Finite Group Databasebeta

← #11781226

Subgroups — #11781226

Order 1152.

240 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 47 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
1Q8×#622C211yesmaximal, characteristic
2#10593395C211yesmaximal, characteristic
3#10591631C212yesmaximal
4#10590042C211yesmaximal, characteristic
5#10590040C212yesmaximal
6Q8×C3⋊Dic3C2211yescharacteristic
7#63919C2212yes—
8C4⋊#622—21no—
9C4⋊#622C2211yescharacteristic
10C4×#622—21no—
11C4×#622C2211yescharacteristic
12#63743—21no—
13#63743—21no—
14C3×#835—22no—
15#63575—22no—
16#63572C2212yes—
17#4793—62no—
18C2×C32×Q8D411yescharacteristic
19C2×#627—22no—
20C2×#622—21no—
21C2×#622D411yescharacteristic
22C2×#622D411yescharacteristic
23C4⋊(C3⋊Dic3)—21no—
24C4⋊(C3⋊Dic3)D411yescharacteristic
25C4×C3⋊Dic3—21no—
26C4×C3⋊Dic3C2311yescharacteristic
27C3×C4⋊Dic3—22no—
28C2×C3×C3⋊C8—22no—
29#3724—22no—
30#1676—91nomaximal, Sylow
31Q8×Dic3—62no—
32#888—62no—
33C3×#103—62no—
34#835—22no—
35#818—62no—
36Dic3⋊C8—62no—
37#807—62no—
38C32×Q8—21no—
39C32×Q8Q1612yes—
40C2×C32×C4—21no—
41C2×C32×C4C2×D411yescharacteristic
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3C2×D411yescharacteristic
44C2×C3⋊Dic3#4111yescharacteristic
45C2×C3×Dic3—42no—
46#627—82no—
47#622—21no—
48#622—41no—
49#622Q1612yes—
50C3×C3⋊C8—42no—
51#500—91no—
52#477—92no—
53C8×Q8—91no—
54#335—91no—
55#333—92no—
56C2×C3×Q8—22no—
57C2×Dic6—122no—
58C2×C3×C8—62no—
59C3×C4⋊C4—62no—
60C4⋊Dic3—22no—
61C4⋊Dic3—62no—
62C4⋊Dic3—122no—
63Dic3⋊C4—122no—
64C4×Dic3—62no—
65C4×Dic3—122no—
66C2×C3⋊C8—22no—
67C22×C32#12111yescharacteristic
68C32×C4—22no—
69C32×C4C2×Q1611yescharacteristic
70C32×C4#13511yescharacteristic
71C3⋊Dic3—21no—
72C3⋊Dic3—41no—
73C3⋊Dic3C2×Q1611yescharacteristic
74C3⋊Dic3#13711yescharacteristic
75C3×Dic3—82no—
76C4⋊Q8—92no—
77C4×Q8—91no—
78#107—182no—
79#107—181no—
80#107—181no—
81C4⋊C8—92no—
82C4⋊C8—91no—
83C4⋊C8—181no—
84#103—62no—
85C4×C8—91no—
86C4×C8—181no—
87C3×Q8—24no—
88C3×Q8—42no—
89C2×C3×C4—22no—
90C2×C3×C4—42no—
91C2×C3×C4—122no—
92C2×Dic3—42no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C2×Dic3—122no—
96Dic6—244no—
97C3×C8—122no—
98C3⋊C8—42no—
99C2×C32#46211yescharacteristic
100C2×C32#46711yescharacteristic
101C2×C32#47211yescharacteristic
102C2×Q8—182no—
103C2×Q8GO+(4,𝔽2)11yescharacteristic
104C2×C8—62no—
105C2×C8—91no—
106C2×C8—91no—
107C2×C8—181no—
108C4⋊C4—62no—
109C4⋊C4—91no—
110C4⋊C4—181no—
111C4⋊C4—182no—
112C42—91no—
113C42—181no—
114C22×C3—22no—
115C3×C4—22no—
116C3×C4—22no—
117C3×C4—44no—
118C3×C4—242no—
119Dic3—62no—
120Dic3—62no—
121Dic3—82no—
122Dic3—122no—
123Dic3—242no—
124C32#167611yescharacteristic, complemented, Sylow
125Q8—21no—
126Q8—722no—
127Q8#377612yes—
128C2×C4—21no—
129C2×C4—91no—
130C2×C4—91no—
131C2×C4—122no—
132C2×C4—181no—
133C2×C4C2×GO+(4,𝔽2)11yescharacteristic
134C8—92no—
135C8—122no—
136C8—181no—
137C8—361no—
138C2×C3—22no—
139C2×C3—22no—
140C2×C3—22no—
141C22#6424211yescharacteristic
142C4—22no—
143C4—91no—
144C4—91no—
145C4—181no—
146C4—242no—
147C4—361no—
148C4#6423711yescharacteristic
149C4C2×#377611yescharacteristic
150C3—22no—
151C2#1059347711yescharacteristic
152C2#1059347911yescharacteristic
153C2#1059352711yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socle, prime radicalC22×C32#121
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1676
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
124. C32#1676semidirect

Maximal subgroups

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

subgroupindex
Q8×#6222
#105933952
#105916312
#105900422
#105900402
#16769