Finite Group Databasebeta

← #25009657

Subgroups — #25009657

Order 11008.

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

normal subgroups only

This group has 342 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#19133636C212yesmaximal
3#19132622C212yesmaximal
4#19132541C211yesmaximal, characteristic
5C43×#2571C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583234—22no—
8#14582939—21no—
9#14582668C2211yescharacteristic
10#14582659—21no—
11#14582635—22no—
12#14582625C2212yes—
13C43×#400—21no—
14C43×#400C2212yes—
15C43×#389—22no—
16C43×#384C2211yescharacteristic
17C43×#382—22no—
18C4×C4⋊C4×C43—21no—
19C2×#10621877—21no—
20#13063324—41no—
21#13063316—41no—
22#13063304—22no—
23#13063284—21no—
24#13063258—41no—
25#13063258—42no—
26#13063256—41no—
27#13063248—42no—
28C22⋊(C43⋊C8)—22no—
29C2×C4⋊C4×C43—21no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43D411yescharacteristic
34C2×C4⋊C4×C43D412yes—
35C2×C4⋊C4×C43C2311yescharacteristic
36C2×C42×C43—22no—
37C2×C42×C43D411yescharacteristic
38#95×C43—21no—
39#95×C43—22no—
40#95×C43—22no—
41#95×C43—22no—
42#95×C43D412yes—
43C22×C4×C43—21no—
44C22×C4×C43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C2×Dic86—22no—
50C4⋊C4×C43—41no—
51C4⋊C4×C43—42no—
52C4⋊C4×C43—41no—
53C4⋊C4×C43—42no—
54C4⋊C4×C43—44no—
55C4⋊C4×C43—42no—
56C4⋊C4×C43—81no—
57C42×C43—21no—
58C42×C43—44no—
59C42×C43Q1612yes—
60C22⋊Dic43—41no—
61C4⋊Dic43—21no—
62C4⋊Dic43—21no—
63C4⋊Dic43—22no—
64Dic43⋊C4—42no—
65C4×Dic43—41no—
66#10621877—22no—
67#10621877—41no—
68C2×C43⋊C8—41no—
69C2×C43⋊C8—42no—
70C23×C43#12011yescharacteristic
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—42no—
78C2×C4×C43—42no—
79C2×C4×C43—42no—
80C2×C4×C43—42no—
81C2×C4×C43—42no—
82C2×C4×C43—42no—
83C2×C4×C43—42no—
84C2×C4×C43—41no—
85C2×C4×C43—42no—
86C2×C4×C43C2×Q1611yescharacteristic
87C2×C4×C43#13711yescharacteristic
88C2×Dic43—41no—
89C2×Dic43—41no—
90Dic86—82no—
91C43⋊C8—42no—
92C43⋊C8—82no—
93#12257—431nomaximal, Sylow
94C22×C43—21no—
95C22×C43—21no—
96C22×C43#45111yescharacteristic
97C22×C43#45611yescharacteristic
98C22×C43B(4,𝔽2)11yescharacteristic
99C4×C43—24no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—42no—
103C4×C43—82no—
104C4×C43—81no—
105C4×C43—82no—
106Dic43—81no—
107Dic43—81no—
108#2571D4311yescharacteristic
109#2060—431no—
110#1617—432no—
111#1353—432no—
112#1325—431no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43#160511yescharacteristic
116C2×C43#219811yescharacteristic
117C2×C43#220411yescharacteristic
118#544—431no—
119#484—862no—
120#428—861no—
121#400—21no—
122#400C2×D4312yes—
123#389—22no—
124#384C2×D4311yescharacteristic
125#382—22no—
126C4×C4⋊C4—21no—
127#343—431no—
128#339—861no—
129#328—862no—
130#324—432no—
131C43#1225711yescharacteristic, complemented, Sylow
132C2×M16—861no—
133C4⋊Q8—1721no—
134#125—1721no—
135C22⋊Q8—862no—
136#117—861no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4C22⋊D4311yescharacteristic
142C2×C4⋊C4C22⋊D4312yes—
143C2×C4⋊C4C22×D4311yescharacteristic
144C2×C42—22no—
145C2×C42C22⋊D4311yescharacteristic
146#107—1721no—
147#107—1722no—
148#106—1721no—
149#103—1722no—
150C22⋊C8—862no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95—22no—
155#95C22⋊D4312yes—
156C2×Q8—862no—
157C22×C4—21no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—21no—
161C22×C4C2×C22⋊D4311yescharacteristic
162C22×C4C2×C22⋊D4312yes—
163M16—862no—
164M16—1721no—
165C2×C8—1722no—
166C2×C8—1721no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—44no—
172C4⋊C4—42no—
173C4⋊C4—81no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C4⋊C4—862no—
177C4⋊C4—1722no—
178C22⋊C4—1721no—
179C42—21no—
180C42—44no—
181C42—1721no—
182C42#1062188512yes—
183C23#1306329411yescharacteristic
184Q8—3442no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—1721no—
201C2×C4—1721no—
202C2×C4C2×#1062188511yescharacteristic
203C2×C4#1306335611yescharacteristic
204C8—3442no—
205C8—1722no—
206C22—21no—
207C22—21no—
208C22#1458305511yescharacteristic
209C22#1458308211yescharacteristic
210C22#1458308611yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—82no—
216C4—81no—
217C4—82no—
218C4—3441no—
219C4—3441no—
220C2—21no—
221C2—21no—
222C2#1913356911yescharacteristic
223C2#1913659111yescharacteristic
224C2#1913662111yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2571C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2571D43
hypocenterC43#12257
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
131. C43#12257semidirect

Maximal subgroups

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

subgroupindex
#191359402
#191336362
#191326222
#191325412
C43×#25712
#1225743