Finite Group Databasebeta

← C3×#10593383 #13166745

Subgroups — C3×#10593383 #13166745

Order 1728.

356 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 70 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×#63870C211yesmaximal, characteristic
3C3×#63777C211yesmaximal, characteristic
4C3×#63743C212yesmaximal
5C3×#63742C212yesmaximal
6#10593383C311yesmaximal, characteristic, direct product factor
7C2×C3×#627—21no—
8C2×C3×#622C2212yes—
9C3×C4×C3⋊Dic3C2211yescharacteristic
10C32×C4⋊Dic3—21no—
11C32×Dic3⋊C4—21no—
12C3×#3724C2211yescharacteristic
13C3×#3724C2211yescharacteristic
14C3×#3724C2212yes—
15C3×Dic3⋊Dic3—21no—
16C3×#889—61no—
17C3×#888—61no—
18#63919C2×C311yescharacteristic
19#63870C2×C311yescharacteristic
20#63777C2×C311yescharacteristic
21#63743C2×C312yes—
22#63742C2×C312yes—
23C2×C33×C4D411yescharacteristic
24C2×C3×C3⋊Dic3D411yescharacteristic
25C2×C3×C3⋊Dic3C2311yescharacteristic
26C2×C32×Dic3—22no—
27C2×C32×Dic3—21no—
28C2×C32×Dic3—21no—
29C3×#627—42no—
30C3×#622Q814yescomplemented
31C3×#501—91nomaximal
32C2×C3×Dic6—62no—
33C2×#627—21no—
34C2×#622C22×C312yes—
35C32×C4⋊C4—61no—
36C32×C4⋊C4—61no—
37C4×C3⋊Dic3C22×C311yescharacteristic
38C3×C4⋊Dic3—21no—
39C3×C4⋊Dic3—21no—
40C3×C4⋊Dic3—41no—
41C3×C4⋊Dic3—61no—
42C3×Dic3⋊C4—21no—
43C3×Dic3⋊C4—21no—
44C3×Dic3⋊C4—41no—
45C3×Dic3⋊C4—62no—
46C3×Dic3⋊C4—61no—
47C3×Dic3⋊C4—61no—
48C3×Dic3⋊C4—61no—
49C3×C4×Dic3—61no—
50C3×C4×Dic3—61no—
51#3724C22×C311yescharacteristic
52#3724C22×C311yescharacteristic
53#3724C22×C312yes—
54Dic3⋊Dic3—21no—
55C22×C33C2×D411yescharacteristic
56C33×C4—21no—
57C3×C3⋊Dic3—21no—
58C3×C3⋊Dic3C2×Q812yes—
59C32×Dic3—41no—
60C32×Dic3—42no—
61C32×Dic3—41no—
62C3×C4⋊Q8—91no—
63C3×#125—91no—
64#889—61no—
65#888—61no—
66C3×#107—92no—
67C3×#106—92no—
68C3×#97—91no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—61no—
74C2×C32×C4—61no—
75C2×C32×C4—62no—
76C2×C32×C4C3×D411yescharacteristic
77C2×C3⋊Dic3C3×D411yescharacteristic
78C2×C3⋊Dic3C23×C311yescharacteristic
79C2×C3×Dic3—21no—
80C2×C3×Dic3—21no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—21no—
83C2×C3×Dic3—21no—
84C2×C3×Dic3—22no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—61no—
89C2×C3×Dic3—61no—
90C2×C3×Dic3—61no—
91C2×C3×Dic3—61no—
92C3×Dic6—124no—
93#627—42no—
94#622C3×Q814yescomplemented
95#501—91noSylow
96C2×C33C4⋊Q811yescharacteristic
97C2×C33AGL(1,ℤ/8)11yescharacteristic
98C2×C33#13711yescharacteristic
99C2×C3×Q8—181no—
100C2×Dic6—62no—
101C2×C3×C8—92no—
102C3×C4⋊C4—61no—
103C3×C4⋊C4—61no—
104C3×C4⋊C4—61no—
105C3×C4⋊C4—61no—
106C3×C4⋊C4—91no—
107C3×C4⋊C4—92no—
108C3×C4⋊C4—91no—
109C3×C4⋊C4—121no—
110C3×C4⋊C4—121no—
111C3×C4⋊C4—181no—
112C3×C42—91no—
113C4⋊Dic3—21no—
114C4⋊Dic3—61no—
115Dic3⋊C4—21no—
116Dic3⋊C4—62no—
117Dic3⋊C4—61no—
118Dic3⋊C4—61no—
119Dic3⋊C4—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—41no—
125C22×C32—41no—
126C22×C32C2×C3×D411yescharacteristic
127C32×C4—22no—
128C32×C4—21no—
129C32×C4—41no—
130C32×C4—42no—
131C32×C4—81no—
132C32×C4—121no—
133C32×C4—122no—
134C32×C4—121no—
135C3⋊Dic3—21no—
136C3⋊Dic3C2×C3×Q812yes—
137C3×Dic3—42no—
138C3×Dic3—41no—
139C3×Dic3—41no—
140C3×Dic3—42no—
141C3×Dic3—42no—
142C3×Dic3—41no—
143C3×Dic3—41no—
144C3×Dic3—62no—
145C3×Dic3—62no—
146C3×Dic3—62no—
147C3×Dic3—82no—
148C3×Dic3—81no—
149C3×Dic3—121no—
150C4⋊Q8—91no—
151#125—91no—
152#107—92no—
153#106—92no—
154#97—91no—
155C33#50111yescharacteristic, complemented, Sylow
156C3×Q8—362no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—61no—
162C2×C3×C4—61no—
163C2×C3×C4—62no—
164C2×C3×C4—61no—
165C2×C3×C4—61no—
166C2×C3×C4—62no—
167C2×C3×C4—91no—
168C2×C3×C4—91no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171C2×C3×C4—122no—
172C2×C3×C4GO+(4,𝔽2)11yescharacteristic
173C2×Dic3—21no—
174C2×Dic3—21no—
175C2×Dic3—22no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180Dic6—124no—
181C3×C8—94no—
182C2×C32—21no—
183C2×C32—21no—
184C2×C32—21no—
185C2×C32—21no—
186C2×C32—21no—
187C2×C32—21no—
188C2×C32—41no—
189C2×C32—41no—
190C2×C32—41no—
191C2×C32—41no—
192C2×C32—41no—
193C2×C32—41no—
194C2×C32C3×C4⋊Q811yescharacteristic
195C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
196C2×C32C3×#13711yescharacteristic
197C2×Q8—181no—
198C2×C8—92no—
199C4⋊C4—61no—
200C4⋊C4—61no—
201C4⋊C4—91no—
202C4⋊C4—92no—
203C4⋊C4—91no—
204C4⋊C4—181no—
205C42—91no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—41no—
209C22×C3—41no—
210C22×C3C2×GO+(4,𝔽2)11yescharacteristic
211C3×C4—22no—
212C3×C4—21no—
213C3×C4—41no—
214C3×C4—42no—
215C3×C4—81no—
216C3×C4—92no—
217C3×C4—122no—
218C3×C4—121no—
219C3×C4—121no—
220C3×C4—122no—
221C3×C4—122no—
222C3×C4—121no—
223C3×C4—121no—
224C3×C4—181no—
225C3×C4—241no—
226C3×C4—242no—
227Dic3—42no—
228Dic3—41no—
229Dic3—41no—
230Dic3—62no—
231Dic3—62no—
232Dic3—62no—
233Dic3—121no—
234C32—21no—
235C32—21no—
236C32—41no—
237C32—41no—
238C32C3×#50111yescharacteristic, complemented
239Q8—362no—
240C2×C4—61no—
241C2×C4—61no—
242C2×C4—62no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4C3×GO+(4,𝔽2)11yescharacteristic
246C8—94no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—41no—
254C2×C3—41no—
255C2×C3—41no—
256C2×C3—41no—
257C2×C3—41no—
258C2×C3—41no—
259C2×C3#6422211yescharacteristic
260C2×C3#6422411yescharacteristic
261C2×C3#6423911yescharacteristic
262C22C2×C3×GO+(4,𝔽2)11yescharacteristic
263C4—21no—
264C4—92no—
265C4—121no—
266C4—122no—
267C4—121no—
268C4—181no—
269C3—21no—
270C3—21no—
271C3—41no—
272C3—41no—
273C3#1059338311yescharacteristic, direct product factor
274C2C3×#6422211yescharacteristic
275C2C3×#6422411yescharacteristic
276C2C3×#6423911yescharacteristic
subgroupG/H
centerC22×C3C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23×C3
FrattiniC22C2×C3×GO+(4,𝔽2)
FittingC2×C33×C4D4
socle, prime radicalC22×C33C2×D4
hypercenterC2×C3×C4GO+(4,𝔽2)
hypocenterC32C3×#501
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
6. #10593383C3direct (N × H)
30. C3×#622Q8semidirect
94. #622C3×Q8semidirect
155. C33#501semidirect
238. C32C3×#501semidirect
273. C3#10593383direct (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×#638702
C3×#637772
C3×#637432
C3×#637422
#105933833
C3×#5019