Finite Group Databasebeta

← D43×#3193 #25967182

Subgroups — D43×#3193 #25967182

Order 11008.

2666 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic, complemented
2C2×#121×D43C211yesmaximal, characteristic
3#19145403C212yesmaximal, complemented
4#19145402C211yesmaximal, characteristic, complemented
5#19145401C211yesmaximal, characteristic, complemented
6#19145400C212yesmaximal, complemented
7#19145399C212yesmaximal, complemented
8#19145398C212yesmaximal, complemented
9#19145397C211yesmaximal, characteristic, complemented
10#19145396C214yesmaximal, complemented
11#484×D43C212yesmaximal, complemented
12#480×D43C212yesmaximal, complemented
13#468×D43C214yesmaximal, complemented
14#448×D43C212yesmaximal, complemented
15#450×D43C212yesmaximal, complemented
16#407×D43C211yesmaximal, characteristic, complemented
17C43×#3193C211yesmaximal, characteristic, complemented
18C22×Q8×D43C2211yescharacteristic, complemented
19C22×D4×D43—21no—
20C22×D4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×SD16×D43C2214yescomplemented
23C2×M16×D43C2212yescomplemented
24C2×#13063305C2211yescharacteristic, complemented
25C2×#13063304C2211yescharacteristic, complemented
26C2×#13063303—21no—
27C2×#13063302—21no—
28C2×#13063301C2211yescharacteristic, complemented
29C22⋊Q8×D43—21no—
30C22⋊Q8×D43—21no—
31C22⋊Q8×D43—21no—
32C22⋊Q8×D43—21no—
33C22⋊Q8×D43C2212yes—
34C22⋊Q8×D43C2212yescomplemented
35C22⋊Q8×D43C2212yescomplemented
36C22⋊Q8×D43C2212yescomplemented
37C2×#13063300C2211yescharacteristic
38C2×#13063299C2211yescharacteristic
39C2×#13063298—21no—
40C2×#13063297—21no—
41C2×#13063296C2211yescharacteristic
42#121×D43—21no—
43#121×D43—21no—
44#121×D43—21no—
45#121×D43—21no—
46#121×D43C2212yes—
47#121×D43C2212yes—
48#121×D43C2212yes—
49#121×D43C2212yes—
50C2×C4⋊C4×D43—21no—
51C2×C4⋊C4×D43C2211yescharacteristic
52C2×C4⋊C4×D43C2211yescharacteristic, complemented
53C2×C22⋊C4×D43—21no—
54C2×C22⋊C4×D43—21no—
55#14583236C2214yescomplemented
56#14583235C2212yescomplemented
57#14583234C2212yescomplemented
58#14583233C2214yescomplemented
59#14583232C2212yescomplemented
60#14583214C2214yescomplemented
61#14583213C2212yescomplemented
62#14583212C2212yescomplemented
63#14583211C2214yescomplemented
64#14583210C2212yescomplemented
65#14583148C2214yescomplemented
66#14583147C2214yescomplemented
67#14583146C2214yescomplemented
68#14583145C2214yescomplemented
69#14583144C2214yescomplemented
70#14583143C2214yescomplemented
71#14583142C2214yescomplemented
72#14583052C2212yescomplemented
73#14583051C2214yescomplemented
74#14583050C2212yescomplemented
75#14583049C2212yescomplemented
76#14583048C2214yescomplemented
77#14583040C2212yescomplemented
78#14583039C2214yescomplemented
79#14583038C2212yescomplemented
80#14583037C2212yescomplemented
81#14583036C2214yescomplemented
82#107×D43C2214yescomplemented
83#103×D43C2214yescomplemented
84#102×D43C2214yescomplemented
85#14582863C2211yescharacteristic, complemented
86#14582862C2212yescomplemented
87#14582861C2212yescomplemented
88#14582861C2212yescomplemented
89C22⋊C8×D43C2212yes—
90C22⋊C8×D43C2212yescomplemented
91C2×C22⋊Q8×C43C2211yescharacteristic, complemented
92C2×#121×C43C2211yescharacteristic
93C43×#484C2212yescomplemented
94C43×#480C2212yescomplemented
95C43×#468C2214yescomplemented
96C43×#450C2212yescomplemented
97C43×#448C2212yescomplemented
98C43×#407C2211yescharacteristic, complemented
99C24×D43—21no—
100C24×D43D411yescharacteristic
101C22×Dic86—21no—
102C22×Dic86C2311yescharacteristic, complemented
103C2×Q8×D43—21no—
104C2×Q8×D43—21no—
105C2×Q8×D43—44no—
106C2×Q8×D43C2312yes—
107C2×Q8×D43C2312yescomplemented
108C22×D172—21no—
109C22×D172C2311yescharacteristic
110C22×C22⋊D43—21no—
111C22×C22⋊D43—21no—
112C22×C22⋊D43—21no—
113C2×D4×D43—22no—
114C2×D4×D43—22no—
115C2×D4×D43—22no—
116C2×D4×D43—22no—
117C2×D4×D43—21no—
118C2×D4×D43—21no—
119C2×D4×D43—44no—
120C2×D4×D43—48no—
121C2×D4×D43C2312yes—
122C2×D4×D43C2312yes—
123C23×Dic43D411yescharacteristic
124C22×C4×D43—21no—
125C22×C4×D43—21no—
126C22×C4×D43—21no—
127C22×C4×D43—44no—
128C22×C4×D43D411yescharacteristic
129C22×C4×D43D411yescharacteristic
130C22×C4×D43D411yescharacteristic
131C22×C4×D43D411yescharacteristic
132C22×C4×D43D411yescharacteristic
133C22×C4×D43D411yescharacteristic
134C22×C4×D43C2311yescharacteristic
135C22×C4×D43C2311yescharacteristic
136C22×C4×D43C2311yescharacteristic
137C22×C4×D43C2311yescharacteristic
138C22×C4×D43C2311yescharacteristic
139C22×C4×D43C2311yescharacteristic
140C2×#10621873C2314yescomplemented
141C2×#10621883C2314yescomplemented
142C2×#10621884C2314yescomplemented
143SD16×D43—48no—
144C2×#10621877C2312yescomplemented
145C2×#10621872C2314yescomplemented
146M16×D43—44no—
147C2×C8×D43C2314yes—
148#13063305—21no—
149#13063305—21no—
150#13063305C2312yes—
151#13063305C2312yescomplemented
152#13063304—21no—
153#13063304—21no—
154#13063304C2312yes—
155#13063304C2312yescomplemented
156#13063303—22no—
157#13063303—22no—
158#13063303—22no—
159#13063303—22no—
160#13063302—22no—
161#13063302—22no—
162#13063302—22no—
163#13063302—22no—
164#13063301—21no—
165#13063301—21no—
166#13063301C2312yes—
167#13063301C2312yescomplemented
168#13063300—21no—
169#13063300—21no—
170#13063300C2312yes—
171#13063300C2312yes—
172#13063299—21no—
173#13063299—21no—
174#13063299C2312yes—
175#13063299C2312yes—
176#13063298—22no—
177#13063298—22no—
178#13063298—22no—
179#13063298—22no—
180#13063297—22no—
181#13063297—22no—
182#13063297—22no—
183#13063297—22no—
184#13063296—21no—
185#13063296—21no—
186#13063296C2312yes—
187#13063296C2312yes—
188C2×C4⋊Dic43—21no—
189C2×C4⋊Dic43C2311yescharacteristic
190C2×C4⋊Dic43C2311yescharacteristic, complemented
191C2×Dic43⋊C4—21no—
192C2×Dic43⋊C4—21no—
193C2×Dic43⋊C4—21no—
194C2×Dic43⋊C4—21no—
195C4⋊C4×D43—22no—
196C4⋊C4×D43—22no—
197C4⋊C4×D43—22no—
198C4⋊C4×D43—22no—
199C4⋊C4×D43—21no—
200C4⋊C4×D43—21no—
201C4⋊C4×D43—21no—
202C4⋊C4×D43—21no—
203C4⋊C4×D43C2312yes—
204C4⋊C4×D43C2312yes—
205C4⋊C4×D43C2312yes—
206C4⋊C4×D43C2312yescomplemented
207C2×C22⋊Dic43—21no—
208C2×C22⋊Dic43—21no—
209C2×(C2×D43)⋊C4—21no—
210C2×(C2×D43)⋊C4—21no—
211C2×(C2×D43)⋊C4—21no—
212C2×(C2×D43)⋊C4—21no—
213C22⋊C4×D43—22no—
214C22⋊C4×D43—22no—
215C22⋊C4×D43—22no—
216C22⋊C4×D43—22no—
217C22⋊C4×D43—22no—
218C22⋊C4×D43—22no—
219C22⋊C4×D43—22no—
220C22⋊C4×D43—22no—
221#13063259C2314yescomplemented
222#13063258C2314yescomplemented
223#13063258C2314yescomplemented
224#13063250C2314yescomplemented
225#13063249C2314yescomplemented
226#13063248C2314yescomplemented
227#13063247C2314yescomplemented
228#13063246C2314yescomplemented
229#13063245C2314yescomplemented
230C22⋊(C43⋊C8)C2312yes—
231C22⋊(C43⋊C8)C2312yescomplemented
232(C2×D43)⋊C8C2314yes—
233(C2×D43)⋊C8C2314yescomplemented
234C22×Q8×C43C2311yescharacteristic, complemented
235C22×D4×C43—21no—
236C22×D4×C43C2311yescharacteristic
237C23×C4×C43C2311yescharacteristic
238C2×SD16×C43C2314yescomplemented
239C2×M16×C43C2312yescomplemented
240C22⋊Q8×C43—21no—
241C22⋊Q8×C43—21no—
242C22⋊Q8×C43C2312yes—
243C22⋊Q8×C43C2312yescomplemented
244#121×C43—21no—
245#121×C43—21no—
246#121×C43C2312yes—
247#121×C43C2312yes—
248C2×C4⋊C4×C43—21no—
249C2×C4⋊C4×C43C2311yescharacteristic
250C2×C4⋊C4×C43C2311yescharacteristic, complemented
251C2×C22⋊C4×C43—21no—
252C2×C22⋊C4×C43—21no—
253#107×C43C2314yescomplemented
254#103×C43C2314yescomplemented
255#102×C43C2314yescomplemented
256C22⋊C8×C43C2312yes—
257C22⋊C8×C43C2312yescomplemented
258C24×C43—21no—
259C24×C43C2×D411yescharacteristic
260C23×D43—24no—
261C23×D43—24no—
262C23×D43—21no—
263C23×D43—22no—
264C23×D43—22no—
265C23×D43—42no—
266C23×D43—44no—
267C23×D43—44no—
268C23×D43—44no—
269C23×D43C2×D411yescharacteristic
270C23×D43C2×D411yescharacteristic
271C23×D43C2×D411yescharacteristic
272C23×D43C2×D411yescharacteristic
273C23×D43C2×D411yescharacteristic
274C23×D43C2×D411yescharacteristic
275C2×Q8×C43—21no—
276C2×Q8×C43—42no—
277C2×Q8×C43C2412yes—
278C2×D4×C43—21no—
279C2×D4×C43—22no—
280C2×D4×C43—22no—
281C2×D4×C43—44no—
282C2×D4×C43—42no—
283C2×D4×C43C2412yes—
284C22×C4×C43—21no—
285C22×C4×C43—21no—
286C22×C4×C43—21no—
287C22×C4×C43—42no—
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2×D411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C2×C22⋊D43—22no—
295C2×C22⋊D43—22no—
296C2×C22⋊D43—22no—
297C2×C22⋊D43—22no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C2×C22⋊D43—44no—
301C2×C22⋊D43—44no—
302C2×C22⋊D43—44no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—42no—
307C22×Dic43C2×D411yescharacteristic
308C22×Dic43C2×D411yescharacteristic
309C22×Dic43C2×D411yescharacteristic
310C22×Dic43C2×D411yescharacteristic
311C22×Dic43C2×D411yescharacteristic
312C22×Dic43C2×D411yescharacteristic
313Q8×D43—28no—
314Q8×D43—44no—
315Q8×D43—44no—
316Q8×D43—44no—
317D4×D43—28no—
318D4×D43—48no—
319D4×D43—48no—
320D4×D43—48no—
321D4×D43—44no—
322D4×D43—44no—
323D4×D43—44no—
324D4×D43—48no—
325C2×D172—21no—
326C2×D172—22no—
327C2×D172—22no—
328C2×D172—44no—
329C2×D172—42no—
330C2×D172C2412yes—
331C2×C4×D43—24no—
332C2×C4×D43—24no—
333C2×C4×D43—24no—
334C2×C4×D43—22no—
335C2×C4×D43—22no—
336C2×C4×D43—22no—
337C2×C4×D43—22no—
338C2×C4×D43—22no—
339C2×C4×D43—22no—
340C2×C4×D43—42no—
341C2×C4×D43—42no—
342C2×C4×D43—42no—
343C2×C4×D43—44no—
344C2×C4×D43—44no—
345C2×C4×D43—42no—
346C2×C4×D43—42no—
347C2×C4×D43—42no—
348C2×C4×D43—42no—
349C2×C4×D43—42no—
350C2×C4×D43—42no—
351C2×C4×D43—44no—
352C2×C4×D43C2×D411yescharacteristic
353C2×C4×D43C2×D411yescharacteristic
354C2×C4×D43C2×D411yescharacteristic
355C2×C4×D43C2×D411yescharacteristic
356C2×C4×D43C2×D411yescharacteristic
357C2×C4×D43C2×D411yescharacteristic
358C2×C4×D43C2×D411yescharacteristic
359C2×C4×D43C2×D411yescharacteristic
360C2×C4×D43C2×D411yescharacteristic
361C2×C4×D43C2×D411yescharacteristic
362C2×C4×D43C2×D411yescharacteristic
363C2×C4×D43C2×D411yescharacteristic
364C2×C4×D43C2411yescharacteristic
365C2×C4×D43C2411yescharacteristic
366C2×C4×D43C2411yescharacteristic
367C2×C4×D43C2411yescharacteristic
368C2×Dic86—21no—
369C2×Dic86—22no—
370C2×Dic86—22no—
371C2×Dic86—42no—
372C2×Dic86—44no—
373C2×Dic86C2412yes—
374SD16×C43—44no—
375M16×C43—42no—
376C2×C8×C43C2414yes—
377C4⋊C4×C43—22no—
378C4⋊C4×C43—22no—
379C4⋊C4×C43—21no—
380C4⋊C4×C43—21no—
381C4⋊C4×C43C2412yes—
382C4⋊C4×C43C2412yes—
383C22⋊C4×C43—22no—
384C22⋊C4×C43—22no—
385C22⋊C4×C43—22no—
386C22⋊C4×C43—22no—
387C22⋊Dic43—22no—
388C22⋊Dic43—22no—
389C22⋊Dic43—22no—
390C22⋊Dic43—22no—
391#10621884—44no—
392#10621883—44no—
393(C2×D43)⋊C4—22no—
394(C2×D43)⋊C4—22no—
395(C2×D43)⋊C4—22no—
396(C2×D43)⋊C4—22no—
397(C2×D43)⋊C4—22no—
398(C2×D43)⋊C4—22no—
399(C2×D43)⋊C4—22no—
400(C2×D43)⋊C4—22no—
401C4⋊Dic43—21no—
402C4⋊Dic43—21no—
403C4⋊Dic43—22no—
404C4⋊Dic43—22no—
405C4⋊Dic43C2412yes—
406C4⋊Dic43C2412yes—
407Dic43⋊C4—22no—
408Dic43⋊C4—22no—
409Dic43⋊C4—22no—
410Dic43⋊C4—22no—
411Dic43⋊C4—22no—
412Dic43⋊C4—22no—
413Dic43⋊C4—22no—
414Dic43⋊C4—22no—
415#10621877—42no—
416C2×C43⋊C8C2414yes—
417#10621873—44no—
418#10621872—44no—
419C8×D43—28no—
420C23×C43—22no—
421C23×C43—22no—
422C23×C43—22no—
423C23×C43—41no—
424C23×C43—42no—
425C23×C43—42no—
426C23×C43—42no—
427C23×C43C22×D411yescharacteristic
428C23×C43C22×D411yescharacteristic
429C23×C43C22×D411yescharacteristic
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—22no—
433C22×D43—22no—
434C22×D43—22no—
435C22×D43—22no—
436C22×D43—22no—
437C22×D43—22no—
438C22×D43—22no—
439C22×D43—22no—
440C22×D43—22no—
441C22×D43—22no—
442C22×D43—22no—
443C22×D43—22no—
444C22×D43—41no—
445C22×D43—41no—
446C22×D43—41no—
447C22×D43—416no—
448C22×D43—44no—
449C22×D43—44no—
450C22×D43—42no—
451C22×D43—42no—
452C22×D43—42no—
453C22×D43—44no—
454C22×D43—44no—
455C22×D43—44no—
456C22×D43—44no—
457C22×D43—816no—
458C22×D43AGL(1,ℤ/8)14yes—
459C22×D43#13714yes—
460C22×D43C22×D411yescharacteristic
461C22×D43C22×D411yescharacteristic
462C22×D43C22×D411yescharacteristic
463C22×D43C22×D411yescharacteristic
464Q8×C43—24no—
465Q8×C43—42no—
466D4×C43—24no—
467D4×C43—42no—
468D4×C43—44no—
469D4×C43—44no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—22no—
476C2×C4×C43—41no—
477C2×C4×C43—41no—
478C2×C4×C43—41no—
479C2×C4×C43—42no—
480C2×C4×C43—42no—
481C2×C4×C43—42no—
482C2×C4×C43C22×D411yescharacteristic
483C2×C4×C43C22×D411yescharacteristic
484C2×C4×C43C22×D411yescharacteristic
485C2×C4×C43C2511yescharacteristic
486C22⋊D43—44no—
487C22⋊D43—44no—
488C22⋊D43—44no—
489C22⋊D43—44no—
490C22⋊D43—44no—
491C22⋊D43—44no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—22no—
496C2×Dic43—22no—
497C2×Dic43—22no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—42no—
502C2×Dic43—42no—
503C2×Dic43—42no—
504C2×Dic43C22×D411yescharacteristic
505C2×Dic43C22×D411yescharacteristic
506C2×Dic43C22×D411yescharacteristic
507C2×Dic43C22×D411yescharacteristic
508D172—24no—
509D172—42no—
510D172—44no—
511D172—44no—
512C4×D43—22no—
513C4×D43—22no—
514C4×D43—22no—
515C4×D43—22no—
516C4×D43—22no—
517C4×D43—22no—
518C4×D43—22no—
519C4×D43—22no—
520C4×D43—22no—
521C4×D43—41no—
522C4×D43—41no—
523C4×D43—41no—
524C4×D43—41no—
525C4×D43—41no—
526C4×D43—41no—
527C4×D43—44no—
528C4×D43—44no—
529C4×D43—44no—
530C4×D43—44no—
531C4×D43—44no—
532C4×D43—44no—
533C4×D43H(5,𝔽2)14yes—
534Dic86—24no—
535Dic86—44no—
536Dic86—42no—
537Dic86—44no—
538C8×C43—24no—
539C43⋊C8—24no—
540C2×#3193—431nomaximal, Sylow
541C22×C43—21no—
542C22×C43—21no—
543C22×C43—21no—
544C22×C43—21no—
545C22×C43—21no—
546C22×C43—21no—
547C22×C43—21no—
548C22×C43—44no—
549C22×C43—42no—
550C22×C43—42no—
551C22×C43—42no—
552C22×C43—84no—
553C22×C43C2×AGL(1,ℤ/8)12yes—
554C22×C43C2×#13712yes—
555C22×C43C23×D411yescharacteristic
556C2×D43—21no—
557C2×D43—21no—
558C2×D43—21no—
559C2×D43—21no—
560C2×D43—28no—
561C2×D43—28no—
562C2×D43—21no—
563C2×D43—21no—
564C2×D43—21no—
565C2×D43—44no—
566C2×D43—44no—
567C2×D43—44no—
568C2×D43—44no—
569C2×D43—42no—
570C2×D43—42no—
571C2×D43—42no—
572C2×D43—88no—
573C2×D43—84no—
574C2×D43—88no—
575C2×D43#53412yes—
576C2×D43C2×AGL(1,ℤ/8)12yes—
577C2×D43C2×AGL(1,ℤ/8)12yes—
578C2×D43C2×#13712yes—
579C2×D43C2×#13712yes—
580C4×C43—21no—
581C4×C43—21no—
582C4×C43—21no—
583C4×C43—42no—
584C4×C43—42no—
585C4×C43—42no—
586C4×C43C2×H(5,𝔽2)12yes—
587Dic43—21no—
588Dic43—21no—
589Dic43—21no—
590Dic43—42no—
591Dic43—42no—
592Dic43—42no—
593Dic43#53412yes—
594C22×C22⋊Q8—431no—
595C22×#121—431no—
596#3193—432no—
597#3193—432no—
598#3193—434no—
599#3193—432no—
600#3193—432no—
601#3193—431no—
602#3193—431no—
603#3193—431no—
604#3193D4311yescharacteristic, direct product factor
605C2×#484—432no—
606C2×#480—432no—
607C2×#468—434no—
608C2×#448—432no—
609C2×#450—432no—
610C2×#407—431no—
611C2×C43—22no—
612C2×C43—22no—
613C2×C43—41no—
614C2×C43—82no—
615C2×C43C2×#53411yescharacteristic
616C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
617C2×C43C22×#13711yescharacteristic
618D43—22no—
619D43—22no—
620D43—41no—
621D43—82no—
622D43#319314yesdirect product factor
623C23×Q8—431no—
624C23×D4—431no—
625C23×D4—861no—
626C24×C4—431no—
627C22×SD16—434no—
628C22×M16—432no—
629C2×C22⋊Q8—431no—
630C2×C22⋊Q8—431no—
631C2×C22⋊Q8—432no—
632C2×C22⋊Q8—432no—
633C2×C22⋊Q8—432no—
634C2×C22⋊Q8—432no—
635C2×C22⋊Q8—431no—
636C2×C22⋊Q8—861no—
637C2×C22⋊Q8—861no—
638C2×C22⋊Q8—861no—
639C2×C22⋊Q8—861no—
640C2×C22⋊Q8—861no—
641C2×C22⋊Q8—861no—
642C2×C22⋊Q8C2×D4311yescharacteristic, complemented
643C2×#121—431no—
644C2×#121—431no—
645C2×#121—432no—
646C2×#121—432no—
647C2×#121—432no—
648C2×#121—432no—
649C2×#121—431no—
650C2×#121—861no—
651C2×#121—861no—
652C2×#121—861no—
653C2×#121—861no—
654C2×#121—861no—
655C2×#121—861no—
656C2×#121C2×D4311yescharacteristic
657C22×C4⋊C4—431no—
658C22×C4⋊C4—431no—
659C22×C4⋊C4—861no—
660C22×C22⋊C4—861no—
661C22×C22⋊C4—861no—
662#484—432no—
663#484—432no—
664#484—434no—
665#484—434no—
666#484—432no—
667#484C2×D4312yescomplemented
668#480—432no—
669#480—432no—
670#480—434no—
671#480—434no—
672#480—432no—
673#480C2×D4312yescomplemented
674#468—434no—
675#468—434no—
676#468—434no—
677#468—434no—
678#468—434no—
679#468—434no—
680#468—434no—
681#468C2×D4314yescomplemented
682#450—432no—
683#450—434no—
684#450—432no—
685#450—434no—
686#450—432no—
687#450C2×D4312yescomplemented
688#448—432no—
689#448—434no—
690#448—432no—
691#448—434no—
692#448—432no—
693#448C2×D4312yescomplemented
694C2×#107—434no—
695C2×#103—434no—
696C2×#102—434no—
697#407—431no—
698#407—432no—
699#407—432no—
700#407—432no—
701#407C2×D4311yescharacteristic, complemented
702C2×C22⋊C8—432no—
703C2×C22⋊C8—432no—
704C43C2×#319311yescharacteristic, complemented, Sylow
705C25—431no—
706C25—861no—
707C22×Q8—432no—
708C22×Q8—432no—
709C22×Q8—431no—
710C22×Q8—861no—
711C22×Q8—861no—
712C22×Q8—861no—
713C22×Q8—1724no—
714C22×Q8C22×D4311yescharacteristic, complemented
715C22×D4—21no—
716C22×D4—432no—
717C22×D4—432no—
718C22×D4—431no—
719C22×D4—861no—
720C22×D4—861no—
721C22×D4—861no—
722C22×D4—861no—
723C22×D4—862no—
724C22×D4—862no—
725C22×D4—862no—
726C22×D4—862no—
727C22×D4—861no—
728C22×D4—861no—
729C22×D4—1724no—
730C22×D4—1728no—
731C22×D4C22×D4311yescharacteristic
732C23×C4—431no—
733C23×C4—431no—
734C23×C4—431no—
735C23×C4—431no—
736C23×C4—431no—
737C23×C4—431no—
738C23×C4—431no—
739C23×C4—431no—
740C23×C4—431no—
741C23×C4—431no—
742C23×C4—431no—
743C23×C4—431no—
744C23×C4—431no—
745C23×C4—861no—
746C23×C4—861no—
747C23×C4—861no—
748C23×C4—1724no—
749C23×C4C22×D4311yescharacteristic
750C2×SD16—434no—
751C2×SD16—434no—
752C2×SD16—434no—
753C2×SD16—1728no—
754C2×SD16C22×D4314yescomplemented
755C2×M16—432no—
756C2×M16—434no—
757C2×M16—1724no—
758C2×M16C22×D4312yescomplemented
759C22×C8—434no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—432no—
763C22⋊Q8—432no—
764C22⋊Q8—432no—
765C22⋊Q8—432no—
766C22⋊Q8—432no—
767C22⋊Q8—432no—
768C22⋊Q8—862no—
769C22⋊Q8—862no—
770C22⋊Q8—862no—
771C22⋊Q8—862no—
772C22⋊Q8—862no—
773C22⋊Q8—862no—
774C22⋊Q8—862no—
775C22⋊Q8—862no—
776C22⋊Q8—861no—
777C22⋊Q8—861no—
778C22⋊Q8—861no—
779C22⋊Q8—861no—
780C22⋊Q8—861no—
781C22⋊Q8—861no—
782C22⋊Q8C22×D4312yes—
783C22⋊Q8C22×D4312yescomplemented
784#121—21no—
785#121—21no—
786#121—432no—
787#121—432no—
788#121—432no—
789#121—432no—
790#121—432no—
791#121—432no—
792#121—862no—
793#121—862no—
794#121—862no—
795#121—862no—
796#121—861no—
797#121—861no—
798#121—861no—
799#121—861no—
800#121—862no—
801#121—862no—
802#121—862no—
803#121—862no—
804#121—861no—
805#121—861no—
806#121C22×D4312yes—
807#121C22×D4312yes—
808C2×C4⋊C4—21no—
809C2×C4⋊C4—431no—
810C2×C4⋊C4—431no—
811C2×C4⋊C4—432no—
812C2×C4⋊C4—432no—
813C2×C4⋊C4—432no—
814C2×C4⋊C4—432no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4—861no—
817C2×C4⋊C4—861no—
818C2×C4⋊C4—861no—
819C2×C4⋊C4—862no—
820C2×C4⋊C4—862no—
821C2×C4⋊C4—862no—
822C2×C4⋊C4—862no—
823C2×C4⋊C4—861no—
824C2×C4⋊C4—861no—
825C2×C4⋊C4—861no—
826C2×C4⋊C4—861no—
827C2×C4⋊C4—861no—
828C2×C4⋊C4C22×D4311yescharacteristic
829C2×C4⋊C4C22×D4311yescharacteristic, complemented
830C2×C22⋊C4—21no—
831C2×C22⋊C4—21no—
832C2×C22⋊C4—862no—
833C2×C22⋊C4—862no—
834C2×C22⋊C4—862no—
835C2×C22⋊C4—862no—
836C2×C22⋊C4—862no—
837C2×C22⋊C4—862no—
838C2×C22⋊C4—862no—
839C2×C22⋊C4—862no—
840C2×C22⋊C4—861no—
841C2×C22⋊C4—861no—
842C2×C22⋊C4—861no—
843C2×C22⋊C4—861no—
844C2×C22⋊C4—861no—
845C2×C22⋊C4—861no—
846#107—434no—
847#107—434no—
848#107—434no—
849#107C22×D4314yescomplemented
850#103—434no—
851#103—434no—
852#103—434no—
853#103C22×D4314yescomplemented
854#102—434no—
855#102—434no—
856#102—434no—
857#102C22×D4314yescomplemented
858C22⋊C8—432no—
859C22⋊C8—432no—
860C22⋊C8—434no—
861C22⋊C8—434no—
862C22⋊C8C22×D4312yes—
863C22⋊C8C22×D4312yescomplemented
864C24—21no—
865C24—431no—
866C24—431no—
867C24—431no—
868C24—431no—
869C24—431no—
870C24—431no—
871C24—864no—
872C24—864no—
873C24—862no—
874C24—862no—
875C24—861no—
876C24—1724no—
877C24—1722no—
878C24—1724no—
879C24—1724no—
880C24D4×D4311yescharacteristic
881C2×Q8—21no—
882C2×Q8—42no—
883C2×Q8—432no—
884C2×Q8—862no—
885C2×Q8—862no—
886C2×Q8—868no—
887C2×Q8—861no—
888C2×Q8—1722no—
889C2×Q8—1724no—
890C2×Q8—1724no—
891C2×Q8—1724no—
892C2×Q8—1724no—
893C2×Q8C23×D4312yes—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—21no—
897C2×D4—42no—
898C2×D4—44no—
899C2×D4—432no—
900C2×D4—862no—
901C2×D4—862no—
902C2×D4—868no—
903C2×D4—862no—
904C2×D4—862no—
905C2×D4—862no—
906C2×D4—862no—
907C2×D4—862no—
908C2×D4—862no—
909C2×D4—861no—
910C2×D4—1722no—
911C2×D4—1724no—
912C2×D4—1724no—
913C2×D4—1724no—
914C2×D4—1724no—
915C2×D4—1724no—
916C2×D4—1728no—
917C2×D4—1728no—
918C2×D4—1728no—
919C2×D4—1728no—
920C2×D4—1724no—
921C2×D4—1724no—
922C2×D4C23×D4312yes—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—42no—
927C22×C4—431no—
928C22×C4—431no—
929C22×C4—431no—
930C22×C4—431no—
931C22×C4—431no—
932C22×C4—431no—
933C22×C4—431no—
934C22×C4—431no—
935C22×C4—431no—
936C22×C4—431no—
937C22×C4—431no—
938C22×C4—431no—
939C22×C4—431no—
940C22×C4—431no—
941C22×C4—431no—
942C22×C4—431no—
943C22×C4—431no—
944C22×C4—431no—
945C22×C4—431no—
946C22×C4—431no—
947C22×C4—431no—
948C22×C4—431no—
949C22×C4—864no—
950C22×C4—864no—
951C22×C4—864no—
952C22×C4—862no—
953C22×C4—862no—
954C22×C4—862no—
955C22×C4—862no—
956C22×C4—862no—
957C22×C4—862no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—1722no—
962C22×C4—1722no—
963C22×C4—1722no—
964C22×C4—1722no—
965C22×C4—1722no—
966C22×C4—1722no—
967C22×C4—1722no—
968C22×C4—1722no—
969C22×C4—1722no—
970C22×C4—1724no—
971C22×C4—1724no—
972C22×C4—1724no—
973C22×C4—1722no—
974C22×C4D4×D4311yescharacteristic
975C22×C4D4×D4311yescharacteristic
976C22×C4D4×D4311yescharacteristic
977C22×C4C23×D4311yescharacteristic
978C22×C4C23×D4311yescharacteristic
979C22×C4C23×D4311yescharacteristic
980SD16—44no—
981SD16—1724no—
982SD16—1724no—
983SD16—1724no—
984M16—42no—
985M16—1724no—
986M16—1722no—
987C2×C8—434no—
988C2×C8—868no—
989C2×C8C23×D4314yes—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—432no—
995C4⋊C4—432no—
996C4⋊C4—862no—
997C4⋊C4—862no—
998C4⋊C4—862no—
999C4⋊C4—862no—
1000C4⋊C4—862no—
1001C4⋊C4—862no—
1002C4⋊C4—862no—
1003C4⋊C4—862no—
1004C4⋊C4—861no—
1005C4⋊C4—861no—
1006C4⋊C4—862no—
1007C4⋊C4—862no—
1008C4⋊C4C23×D4312yes—
1009C4⋊C4C23×D4312yes—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—862no—
1015C22⋊C4—862no—
1016C22⋊C4—862no—
1017C22⋊C4—862no—
1018C22⋊C4—862no—
1019C22⋊C4—862no—
1020C22⋊C4—862no—
1021C22⋊C4—862no—
1022C22⋊C4—862no—
1023C22⋊C4—862no—
1024C22⋊C4—862no—
1025C22⋊C4—862no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—431no—
1034C23—434no—
1035C23—434no—
1036C23—431no—
1037C23—431no—
1038C23—431no—
1039C23—862no—
1040C23—862no—
1041C23—862no—
1042C23—862no—
1043C23—862no—
1044C23—862no—
1045C23—862no—
1046C23—862no—
1047C23—862no—
1048C23—862no—
1049C23—862no—
1050C23—862no—
1051C23—862no—
1052C23—862no—
1053C23—34416no—
1054C23—1721no—
1055C23—1721no—
1056C23—1721no—
1057C23—1722no—
1058C23—1722no—
1059C23—1724no—
1060C23—1724no—
1061C23—1724no—
1062C23—1724no—
1063C23—17216no—
1064C23—1724no—
1065C23—1724no—
1066C23—1722no—
1067C23C2×D4×D4311yescharacteristic
1068C23C2×D4×D4311yescharacteristic
1069C23C2×D4×D4311yescharacteristic
1070Q8—24no—
1071Q8—42no—
1072Q8—864no—
1073Q8—1722no—
1074Q8—1724no—
1075Q8—1724no—
1076D4—24no—
1077D4—42no—
1078D4—44no—
1079D4—44no—
1080D4—864no—
1081D4—1722no—
1082D4—1724no—
1083D4—1724no—
1084D4—1724no—
1085D4—1724no—
1086D4—1724no—
1087D4—1724no—
1088D4—1724no—
1089D4—1724no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—431no—
1103C2×C4—434no—
1104C2×C4—431no—
1105C2×C4—431no—
1106C2×C4—431no—
1107C2×C4—862no—
1108C2×C4—862no—
1109C2×C4—862no—
1110C2×C4—862no—
1111C2×C4—862no—
1112C2×C4—862no—
1113C2×C4—862no—
1114C2×C4—862no—
1115C2×C4—862no—
1116C2×C4—862no—
1117C2×C4—862no—
1118C2×C4—862no—
1119C2×C4—862no—
1120C2×C4—862no—
1121C2×C4—862no—
1122C2×C4—1721no—
1123C2×C4—1721no—
1124C2×C4—1721no—
1125C2×C4—1721no—
1126C2×C4—1721no—
1127C2×C4—1721no—
1128C2×C4—1724no—
1129C2×C4—1724no—
1130C2×C4—1724no—
1131C2×C4—1724no—
1132C2×C4—1724no—
1133C2×C4—1724no—
1134C2×C4—1721no—
1135C2×C4—1721no—
1136C2×C4—1721no—
1137C2×C4—1722no—
1138C2×C4—1722no—
1139C2×C4—1722no—
1140C2×C4C2×D4×D4311yescharacteristic
1141C2×C4C2×D4×D4311yescharacteristic
1142C2×C4C2×D4×D4311yescharacteristic
1143C2×C4C24×D4311yescharacteristic
1144C8—24no—
1145C8—864no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—44no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—84no—
1158C22—432no—
1159C22—432no—
1160C22—432no—
1161C22—432no—
1162C22—432no—
1163C22—868no—
1164C22—868no—
1165C22—861no—
1166C22—861no—
1167C22—861no—
1168C22—861no—
1169C22—861no—
1170C22—861no—
1171C22—861no—
1172C22—3444no—
1173C22—3448no—
1174C22—3448no—
1175C22—1724no—
1176C22—1724no—
1177C22—1724no—
1178C22—1724no—
1179C22—1722no—
1180C22—1722no—
1181C22—1722no—
1182C22AGL(1,ℤ/8)×D4312yes—
1183C22#137×D4312yes—
1184C22C22×D4×D4311yescharacteristic
1185C4—21no—
1186C4—21no—
1187C4—21no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—432no—
1192C4—861no—
1193C4—861no—
1194C4—861no—
1195C4—1722no—
1196C4—1722no—
1197C4—1722no—
1198C4H(5,𝔽2)×D4312yes—
1199C2—22no—
1200C2—22no—
1201C2—41no—
1202C2—82no—
1203C2—434no—
1204C2—862no—
1205C2—862no—
1206C2—3442no—
1207C2—1721no—
1208C2#534×D4311yescharacteristic
1209C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1210C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3193C2
socleC22×C43C23×D4
prime radicalC2×#121×D43C2
hypercenter#3193D43
hypocenterC43C2×#3193
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊Q8×D43C2semidirect
3. #19145403C2semidirect
4. #19145402C2semidirect
5. #19145401C2semidirect
6. #19145400C2semidirect
7. #19145399C2semidirect
8. #19145398C2semidirect
9. #19145397C2semidirect
10. #19145396C2semidirect
11. #484×D43C2semidirect
12. #480×D43C2semidirect
13. #468×D43C2semidirect
14. #448×D43C2semidirect
15. #450×D43C2semidirect
16. #407×D43C2semidirect
17. C43×#3193C2semidirect
18. C22×Q8×D43C22semidirect
22. C2×SD16×D43C22semidirect
23. C2×M16×D43C22semidirect
24. C2×#13063305C22semidirect
25. C2×#13063304C22semidirect
28. C2×#13063301C22semidirect
34. C22⋊Q8×D43C22semidirect
35. C22⋊Q8×D43C22semidirect
36. C22⋊Q8×D43C22semidirect
52. C2×C4⋊C4×D43C22semidirect
55. #14583236C22semidirect
56. #14583235C22semidirect
57. #14583234C22semidirect
58. #14583233C22semidirect
59. #14583232C22semidirect
60. #14583214C22semidirect
61. #14583213C22semidirect
62. #14583212C22semidirect
63. #14583211C22semidirect
64. #14583210C22semidirect
65. #14583148C22semidirect
66. #14583147C22semidirect
67. #14583146C22semidirect
68. #14583145C22semidirect
69. #14583144C22semidirect
70. #14583143C22semidirect
71. #14583142C22semidirect
72. #14583052C22semidirect
73. #14583051C22semidirect
74. #14583050C22semidirect
75. #14583049C22semidirect
76. #14583048C22semidirect
77. #14583040C22semidirect
78. #14583039C22semidirect
79. #14583038C22semidirect
80. #14583037C22semidirect
81. #14583036C22semidirect
82. #107×D43C22semidirect
83. #103×D43C22semidirect
84. #102×D43C22semidirect
85. #14582863C22semidirect
86. #14582862C22semidirect
87. #14582861C22semidirect
88. #14582861C22semidirect
90. C22⋊C8×D43C22semidirect
91. C2×C22⋊Q8×C43C22semidirect
93. C43×#484C22semidirect
94. C43×#480C22semidirect
95. C43×#468C22semidirect
96. C43×#450C22semidirect
97. C43×#448C22semidirect
98. C43×#407C22semidirect
102. C22×Dic86C23semidirect
107. C2×Q8×D43C23semidirect
140. C2×#10621873C23semidirect
141. C2×#10621883C23semidirect
142. C2×#10621884C23semidirect
144. C2×#10621877C23semidirect
145. C2×#10621872C23semidirect
151. #13063305C23semidirect
155. #13063304C23semidirect
167. #13063301C23semidirect
190. C2×C4⋊Dic43C23semidirect
206. C4⋊C4×D43C23semidirect
221. #13063259C23semidirect
222. #13063258C23semidirect
223. #13063258C23semidirect
224. #13063250C23semidirect
225. #13063249C23semidirect
226. #13063248C23semidirect
227. #13063247C23semidirect
228. #13063246C23semidirect
229. #13063245C23semidirect
231. C22⋊(C43⋊C8)C23semidirect
233. (C2×D43)⋊C8C23semidirect
234. C22×Q8×C43C23semidirect
238. C2×SD16×C43C23semidirect
239. C2×M16×C43C23semidirect
243. C22⋊Q8×C43C23semidirect
250. C2×C4⋊C4×C43C23semidirect
253. #107×C43C23semidirect
254. #103×C43C23semidirect
255. #102×C43C23semidirect
257. C22⋊C8×C43C23semidirect
604. #3193D43direct (N × H)
622. D43#3193direct (N × H)
642. C2×C22⋊Q8C2×D43semidirect
667. #484C2×D43semidirect
673. #480C2×D43semidirect
681. #468C2×D43semidirect
687. #450C2×D43semidirect
693. #448C2×D43semidirect
701. #407C2×D43semidirect
704. C43C2×#3193semidirect
714. C22×Q8C22×D43semidirect
754. C2×SD16C22×D43semidirect
758. C2×M16C22×D43semidirect
783. C22⋊Q8C22×D43semidirect
829. C2×C4⋊C4C22×D43semidirect
849. #107C22×D43semidirect
853. #103C22×D43semidirect
857. #102C22×D43semidirect
863. C22⋊C8C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#121×D432
#191454032
#191454022
#191454012
#191454002
#191453992
#191453982
#191453972
#191453962
#484×D432
#480×D432
#468×D432
#448×D432
#450×D432
#407×D432
C43×#31932
C2×#319343