Finite Group Databasebeta

← #11797129

Subgroups — #11797129

Order 1152.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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×#63770C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic
3C3⋊D3×M32C211yesmaximal, characteristic
4#10590137C214yesmaximal, complemented
5#64286—21no—
6C2×#3788—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8#63770—21no—
9#63770C2212yes—
10#63769—21no—
11#63768C2212yes—
12C32×M32C411yescharacteristic, complemented
13#63639C411yescharacteristic, complemented
14#63625C2212yes—
15C16×C3⋊D3C412yescomplemented
16D3×M32—62no—
17C2×C4×C3⋊D3D411yescharacteristic
18C22⋊#157—41no—
19C2×#622—41no—
20C4⋊#157—22no—
21C4×#157—41no—
22#3788—22no—
23#3788—41no—
24C2×C32×C8C2×C411yescharacteristic
25C2×C3⋊(C3⋊C8)Q811yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3D411yescharacteristic
28C8×C3⋊D3Q811yescharacteristic
29C8×C3⋊D3C2311yescharacteristic
30C32×C16C2×C412yes—
31C3⋊(C3⋊C16)C2×C412yes—
32#2155—91nomaximal, Sylow
33C2×D3×C8—62no—
34C3×M32—22no—
35#812—62no—
36#798—64no—
37D3×C16—64no—
38C22×C3⋊D3SD1611yescharacteristic
39C2×#157—42no—
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C3⋊Dic3SD1611yescharacteristic
42C4×C3⋊D3C4⋊C411yescharacteristic
43C4×C3⋊D3SD1611yescharacteristic
44C4×C3⋊D3SD1611yescharacteristic
45C4×C3⋊D3C2×D411yescharacteristic
46#622—42no—
47C32×C8C4⋊C411yescharacteristic
48C32×C8C22×C411yescharacteristic
49C3⋊(C3⋊C8)C4⋊C411yescharacteristic
50C3⋊(C3⋊C8)C2×Q811yescharacteristic
51C2×M32—91no—
52C2×#108—91no—
53#427—91no—
54#365—94no—
55C2×C4×D3—62no—
56C2×C3×C8—22no—
57C2×C3⋊C8—62no—
58D3×C8—62no—
59D3×C8—62no—
60D3×C8—62no—
61D3×C8—62no—
62C3×C16—24no—
63C3⋊C16—64no—
64C22×C32#10611yescharacteristic
65C2×C3⋊D3—41no—
66C2×C3⋊D3#10611yescharacteristic
67C2×C3⋊D3C2×SD1611yescharacteristic
68#157—82no—
69C32×C4#10611yescharacteristic
70C32×C4C2×C4⋊C411yescharacteristic
71C3⋊Dic3#10611yescharacteristic
72C3⋊Dic3C2×SD1611yescharacteristic
73C2×M16—181no—
74C22×C8—91no—
75#117—181no—
76M32—91no—
77M32—92no—
78M32#15711yescharacteristic, complemented
79C2×C16—92no—
80#108—92no—
81#108—181no—
82#107—181no—
83#106—92no—
84C22×D3—62no—
85C2×C3×C4—22no—
86C2×Dic3—62no—
87C4×D3—62no—
88C4×D3—62no—
89C4×D3—62no—
90C4×D3—62no—
91C3×C8—22no—
92C3×C8—22no—
93C3⋊C8—62no—
94C3⋊C8—62no—
95C2×C32—21no—
96C2×C32C2×#10611yescharacteristic
97C3⋊D3—21no—
98C3⋊D3—21no—
99C22×C4—91no—
100M16—182no—
101M16—361no—
102C2×C8—91no—
103C2×C8—91no—
104C2×C8—91no—
105C2×C8—91no—
106C2×C8—91no—
107C2×C8—361no—
108C2×C8C2×#15711yescharacteristic
109C4⋊C4—182no—
110C22⋊C4—361no—
111C42—361no—
112C16—92no—
113C16C2×#15712yes—
114C22×C3—22no—
115C2×D3—62no—
116C2×D3—62no—
117C2×D3—124no—
118C3×C4—22no—
119C3×C4—22no—
120Dic3—62no—
121Dic3—62no—
122C32#215511yescharacteristic, complemented, Sylow
123C23—91no—
124C2×C4—91no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—362no—
130C2×C4C4⋊#15711yescharacteristic
131C8—91no—
132C8—91no—
133C8—362no—
134C8C4⋊#15711yescharacteristic
135C8C22×#15711yescharacteristic
136C2×C3—22no—
137C2×C3—42no—
138D3—64no—
139D3—122no—
140C22—91no—
141C22—91no—
142C22—361no—
143C22#6376811yescharacteristic
144C4—91no—
145C4—91no—
146C4—722no—
147C4#6376811yescharacteristic
148C4C2×C4⋊#15711yescharacteristic
149C3—22no—
150C2—21no—
151C2—181no—
152C2—181no—
153C2C2×#6376811yescharacteristic
subgroupG/H
centerC2C2×#63768
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×M32C4
socleC2×C32C2×#106
prime radicalC22×C3⋊D3SD16
cosocleC8×C3⋊D3C23
hypercenterM32#157
hypocenterC32#2155
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
4. #10590137C2semidirect
12. C32×M32C4semidirect
13. #63639C4semidirect
15. C16×C3⋊D3C4semidirect
78. M32#157semidirect
122. C32#2155semidirect

Maximal subgroups

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

subgroupindex
C2×#637702
#105937682
C3⋊D3×M322
#105901372
#21559