Finite Group Databasebeta

← #11800081

Subgroups — #11800081

Order 1152.

250 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 51 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#10590387C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic
3C4×#3708C211yesmaximal, characteristic
4#10590062C214yesmaximal
5C3×#869—21no—
6C3×#869—21no—
7C2×#3718—21no—
8C2×#3718C2212yes—
9C2×#3708C2212yes—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11#63576—21no—
12#63576C2212yes—
13#5092—61no—
14#5078—61no—
15C2×C3×Dic6—22no—
16C2×C3×Dic6—41no—
17C32×C42D411yescharacteristic
18C2×C3⋊(C3⋊C8)D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2311yescharacteristic
20C3×C4⋊Dic3—22no—
21C3×C4⋊Dic3—41no—
22C3×C4⋊Dic3—41no—
23C3×C4⋊Dic3—41no—
24#3718—24no—
25#3718—42no—
26#3708—22no—
27#2241—91nomaximal, Sylow
28C3×C4⋊Q8—61no—
29C3×C4⋊Q8—61no—
30C2×#216—62no—
31C2×#216—62no—
32#869—21no—
33#869—21no—
34#807—62no—
35#807—62no—
36C4×C3⋊C8—61no—
37C4×C3⋊C8—61no—
38C2×C32×C4D811yescharacteristic
39C2×C32×C4D811yescharacteristic
40C2×C32×C4C2×D411yescharacteristic
41C2×C3×Dic3—42no—
42C2×C3×Dic3—42no—
43C3×Dic6—42no—
44C3×Dic6—42no—
45C3×Dic6—82no—
46C3⋊(C3⋊C8)SD1612yes—
47C3⋊(C3⋊C8)#4112yes—
48#500—91no—
49#494—91no—
50#358—94no—
51C4×C16—91no—
52C2×C3×Q8—62no—
53C2×C3×Q8—121no—
54C2×Dic6—22no—
55C2×Dic6—41no—
56C3×C4⋊C4—62no—
57C3×C4⋊C4—121no—
58C3×C4⋊C4—121no—
59C3×C4⋊C4—121no—
60C3×C42—21no—
61C3×C42—21no—
62#216—124no—
63#216—124no—
64C4⋊Dic3—22no—
65C4⋊Dic3—41no—
66C4⋊Dic3—41no—
67C4⋊Dic3—41no—
68C2×C3⋊C8—61no—
69C2×C3⋊C8—61no—
70C2×C3⋊C8—61no—
71C2×C3⋊C8—61no—
72C22×C32C2×D811yescharacteristic
73C32×C4SD3212yes—
74C32×C4Q3212yes—
75C32×C4#12411yescharacteristic
76C32×C4C2×SD1611yescharacteristic
77C3×Dic3—82no—
78C3×Dic3—82no—
79C2×Q16—92no—
80C2×Q16—181no—
81C4⋊Q8—61no—
82C4⋊Q8—61no—
83C2×C16—92no—
84#107—92no—
85#107—181no—
86C4×C8—91no—
87C3×Q8—122no—
88C3×Q8—122no—
89C3×Q8—242no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4—21no—
96C2×C3×C4—122no—
97C2×C3×C4—122no—
98C2×Dic3—42no—
99C2×Dic3—42no—
100Dic6—42no—
101Dic6—42no—
102Dic6—82no—
103C3⋊C8—62no—
104C3⋊C8—62no—
105C3⋊C8—62no—
106C3⋊C8—62no—
107C2×C32#48611yescharacteristic
108C2×C32C2×SD3211yescharacteristic
109C2×C32C2×Q3211yescharacteristic
110C2×Q8—62no—
111C2×Q8—121no—
112Q16—184no—
113Q16—362no—
114C2×C8—91no—
115C2×C8—91no—
116C4⋊C4—62no—
117C4⋊C4—121no—
118C4⋊C4—121no—
119C4⋊C4—121no—
120C42GO+(4,𝔽2)11yescharacteristic
121C16—182no—
122C22×C3—21no—
123C22×C3—21no—
124C3×C4—21no—
125C3×C4—21no—
126C3×C4—21no—
127C3×C4—21no—
128C3×C4—22no—
129C3×C4—22no—
130C3×C4—22no—
131C3×C4—22no—
132C3×C4—242no—
133C3×C4—242no—
134Dic3—82no—
135Dic3—82no—
136C32#224111yescharacteristic, complemented, Sylow
137Q8—122no—
138Q8—122no—
139Q8—242no—
140C2×C4—122no—
141C2×C4—122no—
142C2×C4#377411yescharacteristic
143C2×C4#377411yescharacteristic
144C2×C4C2×GO+(4,𝔽2)11yescharacteristic
145C8—92no—
146C8—92no—
147C2×C3—21no—
148C2×C3—21no—
149C2×C3—21no—
150C2×C3—21no—
151C2×C3—21no—
152C2×C3—21no—
153C22C2×#377411yescharacteristic
154C4—242no—
155C4—242no—
156C4#6373512yes—
157C4#6373612yes—
158C4#6422111yescharacteristic
159C4#6422711yescharacteristic
160C3—21no—
161C3—21no—
162C2C2×#6373511yescharacteristic
163C2C2×#6373611yescharacteristic
164C2#1059334811yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socle, prime radicalC22×C32C2×D8
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2241
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
136. C32#2241semidirect

Maximal subgroups

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

subgroupindex
#105903872
#105903122
C4×#37082
#105900622
#22419