Finite Group Databasebeta

← C3×#67531 #11771423

Subgroups — C3×#67531 #11771423

Order 1152.

253 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 253 conjugacy classes of subgroups — too many to draw. Only its 66 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×#5129C211yesmaximal, characteristic
2C32×#349C211yesmaximal, characteristic, complemented
3C3×#4553C211yesmaximal, characteristic, complemented
4C3×#1321—31nomaximal
5#67531C311yesmaximal, characteristic, direct product factor
6C2×C3×#235C411yescharacteristic
7C2×C32×M16C2211yescharacteristic
8C22×C3×C3⋊C8C411yescharacteristic
9C32×M32—21no—
10C3×(C2×D3)⋊C8—21no—
11C3×(C2×D3)⋊C8—21no—
12C3×#812—21no—
13C3×#408—31no—
14#5129C2×C311yescharacteristic
15C3×#349—21no—
16C3×#349—31no—
17C3×#349D311yescharacteristic, complemented
18C3×#349C2×C311yescharacteristic, complemented
19#4553C2×C311yescharacteristic, complemented
20C22×C32×C4C2×C411yescharacteristic
21C2×C3×#67—21no—
22C3×#235—41no—
23C3×#235—41no—
24C2×C3×D12C811yescharacteristic
25C2×C3×C4×D3—21no—
26C2×C3×Dic6C811yescharacteristic
27C32×M16—41no—
28C2×C32×C8D411yescharacteristic
29C2×C32×C8D411yescharacteristic
30C2×C3×C3⋊C8—21no—
31C2×C3×C3⋊C8—41no—
32C32×C16—41no—
33C3×C3⋊C16—41no—
34#1321—31noSylow
35C2×C3×#41—31no—
36C2×#235C3×C411yescharacteristic
37C2×C3×M16—21no—
38C2×C3×M16C2×D311yescharacteristic
39C2×C3×M16C22×C311yescharacteristic
40C22×C3×C8—31no—
41C22×C3⋊C8C3×C411yescharacteristic
42C3×M32—22no—
43C3×M32—21no—
44C3×M32—21no—
45C3×M32—61no—
46C3×C22⋊C8—61no—
47C3×C22⋊C8—61no—
48(C2×D3)⋊C8—21no—
49(C2×D3)⋊C8—21no—
50#812—21no—
51C23×C32M1611yescharacteristic
52C22×C3×D3—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C2×C811yescharacteristic
57C3×#67—42no—
58C2×C3×Dic3—21no—
59C3×D12—41no—
60C3×C4×D3—41no—
61C3×C4×D3—41no—
62C3×Dic6—41no—
63C32×C8—21no—
64C32×C8—21no—
65C3×C3⋊C8—41no—
66#408—31no—
67#349—31no—
68#349C3×D311yescharacteristic, complemented
69C3×#41—121no—
70C3×#41—121no—
71C2×C3×Q8—31no—
72C2×C3×D4—31no—
73C2×C3×D4—61no—
74C22×C3×C4—21no—
75C22×C3×C4—61no—
76C22×C3×C4C4×D311yescharacteristic
77C22×C3×C4C2×C3×C411yescharacteristic
78C2×#67—21no—
79#235—41no—
80#235—41no—
81C2×D12C3×C811yescharacteristic
82C2×C4×D3—21no—
83C2×Dic6C3×C811yescharacteristic
84C3×M16—41no—
85C3×M16—41no—
86C3×M16—42no—
87C2×C3×C8—21no—
88C2×C3×C8—21no—
89C2×C3×C8—61no—
90C2×C3×C8—121no—
91C2×C3×C8D1211yescharacteristic
92C2×C3×C8#6711yescharacteristic
93C2×C3×C8C3×D411yescharacteristic
94C2×C3×C8C3×D411yescharacteristic
95C2×C3⋊C8—21no—
96C2×C3⋊C8—41no—
97C3×C16—42no—
98C3×C16—41no—
99C3×C16—41no—
100C3×C16—121no—
101C3⋊C16—41no—
102C22×C32—21no—
103C22×C32—41no—
104C22×C32C22⋊C811yescharacteristic
105C2×C3×D3—42no—
106C2×C3×D3—41no—
107C32×C4—21no—
108C32×C4#9911yescharacteristic
109C32×C4#10011yescharacteristic
110C3×Dic3—41no—
111C2×#41—31no—
112C2×M16C2×C3×D311yescharacteristic
113C22×C8—31no—
114M32—21no—
115M32—61no—
116C22⋊C8—61no—
117C22⋊C8—61no—
118C23×C3—21no—
119C23×C3—61no—
120C23×C3ΓL(1,𝔽25)11yescharacteristic
121C23×C3C3×M1611yescharacteristic
122C22×D3—21no—
123C3×Q8—121no—
124C3×D4—121no—
125C3×D4—122no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—41no—
133C2×C3×C4—41no—
134C2×C3×C4—61no—
135C2×C3×C4—121no—
136C2×C3×C4—121no—
137C2×C3×C4D3×C811yescharacteristic
138C2×C3×C4(C2×D3)⋊C411yescharacteristic
139C2×C3×C4C3×C22⋊C411yescharacteristic
140C2×C3×C4C2×C3×C811yescharacteristic
141#67—42no—
142C2×Dic3—21no—
143D12—41no—
144C4×D3—41no—
145C4×D3—41no—
146Dic6—41no—
147C3×C8—22no—
148C3×C8—21no—
149C3×C8—21no—
150C3×C8—21no—
151C3×C8—21no—
152C3×C8—41no—
153C3×C8—121no—
154C3⋊C8—41no—
155C2×C32—21no—
156C2×C32—41no—
157C2×C32#32311yescharacteristic
158C3×D3—81no—
159#41—121no—
160#41—121no—
161C2×Q8—31no—
162C2×D4—31no—
163C2×D4—61no—
164C22×C4—61no—
165C22×C4C3×C4×D311yescharacteristic
166M16—41no—
167C2×C8—61no—
168C2×C8—121no—
169C2×C8C3×D1211yescharacteristic
170C2×C8C3×#6711yescharacteristic
171C16—41no—
172C16—121no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—41no—
177C22×C3—41no—
178C22×C3—41no—
179C22×C3—81no—
180C22×C3—122no—
181C22×C3—121no—
182C22×C3(C2×D3)⋊C811yescharacteristic
183C22×C3C3×C22⋊C811yescharacteristic
184C2×D3—42no—
185C2×D3—41no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—21no—
190C3×C4—41no—
191C3×C4—121no—
192C3×C4#80611yescharacteristic
193C3×C4#82311yescharacteristic
194C3×C4C3×#9911yescharacteristic
195C3×C4C3×#10011yescharacteristic
196Dic3—41no—
197C32#132111yescharacteristic, complemented, Sylow
198C23—61no—
199C23C3×ΓL(1,𝔽25)11yescharacteristic
200Q8—121no—
201D4—121no—
202D4—122no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—61no—
206C2×C4—121no—
207C2×C4—121no—
208C2×C4C3×D3×C811yescharacteristic
209C2×C4C3×(C2×D3)⋊C411yescharacteristic
210C8—21no—
211C8—21no—
212C8—121no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—41no—
217C2×C3—41no—
218C2×C3—41no—
219C2×C3—81no—
220C2×C3—241no—
221C2×C3#446811yescharacteristic
222C2×C3C3×#32311yescharacteristic
223D3—81no—
224C22—21no—
225C22—41no—
226C22—122no—
227C22—121no—
228C22C3×(C2×D3)⋊C811yescharacteristic
229C4—21no—
230C4—121no—
231C4C3×#80611yescharacteristic
232C4C3×#82311yescharacteristic
233C3—21no—
234C3#6753111yescharacteristic, direct product factor
235C3C3×#132111yescharacteristic, complemented
236C2—21no—
237C2—41no—
238C2—241no—
239C2C3×#446811yescharacteristic
subgroupG/H
centerC3×C4#806
commutatorC2×C3×C4C2×C3×C8
FrattiniC2×M16C2×C3×D3
FittingC32×#349C2
socleC2×C32#323
prime radicalC2×C3×#235C4
cosocleC2×C3×M16C22×C3
hypercenterC3×#349D3
hypocenterC3C3×#1321
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ C3×#349

Complements

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

NH ≅ G/Ntype
2. C32×#349C2semidirect
3. C3×#4553C2semidirect
5. #67531C3direct (N × H)
17. C3×#349D3semidirect
18. C3×#349C2×C3semidirect
19. #4553C2×C3semidirect
68. #349C3×D3semidirect
197. C32#1321semidirect
234. C3#67531direct (N × H)
235. C3C3×#1321semidirect

Maximal subgroups

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

subgroupindex
C3×#51292
C32×#3492
C3×#45532
C3×#13213
#675313