Finite Group Databasebeta

← C3×#73133 #11920911

Subgroups — C3×#73133 #11920911

Order 1152.

246 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 36 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×D8C211yesmaximal, characteristic, complemented
2C3×#5402C211yesmaximal, characteristic, complemented
3C3×A4⋊C16C211yesmaximal, characteristic, complemented
4#73133C311yesmaximal, characteristic, direct product factor
5C3×#2184—31nomaximal
6C3×D4×A4—21no—
7C3×C4⋊S4—21no—
8C3×C8×A4C2211yescharacteristic
9C3×#826—41nomaximal
10C22×C3×D8D311yescharacteristic, complemented
11A4×D8—21no—
12A4×D8C2×C311yescharacteristic, complemented
13#5402C2×C311yescharacteristic, complemented
14C2×C3×D16—31no—
15C2×C3×D16—31no—
16C3×#466—31no—
17A4⋊C16C2×C311yescharacteristic, complemented
18C3×#357—31no—
19C3×#357—31no—
20C3×C22⋊C16—31no—
21C22×C3×A4—41no—
22C2×C3×S4—41no—
23C3×C4×A4D411yescharacteristic
24C32×D8—41no—
25C3×D24—41no—
26C3×C3⋊C16—41no—
27#2184—31noSylow
28C22×C3×D4—21no—
29D4×A4—22no—
30D4×A4—21no—
31C4⋊S4—21no—
32C2×C3×D8—31no—
33C2×C3×D8—31no—
34C2×C3×D8—31no—
35C2×C3×D8—61no—
36C22×C3×C8C2×D311yescharacteristic
37C3×#121—61no—
38C8×A4—21no—
39C8×A4C22×C311yescharacteristic
40C3×D16—62no—
41C3×D16—61no—
42C3×D16—61no—
43C2×C3×C16—31no—
44C2×C3×C16—31no—
45C3×#107—31no—
46C3×#102—61no—
47#826—41no—
48C2×C3×A4—81no—
49C2×C3×A4D811yescharacteristic
50C3×S4—81no—
51C32×D4—81no—
52C3×D12—81no—
53C32×C8—41no—
54C22×D8C3×D311yescharacteristic, complemented
55C2×D16—31no—
56C2×D16—31no—
57#466—31no—
58#357—31no—
59#357—31no—
60C22⋊C16—31no—
61C24×C3—41no—
62C22×A4—42no—
63C22×A4—41no—
64C2×S4—41no—
65C2×C3×D4—61no—
66C2×C3×D4—61no—
67C2×C3×D4—61no—
68C2×C3×D4—121no—
69C2×C3×D4—121no—
70C22×C3×C4#6711yescharacteristic
71C4×A4—21no—
72C4×A4C3×D411yescharacteristic
73C3×D8—32no—
74C3×D8—31no—
75C3×D8—41no—
76C3×D8—61no—
77C3×D8—61no—
78C3×D8—61no—
79C3×D8—81no—
80C3×D8S411yescharacteristic, complemented
81C2×C3×C8—31no—
82C2×C3×C8—31no—
83C3×C4⋊C4—61no—
84C3×C22⋊C4—121no—
85D24—41no—
86C3×C16—61no—
87C3×C16—61no—
88C3⋊C16—41no—
89C22×C32—161no—
90C2×C3×D3—161no—
91C3×A4D1611yescharacteristic, complemented
92C32×C4—41no—
93C22×D4—21no—
94C2×D8—31no—
95C2×D8—31no—
96C2×D8—31no—
97C2×D8—61no—
98C22×C8C2×C3×D311yescharacteristic
99#121—61no—
100D16—62no—
101D16—61no—
102D16—61no—
103C2×C16—31no—
104C2×C16—31no—
105#107—31no—
106#102—61no—
107C23×C3—81no—
108C23×C3—121no—
109C23×C3—121no—
110C23×C3—121no—
111C23×C3—241no—
112C23×C3#21311yescharacteristic
113C2×A4—21no—
114C2×A4—82no—
115C2×A4—81no—
116C2×A4C3×D811yescharacteristic
117S4—81no—
118C3×D4—21no—
119C3×D4—61no—
120C3×D4—81no—
121C3×D4—82no—
122C3×D4—121no—
123C3×D4—121no—
124C3×D4—121no—
125C3×D4—121no—
126C3×D4—241no—
127C3×D4—241no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—121no—
131D12—81no—
132C3×C8—31no—
133C3×C8—41no—
134C3×C8—81no—
135C3×C8C2×S411yescharacteristic
136C2×C32—41no—
137C2×C32—321no—
138C3×D3—321no—
139C24—41no—
140C2×D4—61no—
141C2×D4—61no—
142C2×D4—61no—
143C2×D4—121no—
144C2×D4—121no—
145C22×C4C3×#6711yescharacteristic
146D8—32no—
147D8—31no—
148D8—61no—
149D8—61no—
150D8—61no—
151D8C3×S411yescharacteristic, complemented
152C2×C8—31no—
153C2×C8—31no—
154C4⋊C4—61no—
155C22⋊C4—121no—
156C16—61no—
157C16—61no—
158C22×C3—31no—
159C22×C3—31no—
160C22×C3—41no—
161C22×C3—121no—
162C22×C3—161no—
163C22×C3—162no—
164C22×C3—241no—
165C22×C3—241no—
166C22×C3—241no—
167C22×C3—241no—
168C22×C3—241no—
169C22×C3—241no—
170C22×C3—241no—
171C22×C3#82611yescharacteristic, complemented
172C2×D3—161no—
173A4—21no—
174A4C3×D1611yescharacteristic, complemented
175C3×C4—31no—
176C3×C4—41no—
177C3×C4—81no—
178C3×C4—241no—
179C3×C4GL(2,ℤ/4)11yescharacteristic
180C32—41noSylow
181C23—81no—
182C23—121no—
183C23—121no—
184C23—121no—
185C23—241no—
186C23C3×#21311yescharacteristic
187D4—21no—
188D4—61no—
189D4—121no—
190D4—121no—
191D4—121no—
192D4—121no—
193D4—241no—
194D4—241no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—121no—
198C8—31no—
199C8C2×C3×S411yescharacteristic
200C2×C3—31no—
201C2×C3—31no—
202C2×C3—41no—
203C2×C3—81no—
204C2×C3—81no—
205C2×C3—241no—
206C2×C3—321no—
207C2×C3—322no—
208C2×C3—481no—
209C2×C3#541511yescharacteristic
210D3—321no—
211C22—31no—
212C22—31no—
213C22—41no—
214C22—121no—
215C22—241no—
216C22—241no—
217C22—241no—
218C22—241no—
219C22—241no—
220C22—241no—
221C22—241no—
222C22C3×#82611yescharacteristic, complemented
223C4—31no—
224C4—241no—
225C4C3×GL(2,ℤ/4)11yescharacteristic
226C3—41no—
227C3—81no—
228C3#7313311yescharacteristic, direct product factor
229C2—31no—
230C2—31no—
231C2—81no—
232C2—241no—
233C2—481no—
234C2C3×#541511yescharacteristic
subgroupG/H
centerC2×C3#5415
commutator, cosocleC8×A4C22×C3
FrattiniC8C2×C3×S4
FittingC22×C3×D8D3
socleC23×C3#213
hypercenterC3×D8S4
hypocenterA4C3×D16
LCSG ▷ C8×A4 ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D8

Complements

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

NH ≅ G/Ntype
1. C3×A4×D8C2semidirect
2. C3×#5402C2semidirect
3. C3×A4⋊C16C2semidirect
4. #73133C3direct (N × H)
10. C22×C3×D8D3semidirect
12. A4×D8C2×C3semidirect
13. #5402C2×C3semidirect
17. A4⋊C16C2×C3semidirect
54. C22×D8C3×D3semidirect
80. C3×D8S4semidirect
91. C3×A4D16semidirect
151. D8C3×S4semidirect
171. C22×C3#826semidirect
174. A4C3×D16semidirect
222. C22C3×#826semidirect
228. C3#73133direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×D82
C3×#54022
C3×A4⋊C162
#731333
C3×#21843
C3×#8264