Finite Group Databasebeta

← C2×#63741 #10593505

Subgroups — C2×#63741 #10593505

Order 576.

306 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 49 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
3C2×Dic32C211yesmaximal, characteristic, complemented
4#63741C214yesmaximal, direct product factor
5C22×C3⋊Dic3C2211yescharacteristic
6C2×C3×#67—21no—
7C22×C3×Dic3—21no—
8C2×#627C411yescharacteristic, complemented
9C2×#625C411yescharacteristic, complemented
10#3805—21no—
11#3805—21no—
12#3805C412yescomplemented
13#3805C2212yes—
14C2×D3×Dic3—21no—
15#3792—21no—
16#3792C2212yescomplemented
17C2×#622—21no—
18Dic32—21no—
19Dic32C2212yescomplemented
20C2×#237—61no—
21C2×C4×Dic3—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—24no—
33C2×C3×Dic3—21no—
34C2×C3×Dic3—22no—
35#627—21no—
36#627C2×C412yescomplemented
37#625—21no—
38#625C2×C412yescomplemented
39D3×Dic3—22no—
40D3×Dic3—22no—
41#622—22no—
42C2×#104—91nomaximal, Sylow
43C2×C3×D4—61no—
44C22×C3×C4—61no—
45C2×#67—21no—
46C2×#67—61no—
47C22×Dic3—21no—
48C22×Dic3—61no—
49C22×Dic3—61no—
50C22×Dic3—61no—
51#237—62no—
52#237—62no—
53#237—62no—
54#237—62no—
55C2×C4×D3—61no—
56C2×Dic6—61no—
57C4×Dic3—62no—
58C4×Dic3—62no—
59C22×C32—22no—
60C22×C32C22⋊C411yescharacteristic
61C22×C32C22⋊C411yescharacteristic
62C22×C32C2×D411yescharacteristic
63C2×C3×D3—22no—
64C2×C3×D3—42no—
65C3⋊Dic3C22⋊C411yescharacteristic
66C3⋊Dic3C22⋊C411yescharacteristic
67C3⋊Dic3C22×C411yescharacteristic
68C3⋊Dic3C2×D411yescharacteristic
69C3×Dic3—24no—
70C3×Dic3—22no—
71C2×#41—91no—
72C2×M16—91no—
73C2×C42—91no—
74#104—94no—
75C23×C3—21no—
76C23×C3—21no—
77C23×C3—61no—
78C22×D3—21no—
79C3×D4—62no—
80C3×D4—62no—
81C2×C3×C4—62no—
82C2×C3×C4—61no—
83C2×C3×C4—64no—
84#67—22no—
85#67—22no—
86#67—62no—
87#67—62no—
88C2×Dic3—22no—
89C2×Dic3—21no—
90C2×Dic3—24no—
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—61no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103C2×Dic3—62no—
104C2×Dic3—62no—
105C4×D3—62no—
106C4×D3—62no—
107Dic6—62no—
108Dic6—62no—
109C2×C32—21no—
110C2×C32—21no—
111C2×C32#10412yescomplemented
112C2×C32C2×C22⋊C411yescharacteristic
113C3×D3—42no—
114#41—92no—
115#41—92no—
116#41—181no—
117#41—181no—
118C2×Q8—91no—
119C2×D4—61no—
120C2×D4—91no—
121C22×C4—61no—
122C22×C4—91no—
123C22×C4—181no—
124M16—92no—
125M16—181no—
126C2×C8—181no—
127C42—92no—
128C42—181no—
129C22×C3—22no—
130C22×C3—22no—
131C22×C3—21no—
132C22×C3—21no—
133C22×C3—21no—
134C22×C3—21no—
135C22×C3—21no—
136C22×C3—21no—
137C22×C3—42no—
138C22×C3—62no—
139C22×C3—122no—
140C2×D3—22no—
141C2×D3—42no—
142C3×C4—62no—
143C3×C4—64no—
144Dic3—22no—
145Dic3—24no—
146Dic3—61no—
147Dic3—61no—
148Dic3—61no—
149Dic3—61no—
150Dic3—61no—
151Dic3—61no—
152Dic3—61no—
153Dic3—61no—
154C32C2×#10411yescharacteristic, complemented, Sylow
155C23—61no—
156C23GO+(4,𝔽2)11yescharacteristic
157Q8—92no—
158Q8—181no—
159D4—62no—
160D4—62no—
161D4—92no—
162D4—181no—
163C2×C4—64no—
164C2×C4—62no—
165C2×C4—61no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—182no—
173C2×C4—182no—
174C8—182no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—22no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—22no—
181C2×C3—22no—
182C2×C3—41no—
183C2×C3—41no—
184C2×C3—122no—
185D3—42no—
186C22—22no—
187C22—62no—
188C22—122no—
189C22D32⋊C411yescharacteristic
190C22D32⋊C411yescharacteristic
191C22C2×GO+(4,𝔽2)11yescharacteristic
192C4—64no—
193C4—62no—
194C4—91no—
195C4—91no—
196C4—91no—
197C4—91no—
198C3—21no—
199C3—21no—
200C2—21no—
201C2—21no—
202C2—122no—
203C2#6374112yesdirect product factor
204C2C2×D32⋊C411yescharacteristic
subgroupG/H
centerC22D32⋊C4
commutatorC3⋊Dic3C22×C4
FrattiniC22C2×GO+(4,𝔽2)
FittingC23×C32D4
socleC22×C32C22⋊C4
prime radicalC2×#3805C2
cosocleC2×C3⋊Dic3C23
hypercenterC23GO+(4,𝔽2)
hypocenterC32C2×#104
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#3792C2semidirect
3. C2×Dic32C2semidirect
4. #63741C2direct (N × H)
8. C2×#627C4semidirect
9. C2×#625C4semidirect
12. #3805C4semidirect
16. #3792C22semidirect
19. Dic32C22semidirect
36. #627C2×C4semidirect
38. #625C2×C4semidirect
111. C2×C32#104semidirect
154. C32C2×#104semidirect
203. C2#63741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#38052
C2×#37922
C2×Dic322
#637412
C2×#1049