Finite Group Databasebeta

← A4×#103 #73236

Subgroups — A4×#103 #73236

Order 384.

206 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 42 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×Q8×A4C211yesmaximal, characteristic
2C2×C8×A4C211yesmaximal, characteristic
3A4×C4⋊C4C211yesmaximal, characteristic
4C22×#103C311yesmaximal, characteristic, complemented, Sylow
5Q8×A4—21no—
6Q8×A4C412yescomplemented
7C2×C4×A4—21no—
8C2×C4×A4—21no—
9C2×C4×A4C2211yescharacteristic
10C8×A4—21no—
11C3×#103—41nomaximal
12C23×Q8C2×C311yescharacteristic
13C23×C8C2×C311yescharacteristic
14C22×C4⋊C4C2×C311yescharacteristic
15C2×#103—31no—
16C2×#103—31no—
17C2×#103—31no—
18C2×#103—31no—
19C22×A4D411yescharacteristic
20C2×C3×Q8—41no—
21C4×A4—22no—
22C4×A4—41no—
23C4×A4C2×C411yescharacteristic
24C4×A4D411yescharacteristic
25C2×C3×C8—41no—
26C3×C4⋊C4—41no—
27C22×Q8—21no—
28C22×Q8—32no—
29C22×Q8—31no—
30C22×Q8—31no—
31C22×Q8—61no—
32C22×Q8—61no—
33C22×Q8C3×C412yescomplemented
34C23×C4—21no—
35C23×C4—21no—
36C23×C4C22×C311yescharacteristic
37C22×C8—21no—
38C22×C8—31no—
39C22×C8—31no—
40C22×C8—61no—
41C2×C4⋊C4—31no—
42C2×C4⋊C4—31no—
43C2×C4⋊C4—61no—
44#103—32no—
45#103—31no—
46#103—31no—
47#103—31no—
48#103A411yescharacteristic, direct product factor
49C2×A4C22⋊C411yescharacteristic
50C2×A4SD1611yescharacteristic
51C2×A4Q1611yescharacteristic
52C3×Q8—42no—
53C3×Q8—81no—
54C2×C3×C4—41no—
55C2×C3×C4—81no—
56C2×C3×C4—81no—
57C3×C8—81no—
58C24C3×D411yescharacteristic
59C2×Q8—32no—
60C2×Q8—32no—
61C2×Q8—32no—
62C2×Q8—32no—
63C2×Q8—31no—
64C2×Q8—61no—
65C2×Q8—61no—
66C2×Q8—61no—
67C2×Q8—62no—
68C2×Q8—61no—
69C2×Q8—62no—
70C2×Q8—61no—
71C2×Q8—64no—
72C2×Q8—61no—
73C2×Q8C2×A411yescharacteristic
74C22×C4—22no—
75C22×C4—31no—
76C22×C4—31no—
77C22×C4—31no—
78C22×C4—31no—
79C22×C4—41no—
80C22×C4—61no—
81C22×C4—61no—
82C22×C4—62no—
83C22×C4—61no—
84C22×C4—61no—
85C22×C4—121no—
86C22×C4C2×C3×C411yescharacteristic
87C22×C4C3×D411yescharacteristic
88C2×C8—31no—
89C2×C8—61no—
90C2×C8—61no—
91C2×C8—61no—
92C2×C8—61no—
93C2×C8C2×A411yescharacteristic
94C4⋊C4—31no—
95C4⋊C4—61no—
96C4⋊C4—61no—
97C4⋊C4C2×A411yescharacteristic
98C22×C3—41no—
99A4#10311yescharacteristic, direct product factor
100C3×C4—41no—
101C3×C4—41no—
102C3×C4—82no—
103C3×C4—161no—
104C23—31no—
105C23—31no—
106C23—31no—
107C23—31no—
108C23C3×C22⋊C411yescharacteristic
109C23C3×SD1611yescharacteristic
110C23C3×Q1611yescharacteristic
111Q8—21no—
112Q8—32no—
113Q8—62no—
114Q8—62no—
115Q8—62no—
116Q8—62no—
117Q8—61no—
118Q8C4×A412yescomplemented
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—32no—
122C2×C4—31no—
123C2×C4—31no—
124C2×C4—31no—
125C2×C4—31no—
126C2×C4—31no—
127C2×C4—31no—
128C2×C4—31no—
129C2×C4—62no—
130C2×C4—62no—
131C2×C4—62no—
132C2×C4—61no—
133C2×C4—62no—
134C2×C4—61no—
135C2×C4—121no—
136C2×C4—121no—
137C2×C4—121no—
138C2×C4—121no—
139C2×C4C22×A411yescharacteristic
140C8—21no—
141C8—61no—
142C2×C3—41no—
143C2×C3—41no—
144C2×C3—41no—
145C22—31no—
146C22—31no—
147C22—31no—
148C22—32no—
149C22—31no—
150C22—31no—
151C22—31no—
152C22—31no—
153C22—31no—
154C22—31no—
155C22C3×#10311yescharacteristic, complemented
156C22D4×A411yescharacteristic
157C4—22no—
158C4—31no—
159C4—31no—
160C4—41no—
161C4—62no—
162C4—121no—
163C4C2×C4×A411yescharacteristic
164C4D4×A411yescharacteristic
165C3—41noSylow
166C2—31no—
167C2—31no—
168C2—31no—
169C2—31no—
170C2A4×C22⋊C411yescharacteristic
171C2A4×SD1611yescharacteristic
172C2A4×Q1611yescharacteristic
subgroupG/H
centerC22D4×A4
commutatorC22×C4C2×C3×C4
FrattiniC2×C4C22×A4
FittingC22×#103C3
socleC24C3×D4
prime radicalC22×A4D4
cosocleC23×C4C22×C3
hypercenter#103A4
hypocenterC22C3×#103
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. C22×#103C3semidirect
6. Q8×A4C4semidirect
33. C22×Q8C3×C4semidirect
48. #103A4direct (N × H)
99. A4#103direct (N × H)
118. Q8C4×A4semidirect
155. C22C3×#103semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×A42
C2×C8×A42
A4×C4⋊C42
C22×#1033
C3×#1034