Finite Group Databasebeta

← #11777112

Subgroups — #11777112

Order 1152.

276 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 64 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
1#10593728C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4#10590172C212yesmaximal, complemented
5#10590171C212yesmaximal, complemented
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8#63778—21no—
9C4⋊#622—21no—
10C4⋊#622C2211yescharacteristic
11C4⋊#622C2211yescharacteristic
12C4⋊#622C2212yes—
13C4×#622—21no—
14C32×C4⋊C8C411yescharacteristic
15#63647C412yes—
16C8×C3⋊Dic3C2212yes—
17C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
18#4833—62no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×C4×C3⋊D3D411yescharacteristic
21C2×C4×C3⋊D3Q811yescharacteristic
22C2×#622—22no—
23C2×#622—21no—
24C2×#622—21no—
25#3788—42no—
26C2×C32×C8C2×C412yes—
27C32×C42C2×C411yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C4×C3⋊Dic3Q811yescharacteristic
30C4×C3⋊Dic3C2311yescharacteristic
31C2×C3⋊(C3⋊C8)C2×C412yes—
32#1574—91nomaximal, Sylow
33C42×D3—62no—
34C3×C4⋊C8—22no—
35(C2×D3)⋊C8—64no—
36C8×Dic3—64no—
37C4⋊(C3⋊C8)—62no—
38C22×C3⋊D3C4⋊C411yescharacteristic
39C2×C32×C4C4⋊C411yescharacteristic
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C32×C4C22×C411yescharacteristic
42C2×C3⋊Dic3C4⋊C411yescharacteristic
43C2×C3⋊Dic3C2×D411yescharacteristic
44C2×C3⋊Dic3C2×Q811yescharacteristic
45C4×C3⋊D3—22no—
46C4×C3⋊D3—21no—
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49C4×C3⋊D3—21no—
50#622—42no—
51#622—41no—
52#622—41no—
53C32×C8—22no—
54C3⋊(C3⋊C8)—22no—
55#431—91no—
56#431—91no—
57#423—91no—
58#335—92no—
59#334—92no—
60C2×C4×D3—62no—
61C2×C4×D3—62no—
62C2×C4×D3—62no—
63C2×C3×C8—24no—
64C3×C42—22no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C4×Dic3—62no—
68C2×C3⋊C8—64no—
69C22×C32C2×C4⋊C411yescharacteristic
70C2×C3⋊D3—21no—
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C32×C4—21no—
74C32×C4#10812yes—
75C32×C4#13111yescharacteristic
76C32×C4#13111yescharacteristic
77C3⋊Dic3—21no—
78C3⋊Dic3—21no—
79C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
80C3⋊Dic3#13711yescharacteristic
81C2×M16—181no—
82C2×C42—91no—
83C4⋊C8—91no—
84C4⋊C8—92no—
85C4⋊C8—91no—
86C4⋊C8—91no—
87C4⋊C8—181no—
88C4⋊C8#15711yescharacteristic
89C22⋊C8—92no—
90C22⋊C8—181no—
91C4×C8—92no—
92C4×C8—181no—
93C22×D3—62no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C4×D3—68no—
101C4×D3—122no—
102C4×D3—122no—
103C4×D3—122no—
104C4×D3—122no—
105C3×C8—44no—
106C3⋊C8—124no—
107C2×C32#42411yescharacteristic
108C2×C32#42811yescharacteristic
109C2×C32C2×#10811yescharacteristic
110C3⋊D3—41no—
111C22×C4—91no—
112C22×C4—91no—
113C22×C4—91no—
114M16—362no—
115C2×C8—92no—
116C2×C8—181no—
117C2×C8—181no—
118C2×C8—182no—
119C2×C8C2×#15712yes—
120C42—91no—
121C42—91no—
122C42—91no—
123C42C2×#15711yescharacteristic
124C22×C3—22no—
125C2×D3—64no—
126C2×D3—122no—
127C2×D3—122no—
128C3×C4—24no—
129C3×C4—22no—
130C3×C4—22no—
131C3×C4—42no—
132Dic3—62no—
133Dic3—62no—
134Dic3—64no—
135Dic3—122no—
136C32#157411yescharacteristic, complemented, Sylow
137C23—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—91no—
141C2×C4—181no—
142C2×C4—181no—
143C2×C4—182no—
144C2×C4—181no—
145C2×C4—181no—
146C2×C4C4⋊#15711yescharacteristic
147C2×C4C4⋊#15711yescharacteristic
148C2×C4C22×#15711yescharacteristic
149C8—22no—
150C8—182no—
151C8—362no—
152C8—361no—
153C8—361no—
154C2×C3—22no—
155C2×C3—22no—
156C2×C3—22no—
157D3—124no—
158C22—181no—
159C22—181no—
160C22—181no—
161C22C2×C4⋊#15711yescharacteristic
162C4—21no—
163C4—91no—
164C4—91no—
165C4—181no—
166C4—181no—
167C4#6377112yes—
168C4#6428711yescharacteristic
169C4#6428911yescharacteristic
170C3—22no—
171C2—361no—
172C2#1059375511yescharacteristic
173C2C2×#6377111yescharacteristic
174C2#1059377411yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC4⋊C8#157
hypocenterC32#1574
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10590172C2semidirect
5. #10590171C2semidirect
136. C32#1574semidirect

Maximal subgroups

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

subgroupindex
#105937282
#105937272
#105925322
#105901722
#105901712
#15749