Finite Group Databasebeta

← D43×#2994 #25961691

Subgroups — D43×#2994 #25961691

Order 11008.

1982 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#19143758C211yesmaximal, characteristic, complemented
3#19143757C211yesmaximal, characteristic, complemented
4#19143756C211yesmaximal, characteristic, complemented
5#19143755C211yesmaximal, characteristic, complemented
6#19143754C211yesmaximal, characteristic, complemented
7#19143753C212yesmaximal, complemented
8#19143752C212yesmaximal, complemented
9#19143751C211yesmaximal, characteristic, complemented
10#19143750C211yesmaximal, characteristic, complemented
11#19143749C212yesmaximal, complemented
12#19143748C212yesmaximal, complemented
13#446×D43C211yesmaximal, characteristic, complemented
14C8×Q8×D43C211yesmaximal, characteristic, complemented
15#436×D43C211yesmaximal, characteristic, complemented
16#435×D43C212yesmaximal, complemented
17C8×D4×D43C211yesmaximal, characteristic, complemented
18C8×D4×D43C212yesmaximal, complemented
19#433×D43C212yesmaximal, complemented
20#431×D43C211yesmaximal, characteristic, complemented
21#424×D43C212yesmaximal, complemented
22C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
23C43×#2994C211yesmaximal, characteristic, complemented
24C2×M16×D43C2212yes—
25C22×C8×D43C2212yes—
26C22×C8×D43C2212yes—
27#14583436C2211yescharacteristic
28#14583435C411yescharacteristic
29#14583434C411yescharacteristic
30#14583433C2211yescharacteristic
31#14583432C412yes—
32#14583431C2211yescharacteristic
33#14583430C411yescharacteristic
34#14583429C2212yes—
35#14583428C411yescharacteristic
36#14583427C2212yes—
37#14583426C412yes—
38#126×D43C412yes—
39#125×D43C411yescharacteristic
40#124×D43C411yescharacteristic
41#123×D43C412yes—
42C22⋊Q8×D43C411yescharacteristic
43#121×D43C411yescharacteristic
44C4×Q8×D43C2211yescharacteristic
45C4×D4×D43C2212yes—
46C4×D4×D43C2211yescharacteristic
47#117×D43C2212yes—
48C2×C42×D43C2211yescharacteristic
49#14583030C2211yescharacteristic, complemented
50#14583029C2211yescharacteristic, complemented
51#14583028C2212yescomplemented
52#14583027C2212yescomplemented
53#14583026C2211yescharacteristic, complemented
54Q8×C43⋊C8C2211yescharacteristic, complemented
55C8×Dic86C2212yescomplemented
56C8×Dic86C2211yescharacteristic, complemented
57#14583023C2212yescomplemented
58#14583023C2211yescharacteristic, complemented
59#14582978C2211yescharacteristic, complemented
60#14582977C2211yescharacteristic, complemented
61#14582976C2211yescharacteristic, complemented
62#14582975C2212yescomplemented
63#14582974C2212yescomplemented
64#14582973C2212yescomplemented
65#14582972C2212yescomplemented
66#14582971C2212yescomplemented
67#14582970C2212yescomplemented
68#14582969C2212yescomplemented
69#14582968C2212yescomplemented
70#14582967C2212yescomplemented
71C8×D172C2212yescomplemented
72C8×D172C2211yescharacteristic, complemented
73D4×C43⋊C8C2212yescomplemented
74D4×C43⋊C8C2211yescharacteristic, complemented
75#14582964C2211yescharacteristic, complemented
76#14582964C2212yescomplemented
77C8×C22⋊D43C2212yescomplemented
78C8×C22⋊D43C2212yescomplemented
79C8×C22⋊D43C2212yescomplemented
80(C22⋊D43)⋊C8C2212yescomplemented
81(C22⋊D43)⋊C8C2212yescomplemented
82(C22⋊D43)⋊C8C2212yescomplemented
83#14582961C2212yescomplemented
84#14582960C2212yescomplemented
85#14582959C2212yescomplemented
86#14582959C2212yescomplemented
87#14582958C2212yescomplemented
88#14582957C2212yescomplemented
89#14582957C2212yescomplemented
90#14582952C2211yescharacteristic, complemented
91#14582951C2211yescharacteristic, complemented
92#14582951C2211yescharacteristic, complemented
93#14582950C2211yescharacteristic, complemented
94#14582950C2211yescharacteristic, complemented
95#14582949C2211yescharacteristic, complemented
96#14582949C2211yescharacteristic, complemented
97#14582927C2212yescomplemented
98#14582926C2212yescomplemented
99#14582925C2212yescomplemented
100#14582924C2212yescomplemented
101#14582924C2212yescomplemented
102#14582924C2212yescomplemented
103#14582924C2212yescomplemented
104C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
105C2×Dic43⋊C8C2212yescomplemented
106C4⋊C8×D43C2211yescharacteristic
107C4⋊C8×D43C2211yescharacteristic
108C4⋊C8×D43C2212yes—
109C4⋊C8×D43C2211yescharacteristic
110C4⋊C8×D43C2212yes—
111C4⋊C8×D43C2212yes—
112C4⋊C8×D43C2211yescharacteristic
113C4⋊C8×D43C2212yescomplemented
114C4⋊C8×D43C2211yescharacteristic, complemented
115C4⋊C8×D43C2211yescharacteristic, complemented
116C22⋊C8×D43C2211yescharacteristic
117C22⋊C8×D43C2211yescharacteristic
118C22⋊C8×D43C2212yes—
119C22⋊C8×D43C2212yes—
120#97×D43C2212yes—
121C4×C8×D43C2211yescharacteristic
122C4×C8×D43C2211yescharacteristic
123C4×C8×D43C2212yes—
124C43×#529C2211yescharacteristic
125C43×#446C2211yescharacteristic, complemented
126C8×Q8×C43C2211yescharacteristic, complemented
127C43×#436C2211yescharacteristic, complemented
128C43×#435C2212yescomplemented
129C8×D4×C43C2211yescharacteristic, complemented
130C8×D4×C43C2212yescomplemented
131C43×#433C2212yescomplemented
132C43×#431C2211yescharacteristic, complemented
133C43×#424C2212yescomplemented
134C2×C4⋊C8×C43C2211yescharacteristic, complemented
135C2×Q8×D43C2×C411yescharacteristic
136C2×D4×D43C2×C412yes—
137C2×D4×D43C2×C411yescharacteristic
138C22×C4×D43C2×C411yescharacteristic
139C22×C4×D43C2×C411yescharacteristic
140C22×C4×D43C2311yescharacteristic
141C22×C4×D43C2312yes—
142C2×#10621877C2312yes—
143C2×#10621872C2312yes—
144C2×#10621872C2312yes—
145M16×D43—44no—
146C22×C43⋊C8C2312yes—
147C22×C43⋊C8C2312yes—
148C2×C8×D43—44no—
149C2×C8×D43—44no—
150C2×C8×D43C2311yescharacteristic
151C2×C8×D43C2311yescharacteristic
152C2×C8×D43C2311yescharacteristic
153C2×C8×D43C2312yes—
154C2×C8×D43C2311yescharacteristic
155C2×C8×D43C2312yes—
156C2×C8×D43C2312yes—
157C2×C8×D43C2312yes—
158C2×C8×D43C2312yes—
159C2×C8×D43C2312yes—
160#13063320C2×C412yes—
161#13063320C2×C412yes—
162#13063320C2×C412yes—
163#13063319C2×C412yes—
164#13063318C2×C412yes—
165#13063318C2×C412yes—
166#13063318C2×C412yes—
167#13063317C2×C411yescharacteristic
168#13063316C2×C411yescharacteristic
169#13063316C2×C411yescharacteristic
170#13063315C2×C412yes—
171#13063315C2×C412yes—
172#13063314C2×C411yescharacteristic
173#13063313C2×C411yescharacteristic
174#13063312C2×C411yescharacteristic
175#13063311C2×C412yes—
176#13063311C2×C412yes—
177#13063310C2×C412yes—
178#13063310C2×C412yes—
179#13063309C2×C412yes—
180#13063308C2×C412yes—
181#13063307C2×C412yes—
182#13063307C2×C412yes—
183#13063306C2×C412yes—
184#13063305C2×C411yescharacteristic
185#13063304C2×C411yescharacteristic
186#13063303C2×C412yes—
187#13063302C2×C412yes—
188#13063301C2×C411yescharacteristic
189#13063300C2×C411yescharacteristic
190#13063299C2×C411yescharacteristic
191#13063298C2×C412yes—
192#13063297C2×C412yes—
193#13063296C2×C411yescharacteristic
194Q8×Dic43C2×C411yescharacteristic
195C4×Dic86C2312yes—
196C4×Dic86C2311yescharacteristic
197#13063290C2×C412yes—
198#13063290C2×C411yescharacteristic
199C4×D172C2312yes—
200C4×D172C2311yescharacteristic
201D4×Dic43C2×C412yes—
202D4×Dic43C2×C411yescharacteristic
203#13063287C2×C412yes—
204#13063287C2×C411yescharacteristic
205C4×C22⋊D43C2312yes—
206C4×C22⋊D43C2312yes—
207C4×C22⋊D43C2312yes—
208(C22⋊D43)⋊C4C2×C412yes—
209(C22⋊D43)⋊C4C2×C412yes—
210(C22⋊D43)⋊C4C2×C412yes—
211#13063284C2312yes—
212#13063283C2×C412yes—
213#13063283C2×C412yes—
214#13063282C2312yes—
215#13063282C2312yes—
216#13063281C2×C412yes—
217#13063281C2×C412yes—
218C4⋊C4×D43C2×C412yes—
219C4⋊C4×D43C2×C412yes—
220C4⋊C4×D43C2×C411yescharacteristic
221C4⋊C4×D43C2×C412yes—
222C4⋊C4×D43C2×C411yescharacteristic
223C4⋊C4×D43C2×C412yes—
224C22⋊C4×D43C2×C412yes—
225C22⋊C4×D43C2×C412yes—
226C22⋊C4×D43C2×C412yes—
227C22⋊C4×D43C2×C412yes—
228C22⋊C4×D43C2×C412yes—
229C2×C4×Dic43C2×C411yescharacteristic
230C2×C4×Dic43C2×C411yescharacteristic
231C2×C4×Dic43C2311yescharacteristic
232C42×D43C2×C411yescharacteristic
233C42×D43C2×C411yescharacteristic
234C42×D43C2×C411yescharacteristic
235C42×D43C2×C411yescharacteristic
236C42×D43C2311yescharacteristic
237C42×D43C2311yescharacteristic
238C42×D43C2311yescharacteristic
239C42×D43C2311yescharacteristic
240C42×D43C2312yes—
241C4⋊(C43⋊C8)C2312yes—
242C4⋊(C43⋊C8)C2311yescharacteristic
243C4⋊(C43⋊C8)C2311yescharacteristic
244C4⋊(C43⋊C8)C2311yescharacteristic
245C4⋊(C43⋊C8)C2312yes—
246C4⋊(C43⋊C8)C2312yes—
247C4⋊(C43⋊C8)C2311yescharacteristic
248Dic43⋊C8C2312yes—
249Dic43⋊C8C2312yes—
250Dic43⋊C8C2312yes—
251Dic43⋊C8C2312yes—
252Dic43⋊C8C2311yescharacteristic
253Dic43⋊C8C2311yescharacteristic
254Dic43⋊C8C2312yes—
255Dic43⋊C8C2312yes—
256Dic43⋊C8C2312yes—
257Dic43⋊C8C2312yes—
258Dic43⋊C8C2311yescharacteristic
259Dic43⋊C8C2311yescharacteristic
260C22⋊(C43⋊C8)C2311yescharacteristic
261C22⋊(C43⋊C8)C2311yescharacteristic
262C22⋊(C43⋊C8)C2312yes—
263C22⋊(C43⋊C8)C2312yes—
264(C2×D43)⋊C8C2311yescharacteristic
265(C2×D43)⋊C8C2311yescharacteristic
266(C2×D43)⋊C8C2311yescharacteristic
267(C2×D43)⋊C8C2311yescharacteristic
268(C2×D43)⋊C8C2312yes—
269(C2×D43)⋊C8C2312yes—
270(C2×D43)⋊C8C2312yes—
271(C2×D43)⋊C8C2312yes—
272#13063236C2312yes—
273#13063235C2312yes—
274#13063235C2312yes—
275C4×C43⋊C8C2311yescharacteristic
276C4×C43⋊C8C2311yescharacteristic
277C4×C43⋊C8C2312yes—
278C8×Dic43C2311yescharacteristic
279C8×Dic43C2311yescharacteristic
280C8×Dic43C2311yescharacteristic
281C8×Dic43C2311yescharacteristic
282C8×Dic43C2312yes—
283C8×Dic43C2312yes—
284C2×M16×C43C2312yes—
285C22×C8×C43C2312yes—
286C22×C8×C43C2312yes—
287#126×C43C2×C412yes—
288#125×C43C2×C411yescharacteristic
289#124×C43C2×C411yescharacteristic
290#123×C43C2×C412yes—
291C22⋊Q8×C43C2×C411yescharacteristic
292#121×C43C2×C411yescharacteristic
293C4×Q8×C43C2311yescharacteristic
294C4×D4×C43C2312yes—
295C4×D4×C43C2311yescharacteristic
296#117×C43C2312yes—
297C2×C42×C43C2311yescharacteristic
298C4⋊C8×C43C2312yes—
299C4⋊C8×C43C2311yescharacteristic
300C4⋊C8×C43C2311yescharacteristic
301C4⋊C8×C43C2311yescharacteristic
302C4⋊C8×C43C2312yes—
303C4⋊C8×C43C2312yes—
304C4⋊C8×C43C2311yescharacteristic
305C22⋊C8×C43C2311yescharacteristic
306C22⋊C8×C43C2311yescharacteristic
307C22⋊C8×C43C2312yes—
308C22⋊C8×C43C2312yes—
309#97×C43C2312yes—
310C4×C8×C43C2311yescharacteristic
311C4×C8×C43C2311yescharacteristic
312C4×C8×C43C2312yes—
313C23×D43C22×C412yes—
314C23×D43C22×C411yescharacteristic
315C2×Q8×C43C22×C411yescharacteristic
316C2×D4×C43C22×C412yes—
317C2×D4×C43C22×C411yescharacteristic
318C22×C4×C43C22×C411yescharacteristic
319C22×C4×C43C22×C411yescharacteristic
320C22×C4×C43C2411yescharacteristic
321C22×C4×C43C2412yes—
322C2×C22⋊D43C22×C412yes—
323C2×C22⋊D43C22×C412yes—
324C2×C22⋊D43C22×C412yes—
325C22×Dic43C22×C411yescharacteristic
326C22×Dic43C22×C411yescharacteristic
327C22×Dic43C22×C411yescharacteristic
328C22×Dic43C22×C412yes—
329Q8×D43—24no—
330D4×D43—24no—
331D4×D43—28no—
332C2×D172C22×C412yes—
333C2×D172C22×C411yescharacteristic
334C2×C4×D43—24no—
335C2×C4×D43—22no—
336C2×C4×D43—24no—
337C2×C4×D43—22no—
338C2×C4×D43—24no—
339C2×C4×D43—24no—
340C2×C4×D43C22×C411yescharacteristic
341C2×C4×D43C22×C411yescharacteristic
342C2×C4×D43C22×C411yescharacteristic
343C2×C4×D43C22×C411yescharacteristic
344C2×C4×D43C22×C411yescharacteristic
345C2×C4×D43C22×C411yescharacteristic
346C2×C4×D43C22×C411yescharacteristic
347C2×C4×D43C22×C411yescharacteristic
348C2×C4×D43C22×C411yescharacteristic
349C2×C4×D43C22×C412yes—
350C2×C4×D43C22×C412yes—
351C2×C4×D43C22×C412yes—
352C2×C4×D43C22×C412yes—
353C2×C4×D43C22×C411yescharacteristic
354C2×C4×D43C2411yescharacteristic
355C2×C4×D43C2412yes—
356C2×C4×D43C2411yescharacteristic
357C2×Dic86C22×C412yes—
358C2×Dic86C22×C411yescharacteristic
359M16×C43—42no—
360C2×C8×C43—42no—
361C2×C8×C43—42no—
362C2×C8×C43C2411yescharacteristic
363C2×C8×C43C2411yescharacteristic
364C2×C8×C43C2411yescharacteristic
365C2×C8×C43C2412yes—
366C2×C8×C43C2411yescharacteristic
367C2×C8×C43C2412yes—
368C4⋊C4×C43C22×C412yes—
369C4⋊C4×C43C22×C412yes—
370C4⋊C4×C43C22×C411yescharacteristic
371C4⋊C4×C43C22×C412yes—
372C4⋊C4×C43C22×C411yescharacteristic
373C4⋊C4×C43C22×C412yes—
374C22⋊C4×C43C22×C412yes—
375C22⋊C4×C43C22×C412yes—
376C22⋊C4×C43C22×C412yes—
377C22⋊C4×C43C22×C412yes—
378C22⋊C4×C43C22×C412yes—
379C42×C43C22×C411yescharacteristic
380C42×C43C22×C411yescharacteristic
381C42×C43C2411yescharacteristic
382C42×C43C2412yes—
383C42×C43C2411yescharacteristic
384C22⋊Dic43C22×C412yes—
385C22⋊Dic43C22×C412yes—
386C22⋊Dic43C22×C412yes—
387C22⋊Dic43C22×C412yes—
388C22⋊Dic43C22×C412yes—
389(C2×D43)⋊C4C22×C412yes—
390(C2×D43)⋊C4C22×C412yes—
391(C2×D43)⋊C4C22×C412yes—
392(C2×D43)⋊C4C22×C412yes—
393(C2×D43)⋊C4C22×C412yes—
394(C2×D43)⋊C4C22×C412yes—
395(C2×D43)⋊C4C22×C412yes—
396(C2×D43)⋊C4C22×C412yes—
397(C2×D43)⋊C4C22×C412yes—
398(C2×D43)⋊C4C22×C412yes—
399C4⋊Dic43C22×C412yes—
400C4⋊Dic43C22×C412yes—
401C4⋊Dic43C22×C411yescharacteristic
402C4⋊Dic43C22×C412yes—
403C4⋊Dic43C22×C411yescharacteristic
404C4⋊Dic43C22×C412yes—
405Dic43⋊C4C22×C412yes—
406Dic43⋊C4C22×C412yes—
407Dic43⋊C4C22×C412yes—
408Dic43⋊C4C22×C412yes—
409Dic43⋊C4C22×C412yes—
410Dic43⋊C4C22×C412yes—
411Dic43⋊C4C22×C412yes—
412Dic43⋊C4C22×C412yes—
413Dic43⋊C4C22×C412yes—
414Dic43⋊C4C22×C412yes—
415C4×Dic43C22×C411yescharacteristic
416C4×Dic43C22×C411yescharacteristic
417C4×Dic43C22×C411yescharacteristic
418C4×Dic43C22×C411yescharacteristic
419C4×Dic43C22×C411yescharacteristic
420C4×Dic43C22×C411yescharacteristic
421C4×Dic43C22×C411yescharacteristic
422C4×Dic43C22×C411yescharacteristic
423C4×Dic43C22×C411yescharacteristic
424C4×Dic43C22×C411yescharacteristic
425C4×Dic43C22×C412yes—
426C4×Dic43C22×C412yes—
427C4×Dic43C2411yescharacteristic
428C4×Dic43C2412yes—
429C4×Dic43C2411yescharacteristic
430#10621877—42no—
431C2×C43⋊C8—42no—
432C2×C43⋊C8—42no—
433C2×C43⋊C8C2411yescharacteristic
434C2×C43⋊C8C2411yescharacteristic
435C2×C43⋊C8C2411yescharacteristic
436C2×C43⋊C8C2412yes—
437C2×C43⋊C8C2411yescharacteristic
438C2×C43⋊C8C2412yes—
439#10621872—42no—
440#10621872—42no—
441C8×D43—22no—
442C8×D43—24no—
443C8×D43—24no—
444C8×D43—22no—
445C8×D43—22no—
446C8×D43—22no—
447C8×D43—42no—
448C8×D43—42no—
449C8×D43—42no—
450C8×D43—42no—
451C23×C43C23×C412yes—
452C23×C43C23×C411yescharacteristic
453C22×D43—22no—
454C22×D43—22no—
455C22×D43—24no—
456C22×D43—24no—
457C22×D43—24no—
458C22×D43#13114yes—
459C22×D43C23×C412yes—
460C22×D43C23×C411yescharacteristic
461C22×D43C23×C411yescharacteristic
462Q8×C43—22no—
463D4×C43—24no—
464D4×C43—22no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—21no—
468C2×C4×C43—22no—
469C2×C4×C43—21no—
470C2×C4×C43—22no—
471C2×C4×C43C23×C411yescharacteristic
472C2×C4×C43C23×C411yescharacteristic
473C2×C4×C43C23×C411yescharacteristic
474C2×C4×C43C23×C411yescharacteristic
475C2×C4×C43C23×C412yes—
476C2×C4×C43C23×C412yes—
477C2×C4×C43C23×C412yes—
478C2×C4×C43C23×C411yescharacteristic
479C2×C4×C43C2511yescharacteristic
480C22⋊D43—24no—
481C22⋊D43—24no—
482C22⋊D43—24no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—24no—
486C2×Dic43—22no—
487C2×Dic43C23×C411yescharacteristic
488C2×Dic43C23×C411yescharacteristic
489C2×Dic43C23×C411yescharacteristic
490C2×Dic43C23×C411yescharacteristic
491C2×Dic43C23×C412yes—
492C2×Dic43C23×C412yes—
493C2×Dic43C23×C412yes—
494C2×Dic43C23×C411yescharacteristic
495C2×Dic43C23×C411yescharacteristic
496D172—24no—
497D172—22no—
498C4×D43—22no—
499C4×D43—24no—
500C4×D43—22no—
501C4×D43—22no—
502C4×D43—22no—
503C4×D43—22no—
504C4×D43—22no—
505C4×D43—24no—
506C4×D43—24no—
507C4×D43—22no—
508C4×D43—21no—
509C4×D43—22no—
510C4×D43—21no—
511C4×D43—22no—
512C4×D43—22no—
513C4×D43—24no—
514C4×D43—22no—
515C4×D43#13114yes—
516C4×D43H(5,𝔽2)12yes—
517C4×D432−1+412yes—
518Dic86—22no—
519Dic86—24no—
520C8×C43—21no—
521C8×C43—22no—
522C8×C43—22no—
523C8×C43—21no—
524C8×C43—21no—
525C8×C43—21no—
526C43⋊C8—21no—
527C43⋊C8—22no—
528C43⋊C8—22no—
529C43⋊C8—21no—
530C43⋊C8—21no—
531C43⋊C8—21no—
532C2×#2994—431nomaximal, Sylow
533C22×C43—21no—
534C22×C43—21no—
535C22×C43—22no—
536C22×C43—22no—
537C22×C43—22no—
538C22×C43C2×#13112yes—
539C22×C43C24×C411yescharacteristic
540C2×D43—21no—
541C2×D43—21no—
542C2×D43—28no—
543C2×D43—22no—
544C2×D43—22no—
545C2×D43—22no—
546C2×D43—48no—
547C2×D43#52012yes—
548C2×D43C2×#13112yes—
549C2×D43C2×#13112yes—
550C2×D43C2×#13112yes—
551C4×C43—21no—
552C4×C43—22no—
553C4×C43—22no—
554C4×C43—21no—
555C4×C43—21no—
556C4×C43—21no—
557C4×C43—22no—
558C4×C43C2×#13112yes—
559C4×C43C2×H(5,𝔽2)11yescharacteristic
560C4×C43C2×2−1+411yescharacteristic
561Dic43—21no—
562Dic43—22no—
563Dic43—22no—
564Dic43—21no—
565Dic43—21no—
566Dic43—21no—
567Dic43—22no—
568Dic43#52012yes—
569Dic43C2×#13112yes—
570C2×#529—431no—
571#2994—431no—
572#2994—431no—
573#2994—431no—
574#2994—432no—
575#2994—431no—
576#2994—432no—
577#2994—432no—
578#2994—431no—
579#2994—432no—
580#2994—431no—
581#2994—431no—
582#2994D4311yescharacteristic, direct product factor
583C2×#446—431no—
584C2×C8×Q8—431no—
585C2×#436—431no—
586C2×#435—432no—
587C2×C8×D4—432no—
588C2×C8×D4—431no—
589C2×#433—432no—
590C2×#431—431no—
591C2×#424—432no—
592C22×C4⋊C8—431no—
593C2×C43—22no—
594C2×C43—42no—
595C2×C43C2×#52011yescharacteristic
596C2×C43C22×#13111yescharacteristic
597C2×C43C22×#13111yescharacteristic
598D43—22no—
599D43—42no—
600D43#299414yesdirect product factor
601C22×M16—432no—
602C23×C8—432no—
603C23×C8—432no—
604#529—432no—
605#529—431no—
606#529—431no—
607#529—432no—
608#529—431no—
609#529—431no—
610#529—431no—
611#529—432no—
612#529—431no—
613#529—432no—
614#529—431no—
615#529C2×D4311yescharacteristic
616C2×#126—432no—
617C2×#125—431no—
618C2×#124—431no—
619C2×#123—432no—
620C2×C22⋊Q8—431no—
621C2×#121—431no—
622C2×C4×Q8—431no—
623C2×C4×D4—432no—
624C2×C4×D4—431no—
625C2×#117—432no—
626C22×C42—431no—
627#446—431no—
628#446—431no—
629#446—432no—
630#446—432no—
631#446—431no—
632#446C2×D4311yescharacteristic, complemented
633C8×Q8—431no—
634C8×Q8—432no—
635C8×Q8—431no—
636C8×Q8—432no—
637C8×Q8—431no—
638C8×Q8C2×D4311yescharacteristic, complemented
639#436—432no—
640#436—431no—
641#436—431no—
642#436—432no—
643#436—431no—
644#436C2×D4311yescharacteristic, complemented
645#435—432no—
646#435—432no—
647#435—432no—
648#435—432no—
649#435—432no—
650#435—432no—
651#435—432no—
652#435C2×D4312yescomplemented
653C8×D4—432no—
654C8×D4—432no—
655C8×D4—432no—
656C8×D4—431no—
657C8×D4—432no—
658C8×D4—431no—
659C8×D4—432no—
660C8×D4—432no—
661C8×D4—432no—
662C8×D4—432no—
663C8×D4—431no—
664C8×D4—432no—
665C8×D4C2×D4311yescharacteristic, complemented
666C8×D4C2×D4312yescomplemented
667#433—432no—
668#433—432no—
669#433—432no—
670#433—432no—
671#433—432no—
672#433—432no—
673#433—432no—
674#433C2×D4312yescomplemented
675#431—431no—
676#431—431no—
677#431—431no—
678#431—431no—
679#431—431no—
680#431—431no—
681#431—431no—
682#431C2×D4311yescharacteristic, complemented
683#424—432no—
684#424—432no—
685#424—432no—
686#424—432no—
687#424—432no—
688#424—432no—
689#424—432no—
690#424C2×D4312yescomplemented
691C2×C4⋊C8—432no—
692C2×C4⋊C8—431no—
693C2×C4⋊C8—432no—
694C2×C4⋊C8—431no—
695C2×C4⋊C8—431no—
696C2×C4⋊C8—431no—
697C2×C4⋊C8—431no—
698C2×C4⋊C8—432no—
699C2×C4⋊C8—431no—
700C2×C4⋊C8—432no—
701C2×C4⋊C8—432no—
702C2×C4⋊C8—431no—
703C2×C4⋊C8C2×D4311yescharacteristic, complemented
704C2×C22⋊C8—431no—
705C2×C22⋊C8—431no—
706C2×C22⋊C8—432no—
707C2×C22⋊C8—432no—
708C2×#97—432no—
709C2×C4×C8—431no—
710C2×C4×C8—431no—
711C2×C4×C8—432no—
712C43C2×#299411yescharacteristic, complemented, Sylow
713C22×Q8—431no—
714C22×D4—432no—
715C22×D4—431no—
716C23×C4—431no—
717C23×C4—431no—
718C23×C4—432no—
719C23×C4—431no—
720C2×M16—432no—
721C2×M16—432no—
722C2×M16—432no—
723C2×M16—1724no—
724C2×M16C22×D4312yes—
725C22×C8—432no—
726C22×C8—432no—
727C22×C8—432no—
728C22×C8—431no—
729C22×C8—432no—
730C22×C8—431no—
731C22×C8—431no—
732C22×C8—431no—
733C22×C8—432no—
734C22×C8—432no—
735C22×C8—432no—
736C22×C8—432no—
737C22×C8—1724no—
738C22×C8—1724no—
739C22×C8C22×D4312yes—
740C22×C8C22×D4312yes—
741#126—432no—
742#126—432no—
743#126—432no—
744#126—432no—
745#126—432no—
746#126—432no—
747#126—432no—
748#126C4×D4312yes—
749#125—432no—
750#125—432no—
751#125—431no—
752#125—431no—
753#125—431no—
754#125C4×D4311yescharacteristic
755#124—431no—
756#124—431no—
757#124—432no—
758#124—432no—
759#124—431no—
760#124C4×D4311yescharacteristic
761#123—432no—
762#123—432no—
763#123—432no—
764#123—432no—
765#123—432no—
766#123—432no—
767#123—432no—
768#123C4×D4312yes—
769C22⋊Q8—431no—
770C22⋊Q8—431no—
771C22⋊Q8—432no—
772C22⋊Q8—431no—
773C22⋊Q8—432no—
774C22⋊Q8C4×D4311yescharacteristic
775#121—431no—
776#121—432no—
777#121—431no—
778#121—431no—
779#121—432no—
780#121C4×D4311yescharacteristic
781C4×Q8—431no—
782C4×Q8—432no—
783C4×Q8—431no—
784C4×Q8—432no—
785C4×Q8—431no—
786C4×Q8C22×D4311yescharacteristic
787C4×D4—431no—
788C4×D4—432no—
789C4×D4—432no—
790C4×D4—432no—
791C4×D4—432no—
792C4×D4—431no—
793C4×D4—432no—
794C4×D4—432no—
795C4×D4—432no—
796C4×D4—432no—
797C4×D4—432no—
798C4×D4—431no—
799C4×D4C22×D4312yes—
800C4×D4C22×D4311yescharacteristic
801#117—432no—
802#117—432no—
803#117—432no—
804#117—432no—
805#117—432no—
806#117—432no—
807#117—432no—
808#117C22×D4312yes—
809C2×C4⋊C4—432no—
810C2×C4⋊C4—432no—
811C2×C4⋊C4—431no—
812C2×C4⋊C4—432no—
813C2×C4⋊C4—431no—
814C2×C4⋊C4—432no—
815C2×C22⋊C4—432no—
816C2×C22⋊C4—432no—
817C2×C22⋊C4—432no—
818C2×C22⋊C4—432no—
819C2×C22⋊C4—432no—
820C2×C42—431no—
821C2×C42—431no—
822C2×C42—431no—
823C2×C42—431no—
824C2×C42—431no—
825C2×C42—431no—
826C2×C42—431no—
827C2×C42—431no—
828C2×C42—432no—
829C2×C42—431no—
830C2×C42—431no—
831C2×C42—431no—
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—432no—
834C4⋊C8—432no—
835C4⋊C8—432no—
836C4⋊C8—432no—
837C4⋊C8—431no—
838C4⋊C8—431no—
839C4⋊C8—432no—
840C4⋊C8—432no—
841C4⋊C8—432no—
842C4⋊C8—432no—
843C4⋊C8—431no—
844C4⋊C8—431no—
845C4⋊C8—432no—
846C4⋊C8—431no—
847C4⋊C8—431no—
848C4⋊C8—431no—
849C4⋊C8—432no—
850C4⋊C8—432no—
851C4⋊C8—431no—
852C4⋊C8C22×D4312yes—
853C4⋊C8C22×D4311yescharacteristic
854C4⋊C8C22×D4311yescharacteristic
855C4⋊C8C22×D4311yescharacteristic
856C4⋊C8C22×D4312yes—
857C4⋊C8C22×D4312yes—
858C4⋊C8C22×D4311yescharacteristic
859C22⋊C8—431no—
860C22⋊C8—431no—
861C22⋊C8—432no—
862C22⋊C8—432no—
863C22⋊C8—431no—
864C22⋊C8—431no—
865C22⋊C8—431no—
866C22⋊C8—431no—
867C22⋊C8—432no—
868C22⋊C8—432no—
869C22⋊C8—432no—
870C22⋊C8—432no—
871C22⋊C8C22×D4311yescharacteristic
872C22⋊C8C22×D4311yescharacteristic
873C22⋊C8C22×D4312yes—
874C22⋊C8C22×D4312yes—
875#97—432no—
876#97—432no—
877#97—432no—
878#97C22×D4312yes—
879C4×C8—431no—
880C4×C8—431no—
881C4×C8—431no—
882C4×C8—431no—
883C4×C8—432no—
884C4×C8—432no—
885C4×C8—431no—
886C4×C8—431no—
887C4×C8—432no—
888C4×C8C22×D4311yescharacteristic
889C4×C8C22×D4311yescharacteristic
890C4×C8C22×D4312yes—
891C24—431no—
892C24—432no—
893C2×Q8—432no—
894C2×Q8—431no—
895C2×Q8—864no—
896C2×Q8C2×C4×D4311yescharacteristic
897C2×D4—432no—
898C2×D4—432no—
899C2×D4—432no—
900C2×D4—432no—
901C2×D4—431no—
902C2×D4—864no—
903C2×D4—868no—
904C2×D4C2×C4×D4312yes—
905C2×D4C2×C4×D4311yescharacteristic
906C22×C4—431no—
907C22×C4—431no—
908C22×C4—431no—
909C22×C4—431no—
910C22×C4—431no—
911C22×C4—432no—
912C22×C4—431no—
913C22×C4—431no—
914C22×C4—431no—
915C22×C4—431no—
916C22×C4—431no—
917C22×C4—431no—
918C22×C4—431no—
919C22×C4—431no—
920C22×C4—431no—
921C22×C4—432no—
922C22×C4—432no—
923C22×C4—432no—
924C22×C4—432no—
925C22×C4—431no—
926C22×C4—432no—
927C22×C4—862no—
928C22×C4—864no—
929C22×C4—864no—
930C22×C4—862no—
931C22×C4—864no—
932C22×C4—864no—
933C22×C4C2×C4×D4311yescharacteristic
934C22×C4C2×C4×D4311yescharacteristic
935C22×C4C23×D4311yescharacteristic
936C22×C4C23×D4312yes—
937M16—42no—
938M16—1722no—
939M16—1722no—
940M16—1722no—
941C2×C8—42no—
942C2×C8—42no—
943C2×C8—431no—
944C2×C8—431no—
945C2×C8—431no—
946C2×C8—432no—
947C2×C8—431no—
948C2×C8—432no—
949C2×C8—864no—
950C2×C8—862no—
951C2×C8—864no—
952C2×C8—862no—
953C2×C8—862no—
954C2×C8—862no—
955C2×C8—1722no—
956C2×C8—1722no—
957C2×C8—1722no—
958C2×C8—1722no—
959C2×C8—1722no—
960C2×C8—1722no—
961C2×C8C23×D4311yescharacteristic
962C2×C8C23×D4311yescharacteristic
963C2×C8C23×D4311yescharacteristic
964C2×C8C23×D4312yes—
965C2×C8C23×D4311yescharacteristic
966C2×C8C23×D4312yes—
967C4⋊C4—432no—
968C4⋊C4—432no—
969C4⋊C4—432no—
970C4⋊C4—432no—
971C4⋊C4—432no—
972C4⋊C4—432no—
973C4⋊C4—432no—
974C4⋊C4—431no—
975C4⋊C4—432no—
976C4⋊C4—432no—
977C4⋊C4—432no—
978C4⋊C4—432no—
979C4⋊C4—431no—
980C4⋊C4—432no—
981C4⋊C4—432no—
982C4⋊C4—432no—
983C4⋊C4C2×C4×D4312yes—
984C4⋊C4C2×C4×D4312yes—
985C4⋊C4C2×C4×D4311yescharacteristic
986C4⋊C4C2×C4×D4312yes—
987C4⋊C4C2×C4×D4311yescharacteristic
988C4⋊C4C2×C4×D4312yes—
989C22⋊C4—432no—
990C22⋊C4—432no—
991C22⋊C4—432no—
992C22⋊C4—432no—
993C22⋊C4—432no—
994C22⋊C4—432no—
995C22⋊C4—432no—
996C22⋊C4—432no—
997C22⋊C4—432no—
998C22⋊C4—432no—
999C22⋊C4—432no—
1000C22⋊C4—432no—
1001C22⋊C4—432no—
1002C22⋊C4—432no—
1003C22⋊C4—432no—
1004C22⋊C4C2×C4×D4312yes—
1005C22⋊C4C2×C4×D4312yes—
1006C22⋊C4C2×C4×D4312yes—
1007C22⋊C4C2×C4×D4312yes—
1008C22⋊C4C2×C4×D4312yes—
1009C42—431no—
1010C42—431no—
1011C42—431no—
1012C42—431no—
1013C42—431no—
1014C42—431no—
1015C42—431no—
1016C42—431no—
1017C42—431no—
1018C42—431no—
1019C42—432no—
1020C42—432no—
1021C42—431no—
1022C42—432no—
1023C42—431no—
1024C42C2×C4×D4311yescharacteristic
1025C42C2×C4×D4311yescharacteristic
1026C42C23×D4311yescharacteristic
1027C42C23×D4312yes—
1028C42C23×D4311yescharacteristic
1029C23—431no—
1030C23—434no—
1031C23—431no—
1032C23—432no—
1033C23—862no—
1034C23—862no—
1035C23—864no—
1036C23—864no—
1037C23—864no—
1038C23C22×C4×D4312yes—
1039C23C22×C4×D4311yescharacteristic
1040Q8—22no—
1041Q8—864no—
1042Q8—862no—
1043D4—24no—
1044D4—22no—
1045D4—864no—
1046D4—864no—
1047D4—864no—
1048D4—864no—
1049D4—862no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—431no—
1057C2×C4—431no—
1058C2×C4—434no—
1059C2×C4—432no—
1060C2×C4—432no—
1061C2×C4—431no—
1062C2×C4—431no—
1063C2×C4—431no—
1064C2×C4—431no—
1065C2×C4—432no—
1066C2×C4—432no—
1067C2×C4—432no—
1068C2×C4—862no—
1069C2×C4—864no—
1070C2×C4—862no—
1071C2×C4—862no—
1072C2×C4—864no—
1073C2×C4—862no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—864no—
1079C2×C4—864no—
1080C2×C4—862no—
1081C2×C4—864no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—861no—
1086C2×C4—862no—
1087C2×C4—861no—
1088C2×C4—862no—
1089C2×C4C22×C4×D4311yescharacteristic
1090C2×C4C22×C4×D4311yescharacteristic
1091C2×C4C22×C4×D4311yescharacteristic
1092C2×C4C22×C4×D4311yescharacteristic
1093C2×C4C22×C4×D4312yes—
1094C2×C4C22×C4×D4312yes—
1095C2×C4C22×C4×D4312yes—
1096C2×C4C22×C4×D4311yescharacteristic
1097C2×C4C24×D4311yescharacteristic
1098C8—21no—
1099C8—22no—
1100C8—22no—
1101C8—21no—
1102C8—21no—
1103C8—21no—
1104C8—861no—
1105C8—862no—
1106C8—862no—
1107C8—861no—
1108C8—861no—
1109C8—861no—
1110C22—21no—
1111C22—21no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—432no—
1116C22—432no—
1117C22—432no—
1118C22—432no—
1119C22—868no—
1120C22—861no—
1121C22—861no—
1122C22—862no—
1123C22—862no—
1124C22—862no—
1125C22—1728no—
1126C22#131×D4312yes—
1127C22C23×C4×D4311yescharacteristic
1128C4—21no—
1129C4—22no—
1130C4—21no—
1131C4—21no—
1132C4—21no—
1133C4—22no—
1134C4—22no—
1135C4—432no—
1136C4—432no—
1137C4—861no—
1138C4—862no—
1139C4—861no—
1140C4—861no—
1141C4—861no—
1142C4—862no—
1143C4—862no—
1144C4#131×D4312yes—
1145C4H(5,𝔽2)×D4311yescharacteristic
1146C42−1+4×D4311yescharacteristic
1147C2—22no—
1148C2—42no—
1149C2—434no—
1150C2—862no—
1151C2—1722no—
1152C2#520×D4311yescharacteristic
1153C2C2×#131×D4311yescharacteristic
1154C2C2×#131×D4311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2994C2
prime radical#121×D43C4
cosocleC2×C4×C43C25
hypercenter#2994D43
hypocenterC43C2×#2994
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #19143758C2semidirect
3. #19143757C2semidirect
4. #19143756C2semidirect
5. #19143755C2semidirect
6. #19143754C2semidirect
7. #19143753C2semidirect
8. #19143752C2semidirect
9. #19143751C2semidirect
10. #19143750C2semidirect
11. #19143749C2semidirect
12. #19143748C2semidirect
13. #446×D43C2semidirect
14. C8×Q8×D43C2semidirect
15. #436×D43C2semidirect
16. #435×D43C2semidirect
17. C8×D4×D43C2semidirect
18. C8×D4×D43C2semidirect
19. #433×D43C2semidirect
20. #431×D43C2semidirect
21. #424×D43C2semidirect
22. C2×C4⋊C8×D43C2semidirect
23. C43×#2994C2semidirect
49. #14583030C22semidirect
50. #14583029C22semidirect
51. #14583028C22semidirect
52. #14583027C22semidirect
53. #14583026C22semidirect
54. Q8×C43⋊C8C22semidirect
55. C8×Dic86C22semidirect
56. C8×Dic86C22semidirect
57. #14583023C22semidirect
58. #14583023C22semidirect
59. #14582978C22semidirect
60. #14582977C22semidirect
61. #14582976C22semidirect
62. #14582975C22semidirect
63. #14582974C22semidirect
64. #14582973C22semidirect
65. #14582972C22semidirect
66. #14582971C22semidirect
67. #14582970C22semidirect
68. #14582969C22semidirect
69. #14582968C22semidirect
70. #14582967C22semidirect
71. C8×D172C22semidirect
72. C8×D172C22semidirect
73. D4×C43⋊C8C22semidirect
74. D4×C43⋊C8C22semidirect
75. #14582964C22semidirect
76. #14582964C22semidirect
77. C8×C22⋊D43C22semidirect
78. C8×C22⋊D43C22semidirect
79. C8×C22⋊D43C22semidirect
80. (C22⋊D43)⋊C8C22semidirect
81. (C22⋊D43)⋊C8C22semidirect
82. (C22⋊D43)⋊C8C22semidirect
83. #14582961C22semidirect
84. #14582960C22semidirect
85. #14582959C22semidirect
86. #14582959C22semidirect
87. #14582958C22semidirect
88. #14582957C22semidirect
89. #14582957C22semidirect
90. #14582952C22semidirect
91. #14582951C22semidirect
92. #14582951C22semidirect
93. #14582950C22semidirect
94. #14582950C22semidirect
95. #14582949C22semidirect
96. #14582949C22semidirect
97. #14582927C22semidirect
98. #14582926C22semidirect
99. #14582925C22semidirect
100. #14582924C22semidirect
101. #14582924C22semidirect
102. #14582924C22semidirect
103. #14582924C22semidirect
104. C2×C4⋊(C43⋊C8)C22semidirect
105. C2×Dic43⋊C8C22semidirect
113. C4⋊C8×D43C22semidirect
114. C4⋊C8×D43C22semidirect
115. C4⋊C8×D43C22semidirect
125. C43×#446C22semidirect
126. C8×Q8×C43C22semidirect
127. C43×#436C22semidirect
128. C43×#435C22semidirect
129. C8×D4×C43C22semidirect
130. C8×D4×C43C22semidirect
131. C43×#433C22semidirect
132. C43×#431C22semidirect
133. C43×#424C22semidirect
134. C2×C4⋊C8×C43C22semidirect
582. #2994D43direct (N × H)
600. D43#2994direct (N × H)
632. #446C2×D43semidirect
638. C8×Q8C2×D43semidirect
644. #436C2×D43semidirect
652. #435C2×D43semidirect
665. C8×D4C2×D43semidirect
666. C8×D4C2×D43semidirect
674. #433C2×D43semidirect
682. #431C2×D43semidirect
690. #424C2×D43semidirect
703. C2×C4⋊C8C2×D43semidirect
712. C43C2×#2994semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#191437582
#191437572
#191437562
#191437552
#191437542
#191437532
#191437522
#191437512
#191437502
#191437492
#191437482
#446×D432
C8×Q8×D432
#436×D432
#435×D432
C8×D4×D432
#433×D432
#431×D432
#424×D432
C2×C4⋊C8×D432
C43×#29942
C2×#299443