Finite Group Databasebeta

← #11856155

Subgroups — #11856155

Order 1152.

10266 conjugacy classes of subgroups; only the 505 normal subgroups are shown.

normal subgroups only

This group has 10266 conjugacy classes of subgroups — too many to draw. Only its 505 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
1C25×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×#120C211yesmaximal, characteristic, complemented
3C2×#64146C216yesmaximal, complemented
4#10592946C211yesmaximal, characteristic, complemented
5#10592654C216yesmaximal, complemented
6#82612—34nomaximal
7C25×C32C2211yescharacteristic
8C24×C3⋊D3—24no—
9C24×C3⋊D3—224no—
10C24×C3⋊D3C2216yes—
11C22×C32×D4C2213yescomplemented
12C22×#638C2214yescomplemented
13C32×#120—24no—
14C2×C32×C22⋊C4C2213yescomplemented
15C2×#3757C2216yescomplemented
16#64146—224no—
17C2×#3752C22112yescomplemented
18C25×D3—34no—
19C2×C3×#120D314yescomplemented
20C2×#937—324no—
21#5247—34no—
22#4955—324no—
23C24×C32—212no—
24C24×C32D414yescomplemented
25C24×C32C2313yes—
26C24×C32C2311yescharacteristic, complemented
27C23×C3⋊D3—296no—
28C23×C3⋊D3—2128no—
29C23×C3⋊D3—212no—
30C23×C3⋊D3—212no—
31C23×C3⋊D3—248no—
32C23×C3⋊D3D4124yescomplemented
33C23×C3⋊D3C2314yes—
34C2×C32×D4—212no—
35C2×C32×D4—26no—
36C22×C32×C4C2313yescomplemented
37C2×#638—224no—
38C22×C3⋊Dic3C2314yescomplemented
39C32×C22⋊C4—26no—
40#3757—212no—
41#3752—224no—
42#2846—91noSylow
43C25×C3C2×D314yes—
44C24×D3—324no—
45C24×D3—696no—
46C24×D3—616no—
47C22×C3×D4C2×D3112yescomplemented
48C22×#67—316no—
49C3×#120—216no—
50C2×C3×C22⋊C4C2×D3112yescomplemented
51C2×#217—324no—
52#937—696no—
53C2×(C2×D3)⋊C4—348no—
54C23×C32—232no—
55C23×C32—224no—
56C23×C32—212no—
57C23×C32—26no—
58C23×C32—21no—
59C23×C32C2×D4112yes—
60C23×C32C2×D416yes—
61C23×C32C2411yescharacteristic
62C22×C3⋊D3—2256no—
63C22×C3⋊D3—296no—
64C22×C3⋊D3—296no—
65C22×C3⋊D3—248no—
66C22×C3⋊D3—212no—
67C22×C3⋊D3—24no—
68C22×C3⋊D3—296no—
69C22×C3⋊D3C2×D4124yes—
70C32×D4—412no—
71C2×C32×C4—26no—
72C2×C32×C4—23no—
73#638—416no—
74C2×C3⋊Dic3—212no—
75C26—91no—
76C2×#120—96no—
77C2×#120C3⋊D311yescharacteristic, complemented
78#379—91no—
79#379—96no—
80C24×C3—248no—
81C24×C3#67116yescomplemented
82C24×C3C22×D3112yes—
83C24×C3C22×D314yescomplemented
84C23×D3—316no—
85C23×D3—396no—
86C23×D3—6192no—
87C23×D3—6512no—
88C23×D3—6384no—
89C23×D3—648no—
90C23×D3—648no—
91C2×C3×D4—248no—
92C2×C3×D4—224no—
93C22×C3×C4C22×D3112yescomplemented
94C2×#67—696no—
95C22×Dic3—316no—
96C3×C22⋊C4—224no—
97#217—648no—
98(C2×D3)⋊C4—696no—
99C22×C32—232no—
100C22×C32—212no—
101C22×C32—224no—
102C22×C32—44no—
103C22×C32—43no—
104C22×C32#120112yescomplemented
105C22×C32C22×D416yes—
106C22×C32C22×D411yescharacteristic
107C2×C3⋊D3—2192no—
108C2×C3⋊D3—224no—
109C2×C3⋊D3—224no—
110C2×C3⋊D3#120116yescomplemented
111C32×C4—43no—
112C3⋊Dic3—44no—
113C25—96no—
114C25—1824no—
115C25—184no—
116C25C2×C3⋊D311yescharacteristic
117C22×D4—94no—
118C22×D4C2×C3⋊D313yescomplemented
119#120—24no—
120#120—1824no—
121C2×C22⋊C4—96no—
122C2×C22⋊C4—912no—
123C2×C22⋊C4C2×C3⋊D313yescomplemented
124C23×C3—2128no—
125C23×C3—296no—
126C23×C3—248no—
127C23×C3—224no—
128C23×C3—24no—
129C23×C3D3×D4148yes—
130C23×C3C2×#67124yes—
131C23×C3C23×D314yes—
132C22×D3—396no—
133C22×D3—6384no—
134C22×D3—61024no—
135C22×D3—6384no—
136C22×D3—6384no—
137C22×D3—6192no—
138C22×D3—648no—
139C22×D3—616no—
140C3×D4—448no—
141C2×C3×C4—224no—
142C2×C3×C4—212no—
143#67—1264no—
144C2×Dic3—648no—
145C2×C32—212no—
146C2×C32—81no—
147C2×C32C2×#12013yes—
148C2×C32C2×#12014yes—
149C3⋊D3—216no—
150C24—212no—
151C24—94no—
152C24—924no—
153C24—1848no—
154C24—18128no—
155C24—1896no—
156C24—1812no—
157C24—1812no—
158C24#63814yescomplemented
159C24C22×C3⋊D313yes—
160C24C22×C3⋊D311yescharacteristic, complemented
161C2×D4—212no—
162C2×D4—26no—
163C2×D4—1824no—
164C22×C4—94no—
165C22×C4C22×C3⋊D313yescomplemented
166C22⋊C4—26no—
167C22⋊C4—1824no—
168C22⋊C4—1812no—
169C22×C3—2128no—
170C22×C3—248no—
171C22×C3—296no—
172C22×C3—412no—
173C22×C3—416no—
174C22×C3#937148yescomplemented
175C22×C3C2×D3×D4124yes—
176C22×C3C22×#6714yes—
177C2×D3—364no—
178C2×D3—6768no—
179C2×D3—696no—
180C2×D3—696no—
181C3×C4—412no—
182Dic3—1216no—
183C32#284611yescharacteristic, complemented, Sylow
184C23—232no—
185C23—212no—
186C23—224no—
187C23—26no—
188C23—21no—
189C23—924no—
190C23—1896no—
191C23—18256no—
192C23—1896no—
193C23—1896no—
194C23—1812no—
195C23—184no—
196C23—1848no—
197C23D4×C3⋊D3112yes—
198C23C2×#63816yes—
199C23C23×C3⋊D311yescharacteristic
200D4—412no—
201D4—3616no—
202C2×C4—26no—
203C2×C4—23no—
204C2×C4—1812no—
205C2×C3—248no—
206C2×C3—84no—
207C2×C3D3×#120116yes—
208C2×C3C2×#937112yes—
209D3—664no—
210C22—232no—
211C22—212no—
212C22—224no—
213C22—43no—
214C22—44no—
215C22—916no—
216C22—18192no—
217C22—1824no—
218C22—1824no—
219C22#64146112yescomplemented
220C22C2×D4×C3⋊D316yes—
221C22C22×#63811yescharacteristic
222C4—43no—
223C4—364no—
224C3#8261214yescomplemented
225C2—212no—
226C2—81no—
227C2—1816no—
228C2C3⋊D3×#12014yes—
229C2C2×#6414613yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×#120C2
hypercenterC2×#120C3⋊D3
hypocenterC32#2846
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C25×C3⋊D3C2semidirect
2. C2×C32×#120C2semidirect
3. C2×#64146C2semidirect
4. #10592946C2semidirect
5. #10592654C2semidirect
11. C22×C32×D4C22semidirect
12. C22×#638C22semidirect
14. C2×C32×C22⋊C4C22semidirect
15. C2×#3757C22semidirect
17. C2×#3752C22semidirect
19. C2×C3×#120D3semidirect
24. C24×C32D4semidirect
26. C24×C32C23semidirect
32. C23×C3⋊D3D4semidirect
36. C22×C32×C4C23semidirect
38. C22×C3⋊Dic3C23semidirect
47. C22×C3×D4C2×D3semidirect
50. C2×C3×C22⋊C4C2×D3semidirect
77. C2×#120C3⋊D3semidirect
81. C24×C3#67semidirect
83. C24×C3C22×D3semidirect
93. C22×C3×C4C22×D3semidirect
104. C22×C32#120semidirect
110. C2×C3⋊D3#120semidirect
118. C22×D4C2×C3⋊D3semidirect
123. C2×C22⋊C4C2×C3⋊D3semidirect
158. C24#638semidirect
160. C24C22×C3⋊D3semidirect
165. C22×C4C22×C3⋊D3semidirect
174. C22×C3#937semidirect
183. C32#2846semidirect
219. C22#64146semidirect
224. C3#82612semidirect

Maximal subgroups

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

subgroupindex
C25×C3⋊D32
C2×C32×#1202
C2×#641462
#105929462
#105926542
#826123