Finite Group Databasebeta

← #25027613

Subgroups — #25027613

Order 11008.

3274 conjugacy classes of subgroups; only the 411 normal subgroups are shown.

normal subgroups only

This group has 3274 conjugacy classes of subgroups — too many to draw. Only its 411 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×#14582755C212yesmaximal, complemented
2#19132844C216yesmaximal, complemented
3#19132836C216yesmaximal, complemented
4C22×#120×C43C211yesmaximal, characteristic
5C22×C22⋊Dic43C22112yes—
6C22×C22⋊Dic43C2214yescomplemented
7#14582755—28no—
8C2×C43⋊#95C22112yescomplemented
9C26×C43C2211yescharacteristic
10C23×D4×C43C2213yes—
11C2×#120×C43—28no—
12C2×#120×C43C418yescomplemented
13C22×C22⋊C4×C43C2213yes—
14C23×Dic43C2318yes—
15C2×C22⋊Dic43—224no—
16C2×C22⋊Dic43—424no—
17C2×C22⋊Dic43—412no—
18C43⋊#95—412no—
19C25×C43—412no—
20C25×C43C2×C414yes—
21C25×C43D418yes—
22C25×C43C2311yescharacteristic
23C25×C43C2313yes—
24C22×D4×C43—212no—
25C22×D4×C43—412no—
26C22×D4×C43C2×C4112yes—
27C23×C4×C43C2313yes—
28#120×C43—232no—
29C2×C22⋊C4×C43—212no—
30C2×C22⋊C4×C43C2×C4112yes—
31C24×C43—212no—
32C24×C43—224no—
33C24×C43—22no—
34C24×C43—212no—
35C24×C43—424no—
36C24×C43—448no—
37C24×C43—448no—
38C24×C43—416no—
39C24×C43C22⋊C4116yescomplemented
40C24×C43C22×C412yes—
41C24×C43C22×C416yes—
42C24×C43C2×D4112yes—
43C24×C43C2411yescharacteristic
44C2×D4×C43—224no—
45C2×D4×C43—424no—
46C2×D4×C43—448no—
47C22×C4×C43—26no—
48C22×C4×C43—212no—
49C22×C4×C43C22×C416yes—
50C22×Dic43—28no—
51C22×Dic43—224no—
52C22×Dic43—224no—
53C22⋊C4×C43—224no—
54C22⋊Dic43—448no—
55C22⋊Dic43—416no—
56C23×C43—212no—
57C23×C43—224no—
58C23×C43—224no—
59C23×C43—224no—
60C23×C43—224no—
61C23×C43—22no—
62C23×C43—212no—
63C23×C43—448no—
64C23×C43—464no—
65C23×C43—4128no—
66C23×C43—436no—
67C23×C43—412no—
68C23×C43—412no—
69C23×C43—412no—
70C23×C43—44no—
71C23×C43C2×C22⋊C4112yes—
72C23×C43C23×C411yescharacteristic
73C23×C43C22×D412yes—
74C23×C43H(5,𝔽2)112yes—
75D4×C43—448no—
76C2×C4×C43—26no—
77C2×C4×C43—212no—
78C2×C4×C43—412no—
79C2×Dic43—424no—
80C2×Dic43—424no—
81C2×Dic43—48no—
82#14657—431nomaximal, Sylow
83C22×C43—224no—
84C22×C43—212no—
85C22×C43—464no—
86C22×C43—424no—
87C22×C43—448no—
88C22×C43—46no—
89C22×C43—48no—
90C22×C43—88no—
91C22×C43C22×C22⋊C411yescharacteristic
92C22×C43#51816yes—
93C22×C43#534112yes—
94C22×C43#560112yes—
95C22×C43H(3,𝔽4)14yes—
96C4×C43—46no—
97Dic43—88no—
98C22×#120D4311yescharacteristic
99C2×#379—432no—
100#1440—436no—
101#1438—436no—
102C2×C43—412no—
103C2×C43—82no—
104C2×C43#230813yes—
105C2×C43#237514yes—
106C2×C43#281218yes—
107C26C2×D4311yescharacteristic
108C23×D4C2×D4313yes—
109C2×#120—28no—
110C2×#120Dic4318yescomplemented
111C22×C22⋊C4—4312no—
112C22×C22⋊C4—434no—
113C22×C22⋊C4C2×D4313yes—
114#379—868no—
115C2×#95—4312no—
116C43#1465711yescharacteristic, complemented, Sylow
117C25—412no—
118C25C2×Dic4314yes—
119C25C22⋊D4318yes—
120C25C22×D4311yescharacteristic
121C25C22×D4313yes—
122C22×D4—212no—
123C22×D4—412no—
124C22×D4C2×Dic43112yes—
125C23×C4—438no—
126C23×C4C22×D4313yes—
127#120—232no—
128C2×C22⋊C4—212no—
129C2×C22⋊C4—8624no—
130C2×C22⋊C4—17224no—
131C2×C22⋊C4—17212no—
132C2×C22⋊C4C2×Dic43112yes—
133#95—17212no—
134C24—224no—
135C24—212no—
136C24—22no—
137C24—212no—
138C24—424no—
139C24—448no—
140C24—448no—
141C24—416no—
142C24C22⋊Dic43116yescomplemented
143C24C22×Dic4312yes—
144C24C22×Dic4316yes—
145C24C2×C22⋊D43112yes—
146C24C23×D4311yescharacteristic
147C2×D4—224no—
148C2×D4—424no—
149C2×D4—448no—
150C22×C4—26no—
151C22×C4—212no—
152C22×C4—868no—
153C22×C4—8624no—
154C22×C4—8624no—
155C22×C4C22×Dic4316yes—
156C22⋊C4—224no—
157C22⋊C4—17248no—
158C22⋊C4—17216no—
159C23—212no—
160C23—224no—
161C23—224no—
162C23—224no—
163C23—224no—
164C23—22no—
165C23—212no—
166C23—448no—
167C23—4128no—
168C23—464no—
169C23—436no—
170C23—412no—
171C23—412no—
172C23—44no—
173C23—412no—
174C23C2×C22⋊Dic43112yes—
175C23C23×Dic4311yescharacteristic
176C23C22×C22⋊D4312yes—
177C23#13063370112yes—
178D4—448no—
179C2×C4—26no—
180C2×C4—212no—
181C2×C4—412no—
182C2×C4—17224no—
183C2×C4—1728no—
184C2×C4—17224no—
185C22—212no—
186C22—224no—
187C22—464no—
188C22—448no—
189C22—424no—
190C22—46no—
191C22—48no—
192C22—88no—
193C22C22×C22⋊Dic4311yescharacteristic
194C22#1458337416yes—
195C22#14583458112yes—
196C22#14583638112yes—
197C22#1458364214yes—
198C4—46no—
199C4—3448no—
200C2—412no—
201C2—82no—
202C2#1913717313yes—
203C2#1913773614yes—
204C2#1914259018yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
Fitting, prime radicalC22×#120×C43C2
socle, cosocleC24×C43C24
hypercenterC22×#120D43
hypocenterC43#14657
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14582755C2semidirect
2. #19132844C2semidirect
3. #19132836C2semidirect
6. C22×C22⋊Dic43C22semidirect
8. C2×C43⋊#95C22semidirect
12. C2×#120×C43C4semidirect
39. C24×C43C22⋊C4semidirect
110. C2×#120Dic43semidirect
116. C43#14657semidirect
142. C24C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827552
#191328442
#191328362
C22×#120×C432
#1465743