Finite Group Databasebeta

← C3×#71304 #11779481

Subgroups — C3×#71304 #11779481

Order 1152.

497 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 497 conjugacy classes of subgroups — too many to draw. Only its 106 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×#5734C211yesmaximal, characteristic
2C32×#494C211yesmaximal, characteristic, complemented
3C3×#5084C212yesmaximal, complemented
4C3×#4546C211yesmaximal, characteristic, complemented
5C3×#4459C212yesmaximal, complemented
6C3×#1634—31nomaximal
7#71304C311yesmaximal, characteristic, direct product factor
8C2×C32×Q16—22no—
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C3×#947—22no—
12C3×#895—22no—
13C3×#892—22no—
14C3×C4×D12C2212yes—
15C32×C4×C8C2211yescharacteristic
16C3×#809—22no—
17C3×#808—22no—
18C3×C4⋊(C3⋊C8)C2212yes—
19C3×#555—31no—
20#5734C2×C311yescharacteristic
21C3×#494—21no—
22C3×#494D311yescharacteristic, complemented
23C3×#494C2×C311yescharacteristic, complemented
24C3×#476—32no—
25#5084C2×C312yescomplemented
26C3×#333—31no—
27C3×D4⋊C8—32no—
28#4546C2×C311yescharacteristic, complemented
29#4459C2×C312yescomplemented
30C2×C32×Q8—21no—
31C2×C32×Q8D412yes—
32C2×C3×D12—22no—
33C2×C3×D12D412yes—
34C2×C3×C4×D3—22no—
35C32×Q16—44no—
36C2×C32×C8—21no—
37C32×C4⋊C4—22no—
38C32×C4⋊C4—22no—
39C32×C42C2311yescharacteristic
40C3×(C2×D3)⋊C4—24no—
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3D412yes—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—22no—
45#1634—31noSylow
46C2×C3×Q16—24no—
47C2×C3×Q16—22no—
48C2×C3×Q16—22no—
49C3×C4⋊Q8—21no—
50C3×C4⋊Q8—21no—
51C3×C4⋊Q8C2×D311yescharacteristic
52C3×C4⋊Q8C2×D311yescharacteristic
53C3×C4⋊Q8C22×C311yescharacteristic
54C3×C4⋊Q8C22×C311yescharacteristic
55C3×#124—62no—
56C3×#121—62no—
57C3×C4×D4—32no—
58C3×#117—62no—
59#947—22no—
60#895—22no—
61#892—22no—
62C4×D12C22×C312yes—
63C3×#106—62no—
64C3×C4⋊C8—32no—
65C3×#102—62no—
66C3×C4×C8—21no—
67C3×C4×C8C2×D311yescharacteristic
68C3×C4×C8C22×C311yescharacteristic
69#809—22no—
70#808—22no—
71C4⋊(C3⋊C8)C22×C312yes—
72C22×C3×D3—22no—
73C32×Q8—42no—
74C32×Q8—42no—
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4C2×D412yes—
78C2×C32×C4C2×D411yescharacteristic
79C2×C3×Dic3—22no—
80C3×D12—22no—
81C3×D12—22no—
82C3×D12—82no—
83C3×C4×D3—42no—
84C3×C4×D3—42no—
85C32×C8—22no—
86C3×C3⋊C8—42no—
87#555—31no—
88#494C3×D311yescharacteristic, complemented
89#476—32no—
90#333—31no—
91D4⋊C8—32no—
92C2×C3×Q8—22no—
93C2×C3×Q8—21no—
94C2×C3×Q8—21no—
95C2×C3×Q8—22no—
96C2×C3×Q8#6712yes—
97C2×C3×Q8C3×D412yes—
98C2×C3×D4—32no—
99C2×C3×D4—62no—
100C22×C3×C4—62no—
101C2×D12—22no—
102C2×D12C3×D412yes—
103C2×C4×D3—22no—
104C3×Q16—44no—
105C3×Q16—44no—
106C3×Q16—48no—
107C2×C3×C8—22no—
108C2×C3×C8—21no—
109C2×C3×C8—21no—
110C2×C3×C8—62no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—32no—
116C3×C4⋊C4—42no—
117C3×C4⋊C4—42no—
118C3×C22⋊C4—64no—
119C3×C22⋊C4—62no—
120C3×C42—21no—
121C3×C42—62no—
122C3×C42C22×D311yescharacteristic
123C3×C42C23×C311yescharacteristic
124(C2×D3)⋊C4—24no—
125(C2×D3)⋊C4—22no—
126C4⋊Dic3C3×D412yes—
127C4×Dic3—22no—
128C2×C3⋊C8—22no—
129C22×C32#12011yescharacteristic
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C32×C4—21no—
134C32×C4—42no—
135C32×C4—81no—
136C32×C4#13512yes—
137C32×C4#13712yes—
138C3×Dic3—42no—
139C2×Q16—22no—
140C4⋊Q8C2×C3×D311yescharacteristic
141C4⋊Q8C2×C3×D311yescharacteristic
142#124—62no—
143#121—62no—
144C4×D4—32no—
145#117—62no—
146#106—62no—
147C4⋊C8—32no—
148#102—62no—
149C4×C8C2×C3×D311yescharacteristic
150C23×C3—62no—
151C22×D3—22no—
152C3×Q8—42no—
153C3×Q8—42no—
154C3×Q8—44no—
155C3×Q8—44no—
156C3×Q8—42no—
157C3×Q8—42no—
158C3×D4—62no—
159C3×D4—62no—
160C3×D4—242no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—21no—
165C2×C3×C4—42no—
166C2×C3×C4—42no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4—62no—
170C2×C3×C4—122no—
171C2×C3×C4—122no—
172C2×C3×C4D3×D412yes—
173C2×C3×C4C2×#6711yescharacteristic
174C2×C3×C4C2×C3×D412yes—
175C2×C3×C4C2×C3×D411yescharacteristic
176C2×Dic3—22no—
177D12—22no—
178D12—22no—
179D12—82no—
180C4×D3—42no—
181C4×D3—42no—
182C3×C8—24no—
183C3×C8—22no—
184C3×C8—22no—
185C3×C8—122no—
186C3⋊C8—42no—
187C2×C32#45212yes—
188C2×C32#45311yescharacteristic
189C3×D3—82no—
190C2×Q8—21no—
191C2×Q8C3×#6712yes—
192C2×D4—32no—
193C2×D4—62no—
194C22×C4—62no—
195Q16—44no—
196C2×C8—21no—
197C2×C8—62no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—32no—
201C22⋊C4—64no—
202C22⋊C4—62no—
203C42—62no—
204C42C22×C3×D311yescharacteristic
205C22×C3—21no—
206C22×C3—122no—
207C22×C3—122no—
208C22×C3—122no—
209C22×C3#93711yescharacteristic
210C22×C3C3×#12011yescharacteristic
211C2×D3—42no—
212C2×D3—42no—
213C2×D3—42no—
214C3×C4—22no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—22no—
218C3×C4—22no—
219C3×C4—42no—
220C3×C4—42no—
221C3×C4—82no—
222C3×C4—82no—
223C3×C4—81no—
224C3×C4—81no—
225C3×C4—122no—
226C3×C4#91812yes—
227C3×C4#91912yes—
228C3×C4C3×#13512yes—
229C3×C4C3×#13712yes—
230Dic3—42no—
231C32#163411yescharacteristic, complemented, Sylow
232C23—62no—
233Q8—42no—
234Q8—42no—
235D4—62no—
236D4—62no—
237D4—242no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—62no—
241C2×C4—122no—
242C2×C4—122no—
243C2×C4C3×D3×D412yes—
244C2×C4C2×C3×#6711yescharacteristic
245C8—22no—
246C8—122no—
247C2×C3—22no—
248C2×C3—21no—
249C2×C3—242no—
250C2×C3#507711yescharacteristic
251C2×C3#518712yes—
252C2×C3C3×#45212yes—
253C2×C3C3×#45311yescharacteristic
254D3—82no—
255C22—122no—
256C22—122no—
257C22—122no—
258C22C3×#93711yescharacteristic
259C4—21no—
260C4—42no—
261C4—81no—
262C4—122no—
263C4C3×#91812yes—
264C4C3×#91912yes—
265C3—21no—
266C3#7130411yescharacteristic, direct product factor
267C3C3×#163411yescharacteristic, complemented
268C2—242no—
269C2C3×#507711yescharacteristic
270C2C3×#518712yes—
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#494C2
socleC22×C32#120
prime radicalC3×#5734C2
hypercenterC3×#494D3
hypocenterC3C3×#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#494

Complements

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

NH ≅ G/Ntype
2. C32×#494C2semidirect
3. C3×#5084C2semidirect
4. C3×#4546C2semidirect
5. C3×#4459C2semidirect
7. #71304C3direct (N × H)
22. C3×#494D3semidirect
23. C3×#494C2×C3semidirect
25. #5084C2×C3semidirect
28. #4546C2×C3semidirect
29. #4459C2×C3semidirect
88. #494C3×D3semidirect
231. C32#1634semidirect
266. C3#71304direct (N × H)
267. C3C3×#1634semidirect

Maximal subgroups

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

subgroupindex
C3×#57342
C32×#4942
C3×#50842
C3×#45462
C3×#44592
C3×#16343
#713043