Finite Group Databasebeta

← #10593422

Subgroups — #10593422

Order 576.

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

normal subgroups only

This group has 209 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×#3775C211yesmaximal, characteristic, complemented
2C2×#3774C211yesmaximal, characteristic
3#63915C211yesmaximal, characteristic, complemented
4C4×#625C211yesmaximal, characteristic, complemented
5#63779C211yesmaximal, characteristic, complemented
6#63740C211yesmaximal, characteristic, complemented
7#63739C211yesmaximal, characteristic, complemented
8C2×C3×C4×D3—21no—
9C2×#627C2211yescharacteristic
10C2×#625C2211yescharacteristic
11C2×#625C2211yescharacteristic
12C2×#622C2211yescharacteristic
13C2×#622C2211yescharacteristic
14#3775—22no—
15#3774—22no—
16C4×C3⋊Dic3C2211yescharacteristic
17C3×(C2×D3)⋊C4—21no—
18#3724C2211yescharacteristic
19(C2×D3)⋊Dic3—21no—
20(C2×D3)⋊Dic3—21no—
21C4×#67—61no—
22#885—61no—
23C22×C3×D3—21no—
24C22×C3×D3—21no—
25C2×C32×C4D411yescharacteristic
26C2×C3⋊Dic3D411yescharacteristic
27C2×C3⋊Dic3C2311yescharacteristic
28C2×C3×Dic3—21no—
29C2×C3×Dic3—21no—
30C3×C4×D3—42no—
31#627—21no—
32#627—21no—
33#625—21no—
34#625—21no—
35#625—21no—
36#625D412yes—
37#622—21no—
38#622—21no—
39#463—91nomaximal, Sylow
40C22×C3×C4—61no—
41C2×#67—61no—
42C2×#67—61no—
43C2×C4×D3—21no—
44C2×Dic6—61no—
45C3×C22⋊C4—61no—
46#217—61no—
47#217—61no—
48(C2×D3)⋊C4—21no—
49(C2×D3)⋊C4—61no—
50(C2×D3)⋊C4—61no—
51Dic3⋊C4—61no—
52C4×Dic3—61no—
53C4×Dic3—61no—
54C22×C32C2×D411yescharacteristic
55C2×C3×D3—22no—
56C2×C3×D3—41no—
57C2×C3×D3—41no—
58C2×C3×D3—41no—
59C2×C3×D3—41no—
60C2×C3×D3—41no—
61C32×C4—21no—
62C3⋊Dic3—21no—
63C3⋊Dic3C2×D411yescharacteristic
64C3⋊Dic3#4111yescharacteristic
65C3×Dic3—41no—
66C3×Dic3—41no—
67C2×SD16—91no—
68C2×D8—91no—
69#124—91no—
70C4×D4—91no—
71C4⋊C8—91no—
72#103—91no—
73#102—91no—
74C23×C3—61no—
75C23×C3—61no—
76C22×D3—21no—
77C22×D3—21no—
78C2×C3×C4—21no—
79C2×C3×C4—21no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—122no—
83#67—62no—
84#67—62no—
85#67—121no—
86#67—121no—
87C2×Dic3—21no—
88C2×Dic3—21no—
89C2×Dic3—61no—
90C2×Dic3—61no—
91C2×Dic3—61no—
92C2×Dic3—61no—
93C4×D3—42no—
94Dic6—121no—
95Dic6—121no—
96C2×C32#12111yescharacteristic
97C2×C32#13511yescharacteristic
98C2×C32AGL(1,ℤ/8)11yescharacteristic
99C3×D3—42no—
100C3×D3—81no—
101C2×Q8—91no—
102C2×D4—91no—
103C2×D4—91no—
104C22×C4—61no—
105SD16—182no—
106D8—182no—
107C2×C8—91no—
108C2×C8—91no—
109C4⋊C4—91no—
110C22⋊C4—61no—
111C22⋊C4—181no—
112C22⋊C4—181no—
113C42—91no—
114C22×C3—21no—
115C22×C3—21no—
116C22×C3—62no—
117C22×C3—121no—
118C22×C3—121no—
119C22×C3—121no—
120C22×C3—121no—
121C22×C3—121no—
122C2×D3—22no—
123C2×D3—41no—
124C2×D3—41no—
125C2×D3—41no—
126C2×D3—41no—
127C2×D3—41no—
128C3×C4—22no—
129C3×C4—41no—
130C3×C4—121no—
131C3×C4—121no—
132Dic3—41no—
133Dic3—41no—
134Dic3—61no—
135Dic3—61no—
136Dic3—61no—
137Dic3—61no—
138Dic3—121no—
139Dic3—121no—
140C32#46311yescharacteristic, complemented, Sylow
141C23—61no—
142C23—61no—
143Q8—181no—
144Q8—181no—
145D4—92no—
146D4—181no—
147D4—181no—
148D4—181no—
149C2×C4—61no—
150C2×C4—61no—
151C2×C4—91no—
152C2×C4—91no—
153C2×C4—122no—
154C2×C4GO+(4,𝔽2)11yescharacteristic
155C8—181no—
156C8—181no—
157C2×C3—21no—
158C2×C3—21no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3—21no—
162C2×C3—21no—
163C2×C3—122no—
164C2×C3—241no—
165D3—42no—
166D3—81no—
167C22—62no—
168C22—121no—
169C22—121no—
170C22—121no—
171C22—121no—
172C22—121no—
173C22C2×GO+(4,𝔽2)11yescharacteristic
174C4—21no—
175C4—91no—
176C4—91no—
177C4—121no—
178C4—121no—
179C4—181no—
180C3—21no—
181C3—21no—
182C2—122no—
183C2—241no—
184C2#6422311yescharacteristic
185C2#6423011yescharacteristic
186C2#6423611yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radicalC2×#3774C2
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#463
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×#3775C2semidirect
3. #63915C2semidirect
4. C4×#625C2semidirect
5. #63779C2semidirect
6. #63740C2semidirect
7. #63739C2semidirect
140. C32#463semidirect

Maximal subgroups

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

subgroupindex
C2×#37752
C2×#37742
#639152
C4×#6252
#637792
#637402
#637392
#4639