Finite Group Databasebeta

← #25070702

Subgroups — #25070702

Order 11008.

1516 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583461C211yesmaximal, characteristic, complemented
2#19145392C212yesmaximal, complemented
3#19133614C214yesmaximal, complemented
4#19133512C214yesmaximal, complemented
5#19133110C212yesmaximal, complemented
6#19132922C211yesmaximal, characteristic, complemented
7C43×#2539C211yesmaximal, characteristic, complemented
8C23×C22⋊D43—21no—
9#14583461—24no—
10#14583461—22no—
11#14583461C2214yes—
12C2×#13063309—22no—
13C2×#13063299—21no—
14C2×#13063299C2212yes—
15C2×#13063295—22no—
16#14583217C2214yescomplemented
17#14583215—22no—
18#14583150—24no—
19#14583033C2214yescomplemented
20#14583032—22no—
21#14582863C2212yescomplemented
22#14582632C2218yescomplemented
23#14582623C2214yescomplemented
24C2×#123×C43—21no—
25C2×#121×C43C2211yescharacteristic, complemented
26C2×#120×C43—21no—
27C22×C22⋊C4×C43C2211yescharacteristic
28C43×#399C2212yescomplemented
29C43×#392C2212yescomplemented
30C43×#390—22no—
31C4×C22⋊C4×C43C2211yescharacteristic, complemented
32C24×D43—21no—
33C22×D172—21no—
34C22×D172D412yescomplemented
35C22×C22⋊D43—22no—
36C22×C22⋊D43—24no—
37C22×C22⋊D43—22no—
38C22×C22⋊D43—24no—
39C22×C22⋊D43—48no—
40C23×Dic43—21no—
41C2×#10621882—24no—
42C2×#10621877—22no—
43#13063309—28no—
44#13063309—28no—
45#13063299—24no—
46#13063299—24no—
47#13063299—22no—
48#13063299—22no—
49#13063299D414yescomplemented
50#13063299C2314yes—
51#13063295—28no—
52#13063295—28no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43D412yescomplemented
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57#13063256—24no—
58#13063246—24no—
59#13063245—24no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)C2314yescomplemented
62C25×C43D411yescharacteristic
63C22×D4×C43—21no—
64C22×D4×C43—22no—
65C22×D4×C43C2311yescharacteristic, complemented
66C23×C4×C43D411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68#123×C43—44no—
69#121×C43—22no—
70#121×C43—22no—
71#120×C43—44no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43C2311yescharacteristic, complemented
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43D412yes—
81C2×C22⋊C4×C43C2312yes—
82C2×C42×C43—21no—
83#95×C43C2312yescomplemented
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—24no—
87C24×C43—21no—
88C24×C43—42no—
89C24×C43—81no—
90C24×C43C2×D411yescharacteristic
91C24×C43C2×D412yes—
92C23×D43—22no—
93C23×D43—24no—
94C23×D43—44no—
95C23×D43—82no—
96C23×D43—82no—
97C2×D4×C43—22no—
98C2×D4×C43—42no—
99C2×D4×C43—42no—
100C2×D4×C43—44no—
101C2×D4×C43—41no—
102C2×D4×C43—41no—
103C2×D4×C43—44no—
104C2×D4×C43—81no—
105C2×D4×C43—82no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—21no—
110C22×C4×C43—42no—
111C22×C4×C43—81no—
112C22×C4×C43C2×D412yes—
113C22×C4×C43C2×D412yes—
114C22×C4×C43C2×D412yes—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2411yescharacteristic
117C2×C22⋊D43—28no—
118C2×C22⋊D43—24no—
119C2×C22⋊D43—24no—
120C2×C22⋊D43—48no—
121C2×C22⋊D43—416no—
122C2×C22⋊D43—48no—
123C2×C22⋊D43—48no—
124C2×C22⋊D43—48no—
125C22×Dic43—24no—
126C22×Dic43—22no—
127C22×Dic43—44no—
128C2×D172—24no—
129C2×D172—22no—
130C2×D172—82no—
131C2×D172—82no—
132C2×D172C2×D414yes—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—44no—
135C22⋊C4×C43—24no—
136C22⋊C4×C43—24no—
137C22⋊C4×C43—24no—
138C22⋊C4×C43—44no—
139C22⋊C4×C43—44no—
140C22⋊C4×C43—42no—
141C42×C43—81no—
142#10621882—84no—
143(C2×D43)⋊C4—28no—
144(C2×D43)⋊C4—24no—
145(C2×D43)⋊C4—24no—
146C4⋊Dic43—24no—
147C4⋊Dic43—22no—
148C4⋊Dic43C2×D414yes—
149#10621877—82no—
150C2×C43⋊C8—24no—
151C23×C43—24no—
152C23×C43—24no—
153C23×C43—22no—
154C23×C43—22no—
155C23×C43—22no—
156C23×C43—22no—
157C23×C43—41no—
158C23×C43—42no—
159C23×C43—42no—
160C23×C43—42no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43—42no—
164C23×C43—42no—
165C23×C43—41no—
166C23×C43—42no—
167C23×C43—81no—
168C23×C43—81no—
169C23×C43—88no—
170C23×C43#12011yescharacteristic
171C23×C43#12011yescharacteristic
172C23×C43AGL(1,ℤ/8)14yes—
173C23×C43C22×D411yescharacteristic
174C22×D43—24no—
175C22×D43—44no—
176C22×D43—44no—
177C22×D43—48no—
178C22×D43—44no—
179C22×D43—84no—
180C22×D43—84no—
181C22×D43—816no—
182D4×C43—44no—
183D4×C43—88no—
184D4×C43—82no—
185D4×C43—82no—
186C2×C4×C43—24no—
187C2×C4×C43—22no—
188C2×C4×C43—42no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—81no—
200C2×C4×C43#12012yes—
201C2×C4×C43C22×D412yes—
202C22⋊D43—416no—
203C22⋊D43—48no—
204C22⋊D43—48no—
205C2×Dic43—24no—
206C2×Dic43—44no—
207C2×Dic43—48no—
208D172—44no—
209D172—82no—
210D172—84no—
211C43⋊C8—44no—
212#18316—431nomaximal, Sylow
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—24no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—44no—
222C22×C43—44no—
223C22×C43—48no—
224C22×C43—42no—
225C22×C43—42no—
226C22×C43—82no—
227C22×C43—82no—
228C22×C43—82no—
229C22×C43—84no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43#45312yes—
234C22×C43C2×#12011yescharacteristic
235C22×C43C2×AGL(1,ℤ/8)12yes—
236C2×D43—44no—
237C2×D43—44no—
238C2×D43—44no—
239C2×D43—88no—
240C2×D43—816no—
241C4×C43—22no—
242C4×C43—22no—
243C4×C43—44no—
244C4×C43—42no—
245C4×C43—81no—
246Dic43—44no—
247C2×#534—431no—
248#3192—432no—
249#2539D4311yescharacteristic, complemented
250#1613—434no—
251#1595—434no—
252#1507—432no—
253#1462—431no—
254C2×C43—22no—
255C2×C43—22no—
256C2×C43—44no—
257C2×C43—41no—
258C2×C43—161no—
259C2×C43#300311yescharacteristic
260C2×C43C2×#45311yescharacteristic
261C2×C43#302611yescharacteristic
262D43—84no—
263C23×D4—861no—
264#534—434no—
265#534—864no—
266#534—862no—
267C2×#123—21no—
268C2×#123—862no—
269C2×#121—432no—
270C2×#121—861no—
271C2×#121C2×D4311yescharacteristic, complemented
272C2×#120—21no—
273C2×#120—862no—
274C22×C22⋊C4C2×D4311yescharacteristic
275#481—434no—
276#481—862no—
277#469—864no—
278#447—434no—
279#447—862no—
280#407—432no—
281#399C2×D4312yescomplemented
282#392C2×D4312yescomplemented
283#390—22no—
284C4×C22⋊C4C2×D4311yescharacteristic, complemented
285#327—438no—
286#323—434no—
287C43#1831611yescharacteristic, complemented, Sylow
288C25—861no—
289C25C22⋊D4311yescharacteristic
290C22×D4—21no—
291C22×D4—22no—
292C22×D4—432no—
293C22×D4—861no—
294C22×D4—862no—
295C22×D4—864no—
296C22×D4—862no—
297C22×D4—864no—
298C22×D4—1728no—
299C22×D4C22×D4311yescharacteristic, complemented
300C23×C4—861no—
301C23×C4C22⋊D4311yescharacteristic
302C23×C4C22×D4311yescharacteristic
303C2×D8—864no—
304C2×M16—862no—
305#123—44no—
306#123—868no—
307#123—868no—
308#121—22no—
309#121—22no—
310#121—434no—
311#121—434no—
312#121—864no—
313#121—862no—
314#121—862no—
315#121—864no—
316#120—44no—
317#120—868no—
318#120—868no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—432no—
321C2×C4⋊C4—861no—
322C2×C4⋊C4C22×D4311yescharacteristic, complemented
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—862no—
330C2×C22⋊C4—862no—
331C2×C22⋊C4C22⋊D4312yes—
332C2×C22⋊C4C22×D4312yes—
333C2×C42—21no—
334#106—864no—
335#102—864no—
336#102—864no—
337C22⋊C8—434no—
338C22⋊C8—862no—
339#95C22×D4312yescomplemented
340C24—21no—
341C24—21no—
342C24—24no—
343C24—21no—
344C24—42no—
345C24—81no—
346C24—864no—
347C24—862no—
348C24—3442no—
349C24—3442no—
350C24—1724no—
351C24C2×C22⋊D4311yescharacteristic
352C24C2×C22⋊D4312yes—
353C2×D4—22no—
354C2×D4—44no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—44no—
360C2×D4—81no—
361C2×D4—82no—
362C2×D4—434no—
363C2×D4—864no—
364C2×D4—868no—
365C2×D4—864no—
366C2×D4—864no—
367C2×D4—862no—
368C2×D4—3442no—
369C2×D4—3442no—
370C2×D4—1728no—
371C2×D4—17216no—
372C2×D4—1728no—
373C2×D4—1728no—
374C2×D4—1728no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—81no—
381C22×C4—864no—
382C22×C4—862no—
383C22×C4—1724no—
384C22×C4D4×D4312yes—
385C22×C4D4×D4312yes—
386C22×C4C2×C22⋊D4312yes—
387C22×C4C2×C22⋊D4311yescharacteristic
388C22×C4C23×D4311yescharacteristic
389D8—3444no—
390M16—3442no—
391C2×C8—864no—
392C4⋊C4—22no—
393C4⋊C4—44no—
394C4⋊C4—434no—
395C4⋊C4—864no—
396C4⋊C4—862no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—42no—
403C22⋊C4—868no—
404C22⋊C4—864no—
405C22⋊C4—864no—
406C42—81no—
407C23—24no—
408C23—24no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—41no—
418C23—41no—
419C23—42no—
420C23—42no—
421C23—41no—
422C23—42no—
423C23—81no—
424C23—81no—
425C23—88no—
426C23—864no—
427C23—34416no—
428C23—3444no—
429C23—3444no—
430C23—1724no—
431C23—1724no—
432C23—1728no—
433C23—1724no—
434C23#1306329311yescharacteristic
435C23#1306329311yescharacteristic
436C23#1306335014yes—
437C23C22×C22⋊D4311yescharacteristic
438D4—44no—
439D4—88no—
440D4—82no—
441D4—82no—
442D4—3442no—
443D4—3444no—
444D4—1724no—
445D4—17216no—
446D4—1728no—
447D4—1728no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—81no—
462C2×C4—864no—
463C2×C4—1724no—
464C2×C4—1728no—
465C2×C4#1306329312yes—
466C2×C4C2×D4×D4312yes—
467C8—1724no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—24no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—48no—
479C22—42no—
480C22—42no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—84no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—3448no—
489C22—34416no—
490C22—1724no—
491C22—1724no—
492C22—1724no—
493C22#1458306612yes—
494C22C2×#1306329311yescharacteristic
495C22C2×#1306335012yes—
496C4—22no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—81no—
501C4—1724no—
502C2—22no—
503C2—22no—
504C2—41no—
505C2—44no—
506C2—161no—
507C2—3444no—
508C2#1914382111yescharacteristic
509C2C2×#1458306611yescharacteristic
510C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2539C2
socleC22×C43C2×#120
hypercenter#2539D43
hypocenterC43#18316
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#14583461C2semidirect
2. #19145392C2semidirect
3. #19133614C2semidirect
4. #19133512C2semidirect
5. #19133110C2semidirect
6. #19132922C2semidirect
7. C43×#2539C2semidirect
16. #14583217C22semidirect
19. #14583033C22semidirect
21. #14582863C22semidirect
22. #14582632C22semidirect
23. #14582623C22semidirect
25. C2×#121×C43C22semidirect
28. C43×#399C22semidirect
29. C43×#392C22semidirect
31. C4×C22⋊C4×C43C22semidirect
34. C22×D172D4semidirect
49. #13063299D4semidirect
54. C2×C4⋊Dic43D4semidirect
61. C22⋊(C43⋊C8)C23semidirect
65. C22×D4×C43C23semidirect
73. C2×C4⋊C4×C43C23semidirect
83. #95×C43C23semidirect
249. #2539D43semidirect
271. C2×#121C2×D43semidirect
281. #399C2×D43semidirect
282. #392C2×D43semidirect
284. C4×C22⋊C4C2×D43semidirect
287. C43#18316semidirect
299. C22×D4C22×D43semidirect
322. C2×C4⋊C4C22×D43semidirect
339. #95C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834612
#191453922
#191336142
#191335122
#191331102
#191329222
C43×#25392
#1831643