Finite Group Databasebeta

← D43×#1871 #25097767

Subgroups — D43×#1871 #25097767

Order 11008.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D43C211yesmaximal, characteristic, complemented
2#525×D43C211yesmaximal, characteristic
3C2×#104×D43C212yesmaximal, complemented
4C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
5#19134898C211yesmaximal, characteristic, complemented
6#19134897C211yesmaximal, characteristic, complemented
7#19134896C212yesmaximal, complemented
8#19134895C211yesmaximal, characteristic, complemented
9#19134894C212yesmaximal, complemented
10#339×D43C212yesmaximal, complemented
11C43×#1871C211yesmaximal, characteristic, complemented
12C2×#41×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×#10621877C2211yescharacteristic, complemented
15C22×#10621872—21no—
16C2×M16×D43—21no—
17C2×M16×D43—21no—
18C2×M16×D43—28no—
19C2×M16×D43C2212yes—
20C2×M16×D43C2212yescomplemented
21C22×C8×D43—21no—
22#14583412C411yescharacteristic, complemented
23#14583412C411yescharacteristic, complemented
24#14583411C2211yescharacteristic
25#14583410C2211yescharacteristic
26#14583409C411yescharacteristic, complemented
27#14583409C411yescharacteristic, complemented
28#14583408—21no—
29#14583408—21no—
30#14583407—21no—
31#14583406C2211yescharacteristic
32#14583405—21no—
33#123×D43—21no—
34C22⋊Q8×D43C411yescharacteristic, complemented
35C22⋊Q8×D43C411yescharacteristic, complemented
36#121×D43C411yescharacteristic, complemented
37#121×D43C411yescharacteristic, complemented
38#120×D43—21no—
39C4×D4×D43—21no—
40C4×D4×D43—21no—
41#117×D43C2211yescharacteristic
42C2×C22⋊C4×D43—21no—
43C2×C42×D43C2212yes—
44C2×#13063253C2212yescomplemented
45C2×#13063252C2212yescomplemented
46C2×#13063251C2212yescomplemented
47#104×D43—28no—
48C22⋊C4×Dic43—21no—
49C4×(C2×D43)⋊C4C2212yescomplemented
50C4×C22⋊Dic43C2211yescharacteristic, complemented
51#14582746—21no—
52#95×D43—21no—
53#14582660C2212yescomplemented
54#14582659C2212yescomplemented
55#14582658C2212yescomplemented
56C22×M16×C43C2211yescharacteristic, complemented
57C43×#525C2211yescharacteristic
58C2×#104×C43C2212yescomplemented
59C4×C22⋊C4×C43C2211yescharacteristic, complemented
60C43×#339C2212yescomplemented
61C24×D43D411yescharacteristic
62C2×#10621902C2×C411yescharacteristic
63C2×#10621898—21no—
64C2×#10621898C2311yescharacteristic
65C2×#10621900—21no—
66C2×#10621900C2×C411yescharacteristic
67#41×D43—24no—
68#41×D43—24no—
69C2×Q8×D43C2×C411yescharacteristic
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72C2×D4×D43—21no—
73C2×D4×D43C2×C411yescharacteristic
74C23×Dic43D411yescharacteristic
75C22×C4×D43—24no—
76C22×C4×D43—24no—
77C22×C4×D43—22no—
78C22×C4×D43—21no—
79C22×C4×D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43D411yescharacteristic
84C22×C4×D43D411yescharacteristic
85C22×C4×D43D411yescharacteristic
86C22×C4×D43D411yescharacteristic
87C22×C4×D43D411yescharacteristic
88C22×C4×D43D411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C2×#10621877—21no—
92C2×#10621877—24no—
93C2×#10621877C2312yes—
94C2×#10621872—28no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97M16×D43—28no—
98M16×D43—28no—
99M16×D43—24no—
100M16×D43—24no—
101M16×D43—24no—
102M16×D43D418yescomplemented
103C22×C43⋊C8—21no—
104C2×C8×D43—28no—
105C2×C8×D43—22no—
106C2×C8×D43—22no—
107#13063310—21no—
108#13063310—21no—
109#13063309—21no—
110#13063308—21no—
111#13063307—21no—
112#13063307—21no—
113#13063306—21no—
114#13063305C2×C411yescharacteristic, complemented
115#13063305C2×C411yescharacteristic, complemented
116#13063304C2×C411yescharacteristic, complemented
117#13063304C2×C411yescharacteristic, complemented
118#13063303—21no—
119#13063303—21no—
120#13063302—21no—
121#13063302—21no—
122#13063301C2×C411yescharacteristic, complemented
123#13063301C2×C411yescharacteristic, complemented
124#13063300C2×C411yescharacteristic, complemented
125#13063300C2×C411yescharacteristic, complemented
126#13063299C2×C411yescharacteristic, complemented
127#13063299C2×C411yescharacteristic, complemented
128#13063298—21no—
129#13063298—21no—
130#13063297—21no—
131#13063297—21no—
132#13063296C2×C411yescharacteristic, complemented
133#13063296C2×C411yescharacteristic, complemented
134#13063295—21no—
135#13063295—21no—
136#13063295—21no—
137#13063294—21no—
138#13063293—21no—
139#13063293—21no—
140#13063293—21no—
141C4×D172—21no—
142C4×D172—21no—
143D4×Dic43—21no—
144D4×Dic43—21no—
145#13063287—21no—
146#13063287—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155#13063284C2311yescharacteristic
156#13063283C2×C411yescharacteristic
157#13063283C2×C411yescharacteristic
158#13063282—21no—
159#13063281—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43—21no—
162C4⋊C4×D43C2×C411yescharacteristic
163C4⋊C4×D43C2×C411yescharacteristic
164C2×C22⋊Dic43—21no—
165C2×(C2×D43)⋊C4—22no—
166C22⋊C4×D43—28no—
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C22⋊C4×D43—21no—
171C22⋊C4×D43—21no—
172C2×C4×Dic43—22no—
173C2×C4×Dic43C2312yes—
174C42×D43—21no—
175C42×D43—24no—
176C42×D43—24no—
177#13063253—24no—
178#13063252—24no—
179#13063251—24no—
180C43⋊#95—21no—
181C43⋊#95—22no—
182C2×#41×C43C2311yescharacteristic
183C23×C4×C43C2311yescharacteristic
184C2×M16×C43—21no—
185C2×M16×C43—24no—
186C2×M16×C43C2312yes—
187C22×C8×C43—21no—
188#123×C43—21no—
189C22⋊Q8×C43C2×C411yescharacteristic, complemented
190C22⋊Q8×C43C2×C411yescharacteristic, complemented
191#121×C43C2×C411yescharacteristic, complemented
192#121×C43C2×C411yescharacteristic, complemented
193#120×C43—21no—
194C4×D4×C43—21no—
195C4×D4×C43—21no—
196#117×C43C2311yescharacteristic
197C2×C22⋊C4×C43—21no—
198C2×C42×C43C2312yes—
199#104×C43—24no—
200#95×C43—21no—
201C24×C43C2×D411yescharacteristic
202C23×D43—24no—
203C23×D43—24no—
204C23×D43—21no—
205C23×D43—42no—
206C23×D43C22⋊C411yescharacteristic
207C23×D43C22⋊C411yescharacteristic
208C23×D43C22⋊C411yescharacteristic
209C23×D43C22⋊C411yescharacteristic
210C23×D43C2×D411yescharacteristic
211C23×D43C2×D411yescharacteristic
212#41×C43—22no—
213#41×C43—22no—
214C2×Q8×C43C22×C411yescharacteristic
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43C22×C411yescharacteristic
219C22×C4×C43—22no—
220C22×C4×C43—22no—
221C22×C4×C43—21no—
222C22×C4×C43—22no—
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C22×Dic43—24no—
237C22×Dic43—21no—
238C22×Dic43—22no—
239C22×Dic43C22⋊C411yescharacteristic
240C22×Dic43C22⋊C411yescharacteristic
241C22×Dic43C22⋊C411yescharacteristic
242C22×Dic43C22⋊C411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245#10621902—24no—
246Q8×D43—24no—
247#10621900—24no—
248#10621900—44no—
249D4×D43—24no—
250D4×D43—44no—
251D4×D43—44no—
252D4×D43—44no—
253#10621898—22no—
254#10621898—22no—
255#10621898—42no—
256#10621898—42no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172C22×C411yescharacteristic
261C2×C4×D43—22no—
262C2×C4×D43—22no—
263C2×C4×D43—24no—
264C2×C4×D43—24no—
265C2×C4×D43—24no—
266C2×C4×D43—24no—
267C2×C4×D43—24no—
268C2×C4×D43—22no—
269C2×C4×D43—22no—
270C2×C4×D43—22no—
271C2×C4×D43—22no—
272C2×C4×D43—22no—
273C2×C4×D43—22no—
274C2×C4×D43—22no—
275C2×C4×D43—22no—
276C2×C4×D43—28no—
277C2×C4×D43—21no—
278C2×C4×D43—21no—
279C2×C4×D43—21no—
280C2×C4×D43—21no—
281C2×C4×D43—21no—
282C2×C4×D43—24no—
283C2×C4×D43—44no—
284C2×C4×D43—42no—
285C2×C4×D43—42no—
286C2×C4×D43—44no—
287C2×C4×D43C22⋊C411yescharacteristic
288C2×C4×D43C22⋊C411yescharacteristic
289C2×C4×D43C22⋊C411yescharacteristic
290C2×C4×D43C22⋊C411yescharacteristic
291C2×C4×D43C22⋊C411yescharacteristic
292C2×C4×D43C22⋊C411yescharacteristic
293C2×C4×D43C22⋊C411yescharacteristic
294C2×C4×D43C22⋊C411yescharacteristic
295C2×C4×D43C22×C411yescharacteristic
296C2×C4×D43C22×C411yescharacteristic
297C2×C4×D43C22×C411yescharacteristic
298C2×C4×D43C22×C411yescharacteristic
299C2×C4×D43C2×D411yescharacteristic
300C2×C4×D43C2×D411yescharacteristic
301C2×C4×D43C2×D411yescharacteristic
302C2×C4×D43C2×D411yescharacteristic
303C2×C4×D43C2×D414yes—
304C2×C4×D43#4114yes—
305C2×Dic86—21no—
306C2×Dic86C22×C411yescharacteristic
307M16×C43—24no—
308M16×C43—22no—
309M16×C43C2×D414yescomplemented
310C2×C8×C43—24no—
311C2×C8×C43—22no—
312C4⋊C4×C43—21no—
313C4⋊C4×C43—21no—
314C4⋊C4×C43C22×C411yescharacteristic
315C4⋊C4×C43C22×C411yescharacteristic
316C22⋊C4×C43—24no—
317C22⋊C4×C43—21no—
318C22⋊C4×C43—21no—
319C22⋊C4×C43—21no—
320C22⋊C4×C43—21no—
321C22⋊C4×C43—21no—
322C42×C43—21no—
323C42×C43—22no—
324C42×C43—22no—
325C22⋊Dic43—24no—
326C22⋊Dic43—21no—
327C22⋊Dic43—21no—
328C22⋊Dic43—21no—
329C22⋊Dic43—21no—
330C22⋊Dic43—21no—
331(C2×D43)⋊C4—28no—
332(C2×D43)⋊C4—21no—
333(C2×D43)⋊C4—21no—
334(C2×D43)⋊C4—21no—
335(C2×D43)⋊C4—21no—
336(C2×D43)⋊C4—21no—
337(C2×D43)⋊C4—21no—
338(C2×D43)⋊C4—21no—
339(C2×D43)⋊C4—21no—
340(C2×D43)⋊C4—21no—
341(C2×D43)⋊C4—21no—
342C4⋊Dic43—21no—
343C4⋊Dic43—21no—
344C4⋊Dic43C22×C411yescharacteristic
345C4⋊Dic43C22×C411yescharacteristic
346Dic43⋊C4—21no—
347Dic43⋊C4—21no—
348Dic43⋊C4—21no—
349Dic43⋊C4—21no—
350Dic43⋊C4—21no—
351Dic43⋊C4—21no—
352C4×Dic43—21no—
353C4×Dic43—21no—
354C4×Dic43—21no—
355C4×Dic43—22no—
356C4×Dic43—22no—
357C4×Dic43—44no—
358#10621877—24no—
359#10621877—22no—
360#10621877C2×D414yescomplemented
361C2×C43⋊C8—24no—
362C2×C43⋊C8—22no—
363#10621872—28no—
364#10621872—28no—
365C8×D43—28no—
366C8×D43—28no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—21no—
370C23×C43—41no—
371C23×C43C2×C22⋊C411yescharacteristic
372C23×C43C2×C22⋊C411yescharacteristic
373C23×C43C22×D411yescharacteristic
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—21no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—416no—
392C22×D43—42no—
393C22×D43—42no—
394C22×D43—42no—
395C22×D43#10414yescomplemented
396C22×D43C2×C22⋊C411yescharacteristic
397C22×D43C2×C22⋊C411yescharacteristic
398C22×D43C2×C22⋊C411yescharacteristic
399C22×D43C2×C22⋊C411yescharacteristic
400C22×D43#12114yes—
401Q8×C43—22no—
402D4×C43—22no—
403D4×C43—42no—
404D4×C43—42no—
405D4×C43—42no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—21no—
410C2×C4×C43—21no—
411C2×C4×C43—21no—
412C2×C4×C43—21no—
413C2×C4×C43—24no—
414C2×C4×C43—21no—
415C2×C4×C43—21no—
416C2×C4×C43—21no—
417C2×C4×C43—42no—
418C2×C4×C43—42no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43C2×C22⋊C411yescharacteristic
422C2×C4×C43C2×C22⋊C411yescharacteristic
423C2×C4×C43C23×C411yescharacteristic
424C2×C4×C43C22×D412yes—
425C2×C4×C43C22×D411yescharacteristic
426C2×C4×C43C2×#4112yes—
427C22⋊D43—42no—
428C22⋊D43—42no—
429C22⋊D43—42no—
430C22⋊D43—42no—
431C22⋊D43—42no—
432C22⋊D43—42no—
433C22⋊D43—42no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—24no—
440C2×Dic43—21no—
441C2×Dic43—21no—
442C2×Dic43—21no—
443C2×Dic43—42no—
444C2×Dic43—42no—
445C2×Dic43—42no—
446C2×Dic43C2×C22⋊C411yescharacteristic
447C2×Dic43C2×C22⋊C411yescharacteristic
448C2×Dic43C2×C22⋊C411yescharacteristic
449C2×Dic43C2×C22⋊C411yescharacteristic
450C2×Dic43#12114yes—
451D172—22no—
452D172—42no—
453D172—42no—
454D172—42no—
455C4×D43—22no—
456C4×D43—22no—
457C4×D43—22no—
458C4×D43—22no—
459C4×D43—22no—
460C4×D43—22no—
461C4×D43—21no—
462C4×D43—21no—
463C4×D43—21no—
464C4×D43—21no—
465C4×D43—22no—
466C4×D43—22no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—416no—
470C4×D43—42no—
471C4×D43—42no—
472C4×D43—42no—
473C4×D43—41no—
474C4×D43—41no—
475C4×D43—42no—
476C4×D43C4×D414yes—
477C4×D43C4×D414yes—
478C4×D43#12012yes—
479C4×D43#12012yes—
480C4×D43#12312yes—
481C4×D43#12312yes—
482Dic86—22no—
483Dic86—42no—
484C8×C43—24no—
485C43⋊C8—24no—
486C2×#1871—431nomaximal, Sylow
487C22×C43—21no—
488C22×C43—21no—
489C22×C43—21no—
490C22×C43—21no—
491C22×C43—21no—
492C22×C43—21no—
493C22×C43—21no—
494C22×C43—44no—
495C22×C43—41no—
496C22×C43—41no—
497C22×C43—41no—
498C22×C43C2×#10412yescomplemented
499C22×C43C22×C22⋊C411yescharacteristic
500C22×C43C2×#12112yes—
501C2×D43—21no—
502C2×D43—21no—
503C2×D43—21no—
504C2×D43—21no—
505C2×D43—28no—
506C2×D43—28no—
507C2×D43—21no—
508C2×D43—21no—
509C2×D43—21no—
510C2×D43—44no—
511C2×D43—44no—
512C2×D43—44no—
513C2×D43—44no—
514C2×D43—41no—
515C2×D43—41no—
516C2×D43—41no—
517C2×D43—84no—
518C2×D43#38612yes—
519C2×D43#38612yes—
520C2×D43C2×#10412yes—
521C2×D43C2×#10412yescomplemented
522C2×D43#42112yes—
523C4×C43—21no—
524C4×C43—21no—
525C4×C43—44no—
526C4×C43—41no—
527C4×C43—41no—
528C4×C43—41no—
529C4×C43C2×C4×D412yes—
530C4×C43C2×#12011yescharacteristic
531C4×C43C2×#12311yescharacteristic
532Dic43—21no—
533Dic43—21no—
534Dic43—44no—
535Dic43—41no—
536Dic43—41no—
537Dic43—41no—
538Dic43#38612yes—
539Dic43#38612yes—
540C23×M16—431no—
541C2×#525—431no—
542C22×#104—432no—
543C2×C4×C22⋊C4—431no—
544#1871—432no—
545#1871—431no—
546#1871—432no—
547#1871—431no—
548#1871—431no—
549#1871D4311yescharacteristic, direct product factor
550C2×#339—432no—
551C2×C43—22no—
552C2×C43—22no—
553C2×C43—41no—
554C2×C43—81no—
555C2×C43C2×#38611yescharacteristic
556C2×C43C22×#10411yescharacteristic
557C2×C43C2×#42111yescharacteristic
558D43—22no—
559D43—22no—
560D43—41no—
561D43—81no—
562D43#187114yesdirect product factor
563C22×#41—431no—
564C24×C4—431no—
565C22×M16—432no—
566C22×M16—431no—
567C22×M16—432no—
568C22×M16—861no—
569C22×M16—868no—
570C22×M16—861no—
571C22×M16—861no—
572C22×M16C2×D4311yescharacteristic, complemented
573C23×C8—861no—
574#525—431no—
575#525—431no—
576#525—431no—
577#525—431no—
578#525—431no—
579#525—431no—
580#525—431no—
581#525—861no—
582#525—861no—
583#525—861no—
584#525—861no—
585#525C2×D4311yescharacteristic
586C2×#123—861no—
587C2×C22⋊Q8—431no—
588C2×C22⋊Q8—431no—
589C2×#121—431no—
590C2×#121—431no—
591C2×#120—861no—
592C2×C4×D4—861no—
593C2×C4×D4—861no—
594C2×#117—431no—
595C22×C22⋊C4—861no—
596C22×C42—432no—
597C2×#104—432no—
598C2×#104—432no—
599C2×#104—432no—
600C2×#104—868no—
601C2×#104C2×D4312yescomplemented
602C4×C22⋊C4—431no—
603C4×C22⋊C4—432no—
604C4×C22⋊C4—861no—
605C4×C22⋊C4—861no—
606C4×C22⋊C4C2×D4311yescharacteristic, complemented
607C2×#95—861no—
608#339—432no—
609#339—432no—
610#339—432no—
611#339C2×D4312yescomplemented
612C43C2×#187111yescharacteristic, complemented, Sylow
613C25—431no—
614C2×#41—431no—
615C2×#41—431no—
616C2×#41—431no—
617C2×#41—861no—
618C2×#41—861no—
619C2×#41—864no—
620C2×#41—864no—
621C2×#41C22×D4311yescharacteristic
622C22×Q8—431no—
623C22×D4—431no—
624C22×D4—861no—
625C22×D4—861no—
626C22×D4—861no—
627C23×C4—431no—
628C23×C4—431no—
629C23×C4—431no—
630C23×C4—431no—
631C23×C4—431no—
632C23×C4—431no—
633C23×C4—431no—
634C23×C4—431no—
635C23×C4—431no—
636C23×C4—431no—
637C23×C4—431no—
638C23×C4—431no—
639C23×C4—431no—
640C23×C4—864no—
641C23×C4—864no—
642C23×C4—861no—
643C23×C4—862no—
644C23×C4C22×D4311yescharacteristic
645C2×M16—21no—
646C2×M16—24no—
647C2×M16—432no—
648C2×M16—438no—
649C2×M16—862no—
650C2×M16—862no—
651C2×M16—868no—
652C2×M16—864no—
653C2×M16—864no—
654C2×M16—868no—
655C2×M16—868no—
656C2×M16—864no—
657C2×M16—861no—
658C2×M16—864no—
659C2×M16C22×D4312yes—
660C22×C8—21no—
661C22×C8—862no—
662C22×C8—862no—
663C22×C8—868no—
664C22×C8—861no—
665#123—21no—
666#123—861no—
667#123—861no—
668#123—861no—
669#123—861no—
670#123—861no—
671#123—861no—
672#123—861no—
673C22⋊Q8—431no—
674C22⋊Q8—431no—
675C22⋊Q8—431no—
676C22⋊Q8—431no—
677C22⋊Q8—431no—
678C22⋊Q8—431no—
679C22⋊Q8—861no—
680C22⋊Q8—861no—
681C22⋊Q8—861no—
682C22⋊Q8—861no—
683C22⋊Q8C4×D4311yescharacteristic, complemented
684C22⋊Q8C4×D4311yescharacteristic, complemented
685#121—431no—
686#121—431no—
687#121—431no—
688#121—431no—
689#121—431no—
690#121—431no—
691#121—861no—
692#121—861no—
693#121—861no—
694#121—861no—
695#121C4×D4311yescharacteristic, complemented
696#121C4×D4311yescharacteristic, complemented
697#120—21no—
698#120—861no—
699#120—861no—
700#120—861no—
701#120—861no—
702#120—861no—
703#120—861no—
704#120—861no—
705C4×D4—21no—
706C4×D4—21no—
707C4×D4—861no—
708C4×D4—861no—
709C4×D4—861no—
710C4×D4—861no—
711C4×D4—861no—
712C4×D4—861no—
713C4×D4—861no—
714C4×D4—861no—
715C4×D4—861no—
716C4×D4—861no—
717C4×D4—861no—
718C4×D4—861no—
719C4×D4—861no—
720C4×D4—861no—
721#117—431no—
722#117—431no—
723#117—431no—
724#117—861no—
725#117—861no—
726#117C22×D4311yescharacteristic
727C2×C4⋊C4—431no—
728C2×C4⋊C4—431no—
729C2×C4⋊C4—861no—
730C2×C4⋊C4—861no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—861no—
733C2×C22⋊C4—861no—
734C2×C22⋊C4—861no—
735C2×C22⋊C4—861no—
736C2×C22⋊C4—861no—
737C2×C22⋊C4—868no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—861no—
740C2×C42—432no—
741C2×C42—861no—
742C2×C42—864no—
743C2×C42—864no—
744C2×C42—862no—
745C2×C42C22×D4312yes—
746#104—24no—
747#104—864no—
748#104—864no—
749#104—864no—
750#95—21no—
751#95—862no—
752#95—861no—
753C24—431no—
754C24—431no—
755C24—431no—
756C24—431no—
757C24—431no—
758C24—431no—
759C24—864no—
760C24—864no—
761C24—861no—
762C24—1722no—
763C24D4×D4311yescharacteristic
764#41—22no—
765#41—22no—
766#41—864no—
767#41—864no—
768#41—862no—
769#41—862no—
770#41—1722no—
771#41—1722no—
772#41—1724no—
773C2×Q8—431no—
774C2×Q8—861no—
775C2×Q8—864no—
776C2×Q8C2×C4×D4311yescharacteristic
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—431no—
781C2×D4—861no—
782C2×D4—861no—
783C2×D4—861no—
784C2×D4—864no—
785C2×D4—861no—
786C2×D4—861no—
787C2×D4—861no—
788C2×D4—861no—
789C2×D4—861no—
790C2×D4—861no—
791C2×D4—861no—
792C2×D4—1724no—
793C2×D4—1724no—
794C2×D4—1724no—
795C2×D4C2×C4×D4311yescharacteristic
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—431no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—434no—
804C22×C4—431no—
805C22×C4—431no—
806C22×C4—434no—
807C22×C4—431no—
808C22×C4—431no—
809C22×C4—431no—
810C22×C4—431no—
811C22×C4—431no—
812C22×C4—431no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—431no—
817C22×C4—431no—
818C22×C4—431no—
819C22×C4—431no—
820C22×C4—431no—
821C22×C4—431no—
822C22×C4—431no—
823C22×C4—431no—
824C22×C4—862no—
825C22×C4—862no—
826C22×C4—862no—
827C22×C4—862no—
828C22×C4—864no—
829C22×C4—864no—
830C22×C4—864no—
831C22×C4—864no—
832C22×C4—864no—
833C22×C4—862no—
834C22×C4—862no—
835C22×C4—862no—
836C22×C4—862no—
837C22×C4—861no—
838C22×C4—864no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—868no—
843C22×C4—864no—
844C22×C4—861no—
845C22×C4—862no—
846C22×C4—862no—
847C22×C4—862no—
848C22×C4—861no—
849C22×C4—1722no—
850C22×C4—1722no—
851C22×C4—1724no—
852C22×C4—1724no—
853C22×C4C2×C4×D4311yescharacteristic
854C22×C4C2×C4×D4311yescharacteristic
855C22×C4D4×D4311yescharacteristic
856C22×C4D4×D4311yescharacteristic
857C22×C4D4×D4311yescharacteristic
858C22×C4C23×D4311yescharacteristic
859M16—24no—
860M16—22no—
861M16—434no—
862M16—868no—
863M16—868no—
864M16—864no—
865M16—862no—
866M16D4×D4314yescomplemented
867C2×C8—24no—
868C2×C8—22no—
869C2×C8—868no—
870C2×C8—868no—
871C2×C8—864no—
872C2×C8—862no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—431no—
876C4⋊C4—431no—
877C4⋊C4—861no—
878C4⋊C4—861no—
879C4⋊C4—861no—
880C4⋊C4—861no—
881C4⋊C4—861no—
882C4⋊C4—861no—
883C4⋊C4—861no—
884C4⋊C4—861no—
885C4⋊C4C2×C4×D4311yescharacteristic
886C4⋊C4C2×C4×D4311yescharacteristic
887C22⋊C4—24no—
888C22⋊C4—21no—
889C22⋊C4—21no—
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—861no—
894C22⋊C4—861no—
895C22⋊C4—861no—
896C22⋊C4—861no—
897C22⋊C4—861no—
898C22⋊C4—861no—
899C22⋊C4—861no—
900C22⋊C4—861no—
901C22⋊C4—868no—
902C22⋊C4—861no—
903C22⋊C4—861no—
904C22⋊C4—864no—
905C22⋊C4—861no—
906C22⋊C4—861no—
907C22⋊C4—861no—
908C22⋊C4—861no—
909C22⋊C4—861no—
910C42—21no—
911C42—22no—
912C42—22no—
913C42—861no—
914C42—861no—
915C42—861no—
916C42—862no—
917C42—862no—
918C42—1724no—
919C23—22no—
920C23—22no—
921C23—21no—
922C23—41no—
923C23—431no—
924C23—431no—
925C23—431no—
926C23—434no—
927C23—434no—
928C23—431no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—861no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1722no—
947C23—1722no—
948C23—1722no—
949C23—17216no—
950C23C22⋊C4×D4311yescharacteristic
951C23C22⋊C4×D4311yescharacteristic
952C23C2×D4×D4311yescharacteristic
953Q8—22no—
954Q8—862no—
955Q8—1722no—
956D4—22no—
957D4—42no—
958D4—42no—
959D4—42no—
960D4—862no—
961D4—1722no—
962D4—1722no—
963D4—1722no—
964D4—1722no—
965D4—1722no—
966D4—1722no—
967D4—1722no—
968D4—1722no—
969D4—1722no—
970D4—1722no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—24no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—431no—
987C2×C4—431no—
988C2×C4—434no—
989C2×C4—434no—
990C2×C4—434no—
991C2×C4—432no—
992C2×C4—432no—
993C2×C4—432no—
994C2×C4—432no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—862no—
1012C2×C4—861no—
1013C2×C4—861no—
1014C2×C4—861no—
1015C2×C4—861no—
1016C2×C4—864no—
1017C2×C4—861no—
1018C2×C4—861no—
1019C2×C4—861no—
1020C2×C4—1722no—
1021C2×C4—1722no—
1022C2×C4—1722no—
1023C2×C4—1722no—
1024C2×C4—17216no—
1025C2×C4—1722no—
1026C2×C4—1722no—
1027C2×C4—1722no—
1028C2×C4—1721no—
1029C2×C4—1721no—
1030C2×C4C22⋊C4×D4311yescharacteristic
1031C2×C4C22⋊C4×D4311yescharacteristic
1032C2×C4C22×C4×D4311yescharacteristic
1033C2×C4C2×D4×D4312yes—
1034C2×C4C2×D4×D4311yescharacteristic
1035C2×C4#41×D4312yes—
1036C8—24no—
1037C8—864no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—44no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—432no—
1050C22—432no—
1051C22—432no—
1052C22—432no—
1053C22—432no—
1054C22—868no—
1055C22—868no—
1056C22—861no—
1057C22—861no—
1058C22—861no—
1059C22—861no—
1060C22—861no—
1061C22—861no—
1062C22—861no—
1063C22—3444no—
1064C22—1724no—
1065C22—1724no—
1066C22—1724no—
1067C22—1724no—
1068C22—1721no—
1069C22—1721no—
1070C22—1721no—
1071C22#104×D4312yescomplemented
1072C22C2×C22⋊C4×D4311yescharacteristic
1073C22#121×D4312yes—
1074C4—21no—
1075C4—21no—
1076C4—44no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—432no—
1081C4—432no—
1082C4—861no—
1083C4—861no—
1084C4—1724no—
1085C4—1721no—
1086C4—1721no—
1087C4—1721no—
1088C4C4×D4×D4312yes—
1089C4#120×D4311yescharacteristic
1090C4#123×D4311yescharacteristic
1091C2—22no—
1092C2—22no—
1093C2—41no—
1094C2—81no—
1095C2—434no—
1096C2—862no—
1097C2—862no—
1098C2—3441no—
1099C2—1721no—
1100C2#386×D4311yescharacteristic
1101C2C2×#104×D4311yescharacteristic
1102C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C22×C22⋊C4
prime radical#525×D43C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43C2×#1871
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
1. C22×M16×D43C2semidirect
3. C2×#104×D43C2semidirect
4. C4×C22⋊C4×D43C2semidirect
5. #19134898C2semidirect
6. #19134897C2semidirect
7. #19134896C2semidirect
8. #19134895C2semidirect
9. #19134894C2semidirect
10. #339×D43C2semidirect
11. C43×#1871C2semidirect
14. C22×#10621877C22semidirect
20. C2×M16×D43C22semidirect
22. #14583412C4semidirect
23. #14583412C4semidirect
26. #14583409C4semidirect
27. #14583409C4semidirect
34. C22⋊Q8×D43C4semidirect
35. C22⋊Q8×D43C4semidirect
36. #121×D43C4semidirect
37. #121×D43C4semidirect
44. C2×#13063253C22semidirect
45. C2×#13063252C22semidirect
46. C2×#13063251C22semidirect
49. C4×(C2×D43)⋊C4C22semidirect
50. C4×C22⋊Dic43C22semidirect
53. #14582660C22semidirect
54. #14582659C22semidirect
55. #14582658C22semidirect
56. C22×M16×C43C22semidirect
58. C2×#104×C43C22semidirect
59. C4×C22⋊C4×C43C22semidirect
60. C43×#339C22semidirect
102. M16×D43D4semidirect
114. #13063305C2×C4semidirect
115. #13063305C2×C4semidirect
116. #13063304C2×C4semidirect
117. #13063304C2×C4semidirect
122. #13063301C2×C4semidirect
123. #13063301C2×C4semidirect
124. #13063300C2×C4semidirect
125. #13063300C2×C4semidirect
126. #13063299C2×C4semidirect
127. #13063299C2×C4semidirect
132. #13063296C2×C4semidirect
133. #13063296C2×C4semidirect
189. C22⋊Q8×C43C2×C4semidirect
190. C22⋊Q8×C43C2×C4semidirect
191. #121×C43C2×C4semidirect
192. #121×C43C2×C4semidirect
309. M16×C43C2×D4semidirect
360. #10621877C2×D4semidirect
395. C22×D43#104semidirect
498. C22×C43C2×#104semidirect
521. C2×D43C2×#104semidirect
549. #1871D43direct (N × H)
562. D43#1871direct (N × H)
572. C22×M16C2×D43semidirect
601. C2×#104C2×D43semidirect
606. C4×C22⋊C4C2×D43semidirect
611. #339C2×D43semidirect
612. C43C2×#1871semidirect
683. C22⋊Q8C4×D43semidirect
684. C22⋊Q8C4×D43semidirect
695. #121C4×D43semidirect
696. #121C4×D43semidirect
866. M16D4×D43semidirect
1071. C22#104×D43semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D432
#525×D432
C2×#104×D432
C4×C22⋊C4×D432
#191348982
#191348972
#191348962
#191348952
#191348942
#339×D432
C43×#18712
C2×#187143