Finite Group Databasebeta

← #10592482

Subgroups — #10592482

Order 576.

456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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×#3830C211yesmaximal, characteristic
2C2×#3754C211yesmaximal, characteristic, complemented
3C2×#3746C211yesmaximal, characteristic, complemented
4#64106C211yesmaximal, characteristic, complemented
5C32×#102C211yesmaximal, characteristic, complemented
6#63647C211yesmaximal, characteristic, complemented
7#63637C211yesmaximal, characteristic, complemented
8#4783—34nomaximal
9C2×C32×D4C2211yescharacteristic
10C2×#638—21no—
11C22×C3⋊Dic3—21no—
12#3830—22no—
13#3830—22no—
14C2×C4×C3⋊D3C2211yescharacteristic
15C2×#634C2211yescharacteristic
16C2×#634C2211yescharacteristic
17C2×C32×C8C2211yescharacteristic
18C32×C4⋊C4C2211yescharacteristic
19#3754—22no—
20#3752—21no—
21C4⋊(C3⋊Dic3)—21no—
22C2×C3⋊(C3⋊C8)C2211yescharacteristic
23#3746—22no—
24C2×#237—34no—
25C2×#214—34no—
26C2×Dic12—34no—
27#897—34no—
28C3×#102D314yescomplemented
29(C2×D3)⋊C8—34no—
30#810—34no—
31C23×C32—21no—
32C22×C3⋊D3D411yescharacteristic
33C32×D4—21no—
34C32×D4D412yes—
35C2×C32×C4—21no—
36C2×C32×C4C2311yescharacteristic
37#638—24no—
38C2×C3⋊Dic3—24no—
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3D411yescharacteristic
42C4×C3⋊D3—21no—
43C4×C3⋊D3—21no—
44#634—21no—
45#634—21no—
46#634—21no—
47#634D412yes—
48C32×C8—21no—
49C3⋊(C3⋊C8)—21no—
50#452—91noSylow
51C2×C3×D4C2×D314yes—
52C2×#67—64no—
53C22×Dic3—64no—
54#237—68no—
55#237—68no—
56C2×C4×D3—34no—
57C2×Dic6—34no—
58C2×Dic6—34no—
59C2×C3×C8C2×D314yes—
60C3×C4⋊C4C2×D314yes—
61#214—68no—
62(C2×D3)⋊C4—64no—
63C4⋊Dic3—64no—
64C2×C3⋊C8—34no—
65Dic12—68no—
66C22×C32—22no—
67C22×C32—41no—
68C22×C32—41no—
69C22×C32C2×D411yescharacteristic
70C2×C3⋊D3—21no—
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C32×C4—41no—
74C32×C4C2×D411yescharacteristic
75C32×C4C2×D411yescharacteristic
76C3⋊Dic3—22no—
77C3⋊Dic3—21no—
78C3⋊Dic3—41no—
79C2×#41—91no—
80C2×Q16—91no—
81C2×SD16—91no—
82C22⋊Q8—91no—
83#103—91no—
84#102C3⋊D311yescharacteristic, complemented
85C22⋊C8—91no—
86C23×C3—24no—
87C22×D3—34no—
88C3×D4—24no—
89C3×D4D1218yes—
90C2×C3×C4—24no—
91C2×C3×C4C22×D314yes—
92#67—616no—
93C2×Dic3—34no—
94C2×Dic3—616no—
95C2×Dic3—64no—
96C2×Dic3—64no—
97C4×D3—64no—
98C4×D3—64no—
99Dic6—38no—
100Dic6—64no—
101Dic6—64no—
102Dic6—64no—
103C3×C8—24no—
104C3⋊C8—64no—
105C2×C32—42no—
106C2×C32#12011yescharacteristic
107C2×C32#13511yescharacteristic
108C2×C32#13711yescharacteristic
109C3⋊D3—41no—
110#41—182no—
111#41—182no—
112C2×Q8—91no—
113C2×Q8—91no—
114C2×D4—181no—
115C2×D4C2×C3⋊D311yescharacteristic
116C22×C4—91no—
117C22×C4—181no—
118Q16—182no—
119SD16—182no—
120C2×C8—91no—
121C2×C8C2×C3⋊D311yescharacteristic
122C4⋊C4—181no—
123C4⋊C4C2×C3⋊D311yescharacteristic
124C22⋊C4—181no—
125C22×C3—28no—
126C22×C3—44no—
127C22×C3—44no—
128C22×C3D3×D414yes—
129C2×D3—64no—
130C2×D3—64no—
131C2×D3—64no—
132C3×C4—44no—
133C3×C4C2×D1214yes—
134C3×C4D3×D414yes—
135Dic3—68no—
136Dic3—64no—
137Dic3—124no—
138C32#45211yescharacteristic, complemented, Sylow
139C23—21no—
140C23—91no—
141Q8—92no—
142Q8—181no—
143Q8—181no—
144Q8—181no—
145D4—21no—
146D4—184no—
147D4C4⋊(C3⋊D3)12yes—
148C2×C4—21no—
149C2×C4—91no—
150C2×C4—184no—
151C2×C4—181no—
152C2×C4—181no—
153C2×C4—181no—
154C2×C4—181no—
155C2×C4C22×C3⋊D311yescharacteristic
156C8—21no—
157C8—181no—
158C2×C3—48no—
159C2×C3#88214yes—
160C2×C3#91214yes—
161C2×C3#91514yes—
162D3—124no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22—181no—
167C22—181no—
168C22—181no—
169C22D4×C3⋊D311yescharacteristic
170C4—41no—
171C4—181no—
172C4—182no—
173C4—361no—
174C4C2×C4⋊(C3⋊D3)11yescharacteristic
175C4D4×C3⋊D311yescharacteristic
176C3#478314yescomplemented
177C2—42no—
178C2—361no—
179C2#6409111yescharacteristic
180C2#6412111yescharacteristic
181C2#6412411yescharacteristic
subgroupG/H
centerC22D4×C3⋊D3
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C22×C3⋊D3
FittingC32×#102C2
socleC22×C32C2×D4
prime radicalC2×#3830C2
hypercenter#102C3⋊D3
hypocenterC32#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#3754C2semidirect
3. C2×#3746C2semidirect
4. #64106C2semidirect
5. C32×#102C2semidirect
6. #63647C2semidirect
7. #63637C2semidirect
28. C3×#102D3semidirect
84. #102C3⋊D3semidirect
138. C32#452semidirect
176. C3#4783semidirect

Maximal subgroups

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

subgroupindex
C2×#38302
C2×#37542
C2×#37462
#641062
C32×#1022
#636472
#636372
#47833