Finite Group Databasebeta

← #11785457

Subgroups — #11785457

Order 1152.

816 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 185 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×#3743C211yesmaximal, characteristic
2#10592825C212yesmaximal
3C2×#63649C212yesmaximal, complemented
4C32×#341C211yesmaximal, characteristic, complemented
5#10589418C211yesmaximal, characteristic, complemented
6#68940—34nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×M16C2212yes—
9C22×C32×C8C2211yescharacteristic
10C2×#3748C2212yes—
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×#3743—24no—
13C2×#3743C414yes—
14#63649—24no—
15#63647—24no—
16C22×ΓL(1,𝔽25)—34no—
17#5126—38no—
18C2×#822—38no—
19C3×#341D314yescomplemented
20#4552—34no—
21C23×C3⋊D3Q811yescharacteristic
22C22×C32×C4C2311yescharacteristic
23C22×C3⋊Dic3Q811yescharacteristic
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3C2×C412yes—
27C2×C4×C3⋊D3D412yes—
28C32×M16—22no—
29C32×M16—22no—
30C2×C32×C8—22no—
31C2×C32×C8—22no—
32C2×C32×C8C2×C412yes—
33#3748—22no—
34#3748—22no—
35C2×C3⋊(C3⋊C8)—22no—
36C2×C3⋊(C3⋊C8)C2×C412yes—
37C2×C3⋊(C3⋊C8)D414yes—
38#3743—28no—
39#1811—91noSylow
40C22×C4×D3—34no—
41C2×C3×M16C2×D318yes—
42C22×C3×C8C2×D314yes—
43C2×#208—38no—
44C22×C3⋊C8—34no—
45C2×ΓL(1,𝔽25)—316no—
46C2×ΓL(1,𝔽25)—616no—
47#822—616no—
48(C2×D3)⋊C8—616no—
49C23×C32C2×Q811yescharacteristic
50C22×C3⋊D3—22no—
51C22×C3⋊D3—42no—
52C22×C3⋊D3C4⋊C412yes—
53C2×C32×C4C22×C411yescharacteristic
54C2×C32×C4C2×D412yes—
55C2×C32×C4C2×D411yescharacteristic
56C2×C32×C4#4112yes—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3C4⋊C412yes—
59C4×C3⋊D3—22no—
60C4×C3⋊D3—22no—
61C4×C3⋊D3—24no—
62C32×C8—22no—
63C32×C8—42no—
64C3⋊(C3⋊C8)—42no—
65C3⋊(C3⋊C8)C22⋊C414yes—
66C22×M16—91no—
67C2×#108—92no—
68#407—92no—
69#341—91no—
70#341C3⋊D311yescharacteristic, complemented
71C23×D3—34no—
72C22×C3×C4C22×D314yes—
73C22×Dic3—34no—
74C2×C4×D3—38no—
75C2×C4×D3—38no—
76C2×C4×D3—68no—
77C2×C4×D3—68no—
78C3×M16—28no—
79C3×M16—28no—
80C2×C3×C8—28no—
81C2×C3×C8—28no—
82C2×C3×C8C4×D318yes—
83#208—68no—
84#208—68no—
85C2×C3⋊C8—38no—
86C2×C3⋊C8—316no—
87C2×C3⋊C8—68no—
88ΓL(1,𝔽25)—632no—
89C22×C32—22no—
90C22×C32C2×C4⋊C411yescharacteristic
91C22×C32C22⋊Q812yes—
92C2×C3⋊D3—22no—
93C2×C3⋊D3—24no—
94C2×C3⋊D3—44no—
95C32×C4C2×C22⋊C411yescharacteristic
96C32×C4#11711yescharacteristic
97C32×C4#12112yes—
98C3⋊Dic3—22no—
99C23×C4—91no—
100C2×M16—94no—
101C2×M16—92no—
102C2×M16—184no—
103C2×M16C2×C3⋊D312yes—
104C22×C8—91no—
105C22×C8C2×C3⋊D311yescharacteristic
106#108—184no—
107C22⋊C8—184no—
108C23×C3D3×Q814yes—
109C22×D3—38no—
110C22×D3—68no—
111C22×D3—128no—
112C2×C3×C4C2×C4×D314yes—
113C2×C3×C4#23518yes—
114C2×C3×C4D3×D418yes—
115C2×C3×C4D3×D414yes—
116C2×Dic3—38no—
117C2×Dic3—68no—
118C4×D3—68no—
119C4×D3—68no—
120C4×D3—616no—
121C3×C8—28no—
122C3×C8—48no—
123C3⋊C8—316no—
124C3⋊C8—128no—
125C2×C32—22no—
126C2×C32#38011yescharacteristic
127C2×C32#43012yes—
128C3⋊D3—42no—
129C24—91no—
130C22×C4—91no—
131C22×C4—92no—
132C22×C4—92no—
133C22×C4—182no—
134C22×C4—182no—
135C22×C4C22×C3⋊D311yescharacteristic
136M16—22no—
137M16—22no—
138M16—188no—
139M16—182no—
140M16—182no—
141C2×C8—22no—
142C2×C8—22no—
143C2×C8—92no—
144C2×C8—94no—
145C2×C8—182no—
146C2×C8C4×C3⋊D312yes—
147C22×C3—28no—
148C22×C3D3×C4⋊C414yes—
149C22×C3#89618yes—
150C2×D3—616no—
151C2×D3—68no—
152C2×D3—1216no—
153C3×C4#87214yes—
154C3×C4D3×C22⋊C414yes—
155C3×C4#88418yes—
156Dic3—68no—
157C32#181111yescharacteristic, complemented, Sylow
158C23—92no—
159C23—182no—
160C23—362no—
161C23Q8×C3⋊D311yescharacteristic
162C2×C4—92no—
163C2×C4—182no—
164C2×C4—182no—
165C2×C4—182no—
166C2×C4—184no—
167C2×C4C2×C4×C3⋊D311yescharacteristic
168C2×C4#382812yes—
169C2×C4D4×C3⋊D312yes—
170C2×C4D4×C3⋊D311yescharacteristic
171C8—22no—
172C8—42no—
173C8—94no—
174C8—362no—
175C2×C3—28no—
176C2×C3#466714yes—
177C2×C3#489318yes—
178D3—128no—
179C22—22no—
180C22—184no—
181C22—182no—
182C22—364no—
183C22C4⋊C4×C3⋊D311yescharacteristic
184C22#6410512yes—
185C4—182no—
186C4#6408111yescharacteristic
187C4C22⋊C4×C3⋊D311yescharacteristic
188C4#6409312yes—
189C3#6894014yescomplemented
190C2—22no—
191C2—362no—
192C2#1059236611yescharacteristic
193C2#1059259212yes—
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#341C2
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC22×C32×C4C23
hypercenter#341C3⋊D3
hypocenterC32#1811
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
3. C2×#63649C2semidirect
4. C32×#341C2semidirect
5. #10589418C2semidirect
19. C3×#341D3semidirect
70. #341C3⋊D3semidirect
157. C32#1811semidirect
189. C3#68940semidirect

Maximal subgroups

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

subgroupindex
C22×#37432
#105928252
C2×#636492
C32×#3412
#105894182
#689403