Finite Group Databasebeta

← A4×#829 #11921348

Subgroups — A4×#829 #11921348

Order 1152.

218 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 39 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
1C3×A4×Q16C211yesmaximal, characteristic
2A4×Dic12C211yesmaximal, characteristic
3A4×C3⋊C16C211yesmaximal, characteristic
4C22×#829C311yesmaximal, characteristic, complemented
5A4×Q32—31nomaximal
6C3×Q8×A4—21no—
7A4×Dic6—21no—
8C3×C8×A4C2211yescharacteristic
9C3×#829—41nomaximal
10C22×C3×Q16C2×C311yescharacteristic
11C22×Dic12C2×C311yescharacteristic
12A4×Q16—21no—
13A4×Q16—31no—
14A4×Q16D311yescharacteristic
15C2×#829—31no—
16C2×#829—31no—
17C2×#829—31no—
18C2×#829—31no—
19C22×C3⋊C16C2×C311yescharacteristic
20A4×C16—31no—
21C3×C4×A4—41no—
22C3×C4×A4D411yescharacteristic
23Dic3×A4—41no—
24C32×Q16—41no—
25C3×Dic12—41no—
26C3×C3⋊C16—41no—
27C22×Q32—31noSylow
28C22×C3×Q8—21no—
29C22×Dic6—21no—
30Q8×A4—22no—
31Q8×A4—21no—
32Q8×A4—61no—
33C2×C3×Q16—31no—
34C2×C3×Q16—31no—
35C2×C3×Q16—61no—
36C22×C3×C8C22×C311yescharacteristic
37C2×Dic12—31no—
38C2×Dic12—31no—
39C2×Dic12—61no—
40C8×A4—21no—
41C8×A4C2×D311yescharacteristic
42C3×Q32—121no—
43#829—32no—
44#829—31no—
45#829—31no—
46#829—31no—
47#829A411yescharacteristic, direct product factor
48C2×C3⋊C16—31no—
49C2×C3⋊C16—31no—
50C2×C3×A4D811yescharacteristic
51C32×Q8—81no—
52C3×Dic6—81no—
53C32×C8—41no—
54C22×Q16—31no—
55C22×Q16C3×D311yescharacteristic
56C2×Q32—91no—
57C2×Q32—91no—
58C2×Q32—91no—
59C2×Q32—91no—
60C22×C16—31no—
61C2×C3×Q8—61no—
62C2×C3×Q8—61no—
63C2×C3×Q8—121no—
64C22×C3×C4—41no—
65C22×C3×C4C3×D411yescharacteristic
66C22×Dic3—41no—
67C2×Dic6—61no—
68C2×Dic6—61no—
69C2×Dic6—121no—
70C4×A4—21no—
71C4×A4—42no—
72C4×A4—41no—
73C4×A4—121no—
74C4×A4#6711yescharacteristic
75C3×Q16—31no—
76C3×Q16—41no—
77C3×Q16—61no—
78C3×Q16—61no—
79C3×Q16—81no—
80C3×Q16—121no—
81C3×Q16C2×A411yescharacteristic
82C2×C3×C8—31no—
83C2×C3×C8—31no—
84Dic12—31no—
85Dic12—61no—
86Dic12—61no—
87Dic12C2×A411yescharacteristic
88C3×C16—121no—
89C3⋊C16—31no—
90C3⋊C16C2×A411yescharacteristic
91C3×A4Q3211yescharacteristic, complemented
92C32×C4—41no—
93C32×C4—161no—
94C3×Dic3—161no—
95C22×Q8—21no—
96C22×Q8—61no—
97C2×Q16—31no—
98C2×Q16—31no—
99C2×Q16—61no—
100C2×Q16—91no—
101C2×Q16—91no—
102C2×Q16—181no—
103C22×C8C2×C3×D311yescharacteristic
104Q32—31no—
105Q32—91no—
106Q32—91no—
107Q32—92no—
108Q32—91no—
109C2×C16—91no—
110C2×C16—91no—
111C23×C3C3×D811yescharacteristic
112C2×A4—21no—
113C2×A4#21311yescharacteristic
114C3×Q8—21no—
115C3×Q8—61no—
116C3×Q8—81no—
117C3×Q8—82no—
118C3×Q8—121no—
119C3×Q8—121no—
120C3×Q8—241no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—121no—
124C2×C3×C4—121no—
125C2×Dic3—121no—
126C2×Dic3—121no—
127Dic6—21no—
128Dic6—61no—
129Dic6—121no—
130Dic6—121no—
131C3×C8—31no—
132C3×C8—41no—
133C3×C8—81no—
134C3×C8C22×A411yescharacteristic
135C2×C32—41no—
136C2×Q8—61no—
137C2×Q8—61no—
138C2×Q8—121no—
139C2×Q8—181no—
140C2×Q8—181no—
141C2×Q8—361no—
142C22×C4—41no—
143C22×C4—121no—
144C22×C4C3×#6711yescharacteristic
145Q16—31no—
146Q16—31no—
147Q16—61no—
148Q16—61no—
149Q16—91no—
150Q16—181no—
151Q16—181no—
152Q16D3×A411yescharacteristic
153C2×C8—31no—
154C2×C8—31no—
155C16—31no—
156C16—91no—
157C22×C3—31no—
158C22×C3—31no—
159C22×C3C3×Q3211yescharacteristic, complemented
160A4—21no—
161A4#82911yescharacteristic, direct product factor
162C3×C4—31no—
163C3×C4—41no—
164C3×C4—41no—
165C3×C4—81no—
166C3×C4—121no—
167C3×C4—161no—
168C3×C4—162no—
169C3×C4—481no—
170C3×C4D4×A411yescharacteristic
171Dic3—41no—
172Dic3—121no—
173C32—41noSylow
174C23C3×#21311yescharacteristic
175Q8—21no—
176Q8—61no—
177Q8—61no—
178Q8—121no—
179Q8—121no—
180Q8—181no—
181Q8—361no—
182Q8—361no—
183C2×C4—31no—
184C2×C4—31no—
185C2×C4—121no—
186C2×C4—121no—
187C2×C4—361no—
188C2×C4—361no—
189C8—31no—
190C8C2×D3×A411yescharacteristic
191C2×C3—31no—
192C2×C3—31no—
193C2×C3—41no—
194C2×C3—81no—
195C2×C3A4×D811yescharacteristic
196C22—31no—
197C22—31no—
198C22C3×#82911yescharacteristic, complemented
199C4—31no—
200C4—41no—
201C4—121no—
202C4—121no—
203C4—361no—
204C4A4×#6711yescharacteristic
205C3—41no—
206C3—81no—
207C3A4×Q3211yescharacteristic, complemented
208C2—31no—
209C2—31no—
210C2A4×#21311yescharacteristic
subgroupG/H
centerC2A4×#213
commutator, cosocleC22×C3×C8C22×C3
FrattiniC8C2×D3×A4
FittingC22×C3×Q16C2×C3
socleC23×C3C3×D8
prime radicalC2×C3×A4D8
hypercenterQ16D3×A4
hypocenterC22×C3C3×Q32
LCSG ▷ C22×C3×C8 ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

Complements

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

NH ≅ G/Ntype
4. C22×#829C3semidirect
47. #829A4direct (N × H)
91. C3×A4Q32semidirect
159. C22×C3C3×Q32semidirect
161. A4#829direct (N × H)
198. C22C3×#829semidirect
207. C3A4×Q32semidirect

Maximal subgroups

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

subgroupindex
C3×A4×Q162
A4×Dic122
A4×C3⋊C162
C22×#8293
A4×Q323
C3×#8294