Finite Group Databasebeta

← A4×C22⋊C8 #73227

Subgroups — A4×C22⋊C8 #73227

Order 384.

262 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C22×C4×A4C211yesmaximal, characteristic
2C2×C8×A4C212yesmaximal, complemented
3C22×C22⋊C8C311yesmaximal, characteristic, complemented, Sylow
4C23×A4C411yescharacteristic
5C2×C4×A4—22no—
6C2×C4×A4C411yescharacteristic
7C2×C4×A4C2211yescharacteristic
8C8×A4—22no—
9C3×C22⋊C8—41nomaximal
10C24×C4C2×C311yescharacteristic
11C23×C8C2×C312yescomplemented
12C2×C22⋊C8—31no—
13C2×C22⋊C8—31no—
14C2×C22⋊C8—32no—
15C22×A4—21no—
16C22×A4—21no—
17C22×A4C812yescomplemented
18C22×A4C2×C411yescharacteristic
19C22×C3×C4—41no—
20C4×A4—21no—
21C4×A4D412yes—
22C2×C3×C8—42no—
23C25C3×C411yescharacteristic
24C23×C4—22no—
25C23×C4—31no—
26C23×C4—31no—
27C23×C4—31no—
28C23×C4—31no—
29C23×C4—62no—
30C23×C4C3×C411yescharacteristic
31C23×C4C22×C311yescharacteristic
32C22×C8—22no—
33C22×C8—32no—
34C22×C8—32no—
35C22×C8—62no—
36C22⋊C8—32no—
37C22⋊C8—31no—
38C22⋊C8—32no—
39C22⋊C8A411yescharacteristic, direct product factor
40C23×C3—41no—
41C2×A4—22no—
42C2×A4C22⋊C411yescharacteristic
43C2×A4C2×C811yescharacteristic
44C2×A4M1611yescharacteristic
45C2×C3×C4—41no—
46C2×C3×C4—41no—
47C2×C3×C4—82no—
48C3×C8—82no—
49C24—21no—
50C24—21no—
51C24—31no—
52C24—32no—
53C24—31no—
54C24—61no—
55C24—61no—
56C24C3×C812yescomplemented
57C24C2×C3×C411yescharacteristic
58C22×C4—21no—
59C22×C4—31no—
60C22×C4—32no—
61C22×C4—31no—
62C22×C4—32no—
63C22×C4—31no—
64C22×C4—31no—
65C22×C4—31no—
66C22×C4—31no—
67C22×C4—31no—
68C22×C4—62no—
69C22×C4—62no—
70C22×C4—62no—
71C22×C4—62no—
72C22×C4—62no—
73C22×C4—62no—
74C22×C4—62no—
75C22×C4—62no—
76C22×C4—61no—
77C22×C4C3×D412yes—
78C22×C4C2×A411yescharacteristic
79C2×C8—32no—
80C2×C8—62no—
81C2×C8—62no—
82C2×C8—62no—
83C2×C8—62no—
84C2×C8C2×A412yescomplemented
85C22×C3—42no—
86C22×C3—41no—
87C22×C3—81no—
88C22×C3—81no—
89A4C22⋊C811yescharacteristic, direct product factor
90C3×C4—42no—
91C3×C4—81no—
92C23—22no—
93C23—31no—
94C23—31no—
95C23—31no—
96C23—31no—
97C23—32no—
98C23—32no—
99C23—32no—
100C23—32no—
101C23—31no—
102C23—61no—
103C23—61no—
104C23—61no—
105C23—61no—
106C23—62no—
107C23—61no—
108C23—61no—
109C23—62no—
110C23—62no—
111C23—61no—
112C23—61no—
113C23—64no—
114C23C3×C22⋊C411yescharacteristic
115C23C2×C3×C811yescharacteristic
116C23C3×M1611yescharacteristic
117C23C4×A411yescharacteristic
118C2×C4—22no—
119C2×C4—32no—
120C2×C4—31no—
121C2×C4—32no—
122C2×C4—32no—
123C2×C4—32no—
124C2×C4—31no—
125C2×C4—62no—
126C2×C4—61no—
127C2×C4—61no—
128C2×C4—62no—
129C2×C4—64no—
130C2×C4—62no—
131C2×C4—61no—
132C2×C4—61no—
133C2×C4C4×A411yescharacteristic
134C2×C4C22×A411yescharacteristic
135C8—22no—
136C8—62no—
137C2×C3—41no—
138C2×C3—41no—
139C2×C3—41no—
140C2×C3—82no—
141C22—21no—
142C22—21no—
143C22—31no—
144C22—31no—
145C22—31no—
146C22—32no—
147C22—31no—
148C22—31no—
149C22—31no—
150C22—31no—
151C22—31no—
152C22—31no—
153C22—32no—
154C22—62no—
155C22—62no—
156C22—62no—
157C22—62no—
158C22—62no—
159C22—62no—
160C22—62no—
161C22—62no—
162C22—61no—
163C22—61no—
164C22C3×C22⋊C811yescharacteristic, complemented
165C22C8×A412yescomplemented
166C22C2×C4×A411yescharacteristic
167C4—21no—
168C4—32no—
169C4—61no—
170C4D4×A412yes—
171C3—41noSylow
172C2—22no—
173C2—31no—
174C2—31no—
175C2—31no—
176C2—31no—
177C2—62no—
178C2A4×C22⋊C411yescharacteristic
179C2C2×C8×A411yescharacteristic
180C2A4×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×A4
commutatorC23C2×C3×C8
FittingC22×C22⋊C8C3
socleC24C2×C3×C4
prime radicalC23×A4C4
cosocleC23×C4C22×C3
hypercenterC22⋊C8A4
hypocenterC22C3×C22⋊C8
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×A4C2semidirect
3. C22×C22⋊C8C3semidirect
11. C23×C8C2×C3semidirect
17. C22×A4C8semidirect
39. C22⋊C8A4direct (N × H)
56. C24C3×C8semidirect
84. C2×C8C2×A4semidirect
89. A4C22⋊C8direct (N × H)
164. C22C3×C22⋊C8semidirect
165. C22C8×A4semidirect

Maximal subgroups

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

subgroupindex
C22×C4×A42
C2×C8×A42
C22×C22⋊C83
C3×C22⋊C84