Finite Group Databasebeta

← #11786263

Subgroups — #11786263

Order 1152.

378 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 87 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×C8×#157C211yesmaximal, characteristic
2#10593396C212yesmaximal
3#10593344C212yesmaximal
4#10590685C212yesmaximal
5C2×C4×#157C2211yescharacteristic
6C2×#3787C2211yescharacteristic
7C2×C8×C3⋊D3C2211yescharacteristic
8#63900C2214yes—
9C8×#157C414yescomplemented
10#63743—24no—
11#63737—24no—
12C3×#817—22no—
13#63574—22no—
14D3×#106—62no—
15C22×#157D412yes—
16C2×C4×C3⋊D3C2311yescharacteristic
17C2×#624—24no—
18C2×#622D412yes—
19C4×#157C2×C412yes—
20C4×#157Q812yes—
21#3787C2×C412yes—
22#3787Q812yes—
23C2×C32×C8D411yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C8×C3⋊D3C2×C412yes—
26C8×C3⋊D3Q812yes—
27C3×C4⋊Dic3—24no—
28#3724—24no—
29#1846—91nomaximal, Sylow
30C2×D3×C8—62no—
31D3×C4⋊C4—64no—
32C3×#106—62no—
33#817—22no—
34#808—64no—
35C22×C3⋊D3C2×D411yescharacteristic
36C2×#157—24no—
37C2×#157C4⋊C414yes—
38C2×C32×C4C2×D411yescharacteristic
39C2×C3⋊Dic3C2×D411yescharacteristic
40C4×C3⋊D3C22×C411yescharacteristic
41C4×C3⋊D3C2×Q811yescharacteristic
42C4×C3⋊D3C2×Q811yescharacteristic
43C4×C3⋊D3C2×Q811yescharacteristic
44C2×C3×Dic3—44no—
45#624—48no—
46#622C4⋊C414yes—
47C32×C8C4⋊C412yes—
48C3⋊(C3⋊C8)C4⋊C412yes—
49C2×#107—92no—
50C2×#106—92no—
51C2×C4×C8—91no—
52#382—92no—
53C2×C4×D3—62no—
54C2×C4×D3—124no—
55C2×C3×C8—22no—
56C3×C4⋊C4—64no—
57C4⋊Dic3—24no—
58Dic3⋊C4—124no—
59C2×C3⋊C8—62no—
60D3×C8—64no—
61D3×C8—64no—
62C22×C32#12711yescharacteristic
63C2×C3⋊D3C2×C4⋊C411yescharacteristic
64C2×C3⋊D3C4⋊Q811yescharacteristic
65C2×C3⋊D3#13514yes—
66#157—24no—
67C32×C4C2×C4⋊C411yescharacteristic
68C32×C4C4⋊Q811yescharacteristic
69C3⋊Dic3C2×C4⋊C411yescharacteristic
70C3⋊Dic3C4⋊Q811yescharacteristic
71C3×Dic3—84no—
72C22×C8—91no—
73C22×C8—91no—
74C2×C4⋊C4—94no—
75C2×C42—91no—
76#107—184no—
77#106—62no—
78#106—182no—
79C4×C8—94no—
80#95—184no—
81C22×D3—62no—
82C2×C3×C4—22no—
83C2×C3×C4—124no—
84C2×Dic3—44no—
85C2×Dic3—62no—
86C4×D3—62no—
87C4×D3—62no—
88C4×D3—62no—
89C4×D3—62no—
90C4×D3—248no—
91C3×C8—24no—
92C3⋊C8—64no—
93C2×C32#38411yescharacteristic
94C2×C32#49512yes—
95C3⋊D3#42712yes—
96C3⋊D3#49912yes—
97C22×C4—91no—
98C22×C4—92no—
99C22×C4—184no—
100C2×C8—92no—
101C2×C8—92no—
102C2×C8—92no—
103C2×C8—91no—
104C2×C8—92no—
105C2×C8—92no—
106C2×C8GO+(4,𝔽2)11yescharacteristic
107C4⋊C4—64no—
108C4⋊C4—184no—
109C42—92no—
110C42—92no—
111C22×C3—22no—
112C2×D3—62no—
113C2×D3—62no—
114C2×D3—68no—
115C3×C4—22no—
116C3×C4—22no—
117C3×C4—244no—
118Dic3—62no—
119Dic3—62no—
120Dic3—84no—
121C32#184611yescharacteristic, complemented, Sylow
122C23—91no—
123C2×C4—91no—
124C2×C4—91no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—94no—
129C2×C4—124no—
130C2×C4—184no—
131C2×C4—368no—
132C2×C4C2×GO+(4,𝔽2)11yescharacteristic
133C8—94no—
134C8—92no—
135C8#377312yes—
136C2×C3—24no—
137C2×C3—22no—
138D3—64no—
139D3—64no—
140C22—94no—
141C22—91no—
142C22—91no—
143C22#6423111yescharacteristic
144C4—91no—
145C4—91no—
146C4—184no—
147C4—244no—
148C4#6422211yescharacteristic
149C4C2×#377311yescharacteristic
150C3—22no—
151C2—92no—
152C2—92no—
153C2#1059329612yes—
154C2#1059341311yescharacteristic
subgroupG/H
centerC22#64231
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#127
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1846
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
9. C8×#157C4semidirect
121. C32#1846semidirect

Maximal subgroups

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

subgroupindex
C2×C8×#1572
#105933962
#105933442
#105906852
#18469