Finite Group Databasebeta

← C3×#10590040 #13154890

Subgroups — C3×#10590040 #13154890

Order 1728.

282 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 54 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×#63919C211yesmaximal, characteristic
2C3×C4⋊#622C211yesmaximal, characteristic
3C3×#63572C211yesmaximal, characteristic
4#10590040C311yesmaximal, characteristic, direct product factor
5C2×C3×#627C412yes—
6C2×C3×#622—21no—
7C3×C4×C3⋊Dic3C2211yescharacteristic
8C32×C4⋊Dic3—21no—
9C2×C32×C3⋊C8—21no—
10C3×#3724—21no—
11C3×#888—61no—
12#63919C2×C311yescharacteristic
13C4⋊#622C2×C311yescharacteristic
14C3×Dic3⋊C8—61no—
15#63572C2×C311yescharacteristic
16C2×C33×C4D411yescharacteristic
17C2×C3×C3⋊Dic3C2×C411yescharacteristic
18C2×C3×C3⋊Dic3D411yescharacteristic
19C2×C32×Dic3—22no—
20C3×#627—42no—
21C3×#622—41no—
22C32×C3⋊C8—41no—
23C3×#333—91nomaximal
24C2×C3×Dic6—62no—
25C2×#627C3×C412yes—
26C2×#622—21no—
27C2×C32×C8—61no—
28C32×C4⋊C4—61no—
29C4×C3⋊Dic3C22×C311yescharacteristic
30C3×C4⋊Dic3—21no—
31C3×C4⋊Dic3—21no—
32C3×C4⋊Dic3—41no—
33C3×Dic3⋊C4—62no—
34C3×C4×Dic3—61no—
35C3×C4×Dic3—61no—
36C2×C3×C3⋊C8—21no—
37C2×C3×C3⋊C8—21no—
38C2×C3×C3⋊C8—41no—
39#3724—21no—
40C22×C33C22⋊C411yescharacteristic
41C33×C4SD1611yescharacteristic
42C33×C4Q1611yescharacteristic
43C3×C3⋊Dic3—21no—
44C3×C3⋊Dic3SD1611yescharacteristic
45C3×C3⋊Dic3Q1611yescharacteristic
46C32×Dic3—42no—
47C3×C4⋊Q8—91no—
48#888—61no—
49C3×C4⋊C8—91no—
50C3×C4⋊C8—91no—
51Dic3⋊C8—61no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—41no—
55C2×C32×C4—41no—
56C2×C32×C4—62no—
57C2×C32×C4C3×D411yescharacteristic
58C2×C3⋊Dic3C2×C3×C411yescharacteristic
59C2×C3⋊Dic3C3×D411yescharacteristic
60C2×C3×Dic3—22no—
61C2×C3×Dic3—22no—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—61no—
64C2×C3×Dic3—61no—
65C2×C3×Dic3—61no—
66C2×C3×Dic3—61no—
67C3×Dic6—124no—
68#627—42no—
69#622—41no—
70C32×C8—121no—
71C3×C3⋊C8—41no—
72C3×C3⋊C8—42no—
73C3×C3⋊C8—41no—
74#333—91noSylow
75C2×C33#10011yescharacteristic
76C2×C33#10311yescharacteristic
77C2×C33#10311yescharacteristic
78C2×C3×Q8—92no—
79C2×Dic6—62no—
80C2×C3×C8—61no—
81C2×C3×C8—61no—
82C2×C3×C8—121no—
83C2×C3×C8—181no—
84C3×C4⋊C4—61no—
85C3×C4⋊C4—61no—
86C3×C4⋊C4—121no—
87C3×C4⋊C4—181no—
88C3×C42—91no—
89C4⋊Dic3—21no—
90Dic3⋊C4—62no—
91C4×Dic3—61no—
92C4×Dic3—61no—
93C2×C3⋊C8—21no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—41no—
97C22×C32—41no—
98C22×C32C3×C22⋊C411yescharacteristic
99C32×C4—21no—
100C32×C4—21no—
101C32×C4—21no—
102C32×C4—21no—
103C32×C4—41no—
104C32×C4—41no—
105C32×C4—41no—
106C32×C4—41no—
107C32×C4—122no—
108C32×C4C3×SD1611yescharacteristic
109C32×C4C3×Q1611yescharacteristic
110C3⋊Dic3—21no—
111C3⋊Dic3C3×SD1611yescharacteristic
112C3⋊Dic3C3×Q1611yescharacteristic
113C3×Dic3—42no—
114C3×Dic3—42no—
115C3×Dic3—61no—
116C3×Dic3—61no—
117C3×Dic3—61no—
118C3×Dic3—61no—
119C3×Dic3—62no—
120C3×Dic3—82no—
121C3×Dic3—121no—
122C4⋊Q8—91no—
123C4⋊C8—91no—
124C4⋊C8—91no—
125C33#33311yescharacteristic, complemented, Sylow
126C3×Q8—362no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—41no—
130C2×C3×C4—41no—
131C2×C3×C4—62no—
132C2×C3×C4—62no—
133C2×C3×C4—91no—
134C2×C3×C4—91no—
135C2×C3×C4—122no—
136C2×C3×C4GO+(4,𝔽2)11yescharacteristic
137C2×Dic3—22no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142Dic6—124no—
143C3×C8—121no—
144C3×C8—122no—
145C3×C8—121no—
146C3×C8—361no—
147C3⋊C8—41no—
148C2×C32—21no—
149C2×C32—21no—
150C2×C32—21no—
151C2×C32—21no—
152C2×C32—21no—
153C2×C32—21no—
154C2×C32—41no—
155C2×C32—41no—
156C2×C32—41no—
157C2×C32—41no—
158C2×C32—41no—
159C2×C32—41no—
160C2×C32C3×#10011yescharacteristic
161C2×C32C3×#10311yescharacteristic
162C2×C32C3×#10311yescharacteristic
163C2×Q8—92no—
164C2×C8—61no—
165C2×C8—181no—
166C4⋊C4—61no—
167C4⋊C4—181no—
168C42—91no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—41no—
172C22×C3—41no—
173C22×C3D32⋊C411yescharacteristic
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—41no—
179C3×C4—41no—
180C3×C4—41no—
181C3×C4—41no—
182C3×C4—91no—
183C3×C4—91no—
184C3×C4—122no—
185C3×C4—122no—
186C3×C4—181no—
187C3×C4—242no—
188C3×C4#377511yescharacteristic
189C3×C4#377611yescharacteristic
190Dic3—42no—
191Dic3—61no—
192Dic3—61no—
193Dic3—61no—
194Dic3—61no—
195Dic3—62no—
196Dic3—121no—
197C32—21no—
198C32—21no—
199C32—41no—
200C32—41no—
201C32C3×#33311yescharacteristic, complemented
202Q8—362no—
203C2×C4—62no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4C3×GO+(4,𝔽2)11yescharacteristic
207C8—121no—
208C8—361no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—41no—
216C2×C3—41no—
217C2×C3—41no—
218C2×C3—41no—
219C2×C3—41no—
220C2×C3—41no—
221C2×C3#6372711yescharacteristic
222C2×C3#6373011yescharacteristic
223C2×C3#6374011yescharacteristic
224C22C3×D32⋊C411yescharacteristic
225C4—91no—
226C4—91no—
227C4—122no—
228C4—181no—
229C4C3×#377511yescharacteristic
230C4C3×#377611yescharacteristic
231C3—21no—
232C3—21no—
233C3—41no—
234C3—41no—
235C3#1059004011yescharacteristic, direct product factor
236C2C3×#6372711yescharacteristic
237C2C3×#6373011yescharacteristic
238C2C3×#6374011yescharacteristic
subgroupG/H
centerC22×C3D32⋊C4
commutatorC2×C3⋊Dic3C2×C3×C4
FrattiniC2×C4C3×GO+(4,𝔽2)
FittingC2×C33×C4D4
socle, prime radicalC22×C33C22⋊C4
cosocleC4×C3⋊Dic3C22×C3
hypercenterC2×C3×C4GO+(4,𝔽2)
hypocenterC32C3×#333
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
4. #10590040C3direct (N × H)
125. C33#333semidirect
201. C32C3×#333semidirect
235. C3#10590040direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#639192
C3×C4⋊#6222
C3×#635722
#105900403
C3×#3339