Finite Group Databasebeta

← #11856161

Subgroups — #11856161

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×#64162C211yesmaximal, characteristic, complemented
3C2×#64091C216yesmaximal, complemented
4C32×#379C211yesmaximal, characteristic, complemented
5#10592654C216yesmaximal, complemented
6#73861—34nomaximal
7C25×C32C2211yescharacteristic
8C24×C3⋊D3—24no—
9C24×C3⋊D3—224no—
10C24×C3⋊D3C2216yes—
11C22×#638C2213yescomplemented
12C22×C4⋊(C3⋊D3)C2214yescomplemented
13C2×C32×C22⋊C4C2216yescomplemented
14#64162—24no—
15C2×#3757C2213yescomplemented
16C2×#3752C22112yescomplemented
17#64091—224no—
18C25×D3—34no—
19C2×#953—34no—
20C2×#882—324no—
21C3×#379D314yescomplemented
22#4955—324no—
23C24×C32—212no—
24C24×C32D414yescomplemented
25C24×C32C2313yes—
26C23×C3⋊D3—296no—
27C23×C3⋊D3—2128no—
28C23×C3⋊D3—212no—
29C23×C3⋊D3—212no—
30C23×C3⋊D3—248no—
31C23×C3⋊D3D4124yescomplemented
32C23×C3⋊D3C2314yes—
33C23×C3⋊D3C2311yescharacteristic, complemented
34C22×C32×C4C2314yescomplemented
35C2×#638—212no—
36C2×#638—26no—
37C22×C3⋊Dic3C2313yescomplemented
38C2×C4⋊(C3⋊D3)—224no—
39C32×C22⋊C4—212no—
40#3757—26no—
41#3752—224no—
42#2846—91noSylow
43C25×C3C2×D314yes—
44C24×D3—324no—
45C24×D3—696no—
46C24×D3—616no—
47C22×#67—312no—
48C22×D12—316no—
49C2×C3×C22⋊C4C2×D3124yescomplemented
50#953—616no—
51C2×#217—312no—
52C2×(C2×D3)⋊C4—348no—
53#882—696no—
54C23×C32—232no—
55C23×C32—224no—
56C23×C32—212no—
57C23×C32C2×D416yes—
58C23×C32C2×D4112yes—
59C23×C32C2411yescharacteristic
60C22×C3⋊D3—2256no—
61C22×C3⋊D3—296no—
62C22×C3⋊D3—296no—
63C22×C3⋊D3—248no—
64C22×C3⋊D3—24no—
65C22×C3⋊D3—212no—
66C22×C3⋊D3—296no—
67C22×C3⋊D3—26no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3C2×D4124yes—
70C2×C32×C4—212no—
71#638—412no—
72C2×C3⋊Dic3—26no—
73C2×C3⋊Dic3—23no—
74C4⋊(C3⋊D3)—416no—
75C26—91no—
76C2×#120—91no—
77C2×#120—96no—
78#379—96no—
79#379C3⋊D311yescharacteristic, complemented
80C24×C3—248no—
81C24×C3D12116yescomplemented
82C24×C3C22×D3112yes—
83C23×D3—316no—
84C23×D3—396no—
85C23×D3—34no—
86C23×D3—6192no—
87C23×D3—6512no—
88C23×D3—6384no—
89C23×D3—648no—
90C23×D3—648no—
91C22×C3×C4C22×D3116yescomplemented
92C2×#67—624no—
93C2×#67—648no—
94C22×Dic3—312no—
95C2×D12—696no—
96C3×C22⋊C4—248no—
97#217—624no—
98(C2×D3)⋊C4—696no—
99C22×C32—232no—
100C22×C32—212no—
101C22×C32—224no—
102C22×C32#120112yescomplemented
103C22×C32C22×D411yescharacteristic
104C22×C32C22×D416yes—
105C2×C3⋊D3—2192no—
106C2×C3⋊D3—224no—
107C2×C3⋊D3—224no—
108C2×C3⋊D3—44no—
109C2×C3⋊D3—43no—
110C2×C3⋊D3#120116yescomplemented
111C32×C4—44no—
112C3⋊Dic3—43no—
113C25—96no—
114C25—1824no—
115C25—184no—
116C25C2×C3⋊D311yescharacteristic
117C22×D4—93no—
118C22×D4—94no—
119#120—1824no—
120#120—184no—
121C2×C22⋊C4—93no—
122C2×C22⋊C4—912no—
123C2×C22⋊C4C2×C3⋊D316yescomplemented
124C23×C3—2128no—
125C23×C3—296no—
126C23×C3—248no—
127C23×C3C2×D12124yes—
128C23×C3D3×D4148yes—
129C23×C3C23×D314yes—
130C22×D3—396no—
131C22×D3—6384no—
132C22×D3—61024no—
133C22×D3—6384no—
134C22×D3—6384no—
135C22×D3—6192no—
136C22×D3—616no—
137C22×D3—648no—
138C22×D3—64no—
139C22×D3—624no—
140C2×C3×C4—248no—
141#67—1248no—
142C2×Dic3—612no—
143C2×Dic3—624no—
144D12—1264no—
145C2×C32—212no—
146C2×C32C2×#12013yes—
147C2×C32C2×#12014yes—
148C3⋊D3—216no—
149C3⋊D3—81no—
150C24—212no—
151C24—94no—
152C24—924no—
153C24—91no—
154C24—1848no—
155C24—18128no—
156C24—1896no—
157C24—1812no—
158C24—1812no—
159C24C4⋊(C3⋊D3)14yescomplemented
160C24C22×C3⋊D313yes—
161C2×D4—1824no—
162C2×D4—186no—
163C2×D4—1812no—
164C22×C4—93no—
165C22×C4C22×C3⋊D314yescomplemented
166C22⋊C4—212no—
167C22⋊C4—1824no—
168C22⋊C4—186no—
169C22×C3—2128no—
170C22×C3—248no—
171C22×C3—296no—
172C22×C3#882148yescomplemented
173C22×C3C22×D1214yes—
174C22×C3C2×D3×D4124yes—
175C2×D3—364no—
176C2×D3—6768no—
177C2×D3—696no—
178C2×D3—696no—
179C2×D3—1212no—
180C2×D3—1216no—
181C3×C4—416no—
182Dic3—1212no—
183C32#284611yescharacteristic, complemented, Sylow
184C23—232no—
185C23—224no—
186C23—212no—
187C23—924no—
188C23—1896no—
189C23—18256no—
190C23—1896no—
191C23—1896no—
192C23—1848no—
193C23—184no—
194C23—1812no—
195C23—181no—
196C23—186no—
197C23C2×C4⋊(C3⋊D3)16yes—
198C23D4×C3⋊D3112yes—
199C23C23×C3⋊D311yescharacteristic
200D4—3616no—
201D4—3612no—
202C2×C4—212no—
203C2×C4—183no—
204C2×C4—186no—
205C2×C3—248no—
206C2×C3C2×#882112yes—
207C2×C3D3×#120116yes—
208D3—664no—
209D3—244no—
210C22—232no—
211C22—212no—
212C22—224no—
213C22—916no—
214C22—18192no—
215C22—1824no—
216C22—1824no—
217C22—363no—
218C22—364no—
219C22#64091112yescomplemented
220C22C22×C4⋊(C3⋊D3)11yescharacteristic
221C22C2×D4×C3⋊D316yes—
222C4—44no—
223C4—363no—
224C3#7386114yescomplemented
225C2—212no—
226C2—1816no—
227C2—721no—
228C2C2×#6409113yes—
229C2C3⋊D3×#12014yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#379C2
hypercenter#379C3⋊D3
hypocenterC32#2846
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C25×C3⋊D3C2semidirect
2. C2×#64162C2semidirect
3. C2×#64091C2semidirect
4. C32×#379C2semidirect
5. #10592654C2semidirect
11. C22×#638C22semidirect
12. C22×C4⋊(C3⋊D3)C22semidirect
13. C2×C32×C22⋊C4C22semidirect
15. C2×#3757C22semidirect
16. C2×#3752C22semidirect
21. C3×#379D3semidirect
24. C24×C32D4semidirect
31. C23×C3⋊D3D4semidirect
33. C23×C3⋊D3C23semidirect
34. C22×C32×C4C23semidirect
37. C22×C3⋊Dic3C23semidirect
49. C2×C3×C22⋊C4C2×D3semidirect
79. #379C3⋊D3semidirect
81. C24×C3D12semidirect
91. C22×C3×C4C22×D3semidirect
102. C22×C32#120semidirect
110. C2×C3⋊D3#120semidirect
123. C2×C22⋊C4C2×C3⋊D3semidirect
159. C24C4⋊(C3⋊D3)semidirect
165. C22×C4C22×C3⋊D3semidirect
172. C22×C3#882semidirect
183. C32#2846semidirect
219. C22#64091semidirect
224. C3#73861semidirect

Maximal subgroups

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

subgroupindex
C25×C3⋊D32
C2×#641622
C2×#640912
C32×#3792
#105926542
#738613