Finite Group Databasebeta

← C3×#10590185 #13157110

Subgroups — C3×#10590185 #13157110

Order 1728.

376 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 76 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×#3788C212yesmaximal
2C2×C3×C8×C3⋊D3C211yesmaximal, characteristic
3#10590185C311yesmaximal, characteristic, direct product factor
4C2×C3×C4×C3⋊D3C2211yescharacteristic
5C2×C3×#622—22no—
6C3×#3788—22no—
7C3×#3788C414yes—
8C2×C33×C8C411yescharacteristic
9C2×C3×C3⋊(C3⋊C8)C411yescharacteristic
10C3×C8×C3⋊D3—22no—
11C2×#3788C2×C312yes—
12C2×C8×C3⋊D3C2×C311yescharacteristic
13C2×C3×D3×C8—62no—
14C22×C3×C3⋊D3Q811yescharacteristic
15C2×C33×C4C2×C411yescharacteristic
16C2×C3×C3⋊Dic3D411yescharacteristic
17C3×C4×C3⋊D3C2×C412yes—
18C3×C4×C3⋊D3D412yes—
19C3×#622—24no—
20C33×C8—21no—
21C3×C3⋊(C3⋊C8)—21no—
22C3×#341—91nomaximal
23C2×C4×C3⋊D3C22×C311yescharacteristic
24C2×C3×C4×D3—62no—
25C2×#622—22no—
26#3788—22no—
27#3788C3×C414yes—
28C2×C32×C8—22no—
29C2×C32×C8—42no—
30C2×C32×C8C3×C411yescharacteristic
31C2×C3⋊(C3⋊C8)C3×C411yescharacteristic
32C8×C3⋊D3—22no—
33C2×C3×C3⋊C8—62no—
34C3×D3×C8—68no—
35C22×C33C4⋊C411yescharacteristic
36C2×C3×C3⋊D3—21no—
37C2×C3×C3⋊D3—21no—
38C2×C3×C3⋊D3C4⋊C412yes—
39C33×C4C4211yescharacteristic
40C33×C4C22⋊C411yescharacteristic
41C3×C3⋊Dic3C22⋊C412yes—
42C2×C3×M16—92no—
43C22×C3×C8—91no—
44C2×D3×C8—62no—
45C22×C3⋊D3C3×Q811yescharacteristic
46C22×C3×D3—62no—
47C2×C32×C4—22no—
48C2×C32×C4—42no—
49C2×C32×C4C2×C3×C411yescharacteristic
50C2×C3⋊Dic3C3×D411yescharacteristic
51C4×C3⋊D3C2×C3×C412yes—
52C4×C3⋊D3C3×D412yes—
53C2×C3×Dic3—62no—
54C3×C4×D3—64no—
55C3×C4×D3—64no—
56#622—24no—
57C32×C8—21no—
58C32×C8—24no—
59C32×C8—44no—
60C3⋊(C3⋊C8)—21no—
61C3×C3⋊C8—64no—
62#341—91noSylow
63C2×C33#9511yescharacteristic
64C2×C33#10811yescharacteristic
65C2×C33#10811yescharacteristic
66C3×C3⋊D3—22no—
67C22×C3×C4—91no—
68C2×C4×D3—62no—
69C3×M16—94no—
70C3×M16—182no—
71C2×C3×C8—22no—
72C2×C3×C8—42no—
73C2×C3×C8—91no—
74C2×C3×C8—182no—
75C2×C3×C8—182no—
76C2×C3×C8#15711yescharacteristic
77C2×C3⋊C8—62no—
78D3×C8—68no—
79C22×C32—22no—
80C22×C32—42no—
81C22×C32C3×C4⋊C411yescharacteristic
82C2×C3⋊D3—21no—
83C2×C3⋊D3—21no—
84C2×C3⋊D3C3×C4⋊C412yes—
85C2×C3×D3—64no—
86C2×C3×D3—64no—
87C2×C3×D3—64no—
88C32×C4—22no—
89C32×C4—22no—
90C32×C4—42no—
91C32×C4—42no—
92C32×C4C3×C4211yescharacteristic
93C32×C4C3×C22⋊C411yescharacteristic
94C3⋊Dic3C3×C22⋊C412yes—
95C3×Dic3—64no—
96C2×M16—92no—
97C22×C8—91no—
98C33#34111yescharacteristic, complemented, Sylow
99C23×C3—91no—
100C22×D3—62no—
101C2×C3×C4—22no—
102C2×C3×C4—42no—
103C2×C3×C4—91no—
104C2×C3×C4—92no—
105C2×C3×C4—92no—
106C2×C3×C4C2×#15711yescharacteristic
107C2×Dic3—62no—
108C4×D3—64no—
109C4×D3—64no—
110C3×C8—24no—
111C3×C8—21no—
112C3×C8—44no—
113C3×C8—184no—
114C3×C8—181no—
115C3⋊C8—64no—
116C2×C32—22no—
117C2×C32—22no—
118C2×C32—22no—
119C2×C32—42no—
120C2×C32—42no—
121C2×C32—42no—
122C2×C32C3×#9511yescharacteristic
123C2×C32C3×#10811yescharacteristic
124C2×C32C3×#10811yescharacteristic
125C3⋊D3—22no—
126C3×D3—68no—
127C22×C4—91no—
128M16—94no—
129M16—182no—
130C2×C8—91no—
131C2×C8—182no—
132C2×C8—182no—
133C2×C8C3×#15711yescharacteristic
134C22×C3—22no—
135C22×C3—42no—
136C22×C3—92no—
137C22×C3—181no—
138C22×C3—181no—
139C22×C3C4⋊#15711yescharacteristic
140C2×D3—64no—
141C2×D3—64no—
142C2×D3—64no—
143C3×C4—22no—
144C3×C4—22no—
145C3×C4—42no—
146C3×C4—42no—
147C3×C4—92no—
148C3×C4C4×#15711yescharacteristic
149C3×C4C22⋊#15711yescharacteristic
150Dic3—64no—
151C32—22no—
152C32—42no—
153C32C3×#34111yescharacteristic, complemented
154C23—91no—
155C2×C4—91no—
156C2×C4—92no—
157C2×C4—92no—
158C2×C4C2×C3×#15711yescharacteristic
159C8—21no—
160C8—184no—
161C8—181no—
162C2×C3—22no—
163C2×C3—22no—
164C2×C3—22no—
165C2×C3—42no—
166C2×C3—42no—
167C2×C3—42no—
168C2×C3—182no—
169C2×C3#6377011yescharacteristic
170C2×C3#6377111yescharacteristic
171C2×C3#6378111yescharacteristic
172D3—68no—
173C22—92no—
174C22—181no—
175C22—181no—
176C22C3×C4⋊#15711yescharacteristic
177C4—92no—
178C4C3×C4×#15711yescharacteristic
179C4C3×C22⋊#15711yescharacteristic
180C3—22no—
181C3—42no—
182C3#1059018511yescharacteristic, direct product factor
183C2—182no—
184C2C3×#6377011yescharacteristic
185C2C3×#6377111yescharacteristic
186C2C3×#6378111yescharacteristic
subgroupG/H
centerC22×C3C4⋊#157
commutatorC32×C4C3×C42
FrattiniC2×C4C2×C3×#157
FittingC2×C33×C8C4
socleC22×C33C4⋊C4
prime radicalC22×C3×C3⋊D3Q8
cosocleC2×C4×C3⋊D3C22×C3
hypercenterC2×C3×C8#157
hypocenterC32C3×#341
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
3. #10590185C3direct (N × H)
98. C33#341semidirect
153. C32C3×#341semidirect
182. C3#10590185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#37882
C2×C3×C8×C3⋊D32
#105901853
C3×#3419