Finite Group Databasebeta

← #24988664

Subgroups — #24988664

Order 11008.

1516 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135402C211yesmaximal, characteristic, complemented
2#19134595C212yesmaximal, complemented
3C2×#14582643C211yesmaximal, characteristic, complemented
4C2×D4⋊(C43⋊C8)C212yesmaximal, complemented
5C2×D42×C43C211yesmaximal, characteristic
6C2×C4⋊(C43⋊C8)C2212yescomplemented
7C2×#13063246—22no—
8C2×#13063246—22no—
9C2×C4×C43⋊C8C2211yescharacteristic, complemented
10#14582769C2211yescharacteristic, complemented
11#14582661—22no—
12#14582643—22no—
13D4⋊(C43⋊C8)—24no—
14C23×D4×C43—22no—
15D42×C43—22no—
16D42×C43—24no—
17D42×C43C414yescomplemented
18C2×#127×C43C2211yescharacteristic
19C2×#121×C43—22no—
20C2×#120×C43—22no—
21C2×C4×D4×C43C2212yes—
22C22×C43⋊C8—21no—
23C22×C43⋊C8—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—22no—
26C4⋊(C43⋊C8)—22no—
27C4⋊(C43⋊C8)—22no—
28#13063246—44no—
29#13063246—44no—
30C4×C43⋊C8—22no—
31C25×C43—22no—
32C22×D4×C43—24no—
33C22×D4×C43—28no—
34C22×D4×C43—28no—
35C22×D4×C43—22no—
36C22×D4×C43—44no—
37C22×D4×C43—44no—
38C22×D4×C43—44no—
39C22×D4×C43—44no—
40C22×D4×C43D412yes—
41C22×D4×C43D412yes—
42C23×C4×C43—22no—
43#127×C43—22no—
44#127×C43C2×C412yes—
45#127×C43D412yes—
46#121×C43—28no—
47#121×C43—28no—
48#120×C43—28no—
49#120×C43—28no—
50C4×D4×C43—22no—
51C4×D4×C43—22no—
52C4×D4×C43C2×C414yes—
53C4×D4×C43D414yes—
54C2×C4⋊C4×C43D412yes—
55C2×C22⋊C4×C43—22no—
56C2×C22⋊C4×C43—22no—
57C2×C42×C43C2311yescharacteristic
58C24×C43—22no—
59C24×C43—28no—
60C24×C43—22no—
61C24×C43—48no—
62C24×C43—48no—
63C24×C43—82no—
64C24×C43—82no—
65C2×D4×C43—216no—
66C2×D4×C43—24no—
67C2×D4×C43—22no—
68C2×D4×C43—24no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—48no—
73C2×D4×C43—48no—
74C2×D4×C43—416no—
75C2×D4×C43—416no—
76C2×D4×C43—416no—
77C2×D4×C43—416no—
78C2×D4×C43—42no—
79C2×D4×C43—42no—
80C2×D4×C43—42no—
81C2×D4×C43—42no—
82C2×D4×C43—42no—
83C2×D4×C43—42no—
84C2×D4×C43C22⋊C414yes—
85C2×D4×C43C22⋊C414yes—
86C2×D4×C43D814yes—
87C2×D4×C43SD1614yes—
88C22×C4×C43—24no—
89C22×C4×C43—24no—
90C22×C4×C43—22no—
91C22×C4×C43—42no—
92C22×C4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43—42no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D412yes—
97C22×Dic43—41no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43C22⋊C414yes—
100C22⋊C4×C43—28no—
101C22⋊C4×C43—24no—
102C22⋊C4×C43—24no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D412yes—
106C4⋊Dic43—42no—
107C4⋊Dic43—42no—
108C4⋊Dic43—42no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—42no—
113C2×C43⋊C8—42no—
114C2×C43⋊C8—42no—
115C23×C43—24no—
116C23×C43—24no—
117C23×C43—24no—
118C23×C43—24no—
119C23×C43—432no—
120C23×C43—42no—
121C23×C43—42no—
122C23×C43—42no—
123C23×C43—42no—
124C23×C43—44no—
125C23×C43—44no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—88no—
129C23×C43—88no—
130C23×C43—88no—
131C23×C43—816no—
132C23×C43#12011yescharacteristic
133D4×C43—24no—
134D4×C43—24no—
135D4×C43—24no—
136D4×C43—44no—
137D4×C43—432no—
138D4×C43—44no—
139D4×C43—44no—
140D4×C43—44no—
141D4×C43—44no—
142D4×C43—82no—
143D4×C43#10218yescomplemented
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—24no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—44no—
150C2×C4×C43—44no—
151C2×C4×C43—44no—
152C2×C4×C43—44no—
153C2×C4×C43C2×C22⋊C411yescharacteristic
154C2×C4×C43C2×C22⋊C412yes—
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12012yes—
157C2×C4×C43C2×D812yes—
158C2×C4×C43C2×SD1612yes—
159C2×C4×C43AGL(1,ℤ/8)12yes—
160C2×C4×C43AGL(1,ℤ/8)12yes—
161C2×Dic43—82no—
162C2×Dic43—81no—
163C43⋊C8—42no—
164C43⋊C8—82no—
165#8443—431nomaximal, Sylow
166C22×C43—28no—
167C22×C43—44no—
168C22×C43—44no—
169C22×C43—44no—
170C22×C43—44no—
171C22×C43—44no—
172C22×C43—44no—
173C22×C43—44no—
174C22×C43—48no—
175C22×C43—832no—
176C22×C43—82no—
177C22×C43—82no—
178C22×C43—84no—
179C22×C43#37911yescharacteristic
180C22×C43#44712yes—
181C22×C43#45012yes—
182C22×C43#45311yescharacteristic
183C22×C43#45511yescharacteristic
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—44no—
187C4×C43C2×#10212yes—
188C4×C43#41812yes—
189C4×C43#44712yes—
190C4×C43#45012yes—
191Dic43—161no—
192C2×D42D4311yescharacteristic
193#1957—431no—
194#1802—432no—
195C2×#331—431no—
196C2×D4⋊C8—432no—
197C2×C43—48no—
198C2×C43—84no—
199C2×C43#161911yescharacteristic
200C2×C43#162911yescharacteristic
201C2×C43#163912yes—
202C2×C43#178612yes—
203C2×C43#179211yescharacteristic
204C23×D4—22no—
205D42—22no—
206D42—24no—
207D42Dic4314yescomplemented
208C2×#127C2×D4311yescharacteristic
209C2×#121—22no—
210C2×#120—22no—
211C2×C4×D4C2×D4312yes—
212C2×C4⋊C8—432no—
213C2×#102—862no—
214C2×#102—862no—
215C2×C4×C8—431no—
216#384—431no—
217#340—862no—
218#331—862no—
219D4⋊C8—864no—
220C43#844311yescharacteristic, complemented, Sylow
221C25—22no—
222C22×D4—24no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—22no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—44no—
230C22×D4C22⋊D4312yes—
231C22×D4C22⋊D4312yes—
232C23×C4—22no—
233C22×C8—861no—
234C22×C8—862no—
235#127—22no—
236#127C2×Dic4312yes—
237#127C22⋊D4312yes—
238#121—28no—
239#121—28no—
240#120—28no—
241#120—28no—
242C4×D4—22no—
243C4×D4—22no—
244C4×D4C2×Dic4314yes—
245C4×D4C22⋊D4314yes—
246C2×C4⋊C4—862no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4C22⋊D4312yes—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C42C22×D4311yescharacteristic
252C4⋊C8—862no—
253C4⋊C8—862no—
254#102—1724no—
255#102—1724no—
256C4×C8—862no—
257C24—22no—
258C24—28no—
259C24—22no—
260C24—48no—
261C24—48no—
262C24—82no—
263C24—82no—
264C2×D4—216no—
265C2×D4—24no—
266C2×D4—22no—
267C2×D4—24no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—416no—
274C2×D4—416no—
275C2×D4—416no—
276C2×D4—48no—
277C2×D4—48no—
278C2×D4—416no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4#1062188214yes—
284C2×D4#1062188314yes—
285C2×D4C22⋊Dic4314yes—
286C2×D4C22⋊Dic4314yes—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—1721no—
295C22×C4C2×C22⋊D4311yescharacteristic
296C22×C4C2×C22⋊D4312yes—
297C2×C8—862no—
298C2×C8—1722no—
299C2×C8—1722no—
300C2×C8—1722no—
301C2×C8—1721no—
302C2×C8—1721no—
303C4⋊C4—22no—
304C4⋊C4—1722no—
305C4⋊C4—1722no—
306C4⋊C4—1722no—
307C4⋊C4C22⋊Dic4314yes—
308C22⋊C4—28no—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C42C22×Dic4311yescharacteristic
312C42C2×C22⋊D4312yes—
313C42C2×C22⋊D4311yescharacteristic
314C23—24no—
315C23—24no—
316C23—24no—
317C23—24no—
318C23—432no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—44no—
324C23—42no—
325C23—42no—
326C23—44no—
327C23—88no—
328C23—88no—
329C23—816no—
330C23—88no—
331C23#1306329411yescharacteristic
332D4—24no—
333D4—24no—
334D4—24no—
335D4—44no—
336D4—432no—
337D4—44no—
338D4—44no—
339D4—44no—
340D4—44no—
341D4—82no—
342D4#1306324618yescomplemented
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—3441no—
353C2×C4—3442no—
354C2×C4C2×C22⋊Dic4311yescharacteristic
355C2×C4C2×C22⋊Dic4312yes—
356C2×C4#1306329411yescharacteristic
357C2×C4#1306329412yes—
358C2×C4C2×#1062188212yes—
359C2×C4C2×#1062188312yes—
360C2×C4#1306335112yes—
361C2×C4#1306335112yes—
362C8—3442no—
363C8—1722no—
364C22—28no—
365C22—44no—
366C22—44no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—48no—
372C22—44no—
373C22—832no—
374C22—82no—
375C22—84no—
376C22—82no—
377C22#1458275511yescharacteristic
378C22#1458303312yes—
379C22#1458305012yes—
380C22#1458306711yescharacteristic
381C22#1458307711yescharacteristic
382C4—21no—
383C4—21no—
384C4—44no—
385C4—6881no—
386C4C2×#1306324612yes—
387C4#1458290412yes—
388C4#1458303312yes—
389C4#1458305012yes—
390C2—48no—
391C2—84no—
392C2#1913364911yescharacteristic
393C2#1913371111yescharacteristic
394C2#1913377412yes—
395C2#1913452612yes—
396C2#1913454911yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC2×D42×C43C2
socleC23×C43#120
cosocleC2×C42×C43C23
hypercenterC2×D42D43
hypocenterC43#8443
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #19135402C2semidirect
2. #19134595C2semidirect
3. C2×#14582643C2semidirect
4. C2×D4⋊(C43⋊C8)C2semidirect
6. C2×C4⋊(C43⋊C8)C22semidirect
9. C2×C4×C43⋊C8C22semidirect
10. #14582769C22semidirect
17. D42×C43C4semidirect
143. D4×C43#102semidirect
207. D42Dic43semidirect
220. C43#8443semidirect
342. D4#13063246semidirect

Maximal subgroups

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

subgroupindex
#191354022
#191345952
C2×#145826432
C2×D4⋊(C43⋊C8)2
C2×D42×C432
#844343