Finite Group Databasebeta

← C2×#64204 #10596461

Subgroups — C2×#64204 #10596461

Order 576.

346 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic3×A4C211yesmaximal, characteristic
2C2×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
3C2×C3×SL(2,ℤ/4)C211yesmaximal, characteristic
4#64204C214yesmaximal, direct product factor
5C2×A4⋊Q8—31nomaximal
6C2×#878—31nomaximal
7C22×C3×A4C2211yescharacteristic
8C2×#627—41nomaximal
9Dic3×A4C2212yes—
10C3⋊SL(2,ℤ/4)C2212yes—
11C3×SL(2,ℤ/4)C2212yes—
12C23×Dic3D311yescharacteristic
13C22×Dic6—31no—
14C2×C4×A4—31no—
15C2×SL(2,ℤ/4)—31no—
16C2×SL(2,ℤ/4)—61no—
17C2×SL(2,ℤ/4)D311yescharacteristic
18A4⋊Q8—34no—
19C2×C3×C22⋊C4—31no—
20C2×#217—31no—
21C2×C4⋊Dic3—31no—
22C2×Dic3⋊C4—31no—
23C2×Dic3⋊C4—31no—
24#878—34no—
25#878—34no—
26C2×C3×A4Q812yescomplemented
27C2×C3×A4C2311yescharacteristic
28C2×C3⋊Dic3—41no—
29C2×C3×Dic3—41no—
30C2×C3×Dic3—41no—
31#627—44no—
32C2×C22⋊Q8—91noSylow
33C24×C3C2×D311yescharacteristic
34C22×A4—21no—
35C22×A4C2×D311yescharacteristic
36C22×C3×C4—31no—
37C22×C3×C4—31no—
38C22×Dic3—31no—
39C22×Dic3—32no—
40C22×Dic3—31no—
41C22×Dic3—31no—
42C22×Dic3—31no—
43C22×Dic3C2×D312yes—
44C2×Dic6—34no—
45C2×Dic6—61no—
46C2×Dic6—62no—
47C2×Dic6—61no—
48C2×Dic6—121no—
49C4×A4—32no—
50SL(2,ℤ/4)—32no—
51SL(2,ℤ/4)—62no—
52SL(2,ℤ/4)C2×D312yes—
53C3×C22⋊C4—32no—
54C3×C22⋊C4—32no—
55#217—32no—
56#217—32no—
57C4⋊Dic3—34no—
58Dic3⋊C4—34no—
59Dic3⋊C4—34no—
60C22×C32—41no—
61C3×A4C2×Q811yescharacteristic, complemented
62C3⋊Dic3—42no—
63C3×Dic3—42no—
64C3×Dic3—42no—
65C22×Q8—91no—
66C23×C4—31no—
67C22⋊Q8—94no—
68C22⋊Q8—94no—
69C2×C4⋊C4—91no—
70C2×C4⋊C4—91no—
71C2×C4⋊C4—91no—
72C2×C22⋊C4—31no—
73C2×C22⋊C4—91no—
74C23×C3—31no—
75C23×C3—31no—
76C23×C3—32no—
77C23×C3Dic612yescomplemented
78C23×C3C22×D311yescharacteristic
79C2×A4—22no—
80C2×A4—21no—
81C2×A4Dic612yescomplemented
82C2×A4C22×D311yescharacteristic
83C2×C3×C4—32no—
84C2×C3×C4—32no—
85C2×C3×C4—61no—
86C2×C3×C4—62no—
87C2×C3×C4—61no—
88C2×C3×C4—121no—
89C2×Dic3—31no—
90C2×Dic3—32no—
91C2×Dic3—32no—
92C2×Dic3—32no—
93C2×Dic3—32no—
94C2×Dic3—32no—
95C2×Dic3—41no—
96C2×Dic3—61no—
97C2×Dic3—61no—
98C2×Dic3—62no—
99C2×Dic3—61no—
100C2×Dic3—121no—
101C2×Dic3—241no—
102C2×Dic3S411yescharacteristic
103Dic6—64no—
104Dic6—64no—
105Dic6—124no—
106C2×C32—42no—
107C2×C32—41no—
108C24D3211yescharacteristic
109C2×Q8—94no—
110C2×Q8—181no—
111C2×Q8—182no—
112C2×Q8—181no—
113C22×C4—31no—
114C22×C4—31no—
115C22×C4—32no—
116C22×C4—91no—
117C22×C4—91no—
118C22×C4—92no—
119C22×C4—91no—
120C22×C4—91no—
121C4⋊C4—94no—
122C4⋊C4—94no—
123C4⋊C4—94no—
124C22⋊C4—32no—
125C22⋊C4—32no—
126C22⋊C4—92no—
127C22⋊C4—92no—
128C22×C3—32no—
129C22×C3—31no—
130C22×C3—32no—
131C22×C3—32no—
132C22×C3—31no—
133C22×C3—31no—
134C22×C3—41no—
135C22×C3—61no—
136C22×C3—81no—
137C22×C3C2×Dic611yescharacteristic, complemented
138C22×C3C2×S411yescharacteristic
139A4—21no—
140A4C2×Dic611yescharacteristic, complemented
141C3×C4—62no—
142C3×C4—62no—
143C3×C4—122no—
144Dic3—32no—
145Dic3—42no—
146Dic3—62no—
147Dic3—62no—
148Dic3—122no—
149Dic3—242no—
150Dic3C2×S412yes—
151C32—41noSylow
152C23—31no—
153C23—31no—
154C23—32no—
155C23#62712yescomplemented
156C23C2×D3211yescharacteristic
157Q8—184no—
158Q8—184no—
159C2×C4—31no—
160C2×C4—32no—
161C2×C4—32no—
162C2×C4—61no—
163C2×C4—62no—
164C2×C4—61no—
165C2×C4—92no—
166C2×C4—92no—
167C2×C4—91no—
168C2×C4—92no—
169C2×C4—92no—
170C2×C4—92no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4—182no—
174C2×C4—181no—
175C2×C3—31no—
176C2×C3—31no—
177C2×C3—32no—
178C2×C3—41no—
179C2×C3—42no—
180C2×C3—81no—
181C2×C3—82no—
182C2×C3A4⋊Q812yescomplemented
183C2×C3C22×S411yescharacteristic
184C22—32no—
185C22—31no—
186C22—31no—
187C22—31no—
188C22—32no—
189C22—32no—
190C22—61no—
191C22C2×#62711yescharacteristic, complemented
192C22D3×S411yescharacteristic
193C4—32no—
194C4—62no—
195C4—62no—
196C4—92no—
197C4—182no—
198C4—182no—
199C3—41no—
200C3—81no—
201C3C2×A4⋊Q811yescharacteristic, complemented
202C2—31no—
203C2—31no—
204C2—32no—
205C2#6420412yesdirect product factor
206C2C2×D3×S411yescharacteristic
subgroupG/H
center, hypercenterC22D3×S4
commutator, cosocleC2×C3×A4C23
FrattiniC2C2×D3×S4
Fitting, socleC24×C3C2×D3
prime radicalC22×C3×A4C22
hypocenterC3×A4C2×Q8
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
4. #64204C2direct (N × H)
26. C2×C3×A4Q8semidirect
61. C3×A4C2×Q8semidirect
77. C23×C3Dic6semidirect
81. C2×A4Dic6semidirect
137. C22×C3C2×Dic6semidirect
140. A4C2×Dic6semidirect
155. C23#627semidirect
182. C2×C3A4⋊Q8semidirect
191. C22C2×#627semidirect
201. C3C2×A4⋊Q8semidirect
205. C2#64204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Dic3×A42
C2×C3⋊SL(2,ℤ/4)2
C2×C3×SL(2,ℤ/4)2
#642042
C2×A4⋊Q83
C2×#8783
C2×#6274