Finite Group Databasebeta

← #10593495

Subgroups — #10593495

Order 576.

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

normal subgroups only

This group has 204 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×#3792C211yesmaximal, characteristic, complemented
2C2×#3775C211yesmaximal, characteristic, complemented
3#63982C211yesmaximal, characteristic, complemented
4#63980C211yesmaximal, characteristic
5#63743C211yesmaximal, characteristic, complemented
6#63740C211yesmaximal, characteristic, complemented
7#63739C211yesmaximal, characteristic, complemented
8C22×C3⋊Dic3C2211yescharacteristic
9C2×C3×#67—21no—
10C2×#627C2211yescharacteristic
11C2×#625C2211yescharacteristic
12#3792—22no—
13C2×#622C2211yescharacteristic
14C2×#622C2211yescharacteristic
15#3775—22no—
16C3×#217—21no—
17#3724C2211yescharacteristic
18#3724C2211yescharacteristic
19Dic3⋊Dic3—21no—
20(C2×D3)⋊Dic3—21no—
21#939—61no—
22#878—61no—
23C23×C32D411yescharacteristic
24C22×C3×D3—21no—
25C2×C3⋊Dic3—21no—
26C2×C3⋊Dic3—21no—
27C2×C3⋊Dic3D411yescharacteristic
28C2×C3⋊Dic3C2311yescharacteristic
29C3×#67—42no—
30C2×C3×Dic3—21no—
31C2×C3×Dic3—21no—
32C2×C3×Dic3—21no—
33#627—21no—
34#627—21no—
35#625—21no—
36#625—21no—
37#622—21no—
38#622D412yescomplemented
39#468—91nomaximal, Sylow
40C2×C3×D4—61no—
41C2×#67—21no—
42C2×#67—61no—
43C22×Dic3—61no—
44C22×Dic3—61no—
45C2×Dic6—61no—
46C3×C22⋊C4—61no—
47#217—21no—
48#217—61no—
49(C2×D3)⋊C4—61no—
50C4⋊Dic3—61no—
51Dic3⋊C4—61no—
52Dic3⋊C4—61no—
53Dic3⋊C4—61no—
54C22×C32—21no—
55C22×C32—21no—
56C22×C32—21no—
57C22×C32C2×D411yescharacteristic
58C2×C3×D3—41no—
59C2×C3×D3—41no—
60C2×C3×D3—41no—
61C3⋊Dic3—21no—
62C3⋊Dic3C2×D411yescharacteristic
63C3⋊Dic3#4111yescharacteristic
64C3×Dic3—41no—
65C3×Dic3—41no—
66C3×Dic3—41no—
67C2×SD16—91no—
68C2×M16—91no—
69C22⋊Q8—91no—
70#121—91no—
71#107—91no—
72#103—91no—
73#102—91no—
74C23×C3—21no—
75C23×C3—21no—
76C23×C3—61no—
77C22×D3—21no—
78C3×D4—122no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82#67—42no—
83#67—121no—
84#67—121no—
85C2×Dic3—21no—
86C2×Dic3—21no—
87C2×Dic3—21no—
88C2×Dic3—61no—
89C2×Dic3—61no—
90C2×Dic3—61no—
91C2×Dic3—61no—
92C2×Dic3—121no—
93C2×Dic3—121no—
94C2×Dic3—121no—
95C2×Dic3—121no—
96Dic6—121no—
97Dic6—121no—
98C2×C32—41no—
99C2×C32#12111yescharacteristic
100C2×C32AGL(1,ℤ/8)11yescharacteristic
101C2×C32#13711yescharacteristic
102C3×D3—81no—
103C2×Q8—91no—
104C2×D4—61no—
105C2×D4—91no—
106C22×C4—91no—
107SD16—182no—
108M16—182no—
109C2×C8—91no—
110C2×C8—91no—
111C4⋊C4—91no—
112C4⋊C4—91no—
113C4⋊C4—181no—
114C22⋊C4—61no—
115C22⋊C4—181no—
116C22×C3—22no—
117C22×C3—22no—
118C22×C3—21no—
119C22×C3—21no—
120C22×C3—41no—
121C22×C3—41no—
122C22×C3—41no—
123C22×C3—41no—
124C22×C3—121no—
125C22×C3—121no—
126C22×C3—121no—
127C2×D3—41no—
128C2×D3—41no—
129C2×D3—41no—
130C3×C4—121no—
131C3×C4—121no—
132C3×C4—121no—
133Dic3—41no—
134Dic3—41no—
135Dic3—41no—
136Dic3—61no—
137Dic3—61no—
138Dic3—61no—
139Dic3—61no—
140Dic3—121no—
141Dic3—121no—
142C32#46811yescharacteristic, complemented, Sylow
143C23—61no—
144C23GO+(4,𝔽2)11yescharacteristic
145Q8—181no—
146Q8—181no—
147D4—122no—
148D4—181no—
149D4—181no—
150C2×C4—61no—
151C2×C4—61no—
152C2×C4—61no—
153C2×C4—91no—
154C2×C4—91no—
155C2×C4—181no—
156C2×C4—181no—
157C8—92no—
158C8—181no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3—21no—
162C2×C3—21no—
163C2×C3—21no—
164C2×C3—21no—
165C2×C3—42no—
166C2×C3—42no—
167C2×C3—241no—
168D3—81no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—121no—
173C22—121no—
174C22—121no—
175C22C2×GO+(4,𝔽2)11yescharacteristic
176C4—91no—
177C4—91no—
178C4—121no—
179C4—121no—
180C4—121no—
181C4—181no—
182C3—21no—
183C3—21no—
184C2—41no—
185C2—241no—
186C2#6423611yescharacteristic
187C2#6423911yescharacteristic
188C2#6424211yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC23×C32D4
socleC22×C32C2×D4
prime radical#63980C2
hypercenterC23GO+(4,𝔽2)
hypocenterC32#468
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#3792C2semidirect
2. C2×#3775C2semidirect
3. #63982C2semidirect
5. #63743C2semidirect
6. #63740C2semidirect
7. #63739C2semidirect
38. #622D4semidirect
142. C32#468semidirect

Maximal subgroups

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

subgroupindex
C2×#37922
C2×#37752
#639822
#639802
#637432
#637402
#637392
#4689