Finite Group Databasebeta

← #25009652

Subgroups — #25009652

Order 11008.

442 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135940C211yesmaximal, characteristic
2#19133568C212yesmaximal
3#19132625C212yesmaximal
4#19132541C211yesmaximal, characteristic
5C43×#2551C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583055—22no—
8#14582939—21no—
9#14582668C2211yescharacteristic
10#14582659—21no—
11#14582635—22no—
12#14582625C2212yes—
13C2×C4⋊Q8×C43—22no—
14C43×#395—21no—
15C43×#395C2212yes—
16C43×#389—22no—
17C43×#384C2211yescharacteristic
18C4×C4⋊C4×C43—21no—
19C2×#10621885—42no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063316—41no—
23#13063304—22no—
24#13063284—21no—
25#13063258—41no—
26#13063256—41no—
27#13063249—42no—
28C22⋊(C43⋊C8)—22no—
29C22×Q8×C43—21no—
30C22×Q8×C43D412yes—
31C4⋊Q8×C43—48no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C4⋊C4×C43C2311yescharacteristic
39C2×C42×C43—22no—
40C2×C42×C43D411yescharacteristic
41#95×C43—21no—
42#95×C43—22no—
43#95×C43D412yes—
44C2×Q8×C43—44no—
45C2×Q8×C43—44no—
46C2×Q8×C43—42no—
47C2×Q8×C43—81no—
48C22×C4×C43—21no—
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—21no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D412yes—
54C2×Dic86—22no—
55C4⋊C4×C43—24no—
56C4⋊C4×C43—24no—
57C4⋊C4×C43—41no—
58C4⋊C4×C43—41no—
59C4⋊C4×C43—44no—
60C4⋊C4×C43—44no—
61C4⋊C4×C43—44no—
62C42×C43—21no—
63C42×C43—44no—
64C42×C43Q1612yescomplemented
65C22⋊Dic43—41no—
66#10621885—84no—
67C4⋊Dic43—22no—
68C4⋊Dic43—21no—
69C4⋊Dic43—21no—
70Dic43⋊C4—42no—
71C4×Dic43—41no—
72#10621877—22no—
73#10621877—41no—
74C2×C43⋊C8—41no—
75C2×C43⋊C8—42no—
76C23×C43#12011yescharacteristic
77Q8×C43—44no—
78Q8×C43—82no—
79Q8×C43—84no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—24no—
86C2×C4×C43—24no—
87C2×C4×C43—22no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43—41no—
95C2×C4×C43C2×Q1611yescharacteristic
96C2×C4×C43#13711yescharacteristic
97C2×Dic43—41no—
98C2×Dic43—41no—
99Dic86—82no—
100C43⋊C8—42no—
101C43⋊C8—82no—
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—44no—
112C4×C43—42no—
113C4×C43—44no—
114C4×C43—81no—
115Dic43—81no—
116Dic43—81no—
117#2551D4311yescharacteristic
118#2060—431no—
119#1605—432no—
120#1354—432no—
121#1325—431no—
122C2×C43—21no—
123C2×C43—21no—
124C2×C43#160511yescharacteristic
125C2×C43#219611yescharacteristic
126C2×C43#220511yescharacteristic
127#544—431no—
128C2×C4⋊Q8—22no—
129#451—862no—
130#428—861no—
131#395—21no—
132#395C2×D4312yes—
133#389—22no—
134#384C2×D4311yescharacteristic
135C4×C4⋊C4—21no—
136#343—431no—
137#339—861no—
138#328—862no—
139#324—432no—
140C43#1225611yescharacteristic, complemented, Sylow
141C22×Q8—21no—
142C22×Q8C22⋊D4312yes—
143C2×Q16—1722no—
144C2×M16—861no—
145C4⋊Q8—48no—
146C4⋊Q8—1721no—
147#125—1721no—
148C22⋊Q8—862no—
149#117—861no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4C22⋊D4311yescharacteristic
156C2×C4⋊C4C22×D4311yescharacteristic
157C2×C42—22no—
158C2×C42C22⋊D4311yescharacteristic
159#107—1721no—
160#106—1721no—
161#103—1722no—
162C22⋊C8—862no—
163#95—21no—
164#95—22no—
165#95C22⋊D4312yes—
166C2×Q8—44no—
167C2×Q8—44no—
168C2×Q8—42no—
169C2×Q8—81no—
170C2×Q8—862no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—21no—
175C22×C4C2×C22⋊D4311yescharacteristic
176C22×C4C2×C22⋊D4312yes—
177Q16—3444no—
178M16—862no—
179M16—1721no—
180C2×C8—1722no—
181C2×C8—1721no—
182C4⋊C4—24no—
183C4⋊C4—24no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—44no—
187C4⋊C4—44no—
188C4⋊C4—44no—
189C4⋊C4—862no—
190C4⋊C4—861no—
191C4⋊C4—861no—
192C4⋊C4—1722no—
193C22⋊C4—1721no—
194C42—21no—
195C42—44no—
196C42—1721no—
197C42#1062188512yescomplemented
198C23#1306329411yescharacteristic
199Q8—44no—
200Q8—82no—
201Q8—84no—
202Q8—3442no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—24no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—1721no—
219C2×C4—1721no—
220C2×C4C2×#1062188511yescharacteristic
221C2×C4#1306335611yescharacteristic
222C8—3442no—
223C8—1722no—
224C22—21no—
225C22—21no—
226C22#1458305511yescharacteristic
227C22#1458308211yescharacteristic
228C22#1458308611yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—44no—
233C4—42no—
234C4—44no—
235C4—81no—
236C4—3441no—
237C4—3441no—
238C2—21no—
239C2—21no—
240C2#1913356911yescharacteristic
241C2#1913657911yescharacteristic
242C2#1913662511yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2551C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2551D43
hypocenterC43#12256
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
64. C42×C43Q16semidirect
140. C43#12256semidirect
197. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191359402
#191335682
#191326252
#191325412
C43×#25512
#1225643