Finite Group Databasebeta

← C3×#10590159 #13157084

Subgroups — C3×#10590159 #13157084

Order 1728.

284 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 44 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×#64099C211yesmaximal, characteristic
2C3×#63777C211yesmaximal, characteristic
3C3×#63777C211yesmaximal, characteristic
4#10590159C311yesmaximal, characteristic, direct product factor
5C2×C3×#622—21no—
6C2×C3×#622—21no—
7C33×C4⋊C4C411yescharacteristic
8C3×C4⋊(C3⋊Dic3)—21no—
9C3×C4⋊(C3⋊Dic3)C411yescharacteristic
10C3×#3750—21no—
11C3×C4×C3⋊Dic3C2211yescharacteristic
12#64099C2×C311yescharacteristic
13C3×#890—62no—
14#63777C2×C311yescharacteristic
15#63777C2×C311yescharacteristic
16C2×C33×C4—21no—
17C2×C33×C4C2×C411yescharacteristic
18C2×C3×C3⋊Dic3—21no—
19C2×C3×C3⋊Dic3D411yescharacteristic
20C2×C3×C3⋊Dic3D411yescharacteristic
21C3×#622—22no—
22C3×#622—22no—
23C3×#330—91nomaximal
24C2×#622—21no—
25C2×#622—21no—
26C32×C4⋊C4—22no—
27C32×C4⋊C4—42no—
28C32×C4⋊C4C3×C411yescharacteristic
29C4⋊(C3⋊Dic3)—21no—
30C4⋊(C3⋊Dic3)C3×C411yescharacteristic
31#3750—21no—
32C4×C3⋊Dic3C22×C311yescharacteristic
33C3×C4⋊Dic3—62no—
34C3×C4⋊Dic3—64no—
35C3×Dic3⋊C4—64no—
36C3×C4×Dic3—62no—
37C22×C33C22⋊C411yescharacteristic
38C33×C4—21no—
39C33×C4—41no—
40C3×C3⋊Dic3—21no—
41C3×C3⋊Dic3—21no—
42C3×C3⋊Dic3—41no—
43C3×#125—91no—
44#890—62no—
45C3×#97—91no—
46C3×#97—91no—
47C2×C32×C4—21no—
48C2×C32×C4—24no—
49C2×C32×C4—22no—
50C2×C32×C4—44no—
51C2×C32×C4—42no—
52C2×C32×C4C2×C3×C411yescharacteristic
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3C3×D411yescharacteristic
55C2×C3⋊Dic3C3×D411yescharacteristic
56C2×C3×Dic3—62no—
57C2×C3×Dic3—62no—
58C2×C3×Dic3—64no—
59#622—22no—
60#622—22no—
61#330—91noSylow
62C2×C33#10111yescharacteristic
63C2×C33#10411yescharacteristic
64C2×C33#10411yescharacteristic
65C2×C3×C8—181no—
66C2×C3×C8—181no—
67C3×C4⋊C4—22no—
68C3×C4⋊C4—42no—
69C3×C4⋊C4—91no—
70C3×C4⋊C4—181no—
71C3×C4⋊C4—181no—
72C3×C4⋊C4#15711yescharacteristic
73C3×C42—91no—
74C4⋊Dic3—62no—
75C4⋊Dic3—64no—
76Dic3⋊C4—64no—
77C4×Dic3—62no—
78C22×C32—22no—
79C22×C32—42no—
80C22×C32C3×C22⋊C411yescharacteristic
81C32×C4—21no—
82C32×C4—24no—
83C32×C4—44no—
84C32×C4—41no—
85C32×C4—44no—
86C32×C4—84no—
87C3⋊Dic3—21no—
88C3⋊Dic3—21no—
89C3⋊Dic3—41no—
90C3×Dic3—122no—
91C3×Dic3—122no—
92C3×Dic3—124no—
93#125—91no—
94#97—91no—
95#97—91no—
96C33#33011yescharacteristic, complemented, Sylow
97C2×C3×C4—24no—
98C2×C3×C4—21no—
99C2×C3×C4—22no—
100C2×C3×C4—44no—
101C2×C3×C4—42no—
102C2×C3×C4—91no—
103C2×C3×C4—91no—
104C2×C3×C4—181no—
105C2×C3×C4C2×#15711yescharacteristic
106C2×Dic3—62no—
107C2×Dic3—62no—
108C2×Dic3—64no—
109C3×C8—182no—
110C3×C8—182no—
111C2×C32—22no—
112C2×C32—22no—
113C2×C32—22no—
114C2×C32—42no—
115C2×C32—42no—
116C2×C32—42no—
117C2×C32C3×#10111yescharacteristic
118C2×C32C3×#10411yescharacteristic
119C2×C32C3×#10411yescharacteristic
120C2×C8—181no—
121C2×C8—181no—
122C4⋊C4—91no—
123C4⋊C4—181no—
124C4⋊C4—181no—
125C4⋊C4C3×#15711yescharacteristic
126C42—91no—
127C22×C3—22no—
128C22×C3—42no—
129C22×C3C22⋊#15711yescharacteristic
130C3×C4—24no—
131C3×C4—21no—
132C3×C4—44no—
133C3×C4—44no—
134C3×C4—41no—
135C3×C4—84no—
136C3×C4—181no—
137C3×C4—181no—
138C3×C4—361no—
139Dic3—122no—
140Dic3—122no—
141Dic3—124no—
142C32—22no—
143C32—42no—
144C32C3×#33011yescharacteristic, complemented
145C2×C4—21no—
146C2×C4—91no—
147C2×C4—91no—
148C2×C4—181no—
149C2×C4C2×C3×#15711yescharacteristic
150C8—182no—
151C8—182no—
152C2×C3—22no—
153C2×C3—22no—
154C2×C3—22no—
155C2×C3—42no—
156C2×C3—42no—
157C2×C3—42no—
158C2×C3#6378011yescharacteristic
159C2×C3#6378311yescharacteristic
160C2×C3#6378511yescharacteristic
161C22C3×C22⋊#15711yescharacteristic
162C4—21no—
163C4—41no—
164C4—181no—
165C4—181no—
166C4—361no—
167C3—22no—
168C3—42no—
169C3#1059015911yescharacteristic, direct product factor
170C2C3×#6378011yescharacteristic
171C2C3×#6378311yescharacteristic
172C2C3×#6378511yescharacteristic
subgroupG/H
centerC22×C3C22⋊#157
commutatorC2×C32×C4C2×C3×C4
FrattiniC2×C4C2×C3×#157
FittingC33×C4⋊C4C4
socle, prime radicalC22×C33C22⋊C4
cosocleC4×C3⋊Dic3C22×C3
hypercenterC3×C4⋊C4#157
hypocenterC32C3×#330
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590159C3direct (N × H)
96. C33#330semidirect
144. C32C3×#330semidirect
169. C3#10590159direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#640992
C3×#637772
#105901593
C3×#3309