Finite Group Databasebeta

← #24995847

Subgroups — #24995847

Order 11008.

522 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583245C211yesmaximal, characteristic
2#19135543C211yesmaximal, characteristic, complemented
3C4⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
4C2×#14582649C211yesmaximal, characteristic, complemented
5C2×#14582647C211yesmaximal, characteristic, complemented
6C2×#14582643C211yesmaximal, characteristic
7C43×#1982C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583245—22no—
10#14583245C414yescomplemented
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×#13063246—21no—
14C2×#13063246—21no—
15C2×C4×C43⋊C8—21no—
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582661—22no—
18#14582654—21no—
19#14582649—22no—
20#14582647—22no—
21#14582643—22no—
22C2×#127×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#102×C43—22no—
25C4×C4⋊C4×C43C2211yescharacteristic
26C22×Dic86—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8D411yescharacteristic
30C22×C43⋊C8D411yescharacteristic
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325C2×C412yes—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)D412yes—
41#13063246—24no—
42#13063246—24no—
43C4×C43⋊C8—42no—
44C4×C43⋊C8C2×C412yes—
45C4×C43⋊C8D412yes—
46C22×D4×C43—21no—
47C22×D4×C43—21no—
48C22×D4×C43—21no—
49C22×C8×C43—21no—
50#127×C43—21no—
51#127×C43—21no—
52#127×C43—21no—
53#127×C43C2×C412yes—
54C2×C4⋊C4×C43D412yes—
55C2×C42×C43—21no—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59#102×C43—44no—
60#95×C43—21no—
61C24×C43—41no—
62C2×D4×C43—22no—
63C2×D4×C43—22no—
64C2×D4×C43—22no—
65C2×D4×C43—41no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43—42no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—42no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—82no—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—41no—
80C2×Dic86—22no—
81C2×Dic86—41no—
82C2×Dic86—82no—
83C2×C8×C43—41no—
84C2×C8×C43—42no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43SD1614yes—
87C42×C43—41no—
88C42×C43—41no—
89C42×C43C22×C411yescharacteristic
90C42×C43C2×D411yescharacteristic
91C42×C43C2×D411yescharacteristic
92C42×C43#4111yescharacteristic
93C4⋊Dic43—22no—
94C4⋊Dic43—22no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—42no—
106C2×C43⋊C8C22⋊C412yes—
107C2×C43⋊C8C22⋊C412yes—
108C23×C43—42no—
109C23×C43—81no—
110C23×C43—81no—
111C23×C43—82no—
112C23×C43—82no—
113C23×C43#12111yescharacteristic
114D4×C43—42no—
115D4×C43—42no—
116D4×C43—44no—
117D4×C43—82no—
118D4×C43—82no—
119D4×C43—81no—
120D4×C43—81no—
121D4×C43—81no—
122D4×C43—81no—
123C2×C4×C43—22no—
124C2×C4×C43—24no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43C2×C22⋊C411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12411yescharacteristic
132C2×C4×C43#12711yescharacteristic
133C2×C4×C43C2×SD1612yes—
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43#13512yes—
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×Dic43—42no—
140C2×Dic43—82no—
141Dic86—82no—
142Dic86—82no—
143C8×C43—81no—
144C43⋊C8—22no—
145C43⋊C8—22no—
146C43⋊C8—42no—
147C43⋊C8—81no—
148#9735—431nomaximal, Sylow
149C22×C43—82no—
150C22×C43—82no—
151C22×C43—82no—
152C22×C43—162no—
153C22×C43—162no—
154C22×C43#39011yescharacteristic
155C22×C43#46311yescharacteristic
156C22×C43#46411yescharacteristic
157C22×C43#46512yes—
158C22×C43#47212yes—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—44no—
162C4×C43#41611yescharacteristic
163C4×C43#41711yescharacteristic
164C4×C43C4×SD1612yes—
165C4×C43#46311yescharacteristic
166C4×C43#46411yescharacteristic
167C4×C43#49211yescharacteristic
168C4×C43#49511yescharacteristic
169Dic43—82no—
170C2×#486—431no—
171#1987—431no—
172#1982D4311yescharacteristic
173C8×C4⋊C4—431no—
174C2×#334—431no—
175C2×#333—431no—
176C2×#331—431no—
177C2×C43—162no—
178C2×C43#167712yes—
179C2×C43#167812yes—
180C2×C43#196811yescharacteristic
181C2×C43#197811yescharacteristic
182C2×C43#198311yescharacteristic
183C2×C4⋊Q8—431no—
184C2×#127C2×D4311yescharacteristic
185#486—434no—
186#486—862no—
187C2×C4⋊C8—431no—
188C2×C4⋊C8—431no—
189C2×C4⋊C8C2×D4311yescharacteristic
190C2×#102—22no—
191C2×#102—861no—
192C2×#102—861no—
193C2×C4×C8—431no—
194C2×C4×C8—861no—
195C4×C4⋊C4C2×D4311yescharacteristic
196#340—862no—
197#336—861no—
198#334—862no—
199#333—862no—
200#331—862no—
201C43#973511yescharacteristic, complemented, Sylow
202C22×Q8—861no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×C8—21no—
207C22×C8—431no—
208C22×C8—431no—
209C22×C8—861no—
210C22×C8—861no—
211C4⋊Q8—432no—
212C4⋊Q8—861no—
213C4⋊Q8—861no—
214C4⋊Q8—861no—
215#127—21no—
216#127—21no—
217#127—21no—
218#127C4×D4312yes—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C22⋊D4312yes—
222C2×C42—21no—
223C2×C42C22×D4311yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—432no—
227C4⋊C8—861no—
228C4⋊C8—861no—
229C4⋊C8—861no—
230#102—44no—
231#102—864no—
232#102—864no—
233C4×C8—432no—
234C4×C8—432no—
235C4×C8—1722no—
236#95—21no—
237C24—41no—
238C2×Q8—862no—
239C2×Q8—3442no—
240C2×Q8—1721no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—42no—
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—82no—
254C22×C4—22no—
255C22×C4—1721no—
256C22×C4D4×D4311yescharacteristic
257C22×C4#1062190011yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259C2×C8—41no—
260C2×C8—42no—
261C2×C8—432no—
262C2×C8—432no—
263C2×C8—861no—
264C2×C8—861no—
265C2×C8—861no—
266C2×C8—861no—
267C2×C8—862no—
268C2×C8—1721no—
269C2×C8—1722no—
270C2×C8—1721no—
271C2×C8—1721no—
272C4⋊C4—22no—
273C4⋊C4—862no—
274C4⋊C4—862no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C4⋊C4#1062188314yes—
278C42—41no—
279C42—41no—
280C42C2×C4×D4311yescharacteristic
281C42#1062189811yescharacteristic
282C42D4×D4311yescharacteristic
283C42D4×D4311yescharacteristic
284C23—42no—
285C23—81no—
286C23—81no—
287C23—82no—
288C23—82no—
289C23#1306329711yescharacteristic
290Q8—3442no—
291Q8—3442no—
292D4—42no—
293D4—42no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—81no—
298D4—81no—
299D4—81no—
300D4—81no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—3442no—
306C2×C4—1722no—
307C2×C4C22⋊C4×D4311yescharacteristic
308C2×C4(C22⋊D43)⋊C411yescharacteristic
309C2×C4C4×C22⋊D4311yescharacteristic
310C2×C4#1306329811yescharacteristic
311C2×C4#1306331111yescharacteristic
312C2×C4#1306332111yescharacteristic
313C2×C4C2×#1062188312yes—
314C2×C4#1306334411yescharacteristic
315C2×C4#1306334512yes—
316C2×C4#1306334611yescharacteristic
317C2×C4#1306334911yescharacteristic
318C2×C4#1306335411yescharacteristic
319C8—81no—
320C8—862no—
321C8—862no—
322C8—3441no—
323C8—1722no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—162no—
328C22—162no—
329C22#1458279911yescharacteristic
330C22#1458311211yescharacteristic
331C22#1458311911yescharacteristic
332C22#1458312612yes—
333C22#1458316712yes—
334C4—21no—
335C4—21no—
336C4—44no—
337C4—3442no—
338C4#1458289211yescharacteristic
339C4#1458289711yescharacteristic
340C4C4×#1062188312yes—
341C4#1458311311yescharacteristic
342C4#1458312011yescharacteristic
343C4#1458327111yescharacteristic
344C4#1458328111yescharacteristic
345C2—162no—
346C2#1913400212yes—
347C2#1913400912yes—
348C2#1913544811yescharacteristic
349C2#1913550411yescharacteristic
350C2#1913552611yescharacteristic
subgroupG/H
centerC23#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1982C2
socleC23×C43#121
prime radicalC2×#127×C43C22
cosocleC2×C42×C43C23
hypercenter#1982D43
hypocenterC43#9735
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #19135543C2semidirect
3. C4⋊C4×C43⋊C8C2semidirect
4. C2×#14582649C2semidirect
5. C2×#14582647C2semidirect
10. #14583245C4semidirect
201. C43#9735semidirect

Maximal subgroups

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

subgroupindex
C2×#145832452
#191355432
C4⋊C4×C43⋊C82
C2×#145826492
C2×#145826472
C2×#145826432
C43×#19822
#973543