Finite Group Databasebeta

← C3×#10588567 #13142195

Subgroups — C3×#10588567 #13142195

Order 1728.

378 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 114 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×C8×D9C211yesmaximal, characteristic
2C2×C3×Dic36C211yesmaximal, characteristic, complemented
3C3×#63459C212yesmaximal
4C3×C9×#107C211yesmaximal, characteristic, complemented
5C3×#63368C212yesmaximal, complemented
6C3×#4887—31nomaximal
7#10588567C311yesmaximal, characteristic, direct product factor
8C2×C3×C4×D9C2211yescharacteristic
9C2×C3×Dic18C2212yes—
10C2×C3×C8×C9C2211yescharacteristic
11C3×C9×C4⋊C4C2212yes—
12C3×(C2×D9)⋊C4—22no—
13C3×C4⋊Dic9—22no—
14C2×C3×C9⋊C8C2211yescharacteristic
15C3×C8×D9—22no—
16C3×Dic36—22no—
17C2×C3×Dic12—31no—
18C2×C3×D3×C8—31no—
19C3×#897—32no—
20C32×#107D311yescharacteristic
21C3×#810—32no—
22C2×C8×D9C2×C311yescharacteristic
23C2×Dic36C2×C311yescharacteristic, complemented
24#63459C2×C312yes—
25C9×#107—21no—
26C9×#107C2×C311yescharacteristic, complemented
27#63368C2×C312yescomplemented
28C22×C3×D9D411yescharacteristic
29C2×C3×C4×C9—22no—
30C2×C3×C4×C9C2311yescharacteristic
31C2×C3×Dic9—22no—
32C2×C3×Dic9D411yescharacteristic
33C3×C4×D9—21no—
34C3×C4×D9—21no—
35C3×Dic18—22no—
36C3×Dic18—22no—
37C3×C8×C9D412yes—
38C3×C9⋊C8—21no—
39C3×#467—91no—
40#4887—31no—
41C2×C3×C4×D3—31no—
42C2×C3×Dic6—32no—
43C2×C32×C8C2×D311yescharacteristic
44C32×C4⋊C4C2×D312yes—
45C3×(C2×D3)⋊C4—62no—
46C3×C4⋊Dic3—62no—
47C2×C3×C3⋊C8—31no—
48C3×Dic12—62no—
49C3×D3×C8—62no—
50C2×C4×D9C22×C311yescharacteristic
51C2×Dic18C22×C312yes—
52C2×C8×C9—21no—
53C2×C8×C9C22×C311yescharacteristic
54C9×C4⋊C4—22no—
55C9×C4⋊C4C22×C312yes—
56(C2×D9)⋊C4—22no—
57C4⋊Dic9—22no—
58C2×C9⋊C8C22×C311yescharacteristic
59C8×D9—22no—
60Dic36—22no—
61C22×C3×C9C2×D411yescharacteristic
62C2×C3×D9—21no—
63C2×C3×D9—21no—
64C2×C3×D9Q1612yescomplemented
65C3×C4×C9—42no—
66C3×C4×C9C2×D411yescharacteristic
67C3×C4×C9#4111yescharacteristic
68C3×Dic9—21no—
69C3×Dic9—42no—
70C2×C3×Q16—91no—
71C22×C3×C8—91no—
72C3×C22⋊Q8—92no—
73C2×Dic12—31no—
74C2×D3×C8—31no—
75#897—32no—
76C3×#107—21no—
77C3×#107D911yescharacteristic, complemented
78C3×#107C3×D311yescharacteristic
79C3×#103—92no—
80#810—32no—
81C22×C3×D3—31no—
82C2×C32×C4—22no—
83C2×C32×C4C22×D311yescharacteristic
84C2×C3×Dic3—31no—
85C2×C3×Dic3—62no—
86C3×C4×D3—61no—
87C3×C4×D3—61no—
88C3×Dic6—62no—
89C3×Dic6—62no—
90C22×D9C3×D411yescharacteristic
91C32×C8D1212yes—
92C3×C3⋊C8—61no—
93C2×C4×C9—22no—
94C2×C4×C9—21no—
95C2×C4×C9—42no—
96C2×C4×C9C23×C311yescharacteristic
97C2×Dic9—22no—
98C2×Dic9C3×D411yescharacteristic
99C4×D9—21no—
100C4×D9—21no—
101Dic18—22no—
102Dic18—22no—
103C8×C9—22no—
104C8×C9C3×D412yes—
105C9⋊C8—21no—
106#467—91noSylow
107C2×C3×C9#12111yescharacteristic
108C2×C3×C9C2×Q1611yescharacteristic
109C2×C3×C9#13511yescharacteristic
110C3×D9—22no—
111C2×C3×Q8—92no—
112C22×C3×C4—91no—
113C2×C4×D3—31no—
114C2×Dic6—32no—
115C3×Q16—182no—
116C2×C3×C8—21no—
117C2×C3×C8—91no—
118C2×C3×C8—182no—
119C2×C3×C8C2×D911yescharacteristic
120C2×C3×C8C2×C3×D311yescharacteristic
121C3×C4⋊C4—22no—
122C3×C4⋊C4—182no—
123C3×C4⋊C4C2×D912yes—
124C3×C4⋊C4C2×C3×D312yes—
125C3×C22⋊C4—182no—
126(C2×D3)⋊C4—62no—
127C4⋊Dic3—62no—
128C2×C3⋊C8—31no—
129Dic12—62no—
130D3×C8—62no—
131C22×C32D3×D411yescharacteristic
132C2×C3×D3—32no—
133C2×C3×D3—61no—
134C2×C3×D3—61no—
135C32×C4—42no—
136C32×C4C2×D1211yescharacteristic
137C32×C4#23911yescharacteristic
138C3×Dic3—61no—
139C3×Dic3—122no—
140C22×C9—21no—
141C22×C9C2×C3×D411yescharacteristic
142C2×D9—21no—
143C2×D9—21no—
144C2×D9C3×Q1612yescomplemented
145C4×C9—21no—
146C4×C9—21no—
147C4×C9—42no—
148C4×C9—82no—
149C4×C9C2×C3×D411yescharacteristic
150C4×C9C3×#4111yescharacteristic
151Dic9—21no—
152Dic9—42no—
153C2×Q16—91no—
154C22×C8—91no—
155C22⋊Q8—92no—
156#107C3×D911yescharacteristic, complemented
157#103—92no—
158C3×C9#46711yescharacteristic, complemented, Sylow
159C23×C3—91no—
160C22×D3—31no—
161C3×Q8—182no—
162C3×Q8—182no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—21no—
166C2×C3×C4—42no—
167C2×C3×C4—91no—
168C2×C3×C4—181no—
169C2×C3×C4—181no—
170C2×C3×C4—182no—
171C2×C3×C4C22×D911yescharacteristic
172C2×C3×C4C22×C3×D311yescharacteristic
173C2×Dic3—31no—
174C2×Dic3—62no—
175C4×D3—61no—
176C4×D3—61no—
177Dic6—62no—
178Dic6—62no—
179C3×C8—22no—
180C3×C8—181no—
181C3×C8D3612yes—
182C3×C8C3×D1212yes—
183C3⋊C8—61no—
184C2×C32#89511yescharacteristic
185C2×C32#91211yescharacteristic
186C2×C32D3×Q1611yescharacteristic
187C3×D3—62no—
188C2×C9—21no—
189C2×C9—21no—
190C2×C9—21no—
191C2×C9C3×#12111yescharacteristic
192C2×C9C2×C3×Q1611yescharacteristic
193C2×C9C3×#13511yescharacteristic
194D9—22no—
195C2×Q8—92no—
196C22×C4—91no—
197Q16—182no—
198C2×C8—91no—
199C2×C8—182no—
200C2×C8C2×C3×D911yescharacteristic
201C4⋊C4—182no—
202C4⋊C4C2×C3×D912yes—
203C22⋊C4—182no—
204C22×C3—21no—
205C22×C3—92no—
206C22×C3—181no—
207C22×C3—181no—
208C22×C3D4×D911yescharacteristic
209C22×C3C3×D3×D411yescharacteristic
210C2×D3—32no—
211C2×D3—61no—
212C2×D3—61no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—42no—
216C3×C4—42no—
217C3×C4—82no—
218C3×C4—181no—
219C3×C4—362no—
220C3×C4C2×D3611yescharacteristic
221C3×C4#370111yescharacteristic
222C3×C4C2×C3×D1211yescharacteristic
223C3×C4C3×#23911yescharacteristic
224Dic3—61no—
225Dic3—122no—
226C32#488711yescharacteristic
227C9—21no—
228C9C3×#46711yescharacteristic, complemented
229C23—91no—
230Q8—182no—
231Q8—182no—
232C2×C4—22no—
233C2×C4—91no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—182no—
237C2×C4C22×C3×D911yescharacteristic
238C8—181no—
239C8C3×D3612yes—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—182no—
244C2×C3#6345711yescharacteristic
245C2×C3#6347411yescharacteristic
246C2×C3Q16×D911yescharacteristic
247C2×C3C3×#89511yescharacteristic
248C2×C3C3×#91211yescharacteristic
249C2×C3C3×D3×Q1611yescharacteristic
250D3—62no—
251C22—92no—
252C22—181no—
253C22—181no—
254C22C3×D4×D911yescharacteristic
255C4—42no—
256C4—181no—
257C4—362no—
258C4C2×C3×D3611yescharacteristic
259C4C3×#370111yescharacteristic
260C3—21no—
261C3#1058856711yescharacteristic, direct product factor
262C3C3×#488711yescharacteristic
263C2—182no—
264C2C3×#6345711yescharacteristic
265C2C3×#6347411yescharacteristic
266C2C3×Q16×D911yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#107C2
socleC22×C32D3×D4
prime radicalC22×C3×D9D4
hypercenterC3×#107D9
hypocenterC9C3×#467
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#107

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic36C2semidirect
4. C3×C9×#107C2semidirect
5. C3×#63368C2semidirect
7. #10588567C3direct (N × H)
23. C2×Dic36C2×C3semidirect
26. C9×#107C2×C3semidirect
27. #63368C2×C3semidirect
64. C2×C3×D9Q16semidirect
77. C3×#107D9semidirect
144. C2×D9C3×Q16semidirect
156. #107C3×D9semidirect
158. C3×C9#467semidirect
228. C9C3×#467semidirect
261. C3#10588567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C8×D92
C2×C3×Dic362
C3×#634592
C3×C9×#1072
C3×#633682
C3×#48873
#105885673