Finite Group Databasebeta

← #25027654

Subgroups — #25027654

Order 11008.

1530 conjugacy classes of subgroups; only the 371 normal subgroups are shown.

normal subgroups only

This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 371 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
1C22×#13063319C211yesmaximal, characteristic
2C2×#14582769C211yesmaximal, characteristic, complemented
3#19132849C216yesmaximal, complemented
4#19132841C216yesmaximal
5C2×C43×#383C211yesmaximal, characteristic, complemented
6C2×#13063319—24no—
7C2×#13063319—24no—
8C2×#13063319C418yescomplemented
9C22×C4⋊Dic43C2216yes—
10C22×Dic43⋊C4C2213yes—
11C22×(C2×D43)⋊C4C2213yes—
12C22×(C2×D43)⋊C4C2214yes—
13#14582769—24no—
14C2×C43⋊#95C22112yes—
15C22×C42×C43C2211yescharacteristic
16C43×#383—24no—
17C2×#95×C43C2216yes—
18C24×D43C2311yescharacteristic
19C23×Dic43C2314yes—
20C23×Dic43C2313yes—
21#13063319—232no—
22C2×C4⋊Dic43—212no—
23C2×C4⋊Dic43—412no—
24C2×Dic43⋊C4—26no—
25C2×Dic43⋊C4—26no—
26C2×Dic43⋊C4C2×C4112yes—
27C2×(C2×D43)⋊C4—26no—
28C2×(C2×D43)⋊C4—26no—
29C2×(C2×D43)⋊C4—412no—
30C2×(C2×D43)⋊C4C2×C4112yes—
31C43⋊#95—412no—
32C23×C4×C43C2314yes—
33C23×C4×C43C2313yes—
34C2×C42×C43C2×C414yes—
35C2×C42×C43D414yes—
36C2×C42×C43D414yes—
37#95×C43—212no—
38C24×C43C2411yescharacteristic
39C23×D43—21no—
40C23×D43—21no—
41C23×D43—26no—
42C23×D43—26no—
43C23×D43C22×C412yes—
44C22×C4×C43—24no—
45C22×C4×C43—26no—
46C22×C4×C43—212no—
47C22×C4×C43—26no—
48C22×C4×C43—212no—
49C22×C4×C43C22×C416yes—
50C22×C4×C43C2×D416yes—
51C22×C4×C43C2×D416yes—
52C22×Dic43—23no—
53C22×Dic43—23no—
54C22×Dic43—24no—
55C22×Dic43—26no—
56C22×Dic43—212no—
57C22×Dic43—212no—
58C22×Dic43—26no—
59C22×Dic43C22×C416yes—
60C42×C43C22⋊C4116yescomplemented
61(C2×D43)⋊C4—224no—
62(C2×D43)⋊C4—416no—
63C4⋊Dic43—424no—
64Dic43⋊C4—224no—
65C23×C43C23×C411yescharacteristic
66C23×C43C22×D411yescharacteristic
67C23×C43C22×D411yescharacteristic
68C23×C43H(5,𝔽2)16yes—
69C23×C432−1+416yes—
70C22×D43—22no—
71C22×D43—212no—
72C22×D43—43no—
73C22×D43—43no—
74C22×D43—46no—
75C22×D43—44no—
76C22×D43—412no—
77C2×C4×C43—212no—
78C2×C4×C43—26no—
79C2×C4×C43—26no—
80C2×C4×C43—212no—
81C2×C4×C43—412no—
82C2×C4×C43—44no—
83C2×C4×C43—412no—
84C2×C4×C43C2×C22⋊C4112yes—
85C2×Dic43—26no—
86C2×Dic43—212no—
87C2×Dic43—43no—
88C2×Dic43—43no—
89C2×Dic43—46no—
90C2×Dic43—412no—
91C2×Dic43—44no—
92C2×Dic43—412no—
93#14665—431nomaximal, Sylow
94C22×C43C22×C22⋊C411yescharacteristic
95C22×C43#52016yes—
96C22×C43#53513yes—
97C22×C43#53613yes—
98C22×C43#53716yes—
99C22×C43#56014yes—
100C22×C43#563112yes—
101C2×D43—46no—
102C2×D43—48no—
103C2×D43—81no—
104C2×D43—83no—
105C2×D43—84no—
106C4×C43—212no—
107C4×C43—84no—
108Dic43—46no—
109Dic43—84no—
110C22×#126—431no—
111C2×#384—431no—
112C2×#383D4311yescharacteristic, complemented
113#1441—436no—
114#1439—436no—
115C2×C43#231113yes—
116C2×C43#238314yes—
117C2×C43#281811yescharacteristic
118C2×C43#282113yes—
119C2×C43#282314yes—
120D43—82no—
121C2×#126—438no—
122C2×#126—864no—
123C2×#126—864no—
124C22×C4⋊C4—433no—
125C22×C4⋊C4—436no—
126C22×C22⋊C4—433no—
127C22×C22⋊C4—434no—
128C22×C42C2×D4311yescharacteristic
129#384—864no—
130#383—24no—
131C2×#95—4312no—
132C2×#95C2×D4316yes—
133C43#1466511yescharacteristic, complemented, Sylow
134C25—431no—
135C23×C4—433no—
136C23×C4—434no—
137C23×C4C22×D4314yes—
138C23×C4C22×D4313yes—
139#126—8632no—
140C2×C4⋊C4—4312no—
141C2×C4⋊C4—866no—
142C2×C4⋊C4—866no—
143C2×C4⋊C4—8612no—
144C2×C4⋊C4—17212no—
145C2×C22⋊C4—4312no—
146C2×C22⋊C4—866no—
147C2×C22⋊C4—866no—
148C2×C22⋊C4—17212no—
149C2×C42C4×D4314yes—
150C2×C42D17214yes—
151C2×C42C22⋊D4314yes—
152#95—212no—
153#95—17212no—
154C24—432no—
155C24—861no—
156C24—861no—
157C24—866no—
158C24—866no—
159C24C23×D4311yescharacteristic
160C22×C4—26no—
161C22×C4—26no—
162C22×C4—24no—
163C22×C4—212no—
164C22×C4—212no—
165C22×C4—436no—
166C22×C4—863no—
167C22×C4—863no—
168C22×C4—866no—
169C22×C4—866no—
170C22×C4—864no—
171C22×C4—8612no—
172C22×C4—8612no—
173C22×C4C2×C4×D4316yes—
174C22×C4C2×D17216yes—
175C22×C4C2×C22⋊D4316yes—
176C4⋊C4—8624no—
177C4⋊C4—17224no—
178C22⋊C4—8624no—
179C22⋊C4—17216no—
180C42(C2×D43)⋊C4116yescomplemented
181C23—862no—
182C23—8612no—
183C23—1724no—
184C23—17212no—
185C23—1723no—
186C23—1723no—
187C23—1726no—
188C23C22×C4×D4311yescharacteristic
189C23C22×C22⋊D4311yescharacteristic
190C23C22×D17211yescharacteristic
191C23#1306337116yes—
192C23#1306337216yes—
193C2×C4—212no—
194C2×C4—26no—
195C2×C4—26no—
196C2×C4—212no—
197C2×C4—44no—
198C2×C4—412no—
199C2×C4—412no—
200C2×C4—866no—
201C2×C4—8612no—
202C2×C4—1724no—
203C2×C4—17212no—
204C2×C4—17212no—
205C2×C4—1723no—
206C2×C4—1723no—
207C2×C4—1726no—
208C2×C4C2×(C2×D43)⋊C4112yes—
209C22—3443no—
210C22—3444no—
211C22—3441no—
212C22—1726no—
213C22—1728no—
214C22C22×(C2×D43)⋊C411yescharacteristic
215C22#1458337916yes—
216C22#1458346813yes—
217C22#1458347513yes—
218C22#1458347716yes—
219C22#1458364014yes—
220C22#14583651112yes—
221C4—212no—
222C4—84no—
223C4—3444no—
224C4—1726no—
225C2—3442no—
226C2#1913718313yes—
227C2#1913778414yes—
228C2#1914263811yescharacteristic
229C2#1914265613yes—
230C2#1914266714yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#383C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#383D43
hypocenterC43#14665
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. C2×#14582769C2semidirect
3. #19132849C2semidirect
5. C2×C43×#383C2semidirect
8. C2×#13063319C4semidirect
60. C42×C43C22⋊C4semidirect
112. C2×#383D43semidirect
133. C43#14665semidirect
180. C42(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633192
C2×#145827692
#191328492
#191328412
C2×C43×#3832
#1466543