Finite Group Databasebeta

← #25102517

Subgroups — #25102517

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063371C211yesmaximal, characteristic, complemented
2C2×#14583068C211yesmaximal, characteristic
3C4×#13063353C211yesmaximal, characteristic, complemented
4C4×#13063350C211yesmaximal, characteristic, complemented
5#19137320C211yesmaximal, characteristic, complemented
6#19134992C211yesmaximal, characteristic, complemented
7#19134972C211yesmaximal, characteristic, complemented
8#19134969C211yesmaximal, characteristic, complemented
9#19134830C211yesmaximal, characteristic, complemented
10#19134829C211yesmaximal, characteristic, complemented
11#19134806C211yesmaximal, characteristic, complemented
12#19134550C211yesmaximal, characteristic, complemented
13#19134406C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C43×#1759C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063353C2211yescharacteristic
18C2×#13063350C2211yescharacteristic
19C2×#13063322C2211yescharacteristic
20#14583382C2211yescharacteristic
21#14583381—21no—
22#14583379—21no—
23#14583379C2211yescharacteristic
24#14583373—21no—
25#14583373C2211yescharacteristic
26#14583371—22no—
27#14583371—21no—
28C4×#10621902—21no—
29C4×#10621898—21no—
30C4×#10621898C2211yescharacteristic
31C2×C4×D172—21no—
32C2×C4×D172C2211yescharacteristic
33C2×C4×D172C2211yescharacteristic, complemented
34C4×D4×D43—22no—
35C4×D4×D43—21no—
36#14583068C418yescomplemented
37#14583012—21no—
38#14583009—21no—
39#14583001—21no—
40#14582997—21no—
41C4×#10621873—21no—
42C4×#10621884—21no—
43C4×D344—21no—
44C4×#10621882—21no—
45#14582942C2211yescharacteristic, complemented
46#14582941C2211yescharacteristic, complemented
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49#14582905C2211yescharacteristic, complemented
50#14582903C2211yescharacteristic, complemented
51#14582901C2211yescharacteristic
52#14582900C2211yescharacteristic
53C2×#13063241C2211yescharacteristic
54C2×#13063241C2211yescharacteristic
55C4×#10621877C2211yescharacteristic, complemented
56#14582801C2211yescharacteristic
57#14582801C2211yescharacteristic, complemented
58#14582777—22no—
59#14582777—22no—
60#14582765C2211yescharacteristic, complemented
61#14582667C2211yescharacteristic, complemented
62#14582667C2211yescharacteristic, complemented
63#14582659C2211yescharacteristic, complemented
64#14582659C2211yescharacteristic, complemented
65C4×#41×C43C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic
68C4×M16×C43C2211yescharacteristic, complemented
69C43×#376C2211yescharacteristic, complemented
70C43×#339C2211yescharacteristic, complemented
71C43×#339C2211yescharacteristic, complemented
72#13063371—22no—
73#13063371—22no—
74#13063371—22no—
75#13063371C2×C414yescomplemented
76C2×#10621902—21no—
77C2×#10621898—21no—
78C2×#10621898C2311yescharacteristic
79C22×D172—21no—
80C22×D172—22no—
81C22×D172C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C2×D4×D43—22no—
84C2×D4×D43—21no—
85C22×C4×D43—22no—
86C22×C4×D43—21no—
87C22×C4×D43D412yes—
88#13063353—22no—
89#13063353C2×C414yescomplemented
90#13063350—22no—
91#13063350C2×C414yescomplemented
92C2×#10621873—21no—
93C2×#10621884—21no—
94C2×D344—21no—
95C2×#10621882—21no—
96C2×#10621877C2311yescharacteristic
97C2×#10621877C2311yescharacteristic
98#13063322—22no—
99#13063322C2×C414yescomplemented
100Q8×Dic43—21no—
101C4×Dic86—21no—
102C4×Dic86D411yescharacteristic, complemented
103C4×Dic86D411yescharacteristic, complemented
104C4×D172—22no—
105C4×D172—22no—
106C4×D172—21no—
107C4×D172—21no—
108C4×D172—21no—
109C4×D172—21no—
110C4×D172—21no—
111C4×D172—21no—
112C4×D172—21no—
113C4×D172—21no—
114C4×D172—21no—
115C4×D172—21no—
116C4×D172—21no—
117C4×D172D411yescharacteristic, complemented
118C4×D172D411yescharacteristic, complemented
119D4×Dic43—21no—
120D4×Dic43—22no—
121#13063287—22no—
122#13063287—22no—
123#13063287—21no—
124#13063287—21no—
125C4×C22⋊D43—22no—
126C4×C22⋊D43—22no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129(C22⋊D43)⋊C4—22no—
130(C22⋊D43)⋊C4—22no—
131(C22⋊D43)⋊C4—22no—
132#13063284—21no—
133#13063284C2311yescharacteristic
134#13063283—22no—
135#13063283—21no—
136#13063282—22no—
137#13063282—21no—
138C2×C4⋊Dic43—21no—
139C2×C4⋊Dic43C2311yescharacteristic
140C2×C4⋊Dic43C2311yescharacteristic
141C4⋊C4×D43—22no—
142C4⋊C4×D43—21no—
143C2×(C2×D43)⋊C4—22no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—22no—
146C2×(C2×D43)⋊C4—22no—
147C2×(C2×D43)⋊C4D412yes—
148C22⋊C4×D43—22no—
149C22⋊C4×D43—22no—
150C22⋊C4×D43—22no—
151C42×D43—22no—
152C42×D43—21no—
153#13063259—21no—
154#13063258—21no—
155#13063257—21no—
156#13063256—21no—
157#13063253—22no—
158#13063253C2×C414yescomplemented
159#13063250—21no—
160#13063249—21no—
161#13063247—21no—
162#13063247—21no—
163#13063247—21no—
164#13063246—21no—
165#13063245—21no—
166#13063245—21no—
167#13063241—22no—
168#13063241C2×C414yescomplemented
169#13063236—21no—
170C4×C43⋊C8—21no—
171C43⋊#95—22no—
172C2×#41×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C2×M16×C43C2311yescharacteristic
175C4×Q8×C43D411yescharacteristic, complemented
176C4×Q8×C43D411yescharacteristic, complemented
177C4×D4×C43—21no—
178C4×D4×C43—21no—
179C4×D4×C43D411yescharacteristic, complemented
180C4×D4×C43D411yescharacteristic, complemented
181#117×C43—21no—
182#117×C43C2311yescharacteristic
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C2×C42×C43C2311yescharacteristic
186C2×C42×C43C2311yescharacteristic
187#104×C43—22no—
188#104×C43C2×C414yescomplemented
189#97×C43—21no—
190C4×C8×C43—21no—
191#95×C43—21no—
192#95×C43—21no—
193C23×D43—22no—
194C23×D43—21no—
195C23×D43C2×D412yes—
196#41×C43—21no—
197#41×C43—21no—
198#41×C43C22×C412yes—
199#41×C43#4112yes—
200C2×Q8×C43C2×D411yescharacteristic
201C2×D4×C43—21no—
202C2×D4×C43C2×D411yescharacteristic
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2411yescharacteristic
211C2×C22⋊D43—22no—
212C2×C22⋊D43—21no—
213C22×Dic43—22no—
214C22×Dic43—21no—
215C22×Dic43C2×D412yes—
216#10621902—24no—
217#10621902—24no—
218D4×D43—24no—
219D4×D43—28no—
220D4×D43—24no—
221D4×D43—28no—
222#10621898—24no—
223#10621898—21no—
224#10621898—21no—
225#10621898—24no—
226#10621898C22×C412yes—
227#10621898#4112yes—
228C2×D172—22no—
229C2×D172—24no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—24no—
235C2×D172—21no—
236C2×D172—28no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—82no—
242C2×D172—82no—
243C2×D172C22×C412yes—
244C2×D172C22×C412yescomplemented
245C2×D172C2×D411yescharacteristic
246C2×D172#4112yes—
247C2×C4×D43—22no—
248C2×C4×D43—21no—
249C2×C4×D43—22no—
250C2×C4×D43—21no—
251C2×C4×D43—22no—
252C2×C4×D43—22no—
253C2×C4×D43—22no—
254C2×C4×D43—21no—
255C2×C4×D43—22no—
256C2×C4×D43—41no—
257C2×C4×D43—41no—
258C2×C4×D43—82no—
259C2×C4×D43—82no—
260C2×C4×D43—84no—
261C2×Dic86C2×D411yescharacteristic
262M16×C43—21no—
263M16×C43—21no—
264M16×C43—21no—
265M16×C43C22×C412yescomplemented
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43C2×D411yescharacteristic
271C4⋊C4×C43C2×D411yescharacteristic
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C42×C43—21no—
276C42×C43—21no—
277C42×C43—21no—
278C42×C43—21no—
279C42×C43—21no—
280C42×C43—21no—
281C42×C43C22×C412yescomplemented
282C42×C43C2×D411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C22⋊Dic43—22no—
287C22⋊Dic43—21no—
288#10621884—24no—
289#10621882—24no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—22no—
297(C2×D43)⋊C4—41no—
298(C2×D43)⋊C4—41no—
299(C2×D43)⋊C4—82no—
300(C2×D43)⋊C4—82no—
301C4⋊Dic43—22no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43C2×D411yescharacteristic
307C4⋊Dic43C2×D411yescharacteristic
308Dic43⋊C4—22no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316#10621877—21no—
317#10621877—21no—
318#10621877—21no—
319#10621877C22×C412yescomplemented
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322D344—24no—
323#10621873—24no—
324C23×C43—21no—
325C23×C43C22×D411yescharacteristic
326C22×D43—22no—
327C22×D43—21no—
328C22×D43—28no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—42no—
334C22×D43—42no—
335C22×D43—41no—
336C22×D43—41no—
337C22×D43—82no—
338C22×D43—82no—
339C22×D43C4×D414yes—
340Q8×C43—21no—
341Q8×C43C4×D412yes—
342D4×C43—22no—
343D4×C43—22no—
344D4×C43—21no—
345D4×C43C4×D412yes—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—42no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—81no—
361C2×C4×C43#12011yescharacteristic
362C2×C4×C43#12011yescharacteristic
363C2×C4×C43#12011yescharacteristic
364C2×C4×C43#12011yescharacteristic
365C2×C4×C43C23×C411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C2×#4111yescharacteristic
369C2×C4×C43C2×#4111yescharacteristic
370C2×C4×C43C2×#4111yescharacteristic
371C22⋊D43—28no—
372C22⋊D43—22no—
373C22⋊D43—22no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—22no—
377C2×Dic43—21no—
378C2×Dic43—42no—
379C2×Dic43—42no—
380C2×Dic43—41no—
381C2×Dic43—82no—
382D172—28no—
383D172—22no—
384D172—22no—
385D172—22no—
386D172—22no—
387D172—21no—
388D172—22no—
389D172—22no—
390D172—41no—
391D172—41no—
392D172—88no—
393D172C4×D412yes—
394C4×D43—28no—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—44no—
398C4×D43—42no—
399C4×D43—81no—
400C4×D43—82no—
401C4×D43—82no—
402C4×D43—82no—
403C4×D43—82no—
404C4×D43—82no—
405C4×D43—82no—
406Dic86—21no—
407Dic86C4×D412yes—
408C8×C43—22no—
409C8×C43—41no—
410C43⋊C8—22no—
411C43⋊C8—41no—
412#21473—431nomaximal, Sylow
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—22no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43C2×C4×D411yescharacteristic
419C22×C43C2×#12011yescharacteristic
420C22×C43#52511yescharacteristic
421C2×D43—22no—
422C2×D43—24no—
423C2×D43—42no—
424C2×D43—41no—
425C2×D43—42no—
426C2×D43—41no—
427C2×D43—44no—
428C2×D43—44no—
429C2×D43—42no—
430C2×D43—82no—
431C2×D43—88no—
432C2×D43—82no—
433C2×D43—81no—
434C2×D43—81no—
435C4×C43—21no—
436C4×C43—21no—
437C4×C43—21no—
438C4×C43—21no—
439C4×C43—22no—
440C4×C43—42no—
441C4×C43—41no—
442C4×C43—41no—
443C4×C43—81no—
444C4×C43C2×C4×D411yescharacteristic
445C4×C43C2×C4×D411yescharacteristic
446C4×C43#52511yescharacteristic
447C4×C43#52511yescharacteristic
448Dic43—22no—
449Dic43—42no—
450Dic43—41no—
451Dic43—41no—
452Dic43—81no—
453C4×H(5,𝔽2)—431no—
454C2×#453—431no—
455C4×AGL(1,ℤ/8)—431no—
456C4×AGL(1,ℤ/8)—431no—
457#2328—431no—
458#1887—431no—
459#1883—431no—
460#1883—431no—
461#1860—431no—
462#1860—431no—
463#1856—431no—
464#1792—431no—
465#1759—431no—
466#1759D4311yescharacteristic, complemented
467C4×#100—431no—
468C2×C43—21no—
469C2×C43—21no—
470C2×C43—42no—
471C2×C43C4×#12011yescharacteristic
472C2×C43#301911yescharacteristic
473C2×C43#302111yescharacteristic
474D43—44no—
475D43—42no—
476D43—82no—
477C2×H(5,𝔽2)—431no—
478C2×AGL(1,ℤ/8)—431no—
479C2×AGL(1,ℤ/8)—431no—
480C2×#127—431no—
481#520—431no—
482#520—431no—
483#520—861no—
484#520—861no—
485#518—431no—
486#518—862no—
487#518—861no—
488#518—861no—
489C4×#41—431no—
490C4×#41—861no—
491C4×#41—861no—
492C4×#41C2×D4311yescharacteristic
493C2×C4×D4—431no—
494C2×C4×D4—431no—
495C2×C4×D4—861no—
496C2×C4×D4—862no—
497C2×C4×D4—861no—
498#453—438no—
499#442—861no—
500#442—861no—
501#440—861no—
502#440—861no—
503C4×SD16—861no—
504C4×SD16—861no—
505C4×D8—861no—
506C4×D8—861no—
507#428—431no—
508#428—431no—
509C2×#104—431no—
510C2×#104—431no—
511C2×#104C2×D4311yescharacteristic
512C2×#104C2×D4311yescharacteristic
513#418—431no—
514#418—431no—
515#417—431no—
516#417—431no—
517C2×#100—431no—
518C2×#100—431no—
519C4×M16—431no—
520C4×M16C2×D4311yescharacteristic, complemented
521#390—431no—
522#390—431no—
523#386—862no—
524#386—862no—
525#382—431no—
526#376C2×D4311yescharacteristic, complemented
527#343—431no—
528#343—431no—
529#339—431no—
530#339—431no—
531#339C2×D4311yescharacteristic, complemented
532#339C2×D4311yescharacteristic, complemented
533C43#2147311yescharacteristic, complemented, Sylow
534H(5,𝔽2)—434no—
535H(5,𝔽2)—862no—
536H(5,𝔽2)—862no—
537H(5,𝔽2)—862no—
538C2×#41—431no—
539C2×#41—861no—
540C2×#41—861no—
541C2×#41C22×D4311yescharacteristic
542C22×D4—431no—
543C22×D4—431no—
544C22×D4—861no—
545C22×D4—862no—
546C22×D4—862no—
547C22×D4—861no—
548C23×C4—432no—
549C23×C4—862no—
550C23×C4—861no—
551AGL(1,ℤ/8)—434no—
552AGL(1,ℤ/8)—434no—
553AGL(1,ℤ/8)—862no—
554AGL(1,ℤ/8)—862no—
555C2×SD16—861no—
556C2×SD16—861no—
557C2×D8—861no—
558C2×D8—861no—
559C2×M16—431no—
560C2×M16—431no—
561C2×M16C22×D4311yescharacteristic
562C2×M16C22×D4311yescharacteristic
563#127—434no—
564#127—862no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—861no—
568C4×Q8—861no—
569C4×Q8D17211yescharacteristic, complemented
570C4×Q8D17211yescharacteristic, complemented
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—431no—
574C4×D4—431no—
575C4×D4—861no—
576C4×D4—861no—
577C4×D4—861no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—862no—
585C4×D4—862no—
586C4×D4—862no—
587C4×D4—862no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4—861no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4—861no—
601C4×D4D17211yescharacteristic, complemented
602C4×D4D17211yescharacteristic, complemented
603#117—21no—
604#117—431no—
605#117—862no—
606#117—862no—
607#117—861no—
608#117—861no—
609#117—861no—
610#117C22×D4311yescharacteristic
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—862no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C22⋊C4—432no—
617C2×C22⋊C4—862no—
618C2×C22⋊C4—862no—
619C2×C22⋊C4—862no—
620C2×C22⋊C4—862no—
621C2×C22⋊C4—862no—
622C2×C22⋊C4—862no—
623C2×C22⋊C4—861no—
624C2×C42—21no—
625C2×C42—862no—
626C2×C42—861no—
627C2×C42C22×D4311yescharacteristic
628C2×C42C22×D4311yescharacteristic
629C2×C42C22×D4311yescharacteristic
630#107—861no—
631#107—861no—
632#106—861no—
633#106—861no—
634#104—22no—
635#104—434no—
636#104—862no—
637#104C4×D4314yescomplemented
638#103—861no—
639#103—861no—
640#102—861no—
641#102—861no—
642#102—861no—
643#102—861no—
644#102—861no—
645#102—861no—
646#100—434no—
647#100—862no—
648#97—21no—
649#97—861no—
650C4×C8—21no—
651C4×C8—861no—
652#95—21no—
653#95—21no—
654#95—862no—
655C24—432no—
656C24—862no—
657C24—861no—
658#41—21no—
659#41—21no—
660#41—432no—
661#41—432no—
662#41—864no—
663#41—864no—
664#41—864no—
665#41—864no—
666#41—861no—
667#41—861no—
668#41C2×C4×D4312yes—
669#41#1062189812yes—
670C2×Q8—431no—
671C2×Q8C2×D17211yescharacteristic
672C2×D4—21no—
673C2×D4—432no—
674C2×D4—432no—
675C2×D4—431no—
676C2×D4—432no—
677C2×D4—864no—
678C2×D4—862no—
679C2×D4—864no—
680C2×D4—868no—
681C2×D4—868no—
682C2×D4—868no—
683C2×D4—864no—
684C2×D4—862no—
685C2×D4—861no—
686C2×D4—864no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4—861no—
691C2×D4—861no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—3442no—
697C2×D4—3442no—
698C2×D4C2×D17211yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—432no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—861no—
710C22×C4—862no—
711C22×C4—861no—
712C22×C4—862no—
713C22×C4—861no—
714C22×C4—862no—
715C22×C4—861no—
716C22×C4—3442no—
717C22×C4—3444no—
718C22×C4—3442no—
719C22×C4—1721no—
720C22×C4—1721no—
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724SD16—864no—
725SD16—864no—
726D8—864no—
727D8—864no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—432no—
732M16—861no—
733M16—861no—
734M16—861no—
735M16C2×C4×D4312yescomplemented
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—861no—
739C2×C8—861no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—431no—
743C4⋊C4—431no—
744C4⋊C4—862no—
745C4⋊C4—862no—
746C4⋊C4—861no—
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4C2×D17211yescharacteristic
753C4⋊C4C2×D17211yescharacteristic
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—862no—
758C22⋊C4—862no—
759C22⋊C4—862no—
760C22⋊C4—862no—
761C22⋊C4—861no—
762C22⋊C4—862no—
763C22⋊C4—862no—
764C22⋊C4—861no—
765C22⋊C4—861no—
766C22⋊C4—3442no—
767C22⋊C4—3442no—
768C22⋊C4—1721no—
769C22⋊C4—1721no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—862no—
777C42—862no—
778C42—861no—
779C42—861no—
780C42—861no—
781C42C2×C4×D4312yescomplemented
782C42C2×D17211yescharacteristic
783C42C2×D17211yescharacteristic
784C42D4×D4311yescharacteristic
785C42D4×D4311yescharacteristic
786C23—21no—
787C23—434no—
788C23—868no—
789C23—862no—
790C23—861no—
791C23—862no—
792C23—862no—
793C23—3442no—
794C23—3442no—
795C23—1722no—
796C23—1722no—
797C23—1722no—
798C23—1722no—
799C23—1721no—
800C23—1721no—
801C23C2×D4×D4311yescharacteristic
802Q8—21no—
803Q8—432no—
804Q8—861no—
805Q8C4×D17212yes—
806D4—22no—
807D4—22no—
808D4—21no—
809D4—432no—
810D4—868no—
811D4—868no—
812D4—862no—
813D4—862no—
814D4—862no—
815D4—862no—
816D4—862no—
817D4—862no—
818D4—861no—
819D4—862no—
820D4—862no—
821D4—3448no—
822D4—1721no—
823D4—1721no—
824D4C4×D17212yes—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—868no—
841C2×C4—861no—
842C2×C4—862no—
843C2×C4—862no—
844C2×C4—861no—
845C2×C4—861no—
846C2×C4—862no—
847C2×C4—3442no—
848C2×C4—3442no—
849C2×C4—3442no—
850C2×C4—3441no—
851C2×C4—3442no—
852C2×C4—3442no—
853C2×C4—3442no—
854C2×C4—3442no—
855C2×C4—1722no—
856C2×C4—1724no—
857C2×C4—1722no—
858C2×C4—1721no—
859C2×C4—1722no—
860C2×C4#1306329511yescharacteristic
861C2×C4#1306329511yescharacteristic
862C2×C4#1306329511yescharacteristic
863C2×C4#1306329511yescharacteristic
864C2×C4C22×C4×D4311yescharacteristic
865C2×C4C2×D4×D4311yescharacteristic
866C2×C4C22×D17211yescharacteristic
867C2×C4#41×D4311yescharacteristic
868C2×C4#41×D4311yescharacteristic
869C2×C4C2×#1062189811yescharacteristic
870C8—22no—
871C8—41no—
872C8—862no—
873C8—1721no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—41no—
878C22—41no—
879C22—862no—
880C22—864no—
881C22—3442no—
882C22—3442no—
883C22—3448no—
884C22—3441no—
885C22—3441no—
886C22—1724no—
887C22—1724no—
888C22—1722no—
889C22—1721no—
890C22—1722no—
891C22—1721no—
892C22—1722no—
893C22C4×D4×D4311yescharacteristic
894C22C2×#1306329511yescharacteristic
895C22#1458340811yescharacteristic
896C4—21no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—22no—
901C4—42no—
902C4—41no—
903C4—41no—
904C4—81no—
905C4—862no—
906C4—3441no—
907C4—1721no—
908C4—1722no—
909C4—1721no—
910C4C4×D4×D4311yescharacteristic
911C4C2×C4×D17211yescharacteristic
912C4#1458340811yescharacteristic
913C4#1458341111yescharacteristic
914C2—21no—
915C2—21no—
916C2—42no—
917C2—3442no—
918C2—1722no—
919C2—1724no—
920C2C4×#1306329511yescharacteristic
921C2#1914395411yescharacteristic
922C2#1914396811yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1759C2
socleC22×C43C2×#120
prime radicalC2×#14583068C2
cosocleC22×C4×C43C24
hypercenter#1759D43
hypocenterC43#21473
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
1. C4×#13063371C2semidirect
3. C4×#13063353C2semidirect
4. C4×#13063350C2semidirect
5. #19137320C2semidirect
6. #19134992C2semidirect
7. #19134972C2semidirect
8. #19134969C2semidirect
9. #19134830C2semidirect
10. #19134829C2semidirect
11. #19134806C2semidirect
12. #19134550C2semidirect
13. #19134406C2semidirect
14. C4×#13063241C2semidirect
15. C43×#1759C2semidirect
33. C2×C4×D172C22semidirect
36. #14583068C4semidirect
45. #14582942C22semidirect
46. #14582941C22semidirect
49. #14582905C22semidirect
50. #14582903C22semidirect
55. C4×#10621877C22semidirect
57. #14582801C22semidirect
60. #14582765C22semidirect
61. #14582667C22semidirect
62. #14582667C22semidirect
63. #14582659C22semidirect
64. #14582659C22semidirect
68. C4×M16×C43C22semidirect
69. C43×#376C22semidirect
70. C43×#339C22semidirect
71. C43×#339C22semidirect
75. #13063371C2×C4semidirect
89. #13063353C2×C4semidirect
91. #13063350C2×C4semidirect
99. #13063322C2×C4semidirect
102. C4×Dic86D4semidirect
103. C4×Dic86D4semidirect
117. C4×D172D4semidirect
118. C4×D172D4semidirect
158. #13063253C2×C4semidirect
168. #13063241C2×C4semidirect
175. C4×Q8×C43D4semidirect
176. C4×Q8×C43D4semidirect
179. C4×D4×C43D4semidirect
180. C4×D4×C43D4semidirect
188. #104×C43C2×C4semidirect
244. C2×D172C22×C4semidirect
265. M16×C43C22×C4semidirect
281. C42×C43C22×C4semidirect
319. #10621877C22×C4semidirect
466. #1759D43semidirect
520. C4×M16C2×D43semidirect
526. #376C2×D43semidirect
531. #339C2×D43semidirect
532. #339C2×D43semidirect
533. C43#21473semidirect
569. C4×Q8D172semidirect
570. C4×Q8D172semidirect
601. C4×D4D172semidirect
602. C4×D4D172semidirect
637. #104C4×D43semidirect
735. M16C2×C4×D43semidirect
781. C42C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C4×#130633712
C2×#145830682
C4×#130633532
C4×#130633502
#191373202
#191349922
#191349722
#191349692
#191348302
#191348292
#191348062
#191345502
#191344062
C4×#130632412
C43×#17592
#2147343