Finite Group Databasebeta

← #83174⋊C3 #11921295

Subgroups — #83174⋊C3 #11921295

Order 1152.

311 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 311 conjugacy classes of subgroups — too many to draw. Only its 43 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×#127⋊C3C211yesmaximal, characteristic
2C3⋊(#383⋊C3)C212yesmaximal, complemented
3#83174C311yesmaximal, characteristic, complemented
4#2380⋊C3—31nomaximal
5C2×Dic3×A4—41nomaximal
6C3×#127⋊C3C412yescomplemented
7C2×C3×C42⋊C3C2211yescharacteristic
8C2×C3×#127C2×C311yescharacteristic
9C2×#127⋊C3—21no—
10C2×#127⋊C3D311yescharacteristic
11#5220—31no—
12#5220—32no—
13#5220—31no—
14#4937C2×C312yescomplemented
15#383⋊C3—32no—
16C22×C3×A4—41no—
17Dic3×A4—42no—
18C3×C42⋊C3C2×C411yescharacteristic, complemented
19#2380—31noSylow
20C22×C3×D4—31no—
21C22×C3×D4—31no—
22C23×Dic3—31no—
23C23×Dic3A411yescharacteristic
24C2×C4×A4—121no—
25C3×#127—32no—
26C3×#127C3×C412yescomplemented
27C2×C3×C42C22×C311yescharacteristic
28C2×#217—31no—
29C2×#217—31no—
30C2×#217—32no—
31#127⋊C3—22no—
32#127⋊C3Dic312yescomplemented
33C2×C42⋊C3—21no—
34C2×C42⋊C3C2×D311yescharacteristic
35C3⋊#95—32no—
36C3⋊#95—32no—
37C2×C3×A4—42no—
38C2×C3×A4—41no—
39C2×C3×Dic3—161no—
40C2×#127C3×D311yescharacteristic
41#386—91no—
42#386—92no—
43#386—91no—
44#383—32no—
45C24×C3—31no—
46C24×C3C2×A411yescharacteristic
47C22×A4—41no—
48C22×A4—81no—
49C2×C3×D4—32no—
50C2×C3×D4—32no—
51C2×C3×D4—32no—
52C2×C3×D4—32no—
53C2×C3×D4—121no—
54C2×C3×D4—121no—
55C2×C3×D4—121no—
56C2×C3×D4—121no—
57C22×C3×C4—31no—
58C22×Dic3—32no—
59C22×Dic3—121no—
60C22×Dic3—122no—
61C22×Dic3—121no—
62C22×Dic3C2×A412yes—
63C4×A4—122no—
64C3×C42—31no—
65C3×C42C2×C3×C411yescharacteristic, complemented
66#217—122no—
67#217—121no—
68#217—121no—
69C42⋊C3—21no—
70C42⋊C3C2×Dic311yescharacteristic, complemented
71C22×C32—161no—
72C3×A4—41no—
73C3×Dic3—162no—
74C22×D4—31no—
75C22×D4—31no—
76C23×C4—31no—
77C23×C4—91no—
78#127—32no—
79#127C3×Dic312yescomplemented
80C2×C22⋊C4—92no—
81C2×C22⋊C4—91no—
82C2×C22⋊C4—91no—
83C2×C42C2×C3×D311yescharacteristic
84#95—92no—
85#95—92no—
86C23×C3—32no—
87C23×C3—61no—
88C23×C3—61no—
89C23×C3—61no—
90C23×C3—62no—
91C23×C3—62no—
92C23×C3—61no—
93C23×C3C4×A412yes—
94C23×C3C22×A411yescharacteristic
95C2×A4—41no—
96C2×A4—42no—
97C2×A4—81no—
98C2×A4—82no—
99C3×D4—122no—
100C3×D4—122no—
101C3×D4—122no—
102C3×D4—122no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4—481no—
108C2×Dic3—41no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113C2×Dic3—121no—
114C2×Dic3—124no—
115C2×C32—162no—
116C2×C32—161no—
117C24—31no—
118C24D3×A411yescharacteristic
119C2×D4—32no—
120C2×D4—32no—
121C2×D4—32no—
122C2×D4—32no—
123C2×D4—121no—
124C2×D4—121no—
125C2×D4—121no—
126C2×D4—121no—
127C22×C4—31no—
128C22×C4—32no—
129C22×C4—92no—
130C22×C4—361no—
131C22×C4—362no—
132C22×C4—361no—
133C22⋊C4—362no—
134C22⋊C4—361no—
135C22⋊C4—361no—
136C42—31no—
137C42C2×C3×Dic311yescharacteristic, complemented
138C22×C3—31no—
139C22×C3—31no—
140C22×C3—41no—
141C22×C3—62no—
142C22×C3—62no—
143C22×C3—64no—
144C22×C3—121no—
145C22×C3—121no—
146C22×C3—122no—
147C22×C3—121no—
148C22×C3—161no—
149C22×C3—321no—
150C22×C3C2×C4×A411yescharacteristic
151A4—41no—
152A4—81no—
153C3×C4—61no—
154C3×C4—61no—
155C3×C4—482no—
156Dic3—42no—
157Dic3—122no—
158C32—161noSylow
159C23—32no—
160C23—61no—
161C23—61no—
162C23—61no—
163C23—62no—
164C23—62no—
165C23—61no—
166C23Dic3×A412yes—
167C23C2×D3×A411yescharacteristic
168D4—122no—
169D4—122no—
170D4—122no—
171D4—122no—
172C2×C4—31no—
173C2×C4—31no—
174C2×C4—61no—
175C2×C4—61no—
176C2×C4—121no—
177C2×C4—182no—
178C2×C4—182no—
179C2×C4—182no—
180C2×C4—182no—
181C2×C4—361no—
182C2×C4—364no—
183C2×C3—31no—
184C2×C3—31no—
185C2×C3—42no—
186C2×C3—122no—
187C2×C3—162no—
188C2×C3—161no—
189C2×C3—322no—
190C2×C3—321no—
191C2×C3#560⋊C311yescharacteristic
192C22—31no—
193C22—31no—
194C22—41no—
195C22—62no—
196C22—62no—
197C22—64no—
198C22—121no—
199C22—121no—
200C22—122no—
201C22—121no—
202C22C2×Dic3×A411yescharacteristic
203C4—61no—
204C4—61no—
205C4—122no—
206C4—362no—
207C3—161no—
208C3—321no—
209C3#2380⋊C311yescharacteristic, complemented
210C2—31no—
211C2—31no—
212C2—42no—
213C2—122no—
214C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC2×C3×#127C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×#127⋊C3C2
cosocleC2×C3×C42C22×C3
LCSG ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(#383⋊C3)C2semidirect
3. #83174C3semidirect
6. C3×#127⋊C3C4semidirect
14. #4937C2×C3semidirect
18. C3×C42⋊C3C2×C4semidirect
26. C3×#127C3×C4semidirect
32. #127⋊C3Dic3semidirect
65. C3×C42C2×C3×C4semidirect
70. C42⋊C3C2×Dic3semidirect
79. #127C3×Dic3semidirect
137. C42C2×C3×Dic3semidirect
209. C3#2380⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
C3⋊(#383⋊C3)2
#831743
#2380⋊C33
C2×Dic3×A44