Finite Group Databasebeta

← #10593441

Subgroups — #10593441

Order 576.

204 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 33 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
1C2×#3788C211yesmaximal, characteristic, complemented
2C2×#3775C211yesmaximal, characteristic, complemented
3#63912C211yesmaximal, characteristic
4#63865C211yesmaximal, characteristic, complemented
5#63743C211yesmaximal, characteristic, complemented
6#63740C211yesmaximal, characteristic, complemented
7#63739C211yesmaximal, characteristic, complemented
8C2×C4×C3⋊D3C2211yescharacteristic
9C2×#627C2211yescharacteristic
10C2×#626—21no—
11C2×#625C2211yescharacteristic
12C2×#622C2211yescharacteristic
13C2×#622C2211yescharacteristic
14#3788—22no—
15#3775—22no—
16C3×(C2×D3)⋊C4—21no—
17C3×Dic3⋊C4—21no—
18#3724C2211yescharacteristic
19#3724C2211yescharacteristic
20#3722—21no—
21#896—61no—
22#884—61no—
23C22×C3⋊D3D411yescharacteristic
24C22×C3×D3—21no—
25C2×C32×C4D411yescharacteristic
26C2×C3⋊Dic3C2311yescharacteristic
27C4×C3⋊D3—21no—
28C4×C3⋊D3—21no—
29C2×C3×Dic3—21no—
30C2×C3×Dic3—21no—
31C2×C3×Dic3—21no—
32#627—21no—
33#627—21no—
34#626—42no—
35#625—21no—
36#625—21no—
37#622—21no—
38#622D412yescomplemented
39#468—91nomaximal, Sylow
40C2×#67—61no—
41C2×#67—61no—
42C2×D12—61no—
43C2×C4×D3—61no—
44C2×C4×D3—61no—
45C2×Dic6—61no—
46C3×C4⋊C4—61no—
47C3×C22⋊C4—61no—
48(C2×D3)⋊C4—21no—
49(C2×D3)⋊C4—61no—
50(C2×D3)⋊C4—61no—
51Dic3⋊C4—21no—
52Dic3⋊C4—61no—
53Dic3⋊C4—61no—
54C22×C32C2×D411yescharacteristic
55C2×C3⋊D3—21no—
56C2×C3⋊D3—21no—
57C2×C3⋊D3—21no—
58C2×C3×D3—41no—
59C2×C3×D3—41no—
60C2×C3×D3—41no—
61C32×C4—21no—
62C3⋊Dic3C2×D411yescharacteristic
63C3⋊Dic3#4111yescharacteristic
64C3×Dic3—41no—
65C3×Dic3—41no—
66C3×Dic3—41no—
67C2×SD16—91no—
68C2×M16—91no—
69C22⋊Q8—91no—
70#121—91no—
71#107—91no—
72#103—91no—
73#102—91no—
74C23×C3—61no—
75C22×D3—21no—
76C22×D3—61no—
77C22×D3—61no—
78C2×C3×C4—21no—
79C2×C3×C4—21no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83#67—121no—
84#67—121no—
85#67—122no—
86C2×Dic3—21no—
87C2×Dic3—21no—
88C2×Dic3—21no—
89C2×Dic3—61no—
90C2×Dic3—61no—
91D12—122no—
92C4×D3—121no—
93C4×D3—121no—
94C4×D3—121no—
95C4×D3—121no—
96Dic6—121no—
97Dic6—121no—
98C2×C32#12111yescharacteristic
99C2×C32AGL(1,ℤ/8)11yescharacteristic
100C2×C32#13711yescharacteristic
101C3⋊D3—41no—
102C3×D3—81no—
103C2×Q8—91no—
104C2×D4—91no—
105C2×D4—181no—
106C22×C4—91no—
107SD16—182no—
108M16—182no—
109C2×C8—91no—
110C2×C8—91no—
111C4⋊C4—61no—
112C4⋊C4—91no—
113C4⋊C4—91no—
114C22⋊C4—61no—
115C22⋊C4—181no—
116C22×C3—21no—
117C22×C3—21no—
118C22×C3—121no—
119C22×C3—121no—
120C22×C3—121no—
121C2×D3—41no—
122C2×D3—41no—
123C2×D3—41no—
124C2×D3—62no—
125C2×D3—62no—
126C2×D3—121no—
127C2×D3—121no—
128C2×D3—121no—
129C2×D3—121no—
130C3×C4—41no—
131C3×C4—41no—
132C3×C4—121no—
133C3×C4—121no—
134C3×C4—121no—
135Dic3—41no—
136Dic3—41no—
137Dic3—41no—
138Dic3—61no—
139Dic3—61no—
140Dic3—61no—
141Dic3—61no—
142C32#46811yescharacteristic, complemented, Sylow
143C23—61no—
144C23—91no—
145Q8—181no—
146Q8—181no—
147D4—181no—
148D4—181no—
149D4—362no—
150C2×C4—61no—
151C2×C4—61no—
152C2×C4—61no—
153C2×C4—91no—
154C2×C4—181no—
155C2×C4—181no—
156C2×C4GO+(4,𝔽2)11yescharacteristic
157C8—92no—
158C8—181no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3—21no—
162C2×C3—21no—
163C2×C3—21no—
164C2×C3—21no—
165C2×C3—241no—
166D3—81no—
167D3—122no—
168D3—122no—
169C22—121no—
170C22—121no—
171C22—121no—
172C22—181no—
173C22—181no—
174C22—181no—
175C22C2×GO+(4,𝔽2)11yescharacteristic
176C4—21no—
177C4—91no—
178C4—91no—
179C4—121no—
180C4—121no—
181C4—121no—
182C3—21no—
183C3—21no—
184C2—241no—
185C2—361no—
186C2#6422411yescharacteristic
187C2#6422611yescharacteristic
188C2#6424211yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radical#63912C2
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#468
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#3788C2semidirect
2. C2×#3775C2semidirect
4. #63865C2semidirect
5. #63743C2semidirect
6. #63740C2semidirect
7. #63739C2semidirect
38. #622D4semidirect
142. C32#468semidirect

Maximal subgroups

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

subgroupindex
C2×#37882
C2×#37752
#639122
#638652
#637432
#637402
#637392
#4689