Finite Group Databasebeta

← #11920053

Subgroups — #11920053

Order 1152.

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

normal subgroups only

This group has 182 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
2#10589493C211yesmaximal, characteristic
3(Q8⋊C9)⋊C8C211yesmaximal, characteristic
4#71940—31nomaximal
5C4×Q8⋊C9—21no—
6C4×Q8⋊C9C2211yescharacteristic
7#63421—21no—
8#63395—41nomaximal
9C3×Q82D311yescharacteristic
10#5092—31no—
11#5021—31no—
12#5021—31no—
13#4546—31no—
14#4535—31no—
15#4535—31no—
16C2×Q8×C9—41no—
17C2×Q8⋊C9D411yescharacteristic
18C4⋊Dic9—41no—
19C2×C9⋊C8—41no—
20#1633—91noSylow
21C3×C4⋊Q8—31no—
22C3×C4⋊Q8—61no—
23C3×C4×Q8—21no—
24C3×C4×Q8—31no—
25C3×C4×Q8C2×D311yescharacteristic
26C2×#216—62no—
27#869—31no—
28#835—61no—
29#835—61no—
30#807—61no—
31#807—61no—
32C4⋊(C3⋊C8)—31no—
33C4⋊(C3⋊C8)—31no—
34C4×C3⋊C8—31no—
35Q8×C9—42no—
36Q8×C9—81no—
37C2×C4×C9—41no—
38C2×C4×C9—81no—
39C2×Dic9—81no—
40Q8⋊C9Q1611yescharacteristic, complemented
41C9⋊C8—81no—
42Q82D911yescharacteristic
43#494—91no—
44#477—91no—
45#477—91no—
46#333—91no—
47Q8⋊C8—91no—
48Q8⋊C8—91no—
49C2×C3×Q8—32no—
50C2×C3×Q8#6711yescharacteristic
51C2×C3×Q8S411yescharacteristic
52C2×Dic6—61no—
53C3×C4⋊C4—31no—
54C3×C4⋊C4—31no—
55C3×C4⋊C4—61no—
56C3×C4⋊C4—61no—
57C3×C42—31no—
58C3×C42—61no—
59#216—124no—
60C4⋊Dic3—61no—
61C4⋊Dic3—61no—
62C2×C3⋊C8—61no—
63C2×C3⋊C8—61no—
64C2×C3⋊C8—61no—
65C22×C9—41no—
66C4×C9—41no—
67C4×C9—41no—
68C4×C9—82no—
69Dic9—161no—
70C2×Q16—182no—
71C4⋊Q8—31no—
72C4⋊Q8—61no—
73C4⋊Q8—91no—
74C4×Q8—21no—
75C4×Q8—31no—
76C4×Q8C2×D911yescharacteristic
77#107—181no—
78#107—181no—
79C4⋊C8—91no—
80C4⋊C8—91no—
81#103—181no—
82#103—181no—
83C4×C8—91no—
84C3×Q8—21no—
85C3×Q8—31no—
86C3×Q8—122no—
87C3×Q8#21611yescharacteristic
88C3×Q8#22612yes—
89C2×C3×C4—21no—
90C2×C3×C4—31no—
91C2×C3×C4—31no—
92C2×C3×C4—61no—
93C2×C3×C4C2×S411yescharacteristic
94C2×Dic3—121no—
95Dic6—122no—
96C3⋊C8—62no—
97C3⋊C8—121no—
98C3⋊C8—121no—
99C2×C9—41no—
100C2×C9—41no—
101C2×C9—41no—
102C2×Q8—32no—
103C2×Q8—181no—
104C2×Q8#61111yescharacteristic
105C2×Q8(C22⋊C9)⋊C211yescharacteristic
106Q16—364no—
107C2×C8—181no—
108C2×C8—181no—
109C2×C8—181no—
110C4⋊C4—31no—
111C4⋊C4—31no—
112C4⋊C4—61no—
113C4⋊C4—61no—
114C4⋊C4—181no—
115C4⋊C4—181no—
116C42—31no—
117C42—61no—
118C22×C3GL(2,ℤ/4)11yescharacteristic
119C3×C4—22no—
120C3×C4—31no—
121C3×C4—31no—
122C3×C4—61no—
123C3×C4—121no—
124C3×C4C2×#22611yescharacteristic
125C3×C4#98311yescharacteristic
126Dic3—241no—
127C9—41noSylow
128Q8—21no—
129Q8—31no—
130Q8—122no—
131Q8—362no—
132Q8#367411yescharacteristic
133Q8#368812yes—
134C2×C4—21no—
135C2×C4—31no—
136C2×C4—31no—
137C2×C4—61no—
138C2×C4—361no—
139C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
140C8—182no—
141C8—361no—
142C8—361no—
143C2×C3#541611yescharacteristic
144C2×C3#541911yescharacteristic
145C2×C3#542911yescharacteristic
146C22#6369411yescharacteristic
147C4—22no—
148C4—31no—
149C4—31no—
150C4—61no—
151C4—121no—
152C4—721no—
153C4C2×#368811yescharacteristic
154C4#6368911yescharacteristic
155C3#7309811yescharacteristic
156C2#1058951811yescharacteristic
157C2#1058952111yescharacteristic
158C2#1058953111yescharacteristic
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⋊C9Q16
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
40. Q8⋊C9Q16semidirect

Maximal subgroups

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

subgroupindex
Q8×Q8⋊C92
#105894932
(Q8⋊C9)⋊C82
#719403
#633954