Finite Group Databasebeta

← #11785530

Subgroups — #11785530

Order 1152.

402 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#64289C211yesmaximal, characteristic
2#10593331C212yesmaximal, complemented
3#10591640C212yesmaximal
4#10590046C212yesmaximal, complemented
5C2×#3832C2211yescharacteristic
6#64289—24no—
7C2×#3788C412yes—
8C2×#3788C2211yescharacteristic
9C2×#3787C412yes—
10C2×#3787C2211yescharacteristic
11#63818C2214yes—
12#63733—24no—
13C3×#836—22no—
14#63559—22no—
15#4751—62no—
16C2×C32×Q8D411yescharacteristic
17#3832—22no—
18#3832—22no—
19C2×C4⋊(C3⋊D3)D411yescharacteristic
20C2×C4⋊(C3⋊D3)Q812yes—
21C2×C4×C3⋊D3C2×C412yes—
22C2×C4×C3⋊D3C2311yescharacteristic
23C2×#622C2×C412yes—
24C2×#622C2×C411yescharacteristic
25C2×#622C2×C411yescharacteristic
26#3788—22no—
27#3788—24no—
28#3787—24no—
29#3787D414yes—
30C3×#208—24no—
31#3712—24no—
32#3710—24no—
33#1813—91nomaximal, Sylow
34C2×#239—62no—
35D3×M16—64no—
36C3×#101—62no—
37#836—22no—
38#823—64no—
39C22×C3⋊D3C4⋊C412yes—
40C22×C3⋊D3C2×Q811yescharacteristic
41C32×Q8—22no—
42C2×C32×C4C4⋊C412yes—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3C22×C411yescharacteristic
45C4⋊(C3⋊D3)—24no—
46C4⋊(C3⋊D3)—22no—
47C4×C3⋊D3—22no—
48C4×C3⋊D3—22no—
49C4×C3⋊D3C2×D412yes—
50C4×C3⋊D3#4112yes—
51#622—22no—
52#622C22⋊C412yes—
53#622C22⋊C412yes—
54C3×C3⋊C8—44no—
55C2×#131—91no—
56C2×#108—92no—
57#413—92no—
58#338—92no—
59C2×C3×Q8—22no—
60#239—124no—
61#239—124no—
62C2×D12—62no—
63C2×D12—64no—
64C2×C4×D3—62no—
65C2×C4×D3—64no—
66C3×M16—64no—
67#208—24no—
68ΓL(1,𝔽25)—124no—
69D3×C8—124no—
70C22×C32C2×C4⋊C411yescharacteristic
71C2×C3⋊D3—22no—
72C2×C3⋊D3—41no—
73C2×C3⋊D3—42no—
74C2×C3⋊D3C22⋊Q812yes—
75C32×C4—22no—
76C32×C4#12112yes—
77C3⋊Dic3C2×C22⋊C411yescharacteristic
78C3⋊Dic3#11711yescharacteristic
79C2×#41—91no—
80#131—184no—
81C2×M16—92no—
82C2×M16—91no—
83C2×M16—94no—
84C22×C8—91no—
85C22×C8—92no—
86#108—184no—
87#101—62no—
88#100—182no—
89C22×D3—62no—
90C22×D3—64no—
91C3×Q8—44no—
92C2×C3×C4—22no—
93C2×C3×C4—24no—
94C2×Dic3—62no—
95D12—124no—
96D12—128no—
97C4×D3—64no—
98C4×D3—64no—
99C4×D3—124no—
100C4×D3—124no—
101C3×C8—124no—
102C3⋊C8—44no—
103C2×C32—21no—
104C2×C32#38011yescharacteristic
105C3⋊D3—22no—
106C3⋊D3—42no—
107#41—182no—
108#41—182no—
109C2×Q8GO+(4,𝔽2)11yescharacteristic
110C2×D4—91no—
111C2×D4—92no—
112C22×C4—91no—
113C22×C4—92no—
114M16—64no—
115M16—184no—
116M16—184no—
117M16—182no—
118C2×C8—94no—
119C2×C8—91no—
120C2×C8—91no—
121C2×C8—92no—
122C2×C8—184no—
123C2×C8—184no—
124C22×C3—22no—
125C2×D3—64no—
126C2×D3—124no—
127C2×D3—242no—
128C2×D3—244no—
129C3×C4—24no—
130C3×C4—44no—
131Dic3—62no—
132Dic3—62no—
133C32#181311yescharacteristic, complemented, Sylow
134C23—91no—
135C23—92no—
136Q8—22no—
137D4—184no—
138D4—182no—
139C2×C4—91no—
140C2×C4—92no—
141C2×C4—92no—
142C2×C4—182no—
143C2×C4—182no—
144C2×C4#377312yes—
145C2×C4C2×GO+(4,𝔽2)11yescharacteristic
146C8—92no—
147C8—92no—
148C8—124no—
149C8—182no—
150C2×C3—22no—
151C2×C3—42no—
152D3—124no—
153D3—244no—
154C22—92no—
155C22—182no—
156C22—361no—
157C22—362no—
158C22C2×#377311yescharacteristic
159C4—22no—
160C4—91no—
161C4—91no—
162C4#6424212yes—
163C3—22no—
164C2—21no—
165C2—182no—
166C2—362no—
167C2#1059351611yescharacteristic
subgroupG/H
centerC2#10593516
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC2×C32#380
prime radicalC2×#3832C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1813
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #10593331C2semidirect
4. #10590046C2semidirect
133. C32#1813semidirect

Maximal subgroups

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

subgroupindex
C2×#642892
#105933312
#105916402
#105900462
#18139