Finite Group Databasebeta

← #11920052

Subgroups — #11920052

Order 1152.

177 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 177 conjugacy classes of subgroups — too many to draw. Only its 37 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×Q8⋊C9C211yesmaximal, characteristic
2C4⋊#3688C211yesmaximal, characteristic
3(Q8⋊C9)⋊C8C211yesmaximal, characteristic
4#71941—31nomaximal
5C2×#3688—21no—
6C4×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8#63395—41nomaximal
9C3×Q82D311yescharacteristic
10#5079—31no—
11#5031—31no—
12#5020—31no—
13#4546—31no—
14#4535—31no—
15#4535—31no—
16C2×Q8×C9—41no—
17C2×Q8⋊C9D411yescharacteristic
18#3688—41no—
19C4⋊Dic9—41no—
20C2×C9⋊C8—41no—
21#1645—91noSylow
22C3×C4⋊Q8—31no—
23C3×C4⋊Q8—61no—
24C3×C4×Q8—21no—
25C3×C4×Q8—31no—
26C3×C4×Q8C2×D311yescharacteristic
27C2×#216—61no—
28#869—31no—
29#835—62no—
30#835—61no—
31#810—61no—
32#808—61no—
33C4⋊(C3⋊C8)—31no—
34C4⋊(C3⋊C8)—31no—
35C4×C3⋊C8—31no—
36Q8×C9—42no—
37Q8×C9—81no—
38C2×C4×C9—41no—
39C2×C4×C9—81no—
40C2×Dic9—81no—
41Q8⋊C9SD1611yescharacteristic
42C9⋊C8—81no—
43Q82D911yescharacteristic
44#487—91no—
45#475—91no—
46#462—91no—
47#333—91no—
48Q8⋊C8—91no—
49Q8⋊C8—91no—
50C2×C3×Q8—32no—
51C2×C3×Q8#6711yescharacteristic
52C2×C3×Q8S411yescharacteristic
53C2×Dic6—61no—
54C3×C4⋊C4—31no—
55C3×C4⋊C4—31no—
56C3×C4⋊C4—61no—
57C3×C4⋊C4—61no—
58C3×C42—31no—
59C3×C42—61no—
60#216—121no—
61#216—121no—
62C4⋊Dic3—61no—
63C4⋊Dic3—61no—
64C2×C3⋊C8—61no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67C22×C9—41no—
68C4×C9—41no—
69C4×C9—41no—
70C4×C9—82no—
71Dic9—161no—
72C2×Q16—181no—
73C4⋊Q8—31no—
74C4⋊Q8—61no—
75C4⋊Q8—91no—
76C4×Q8—21no—
77C4×Q8—31no—
78C4×Q8C2×D911yescharacteristic
79#106—181no—
80C4⋊C8—91no—
81C4⋊C8—91no—
82#103—181no—
83#103—182no—
84#103—181no—
85C4×C8—91no—
86C3×Q8—21no—
87C3×Q8—31no—
88C3×Q8—122no—
89C3×Q8#21511yescharacteristic
90C3×Q8#22612yes—
91C2×C3×C4—21no—
92C2×C3×C4—31no—
93C2×C3×C4—31no—
94C2×C3×C4—61no—
95C2×C3×C4C2×S411yescharacteristic
96C2×Dic3—121no—
97Dic6—121no—
98Dic6—121no—
99C3⋊C8—121no—
100C3⋊C8—121no—
101C3⋊C8—121no—
102C2×C9—41no—
103C2×C9—41no—
104C2×C9—41no—
105C2×Q8—32no—
106C2×Q8—181no—
107C2×Q8#61111yescharacteristic
108C2×Q8(C22⋊C9)⋊C211yescharacteristic
109Q16—361no—
110Q16—361no—
111C2×C8—181no—
112C2×C8—181no—
113C2×C8—181no—
114C4⋊C4—31no—
115C4⋊C4—31no—
116C4⋊C4—61no—
117C4⋊C4—61no—
118C4⋊C4—181no—
119C4⋊C4—181no—
120C42—31no—
121C42—61no—
122C22×C3GL(2,ℤ/4)11yescharacteristic
123C3×C4—22no—
124C3×C4—31no—
125C3×C4—31no—
126C3×C4—61no—
127C3×C4—121no—
128C3×C4C2×#22611yescharacteristic
129C3×C4#98311yescharacteristic
130Dic3—241no—
131C9—41noSylow
132Q8—21no—
133Q8—31no—
134Q8—122no—
135Q8—361no—
136Q8—361no—
137Q8#367511yescharacteristic
138Q8#368812yescomplemented
139C2×C4—21no—
140C2×C4—31no—
141C2×C4—31no—
142C2×C4—61no—
143C2×C4—361no—
144C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
145C8—361no—
146C8—361no—
147C8—361no—
148C2×C3#541711yescharacteristic
149C2×C3#541911yescharacteristic
150C2×C3#542811yescharacteristic
151C22#6369411yescharacteristic
152C4—22no—
153C4—31no—
154C4—31no—
155C4—61no—
156C4—121no—
157C4—721no—
158C4C2×#368811yescharacteristic
159C4#6368911yescharacteristic
160C3#7309711yescharacteristic
161C2#1058951911yescharacteristic
162C2#1058952111yescharacteristic
163C2#1058953011yescharacteristic
subgroupG/H
centerC22#63694
commutator, cosocleC4×Q8⋊C9C22
FrattiniC2×C3×C4C2×S4
FittingC3×Q82D3
socle, prime radicalC22×C3GL(2,ℤ/4)
hypercenterC2×Q8(C22⋊C9)⋊C2
hypocenterQ8⋊C9SD16
LCSG ▷ C4×Q8⋊C9 ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
138. Q8#3688semidirect

Maximal subgroups

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

subgroupindex
Q8×Q8⋊C92
C4⋊#36882
(Q8⋊C9)⋊C82
#719413
#633954