Finite Group Databasebeta

← C3×#73105 #11920883

Subgroups — C3×#73105 #11920883

Order 1152.

276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 60 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×C3×C8×A4C211yesmaximal, characteristic
2C3×#5409C212yesmaximal
3#73105C311yesmaximal, characteristic, direct product factor
4C3×#1810—31nomaximal
5C2×C3×C4×A4C2211yescharacteristic
6C3×C8×A4C412yes—
7C3×A4⋊C8—22no—
8C3×#819—41nomaximal
9C23×C3×C8D311yescharacteristic
10C2×C8×A4—21no—
11C2×C8×A4C2×C311yescharacteristic
12#5409C2×C312yes—
13C2×C3×#108—31no—
14C2×C3×#108—31no—
15C3×#407—32no—
16C3×#341—32no—
17C22×C3×A4Q811yescharacteristic
18C3×C4×A4C2×C411yescharacteristic
19C3×C4×A4D411yescharacteristic
20C2×C32×C8—41no—
21C3×#208—42no—
22#1810—31noSylow
23C23×C3×C4C2×D311yescharacteristic
24C2×C4×A4—21no—
25C2×C4×A4C22×C311yescharacteristic
26C2×C3×M16—32no—
27C2×C3×M16—32no—
28C22×C3×C8—31no—
29C22×C3×C8—32no—
30C22×C3×C8—31no—
31C22×C3×C8Dic312yes—
32C8×A4—22no—
33C8×A4C3×C412yes—
34A4⋊C8—22no—
35C3×#108—61no—
36C3×#108—62no—
37C3×#108—61no—
38C3×C22⋊C8—62no—
39C3×C22⋊C8—62no—
40#819—41no—
41C2×C3×A4—21no—
42C2×C3×A4C4⋊C411yescharacteristic
43C2×C32×C4—41no—
44C32×C8—42no—
45C3×C3⋊C8—82no—
46C23×C8C3×D311yescharacteristic
47C2×#108—31no—
48C2×#108—31no—
49#407—32no—
50#341—32no—
51C24×C3Dic611yescharacteristic
52C22×A4—21no—
53C22×A4C3×Q811yescharacteristic
54C22×C3×C4—31no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×C3×C4D1211yescharacteristic
59C22×C3×C4C2×Dic311yescharacteristic
60C4×A4—21no—
61C4×A4—21no—
62C4×A4C2×C3×C411yescharacteristic
63C4×A4C3×D411yescharacteristic
64C3×M16—62no—
65C3×M16—62no—
66C3×M16—62no—
67C3×M16—62no—
68C2×C3×C8—31no—
69C2×C3×C8—32no—
70C2×C3×C8—32no—
71C2×C3×C8—32no—
72C2×C3×C8—41no—
73C2×C3×C8—61no—
74C2×C3×C8—62no—
75C2×C3×C8—62no—
76C2×C3×C8—81no—
77C2×C3×C8S411yescharacteristic
78#208—42no—
79C22×C32—41no—
80C3×A4#10811yescharacteristic, complemented
81C32×C4—41no—
82C32×C4—41no—
83C23×C4C2×C3×D311yescharacteristic
84C2×M16—32no—
85C2×M16—32no—
86C22×C8—31no—
87C22×C8—31no—
88C22×C8—32no—
89C22×C8C3×Dic312yes—
90#108—61no—
91#108—62no—
92#108—61no—
93C22⋊C8—62no—
94C22⋊C8—62no—
95C23×C3—21no—
96C23×C3—31no—
97C23×C3—31no—
98C23×C3—61no—
99C23×C3C4⋊Dic311yescharacteristic
100C2×A4—22no—
101C2×A4—21no—
102C2×A4—21no—
103C2×A4C3×C4⋊C411yescharacteristic
104C2×C3×C4—31no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—41no—
112C2×C3×C4—61no—
113C2×C3×C4—81no—
114C2×C3×C4C2×S411yescharacteristic
115C3×C8—32no—
116C3×C8—42no—
117C3×C8—82no—
118C3×C8—122no—
119C3×C8—122no—
120C3×C8SL(2,ℤ/4)12yes—
121C3⋊C8—82no—
122C2×C32—41no—
123C2×C32—81no—
124C24C3×Dic611yescharacteristic
125C22×C4—31no—
126C22×C4—31no—
127C22×C4—31no—
128C22×C4—31no—
129C22×C4C3×D1211yescharacteristic
130C22×C4C2×C3×Dic311yescharacteristic
131M16—62no—
132M16—62no—
133M16—62no—
134M16—62no—
135C2×C8—31no—
136C2×C8—32no—
137C2×C8—32no—
138C2×C8—32no—
139C2×C8—61no—
140C2×C8—62no—
141C2×C8—62no—
142C2×C8C3×S411yescharacteristic
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—32no—
146C22×C3—31no—
147C22×C3—41no—
148C22×C3—61no—
149C22×C3—61no—
150C22×C3—61no—
151C22×C3—81no—
152C22×C3#81911yescharacteristic, complemented
153C22×C3A4⋊Q811yescharacteristic
154A4—21no—
155A4C3×#10811yescharacteristic, complemented
156C3×C4—31no—
157C3×C4—31no—
158C3×C4—41no—
159C3×C4—41no—
160C3×C4—81no—
161C3×C4—81no—
162C3×C4C4⋊S411yescharacteristic
163C3×C4C2×SL(2,ℤ/4)11yescharacteristic
164C32—41noSylow
165C23—21no—
166C23—31no—
167C23—31no—
168C23—61no—
169C23C3×C4⋊Dic311yescharacteristic
170C2×C4—31no—
171C2×C4—31no—
172C2×C4—31no—
173C2×C4—31no—
174C2×C4—31no—
175C2×C4—31no—
176C2×C4—31no—
177C2×C4—61no—
178C2×C4C2×C3×S411yescharacteristic
179C8—32no—
180C8—122no—
181C8—122no—
182C8C3×SL(2,ℤ/4)12yes—
183C2×C3—21no—
184C2×C3—31no—
185C2×C3—31no—
186C2×C3—41no—
187C2×C3—61no—
188C2×C3—81no—
189C2×C3—82no—
190C2×C3—81no—
191C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
192C22—31no—
193C22—31no—
194C22—32no—
195C22—31no—
196C22—61no—
197C22—61no—
198C22—61no—
199C22C3×#81911yescharacteristic, complemented
200C22C3×A4⋊Q811yescharacteristic
201C4—31no—
202C4—31no—
203C4C3×C4⋊S411yescharacteristic
204C4C2×C3×SL(2,ℤ/4)11yescharacteristic
205C3—41no—
206C3—81no—
207C3#7310511yescharacteristic, direct product factor
208C2—21no—
209C2—31no—
210C2—31no—
211C2—61no—
212C2C3×C4⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC3×C4C4⋊S4
commutatorC4×A4C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC23×C3×C8D3
socleC23×C3C4⋊Dic3
prime radicalC22×C3×A4Q8
cosocleC2×C4×A4C22×C3
hypercenterC2×C3×C8S4
hypocenterA4C3×#108
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
3. #73105C3direct (N × H)
80. C3×A4#108semidirect
152. C22×C3#819semidirect
155. A4C3×#108semidirect
199. C22C3×#819semidirect
207. C3#73105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C3×#54092
#731053
C3×#18103
C3×#8194