Finite Group Databasebeta

← #11920586

Subgroups — #11920586

Order 1152.

246 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 31 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
1A4×D24C211yesmaximal, characteristic, complemented
2#10593636C211yesmaximal, characteristic, complemented
3C3×A4⋊C16C211yesmaximal, characteristic, complemented
4#73133—31nomaximal
5#69108—31nomaximal
6A4×D12—21no—
7C4⋊(C3⋊S4)—21no—
8C3×C8×A4C2211yescharacteristic
9#63546—41nomaximal
10C22×D24D311yescharacteristic, complemented
11A4×D8—31no—
12#5402—31no—
13#5402—61no—
14#5115—31no—
15C2×D48—31no—
16C2×D48—31no—
17A4⋊C16D311yescharacteristic, complemented
18C3×C22⋊C16—31no—
19#4509—31no—
20#4509—31no—
21C2×D3×A4—41no—
22C2×C3⋊S4—41no—
23C3×C4×A4D411yescharacteristic
24#3745—41no—
25C3×D24—41no—
26C3×C3⋊C16—41no—
27#2184—91noSylow
28C22×D12—21no—
29D4×A4—61no—
30C4⋊S4—62no—
31C4⋊S4—61no—
32C22×C3×C8C2×D311yescharacteristic
33#930—61no—
34C2×D24—31no—
35C2×D24—31no—
36C2×D24—31no—
37C2×D24—61no—
38C8×A4—21no—
39C8×A4C2×D311yescharacteristic
40C2×C3×C16—31no—
41C2×C3×C16—31no—
42#826—121no—
43#821—61no—
44#818—31no—
45D48—62no—
46D48—61no—
47D48—61no—
48C2×C3×A4D811yescharacteristic
49D3×A4—81no—
50C3⋊S4—81no—
51C4⋊(C3⋊D3)—81no—
52C3×D12—81no—
53C32×C8—41no—
54C22×D8—31no—
55C2×D16—91no—
56C2×D16—91no—
57#466—91no—
58#357—91no—
59#357—91no—
60C22⋊C16—31no—
61C23×D3—41no—
62C22×A4—121no—
63C2×S4—122no—
64C2×S4—121no—
65C22×C3×C4#6711yescharacteristic
66C2×#67—121no—
67C2×D12—61no—
68C2×D12—61no—
69C2×D12—61no—
70C2×D12—121no—
71C4×A4—21no—
72C4×A4D1211yescharacteristic
73C3×D8—121no—
74C2×C3×C8—31no—
75C2×C3×C8—31no—
76(C2×D3)⋊C4—121no—
77C4⋊Dic3—61no—
78D24—32no—
79D24—31no—
80D24—61no—
81D24—61no—
82D24—61no—
83D24—121no—
84D24—241no—
85D24S411yescharacteristic, complemented
86C3×C16—61no—
87C3×C16—61no—
88C3⋊C16—41no—
89C2×C3⋊D3—161no—
90C2×C3×D3—161no—
91C3×A4D1611yescharacteristic, complemented
92C32×C4—41no—
93C22×D4—61no—
94C2×D8—91no—
95C2×D8—91no—
96C2×D8—91no—
97C2×D8—181no—
98C22×C8D3211yescharacteristic
99#121—181no—
100D16—181no—
101D16—182no—
102D16—181no—
103C2×C16—31no—
104C2×C16—31no—
105#107—91no—
106#102—181no—
107C23×C3#21311yescharacteristic
108C22×D3—81no—
109C22×D3—121no—
110C22×D3—121no—
111C22×D3—121no—
112C22×D3—241no—
113C2×A4—21no—
114C2×A4—241no—
115C2×A4D2411yescharacteristic
116S4—242no—
117S4—241no—
118C3×D4—241no—
119C2×C3×C4—31no—
120C2×C3×C4—31no—
121#67—241no—
122#67—241no—
123C2×Dic3—121no—
124D12—21no—
125D12—61no—
126D12—121no—
127D12—121no—
128D12—121no—
129D12—121no—
130D12—241no—
131D12—242no—
132C3×C8—31no—
133C3×C8—41no—
134C3×C8—81no—
135C3×C8C2×S411yescharacteristic
136C2×C32—41no—
137C3⋊D3—321no—
138C3×D3—321no—
139C24—121no—
140C2×D4—181no—
141C2×D4—181no—
142C2×D4—181no—
143C2×D4—361no—
144C2×D4—361no—
145C22×C4#62611yescharacteristic
146D8—31no—
147D8—92no—
148D8—91no—
149D8—181no—
150D8—181no—
151D8—181no—
152C2×C8—31no—
153C2×C8—31no—
154C4⋊C4—181no—
155C22⋊C4—361no—
156C16—61no—
157C16—61no—
158C22×C3—31no—
159C22×C3—31no—
160C22×C3—481no—
161C22×C3#82611yescharacteristic, complemented
162C2×D3—41no—
163C2×D3—121no—
164C2×D3—241no—
165C2×D3—241no—
166C2×D3—241no—
167C2×D3—241no—
168C2×D3—241no—
169C2×D3—241no—
170C2×D3—241no—
171C2×D3—481no—
172C2×D3—482no—
173A4—21no—
174A4D4811yescharacteristic, complemented
175C3×C4—31no—
176C3×C4—41no—
177C3×C4—81no—
178C3×C4GL(2,ℤ/4)11yescharacteristic
179Dic3—241no—
180C32—41noSylow
181C23—241no—
182C23—361no—
183C23—361no—
184C23—361no—
185C23—721no—
186C23#371411yescharacteristic
187D4—61no—
188D4—181no—
189D4—361no—
190D4—361no—
191D4—361no—
192D4—361no—
193D4—721no—
194D4—721no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—361no—
198C8—31no—
199C8D3×S411yescharacteristic
200C2×C3—31no—
201C2×C3—31no—
202C2×C3—41no—
203C2×C3—81no—
204C2×C3—961no—
205C2×C3#541511yescharacteristic
206D3—81no—
207D3—241no—
208D3—481no—
209D3—961no—
210D3—962no—
211C22—31no—
212C22—31no—
213C22—121no—
214C22—361no—
215C22—721no—
216C22—721no—
217C22—721no—
218C22—721no—
219C22—721no—
220C22—721no—
221C22—721no—
222C22#6354611yescharacteristic, complemented
223C4—31no—
224C4—721no—
225C4#6421011yescharacteristic
226C3—41no—
227C3—81no—
228C3#7313311yescharacteristic, complemented
229C2—31no—
230C2—31no—
231C2—241no—
232C2—721no—
233C2—1441no—
234C2#1059318411yescharacteristic
subgroupG/H
centerC2#10593184
commutator, cosocleC3×C8×A4C22
Frattini, hypercenterC8D3×S4
FittingC22×C3×C8C2×D3
socleC23×C3#213
hypocenterC3×A4D16
LCSG ▷ C3×C8×A4 ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. A4×D24C2semidirect
2. #10593636C2semidirect
3. C3×A4⋊C16C2semidirect
10. C22×D24D3semidirect
17. A4⋊C16D3semidirect
85. D24S4semidirect
91. C3×A4D16semidirect
161. C22×C3#826semidirect
174. A4D48semidirect
222. C22#63546semidirect
228. C3#73133semidirect

Maximal subgroups

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

subgroupindex
A4×D242
#105936362
C3×A4⋊C162
#731333
#691083
#635464