Finite Group Databasebeta

← #10593506

Subgroups — #10593506

Order 576.

274 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 45 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×#3805C211yesmaximal, characteristic
2C2×#3792C211yesmaximal, characteristic, complemented
3#63957C211yesmaximal, characteristic, complemented
4#63741C214yesmaximal, complemented
5C22×C3⋊Dic3C2211yescharacteristic
6C2×C3×#67—21no—
7C2×#627C411yescharacteristic, complemented
8C2×#625C411yescharacteristic, complemented
9#3805—21no—
10#3805—21no—
11#3805C412yescomplemented
12#3805C2212yes—
13C2×D3×Dic3—21no—
14#3792—21no—
15#3792C2212yescomplemented
16C2×#622—21no—
17C3×#217—21no—
18#3724—21no—
19Dic32C2212yescomplemented
20C2×#237—61no—
21#877—61no—
22C23×C32D411yescharacteristic
23C22×C3×D3—21no—
24C2×C3⋊Dic3C2×C411yescharacteristic
25C2×C3⋊Dic3C2×C411yescharacteristic
26C2×C3⋊Dic3D411yescharacteristic
27C2×C3⋊Dic3D411yescharacteristic
28C2×C3⋊Dic3D411yescharacteristic
29C2×C3⋊Dic3C2311yescharacteristic
30C3×#67—22no—
31C3×#67—22no—
32C2×C3×Dic3—21no—
33C2×C3×Dic3—22no—
34#627—21no—
35#627C2×C412yes—
36#625—21no—
37#625C2×C412yes—
38D3×Dic3—22no—
39D3×Dic3—22no—
40#622—22no—
41#421—91nomaximal, Sylow
42C2×C3×D4—61no—
43C2×#67—21no—
44C2×#67—61no—
45C22×Dic3—61no—
46C22×Dic3—61no—
47C22×Dic3—61no—
48#237—62no—
49#237—62no—
50#237—62no—
51#237—62no—
52C2×C4×D3—61no—
53C2×Dic6—61no—
54C3×C22⋊C4—61no—
55#217—21no—
56Dic3⋊C4—62no—
57C4×Dic3—62no—
58C22×C32—41no—
59C22×C32C22⋊C411yescharacteristic
60C22×C32C22⋊C411yescharacteristic
61C22×C32C2×D411yescharacteristic
62C2×C3×D3—22no—
63C2×C3×D3—42no—
64C3⋊Dic3C22⋊C411yescharacteristic
65C3⋊Dic3C22⋊C411yescharacteristic
66C3⋊Dic3C22×C411yescharacteristic
67C3⋊Dic3C2×D411yescharacteristic
68C3×Dic3—22no—
69C3×Dic3—42no—
70C2×#41—91no—
71C2×M16—91no—
72#117—91no—
73#104—94no—
74C23×C3—21no—
75C23×C3—21no—
76C23×C3—61no—
77C22×D3—21no—
78C3×D4—62no—
79C3×D4—62no—
80C2×C3×C4—61no—
81C2×C3×C4—62no—
82#67—22no—
83#67—22no—
84#67—62no—
85#67—62no—
86C2×Dic3—21no—
87C2×Dic3—22no—
88C2×Dic3—61no—
89C2×Dic3—61no—
90C2×Dic3—61no—
91C2×Dic3—61no—
92C2×Dic3—61no—
93C2×Dic3—61no—
94C2×Dic3—61no—
95C2×Dic3—61no—
96C2×Dic3—61no—
97C2×Dic3—61no—
98C2×Dic3—61no—
99C2×Dic3—61no—
100C2×Dic3—62no—
101C2×Dic3—62no—
102C4×D3—62no—
103C4×D3—62no—
104Dic6—62no—
105Dic6—62no—
106C2×C32—21no—
107C2×C32—21no—
108C2×C32—21no—
109C2×C32C2×C22⋊C411yescharacteristic
110C3×D3—42no—
111#41—92no—
112#41—92no—
113#41—181no—
114#41—181no—
115C2×Q8—91no—
116C2×D4—61no—
117C2×D4—91no—
118C22×C4—91no—
119C22×C4—181no—
120M16—92no—
121M16—181no—
122C2×C8—181no—
123C4⋊C4—181no—
124C22⋊C4—61no—
125C42—92no—
126C22×C3—21no—
127C22×C3—21no—
128C22×C3—21no—
129C22×C3—21no—
130C22×C3—21no—
131C22×C3—21no—
132C22×C3—42no—
133C22×C3—42no—
134C22×C3—62no—
135C22×C3—122no—
136C2×D3—22no—
137C2×D3—42no—
138C3×C4—62no—
139C3×C4—122no—
140Dic3—22no—
141Dic3—42no—
142Dic3—61no—
143Dic3—61no—
144Dic3—61no—
145Dic3—61no—
146Dic3—61no—
147Dic3—61no—
148Dic3—61no—
149Dic3—61no—
150C32#42111yescharacteristic, complemented, Sylow
151C23—61no—
152C23GO+(4,𝔽2)11yescharacteristic
153Q8—92no—
154Q8—181no—
155D4—62no—
156D4—62no—
157D4—92no—
158D4—181no—
159C2×C4—61no—
160C2×C4—62no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—182no—
168C2×C4—182no—
169C8—182no—
170C2×C3—22no—
171C2×C3—22no—
172C2×C3—21no—
173C2×C3—21no—
174C2×C3—41no—
175C2×C3—41no—
176C2×C3—41no—
177C2×C3—41no—
178C2×C3—122no—
179D3—42no—
180C22—41no—
181C22—62no—
182C22—122no—
183C22D32⋊C411yescharacteristic
184C22D32⋊C411yescharacteristic
185C22C2×GO+(4,𝔽2)11yescharacteristic
186C4—62no—
187C4—91no—
188C4—91no—
189C4—91no—
190C4—91no—
191C4—122no—
192C3—21no—
193C3—21no—
194C2—21no—
195C2—21no—
196C2—21no—
197C2—122no—
198C2C2×D32⋊C411yescharacteristic
subgroupG/H
centerC2C2×D32⋊C4
commutatorC3⋊Dic3C22×C4
FrattiniC22C2×GO+(4,𝔽2)
FittingC23×C32D4
socleC2×C32C2×C22⋊C4
prime radicalC2×#3805C2
cosocleC2×C3⋊Dic3C23
hypercenterC23GO+(4,𝔽2)
hypocenterC32#421
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#3792C2semidirect
3. #63957C2semidirect
4. #63741C2semidirect
7. C2×#627C4semidirect
8. C2×#625C4semidirect
11. #3805C4semidirect
15. #3792C22semidirect
19. Dic32C22semidirect
150. C32#421semidirect

Maximal subgroups

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

subgroupindex
C2×#38052
C2×#37922
#639572
#637412
#4219