Finite Group Databasebeta

← #11800082

Subgroups — #11800082

Order 1152.

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

normal subgroups only

This group has 250 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
1#10590905C211yesmaximal, characteristic
2#10590902C211yesmaximal, characteristic
3#10590174C211yesmaximal, characteristic
4#10590062C214yesmaximal
5C2×C3×Dic12—21no—
6#63919—21no—
7#63873—21no—
8C2×#3718C2212yes—
9C2×#3708C2212yes—
10C8×C3⋊Dic3C2211yescharacteristic
11C3×#818—21no—
12#63576C2212yes—
13#5183—61no—
14#4874—61no—
15C2×C3×Dic6—22no—
16C2×#627—41no—
17C2×C32×C8D411yescharacteristic
18C4×C3⋊Dic3D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2311yescharacteristic
20C3×C4⋊Dic3—22no—
21C3×Dic12—42no—
22#3724—41no—
23#3724—41no—
24#3724—41no—
25#3718—24no—
26#3708—22no—
27#2241—91nomaximal, Sylow
28C2×C3×Q16—61no—
29#944—62no—
30C2×#216—62no—
31C2×Dic12—21no—
32#888—62no—
33C3×#107—61no—
34#818—21no—
35C8×Dic3—61no—
36C8×Dic3—61no—
37#807—62no—
38C2×C32×C4C2×D411yescharacteristic
39C2×C3⋊Dic3D811yescharacteristic
40C2×C3⋊Dic3D811yescharacteristic
41C2×C3×Dic3—42no—
42C2×C3×Dic3—42no—
43C3×Dic6—42no—
44C3×Dic6—42no—
45#627—82no—
46C32×C8SD1612yes—
47C3⋊(C3⋊C8)#4112yes—
48#500—91no—
49#494—91no—
50#358—94no—
51C4×C16—91no—
52C2×C3×Q8—62no—
53C2×Dic6—22no—
54C2×Dic6—122no—
55C3×Q16—122no—
56C2×C3×C8—21no—
57C2×C3×C8—21no—
58C3×C4⋊C4—62no—
59#216—124no—
60C4⋊Dic3—22no—
61Dic3⋊C4—122no—
62Dic3⋊C4—122no—
63Dic3⋊C4—122no—
64C4×Dic3—61no—
65C4×Dic3—61no—
66C2×C3⋊C8—61no—
67C2×C3⋊C8—61no—
68Dic12—42no—
69C22×C32C2×D811yescharacteristic
70C32×C4#12411yescharacteristic
71C32×C4C2×SD1611yescharacteristic
72C3⋊Dic3SD3212yes—
73C3⋊Dic3Q3212yes—
74C3×Dic3—82no—
75C3×Dic3—82no—
76C2×Q16—61no—
77C2×Q16—92no—
78C4⋊Q8—181no—
79C4⋊Q8—181no—
80C2×C16—92no—
81#107—61no—
82#107—92no—
83C4×C8—91no—
84C3×Q8—122no—
85C3×Q8—122no—
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4—122no—
89C2×C3×C4—122no—
90C2×Dic3—42no—
91C2×Dic3—42no—
92C2×Dic3—61no—
93C2×Dic3—61no—
94C2×Dic3—61no—
95C2×Dic3—61no—
96Dic6—42no—
97Dic6—42no—
98Dic6—244no—
99C3×C8—22no—
100C3×C8—22no—
101C3⋊C8—62no—
102C3⋊C8—62no—
103C2×C32#48611yescharacteristic
104C2×C32C2×SD3211yescharacteristic
105C2×C32C2×Q3211yescharacteristic
106C2×Q8—62no—
107C2×Q8—361no—
108Q16—122no—
109Q16—184no—
110C2×C8—91no—
111C2×C8GO+(4,𝔽2)11yescharacteristic
112C4⋊C4—62no—
113C4⋊C4—361no—
114C4⋊C4—361no—
115C4⋊C4—361no—
116C42—91no—
117C16—182no—
118C22×C3—21no—
119C22×C3—21no—
120C3×C4—21no—
121C3×C4—21no—
122C3×C4—21no—
123C3×C4—21no—
124C3×C4—242no—
125C3×C4—242no—
126Dic3—62no—
127Dic3—62no—
128Dic3—62no—
129Dic3—62no—
130Dic3—82no—
131Dic3—82no—
132C32#224111yescharacteristic, complemented, Sylow
133Q8—122no—
134Q8—122no—
135Q8—722no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—122no—
139C2×C4—122no—
140C2×C4C2×GO+(4,𝔽2)11yescharacteristic
141C8—92no—
142C8#377512yes—
143C2×C3—21no—
144C2×C3—21no—
145C2×C3—21no—
146C2×C3—21no—
147C2×C3—21no—
148C2×C3—21no—
149C22#6422511yescharacteristic
150C4—92no—
151C4—92no—
152C4—242no—
153C4—242no—
154C4#6422111yescharacteristic
155C4C2×#377511yescharacteristic
156C3—21no—
157C3—21no—
158C2#1059327811yescharacteristic
159C2#1059328011yescharacteristic
160C2#1059336611yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32C2×D8
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2241
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
132. C32#2241semidirect

Maximal subgroups

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

subgroupindex
#105909052
#105909022
#105901742
#105900622
#22419