Finite Group Databasebeta

← #10593404

Subgroups — #10593404

Order 576.

282 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 41 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×D32⋊C4C212yesmaximal
2#63921C211yesmaximal, characteristic
3#63900C211yesmaximal, characteristic, complemented
4#63781C211yesmaximal, characteristic, complemented
5#63737C212yesmaximal, complemented
6C22×D32C2211yescharacteristic
7C22×#157C2212yes—
8C2×C4×C3⋊D3C2211yescharacteristic
9C2×#624C2212yes—
10C2×#624C2211yescharacteristic
11D32⋊C4—24no—
12C3×(C2×D3)⋊C4—21no—
13C3×C4⋊Dic3—21no—
14#3724—21no—
15(C2×D3)⋊Dic3—21no—
16D3×C4⋊C4—61no—
17D3×C22⋊C4—61no—
18C22×C3⋊D3C2311yescharacteristic
19C22×C3×D3—21no—
20C2×D32—21no—
21C2×D32—22no—
22C2×D32—22no—
23C2×D32D412yes—
24C2×#157—22no—
25C2×#157—22no—
26C2×#157—22no—
27C2×C32×C4D411yescharacteristic
28C2×C3⋊Dic3D411yescharacteristic
29C4×C3⋊D3—22no—
30C2×C3×Dic3—21no—
31C2×C3×Dic3—22no—
32#624—22no—
33#624—22no—
34#624—22no—
35#397—91nomaximal, Sylow
36C23×D3—61no—
37C2×C4×D3—61no—
38C2×C4×D3—61no—
39C2×C4×D3—62no—
40C2×C4×D3—61no—
41C3×C4⋊C4—61no—
42C3×C22⋊C4—61no—
43#217—61no—
44(C2×D3)⋊C4—21no—
45(C2×D3)⋊C4—61no—
46C4⋊Dic3—21no—
47Dic3⋊C4—62no—
48C22×C32C2×D411yescharacteristic
49C2×C3⋊D3C2×D411yescharacteristic
50C2×C3⋊D3#4112yes—
51C2×C3⋊D3#4112yes—
52C2×C3⋊D3#4111yescharacteristic
53C2×C3×D3—22no—
54C2×C3×D3—41no—
55C2×C3×D3—41no—
56D32—24no—
57D32—42no—
58#157—42no—
59C32×C4—21no—
60C3⋊Dic3—21no—
61C3×Dic3—42no—
62C3×Dic3—41no—
63C2×C4⋊C4—91no—
64C2×C22⋊C4—91no—
65C2×C22⋊C4—92no—
66#95—91no—
67#95—92no—
68C23×C3—61no—
69C22×D3—21no—
70C22×D3—62no—
71C22×D3—61no—
72C22×D3—61no—
73C22×D3—62no—
74C22×D3—122no—
75C22×D3—122no—
76C2×C3×C4—21no—
77C2×C3×C4—21no—
78C2×C3×C4—62no—
79C2×C3×C4—61no—
80C2×Dic3—22no—
81C2×Dic3—21no—
82C2×Dic3—61no—
83C2×Dic3—61no—
84C4×D3—64no—
85C4×D3—122no—
86C4×D3—122no—
87C4×D3—122no—
88C4×D3—122no—
89C2×C32#12111yescharacteristic
90C2×C32#12311yescharacteristic
91C2×C32#12411yescharacteristic
92C3⋊D3#12312yes—
93C3⋊D3#12612yes—
94C3×D3—42no—
95C24—91no—
96C22×C4—91no—
97C22×C4—92no—
98C22×C4—91no—
99C22×C4—92no—
100C4⋊C4—61no—
101C4⋊C4—181no—
102C22⋊C4—61no—
103C22⋊C4—181no—
104C22⋊C4—184no—
105C22×C3—21no—
106C22×C3—21no—
107C22×C3—62no—
108C22×C3—121no—
109C22×C3—121no—
110C2×D3—22no—
111C2×D3—41no—
112C2×D3—41no—
113C2×D3—62no—
114C2×D3—61no—
115C2×D3—61no—
116C2×D3—62no—
117C2×D3—62no—
118C2×D3—61no—
119C2×D3—61no—
120C2×D3—62no—
121C2×D3—124no—
122C2×D3—124no—
123C3×C4—22no—
124C3×C4—41no—
125C3×C4—121no—
126C3×C4—122no—
127Dic3—41no—
128Dic3—42no—
129Dic3—62no—
130Dic3—121no—
131C32#39711yescharacteristic, complemented, Sylow
132C23—61no—
133C23—92no—
134C23—91no—
135C23—181no—
136C23—182no—
137C23—182no—
138C2×C4—61no—
139C2×C4—62no—
140C2×C4—91no—
141C2×C4—182no—
142C2×C4—182no—
143C2×C4—182no—
144C2×C4—182no—
145C2×C4—182no—
146C2×C4—182no—
147C2×C4—182no—
148C2×C4GO+(4,𝔽2)11yescharacteristic
149C2×C3—21no—
150C2×C3—21no—
151C2×C3—21no—
152C2×C3—21no—
153C2×C3—21no—
154C2×C3—21no—
155C2×C3—122no—
156D3—42no—
157D3—62no—
158D3—62no—
159D3—62no—
160D3—62no—
161C22—62no—
162C22—92no—
163C22—91no—
164C22—91no—
165C22—92no—
166C22—121no—
167C22—121no—
168C22—184no—
169C22—362no—
170C22C2×GO+(4,𝔽2)11yescharacteristic
171C4—21no—
172C4—121no—
173C4—122no—
174C4—181no—
175C4—362no—
176C3—21no—
177C3—21no—
178C2—92no—
179C2—92no—
180C2—122no—
181C2#6422111yescharacteristic
182C2#6423011yescharacteristic
183C2#6423311yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radicalC22×D32C22
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#397
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #63900C2semidirect
4. #63781C2semidirect
5. #63737C2semidirect
131. C32#397semidirect

Maximal subgroups

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

subgroupindex
C2×D32⋊C42
#639212
#639002
#637812
#637372
#3979