Finite Group Databasebeta

← C3×#73135 #11920913

Subgroups — C3×#73135 #11920913

Order 1152.

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

normal subgroups only

This group has 222 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×Q16C211yesmaximal, characteristic, complemented
2C3×#5402C211yesmaximal, characteristic
3C3×A4⋊C16C211yesmaximal, characteristic, complemented
4#73135C311yesmaximal, characteristic, direct product factor
5C3×#2185—31nomaximal
6C3×Q8×A4—21no—
7C3×C4⋊S4—21no—
8C3×C8×A4C2211yescharacteristic
9C3×#828—41nomaximal
10C22×C3×Q16D311yescharacteristic, complemented
11A4×Q16—21no—
12A4×Q16C2×C311yescharacteristic, complemented
13#5402C2×C311yescharacteristic
14C2×C3×SD32—31no—
15C2×C3×SD32—31no—
16C3×#466—31no—
17A4⋊C16C2×C311yescharacteristic, complemented
18C3×#358—31no—
19C3×#358—31no—
20C3×C22⋊C16—31no—
21C2×C3×S4—41no—
22C3×C4×A4—41no—
23C3×C4×A4D411yescharacteristic
24C32×Q16—41no—
25C3×D24—41no—
26C3×C3⋊C16—41no—
27#2185—31noSylow
28C22×C3×Q8—21no—
29Q8×A4—22no—
30Q8×A4—21no—
31C4⋊S4—21no—
32C2×C3×Q16—31no—
33C2×C3×Q16—31no—
34C2×C3×Q16—61no—
35C2×C3×D8—31no—
36C22×C3×C8C2×D311yescharacteristic
37C3×#121—61no—
38C8×A4—21no—
39C8×A4C22×C311yescharacteristic
40C3×SD32—62no—
41C3×SD32—61no—
42C3×SD32—61no—
43C2×C3×C16—31no—
44C2×C3×C16—31no—
45C3×#107—31no—
46C3×#102—61no—
47#828—41no—
48C2×C3×A4D811yescharacteristic
49C3×S4—81no—
50C32×Q8—81no—
51C3×D12—81no—
52C32×C8—41no—
53C22×Q16C3×D311yescharacteristic, complemented
54C2×SD32—31no—
55C2×SD32—31no—
56#466—31no—
57#358—31no—
58#358—31no—
59C22⋊C16—31no—
60C2×S4—41no—
61C2×C3×Q8—61no—
62C2×C3×Q8—61no—
63C2×C3×Q8—121no—
64C2×C3×D4—61no—
65C2×C3×D4—121no—
66C22×C3×C4—41no—
67C22×C3×C4#6711yescharacteristic
68C4×A4—21no—
69C4×A4—42no—
70C4×A4—41no—
71C4×A4C3×D411yescharacteristic
72C3×Q16—32no—
73C3×Q16—31no—
74C3×Q16—41no—
75C3×Q16—61no—
76C3×Q16—81no—
77C3×Q16S411yescharacteristic, complemented
78C3×D8—61no—
79C3×D8—61no—
80C2×C3×C8—31no—
81C2×C3×C8—31no—
82C3×C4⋊C4—61no—
83C3×C22⋊C4—121no—
84D24—41no—
85C3×C16—61no—
86C3×C16—61no—
87C3⋊C16—41no—
88C2×C3×D3—161no—
89C3×A4SD3211yescharacteristic, complemented
90C32×C4—41no—
91C32×C4—161no—
92C22×Q8—21no—
93C2×Q16—31no—
94C2×Q16—31no—
95C2×Q16—61no—
96C2×D8—31no—
97C22×C8C2×C3×D311yescharacteristic
98#121—61no—
99SD32—62no—
100SD32—61no—
101SD32—61no—
102C2×C16—31no—
103C2×C16—31no—
104#107—31no—
105#102—61no—
106C23×C3—121no—
107C23×C3#21311yescharacteristic
108C2×A4—21no—
109C2×A4C3×D811yescharacteristic
110S4—81no—
111C3×Q8—21no—
112C3×Q8—61no—
113C3×Q8—81no—
114C3×Q8—82no—
115C3×Q8—121no—
116C3×Q8—121no—
117C3×D4—121no—
118C3×D4—121no—
119C3×D4—241no—
120C3×D4—241no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—121no—
124C2×C3×C4—121no—
125C2×C3×C4—121no—
126D12—81no—
127C3×C8—31no—
128C3×C8—41no—
129C3×C8—81no—
130C3×C8C2×S411yescharacteristic
131C2×C32—41no—
132C3×D3—321no—
133C2×Q8—61no—
134C2×Q8—61no—
135C2×Q8—121no—
136C2×D4—61no—
137C2×D4—121no—
138C22×C4—41no—
139C22×C4C3×#6711yescharacteristic
140Q16—32no—
141Q16—31no—
142Q16—61no—
143Q16C3×S411yescharacteristic, complemented
144D8—61no—
145D8—61no—
146C2×C8—31no—
147C2×C8—31no—
148C4⋊C4—61no—
149C22⋊C4—121no—
150C16—61no—
151C16—61no—
152C22×C3—31no—
153C22×C3—31no—
154C22×C3—241no—
155C22×C3—241no—
156C22×C3—241no—
157C22×C3#82811yescharacteristic, complemented
158C2×D3—161no—
159A4—21no—
160A4C3×SD3211yescharacteristic, complemented
161C3×C4—31no—
162C3×C4—41no—
163C3×C4—41no—
164C3×C4—81no—
165C3×C4—121no—
166C3×C4—161no—
167C3×C4—162no—
168C3×C4—241no—
169C3×C4GL(2,ℤ/4)11yescharacteristic
170C32—41noSylow
171C23—121no—
172C23C3×#21311yescharacteristic
173Q8—21no—
174Q8—61no—
175Q8—121no—
176Q8—121no—
177D4—121no—
178D4—121no—
179D4—241no—
180D4—241no—
181C2×C4—31no—
182C2×C4—31no—
183C2×C4—121no—
184C2×C4—121no—
185C2×C4—121no—
186C8—31no—
187C8C2×C3×S411yescharacteristic
188C2×C3—31no—
189C2×C3—31no—
190C2×C3—41no—
191C2×C3—81no—
192C2×C3—481no—
193C2×C3#541511yescharacteristic
194D3—321no—
195C22—31no—
196C22—31no—
197C22—241no—
198C22—241no—
199C22—241no—
200C22C3×#82811yescharacteristic, complemented
201C4—31no—
202C4—41no—
203C4—121no—
204C4—241no—
205C4C3×GL(2,ℤ/4)11yescharacteristic
206C3—41no—
207C3—81no—
208C3#7313511yescharacteristic, direct product factor
209C2—31no—
210C2—31no—
211C2—481no—
212C2C3×#541511yescharacteristic
subgroupG/H
centerC2×C3#5415
commutator, cosocleC8×A4C22×C3
FrattiniC8C2×C3×S4
FittingC22×C3×Q16D3
socleC23×C3#213
prime radicalC3×#5402C2
hypercenterC3×Q16S4
hypocenterA4C3×SD32
LCSG ▷ C8×A4 ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

Complements

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

NH ≅ G/Ntype
1. C3×A4×Q16C2semidirect
3. C3×A4⋊C16C2semidirect
4. #73135C3direct (N × H)
10. C22×C3×Q16D3semidirect
12. A4×Q16C2×C3semidirect
17. A4⋊C16C2×C3semidirect
53. C22×Q16C3×D3semidirect
77. C3×Q16S4semidirect
89. C3×A4SD32semidirect
143. Q16C3×S4semidirect
157. C22×C3#828semidirect
160. A4C3×SD32semidirect
200. C22C3×#828semidirect
208. C3#73135direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×Q162
C3×#54022
C3×A4⋊C162
#731353
C3×#21853
C3×#8284