Finite Group Databasebeta

← C3×#72987 #11920765

Subgroups — C3×#72987 #11920765

Order 1152.

234 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 26 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×#376⋊C3C211yesmaximal, characteristic, complemented
2C3×#4622C211yesmaximal, characteristic
3C3×#4621C211yesmaximal, characteristic, complemented
4#72987C311yesmaximal, characteristic, direct product factor
5C3×#1500—31nomaximal
6C3×C4×S4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#529—31no—
9C3×#431—31no—
10C3×#376D311yescharacteristic, complemented
11#376⋊C3—21no—
12#376⋊C3C2×C311yescharacteristic, complemented
13#4622C2×C311yescharacteristic
14#4621C2×C311yescharacteristic, complemented
15C3×#328—31no—
16C3×#328—31no—
17C3×#327—31no—
18C3×#327—31no—
19C2×C3×S4—41no—
20C3×C4×A4—41no—
21C3×SL(2,ℤ/4)—41no—
22#1500—31noSylow
23C4×S4—41no—
24C3×#126—61no—
25C3×#125—31no—
26C3×#124—31no—
27C3×#123—61no—
28C3×C22⋊Q8—31no—
29C3×#121—31no—
30C3×C4×Q8—31no—
31C3×C4×D4—31no—
32C3×C4×D4—61no—
33C3×#117—61no—
34C2×C3×C42—31no—
35C3×C4⋊C8—61no—
36C3×C22⋊C8—31no—
37C3×C22⋊C8—31no—
38C3×C4×C8—61no—
39C3×#95—31no—
40C3×#95C2×D311yescharacteristic
41#95⋊C3—21no—
42#95⋊C3C22×C311yescharacteristic
43C2×C3×A4—41no—
44C3×S4—42no—
45C3×C4×D3—161no—
46#529—31no—
47#431—31no—
48#376C3×D311yescharacteristic, complemented
49#328—31no—
50#328—31no—
51#327—31no—
52#327—31no—
53C2×S4—41no—
54C2×C3×Q8—31no—
55C2×C3×D4—31no—
56C2×C3×D4—61no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—61no—
60C22×C3×C4S411yescharacteristic
61C4×A4—41no—
62C4×A4—81no—
63SL(2,ℤ/4)—41no—
64C2×C3×C8—61no—
65C2×C3×C8—61no—
66C3×C4⋊C4—31no—
67C3×C4⋊C4—31no—
68C3×C4⋊C4—61no—
69C3×C4⋊C4—61no—
70C3×C4⋊C4—61no—
71C3×C4⋊C4—61no—
72C3×C22⋊C4—61no—
73C3×C22⋊C4—61no—
74C3×C22⋊C4—61no—
75C3×C22⋊C4—61no—
76C3×C22⋊C4—61no—
77C3×C42—31no—
78C3×C42—31no—
79C3×C42—31no—
80C3×C42—31no—
81C3×C42—61no—
82C2×C3×D3—161no—
83C3×A4—41no—
84C32×C4—161no—
85C3×Dic3—161no—
86#126—61no—
87#125—31no—
88#124—31no—
89#123—61no—
90C22⋊Q8—31no—
91#121—31no—
92C4×Q8—31no—
93C4×D4—31no—
94C4×D4—61no—
95#117—61no—
96C2×C42—31no—
97C4⋊C8—61no—
98C22⋊C8—31no—
99C22⋊C8—31no—
100C4×C8—61no—
101#95—31no—
102#95C2×C3×D311yescharacteristic
103C23×C3—61no—
104C23×C3C2×S411yescharacteristic
105C2×A4—41no—
106C2×A4—81no—
107S4—42no—
108C3×Q8—121no—
109C3×D4—121no—
110C3×D4—121no—
111C3×D4—121no—
112C2×C3×C4—31no—
113C2×C3×C4—31no—
114C2×C3×C4—31no—
115C2×C3×C4—31no—
116C2×C3×C4—31no—
117C2×C3×C4—31no—
118C2×C3×C4—61no—
119C2×C3×C4—61no—
120C2×C3×C4—61no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×C3×C4—121no—
124C2×C3×C4—121no—
125C2×C3×C4—121no—
126C4×D3—161no—
127C3×C8—121no—
128C3×C8—121no—
129C2×C32—161no—
130C3×D3—162no—
131C2×Q8—31no—
132C2×D4—31no—
133C2×D4—61no—
134C22×C4—31no—
135C22×C4—31no—
136C22×C4—61no—
137C22×C4C3×S411yescharacteristic
138C2×C8—61no—
139C2×C8—61no—
140C4⋊C4—31no—
141C4⋊C4—31no—
142C4⋊C4—61no—
143C4⋊C4—61no—
144C4⋊C4—61no—
145C4⋊C4—61no—
146C22⋊C4—61no—
147C22⋊C4—61no—
148C22⋊C4—61no—
149C22⋊C4—61no—
150C22⋊C4—61no—
151C42—31no—
152C42—31no—
153C42—31no—
154C42—31no—
155C42—61no—
156C22×C3—31no—
157C22×C3—31no—
158C22×C3—121no—
159C22×C3—121no—
160C22×C3—121no—
161C22×C3#98511yescharacteristic
162C2×D3—161no—
163A4—41no—
164A4—81no—
165C3×C4—31no—
166C3×C4—61no—
167C3×C4—61no—
168C3×C4—61no—
169C3×C4—61no—
170C3×C4—121no—
171C3×C4—121no—
172C3×C4—121no—
173C3×C4—161no—
174C3×C4—321no—
175C3×C4#85711yescharacteristic
176Dic3—161no—
177C32—161noSylow
178C23—61no—
179C23C2×C3×S411yescharacteristic
180Q8—121no—
181D4—121no—
182D4—121no—
183D4—121no—
184C2×C4—31no—
185C2×C4—31no—
186C2×C4—31no—
187C2×C4—31no—
188C2×C4—31no—
189C2×C4—31no—
190C2×C4—61no—
191C2×C4—61no—
192C2×C4—61no—
193C2×C4—61no—
194C2×C4—61no—
195C2×C4—121no—
196C2×C4—121no—
197C2×C4—121no—
198C8—121no—
199C8—121no—
200C2×C3—31no—
201C2×C3—31no—
202C2×C3—161no—
203C2×C3—241no—
204C2×C3—321no—
205C2×C3C2×#85711yescharacteristic
206D3—162no—
207C22—31no—
208C22—31no—
209C22—121no—
210C22—121no—
211C22—121no—
212C22C3×#98511yescharacteristic
213C4—31no—
214C4—61no—
215C4—61no—
216C4—61no—
217C4—61no—
218C4—121no—
219C4—121no—
220C4—121no—
221C4C3×#85711yescharacteristic
222C3—161no—
223C3—321no—
224C3#7298711yescharacteristic, direct product factor
225C2—31no—
226C2—31no—
227C2—241no—
228C2C2×C3×#85711yescharacteristic
subgroupG/H
center, hypercenterC3×C4#857
commutator, cosocle, hypocenter#95⋊C3C22×C3
FrattiniC23C2×C3×S4
FittingC3×#376D3
socleC23×C3C2×S4
prime radicalC3×#4622C2
LCSG ▷ #95⋊C3
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#376⋊C3C2semidirect
3. C3×#4621C2semidirect
4. #72987C3direct (N × H)
10. C3×#376D3semidirect
12. #376⋊C3C2×C3semidirect
14. #4621C2×C3semidirect
48. #376C3×D3semidirect
224. C3#72987direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#376⋊C32
C3×#46222
C3×#46212
#729873
C3×#15003
C3×C4×S44