Finite Group Databasebeta

← #3416⋊C9 #11919633

Subgroups — #3416⋊C9 #11919633

Order 1152.

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

normal subgroups only

This group has 176 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
1#578⋊C9C211yesmaximal, characteristic, complemented
2#576⋊C9C211yesmaximal, characteristic, complemented
3#504⋊C9C211yesmaximal, characteristic, complemented
4C3×#3416C311yesmaximal, characteristic
52−1+4⋊C9—21no—
6#63700—21no—
7#131⋊C9C2211yescharacteristic
8C9×SD32—41nomaximal
9C3×#578C2×C311yescharacteristic
10C3×#576C2×C311yescharacteristic
11C3×#510—31no—
12C3×#509—31no—
13C3×#508—31no—
14C2×C3×SD32—31no—
15C3×#504C2×C311yescharacteristic
16#41⋊C9—41no—
17#41⋊C9D411yescharacteristic
18C2×Q8⋊C9—41no—
19C9×Q16—41no—
20C9×D8—41no—
21C9×C16—41no—
22#3416C911yescharacteristic, complemented, Sylow
23C3×2−1+4—21no—
24C3×H(5,𝔽2)—21no—
25C3×#137—61no—
26C3×AGL(1,ℤ/8)—61no—
27C3×#135—31no—
28C3×#135—31no—
29C2×C3×Q16—31no—
30C2×C3×D8—31no—
31C3×#131C22×C311yescharacteristic
32C3×Q32—31no—
33C3×SD32—32no—
34C3×SD32—31no—
35C3×SD32A411yescharacteristic
36C3×D16—31no—
37C3×M32—31no—
38C2×C3×C16—31no—
39Q8×C9—81no—
40D4×C9—81no—
41Q8⋊C9D811yescharacteristic
42C8×C9—41no—
43#578C2×C911yescharacteristic
44#576C2×C911yescharacteristic, complemented
45#510—31no—
46#509—31no—
47#508—31no—
48C2×SD32—31no—
49#504C2×C911yescharacteristic, complemented
50C3×#41—41no—
51C3×#41—61no—
52C3×#41—61no—
53C3×#41—121no—
54C3×#41C3×D411yescharacteristic
55C2×C3×Q8—41no—
56C2×C3×Q8—61no—
57C2×C3×D4—61no—
58C2×C3×D4—121no—
59C3×Q16—31no—
60C3×Q16—61no—
61C3×Q16C2×A411yescharacteristic
62C3×SD16—61no—
63C3×SD16—61no—
64C3×D8—31no—
65C3×D8—61no—
66C3×D8C2×A411yescharacteristic
67C3×M16—31no—
68C2×C3×C8—31no—
69C3×C16—31no—
70C3×C16C2×A411yescharacteristic
71C22×C9—161no—
72C4×C9—41no—
73C4×C9—161no—
742−1+4—21no—
75H(5,𝔽2)—21no—
76#137—61no—
77AGL(1,ℤ/8)—61no—
78#135—31no—
79#135—31no—
80C2×Q16—31no—
81C2×D8—31no—
82#131C22×C911yescharacteristic
83Q32—31no—
84SD32—32no—
85SD32—31no—
86SD32C22⋊C911yescharacteristic
87D16—31no—
88M32—31no—
89C2×C16—31no—
90C23×C3—121no—
91C3×Q8—21no—
92C3×Q8—61no—
93C3×Q8—121no—
94C3×Q8C3×D811yescharacteristic
95C3×D4—21no—
96C3×D4—31no—
97C3×D4—61no—
98C3×D4—121no—
99C3×D4—121no—
100C3×D4—121no—
101C2×C3×C4—31no—
102C2×C3×C4—121no—
103C2×C3×C4—121no—
104C2×C3×C4—121no—
105C3×C8—31no—
106C3×C8C22×A411yescharacteristic
107C2×C9—41no—
108C2×C9—321no—
109#41—41no—
110#41—61no—
111#41—61no—
112#41—121no—
113#41D4×C911yescharacteristic
114C2×Q8—41no—
115C2×Q8—61no—
116C2×D4—61no—
117C2×D4—121no—
118Q16—31no—
119Q16—61no—
120Q16C2×C22⋊C911yescharacteristic
121SD16—61no—
122SD16—61no—
123D8—31no—
124D8—61no—
125D8C2×C22⋊C911yescharacteristic
126M16—31no—
127C2×C8—31no—
128C16—31no—
129C16C2×C22⋊C911yescharacteristic
130C22×C3—31no—
131C22×C3—41no—
132C22×C3—121no—
133C22×C3—481no—
134C3×C4—31no—
135C3×C4—41no—
136C3×C4—121no—
137C3×C4D4×A411yescharacteristic
138C9—41noSylow
139C23—121no—
140Q8—21no—
141Q8—61no—
142Q8—121no—
143Q8C9×D811yescharacteristic
144D4—21no—
145D4—31no—
146D4—61no—
147D4—121no—
148D4—121no—
149D4—121no—
150C2×C4—31no—
151C2×C4—121no—
152C2×C4—121no—
153C2×C4—121no—
154C8—31no—
155C8C22×C22⋊C911yescharacteristic
156C2×C3—61no—
157C2×C3—81no—
158C2×C3—241no—
159C2×C3A4×D811yescharacteristic
160C22—31no—
161C22—41no—
162C22—121no—
163C22—481no—
164C4—31no—
165C4—41no—
166C4—121no—
167C4D4×C22⋊C911yescharacteristic
168C3#3416⋊C311yescharacteristic
169C2—61no—
170C2—81no—
171C2—241no—
172C2D8×C22⋊C911yescharacteristic
subgroupG/H
center, socleC2×C3A4×D8
commutator#131C22×C9
FrattiniC3×C8C22×A4
Fitting, prime radicalC3×#3416C3
cosocleC3×#131C22×C3
hypercenterC3×SD32A4
hypocenterQ8C9×D8
LCSG ▷ #131 ▷ #41 ▷ Q8
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×SD32

Complements

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

NH ≅ G/Ntype
1. #578⋊C9C2semidirect
2. #576⋊C9C2semidirect
3. #504⋊C9C2semidirect
22. #3416C9semidirect
44. #576C2×C9semidirect
49. #504C2×C9semidirect

Maximal subgroups

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

subgroupindex
#578⋊C92
#576⋊C92
#504⋊C92
C3×#34163
C9×SD324