊Dic43C2411yescharacteristic
446C4⋊Dic43C2412yes—
447Dic43⋊C4—21no—
448Dic43⋊C4—22no—
449Dic43⋊C4—21no—
450Dic43⋊C4—22no—
451Dic43⋊C4—22no—
452Dic43⋊C4—22no—
453Dic43⋊C4—22no—
454Dic43⋊C4—21no—
455Dic43⋊C4—22no—
456Dic43⋊C4—22no—
457Dic43⋊C4—22no—
458Dic43⋊C4—21no—
459Dic43⋊C4C2×D412yes—
460C4×Dic43—21no—
461C4×Dic43—21no—
462C4×Dic43—21no—
463C4×Dic43C2×D411yescharacteristic
464C4×Dic43C2×D411yescharacteristic
465C4×Dic43C2411yescharacteristic
466C2×C43⋊C8—42no—
467C2×C43⋊C8C2411yescharacteristic
468C2×C43⋊C8C2411yescharacteristic
469C2×C43⋊C8C2412yes—
470#10621873—22no—
471#10621873—42no—
472C8×D43—22no—
473C8×D43—22no—
474C8×D43—24no—
475C8×D43—42no—
476C8×D43—42no—
477C23×C43—21no—
478C23×C43C22×D412yes—
479C22×D43—24no—
480C22×D43—24no—
481C22×D43—21no—
482C22×D43—42no—
483C22×D43—42no—
484C22×D43—42no—
485C22×D43C2×SD1618yes—
486C22×D43C22×D412yes—
487C22×D43C22×D411yescharacteristic
488Q8×C43—21no—
489Q8×C43—22no—
490Q8×C43—22no—
491Q8×C43—44no—
492Q8×C43—42no—
493Q8×C43C2×#4112yescomplemented
494D4×C43—21no—
495D4×C43—21no—
496D4×C43—44no—
497D4×C43C2×SD1614yescomplemented
498C2×C4×C43—21no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—21no—
502C2×C4×C43—22no—
503C2×C4×C43—22no—
504C2×C4×C43—21no—
505C2×C4×C43—44no—
506C2×C4×C43—44no—
507C2×C4×C43—42no—
508C2×C4×C43C22×D411yescharacteristic
509C2×C4×C43C22×D412yes—
510C2×C4×C43C22×D411yescharacteristic
511C2×C4×C43C2511yescharacteristic
512C22⋊D43—44no—
513C22⋊D43—44no—
514C22⋊D43—42no—
515C22⋊D43C2×SD1618yescomplemented
516C2×Dic43—21no—
517C2×Dic43—24no—
518C2×Dic43—21no—
519C2×Dic43—22no—
520C2×Dic43—22no—
521C2×Dic43—21no—
522C2×Dic43—44no—
523C2×Dic43—44no—
524C2×Dic43—42no—
525C2×Dic43C22×D411yescharacteristic
526C2×Dic43C22×D412yes—
527C2×Dic43C22×D411yescharacteristic
528C2×Dic43C22×D411yescharacteristic
529D172—21no—
530D172—21no—
531D172—44no—
532D172C2×SD1614yescomplemented
533C4×D43—24no—
534C4×D43—24no—
535C4×D43—22no—
536C4×D43—22no—
537C4×D43—22no—
538C4×D43—24no—
539C4×D43—44no—
540C4×D43—44no—
541C4×D43—44no—
542C4×D43—42no—
543C4×D43—44no—
544C4×D43—44no—
545C4×D43—44no—
546C4×D43—42no—
547C4×D43—42no—
548C4×D43—42no—
549C4×D43C2×SD1614yes—
550C4×D43C2×#4112yes—
551C4×D43H(5,𝔽2)12yes—
552Dic86—21no—
553Dic86—24no—
554Dic86—22no—
555Dic86—22no—
556Dic86—44no—
557Dic86—44no—
558Dic86—44no—
559Dic86—42no—
560Dic86—44no—
561Dic86—44no—
562Dic86C2×#4112yescomplemented
563C8×C43—21no—
564C8×C43—21no—
565C8×C43—22no—
566C43⋊C8—21no—
567C43⋊C8—21no—
568C43⋊C8—22no—
569C2×#3298—431nomaximal, Sylow
570C22×C43—22no—
571C22×C43—22no—
572C22×C43—41no—
573C22×C43—41no—
574C22×C43—41no—
575C22×C43C22×SD1614yes—
576C22×C43C23×D411yescharacteristic
577C2×D43—22no—
578C2×D43—22no—
579C2×D43—216no—
580C2×D43—41no—
581C2×D43—41no—
582C2×D43—41no—
583C2×D43—84no—
584C2×D43#54612yes—
585C2×D43C22×SD1614yes—
586C2×D43C22×SD1612yes—
587C2×D43#57812yes—
588C4×C43—22no—
589C4×C43—22no—
590C4×C43—21no—
591C4×C43—42no—
592C4×C43—42no—
593C4×C43—41no—
594C4×C43—41no—
595C4×C43C22×SD1612yes—
596C4×C43C22×#4111yescharacteristic
597C4×C43C2×H(5,𝔽2)11yescharacteristic
598Dic43—22no—
599Dic43—22no—
600Dic43—21no—
601Dic43—42no—
602Dic43—42no—
603Dic43—41no—
604Dic43—41no—
605Dic43#54612yes—
606Dic43C22×SD1612yes—
607C2×D4×Q8—431no—
608C2×#547—431no—
609#3298—431no—
610#3298—432no—
611#3298—431no—
612#3298—432no—
613#3298—431no—
614#3298—432no—
615#3298—431no—
616#3298—431no—
617#3298—432no—
618#3298—431no—
619#3298—431no—
620#3298D4311yescharacteristic, direct product factor
621C2×#487—431no—
622C2×#483—432no—
623C2×#475—431no—
624C2×#465—432no—
625C2×#461—431no—
626C2×#448—432no—
627C2×C4×SD16—431no—
628C2×C8×D4—431no—
629C22×#103—432no—
630C2×C43—24no—
631C2×C43—81no—
632C2×C43C2×#54611yescharacteristic
633C2×C43C23×SD1611yescharacteristic
634C2×C43C2×#57811yescharacteristic
635D43—24no—
636D43—81no—
637D43#329814yesdirect product factor
638C22×#41—861no—
639C23×Q8—432no—
640C22×SD16—431no—
641C22×SD16—432no—
642C23×C8—432no—
643D4×Q8—432no—
644D4×Q8—431no—
645D4×Q8—432no—
646D4×Q8—431no—
647D4×Q8—431no—
648D4×Q8—861no—
649D4×Q8—862no—
650D4×Q8—861no—
651D4×Q8C2×D4311yescharacteristic, complemented
652#547—431no—
653#547—432no—
654#547—431no—
655#547—431no—
656#547—432no—
657#547—861no—
658#547—862no—
659#547—861no—
660#547C2×D4311yescharacteristic
661C2×C4⋊Q8—431no—
662C2×C4⋊Q8—431no—
663C2×C4⋊Q8—861no—
664C2×#123—862no—
665C2×C22⋊Q8—432no—
666C2×C22⋊Q8—862no—
667C2×C22⋊Q8—861no—
668C2×#121—432no—
669C2×C4×Q8—431no—
670C2×C4×D4—431no—
671C2×C4×D4—431no—
672C2×C4×D4—861no—
673C22×C4⋊C4—432no—
674#487—431no—
675#487—431no—
676#487—432no—
677#487—432no—
678#487—431no—
679#487C2×D4311yescharacteristic, complemented
680#483—432no—
681#483—432no—
682#483—432no—
683#483—432no—
684#483—432no—
685#483—432no—
686#483—432no—
687#483C2×D4312yescomplemented
688#475—431no—
689#475—431no—
690#475—432no—
691#475—431no—
692#475—432no—
693#475C2×D4311yescharacteristic, complemented
694#465—432no—
695#465—432no—
696#465—432no—
697#465—432no—
698#465—432no—
699#465—432no—
700#465—432no—
701#465C2×D4312yescomplemented
702#461—432no—
703#461—431no—
704#461—431no—
705#461—431no—
706#461—432no—
707#461C2×D4311yescharacteristic, complemented
708#448—432no—
709#448—432no—
710#448—432no—
711#448—432no—
712#448—432no—
713#448—432no—
714#448—432no—
715#448C2×D4312yescomplemented
716C4×SD16—431no—
717C4×SD16—431no—
718C4×SD16—431no—
719C4×SD16—431no—
720C4×SD16—431no—
721C4×SD16—431no—
722C4×SD16—431no—
723C4×SD16C2×D4311yescharacteristic, complemented
724C8×D4—432no—
725C8×D4—431no—
726C8×D4—431no—
727C8×D4—432no—
728C8×D4—431no—
729C8×D4C2×D4311yescharacteristic, complemented
730C2×#106—432no—
731C2×#106—431no—
732C2×C4⋊C8—431no—
733C2×#103—432no—
734C2×#103—432no—
735C2×#103—432no—
736C2×#103—432no—
737C2×#103—432no—
738C2×#103—432no—
739C2×#103—432no—
740C2×#103—431no—
741C2×#103—432no—
742C2×#103—432no—
743C2×#103—432no—
744C2×#103—432no—
745C2×#103C2×D4312yescomplemented
746C2×#102—431no—
747C2×C22⋊C8—432no—
748C2×C4×C8—431no—
749C43C2×#329811yescharacteristic, complemented, Sylow
750C2×#41—21no—
751C2×#41—862no—
752C2×#41—861no—
753C2×#41—862no—
754C2×#41—861no—
755C2×#41—861no—
756C2×#41—1728no—
757C22×Q8—431no—
758C22×Q8—432no—
759C22×Q8—432no—
760C22×Q8—432no—
761C22×Q8—432no—
762C22×Q8—862no—
763C22×Q8—861no—
764C22×Q8—862no—
765C22×Q8—862no—
766C22×Q8—868no—
767C22×Q8—1724no—
768C22×Q8C22×D4312yes—
769C22×D4—431no—
770C22×D4—431no—
771C22×D4—862no—
772C23×C4—432no—
773C23×C4—861no—
774C23×C4—862no—
775C23×C4—862no—
776C2×SD16—431no—
777C2×SD16—431no—
778C2×SD16—432no—
779C2×SD16—432no—
780C2×SD16—431no—
781C2×SD16—432no—
782C2×SD16—864no—
783C2×SD16—1724no—
784C2×SD16C22×D4311yescharacteristic
785C2×SD16C22×D4312yes—
786C22×C8—432no—
787C22×C8—431no—
788C22×C8—432no—
789C22×C8—431no—
790C22×C8—432no—
791C22×C8—432no—
792C22×C8—1724no—
793C22×C8C22×D4312yes—
794C4⋊Q8—21no—
795C4⋊Q8—432no—
796C4⋊Q8—432no—
797C4⋊Q8—431no—
798C4⋊Q8—431no—
799C4⋊Q8—861no—
800C4⋊Q8—861no—
801C4⋊Q8—861no—
802C4⋊Q8—861no—
803C4⋊Q8—861no—
804C4⋊Q8—862no—
805C4⋊Q8—861no—
806C4⋊Q8—862no—
807C4⋊Q8—861no—
808C4⋊Q8C22×D4311yescharacteristic
809C4⋊Q8C22×D4311yescharacteristic
810#123—22no—
811#123—862no—
812#123—862no—
813#123—862no—
814#123—862no—
815#123—862no—
816#123—862no—
817#123—862no—
818C22⋊Q8—21no—
819C22⋊Q8—22no—
820C22⋊Q8—432no—
821C22⋊Q8—432no—
822C22⋊Q8—432no—
823C22⋊Q8—862no—
824C22⋊Q8—862no—
825C22⋊Q8—862no—
826C22⋊Q8—862no—
827C22⋊Q8—862no—
828C22⋊Q8—862no—
829C22⋊Q8—862no—
830C22⋊Q8—862no—
831C22⋊Q8—862no—
832C22⋊Q8—862no—
833C22⋊Q8—861no—
834C22⋊Q8—861no—
835C22⋊Q8—861no—
836C22⋊Q8—862no—
837C22⋊Q8C22×D4312yes—
838#121—432no—
839#121—432no—
840#121—432no—
841#121—862no—
842#121—862no—
843#121C22×D4312yes—
844C4×Q8—431no—
845C4×Q8—431no—
846C4×Q8—431no—
847C4×Q8—861no—
848C4×Q8—861no—
849C4×Q8C22×D4311yescharacteristic
850C4×D4—21no—
851C4×D4—431no—
852C4×D4—432no—
853C4×D4—431no—
854C4×D4—432no—
855C4×D4—431no—
856C4×D4—431no—
857C4×D4—431no—
858C4×D4—431no—
859C4×D4—861no—
860C4×D4—861no—
861C4×D4—861no—
862C4×D4—862no—
863C4×D4—861no—
864C4×D4—862no—
865C4×D4—861no—
866C4×D4C22×D4311yescharacteristic
867C4×D4C22×D4311yescharacteristic
868C2×C4⋊C4—431no—
869C2×C4⋊C4—432no—
870C2×C4⋊C4—431no—
871C2×C4⋊C4—432no—
872C2×C4⋊C4—432no—
873C2×C4⋊C4—432no—
874C2×C4⋊C4—431no—
875C2×C4⋊C4—862no—
876C2×C4⋊C4—862no—
877C2×C4⋊C4—861no—
878C2×C4⋊C4—861no—
879C2×C4⋊C4—862no—
880C2×C4⋊C4—861no—
881C2×C4⋊C4—861no—
882C2×C4⋊C4—862no—
883C2×C4⋊C4C22×D4312yes—
884C2×C22⋊C4—432no—
885C2×C22⋊C4—861no—
886C2×C22⋊C4—862no—
887C2×C22⋊C4—862no—
888C2×C42—431no—
889C2×C42—861no—
890#106—431no—
891#106—432no—
892#106—431no—
893#106—431no—
894#106—432no—
895#106—432no—
896#106C22×D4311yescharacteristic
897#106C22×D4312yes—
898C4⋊C8—432no—
899C4⋊C8—431no—
900C4⋊C8C22×D4311yescharacteristic
901#103—431no—
902#103—432no—
903#103—432no—
904#103—432no—
905#103—432no—
906#103—431no—
907#103—432no—
908#103—432no—
909#103—432no—
910#103—432no—
911#103—431no—
912#103—432no—
913#103—432no—
914#103—432no—
915#103—432no—
916#103C22×D4311yescharacteristic
917#103C22×D4312yes—
918#103C22×D4312yes—
919#103C22×D4312yes—
920#103C22×D4312yes—
921#102—431no—
922#102—431no—
923#102—431no—
924#102C22×D4311yescharacteristic
925C22⋊C8—432no—
926C22⋊C8—432no—
927C22⋊C8—432no—
928C22⋊C8C22×D4312yes—
929C4×C8—431no—
930C4×C8—431no—
931C4×C8—431no—
932C4×C8C22×D4311yescharacteristic
933C24—432no—
934C24—861no—
935#41—44no—
936#41—1728no—
937#41—1724no—
938#41—1728no—
939#41—1724no—
940#41—1724no—
941C2×Q8—22no—
942C2×Q8—21no—
943C2×Q8—24no—
944C2×Q8—42no—
945C2×Q8—434no—
946C2×Q8—431no—
947C2×Q8—432no—
948C2×Q8—861no—
949C2×Q8—862no—
950C2×Q8—862no—
951C2×Q8—862no—
952C2×Q8—862no—
953C2×Q8—864no—
954C2×Q8—862no—
955C2×Q8—864no—
956C2×Q8—864no—
957C2×Q8—861no—
958C2×Q8—862no—
959C2×Q8—864no—
960C2×Q8—864no—
961C2×Q8—1722no—
962C2×Q8—1728no—
963C2×Q8—1724no—
964C2×Q8—1728no—
965C2×Q8—1722no—
966C2×Q8—1722no—
967C2×Q8—1728no—
968C2×Q8C23×D4312yes—
969C2×Q8C23×D4311yescharacteristic
970C2×D4—22no—
971C2×D4—432no—
972C2×D4—438no—
973C2×D4—431no—
974C2×D4—431no—
975C2×D4—862no—
976C2×D4—862no—
977C2×D4—862no—
978C2×D4—861no—
979C2×D4—862no—
980C2×D4—862no—
981C2×D4—1728no—
982C2×D4D4×D4311yescharacteristic
983C2×D4C23×D4311yescharacteristic
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—21no—
987C22×C4—431no—
988C22×C4—431no—
989C22×C4—432no—
990C22×C4—431no—
991C22×C4—432no—
992C22×C4—432no—
993C22×C4—432no—
994C22×C4—864no—
995C22×C4—864no—
996C22×C4—861no—
997C22×C4—861no—
998C22×C4—861no—
999C22×C4—861no—
1000C22×C4—862no—
1001C22×C4—862no—
1002C22×C4—862no—
1003C22×C4—862no—
1004C22×C4—862no—
1005C22×C4—862no—
1006C22×C4—861no—
1007C22×C4—862no—
1008C22×C4—862no—
1009C22×C4—861no—
1010C22×C4—1724no—
1011C22×C4—1728no—
1012C22×C4—1728no—
1013C22×C4C23×D4312yes—
1014SD16—22no—
1015SD16—42no—
1016SD16—862no—
1017SD16—862no—
1018SD16—862no—
1019SD16—1722no—
1020SD16—1722no—
1021SD16—1722no—
1022C2×C8—42no—
1023C2×C8—431no—
1024C2×C8—431no—
1025C2×C8—432no—
1026C2×C8—862no—
1027C2×C8—864no—
1028C2×C8—862no—
1029C2×C8—1722no—
1030C2×C8—1722no—
1031C2×C8—1722no—
1032C2×C8C23×D4311yescharacteristic
1033C2×C8C23×D4311yescharacteristic
1034C2×C8C23×D4312yes—
1035C4⋊C4—22no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—22no—
1040C4⋊C4—21no—
1041C4⋊C4—432no—
1042C4⋊C4—431no—
1043C4⋊C4—431no—
1044C4⋊C4—431no—
1045C4⋊C4—432no—
1046C4⋊C4—861no—
1047C4⋊C4—862no—
1048C4⋊C4—862no—
1049C4⋊C4—862no—
1050C4⋊C4—861no—
1051C4⋊C4—862no—
1052C4⋊C4—861no—
1053C4⋊C4—861no—
1054C4⋊C4—862no—
1055C4⋊C4—862no—
1056C4⋊C4—862no—
1057C4⋊C4—862no—
1058C4⋊C4—862no—
1059C4⋊C4—861no—
1060C4⋊C4—861no—
1061C4⋊C4—862no—
1062C4⋊C4—861no—
1063C4⋊C4—861no—
1064C4⋊C4D4×D4311yescharacteristic
1065C4⋊C4C23×D4311yescharacteristic
1066C4⋊C4C23×D4311yescharacteristic
1067C4⋊C4C23×D4312yes—
1068C22⋊C4—22no—
1069C22⋊C4—21no—
1070C22⋊C4—22no—
1071C22⋊C4—432no—
1072C22⋊C4—432no—
1073C22⋊C4—432no—
1074C22⋊C4—861no—
1075C22⋊C4—862no—
1076C22⋊C4—862no—
1077C22⋊C4—862no—
1078C22⋊C4—861no—
1079C22⋊C4—862no—
1080C22⋊C4—862no—
1081C22⋊C4—861no—
1082C22⋊C4—862no—
1083C22⋊C4D4×D4312yes—
1084C42—21no—
1085C42—431no—
1086C42—431no—
1087C42—431no—
1088C42—861no—
1089C42—861no—
1090C42—861no—
1091C42C23×D4311yescharacteristic
1092C23—21no—
1093C23—431no—
1094C23—438no—
1095C23—432no—
1096C23—864no—
1097C23—864no—
1098C23—861no—
1099C23—1722no—
1100C23—1722no—
1101C23—1722no—
1102C23C2×D4×D4312yes—
1103Q8—21no—
1104Q8—22no—
1105Q8—22no—
1106Q8—44no—
1107Q8—42no—
1108Q8—432no—
1109Q8—864no—
1110Q8—861no—
1111Q8—862no—
1112Q8—862no—
1113Q8—1724no—
1114Q8—1724no—
1115Q8—1724no—
1116Q8—1724no—
1117Q8—1724no—
1118Q8—1722no—
1119Q8#41×D4312yescomplemented
1120D4—21no—
1121D4—21no—
1122D4—44no—
1123D4—438no—
1124D4—434no—
1125D4—861no—
1126D4—861no—
1127D4—1724no—
1128D4—1722no—
1129D4—1724no—
1130D4—1724no—
1131D4SD16×D4314yescomplemented
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—42no—
1142C2×C4—431no—
1143C2×C4—431no—
1144C2×C4—434no—
1145C2×C4—432no—
1146C2×C4—432no—
1147C2×C4—431no—
1148C2×C4—432no—
1149C2×C4—864no—
1150C2×C4—864no—
1151C2×C4—862no—
1152C2×C4—864no—
1153C2×C4—864no—
1154C2×C4—861no—
1155C2×C4—862no—
1156C2×C4—862no—
1157C2×C4—861no—
1158C2×C4—861no—
1159C2×C4—862no—
1160C2×C4—862no—
1161C2×C4—1724no—
1162C2×C4—1722no—
1163C2×C4—1724no—
1164C2×C4—1722no—
1165C2×C4—1724no—
1166C2×C4—1724no—
1167C2×C4—1724no—
1168C2×C4—1724no—
1169C2×C4—1722no—
1170C2×C4—1722no—
1171C2×C4—1724no—
1172C2×C4—1724no—
1173C2×C4—1722no—
1174C2×C4C2×D4×D4311yescharacteristic
1175C2×C4C2×D4×D4312yes—
1176C2×C4C2×D4×D4311yescharacteristic
1177C2×C4C24×D4311yescharacteristic
1178C8—21no—
1179C8—21no—
1180C8—22no—
1181C8—861no—
1182C8—861no—
1183C8—862no—
1184C22—22no—
1185C22—22no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—432no—
1190C22—432no—
1191C22—432no—
1192C22—434no—
1193C22—8616no—
1194C22—862no—
1195C22—862no—
1196C22—3444no—
1197C22—1721no—
1198C22—1721no—
1199C22—1721no—
1200C22C2×SD16×D4314yes—
1201C22C22×D4×D4311yescharacteristic
1202C4—22no—
1203C4—22no—
1204C4—21no—
1205C4—41no—
1206C4—42no—
1207C4—42no—
1208C4—41no—
1209C4—432no—
1210C4—432no—
1211C4—862no—
1212C4—862no—
1213C4—861no—
1214C4—1721no—
1215C4—1722no—
1216C4—1722no—
1217C4—1721no—
1218C4C2×SD16×D4312yes—
1219C4C2×#41×D4311yescharacteristic
1220C4H(5,𝔽2)×D4311yescharacteristic
1221C2—24no—
1222C2—81no—
1223C2—434no—
1224C2—864no—
1225C2—3441no—
1226C2#546×D4311yescharacteristic
1227C2C22×SD16×D4311yescharacteristic
1228C2#578×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3298C2
socleC22×C43C23×D4
prime radical#547×D43C2
hypercenter#3298D43
hypocenterC43C2×#3298
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3298

Complements

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

NH ≅ G/Ntype
1. D4×Q8×D43C2semidirect
3. #19146463C2semidirect
4. #19146462C2semidirect
5. #19146461C2semidirect
6. #19146460C2semidirect
7. #19146459C2semidirect
8. #19146458C2semidirect
9. #19146457C2semidirect
10. #19146456C2semidirect
11. #19146455C2semidirect
12. #19146454C2semidirect
13. #19146453C2semidirect
14. #487×D43C2semidirect
15. #483×D43C2semidirect
16. #475×D43C2semidirect
17. #465×D43C2semidirect
18. #461×D43C2semidirect
19. #448×D43C2semidirect
20. C4×SD16×D43C2semidirect
21. C8×D4×D43C2semidirect
22. C2×#103×D43C2semidirect
23. C43×#3298C2semidirect
29. Q8×D172C22semidirect
31. D4×Dic86C22semidirect
33. #14583564C22semidirect
34. Q8×C22⋊D43C22semidirect
36. #14583562C22semidirect
58. #14583251C22semidirect
59. #14583250C22semidirect
60. #14583249C22semidirect
61. #14583248C22semidirect
62. #14583248C22semidirect
63. #14583231C22semidirect
64. #14583231C22semidirect
65. #14583230C22semidirect
66. #14583229C22semidirect
67. #14583228C22semidirect
68. #14583228C22semidirect
69. #14583227C22semidirect
70. #14583185C22semidirect
71. #14583184C22semidirect
72. #14583183C22semidirect
73. #14583182C22semidirect
74. #14583181C22semidirect
75. #14583131C22semidirect
76. #14583130C22semidirect
77. #14583129C22semidirect
78. #14583128C22semidirect
79. #14583127C22semidirect
80. #14583126C22semidirect
81. #14583125C22semidirect
82. #14583105C22semidirect
83. #14583104C22semidirect
84. #14583103C22semidirect
85. #14583102C22semidirect
86. #14583101C22semidirect
87. #14583040C22semidirect
88. #14583039C22semidirect
89. #14583039C22semidirect
90. #14583038C22semidirect
91. #14583037C22semidirect
92. #14583036C22semidirect
93. #14583036C22semidirect
94. #14582990C22semidirect
95. C4×#10621873C22semidirect
96. SD16×Dic43C22semidirect
97. C4×#10621884C22semidirect
98. #14582986C22semidirect
99. C4×#10621883C22semidirect
100. #14582984C22semidirect
101. C8×D172C22semidirect
102. D4×C43⋊C8C22semidirect
103. #14582964C22semidirect
104. C8×C22⋊D43C22semidirect
105. (C22⋊D43)⋊C8C22semidirect
109. C2×#13063250C22semidirect
110. C2×#13063249C22semidirect
111. C2×#13063248C22semidirect
117. #103×D43C22semidirect
118. #103×D43C22semidirect
119. #103×D43C22semidirect
120. #103×D43C22semidirect
124. D4×Q8×C43C22semidirect
126. C43×#487C22semidirect
127. C43×#483C22semidirect
128. C43×#475C22semidirect
129. C43×#465C22semidirect
130. C43×#461C22semidirect
131. C43×#448C22semidirect
132. C4×SD16×C43C22semidirect
133. C8×D4×C43C22semidirect
134. C2×#103×C43C22semidirect
353. Q8×D43#41semidirect
359. D4×D43SD16semidirect
493. Q8×C43C2×#41semidirect
497. D4×C43C2×SD16semidirect
515. C22⋊D43C2×SD16semidirect
532. D172C2×SD16semidirect
562. Dic86C2×#41semidirect
620. #3298D43direct (N × H)
637. D43#3298direct (N × H)
651. D4×Q8C2×D43semidirect
679. #487C2×D43semidirect
687. #483C2×D43semidirect
693. #475C2×D43semidirect
701. #465C2×D43semidirect
707. #461C2×D43semidirect
715. #448C2×D43semidirect
723. C4×SD16C2×D43semidirect
729. C8×D4C2×D43semidirect
745. C2×#103C2×D43semidirect
749. C43C2×#3298semidirect
1119. Q8#41×D43semidirect
1131. D4SD16×D43semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×D432
#547×D432
#191464632
#191464622
#191464612
#191464602
#191464592
#191464582
#191464572
#191464562
#191464552
#191464542
#191464532
#487×D432
#483×D432
#475×D432
#465×D432
#461×D432
#448×D432
C4×SD16×D432
C8×D4×D432
C2×#103×D432
C43×#32982
C2×#329843