Finite Group Databasebeta

← #10593436

Subgroups — #10593436

Order 576.

283 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 283 conjugacy classes of subgroups — too many to draw. Only its 37 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×#3797C211yesmaximal, characteristic, complemented
2C2×#3775C212yesmaximal, complemented
3#63912C211yesmaximal, characteristic
4#63778C211yesmaximal, characteristic, complemented
5#63740C212yesmaximal, complemented
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×C3×Dic6—21no—
8C2×#627C2212yes—
9C2×#626—21no—
10C2×#625C2211yescharacteristic
11C2×#624—21no—
12#3797—24no—
13C2×#622C2212yes—
14#3775—24no—
15C3×(C2×D3)⋊C4—21no—
16#3724C2211yescharacteristic
17C2×D3×Q8—61no—
18#884—61no—
19C22×C3⋊D3D411yescharacteristic
20C22×C3×D3—21no—
21C2×C32×C4D411yescharacteristic
22C2×C3⋊Dic3C2311yescharacteristic
23C4×C3⋊D3—22no—
24C2×C3×Dic3—22no—
25C2×C3×Dic3—21no—
26C3×Dic6—24no—
27#627—22no—
28#627D414yescomplemented
29#626—42no—
30#625—22no—
31#624—24no—
32#622—22no—
33#448—91nomaximal, Sylow
34C2×C3×Q8—61no—
35C2×#67—61no—
36C2×#67—61no—
37D3×Q8—68no—
38C2×D12—61no—
39C2×C4×D3—61no—
40C2×C4×D3—61no—
41C2×C4×D3—62no—
42C2×Dic6—21no—
43C2×Dic6—62no—
44C3×C22⋊C4—61no—
45(C2×D3)⋊C4—21no—
46Dic3⋊C4—61no—
47C22×C32C2×D411yescharacteristic
48C2×C3⋊D3—21no—
49C2×C3⋊D3—21no—
50C2×C3⋊D3SD1612yescomplemented
51C2×C3×D3—41no—
52C2×C3×D3—41no—
53C2×C3×D3—41no—
54C32×C4—21no—
55C3⋊Dic3C2×D412yes—
56C3×Dic3—24no—
57C3×Dic3—41no—
58C22×Q8—91no—
59C2×SD16—92no—
60#121—91no—
61#103—92no—
62C22⋊C8—91no—
63C23×C3—61no—
64C22×D3—21no—
65C22×D3—61no—
66C22×D3—61no—
67C3×Q8—64no—
68C2×C3×C4—21no—
69C2×C3×C4—21no—
70C2×C3×C4—62no—
71C2×C3×C4—61no—
72#67—122no—
73#67—122no—
74C2×Dic3—22no—
75C2×Dic3—21no—
76C2×Dic3—61no—
77C2×Dic3—61no—
78D12—122no—
79C4×D3—68no—
80C4×D3—64no—
81C4×D3—122no—
82Dic6—24no—
83Dic6—64no—
84Dic6—64no—
85C2×C32#12011yescharacteristic
86C2×C32C2×SD1611yescharacteristic
87C2×C32#13711yescharacteristic
88C3⋊D3—22no—
89C3×D3—81no—
90C2×Q8—61no—
91C2×Q8—92no—
92C2×Q8—184no—
93C2×D4—91no—
94C2×D4—181no—
95C22×C4—91no—
96C22×C4—181no—
97SD16—184no—
98C2×C8—92no—
99C4⋊C4—91no—
100C22⋊C4—61no—
101C22×C3—21no—
102C22×C3—21no—
103C22×C3—121no—
104C22×C3—121no—
105C22×C3—121no—
106C2×D3—41no—
107C2×D3—41no—
108C2×D3—41no—
109C2×D3—62no—
110C2×D3—62no—
111C2×D3—62no—
112C2×D3—62no—
113C2×D3—121no—
114C2×D3—121no—
115C3×C4—22no—
116C3×C4—41no—
117C3×C4—64no—
118C3×C4—121no—
119Dic3—24no—
120Dic3—41no—
121Dic3—62no—
122Dic3—62no—
123C32#44811yescharacteristic, complemented, Sylow
124C23—61no—
125C23—91no—
126Q8—64no—
127Q8—94no—
128Q8—182no—
129D4—182no—
130D4—362no—
131C2×C4—62no—
132C2×C4—61no—
133C2×C4—91no—
134C2×C4—182no—
135C2×C4—184no—
136C2×C4GO+(4,𝔽2)11yescharacteristic
137C8—182no—
138C2×C3—21no—
139C2×C3—21no—
140C2×C3—21no—
141C2×C3—21no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—241no—
145D3—64no—
146D3—81no—
147D3—122no—
148C22—92no—
149C22—121no—
150C22—121no—
151C22—121no—
152C22—181no—
153C22—181no—
154C22C2×GO+(4,𝔽2)11yescharacteristic
155C4—21no—
156C4—64no—
157C4—92no—
158C4—121no—
159C3—21no—
160C3—21no—
161C2—182no—
162C2—241no—
163C2#6422611yescharacteristic
164C2#6422711yescharacteristic
165C2#6424111yescharacteristic
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#448
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×#3797C2semidirect
2. C2×#3775C2semidirect
4. #63778C2semidirect
5. #63740C2semidirect
28. #627D4semidirect
50. C2×C3⋊D3SD16semidirect
123. C32#448semidirect

Maximal subgroups

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

subgroupindex
C2×#37972
C2×#37752
#639122
#637782
#637402
#4489