Finite Group Databasebeta

← #25072715

Subgroups — #25072715

Order 11008.

982 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 163 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×#14583635C211yesmaximal, characteristic
2#19144721C212yesmaximal, complemented
3#19133778C218yesmaximal, complemented
4#19133309C211yesmaximal, characteristic
5#19133043C212yesmaximal, complemented
6C43×#3138C211yesmaximal, characteristic
7#14583635—24no—
8#14583635—22no—
9#14583635C2214yes—
10C2×#13063312—22no—
11C2×#13063306—22no—
12C2×C4×Dic86C2212yes—
13C2×D4×Dic43—22no—
14#14583227—22no—
15#14583181C2214yescomplemented
16#14583106C2214yescomplemented
17#14583054—22no—
18#14583004—24no—
19#14582956C2212yes—
20#14582643C2214yes—
21#14582631C2218yescomplemented
22C43×#533C2211yescharacteristic
23C2×#127×C43C2211yescharacteristic
24C43×#490—22no—
25C43×#486C2214yes—
26C43×#418—22no—
27C4×M16×C43C2211yescharacteristic
28C22×Dic86D412yes—
29C23×Dic43—22no—
30C2×#10621885—24no—
31#13063312—28no—
32#13063312—28no—
33#13063306—28no—
34#13063306—28no—
35C4×Dic86—22no—
36C4×Dic86—22no—
37C4×Dic86D414yes—
38C4×Dic86C2314yes—
39D4×Dic43—28no—
40D4×Dic43—28no—
41C2×C4⋊Dic43D412yes—
42C2×Dic43⋊C4—22no—
43C2×C22⋊Dic43—24no—
44C2×C22⋊Dic43—22no—
45C2×C4×Dic43—22no—
46#13063256—24no—
47C4⋊(C43⋊C8)C2314yes—
48#13063249—24no—
49#13063248—24no—
50C22⋊(C43⋊C8)—22no—
51#13063236—22no—
52C22×D4×C43—22no—
53C22×D4×C43D412yes—
54C2×M16×C43—21no—
55C4⋊Q8×C43C2312yes—
56#127×C43—22no—
57#127×C43D412yes—
58#127×C43C2312yes—
59#125×C43—21no—
60C22⋊Q8×C43—22no—
61C4×Q8×C43—22no—
62#117×C43—21no—
63C2×C42×C43C2311yescharacteristic
64#102×C43—28no—
65#97×C43—21no—
66C4×C8×C43C2312yes—
67C24×C43—22no—
68C2×Q8×C43—22no—
69C2×D4×C43—24no—
70C2×D4×C43—22no—
71C2×D4×C43—24no—
72C2×D4×C43—48no—
73C2×D4×C43—44no—
74C2×D4×C43C2×D414yes—
75C22×C4×C43C2×D412yes—
76C22×C4×C43C2×D411yescharacteristic
77C22×Dic43—28no—
78C22×Dic43—22no—
79C22×Dic43—22no—
80C22×Dic43—84no—
81C2×Dic86—22no—
82C2×Dic86—44no—
83C2×Dic86C2×D414yes—
84M16×C43—42no—
85C2×C8×C43—22no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—42no—
89C22⋊C4×C43—41no—
90C42×C43—41no—
91C42×C43C2×D412yes—
92C42×C43C2×D411yescharacteristic
93C42×C43C2411yescharacteristic
94C22⋊Dic43—216no—
95C22⋊Dic43—28no—
96#10621885—48no—
97C4⋊Dic43—22no—
98C4⋊Dic43C2×D414yes—
99Dic43⋊C4—24no—
100Dic43⋊C4—24no—
101C4×Dic43—24no—
102C4×Dic43—24no—
103C2×C43⋊C8—24no—
104C23×C43—24no—
105C23×C43—48no—
106C23×C43—44no—
107C23×C43#12011yescharacteristic
108Q8×C43—44no—
109D4×C43—44no—
110D4×C43—48no—
111D4×C43—48no—
112D4×C43—82no—
113C2×C4×C43—22no—
114C2×C4×C43—24no—
115C2×C4×C43—42no—
116C2×C4×C43#12012yes—
117C2×C4×C43#12011yescharacteristic
118C2×C4×C43C22×D412yes—
119C2×C4×C43C22×D411yescharacteristic
120C2×Dic43—24no—
121C2×Dic43—24no—
122C2×Dic43—44no—
123C2×Dic43—44no—
124C2×Dic43—88no—
125Dic86—24no—
126Dic86—24no—
127Dic86—44no—
128C8×C43—42no—
129C43⋊C8—44no—
130#18531—431nomaximal, Sylow
131C22×C43—22no—
132C22×C43—48no—
133C22×C43—44no—
134C22×C43—88no—
135C22×C43#45512yes—
136C22×C43C2×#12011yescharacteristic
137C4×C43—22no—
138C4×C43—21no—
139C4×C43—21no—
140C4×C43—82no—
141C4×C43#57514yes—
142Dic43—44no—
143Dic43—44no—
144C2×#559—431no—
145#3138D4311yescharacteristic
146#3113—432no—
147#1640—438no—
148#1555—431no—
149#1491—432no—
150C2×C43—22no—
151C2×C43—84no—
152C2×C43#300512yes—
153C2×C43C2×#45511yescharacteristic
154#559—434no—
155#559—864no—
156#559—862no—
157#533C2×D4311yescharacteristic
158C2×#127C2×D4311yescharacteristic
159C2×#124—862no—
160C2×#123—862no—
161C2×C4×Q8—432no—
162C2×C4×D4—862no—
163#490—22no—
164#486C2×D4314yes—
165#483—862no—
166#475—434no—
167#462—434no—
168#451—862no—
169#441—864no—
170#432—432no—
171#418—22no—
172C4×M16C2×D4311yescharacteristic
173#331—434no—
174Q8⋊C8—438no—
175C43#1853111yescharacteristic, complemented, Sylow
176C22×Q8—432no—
177C22×D4—22no—
178C22×D4C22⋊D4312yes—
179C23×C4—862no—
180C2×Q16—864no—
181C2×M16—21no—
182C4⋊Q8C22×D4312yes—
183#127—22no—
184#127C22⋊D4312yes—
185#127C22×D4312yes—
186#125—21no—
187#124—868no—
188#124—868no—
189#123—868no—
190#123—868no—
191C22⋊Q8—22no—
192C4×Q8—22no—
193C4×Q8—434no—
194C4×Q8—434no—
195C4×Q8—862no—
196C4×Q8—862no—
197C4×D4—868no—
198C4×D4—868no—
199#117—21no—
200C2×C4⋊C4—432no—
201C2×C4⋊C4—862no—
202C2×C22⋊C4—864no—
203C2×C22⋊C4—862no—
204C2×C42—862no—
205C2×C42C22×D4311yescharacteristic
206#106—864no—
207C4⋊C8—434no—
208#103—864no—
209#103—864no—
210#102—28no—
211C22⋊C8—862no—
212#97—21no—
213#97—862no—
214C4×C8C22×D4312yes—
215C24—22no—
216C2×Q8—22no—
217C2×Q8—434no—
218C2×Q8—862no—
219C2×Q8—1724no—
220C2×D4—24no—
221C2×D4—22no—
222C2×D4—24no—
223C2×D4—48no—
224C2×D4—44no—
225C2×D4C2×C22⋊D4314yes—
226C22×C4—868no—
227C22×C4—862no—
228C22×C4—862no—
229C22×C4—3444no—
230C22×C4D4×D4312yes—
231C22×C4C2×C22⋊D4311yescharacteristic
232Q16—1728no—
233M16—42no—
234C2×C8—22no—
235C2×C8—864no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—434no—
240C4⋊C4—862no—
241C4⋊C4—864no—
242C4⋊C4—864no—
243C22⋊C4—41no—
244C22⋊C4—8616no—
245C22⋊C4—868no—
246C42—41no—
247C42—864no—
248C42—864no—
249C42D4×D4312yes—
250C42C2×C22⋊D4311yescharacteristic
251C42C23×D4311yescharacteristic
252C23—24no—
253C23—48no—
254C23—44no—
255C23#1306329311yescharacteristic
256Q8—44no—
257Q8—864no—
258Q8—864no—
259Q8—1724no—
260D4—44no—
261D4—48no—
262D4—48no—
263D4—82no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—42no—
267C2×C4—864no—
268C2×C4—864no—
269C2×C4—3448no—
270C2×C4—1724no—
271C2×C4—1724no—
272C2×C4#1306329311yescharacteristic
273C2×C4#1306329312yes—
274C2×C4C2×D4×D4312yes—
275C2×C4C22×C22⋊D4311yescharacteristic
276C8—42no—
277C8—1724no—
278C22—22no—
279C22—48no—
280C22—44no—
281C22—88no—
282C22#1458307612yes—
283C22C2×#1306329311yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—82no—
288C4—1724no—
289C4—1724no—
290C4#1458369514yes—
291C2—22no—
292C2—84no—
293C2#1914383412yes—
294C2C2×#1458307611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3138C2
socleC22×C43C2×#120
prime radicalC2×#127×C43C22
hypercenter#3138D43
hypocenterC43#18531
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
2. #19144721C2semidirect
3. #19133778C2semidirect
5. #19133043C2semidirect
15. #14583181C22semidirect
16. #14583106C22semidirect
21. #14582631C22semidirect
175. C43#18531semidirect

Maximal subgroups

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

subgroupindex
C2×#145836352
#191447212
#191337782
#191333092
#191330432
C43×#31382
#1853143