Finite Group Databasebeta

← C3×#63979 #11723304

Subgroups — C3×#63979 #11723304

Order 864.

626 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 108 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×#638C211yesmaximal, characteristic, complemented
2C2×C32×#67C212yesmaximal, complemented
3C2×C3×#626C212yesmaximal, complemented
4C2×C3×#625C211yesmaximal, characteristic, complemented
5C3×Dic32C211yesmaximal, characteristic, complemented
6C3×#940—32nomaximal
7#63979C311yesmaximal, characteristic, direct product factor
8C23×C33C2211yescharacteristic
9C22×C3×C3⋊D3C2211yescharacteristic
10C22×C32×D3C2212yes—
11C3×#638—22no—
12C2×C3×C3⋊Dic3C2211yescharacteristic
13C32×#67—24no—
14C2×C32×Dic3C2212yes—
15C3×#626—24no—
16C3×#625—22no—
17C2×C32×D4—32no—
18C2×#638C2×C311yescharacteristic, complemented
19C2×C3×#67—22no—
20C2×C3×#67—32no—
21C2×C3×#67—32no—
22C2×C3×#67—32no—
23C2×C3×#67—61no—
24C2×C3×#67D312yescomplemented
25C2×C3×#67C2×C312yescomplemented
26C2×C3×D12—32no—
27C2×#626C2×C312yescomplemented
28C2×#625C2×C311yescharacteristic, complemented
29C3×C4×Dic3—32no—
30Dic32C2×C311yescharacteristic, complemented
31C22×C33—22no—
32C22×C33—21no—
33C22×C33C2311yescharacteristic
34C2×C3×C3⋊D3—21no—
35C2×C3×C3⋊D3—22no—
36C2×C32×D3—22no—
37C2×C32×D3—22no—
38C2×C32×D3—22no—
39C3×C3⋊Dic3D412yescomplemented
40C32×Dic3D414yescomplemented
41C3×#127—91no—
42#940—32no—
43C23×C32—21no—
44C23×C32—22no—
45C23×C32—32no—
46C23×C32—41no—
47C23×C32C2×D312yes—
48C23×C32C22×C311yescharacteristic
49C22×C3⋊D3C22×C311yescharacteristic
50C22×C3×D3—22no—
51C22×C3×D3—32no—
52C22×C3×D3—61no—
53C22×C3×D3C2×D312yes—
54C22×C3×D3C22×C312yes—
55C32×D4—64no—
56C2×C32×C4—32no—
57#638—22no—
58C2×C3⋊Dic3C22×C311yescharacteristic
59C3×#67—28no—
60C3×#67—24no—
61C3×#67—24no—
62C3×#67—64no—
63C3×#67—64no—
64C3×#67—64no—
65C3×#67—64no—
66C2×C3×Dic3—22no—
67C2×C3×Dic3—32no—
68C2×C3×Dic3—61no—
69C2×C3×Dic3C2×D312yes—
70C2×C3×Dic3C22×C312yes—
71C3×D12—64no—
72#626—24no—
73#625—22no—
74C2×C33—41no—
75C2×C33C2×D411yescharacteristic
76C2×C33C2×D412yes—
77C3×C3⋊D3—41no—
78C32×D3—42no—
79C2×C3×D4—32no—
80C2×C3×D4—32no—
81C2×C3×D4—62no—
82C2×C3×D4—92no—
83C2×C3×D4—91no—
84C2×C3×D4—91no—
85C2×#67—32no—
86C2×#67—32no—
87C2×#67—32no—
88C2×#67—61no—
89C2×#67C3×D312yescomplemented
90C2×D12—32no—
91C3×C42—91no—
92C4×Dic3—32no—
93C22×C32—22no—
94C22×C32—21no—
95C22×C32—24no—
96C22×C32—22no—
97C22×C32—22no—
98C22×C32—22no—
99C22×C32—22no—
100C22×C32—21no—
101C22×C32—22no—
102C22×C32—41no—
103C22×C32—42no—
104C22×C32—42no—
105C22×C32—42no—
106C22×C32—42no—
107C22×C32—44no—
108C22×C32—62no—
109C22×C32—62no—
110C22×C32—62no—
111C22×C32C22×D312yes—
112C22×C32C23×C311yescharacteristic
113C2×C3⋊D3—21no—
114C2×C3⋊D3—22no—
115C2×C3×D3—24no—
116C2×C3×D3—22no—
117C2×C3×D3—22no—
118C2×C3×D3—22no—
119C2×C3×D3—22no—
120C2×C3×D3—22no—
121C2×C3×D3—22no—
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124C2×C3×D3—62no—
125C2×C3×D3—62no—
126C2×C3×D3—62no—
127C2×C3×D3—62no—
128C2×C3×D3—122no—
129C32×C4—34no—
130C3⋊Dic3C3×D412yescomplemented
131C3×Dic3—24no—
132C3×Dic3—34no—
133C3×Dic3—62no—
134C3×Dic3#6714yescomplemented
135C3×Dic3C3×D414yescomplemented
136#127—91noSylow
137C33#12711yescharacteristic, complemented, Sylow
138C23×C3—22no—
139C23×C3—21no—
140C23×C3—32no—
141C23×C3—32no—
142C23×C3—41no—
143C23×C3—62no—
144C23×C3—91no—
145C23×C3D3211yescharacteristic
146C23×C3C2×C3×D312yes—
147C22×D3—32no—
148C22×D3—61no—
149C22×D3C2×C3×D312yes—
150C3×D4—64no—
151C3×D4—64no—
152C3×D4—68no—
153C3×D4—184no—
154C3×D4—182no—
155C3×D4—182no—
156C2×C3×C4—32no—
157C2×C3×C4—32no—
158C2×C3×C4—62no—
159C2×C3×C4—91no—
160#67—24no—
161#67—64no—
162#67—64no—
163#67—64no—
164#67—64no—
165C2×Dic3—32no—
166C2×Dic3—61no—
167C2×Dic3C2×C3×D312yes—
168D12—64no—
169C2×C32—22no—
170C2×C32—21no—
171C2×C32—22no—
172C2×C32—22no—
173C2×C32—22no—
174C2×C32—42no—
175C2×C32—41no—
176C2×C32—44no—
177C2×C32—42no—
178C2×C32—44no—
179C2×C32—42no—
180C2×C32—41no—
181C2×C32—122no—
182C2×C32D3×D412yes—
183C2×C32D3×D412yes—
184C2×C32C2×#6712yes—
185C2×C32C2×C3×D411yescharacteristic
186C2×C32C2×C3×D412yes—
187C3⋊D3—41no—
188C3×D3—44no—
189C3×D3—42no—
190C3×D3—42no—
191C3×D3—122no—
192C3×D3—122no—
193C2×D4—32no—
194C2×D4—92no—
195C2×D4—91no—
196C2×D4—91no—
197C42—91no—
198C22×C3—22no—
199C22×C3—24no—
200C22×C3—22no—
201C22×C3—21no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—21no—
206C22×C3—22no—
207C22×C3—42no—
208C22×C3—42no—
209C22×C3—42no—
210C22×C3—44no—
211C22×C3—42no—
212C22×C3—41no—
213C22×C3—64no—
214C22×C3—62no—
215C22×C3—62no—
216C22×C3—62no—
217C22×C3—62no—
218C22×C3—62no—
219C22×C3—62no—
220C22×C3—122no—
221C22×C3—122no—
222C22×C3—182no—
223C22×C3—181no—
224C22×C3C2×D3211yescharacteristic
225C22×C3C22×C3×D312yes—
226C2×D3—22no—
227C2×D3—22no—
228C2×D3—22no—
229C2×D3—62no—
230C2×D3—62no—
231C2×D3—62no—
232C2×D3—62no—
233C2×D3—122no—
234C3×C4—34no—
235C3×C4—34no—
236C3×C4—64no—
237C3×C4—92no—
238Dic3—34no—
239Dic3—62no—
240Dic3C3×#6714yescomplemented
241C32—22no—
242C32—21no—
243C32—41no—
244C32#94012yescomplemented
245C32C3×#12711yescharacteristic, complemented
246C23—32no—
247C23—91no—
248C23C3×D3211yescharacteristic
249D4—64no—
250D4—184no—
251D4—182no—
252D4—182no—
253C2×C4—32no—
254C2×C4—91no—
255C2×C3—22no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—21no—
259C2×C3—22no—
260C2×C3—42no—
261C2×C3—44no—
262C2×C3—44no—
263C2×C3—42no—
264C2×C3—41no—
265C2×C3—42no—
266C2×C3—41no—
267C2×C3—124no—
268C2×C3—122no—
269C2×C3—122no—
270C2×C3—361no—
271C2×C3D3×#6712yes—
272C2×C3#381111yescharacteristic
273C2×C3C3×D3×D412yes—
274C2×C3C3×D3×D412yes—
275C2×C3C2×C3×#6712yes—
276D3—42no—
277D3—122no—
278D3—122no—
279C22—22no—
280C22—21no—
281C22—62no—
282C22—62no—
283C22—62no—
284C22—182no—
285C22—181no—
286C22C2×C3×D3211yescharacteristic
287C4—34no—
288C4—92no—
289C3—21no—
290C3—22no—
291C3—41no—
292C3#6397911yescharacteristic, direct product factor
293C3C3×#94012yescomplemented
294C2—41no—
295C2—122no—
296C2—361no—
297C2C3×D3×#6712yes—
298C2C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C2×D32
commutator, cosocleC22×C32C23×C3
FrattiniC22C2×C3×D32
FittingC23×C33C22
socleC22×C33C23
hypercenterC23×C3D32
hypocenterC32C3×#127
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#638C2semidirect
2. C2×C32×#67C2semidirect
3. C2×C3×#626C2semidirect
4. C2×C3×#625C2semidirect
5. C3×Dic32C2semidirect
7. #63979C3direct (N × H)
18. C2×#638C2×C3semidirect
24. C2×C3×#67D3semidirect
25. C2×C3×#67C2×C3semidirect
27. C2×#626C2×C3semidirect
28. C2×#625C2×C3semidirect
30. Dic32C2×C3semidirect
39. C3×C3⋊Dic3D4semidirect
40. C32×Dic3D4semidirect
89. C2×#67C3×D3semidirect
130. C3⋊Dic3C3×D4semidirect
134. C3×Dic3#67semidirect
135. C3×Dic3C3×D4semidirect
137. C33#127semidirect
240. Dic3C3×#67semidirect
244. C32#940semidirect
245. C32C3×#127semidirect
292. C3#63979direct (N × H)
293. C3C3×#940semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#6382
C2×C32×#672
C2×C3×#6262
C2×C3×#6252
C3×Dic322
C3×#9403
#639793