Finite Group Databasebeta

← #10593494

Subgroups — #10593494

Order 576.

191 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 191 conjugacy classes of subgroups — too many to draw. Only its 31 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#63980C211yesmaximal, characteristic
2#63957C211yesmaximal, characteristic, complemented
3C22⋊#622C211yesmaximal, characteristic, complemented
4#63743C211yesmaximal, characteristic, complemented
5#63742C211yesmaximal, characteristic, complemented
6#63739C211yesmaximal, characteristic, complemented
7#63739C211yesmaximal, characteristic, complemented
8C22×C3⋊Dic3C2211yescharacteristic
9C2×C3×#67—21no—
10C2×#625C2211yescharacteristic
11C2×#622C2211yescharacteristic
12C2×#622C2211yescharacteristic
13C3×#217—21no—
14#3724C2211yescharacteristic
15#3724C2211yescharacteristic
16#3724C2211yescharacteristic
17(C2×D3)⋊Dic3—21no—
18Dic32—21no—
19#939—61no—
20#877—61no—
21C23×C32D411yescharacteristic
22C22×C3×D3—21no—
23C2×C3⋊Dic3—21no—
24C2×C3⋊Dic3—21no—
25C2×C3⋊Dic3D411yescharacteristic
26C2×C3⋊Dic3C2311yescharacteristic
27C3×#67—42no—
28C2×C3×Dic3—21no—
29C2×C3×Dic3—21no—
30C2×C3×Dic3—21no—
31#625—21no—
32#625—21no—
33#622—21no—
34#622—21no—
35#482—91nomaximal, Sylow
36C2×C3×D4—61no—
37C2×#67—21no—
38C2×#67—61no—
39C22×Dic3—61no—
40C22×Dic3—61no—
41C3×C22⋊C4—61no—
42#217—21no—
43#217—61no—
44(C2×D3)⋊C4—61no—
45Dic3⋊C4—61no—
46Dic3⋊C4—61no—
47Dic3⋊C4—61no—
48C4×Dic3—61no—
49C4×Dic3—61no—
50C22×C32—21no—
51C22×C32—21no—
52C22×C32—21no—
53C22×C32C2×D411yescharacteristic
54C2×C3×D3—41no—
55C2×C3×D3—41no—
56C2×C3×D3—41no—
57C3⋊Dic3—21no—
58C3⋊Dic3#4111yescharacteristic
59C3⋊Dic3#4111yescharacteristic
60C3×Dic3—41no—
61C3×Dic3—41no—
62C3×Dic3—41no—
63#121—91no—
64#117—91no—
65#107—91no—
66#106—91no—
67#102—91no—
68#102—91no—
69C22⋊C8—91no—
70C23×C3—21no—
71C23×C3—21no—
72C23×C3—61no—
73C22×D3—21no—
74C3×D4—122no—
75C2×C3×C4—61no—
76C2×C3×C4—61no—
77C2×C3×C4—61no—
78#67—42no—
79#67—121no—
80#67—121no—
81C2×Dic3—21no—
82C2×Dic3—21no—
83C2×Dic3—21no—
84C2×Dic3—61no—
85C2×Dic3—61no—
86C2×Dic3—61no—
87C2×Dic3—61no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—121no—
91C2×Dic3—121no—
92C2×C32—41no—
93C2×C32#12311yescharacteristic
94C2×C32#13511yescharacteristic
95C2×C32AGL(1,ℤ/8)11yescharacteristic
96C3×D3—81no—
97C2×D4—61no—
98C2×D4—91no—
99C22×C4—91no—
100C2×C8—91no—
101C2×C8—91no—
102C4⋊C4—91no—
103C4⋊C4—91no—
104C4⋊C4—91no—
105C22⋊C4—61no—
106C22⋊C4—181no—
107C42—181no—
108C22×C3—22no—
109C22×C3—22no—
110C22×C3—21no—
111C22×C3—21no—
112C22×C3—41no—
113C22×C3—41no—
114C22×C3—41no—
115C22×C3—41no—
116C22×C3—121no—
117C22×C3—121no—
118C22×C3—121no—
119C2×D3—41no—
120C2×D3—41no—
121C2×D3—41no—
122C3×C4—121no—
123C3×C4—121no—
124C3×C4—121no—
125Dic3—41no—
126Dic3—41no—
127Dic3—41no—
128Dic3—61no—
129Dic3—61no—
130Dic3—61no—
131Dic3—61no—
132Dic3—62no—
133Dic3—121no—
134C32#48211yescharacteristic, complemented, Sylow
135C23—61no—
136C23GO+(4,𝔽2)11yescharacteristic
137D4—122no—
138D4—181no—
139D4—181no—
140C2×C4—61no—
141C2×C4—61no—
142C2×C4—61no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—181no—
146C2×C4—181no—
147C8—181no—
148C8—181no—
149C2×C3—21no—
150C2×C3—21no—
151C2×C3—21no—
152C2×C3—21no—
153C2×C3—21no—
154C2×C3—21no—
155C2×C3—42no—
156C2×C3—42no—
157C2×C3—241no—
158D3—81no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—121no—
163C22—121no—
164C22—121no—
165C22C2×GO+(4,𝔽2)11yescharacteristic
166C4—91no—
167C4—91no—
168C4—121no—
169C4—121no—
170C4—121no—
171C4—181no—
172C3—21no—
173C3—21no—
174C2—41no—
175C2—241no—
176C2#6423311yescharacteristic
177C2#6423611yescharacteristic
178C2#6423711yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC23×C32D4
socleC22×C32C2×D4
prime radical#63980C2
hypercenterC23GO+(4,𝔽2)
hypocenterC32#482
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #63957C2semidirect
3. C22⋊#622C2semidirect
4. #63743C2semidirect
5. #63742C2semidirect
6. #63739C2semidirect
7. #63739C2semidirect
134. C32#482semidirect

Maximal subgroups

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

subgroupindex
#639802
#639572
C22⋊#6222
#637432
#637422
#637392
#4829