Finite Group Databasebeta

← #25961102

Subgroups — #25961102

Order 11008.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#19143571C211yesmaximal, characteristic, complemented
3#19143570C211yesmaximal, characteristic, complemented
4#19143568C212yesmaximal, complemented
5#19143566C212yesmaximal, complemented
6#19143564C211yesmaximal, characteristic, complemented
7#19143560C211yesmaximal, characteristic, complemented
8#19143558C211yesmaximal, characteristic, complemented
9#19143555C212yesmaximal, complemented
10C8×#10621902C211yesmaximal, characteristic, complemented
11C8×#10621900C211yesmaximal, characteristic, complemented
12C8×#10621900C212yesmaximal, complemented
13#19143526C211yesmaximal, characteristic, complemented
14#19143524C211yesmaximal, characteristic, complemented
15#19143304C211yesmaximal, characteristic, complemented
16#19143302C211yesmaximal, characteristic, complemented
17#19143286C212yesmaximal, complemented
18#19143284C212yesmaximal, complemented
19#19143236C212yesmaximal, complemented
20#19143225C211yesmaximal, characteristic, complemented
21#19143017C212yesmaximal, complemented
22C2×C4×C8×D43C211yesmaximal, characteristic, complemented
23C43×#2966C211yesmaximal, characteristic, complemented
24C2×#13063333C2212yes—
25C2×#13063331C2212yes—
26C22×C8×D43C2211yescharacteristic
27C22×C8×D43C2211yescharacteristic
28#14583455C411yescharacteristic
29#14583453C2211yescharacteristic
30#14583451C411yescharacteristic
31#14583448C411yescharacteristic
32#14583446C2211yescharacteristic
33#14583444C411yescharacteristic
34#14583434C411yescharacteristic
35#14583433C2211yescharacteristic
36#14583432C412yes—
37#14583432C412yes—
38#14583428C411yescharacteristic
39#14583427C2212yes—
40#14583426C412yes—
41#14583412C411yescharacteristic
42#14583409C411yescharacteristic
43#14583408C2212yes—
44#14583407C412yes—
45C4×#10621902C2211yescharacteristic
46#14583367C2212yes—
47C4×#10621900C2212yes—
48C4×#10621900C2211yescharacteristic
49C2×C42×D43C2211yescharacteristic
50#14583030C2211yescharacteristic, complemented
51#14583029C2211yescharacteristic, complemented
52#14583028C2212yescomplemented
53#14583027C2212yescomplemented
54#14583026C2211yescharacteristic, complemented
55Q8×C43⋊C8C2211yescharacteristic, complemented
56C8×Dic86C2212yescomplemented
57C8×Dic86C2211yescharacteristic, complemented
58#14583023C2211yescharacteristic, complemented
59#14583023C2212yescomplemented
60#14582978C2211yescharacteristic, complemented
61#14582977C2211yescharacteristic, complemented
62#14582976C2211yescharacteristic, complemented
63#14582975C2212yescomplemented
64#14582974C2212yescomplemented
65#14582973C2212yes—
66#14582972C2212yes—
67#14582971C2212yes—
68#14582970C2212yes—
69#14582969C2212yes—
70#14582968C2212yes—
71#14582967C2212yes—
72C8×D172C2212yes—
73C8×D172C2211yescharacteristic, complemented
74D4×C43⋊C8C2212yes—
75D4×C43⋊C8C2211yescharacteristic, complemented
76#14582964C2212yes—
77#14582964C2211yescharacteristic, complemented
78C8×C22⋊D43C2212yes—
79C8×C22⋊D43C2212yes—
80C8×C22⋊D43C2212yescomplemented
81(C22⋊D43)⋊C8C2212yes—
82(C22⋊D43)⋊C8C2212yes—
83(C22⋊D43)⋊C8C2212yescomplemented
84#14582961C2212yescomplemented
85#14582960C2212yescomplemented
86#14582958C2212yescomplemented
87#14582956C2211yescharacteristic
88#14582954C2212yes—
89#14582951C2211yescharacteristic
90#14582951C2211yescharacteristic
91#14582951C2212yescomplemented
92#14582951C2212yescomplemented
93#14582949C2212yes—
94#14582949C2212yescomplemented
95#14582949C2212yescomplemented
96#14582924C2212yes—
97#14582924C2212yes—
98#14582921C2211yescharacteristic
99#14582921C2211yescharacteristic
100#14582864C2212yes—
101#14582864C2212yes—
102#14582861C2212yes—
103#14582856C2212yes—
104#14582856C2212yescomplemented
105#14582855C2212yescomplemented
106#14582853C2212yes—
107#14582853C2212yescomplemented
108#14582851C2212yes—
109#14582851C2212yescomplemented
110M16×Dic43C2212yescomplemented
111C2×C4×C43⋊C8C2211yescharacteristic
112C2×C8×Dic43C2211yescharacteristic
113C2×C8×Dic43C2211yescharacteristic
114C2×C8×Dic43C2212yescomplemented
115C4×C8×D43C2211yescharacteristic
116C4×C8×D43C2211yescharacteristic
117C4×C8×D43C2211yescharacteristic
118C4×C8×D43C2211yescharacteristic
119C4×C8×D43C2211yescharacteristic
120C4×C8×D43C2211yescharacteristic
121C4×C8×D43C2211yescharacteristic
122C4×C8×D43C2211yescharacteristic
123C4×C8×D43C2212yescomplemented
124C43×#529C2211yescharacteristic
125C43×#446C2211yescharacteristic, complemented
126C8×Q8×C43C2211yescharacteristic, complemented
127C43×#436C2211yescharacteristic, complemented
128C43×#435C2212yes—
129C8×D4×C43C2212yes—
130C8×D4×C43C2211yescharacteristic, complemented
131C43×#433C2212yescomplemented
132C43×#432C2211yescharacteristic
133C43×#405C2212yescomplemented
134C2×C4×C8×C43C2211yescharacteristic
135C2×#10621902C2×C411yescharacteristic
136C2×#10621898C2312yes—
137C2×#10621900C2×C412yes—
138C2×#10621900C2×C411yescharacteristic
139C22×C4×D43C2×C411yescharacteristic
140C22×C4×D43C2×C411yescharacteristic
141C22×C4×D43C2311yescharacteristic
142#13063333—28no—
143#13063331—28no—
144C2×#10621877C2312yes—
145C2×#10621872C2312yes—
146C2×#10621872C2312yes—
147C2×#10621872C2312yes—
148C2×#10621872C2312yes—
149C22×C43⋊C8C2311yescharacteristic
150C22×C43⋊C8C2311yescharacteristic
151C22×C43⋊C8C2312yes—
152C2×C8×D43—24no—
153C2×C8×D43—24no—
154C2×C8×D43C2311yescharacteristic
155C2×C8×D43C2311yescharacteristic
156C2×C8×D43C2311yescharacteristic
157C2×C8×D43C2311yescharacteristic
158C2×C8×D43C2311yescharacteristic
159C2×C8×D43C2311yescharacteristic
160C2×C8×D43C2312yes—
161C2×C8×D43C2312yes—
162C2×C8×D43C2311yescharacteristic
163C2×C8×D43C2311yescharacteristic
164#13063324C2×C411yescharacteristic
165#13063324C2×C411yescharacteristic
166#13063323C2×C411yescharacteristic
167#13063321C2×C411yescharacteristic
168#13063320C2×C412yes—
169#13063319C2×C412yes—
170#13063318C2×C412yes—
171#13063317C2×C411yescharacteristic
172#13063315C2×C412yes—
173#13063315C2×C412yes—
174#13063313C2×C411yescharacteristic
175#13063311C2×C412yes—
176#13063311C2×C412yes—
177#13063310C2×C412yes—
178#13063310C2×C412yes—
179#13063308C2×C412yes—
180#13063307C2×C412yes—
181#13063307C2×C412yes—
182#13063305C2×C411yescharacteristic
183#13063304C2×C411yescharacteristic
184#13063303C2×C412yes—
185#13063303C2×C412yes—
186#13063303C2×C412yes—
187#13063302C2×C412yes—
188#13063301C2×C411yescharacteristic
189#13063300C2×C411yescharacteristic
190#13063299C2×C411yescharacteristic
191#13063298C2×C412yes—
192#13063298C2×C412yes—
193#13063298C2×C412yes—
194#13063297C2×C412yes—
195#13063296C2×C411yescharacteristic
196#13063295C2×C412yes—
197#13063293C2×C412yes—
198Q8×Dic43C2×C411yescharacteristic
199C4×Dic86C2312yes—
200C4×Dic86C2311yescharacteristic
201#13063290C2×C412yes—
202#13063290C2×C411yescharacteristic
203#13063290C2×C412yes—
204#13063290C2×C412yes—
205C4×D172C2312yes—
206C4×D172C2311yescharacteristic
207D4×Dic43C2×C412yes—
208D4×Dic43C2×C411yescharacteristic
209#13063287C2×C412yes—
210#13063287C2×C412yes—
211#13063287C2×C412yes—
212#13063287C2×C411yescharacteristic
213C4×C22⋊D43C2312yes—
214C4×C22⋊D43C2312yes—
215C4×C22⋊D43C2312yes—
216(C22⋊D43)⋊C4C2×C412yes—
217(C22⋊D43)⋊C4C2×C412yes—
218(C22⋊D43)⋊C4C2×C412yes—
219(C22⋊D43)⋊C4C2×C412yes—
220(C22⋊D43)⋊C4C2×C412yes—
221(C22⋊D43)⋊C4C2×C412yes—
222(C22⋊D43)⋊C4C2×C412yes—
223#13063283C2×C411yescharacteristic
224#13063283C2×C412yes—
225#13063283C2×C411yescharacteristic
226#13063283C2×C412yes—
227#13063282C2312yes—
228#13063282C2312yes—
229#13063281C2×C412yes—
230#13063281C2×C412yes—
231#13063281C2×C412yes—
232C2×C4×Dic43C2×C411yescharacteristic
233C2×C4×Dic43C2×C411yescharacteristic
234C2×C4×Dic43C2311yescharacteristic
235C2×C4×Dic43C2312yes—
236C42×D43C2×C411yescharacteristic
237C42×D43C2×C411yescharacteristic
238C42×D43C2×C411yescharacteristic
239C42×D43C2×C411yescharacteristic
240C42×D43C2311yescharacteristic
241C42×D43C2311yescharacteristic
242C42×D43C2311yescharacteristic
243C42×D43C2311yescharacteristic
244C42×D43C2312yes—
245C4⋊(C43⋊C8)C2311yescharacteristic
246C4⋊(C43⋊C8)C2311yescharacteristic
247C4⋊(C43⋊C8)C2312yes—
248C4⋊(C43⋊C8)C2312yes—
249Dic43⋊C8C2312yes—
250Dic43⋊C8C2312yes—
251Dic43⋊C8C2312yes—
252Dic43⋊C8C2312yes—
253Dic43⋊C8C2312yes—
254Dic43⋊C8C2312yes—
255C22⋊(C43⋊C8)C2312yes—
256C22⋊(C43⋊C8)C2312yes—
257C22⋊(C43⋊C8)C2312yes—
258(C2×D43)⋊C8C2312yes—
259(C2×D43)⋊C8C2312yes—
260(C2×D43)⋊C8C2312yes—
261(C2×D43)⋊C8C2312yes—
262(C2×D43)⋊C8C2312yes—
263(C2×D43)⋊C8C2312yes—
264#13063236C2312yes—
265#13063236C2312yes—
266#13063235C2312yes—
267#13063235C2312yes—
268C4×C43⋊C8C2311yescharacteristic
269C4×C43⋊C8C2311yescharacteristic
270C4×C43⋊C8C2311yescharacteristic
271C4×C43⋊C8C2311yescharacteristic
272C4×C43⋊C8C2312yes—
273C8×Dic43C2311yescharacteristic
274C8×Dic43C2311yescharacteristic
275C8×Dic43C2311yescharacteristic
276C8×Dic43C2311yescharacteristic
277C8×Dic43C2311yescharacteristic
278C8×Dic43C2311yescharacteristic
279C8×Dic43C2311yescharacteristic
280C8×Dic43C2311yescharacteristic
281C8×Dic43C2312yes—
282C8×Dic43C2312yes—
283C8×Dic43C2312yes—
284C8×Dic43C2312yes—
285C2×M16×C43C2312yes—
286C22×C8×C43C2311yescharacteristic
287C22×C8×C43C2311yescharacteristic
288C22×C8×C43C2312yes—
289#126×C43C2×C412yes—
290#125×C43C2×C411yescharacteristic
291#124×C43C2×C411yescharacteristic
292#123×C43C2×C412yes—
293C22⋊Q8×C43C2×C411yescharacteristic
294#121×C43C2×C411yescharacteristic
295C4×Q8×C43C2311yescharacteristic
296C4×D4×C43C2312yes—
297C4×D4×C43C2311yescharacteristic
298#117×C43C2312yes—
299C2×C42×C43C2311yescharacteristic
300C4⋊C8×C43C2311yescharacteristic
301C4⋊C8×C43C2311yescharacteristic
302C4⋊C8×C43C2312yes—
303C4⋊C8×C43C2312yes—
304C22⋊C8×C43C2312yes—
305C22⋊C8×C43C2312yes—
306C22⋊C8×C43C2312yes—
307#97×C43C2312yes—
308#97×C43C2312yes—
309C4×C8×C43C2311yescharacteristic
310C4×C8×C43C2311yescharacteristic
311C4×C8×C43C2311yescharacteristic
312C4×C8×C43C2311yescharacteristic
313C4×C8×C43C2312yes—
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—
325C2×C22⋊D43C22×C412yes—
326C2×C22⋊D43C22×C412yes—
327C22×Dic43C22×C411yescharacteristic
328C22×Dic43C22×C411yescharacteristic
329C22×Dic43C22×C412yes—
330C22×Dic43C22×C412yes—
331C22×Dic43C22×C411yescharacteristic
332#10621902—24no—
333#10621900—28no—
334#10621900—24no—
335#10621898—24no—
336#10621898—24no—
337C2×D172C22×C412yes—
338C2×D172C22×C412yes—
339C2×D172C22×C411yescharacteristic
340C2×C4×D43—24no—
341C2×C4×D43—24no—
342C2×C4×D43—22no—
343C2×C4×D43—22no—
344C2×C4×D43C22×C411yescharacteristic
345C2×C4×D43C22×C411yescharacteristic
346C2×C4×D43C22×C411yescharacteristic
347C2×C4×D43C22×C411yescharacteristic
348C2×C4×D43C22×C411yescharacteristic
349C2×C4×D43C22×C411yescharacteristic
350C2×C4×D43C22×C411yescharacteristic
351C2×C4×D43C22×C411yescharacteristic
352C2×C4×D43C22×C411yescharacteristic
353C2×C4×D43C22×C412yes—
354C2×C4×D43C22×C412yes—
355C2×C4×D43C22×C411yescharacteristic
356C2×C4×D43C2411yescharacteristic
357C2×C4×D43C2412yes—
358C2×C4×D43C2411yescharacteristic
359C2×Dic86C22×C412yes—
360C2×Dic86C22×C412yes—
361C2×Dic86C22×C411yescharacteristic
362M16×C43—24no—
363C2×C8×C43—22no—
364C2×C8×C43—22no—
365C2×C8×C43—24no—
366C2×C8×C43C2411yescharacteristic
367C2×C8×C43C2411yescharacteristic
368C2×C8×C43C2412yes—
369C2×C8×C43C2412yes—
370C2×C8×C43C2411yescharacteristic
371C2×C8×C43C2411yescharacteristic
372C4⋊C4×C43C22×C412yes—
373C4⋊C4×C43C22×C412yes—
374C4⋊C4×C43C22×C411yescharacteristic
375C4⋊C4×C43C22×C412yes—
376C4⋊C4×C43C22×C411yescharacteristic
377C4⋊C4×C43C22×C412yes—
378C22⋊C4×C43C22×C412yes—
379C22⋊C4×C43C22×C412yes—
380C22⋊C4×C43C22×C412yes—
381C22⋊C4×C43C22×C412yes—
382C22⋊C4×C43C22×C412yes—
383C42×C43C22×C411yescharacteristic
384C42×C43C22×C411yescharacteristic
385C42×C43C2411yescharacteristic
386C42×C43C2411yescharacteristic
387C42×C43C2412yes—
388C22⋊Dic43C22×C412yes—
389C22⋊Dic43C22×C412yes—
390C22⋊Dic43C22×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—
399(C2×D43)⋊C4C22×C412yes—
400(C2×D43)⋊C4C22×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×Dic43C22×C412yes—
428C4×Dic43C22×C412yes—
429C4×Dic43C2411yescharacteristic
430C4×Dic43C2411yescharacteristic
431C4×Dic43C2412yes—
432#10621877—24no—
433C2×C43⋊C8—22no—
434C2×C43⋊C8—22no—
435C2×C43⋊C8—24no—
436C2×C43⋊C8C2411yescharacteristic
437C2×C43⋊C8C2411yescharacteristic
438C2×C43⋊C8C2412yes—
439C2×C43⋊C8C2412yes—
440C2×C43⋊C8C2411yescharacteristic
441C2×C43⋊C8C2411yescharacteristic
442#10621872—24no—
443#10621872—24no—
444#10621872—24no—
445#10621872—24no—
446C8×D43—22no—
447C8×D43—22no—
448C8×D43—22no—
449C8×D43—22no—
450C8×D43—24no—
451C8×D43—22no—
452C8×D43—22no—
453C8×D43—24no—
454C8×D43#4114yescomplemented
455C8×D43#4114yescomplemented
456C23×C43C23×C412yes—
457C23×C43C23×C411yescharacteristic
458C22×D43—22no—
459C22×D43—22no—
460C22×D43—22no—
461C22×D43C23×C412yes—
462C22×D43C23×C411yescharacteristic
463C22×D43C23×C411yescharacteristic
464Q8×C43—22no—
465D4×C43—24no—
466D4×C43—22no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43—21no—
470C2×C4×C43—21no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
473C2×C4×C43C23×C411yescharacteristic
474C2×C4×C43C23×C411yescharacteristic
475C2×C4×C43C23×C411yescharacteristic
476C2×C4×C43C23×C411yescharacteristic
477C2×C4×C43C23×C412yes—
478C2×C4×C43C23×C412yes—
479C2×C4×C43C23×C412yes—
480C2×C4×C43C23×C411yescharacteristic
481C2×C4×C43C2511yescharacteristic
482C22⋊D43—24no—
483C22⋊D43—24no—
484C22⋊D43—24no—
485C22⋊D43—24no—
486C22⋊D43—24no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—24no—
490C2×Dic43—24no—
491C2×Dic43#13114yescomplemented
492C2×Dic43C23×C411yescharacteristic
493C2×Dic43C23×C411yescharacteristic
494C2×Dic43C23×C412yes—
495C2×Dic43C23×C412yes—
496C2×Dic43C23×C412yes—
497C2×Dic43C23×C411yescharacteristic
498C2×Dic43C23×C411yescharacteristic
499C2×Dic43C23×C411yescharacteristic
500C2×Dic43C23×C411yescharacteristic
501D172—24no—
502D172—24no—
503D172—22no—
504C4×D43—22no—
505C4×D43—22no—
506C4×D43—22no—
507C4×D43—21no—
508C4×D43—21no—
509C4×D43—22no—
510C4×D43—22no—
511C4×D43—22no—
512C4×D43—22no—
513C4×D43—22no—
514C4×D43—22no—
515C4×D43—22no—
516C4×D43—22no—
517C4×D43—24no—
518C4×D43—24no—
519C4×D43#13114yescomplemented
520C4×D43C2×#4112yes—
521C4×D43C2×#4112yes—
522Dic86—22no—
523Dic86—24no—
524Dic86—24no—
525C8×C43—21no—
526C8×C43—21no—
527C8×C43—22no—
528C8×C43—22no—
529C8×C43C2×#4112yes—
530C8×C43C2×#4112yes—
531C43⋊C8—21no—
532C43⋊C8—21no—
533C43⋊C8—22no—
534C43⋊C8—22no—
535C43⋊C8C2×#4112yes—
536C43⋊C8C2×#4112yes—
537#60204—431nomaximal, Sylow
538C22×C43—21no—
539C22×C43—21no—
540C22×C43—22no—
541C22×C43—22no—
542C22×C43—22no—
543C22×C43C2×#13112yes—
544C22×C43C24×C411yescharacteristic
545C2×D43—28no—
546C2×D43—21no—
547C2×D43—21no—
548C2×D43—21no—
549C2×D43—21no—
550C2×D43—22no—
551C2×D43—22no—
552C2×D43—22no—
553C2×D43C4×#4112yes—
554C2×D43C2×#13112yes—
555C4×C43—22no—
556C4×C43—21no—
557C4×C43—22no—
558C4×C43—21no—
559C4×C43—21no—
560C4×C43—21no—
561C4×C43—22no—
562C4×C43C2×#13112yes—
563C4×C43C22×#4111yescharacteristic
564C4×C43C22×#4111yescharacteristic
565Dic43—22no—
566Dic43—21no—
567Dic43—22no—
568Dic43—22no—
569Dic43—21no—
570Dic43C4×#4112yes—
571Dic43C2×#13112yes—
572Dic43C2×#13112yes—
573Dic43C2×#13112yes—
574#3444—431no—
575#2966—432no—
576#2966—431no—
577#2966—432no—
578#2966—431no—
579#2966—431no—
580#2966D4311yescharacteristic, complemented
581#2965—431no—
582#2965—431no—
583#2965—432no—
584C8×#41—431no—
585C8×#41—432no—
586C8×#41—431no—
587#2960—431no—
588#2960—431no—
589#2931—431no—
590#2931—431no—
591#2929—432no—
592#2929—432no—
593#2922—432no—
594#2920—431no—
595C4×#131—432no—
596C22×C4×C8—431no—
597C2×C43—22no—
598C2×C43—42no—
599C2×C43C2×C4×#4111yescharacteristic
600C2×C43C22×#13111yescharacteristic
601C2×C43C22×#13111yescharacteristic
602D43—22no—
603D43—22no—
604D43—42no—
605C2×#131—432no—
606C2×#131—432no—
607C23×C8—431no—
608C23×C8—431no—
609#533—431no—
610#533—431no—
611#533—431no—
612#532—431no—
613#532—431no—
614#532—431no—
615#529—432no—
616#529—432no—
617#529—431no—
618#529—431no—
619#529—432no—
620#529—432no—
621#529—431no—
622#529C2×D4311yescharacteristic
623#525—432no—
624#525—431no—
625#525—431no—
626#525—432no—
627C4×#41—431no—
628C4×#41—431no—
629C4×#41—432no—
630C4×#41—432no—
631C22×C42—431no—
632#446—431no—
633#446—431no—
634#446—432no—
635#446—432no—
636#446—431no—
637#446C2×D4311yescharacteristic, complemented
638C8×Q8—431no—
639C8×Q8—432no—
640C8×Q8—431no—
641C8×Q8—432no—
642C8×Q8—431no—
643C8×Q8C2×D4311yescharacteristic, complemented
644#436—432no—
645#436—431no—
646#436—431no—
647#436—432no—
648#436—431no—
649#436C2×D4311yescharacteristic, complemented
650#435—432no—
651#435—432no—
652#435—432no—
653#435—432no—
654#435—432no—
655#435—432no—
656#435—432no—
657#435C2×D4312yes—
658C8×D4—432no—
659C8×D4—432no—
660C8×D4—432no—
661C8×D4—432no—
662C8×D4—431no—
663C8×D4—432no—
664C8×D4—431no—
665C8×D4—432no—
666C8×D4—432no—
667C8×D4—432no—
668C8×D4—432no—
669C8×D4—431no—
670C8×D4C2×D4312yes—
671C8×D4C2×D4311yescharacteristic, complemented
672#433—432no—
673#433—432no—
674#433—432no—
675#433C2×D4312yescomplemented
676#432—431no—
677#432—432no—
678#432C2×D4311yescharacteristic
679#431—431no—
680#431—431no—
681#431—432no—
682#431—432no—
683#431—432no—
684#431—432no—
685#431—432no—
686#424—432no—
687#424—432no—
688#423—431no—
689#423—431no—
690#408—432no—
691#408—432no—
692#407—432no—
693#405—432no—
694#405—432no—
695#405—432no—
696#405—432no—
697#405—432no—
698#405C2×D4312yescomplemented
699C4×M16—432no—
700C4×M16—432no—
701C4×M16—432no—
702C2×C4×C8—431no—
703C2×C4×C8—431no—
704C2×C4×C8—432no—
705C2×C4×C8—431no—
706C2×C4×C8—431no—
707C2×C4×C8—431no—
708C2×C4×C8—431no—
709C2×C4×C8—431no—
710C2×C4×C8—431no—
711C2×C4×C8—431no—
712C2×C4×C8—431no—
713C2×C4×C8—431no—
714C2×C4×C8—432no—
715C2×C4×C8C2×D4311yescharacteristic
716C43#6020411yescharacteristic, complemented, Sylow
717C2×#41—431no—
718C2×#41—432no—
719C2×#41—431no—
720C2×#41—432no—
721C23×C4—431no—
722C23×C4—431no—
723C23×C4—431no—
724#131—868no—
725#131—868no—
726C2×M16—432no—
727C2×M16—432no—
728C2×M16—432no—
729C2×M16—432no—
730C2×M16—432no—
731C2×M16C22×D4312yes—
732C22×C8—431no—
733C22×C8—431no—
734C22×C8—431no—
735C22×C8—431no—
736C22×C8—432no—
737C22×C8—431no—
738C22×C8—431no—
739C22×C8—431no—
740C22×C8—431no—
741C22×C8—431no—
742C22×C8—432no—
743C22×C8—431no—
744C22×C8—432no—
745C22×C8—864no—
746C22×C8—864no—
747C22×C8C22×D4311yescharacteristic
748C22×C8C22×D4311yescharacteristic
749C22×C8C22×D4312yes—
750C4⋊Q8—431no—
751C4⋊Q8—431no—
752C4⋊Q8—431no—
753#127—431no—
754#126—432no—
755#126—432no—
756#126—432no—
757#126C4×D4312yes—
758#125—432no—
759#125—432no—
760#125—431no—
761#125C4×D4311yescharacteristic
762#124—432no—
763#124—432no—
764#124—431no—
765#124C4×D4311yescharacteristic
766#123—432no—
767#123—432no—
768#123—432no—
769#123—432no—
770#123—432no—
771#123C4×D4312yes—
772C22⋊Q8—431no—
773C22⋊Q8—431no—
774C22⋊Q8—432no—
775C22⋊Q8—432no—
776C22⋊Q8—432no—
777C22⋊Q8—431no—
778C22⋊Q8—432no—
779C22⋊Q8C4×D4311yescharacteristic
780#121—431no—
781#121—432no—
782#121—431no—
783#121—431no—
784#121—432no—
785#121—432no—
786#121—432no—
787#121C4×D4311yescharacteristic
788#120—432no—
789#120—432no—
790C4×Q8—431no—
791C4×Q8—432no—
792C4×Q8—432no—
793C4×Q8—432no—
794C4×Q8—431no—
795C4×Q8—432no—
796C4×Q8—431no—
797C4×Q8C22×D4311yescharacteristic
798C4×D4—432no—
799C4×D4—431no—
800C4×D4—432no—
801C4×D4—432no—
802C4×D4—432no—
803C4×D4—432no—
804C4×D4—432no—
805C4×D4—432no—
806C4×D4—431no—
807C4×D4—432no—
808C4×D4—432no—
809C4×D4—432no—
810C4×D4—432no—
811C4×D4—432no—
812C4×D4—432no—
813C4×D4—432no—
814C4×D4—432no—
815C4×D4—431no—
816C4×D4C22×D4312yes—
817C4×D4C22×D4311yescharacteristic
818#117—431no—
819#117—431no—
820#117—432no—
821#117—432no—
822#117—432no—
823#117—432no—
824#117—432no—
825#117—432no—
826#117—432no—
827#117C22×D4312yes—
828C2×C42—431no—
829C2×C42—431no—
830C2×C42—432no—
831C2×C42—431no—
832C2×C42—431no—
833C2×C42—431no—
834C2×C42—431no—
835C2×C42—431no—
836C2×C42—432no—
837C2×C42—431no—
838C2×C42—431no—
839C2×C42—431no—
840C2×C42—431no—
841C2×C42C22×D4311yescharacteristic
842C4⋊C8—432no—
843C4⋊C8—432no—
844C4⋊C8—432no—
845C4⋊C8—432no—
846C4⋊C8—432no—
847C4⋊C8—432no—
848C4⋊C8—431no—
849C4⋊C8—431no—
850C4⋊C8—432no—
851C4⋊C8—432no—
852C4⋊C8C22×D4311yescharacteristic
853C4⋊C8C22×D4311yescharacteristic
854C4⋊C8C22×D4312yes—
855C4⋊C8C22×D4312yes—
856C22⋊C8—432no—
857C22⋊C8—432no—
858C22⋊C8—432no—
859C22⋊C8—432no—
860C22⋊C8—432no—
861C22⋊C8—432no—
862C22⋊C8—432no—
863C22⋊C8—432no—
864C22⋊C8—432no—
865C22⋊C8C22×D4312yes—
866C22⋊C8C22×D4312yes—
867C22⋊C8C22×D4312yes—
868#97—432no—
869#97—432no—
870#97—432no—
871#97—432no—
872#97C22×D4312yes—
873#97C22×D4312yes—
874C4×C8—431no—
875C4×C8—431no—
876C4×C8—431no—
877C4×C8—431no—
878C4×C8—431no—
879C4×C8—431no—
880C4×C8—432no—
881C4×C8—432no—
882C4×C8—432no—
883C4×C8—431no—
884C4×C8—431no—
885C4×C8—432no—
886C4×C8—431no—
887C4×C8—431no—
888C4×C8—431no—
889C4×C8—431no—
890C4×C8—432no—
891C4×C8C22×D4311yescharacteristic
892C4×C8C22×D4311yescharacteristic
893C4×C8C22×D4311yescharacteristic
894C4×C8C22×D4311yescharacteristic
895C4×C8C22×D4312yes—
896C24—431no—
897#41—864no—
898#41—864no—
899#41—868no—
900#41—864no—
901#41—864no—
902C2×Q8—432no—
903C2×Q8—432no—
904C2×Q8—431no—
905C2×Q8C2×C4×D4311yescharacteristic
906C2×D4—432no—
907C2×D4—432no—
908C2×D4—432no—
909C2×D4—432no—
910C2×D4—432no—
911C2×D4—432no—
912C2×D4—432no—
913C2×D4—431no—
914C2×D4C2×C4×D4312yes—
915C2×D4C2×C4×D4311yescharacteristic
916C22×C4—431no—
917C22×C4—431no—
918C22×C4—431no—
919C22×C4—431no—
920C22×C4—431no—
921C22×C4—432no—
922C22×C4—432no—
923C22×C4—431no—
924C22×C4—431no—
925C22×C4—431no—
926C22×C4—431no—
927C22×C4—431no—
928C22×C4—431no—
929C22×C4—431no—
930C22×C4—431no—
931C22×C4—431no—
932C22×C4—432no—
933C22×C4—432no—
934C22×C4—431no—
935C22×C4—432no—
936C22×C4—862no—
937C22×C4—862no—
938C22×C4—864no—
939C22×C4—864no—
940C22×C4C2×C4×D4311yescharacteristic
941C22×C4C2×C4×D4311yescharacteristic
942C22×C4C23×D4311yescharacteristic
943C22×C4C23×D4312yes—
944M16—24no—
945M16—864no—
946M16—864no—
947M16—864no—
948M16—864no—
949M16—864no—
950C2×C8—22no—
951C2×C8—22no—
952C2×C8—24no—
953C2×C8—431no—
954C2×C8—431no—
955C2×C8—434no—
956C2×C8—434no—
957C2×C8—431no—
958C2×C8—431no—
959C2×C8—432no—
960C2×C8—432no—
961C2×C8—862no—
962C2×C8—862no—
963C2×C8—864no—
964C2×C8—862no—
965C2×C8—862no—
966C2×C8—862no—
967C2×C8—862no—
968C2×C8—864no—
969C2×C8—862no—
970C2×C8—862no—
971C2×C8—864no—
972C2×C8C23×D4311yescharacteristic
973C2×C8C23×D4311yescharacteristic
974C2×C8C23×D4312yes—
975C2×C8C23×D4312yes—
976C2×C8C23×D4311yescharacteristic
977C2×C8C23×D4311yescharacteristic
978C4⋊C4—432no—
979C4⋊C4—432no—
980C4⋊C4—432no—
981C4⋊C4—432no—
982C4⋊C4—431no—
983C4⋊C4—431no—
984C4⋊C4—432no—
985C4⋊C4—432no—
986C4⋊C4—432no—
987C4⋊C4—432no—
988C4⋊C4—432no—
989C4⋊C4—432no—
990C4⋊C4—432no—
991C4⋊C4—432no—
992C4⋊C4C2×C4×D4311yescharacteristic
993C4⋊C4C2×C4×D4312yes—
994C4⋊C4C2×C4×D4311yescharacteristic
995C4⋊C4C2×C4×D4312yes—
996C4⋊C4C2×C4×D4312yes—
997C4⋊C4C2×C4×D4312yes—
998C22⋊C4—432no—
999C22⋊C4—432no—
1000C22⋊C4—432no—
1001C22⋊C4—432no—
1002C22⋊C4—432no—
1003C22⋊C4—432no—
1004C22⋊C4—432no—
1005C22⋊C4—432no—
1006C22⋊C4—432no—
1007C22⋊C4—432no—
1008C22⋊C4—432no—
1009C22⋊C4—432no—
1010C22⋊C4—432no—
1011C22⋊C4C2×C4×D4312yes—
1012C22⋊C4C2×C4×D4312yes—
1013C22⋊C4C2×C4×D4312yes—
1014C22⋊C4C2×C4×D4312yes—
1015C22⋊C4C2×C4×D4312yes—
1016C42—431no—
1017C42—431no—
1018C42—431no—
1019C42—431no—
1020C42—431no—
1021C42—431no—
1022C42—431no—
1023C42—431no—
1024C42—431no—
1025C42—431no—
1026C42—432no—
1027C42—432no—
1028C42—432no—
1029C42—432no—
1030C42—431no—
1031C42—431no—
1032C42—432no—
1033C42C2×C4×D4311yescharacteristic
1034C42C2×C4×D4311yescharacteristic
1035C42C23×D4311yescharacteristic
1036C42C23×D4311yescharacteristic
1037C42C23×D4312yes—
1038C23—431no—
1039C23—431no—
1040C23—432no—
1041C23—862no—
1042C23—862no—
1043C23—862no—
1044C23C22×C4×D4312yes—
1045C23C22×C4×D4311yescharacteristic
1046Q8—22no—
1047Q8—864no—
1048Q8—864no—
1049Q8—862no—
1050D4—24no—
1051D4—22no—
1052D4—864no—
1053D4—864no—
1054D4—864no—
1055D4—864no—
1056D4—864no—
1057D4—864no—
1058D4—864no—
1059D4—862no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—434no—
1067C2×C4—431no—
1068C2×C4—431no—
1069C2×C4—431no—
1070C2×C4—431no—
1071C2×C4—434no—
1072C2×C4—432no—
1073C2×C4—432no—
1074C2×C4—431no—
1075C2×C4—431no—
1076C2×C4—432no—
1077C2×C4—432no—
1078C2×C4—432no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—864no—
1086C2×C4—864no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—864no—
1092C2×C4—864no—
1093C2×C4—862no—
1094C2×C4—861no—
1095C2×C4—861no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4C22×C4×D4311yescharacteristic
1099C2×C4C22×C4×D4311yescharacteristic
1100C2×C4C22×C4×D4311yescharacteristic
1101C2×C4C22×C4×D4311yescharacteristic
1102C2×C4C22×C4×D4312yes—
1103C2×C4C22×C4×D4312yes—
1104C2×C4C22×C4×D4312yes—
1105C2×C4C22×C4×D4311yescharacteristic
1106C2×C4C24×D4311yescharacteristic
1107C8—21no—
1108C8—21no—
1109C8—22no—
1110C8—22no—
1111C8—432no—
1112C8—432no—
1113C8—861no—
1114C8—861no—
1115C8—862no—
1116C8—862no—
1117C8#41×D4312yes—
1118C8#41×D4312yes—
1119C22—21no—
1120C22—21no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—432no—
1125C22—432no—
1126C22—868no—
1127C22—861no—
1128C22—861no—
1129C22—861no—
1130C22—861no—
1131C22—862no—
1132C22—862no—
1133C22—862no—
1134C22#131×D4312yes—
1135C22C23×C4×D4311yescharacteristic
1136C4—21no—
1137C4—21no—
1138C4—21no—
1139C4—22no—
1140C4—22no—
1141C4—21no—
1142C4—22no—
1143C4—432no—
1144C4—432no—
1145C4—432no—
1146C4—432no—
1147C4—861no—
1148C4—862no—
1149C4—862no—
1150C4—861no—
1151C4—862no—
1152C4#131×D4312yes—
1153C4C2×#41×D4311yescharacteristic
1154C4C2×#41×D4311yescharacteristic
1155C2—22no—
1156C2—42no—
1157C2—862no—
1158C2—862no—
1159C2—1722no—
1160C2C4×#41×D4311yescharacteristic
1161C2C2×#131×D4311yescharacteristic
1162C2C2×#131×D4311yescharacteristic
subgroupG/H
centerC2×C8C23×D43
commutator, socleC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC43×#2966C2
prime radical#19147889C2
cosocleC2×C4×C43C25
hypercenter#2966D43
hypocenterC43#60204
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #19143571C2semidirect
3. #19143570C2semidirect
4. #19143568C2semidirect
5. #19143566C2semidirect
6. #19143564C2semidirect
7. #19143560C2semidirect
8. #19143558C2semidirect
9. #19143555C2semidirect
10. C8×#10621902C2semidirect
11. C8×#10621900C2semidirect
12. C8×#10621900C2semidirect
13. #19143526C2semidirect
14. #19143524C2semidirect
15. #19143304C2semidirect
16. #19143302C2semidirect
17. #19143286C2semidirect
18. #19143284C2semidirect
19. #19143236C2semidirect
20. #19143225C2semidirect
21. #19143017C2semidirect
22. C2×C4×C8×D43C2semidirect
23. C43×#2966C2semidirect
50. #14583030C22semidirect
51. #14583029C22semidirect
52. #14583028C22semidirect
53. #14583027C22semidirect
54. #14583026C22semidirect
55. Q8×C43⋊C8C22semidirect
56. C8×Dic86C22semidirect
57. C8×Dic86C22semidirect
58. #14583023C22semidirect
59. #14583023C22semidirect
60. #14582978C22semidirect
61. #14582977C22semidirect
62. #14582976C22semidirect
63. #14582975C22semidirect
64. #14582974C22semidirect
73. C8×D172C22semidirect
75. D4×C43⋊C8C22semidirect
77. #14582964C22semidirect
80. C8×C22⋊D43C22semidirect
83. (C22⋊D43)⋊C8C22semidirect
84. #14582961C22semidirect
85. #14582960C22semidirect
86. #14582958C22semidirect
91. #14582951C22semidirect
92. #14582951C22semidirect
94. #14582949C22semidirect
95. #14582949C22semidirect
104. #14582856C22semidirect
105. #14582855C22semidirect
107. #14582853C22semidirect
109. #14582851C22semidirect
110. M16×Dic43C22semidirect
114. C2×C8×Dic43C22semidirect
123. C4×C8×D43C22semidirect
125. C43×#446C22semidirect
126. C8×Q8×C43C22semidirect
127. C43×#436C22semidirect
130. C8×D4×C43C22semidirect
131. C43×#433C22semidirect
133. C43×#405C22semidirect
454. C8×D43#41semidirect
455. C8×D43#41semidirect
491. C2×Dic43#131semidirect
519. C4×D43#131semidirect
580. #2966D43semidirect
637. #446C2×D43semidirect
643. C8×Q8C2×D43semidirect
649. #436C2×D43semidirect
671. C8×D4C2×D43semidirect
675. #433C2×D43semidirect
698. #405C2×D43semidirect
716. C43#60204semidirect

Maximal subgroups

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

subgroupindex
#191478892
#191435712
#191435702
#191435682
#191435662
#191435642
#191435602
#191435582
#191435552
C8×#106219022
C8×#106219002
#191435262
#191435242
#191433042
#191433022
#191432862
#191432842
#191432362
#191432252
#191430172
C2×C4×C8×D432
C43×#29662
#6020443