Finite Group Databasebeta

← #25961257

Subgroups — #25961257

Order 11008.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148162C211yesmaximal, characteristic
2#19143608C212yesmaximal, complemented
3#19143598C212yesmaximal, complemented
4#19143588C212yesmaximal, complemented
5#19143588C212yesmaximal, complemented
6#19143579C212yesmaximal, complemented
7#19143579C212yesmaximal, complemented
8#19143572C212yesmaximal, complemented
9#19143560C212yesmaximal, complemented
10#19143536C211yesmaximal, characteristic, complemented
11M16×D172C211yesmaximal, characteristic, complemented
12#19143323C211yesmaximal, characteristic, complemented
13#19143323C211yesmaximal, characteristic, complemented
14#19143297C211yesmaximal, characteristic, complemented
15#19143288C211yesmaximal, characteristic, complemented
16C2×#14582969C211yesmaximal, characteristic, complemented
17#19143260C211yesmaximal, characteristic, complemented
18#19143252C211yesmaximal, characteristic, complemented
19#19143252C211yesmaximal, characteristic, complemented
20#19143024C211yesmaximal, characteristic, complemented
21#19143011C211yesmaximal, characteristic, complemented
22#405×D43C211yesmaximal, characteristic, complemented
23C43×#2962C211yesmaximal, characteristic, complemented
24C2×#13063333C2211yescharacteristic
25C2×#13063333C2211yescharacteristic
26C22×#10621872C2211yescharacteristic
27C2×M16×D43C2211yescharacteristic
28C2×M16×D43C2211yescharacteristic
29C22×C8×D43C2211yescharacteristic
30#14583623C411yescharacteristic
31#14583615C411yescharacteristic
32#14583610C411yescharacteristic
33#14583602C411yescharacteristic
34#14583602C411yescharacteristic
35#14583591C412yes—
36#14583587C411yescharacteristic
37#14583587C411yescharacteristic
38#14583576C412yes—
39#14583576C412yes—
40#14583552C411yescharacteristic
41#14583540C412yes—
42#14583436C2212yes—
43#14583436C2212yes—
44#14583436C2212yes—
45#14583411C2211yescharacteristic
46#14583411C2211yescharacteristic
47C4×#10621902C2212yes—
48C4×#10621898C2211yescharacteristic
49C2×C4×D172C2211yescharacteristic
50#117×D43C2211yescharacteristic
51#117×D43C2211yescharacteristic
52#14583030C2212yescomplemented
53#14583030C2212yescomplemented
54#14583030C2212yescomplemented
55#14583030C2212yescomplemented
56#14582978C2212yes—
57#14582978C2212yescomplemented
58#14582978C2212yescomplemented
59#14582976C2212yescomplemented
60#14582976C2212yescomplemented
61#14582972C2212yes—
62#14582972C2212yes—
63#14582972C2212yescomplemented
64#14582972C2212yescomplemented
65#14582972C2212yescomplemented
66#14582972C2212yescomplemented
67#14582969C2211yescharacteristic
68#14582969C2211yescharacteristic
69#14582969C2211yescharacteristic
70#14582969C2211yescharacteristic
71#14582969C2211yescharacteristic
72#14582969C2211yescharacteristic
73#14582969C2211yescharacteristic
74#14582969C2211yescharacteristic
75#14582969C2212yescomplemented
76#14582969C2212yescomplemented
77#14582969C2212yescomplemented
78#14582969C2212yescomplemented
79C8×D172C2212yes—
80C8×D172C2212yescomplemented
81C8×D172C2212yescomplemented
82#14582964C2212yescomplemented
83#14582964C2212yescomplemented
84#14582959C2212yescomplemented
85#14582959C2212yescomplemented
86#14582959C2212yescomplemented
87#14582959C2212yescomplemented
88#14582959C2212yescomplemented
89#14582959C2212yescomplemented
90#14582955C2212yescomplemented
91#14582955C2212yescomplemented
92#14582955C2212yescomplemented
93#14582951C2212yescomplemented
94#14582951C2212yescomplemented
95#14582951C2212yescomplemented
96#14582926C2211yescharacteristic
97#14582926C2211yescharacteristic
98#14582923C2211yescharacteristic
99#14582865C2211yescharacteristic
100#14582865C2211yescharacteristic
101#14582862C2211yescharacteristic
102#14582862C2211yescharacteristic
103C2×(C2×D43)⋊C8C2211yescharacteristic
104C2×(C2×D43)⋊C8C2211yescharacteristic
105#14582857C2211yescharacteristic
106#14582857C2211yescharacteristic
107#14582856C2212yescomplemented
108#14582856C2212yescomplemented
109#14582855C2211yescharacteristic
110#14582855C2211yescharacteristic
111#14582854C2211yescharacteristic
112#14582854C2211yescharacteristic
113#14582853C2212yescomplemented
114#14582853C2212yescomplemented
115#14582853C2212yescomplemented
116#14582853C2212yescomplemented
117#14582851C2212yescomplemented
118#14582851C2212yescomplemented
119C4×#10621872C2212yescomplemented
120C2×#13063236C2211yescharacteristic
121#97×D43C2212yescomplemented
122#97×D43C2212yescomplemented
123C4×C8×D43C2212yescomplemented
124C43×#533C2211yescharacteristic
125C43×#446C2212yescomplemented
126C43×#446C2212yescomplemented
127C43×#446C2212yescomplemented
128C8×Q8×C43C2212yescomplemented
129C43×#424C2211yescharacteristic
130C43×#424C2211yescharacteristic
131C2×C4⋊C8×C43C2211yescharacteristic
132C43×#405C2211yescharacteristic
133C43×#405C2211yescharacteristic
134C4×M16×C43C2211yescharacteristic
135C2×#10621902C2×C412yes—
136C2×#10621898C2311yescharacteristic
137C22×D172C2×C411yescharacteristic
138C22×C4×D43C2311yescharacteristic
139C22×C4×D43C2311yescharacteristic
140#13063333—24no—
141#13063333—24no—
142C2×#10621877C2311yescharacteristic
143C2×#10621877C2311yescharacteristic
144C2×#10621872—24no—
145C2×#10621872C2311yescharacteristic
146C2×#10621872C2312yes—
147C2×#10621872C2311yescharacteristic
148C2×#10621872C2312yes—
149C2×#10621872C2312yes—
150C2×#10621872C2311yescharacteristic
151C2×#10621872C2312yes—
152C2×#10621872C2311yescharacteristic
153M16×D43—24no—
154M16×D43—24no—
155C22×C43⋊C8C2311yescharacteristic
156C22×C43⋊C8C2311yescharacteristic
157C2×C8×D43—24no—
158C2×C8×D43C2311yescharacteristic
159C2×C8×D43C2312yes—
160C2×C8×D43C2311yescharacteristic
161C2×C8×D43C2312yes—
162C2×C8×D43C2312yes—
163C2×C8×D43C2311yescharacteristic
164C2×C8×D43C2312yes—
165C2×C8×D43C2311yescharacteristic
166#13063320C2×C412yes—
167#13063320C2×C412yes—
168#13063320C2×C412yes—
169#13063320C2×C412yes—
170#13063320C2×C412yes—
171#13063320C2×C412yes—
172#13063316C2×C412yes—
173#13063316C2×C412yes—
174#13063316C2×C412yes—
175#13063314C2×C412yes—
176#13063314C2×C412yes—
177#13063314C2×C412yes—
178#13063310C2×C412yes—
179#13063310C2×C412yes—
180#13063310C2×C412yes—
181#13063310C2×C412yes—
182#13063310C2×C412yes—
183#13063310C2×C412yes—
184#13063309C2×C412yes—
185#13063309C2×C412yes—
186#13063305C2×C411yescharacteristic
187#13063305C2×C411yescharacteristic
188#13063305C2×C411yescharacteristic
189#13063305C2×C411yescharacteristic
190#13063301C2×C412yes—
191#13063301C2×C412yes—
192#13063301C2×C412yes—
193#13063300C2×C411yescharacteristic
194#13063300C2×C411yescharacteristic
195#13063300C2×C411yescharacteristic
196#13063300C2×C411yescharacteristic
197#13063300C2×C412yes—
198#13063300C2×C412yes—
199#13063300C2×C412yes—
200#13063295C2×C412yes—
201#13063295C2×C412yes—
202Q8×Dic43C2×C412yes—
203C4×Dic86C2×C411yescharacteristic
204C4×Dic86C2×C411yescharacteristic
205C4×D172C2×C411yescharacteristic
206C4×D172C2×C411yescharacteristic
207C4×D172C2×C411yescharacteristic
208C4×D172C2×C411yescharacteristic
209C4×D172C2×C411yescharacteristic
210C4×D172C2×C411yescharacteristic
211C4×D172C2311yescharacteristic
212C4×D172C2311yescharacteristic
213C4×D172C2311yescharacteristic
214C4×D172C2311yescharacteristic
215C4×D172C2312yes—
216C4×D172C2312yes—
217C4×D172C2312yes—
218C4×D172C2312yes—
219#13063287C2×C412yes—
220#13063287C2×C412yes—
221#13063287C2×C412yes—
222C4×C22⋊D43C2×C412yes—
223C4×C22⋊D43C2×C412yes—
224#13063284C2311yescharacteristic
225#13063283C2×C412yes—
226#13063283C2×C412yes—
227#13063283C2×C411yescharacteristic
228#13063283C2×C411yescharacteristic
229#13063283C2×C412yes—
230#13063283C2×C411yescharacteristic
231#13063283C2×C411yescharacteristic
232#13063282C2312yes—
233#13063282C2312yes—
234#13063282C2312yes—
235#13063281C2×C412yes—
236#13063281C2×C412yes—
237C2×C4⋊Dic43C2×C411yescharacteristic
238C4⋊C4×D43C2×C411yescharacteristic
239C4⋊C4×D43C2×C411yescharacteristic
240C4⋊C4×D43C2×C411yescharacteristic
241C4⋊C4×D43C2×C411yescharacteristic
242C2×(C2×D43)⋊C4C2×C411yescharacteristic
243C2×(C2×D43)⋊C4C2×C411yescharacteristic
244C22⋊C4×D43C2×C412yes—
245C22⋊C4×D43C2×C412yes—
246C42×D43C2312yes—
247C42×D43C2312yes—
248C42×D43C2312yes—
249C4⋊(C43⋊C8)C2312yes—
250C4⋊(C43⋊C8)C2312yes—
251C4⋊(C43⋊C8)C2312yes—
252C4⋊(C43⋊C8)C2312yes—
253C4⋊(C43⋊C8)C2312yes—
254C4⋊(C43⋊C8)C2312yes—
255(C2×D43)⋊C8C2311yescharacteristic
256(C2×D43)⋊C8C2311yescharacteristic
257(C2×D43)⋊C8C2311yescharacteristic
258(C2×D43)⋊C8C2311yescharacteristic
259(C2×D43)⋊C8C2311yescharacteristic
260(C2×D43)⋊C8C2311yescharacteristic
261(C2×D43)⋊C8C2311yescharacteristic
262(C2×D43)⋊C8C2311yescharacteristic
263(C2×D43)⋊C8C2312yes—
264(C2×D43)⋊C8C2312yes—
265(C2×D43)⋊C8C2312yes—
266(C2×D43)⋊C8C2312yes—
267(C2×D43)⋊C8C2312yes—
268(C2×D43)⋊C8C2312yes—
269(C2×D43)⋊C8C2312yes—
270(C2×D43)⋊C8C2312yes—
271#13063236C2311yescharacteristic
272#13063236C2312yes—
273#13063236C2311yescharacteristic
274#13063236C2311yescharacteristic
275#13063236C2311yescharacteristic
276#13063236C2312yes—
277#13063235C2312yes—
278#13063235C2312yes—
279#13063235C2312yes—
280#13063235C2312yes—
281C4×C43⋊C8C2312yes—
282C4×C43⋊C8C2312yes—
283C8×Dic43C2312yes—
284C8×Dic43C2312yes—
285C8×Dic43C2312yes—
286C8×Dic43C2312yes—
287C2×M16×C43C2311yescharacteristic
288C2×M16×C43C2311yescharacteristic
289C22×C8×C43C2311yescharacteristic
290C22×C8×C43C2311yescharacteristic
291C4⋊Q8×C43C2×C411yescharacteristic
292C4⋊Q8×C43C2×C411yescharacteristic
293#125×C43C2×C411yescharacteristic
294#125×C43C2×C411yescharacteristic
295C22⋊Q8×C43C2×C412yes—
296C22⋊Q8×C43C2×C412yes—
297C4×Q8×C43C2312yes—
298C4×Q8×C43C2312yes—
299#117×C43C2311yescharacteristic
300#117×C43C2311yescharacteristic
301C2×C42×C43C2311yescharacteristic
302C4⋊C8×C43C2311yescharacteristic
303C4⋊C8×C43C2312yes—
304C4⋊C8×C43C2312yes—
305C4⋊C8×C43C2311yescharacteristic
306C4⋊C8×C43C2312yes—
307C4⋊C8×C43C2312yes—
308C4⋊C8×C43C2311yescharacteristic
309C4⋊C8×C43C2311yescharacteristic
310#97×C43C2312yes—
311#97×C43C2312yes—
312#97×C43C2312yes—
313C4×C8×C43C2312yes—
314C4×C8×C43C2312yes—
315C4×C8×C43C2312yes—
316C23×D43C22×C411yescharacteristic
317C23×D43C22×C411yescharacteristic
318C2×Q8×C43C22×C412yes—
319C2×Q8×C43C22×C412yes—
320C22×C4×C43C22×C411yescharacteristic
321C22×C4×C43C22×C411yescharacteristic
322C22×C4×C43C2411yescharacteristic
323C2×C22⋊D43C22×C412yes—
324C22×Dic43C22×C411yescharacteristic
325C22×Dic43C22×C411yescharacteristic
326#10621902—44no—
327#10621898—22no—
328#10621898—22no—
329C2×D172—42no—
330C2×D172C22×C411yescharacteristic
331C2×D172C22×C412yes—
332C2×D172C22×C411yescharacteristic
333C2×D172C22×C411yescharacteristic
334C2×D172C22×C412yes—
335C2×D172C22×C411yescharacteristic
336C2×D172C22×C411yescharacteristic
337C2×D172C22×C412yes—
338C2×D172C22×C412yes—
339C2×C4×D43—22no—
340C2×C4×D43—22no—
341C2×C4×D43—22no—
342C2×C4×D43—22no—
343C2×C4×D43C22×C412yes—
344C2×C4×D43C22×C411yescharacteristic
345C2×C4×D43C22×C411yescharacteristic
346C2×C4×D43C22×C411yescharacteristic
347C2×C4×D43C22×C411yescharacteristic
348C2×C4×D43C22×C412yes—
349C2×C4×D43C22×C412yes—
350C2×C4×D43C22×C412yes—
351C2×C4×D43C22×C412yes—
352C2×C4×D43C22×C412yes—
353C2×C4×D43C2411yescharacteristic
354C2×C4×D43C2411yescharacteristic
355C2×C4×D43C2412yes—
356C2×C4×D43C2411yescharacteristic
357C2×C4×D43C2411yescharacteristic
358C2×Dic86C22×C411yescharacteristic
359M16×C43—22no—
360M16×C43#4114yescomplemented
361C2×C8×C43—22no—
362C2×C8×C43—22no—
363C2×C8×C43C2411yescharacteristic
364C2×C8×C43C2411yescharacteristic
365C2×C8×C43C2412yes—
366C2×C8×C43C2411yescharacteristic
367C2×C8×C43C2411yescharacteristic
368C2×C8×C43C2412yes—
369C4⋊C4×C43C22×C411yescharacteristic
370C4⋊C4×C43C22×C411yescharacteristic
371C4⋊C4×C43C22×C411yescharacteristic
372C4⋊C4×C43C22×C411yescharacteristic
373C4⋊C4×C43C22×C412yes—
374C4⋊C4×C43C22×C412yes—
375C4⋊C4×C43C22×C412yes—
376C4⋊C4×C43C22×C412yes—
377C4⋊C4×C43C22×C412yes—
378C4⋊C4×C43C22×C412yes—
379C22⋊C4×C43C22×C412yes—
380C22⋊C4×C43C22×C412yes—
381C42×C43C22×C411yescharacteristic
382C42×C43C22×C411yescharacteristic
383C42×C43C2411yescharacteristic
384C42×C43C2412yes—
385C42×C43C2412yes—
386C42×C43C2411yescharacteristic
387C22⋊Dic43C22×C412yes—
388(C2×D43)⋊C4C22×C412yes—
389(C2×D43)⋊C4C22×C412yes—
390(C2×D43)⋊C4C22×C412yes—
391(C2×D43)⋊C4C22×C412yes—
392(C2×D43)⋊C4C22×C411yescharacteristic
393(C2×D43)⋊C4C22×C411yescharacteristic
394(C2×D43)⋊C4C22×C411yescharacteristic
395(C2×D43)⋊C4C22×C411yescharacteristic
396(C2×D43)⋊C4C22×C411yescharacteristic
397(C2×D43)⋊C4C22×C411yescharacteristic
398(C2×D43)⋊C4C22×C411yescharacteristic
399(C2×D43)⋊C4C22×C411yescharacteristic
400(C2×D43)⋊C4C22×C412yes—
401(C2×D43)⋊C4C22×C412yes—
402(C2×D43)⋊C4C22×C412yes—
403(C2×D43)⋊C4C22×C412yes—
404(C2×D43)⋊C4C22×C412yes—
405(C2×D43)⋊C4C22×C412yes—
406(C2×D43)⋊C4C22×C412yes—
407(C2×D43)⋊C4C22×C412yes—
408(C2×D43)⋊C4C22×C412yes—
409(C2×D43)⋊C4C22×C412yes—
410C4⋊Dic43C22×C411yescharacteristic
411C4⋊Dic43C22×C411yescharacteristic
412C4⋊Dic43C22×C411yescharacteristic
413C4⋊Dic43C22×C411yescharacteristic
414C4⋊Dic43C22×C411yescharacteristic
415C4⋊Dic43C22×C411yescharacteristic
416C4⋊Dic43C22×C412yes—
417C4⋊Dic43C22×C412yes—
418C4⋊Dic43C22×C412yes—
419C4⋊Dic43C22×C412yes—
420Dic43⋊C4C22×C412yes—
421Dic43⋊C4C22×C412yes—
422Dic43⋊C4C22×C412yes—
423Dic43⋊C4C22×C412yes—
424Dic43⋊C4C22×C412yes—
425Dic43⋊C4C22×C412yes—
426C4×Dic43C22×C412yes—
427C4×Dic43C22×C412yes—
428C4×Dic43C22×C412yes—
429C4×Dic43C22×C412yes—
430C4×Dic43C22×C412yes—
431C4×Dic43C22×C412yes—
432C4×Dic43C2412yes—
433#10621877—22no—
434#10621877—22no—
435C2×C43⋊C8—22no—
436C2×C43⋊C8#4114yescomplemented
437C2×C43⋊C8C2411yescharacteristic
438C2×C43⋊C8C2412yes—
439C2×C43⋊C8C2412yes—
440C2×C43⋊C8C2411yescharacteristic
441C2×C43⋊C8C2411yescharacteristic
442C2×C43⋊C8C2411yescharacteristic
443#10621872—24no—
444#10621872—24no—
445#10621872—24no—
446#10621872—22no—
447#10621872—22no—
448#10621872—22no—
449#10621872—22no—
450#10621872—24no—
451C8×D43—24no—
452C8×D43—24no—
453C8×D43—24no—
454C8×D43—22no—
455C8×D43—22no—
456C8×D43—22no—
457C8×D43—22no—
458C8×D43—24no—
459C23×C43C23×C411yescharacteristic
460C22×D43—22no—
461C22×D43—22no—
462C22×D43—22no—
463C22×D43—41no—
464C22×D43—41no—
465C22×D43—41no—
466C22×D43C23×C411yescharacteristic
467C22×D43C23×C411yescharacteristic
468C22×D43C23×C412yes—
469C22×D43C23×C411yescharacteristic
470C22×D43C23×C411yescharacteristic
471Q8×C43—42no—
472Q8×C43—42no—
473C2×C4×C43—41no—
474C2×C4×C43—41no—
475C2×C4×C43C23×C411yescharacteristic
476C2×C4×C43C23×C411yescharacteristic
477C2×C4×C43C23×C412yes—
478C2×C4×C43C23×C412yes—
479C2×C4×C43C23×C412yes—
480C2×C4×C43C23×C412yes—
481C2×C4×C43C23×C411yescharacteristic
482C2×C4×C43C23×C411yescharacteristic
483C2×C4×C43C23×C411yescharacteristic
484C2×C4×C43C2×#4112yes—
485C2×C4×C43C2×#4112yes—
486C2×C4×C43C2511yescharacteristic
487C22⋊D43—24no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43C23×C411yescharacteristic
491C2×Dic43C23×C411yescharacteristic
492C2×Dic43C23×C412yes—
493C2×Dic43C23×C412yes—
494C2×Dic43C23×C412yes—
495C2×Dic43C23×C411yescharacteristic
496C2×Dic43C23×C411yescharacteristic
497D172—22no—
498D172—22no—
499D172—24no—
500D172—22no—
501D172—41no—
502D172—41no—
503D172—42no—
504D172—42no—
505D172—42no—
506C4×D43—24no—
507C4×D43—22no—
508C4×D43—22no—
509C4×D43—22no—
510C4×D43—22no—
511C4×D43—21no—
512C4×D43—21no—
513C4×D43—21no—
514C4×D43—21no—
515C4×D43—22no—
516C4×D43—22no—
517C4×D43—21no—
518C4×D43—21no—
519C4×D43—21no—
520C4×D43—21no—
521C4×D43—42no—
522C4×D43—42no—
523C4×D43—42no—
524C4×D43—42no—
525C4×D43—42no—
526Dic86—22no—
527C8×C43—21no—
528C8×C43—21no—
529C8×C43—22no—
530C8×C43—21no—
531C8×C43—21no—
532C8×C43C2×#4114yes—
533C43⋊C8—21no—
534C43⋊C8—22no—
535C43⋊C8—22no—
536C43⋊C8—21no—
537C43⋊C8C2×#4112yes—
538C43⋊C8C2×#4112yes—
539#60216—431nomaximal, Sylow
540C22×C43—21no—
541C22×C43—21no—
542C22×C43C4×#4112yes—
543C22×C43C24×C411yescharacteristic
544C2×D43—21no—
545C2×D43—21no—
546C2×D43—21no—
547C2×D43—21no—
548C2×D43—21no—
549C2×D43—22no—
550C2×D43—21no—
551C2×D43—21no—
552C2×D43—21no—
553C2×D43—22no—
554C2×D43—21no—
555C2×D43—21no—
556C2×D43—21no—
557C2×D43—22no—
558C2×D43—44no—
559C2×D43—82no—
560C2×D43#56812yes—
561C4×C43—22no—
562C4×C43—21no—
563C4×C43—22no—
564C4×C43—21no—
565C4×C43—21no—
566C4×C43—22no—
567C4×C43—22no—
568C4×C43—21no—
569C4×C43C4×#4112yes—
570C4×C43C22×#4111yescharacteristic
571C4×C43C22×#4111yescharacteristic
572Dic43—22no—
573Dic43—21no—
574Dic43—21no—
575Dic43—21no—
576Dic43—21no—
577Dic43—22no—
578Dic43—22no—
579#3475—431no—
580#2970—432no—
581#2969—432no—
582#2968—432no—
583#2968—432no—
584#2967—432no—
585#2967—432no—
586#2966—432no—
587#2965—432no—
588#2962D4311yescharacteristic, complemented
589#2961—431no—
590D4×M16—431no—
591#2933—431no—
592#2933—431no—
593#2930—431no—
594#2929—431no—
595C2×#435—431no—
596#2925—431no—
597#2924—431no—
598#2924—431no—
599#2875—431no—
600#2873—431no—
601C2×#405—431no—
602C2×C43—22no—
603C2×C43C2×C4×#4111yescharacteristic
604C2×C43C2×#56811yescharacteristic
605C2×C43#357311yescharacteristic
606D43—22no—
607D43—42no—
608D43—41no—
609D43—41no—
610D43—41no—
611C2×#131—431no—
612C2×#131—431no—
613C22×M16—431no—
614C22×M16—431no—
615C22×M16—431no—
616C23×C8—431no—
617#556—431no—
618#555—431no—
619#554—431no—
620#553—431no—
621#553—431no—
622#552—431no—
623#552—431no—
624#552—432no—
625#551—432no—
626#551—432no—
627#547—431no—
628#546—432no—
629#533C2×D4311yescharacteristic
630#529—432no—
631#529—432no—
632#529—432no—
633#525—431no—
634#525—431no—
635C4×#41—432no—
636C4×#41—431no—
637C2×C4×D4—431no—
638C2×#117—431no—
639C2×#117—431no—
640#446—432no—
641#446—432no—
642#446—432no—
643#446—432no—
644#446C2×D4312yescomplemented
645#446C2×D4312yescomplemented
646#446C2×D4312yescomplemented
647C8×Q8C2×D4312yescomplemented
648#436—432no—
649#436—432no—
650#436—432no—
651#436—432no—
652#436—432no—
653#435—431no—
654#435—431no—
655#435—431no—
656#435—431no—
657#435—431no—
658#435—431no—
659#435—431no—
660#435—431no—
661#435—432no—
662#435—432no—
663#435—432no—
664#435—432no—
665#435—432no—
666#435—432no—
667#435—432no—
668#435—432no—
669#435—432no—
670#435—432no—
671C8×D4—432no—
672C8×D4—432no—
673C8×D4—432no—
674C8×D4—432no—
675C8×D4—432no—
676#433—432no—
677#433—432no—
678#433—432no—
679#433—432no—
680#433—432no—
681#433—432no—
682#432—432no—
683#432—432no—
684#432—432no—
685#431—432no—
686#431—432no—
687#431—432no—
688#424—431no—
689#424—431no—
690#424C2×D4311yescharacteristic
691#424C2×D4311yescharacteristic
692#423—431no—
693C2×C4⋊C8C2×D4311yescharacteristic
694#408—431no—
695#408—431no—
696#407—431no—
697#407—431no—
698C2×C22⋊C8—431no—
699C2×C22⋊C8—431no—
700#405—431no—
701#405—431no—
702#405—431no—
703#405—431no—
704#405—431no—
705#405—431no—
706#405—432no—
707#405—432no—
708#405—432no—
709#405—432no—
710#405—432no—
711#405—432no—
712#405C2×D4311yescharacteristic
713#405C2×D4311yescharacteristic
714C4×M16—432no—
715C4×M16—432no—
716C4×M16—432no—
717C4×M16C2×D4311yescharacteristic
718C2×#97—431no—
719C2×#97—432no—
720C2×#97—432no—
721C2×C4×C8—432no—
722C43#6021611yescharacteristic, complemented, Sylow
723C2×#41—432no—
724C2×#41—431no—
725C22×D4—431no—
726C23×C4—431no—
727C23×C4—431no—
728#131—864no—
729#131—864no—
730C2×M16—431no—
731C2×M16—431no—
732C2×M16—431no—
733C2×M16—431no—
734C2×M16—432no—
735C2×M16—431no—
736C2×M16—431no—
737C2×M16—432no—
738C2×M16—432no—
739C2×M16—432no—
740C2×M16—864no—
741C2×M16—864no—
742C2×M16—864no—
743C2×M16C22×D4311yescharacteristic
744C2×M16C22×D4311yescharacteristic
745C22×C8—431no—
746C22×C8—431no—
747C22×C8—431no—
748C22×C8—431no—
749C22×C8—431no—
750C22×C8—431no—
751C22×C8—432no—
752C22×C8—432no—
753C22×C8—432no—
754C22×C8—432no—
755C22×C8—864no—
756C22×C8C22×D4311yescharacteristic
757C22×C8C22×D4311yescharacteristic
758C4⋊Q8C4×D4311yescharacteristic
759C4⋊Q8C4×D4311yescharacteristic
760#126—432no—
761#126—432no—
762#126—432no—
763#126—432no—
764#126—432no—
765#126—432no—
766#125—432no—
767#125—432no—
768#125—432no—
769#125C4×D4311yescharacteristic
770#125C4×D4311yescharacteristic
771#124—432no—
772#124—432no—
773#124—432no—
774#123—432no—
775#123—432no—
776#123—432no—
777#123—432no—
778#123—432no—
779#123—432no—
780#123—432no—
781#123—432no—
782C22⋊Q8—432no—
783C22⋊Q8—432no—
784C22⋊Q8—432no—
785C22⋊Q8—431no—
786C22⋊Q8—431no—
787C22⋊Q8—431no—
788C22⋊Q8—431no—
789C22⋊Q8C4×D4312yes—
790C22⋊Q8C4×D4312yes—
791#121—431no—
792#121—431no—
793#121—431no—
794#121—431no—
795#121—432no—
796#121—432no—
797#121—432no—
798#120—432no—
799#120—432no—
800C4×Q8—432no—
801C4×Q8—431no—
802C4×Q8—431no—
803C4×Q8C22×D4312yes—
804C4×Q8C22×D4312yes—
805C4×D4—432no—
806C4×D4—432no—
807C4×D4—432no—
808C4×D4—432no—
809C4×D4—432no—
810C4×D4—431no—
811C4×D4—431no—
812C4×D4—431no—
813C4×D4—431no—
814C4×D4—431no—
815C4×D4—431no—
816C4×D4—431no—
817C4×D4—431no—
818C4×D4—431no—
819C4×D4—431no—
820C4×D4—432no—
821C4×D4—432no—
822C4×D4—432no—
823C4×D4—432no—
824#117—431no—
825#117—431no—
826#117—431no—
827#117—431no—
828#117—431no—
829#117—432no—
830#117—432no—
831#117—432no—
832#117—432no—
833#117—432no—
834#117—432no—
835#117—432no—
836#117—432no—
837#117C22×D4311yescharacteristic
838#117C22×D4311yescharacteristic
839C2×C4⋊C4—431no—
840C2×C4⋊C4—431no—
841C2×C4⋊C4—431no—
842C2×C4⋊C4—431no—
843C2×C4⋊C4—431no—
844C2×C22⋊C4—431no—
845C2×C22⋊C4—431no—
846C2×C22⋊C4—432no—
847C2×C22⋊C4—432no—
848C2×C42—432no—
849C2×C42—432no—
850C2×C42—432no—
851C2×C42C22×D4311yescharacteristic
852C4⋊C8—432no—
853C4⋊C8—432no—
854C4⋊C8—432no—
855C4⋊C8—432no—
856C4⋊C8—432no—
857C4⋊C8—432no—
858C4⋊C8C22×D4311yescharacteristic
859C4⋊C8C22×D4311yescharacteristic
860C4⋊C8C22×D4311yescharacteristic
861C4⋊C8C22×D4311yescharacteristic
862C4⋊C8C22×D4312yes—
863C4⋊C8C22×D4312yes—
864C4⋊C8C22×D4312yes—
865C4⋊C8C22×D4312yes—
866C22⋊C8—431no—
867C22⋊C8—431no—
868C22⋊C8—431no—
869C22⋊C8—431no—
870C22⋊C8—431no—
871C22⋊C8—431no—
872C22⋊C8—431no—
873C22⋊C8—431no—
874C22⋊C8—432no—
875C22⋊C8—432no—
876C22⋊C8—432no—
877C22⋊C8—432no—
878C22⋊C8—432no—
879C22⋊C8—432no—
880C22⋊C8—432no—
881C22⋊C8—432no—
882#97—432no—
883#97—432no—
884#97—432no—
885#97—432no—
886#97—431no—
887#97—431no—
888#97—432no—
889#97—431no—
890#97—431no—
891#97—432no—
892#97C22×D4312yes—
893#97C22×D4312yes—
894#97C22×D4312yes—
895C4×C8—432no—
896C4×C8—432no—
897C4×C8—432no—
898C4×C8—432no—
899C4×C8—432no—
900C4×C8—432no—
901C4×C8C22×D4312yes—
902C4×C8C22×D4312yes—
903C4×C8C22×D4312yes—
904C24—431no—
905C24—431no—
906#41—862no—
907#41—862no—
908#41—1724no—
909C2×Q8—431no—
910C2×Q8C2×C4×D4312yes—
911C2×Q8C2×C4×D4312yes—
912C2×D4—432no—
913C2×D4—431no—
914C2×D4—432no—
915C2×D4—431no—
916C2×D4—431no—
917C2×D4—432no—
918C2×D4—431no—
919C2×D4—431no—
920C2×D4—432no—
921C2×D4—432no—
922C2×D4—1722no—
923C22×C4—431no—
924C22×C4—431no—
925C22×C4—432no—
926C22×C4—431no—
927C22×C4—431no—
928C22×C4—431no—
929C22×C4—431no—
930C22×C4—431no—
931C22×C4—431no—
932C22×C4—432no—
933C22×C4—431no—
934C22×C4—431no—
935C22×C4—432no—
936C22×C4—432no—
937C22×C4—432no—
938C22×C4—432no—
939C22×C4—432no—
940C22×C4—862no—
941C22×C4—862no—
942C22×C4—862no—
943C22×C4—862no—
944C22×C4C2×C4×D4311yescharacteristic
945C22×C4C2×C4×D4311yescharacteristic
946C22×C4C23×D4311yescharacteristic
947M16—22no—
948M16—862no—
949M16—862no—
950M16—862no—
951M16—862no—
952M16—864no—
953M16—862no—
954M16—862no—
955M16—864no—
956M16—864no—
957M16—864no—
958M16#1062190214yescomplemented
959C2×C8—22no—
960C2×C8—22no—
961C2×C8—434no—
962C2×C8—431no—
963C2×C8—431no—
964C2×C8—432no—
965C2×C8—431no—
966C2×C8—432no—
967C2×C8—431no—
968C2×C8—862no—
969C2×C8—862no—
970C2×C8—862no—
971C2×C8—862no—
972C2×C8—864no—
973C2×C8—862no—
974C2×C8—864no—
975C2×C8—864no—
976C2×C8—864no—
977C2×C8C23×D4311yescharacteristic
978C2×C8C23×D4311yescharacteristic
979C2×C8C23×D4312yes—
980C2×C8C23×D4311yescharacteristic
981C2×C8C23×D4311yescharacteristic
982C2×C8C23×D4312yes—
983C4⋊C4—431no—
984C4⋊C4—431no—
985C4⋊C4—431no—
986C4⋊C4—432no—
987C4⋊C4—432no—
988C4⋊C4—432no—
989C4⋊C4—432no—
990C4⋊C4—431no—
991C4⋊C4—431no—
992C4⋊C4—431no—
993C4⋊C4—432no—
994C4⋊C4—432no—
995C4⋊C4—432no—
996C4⋊C4—432no—
997C4⋊C4—432no—
998C4⋊C4—432no—
999C4⋊C4C2×C4×D4311yescharacteristic
1000C4⋊C4C2×C4×D4311yescharacteristic
1001C4⋊C4C2×C4×D4311yescharacteristic
1002C4⋊C4C2×C4×D4311yescharacteristic
1003C4⋊C4C2×C4×D4312yes—
1004C4⋊C4C2×C4×D4312yes—
1005C4⋊C4C2×C4×D4312yes—
1006C4⋊C4C2×C4×D4312yes—
1007C4⋊C4C2×C4×D4312yes—
1008C4⋊C4C2×C4×D4312yes—
1009C22⋊C4—432no—
1010C22⋊C4—431no—
1011C22⋊C4—431no—
1012C22⋊C4—432no—
1013C22⋊C4—432no—
1014C22⋊C4—432no—
1015C22⋊C4—432no—
1016C22⋊C4—431no—
1017C22⋊C4—431no—
1018C22⋊C4—431no—
1019C22⋊C4—431no—
1020C22⋊C4—431no—
1021C22⋊C4—431no—
1022C22⋊C4—432no—
1023C22⋊C4—432no—
1024C22⋊C4—432no—
1025C22⋊C4—432no—
1026C22⋊C4—432no—
1027C22⋊C4—432no—
1028C22⋊C4—432no—
1029C22⋊C4—432no—
1030C22⋊C4—432no—
1031C22⋊C4—432no—
1032C22⋊C4C2×C4×D4312yes—
1033C22⋊C4C2×C4×D4312yes—
1034C42—432no—
1035C42—432no—
1036C42—432no—
1037C42—432no—
1038C42—432no—
1039C42—432no—
1040C42—432no—
1041C42C2×C4×D4311yescharacteristic
1042C42C2×C4×D4311yescharacteristic
1043C42C23×D4312yes—
1044C42C23×D4312yes—
1045C42C23×D4311yescharacteristic
1046C42C23×D4311yescharacteristic
1047C23—431no—
1048C23—431no—
1049C23—431no—
1050C23—432no—
1051C23—431no—
1052C23—862no—
1053C23—862no—
1054C23—862no—
1055C23—1721no—
1056C23—1721no—
1057C23—1721no—
1058C23C22×C4×D4311yescharacteristic
1059Q8—42no—
1060Q8—42no—
1061Q8—862no—
1062D4—862no—
1063D4—862no—
1064D4—864no—
1065D4—864no—
1066D4—862no—
1067D4—1721no—
1068D4—1721no—
1069D4—1722no—
1070D4—1722no—
1071D4—1722no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—431no—
1075C2×C4—431no—
1076C2×C4—432no—
1077C2×C4—432no—
1078C2×C4—432no—
1079C2×C4—431no—
1080C2×C4—431no—
1081C2×C4—864no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—861no—
1089C2×C4—861no—
1090C2×C4—862no—
1091C2×C4—861no—
1092C2×C4—861no—
1093C2×C4—861no—
1094C2×C4—861no—
1095C2×C4—862no—
1096C2×C4—861no—
1097C2×C4—861no—
1098C2×C4—1722no—
1099C2×C4—1722no—
1100C2×C4—1722no—
1101C2×C4—1722no—
1102C2×C4—1722no—
1103C2×C4C22×C4×D4311yescharacteristic
1104C2×C4C22×C4×D4311yescharacteristic
1105C2×C4C22×C4×D4312yes—
1106C2×C4C22×C4×D4312yes—
1107C2×C4C22×C4×D4312yes—
1108C2×C4C22×C4×D4312yes—
1109C2×C4C22×C4×D4311yescharacteristic
1110C2×C4C22×C4×D4311yescharacteristic
1111C2×C4C22×C4×D4311yescharacteristic
1112C2×C4#41×D4312yes—
1113C2×C4C2×#1062190212yes—
1114C2×C4C24×D4311yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—22no—
1120C8—432no—
1121C8—432no—
1122C8—861no—
1123C8—861no—
1124C8—862no—
1125C8—862no—
1126C8C2×#1062190214yes—
1127C22—21no—
1128C22—21no—
1129C22—432no—
1130C22—861no—
1131C22—861no—
1132C22—861no—
1133C22—861no—
1134C22—861no—
1135C22—862no—
1136C22—861no—
1137C22—862no—
1138C22—861no—
1139C22—861no—
1140C22—861no—
1141C22—862no—
1142C22—861no—
1143C22—861no—
1144C22—3442no—
1145C22—1724no—
1146C22C4×#1062190212yes—
1147C22C23×C4×D4311yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—22no—
1152C4—21no—
1153C4—21no—
1154C4—22no—
1155C4—22no—
1156C4—861no—
1157C4—861no—
1158C4—861no—
1159C4—861no—
1160C4—862no—
1161C4—862no—
1162C4—862no—
1163C4C4×#1062190212yes—
1164C4C2×#41×D4311yescharacteristic
1165C4C22×#1062190211yescharacteristic
1166C2—22no—
1167C2—862no—
1168C2—1721no—
1169C2—1721no—
1170C2—1721no—
1171C2—1722no—
1172C2C2×C4×#1062190211yescharacteristic
1173C2#568×D4311yescharacteristic
1174C2#1914930611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2962C2
prime radical#19148162C2
cosocleC2×C4×C43C25
hypercenter#2962D43
hypocenterC43#60216
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2962

Complements

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

NH ≅ G/Ntype
2. #19143608C2semidirect
3. #19143598C2semidirect
4. #19143588C2semidirect
5. #19143588C2semidirect
6. #19143579C2semidirect
7. #19143579C2semidirect
8. #19143572C2semidirect
9. #19143560C2semidirect
10. #19143536C2semidirect
11. M16×D172C2semidirect
12. #19143323C2semidirect
13. #19143323C2semidirect
14. #19143297C2semidirect
15. #19143288C2semidirect
16. C2×#14582969C2semidirect
17. #19143260C2semidirect
18. #19143252C2semidirect
19. #19143252C2semidirect
20. #19143024C2semidirect
21. #19143011C2semidirect
22. #405×D43C2semidirect
23. C43×#2962C2semidirect
52. #14583030C22semidirect
53. #14583030C22semidirect
54. #14583030C22semidirect
55. #14583030C22semidirect
57. #14582978C22semidirect
58. #14582978C22semidirect
59. #14582976C22semidirect
60. #14582976C22semidirect
63. #14582972C22semidirect
64. #14582972C22semidirect
65. #14582972C22semidirect
66. #14582972C22semidirect
75. #14582969C22semidirect
76. #14582969C22semidirect
77. #14582969C22semidirect
78. #14582969C22semidirect
80. C8×D172C22semidirect
81. C8×D172C22semidirect
82. #14582964C22semidirect
83. #14582964C22semidirect
84. #14582959C22semidirect
85. #14582959C22semidirect
86. #14582959C22semidirect
87. #14582959C22semidirect
88. #14582959C22semidirect
89. #14582959C22semidirect
90. #14582955C22semidirect
91. #14582955C22semidirect
92. #14582955C22semidirect
93. #14582951C22semidirect
94. #14582951C22semidirect
95. #14582951C22semidirect
107. #14582856C22semidirect
108. #14582856C22semidirect
113. #14582853C22semidirect
114. #14582853C22semidirect
115. #14582853C22semidirect
116. #14582853C22semidirect
117. #14582851C22semidirect
118. #14582851C22semidirect
119. C4×#10621872C22semidirect
121. #97×D43C22semidirect
122. #97×D43C22semidirect
123. C4×C8×D43C22semidirect
125. C43×#446C22semidirect
126. C43×#446C22semidirect
127. C43×#446C22semidirect
128. C8×Q8×C43C22semidirect
360. M16×C43#41semidirect
436. C2×C43⋊C8#41semidirect
588. #2962D43semidirect
644. #446C2×D43semidirect
645. #446C2×D43semidirect
646. #446C2×D43semidirect
647. C8×Q8C2×D43semidirect
722. C43#60216semidirect
958. M16#10621902semidirect

Maximal subgroups

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

subgroupindex
#191481622
#191436082
#191435982
#191435882
#191435792
#191435722
#191435602
#191435362
M16×D1722
#191433232
#191432972
#191432882
C2×#145829692
#191432602
#191432522
#191430242
#191430112
#405×D432
C43×#29622
#6021643