Finite Group Databasebeta

← #24987490

Subgroups — #24987490

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137101C211yesmaximal, characteristic
2#19134359C211yesmaximal, characteristic, complemented
3C2×#14582634C211yesmaximal, characteristic
4C2×#14582632C211yesmaximal, characteristic
5#95×Dic43C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063287C411yescharacteristic, complemented
10C2×(C22⋊D43)⋊C4—21no—
11C22×C4×Dic43—21no—
12C22×C4×Dic43C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063235—21no—
15#14582800C411yescharacteristic, complemented
16#14582795C411yescharacteristic, complemented
17#14582788—21no—
18#14582776—21no—
19C4⋊C4×Dic43C411yescharacteristic, complemented
20#14582746—21no—
21C2×C43⋊#95—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582653—21no—
24#14582634C414yescomplemented
25#14582632C414yescomplemented
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C2×#95×C43C2211yescharacteristic
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C23×Dic43—21no—
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34C22×C4×D43—21no—
35C22×C43⋊C8—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299C2×C412yes—
39#13063299C2×C412yes—
40#13063287—42no—
41(C22⋊D43)⋊C4—42no—
42(C22⋊D43)⋊C4—42no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×C4×Dic43—24no—
50C2×C4×Dic43—21no—
51C2×C4×Dic43—42no—
52C2×C4×Dic43—42no—
53C2×C4×Dic43—42no—
54C2×C4×Dic43C2×C411yescharacteristic
55C2×C4×Dic43C2×C411yescharacteristic
56C2×C4×Dic43D411yescharacteristic
57C2×C4×Dic43D411yescharacteristic
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)C2×C412yescomplemented
60#13063235—42no—
61C43⋊#95—24no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95C2×C412yescomplemented
66C23×C4×C43—21no—
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69C2×C4⋊C4×C43C2×C411yescharacteristic
70C2×C4⋊C4×C43C2×C411yescharacteristic
71C2×C22⋊C4×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43C2×C412yescomplemented
74#95×C43—21no—
75#95×C43—21no—
76#95×C43C2×C412yescomplemented
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C22×C411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×C22⋊D43—22no—
97C2×C22⋊D43—22no—
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C22×Dic43—22no—
103C22×Dic43—22no—
104C22×Dic43—22no—
105C22×Dic43—22no—
106C22×Dic43—22no—
107C22×Dic43—21no—
108C22×Dic43—22no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43—41no—
117C22×Dic43—41no—
118C22×Dic43C22⋊C411yescharacteristic
119C22×Dic43C22⋊C411yescharacteristic
120C22×Dic43C22⋊C411yescharacteristic
121C22×Dic43C22⋊C411yescharacteristic
122C2×D172—21no—
123C2×D172—41no—
124C2×D172—41no—
125C2×D172C4212yescomplemented
126C2×C4×D43—42no—
127C2×C4×D43—42no—
128C2×C4×D43—42no—
129C2×C8×C43—22no—
130C2×C8×C43—41no—
131C2×C8×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C22⋊C4×C43—41no—
136(C2×D43)⋊C4—22no—
137(C2×D43)⋊C4—22no—
138(C2×D43)⋊C4—42no—
139(C2×D43)⋊C4—42no—
140(C2×D43)⋊C4—42no—
141C4⋊Dic43—21no—
142C4⋊Dic43C4212yescomplemented
143Dic43⋊C4—42no—
144C4×Dic43—22no—
145C4×Dic43—22no—
146C4×Dic43—41no—
147C4×Dic43—41no—
148C4×Dic43—48no—
149C4×Dic43—42no—
150C2×C43⋊C8—22no—
151C2×C43⋊C8—41no—
152C2×C43⋊C8—41no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43C2×C22⋊C411yescharacteristic
158C23×C43C4×D411yescharacteristic
159C23×C43C4×D411yescharacteristic
160C23×C43AGL(1,ℤ/8)11yescharacteristic
161C23×C43AGL(1,ℤ/8)11yescharacteristic
162C23×C43AGL(1,ℤ/8)11yescharacteristic
163C23×C43#13711yescharacteristic
164C22×D43—22no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—24no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43C2×C4211yescharacteristic
193C2×C4×C43#11711yescharacteristic
194C2×C4×C43C4×D411yescharacteristic
195C2×C4×C43C4×D411yescharacteristic
196C22⋊D43—42no—
197C22⋊D43—42no—
198C22⋊D43—42no—
199C22⋊D43—42no—
200C2×Dic43—24no—
201C2×Dic43—24no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—24no—
209C2×Dic43—22no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—42no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—42no—
223C2×Dic43#9912yes—
224C2×Dic43#10412yes—
225C2×Dic43#10412yes—
226D172—42no—
227D172—42no—
228C4×D43—84no—
229C8×C43—42no—
230C43⋊C8—42no—
231#8218—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43C4×C22⋊C411yescharacteristic
245C22×C43C2×#9911yescharacteristic
246C22×C43#41011yescharacteristic
247C22×C43#41711yescharacteristic
248C22×C43#41811yescharacteristic
249C22×C43C2×#10411yescharacteristic
250C22×C43C2×#10411yescharacteristic
251C22×C43#44011yescharacteristic
252C22×C43#44011yescharacteristic
253C22×C43#44211yescharacteristic
254C22×C43#44211yescharacteristic
255C2×D43—42no—
256C2×D43—42no—
257C2×D43—42no—
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43—81no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—44no—
267C4×C43—81no—
268C4×C43—81no—
269Dic43—22no—
270Dic43—22no—
271Dic43—22no—
272Dic43—44no—
273Dic43—42no—
274Dic43—41no—
275C4×#121—431no—
276#1749—431no—
277C2×#327—431no—
278C2×#327—431no—
279C4×#95—431no—
280#1294—431no—
281#1294D4311yescharacteristic, complemented
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—21no—
285C2×C43—21no—
286C2×C43#150411yescharacteristic
287C2×C43#150511yescharacteristic
288C2×C43#150711yescharacteristic
289C2×C43#150911yescharacteristic
290C2×C43C4×#9911yescharacteristic
291C2×C43C4×#10411yescharacteristic
292C2×C43#176211yescharacteristic
293D43—82no—
294C2×#121—431no—
295C2×C4×D4—431no—
296C2×C4×D4—861no—
297C22×C42—431no—
298C22×C42—861no—
299C2×C22⋊C8—431no—
300C2×C22⋊C8C2×D4311yescharacteristic
301C2×#97—861no—
302#390—431no—
303#389—431no—
304#388—861no—
305#386—861no—
306#380C2×D4311yescharacteristic
307C4×C4⋊C4—431no—
308C4×C22⋊C4—861no—
309C2×#95—431no—
310C2×#95—861no—
311C2×#95C2×D4311yescharacteristic
312#336—861no—
313#327—434no—
314#327—434no—
315C43#821811yescharacteristic, complemented, Sylow
316C22×D4—431no—
317C22×D4—861no—
318C23×C4—21no—
319C23×C4—431no—
320C23×C4—431no—
321C23×C4—861no—
322C23×C4—861no—
323C23×C4C22×D4311yescharacteristic
324C22×C8—21no—
325C22×C8—861no—
326#121—432no—
327#121—432no—
328#121—861no—
329#121—861no—
330C4×D4—1722no—
331C4×D4—1722no—
332C4×D4—1722no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4C4×D4311yescharacteristic
336C2×C4⋊C4C4×D4311yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341C2×C22⋊C4—861no—
342C2×C42—431no—
343C2×C42—431no—
344C2×C42—431no—
345C2×C42—431no—
346C2×C42—861no—
347C2×C42—864no—
348C2×C42—1722no—
349C2×C42—1722no—
350C2×C42—1722no—
351C22⋊C8—21no—
352C22⋊C8—432no—
353C22⋊C8—861no—
354C22⋊C8C4×D4312yescomplemented
355#97—1722no—
356#95—21no—
357#95—21no—
358#95—432no—
359#95—861no—
360#95—861no—
361#95—864no—
362#95—861no—
363#95C4×D4312yescomplemented
364C24—861no—
365C24D4×D4311yescharacteristic
366C2×D4—432no—
367C2×D4—862no—
368C2×D4—862no—
369C2×D4—861no—
370C2×D4—1721no—
371C2×D4—1721no—
372C2×D4—1721no—
373C2×D4—1721no—
374C2×D4—1721no—
375C2×D4—1721no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—431no—
388C22×C4—431no—
389C22×C4—431no—
390C22×C4—431no—
391C22×C4—862no—
392C22×C4—862no—
393C22×C4—862no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—862no—
397C22×C4—862no—
398C22×C4—861no—
399C22×C4—862no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—1722no—
403C22×C4—1722no—
404C22×C4—1722no—
405C22×C4—1721no—
406C22×C4—1721no—
407C22×C4—1721no—
408C22×C4—1721no—
409C22×C4—1721no—
410C22×C4C2×C4×D4311yescharacteristic
411C22×C4C2×C4×D4311yescharacteristic
412C22×C4C2×C4×D4311yescharacteristic
413C22×C4D4×D4311yescharacteristic
414C22×C4#1062190011yescharacteristic
415C22×C4#1062190211yescharacteristic
416C2×C8—22no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—862no—
420C2×C8—1721no—
421C2×C8—1721no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—432no—
425C4⋊C4—861no—
426C4⋊C4—1722no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—862no—
430C22⋊C4—862no—
431C22⋊C4—1722no—
432C22⋊C4—1722no—
433C22⋊C4—1722no—
434C42—862no—
435C42—862no—
436C42—1721no—
437C42—1721no—
438C42—1728no—
439C42—1722no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—862no—
445C23—1721no—
446C23—1721no—
447C23—1721no—
448C23—1721no—
449C23—1721no—
450C23—1721no—
451C23C22⋊C4×D4311yescharacteristic
452C23(C22⋊D43)⋊C411yescharacteristic
453C23#1306328711yescharacteristic
454C23#1306334911yescharacteristic
455C23#1306335211yescharacteristic
456C23#1306335211yescharacteristic
457C23#1306335711yescharacteristic
458D4—1722no—
459D4—1722no—
460D4—1722no—
461D4—1722no—
462D4—1722no—
463D4—1722no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—432no—
486C2×C4—432no—
487C2×C4—432no—
488C2×C4—864no—
489C2×C4—864no—
490C2×C4—861no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—864no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—862no—
501C2×C4—3444no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4—1722no—
507C2×C4—1722no—
508C2×C4—1722no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1722no—
512C2×C4C42×D4311yescharacteristic
513C2×C4#1306328311yescharacteristic
514C2×C4(C22⋊D43)⋊C411yescharacteristic
515C2×C4#1306328711yescharacteristic
516C8—42no—
517C8—1722no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—3441no—
531C22—3441no—
532C22—3441no—
533C22—3441no—
534C22—1722no—
535C22—1722no—
536C22—1722no—
537C22#1458274611yescharacteristic
538C22#99×D4311yescharacteristic
539C22#1458287111yescharacteristic
540C22#1458289911yescharacteristic
541C22#1458290211yescharacteristic
542C22#104×D4311yescharacteristic
543C22#104×D4311yescharacteristic
544C22#1458299811yescharacteristic
545C22#1458300211yescharacteristic
546C22#1458300811yescharacteristic
547C22#1458301011yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—44no—
553C4—81no—
554C4—81no—
555C4—862no—
556C4—862no—
557C4—862no—
558C4—1724no—
559C4—1721no—
560C4—1722no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—3442no—
566C2#1913309811yescharacteristic
567C2#1913310111yescharacteristic
568C2#1913310911yescharacteristic
569C2#1913311911yescharacteristic
570C2#1913438211yescharacteristic
571C2#1913439911yescharacteristic
572C2#1913441911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#8218
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #19134359C2semidirect
5. #95×Dic43C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
9. C2×#13063287C4semidirect
15. #14582800C4semidirect
16. #14582795C4semidirect
19. C4⋊C4×Dic43C4semidirect
24. #14582634C4semidirect
25. #14582632C4semidirect
59. C22⋊(C43⋊C8)C2×C4semidirect
65. C43⋊#95C2×C4semidirect
73. C22⋊C8×C43C2×C4semidirect
76. #95×C43C2×C4semidirect
125. C2×D172C42semidirect
142. C4⋊Dic43C42semidirect
281. #1294D43semidirect
315. C43#8218semidirect
354. C22⋊C8C4×D43semidirect
363. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191371012
#191343592
C2×#145826342
C2×#145826322
#95×Dic432
#191324732
C43×#12942
#821843