Finite Group Databasebeta

← #25009654

Subgroups — #25009654

Order 11008.

442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#19139624C211yesmaximal, characteristic
2#19135940C211yesmaximal, characteristic
3#19133571C212yesmaximal
4#19132626C212yesmaximal
5C43×#1325C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7C2×#13063324—22no—
8#14583057—22no—
9#14582939—21no—
10#14582819—21no—
11#14582819C2212yes—
12#14582795—22no—
13C4×C4⋊Dic43—21no—
14#14582668C2211yescharacteristic
15#14582659—21no—
16#14582637—22no—
17C43×#384C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86—21no—
20C22×Dic86D412yes—
21C2×Dic172—42no—
22C2×#10621877—21no—
23#13063324—41no—
24#13063324—48no—
25#13063316—41no—
26#13063304—22no—
27#13063284—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×C4×Dic43—22no—
33#13063258—41no—
34#13063256—41no—
35#13063250—42no—
36C43⋊#95—21no—
37C43⋊#95—22no—
38C43⋊#95D412yes—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C42×C43D411yescharacteristic
43C22⋊C8×C43—22no—
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43C2×D411yescharacteristic
47C22×C4×C43C2×D412yes—
48C22×Dic43—22no—
49C22×Dic43—22no—
50C2×Dic86—22no—
51C2×Dic86—42no—
52C2×Dic86—44no—
53C2×Dic86—44no—
54C2×Dic86—81no—
55C2×C8×C43—42no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C4⋊C4×C43—44no—
59C42×C43—21no—
60C42×C43Q1612yescomplemented
61C22⋊Dic43—41no—
62C4⋊Dic43—24no—
63C4⋊Dic43—24no—
64C4⋊Dic43—22no—
65C4⋊Dic43—21no—
66C4⋊Dic43—21no—
67Dic43⋊C4—44no—
68Dic43⋊C4—44no—
69Dic43⋊C4—42no—
70C4×Dic43—44no—
71C4×Dic43—41no—
72#10621877—22no—
73#10621877—41no—
74C2×C43⋊C8—41no—
75Dic172—84no—
76C23×C43#12011yescharacteristic
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—41no—
86C2×C4×C43C2×Q1611yescharacteristic
87C2×C4×C43#13711yescharacteristic
88C2×Dic43—24no—
89C2×Dic43—24no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—41no—
95C2×Dic43—41no—
96Dic86—44no—
97Dic86—82no—
98Dic86—84no—
99Dic86—82no—
100C8×C43—82no—
101C43⋊C8—42no—
102#12256—431nomaximal, Sylow
103C22×C43—21no—
104C22×C43—21no—
105C22×C43#45111yescharacteristic
106C22×C43#45611yescharacteristic
107C22×C43B(4,𝔽2)11yescharacteristic
108C4×C43—24no—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43—42no—
112C4×C43—81no—
113Dic43—44no—
114Dic43—44no—
115Dic43—81no—
116Dic43—81no—
117#2551—431no—
118#2060—431no—
119#1605—432no—
120#1354—432no—
121#1325D4311yescharacteristic
122C2×C43—21no—
123C2×C43—21no—
124C2×C43#160511yescharacteristic
125C2×C43#219611yescharacteristic
126C2×C43#220511yescharacteristic
127#544—431no—
128C2×C4⋊Q8—862no—
129#451—862no—
130#428—861no—
131#395—432no—
132#395—861no—
133#389—862no—
134#384C2×D4311yescharacteristic
135C4×C4⋊C4—861no—
136#343—431no—
137#339—861no—
138#328—862no—
139#324C2×D4312yes—
140C43#1225611yescharacteristic, complemented, Sylow
141C22×Q8—432no—
142C22×Q8—861no—
143C2×Q16—1722no—
144C2×M16—861no—
145C4⋊Q8—1721no—
146C4⋊Q8—1728no—
147#125—1721no—
148C22⋊Q8—862no—
149#117—861no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—861no—
152C2×C4⋊C4—861no—
153C2×C4⋊C4—862no—
154C2×C4⋊C4—862no—
155C2×C4⋊C4D17211yescharacteristic
156C2×C4⋊C4C22×D4311yescharacteristic
157C2×C42—862no—
158C2×C42D17211yescharacteristic
159#107—1721no—
160#106—1721no—
161#103—1722no—
162C22⋊C8—22no—
163#95—432no—
164#95—861no—
165#95—862no—
166C2×Q8—862no—
167C2×Q8—3441no—
168C2×Q8—1722no—
169C2×Q8—1724no—
170C2×Q8—1724no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—862no—
174C22×C4—862no—
175C22×C4C2×D17211yescharacteristic
176C22×C4D4×D4312yes—
177Q16—3444no—
178M16—862no—
179M16—1721no—
180C2×C8—42no—
181C2×C8—1721no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—44no—
185C4⋊C4—864no—
186C4⋊C4—864no—
187C4⋊C4—862no—
188C4⋊C4—861no—
189C4⋊C4—861no—
190C4⋊C4—1722no—
191C4⋊C4—1724no—
192C4⋊C4—1724no—
193C22⋊C4—1721no—
194C42—21no—
195C42—1724no—
196C42—1721no—
197C42Dic17212yescomplemented
198C23#1306329511yescharacteristic
199Q8—3442no—
200Q8—3442no—
201Q8—3444no—
202Q8—1724no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—864no—
213C2×C4—864no—
214C2×C4—1721no—
215C2×C4—1721no—
216C2×C4—1722no—
217C2×C4—1722no—
218C2×C4—1722no—
219C2×C4—1722no—
220C2×C4C2×Dic17211yescharacteristic
221C2×C4#1306335811yescharacteristic
222C8—82no—
223C8—1722no—
224C22—21no—
225C22—21no—
226C22#1458305711yescharacteristic
227C22#1458308411yescharacteristic
228C22#1458308711yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—81no—
234C4—3441no—
235C4—3441no—
236C4—1724no—
237C4—1724no—
238C2—21no—
239C2—21no—
240C2#1913357111yescharacteristic
241C2#1913658111yescharacteristic
242C2#1913662611yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1325C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1325D43
hypocenterC43#12256
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
60. C42×C43Q16semidirect
140. C43#12256semidirect
197. C42Dic172semidirect

Maximal subgroups

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

subgroupindex
#191396242
#191359402
#191335712
#191326262
C43×#13252
#1225643