Finite Group Databasebeta

← C3×#67453 #11771473

Subgroups — C3×#67453 #11771473

Order 1152.

307 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 307 conjugacy classes of subgroups — too many to draw. Only its 74 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×#4975C211yesmaximal, characteristic
2C32×#324C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4C3×#1325—31nomaximal
5#67453C311yesmaximal, characteristic, direct product factor
6C2×C32×C4⋊C4C2211yescharacteristic
7C2×C3×C4⋊Dic3C411yescharacteristic
8C2×C3×Dic3⋊C4—21no—
9C2×C3×Dic3⋊C4—21no—
10C2×C3×C4×Dic3C411yescharacteristic
11C32×C22⋊C8—21no—
12C3×#830—21no—
13C3×#384—31no—
14#4975C2×C311yescharacteristic
15C3×#324—21no—
16C3×#324—31no—
17C3×#324D311yescharacteristic
18C3×#324C2×C311yescharacteristic
19#4528C2×C311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3×Dic3—21no—
24C22×C3×Dic3—21no—
25C2×C32×C8—41no—
26C32×C4⋊C4—41no—
27C3×C4⋊Dic3—41no—
28C3×Dic3⋊C4—42no—
29C3×Dic3⋊C4—42no—
30C3×C4×Dic3—21no—
31C3×C4×Dic3C812yescomplemented
32C2×C3×C3⋊C8—41no—
33#1325—31noSylow
34C2×C3×C4⋊C4—21no—
35C2×C3×C4⋊C4—31no—
36C2×C3×C4⋊C4—61no—
37C2×C3×C4⋊C4—61no—
38C2×C3×C4⋊C4C2×D311yescharacteristic
39C2×C3×C4⋊C4C22×C311yescharacteristic
40C2×C3×C42—31no—
41C2×C4⋊Dic3C3×C411yescharacteristic
42C2×Dic3⋊C4—21no—
43C2×Dic3⋊C4—21no—
44C2×C4×Dic3C3×C411yescharacteristic
45C3×C22⋊C8—22no—
46C3×C22⋊C8—21no—
47C3×C22⋊C8—21no—
48C3×C22⋊C8—61no—
49#830—21no—
50C23×C32C22⋊C411yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4C2×C811yescharacteristic
58C2×C32×C4M1611yescharacteristic
59C2×C3×Dic3—22no—
60C2×C3×Dic3—22no—
61C2×C3×Dic3—22no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C32×C8—81no—
66C3×C3⋊C8—81no—
67#384—31no—
68#324—31no—
69#324C3×D311yescharacteristic
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4—21no—
73C22×C3×C4—61no—
74C22×C3×C4—61no—
75C22×C3×C4C4×D311yescharacteristic
76C22×C3×C4D1211yescharacteristic
77C22×C3×C4#6711yescharacteristic
78C22×C3×C4C2×C3×C411yescharacteristic
79C22×C3×C4C3×D411yescharacteristic
80C22×C3×C4C3×D411yescharacteristic
81C22×Dic3—21no—
82C22×Dic3—21no—
83C2×C3×C8—42no—
84C2×C3×C8—41no—
85C2×C3×C8—41no—
86C2×C3×C8—121no—
87C3×C4⋊C4—41no—
88C3×C4⋊C4—41no—
89C3×C4⋊C4—42no—
90C3×C4⋊C4—121no—
91C3×C4⋊C4—122no—
92C3×C4⋊C4—122no—
93C3×C42—32no—
94C3×C42—61no—
95C4⋊Dic3—41no—
96Dic3⋊C4—42no—
97Dic3⋊C4—42no—
98C4×Dic3—21no—
99C4×Dic3C3×C812yescomplemented
100C2×C3⋊C8—41no—
101C22×C32—21no—
102C22×C32—21no—
103C22×C32C22⋊C811yescharacteristic
104C22×C32#9911yescharacteristic
105C22×C32#10111yescharacteristic
106C32×C4—21no—
107C32×C4—21no—
108C32×C4—41no—
109C32×C4—41no—
110C3×Dic3—24no—
111C3×Dic3—81no—
112C2×C4⋊C4—31no—
113C2×C4⋊C4—61no—
114C2×C4⋊C4—61no—
115C2×C4⋊C4C2×C3×D311yescharacteristic
116C2×C42—31no—
117C22⋊C8—21no—
118C22⋊C8—61no—
119C23×C3—21no—
120C23×C3(C2×D3)⋊C411yescharacteristic
121C23×C3C3×C22⋊C411yescharacteristic
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—22no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—41no—
134C2×C3×C4—41no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×C3×C4—62no—
141C2×C3×C4—62no—
142C2×C3×C4—62no—
143C2×C3×C4—81no—
144C2×C3×C4—81no—
145C2×C3×C4—121no—
146C2×C3×C4—121no—
147C2×C3×C4—121no—
148C2×C3×C4D3×C811yescharacteristic
149C2×C3×C4ΓL(1,𝔽25)11yescharacteristic
150C2×C3×C4C2×C3×C811yescharacteristic
151C2×C3×C4C3×M1611yescharacteristic
152C2×Dic3—22no—
153C2×Dic3—22no—
154C2×Dic3—22no—
155C2×Dic3—41no—
156C2×Dic3—41no—
157C2×Dic3—41no—
158C3×C8—82no—
159C3×C8—81no—
160C3×C8—81no—
161C3×C8—241no—
162C3⋊C8—81no—
163C2×C32—21no—
164C2×C32—21no—
165C2×C32#32411yescharacteristic
166C2×C32#35311yescharacteristic
167C2×C32#35611yescharacteristic
168C22×C4—61no—
169C22×C4—61no—
170C22×C4C3×C4×D311yescharacteristic
171C22×C4C3×D1211yescharacteristic
172C22×C4C3×#6711yescharacteristic
173C2×C8—41no—
174C2×C8—121no—
175C4⋊C4—41no—
176C4⋊C4—121no—
177C4⋊C4—122no—
178C4⋊C4—122no—
179C42—32no—
180C42—61no—
181C22×C3—21no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—41no—
189C22×C3—41no—
190C22×C3#80611yescharacteristic
191C22×C3(C2×D3)⋊C811yescharacteristic
192C22×C3#82411yescharacteristic
193C22×C3C3×C22⋊C811yescharacteristic
194C22×C3C3×#9911yescharacteristic
195C22×C3C3×#10111yescharacteristic
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—41no—
201C3×C4—41no—
202C3×C4—42no—
203C3×C4—41no—
204C3×C4—41no—
205C3×C4—41no—
206C3×C4—41no—
207C3×C4—64no—
208C3×C4—81no—
209C3×C4—241no—
210Dic3—24no—
211Dic3—81no—
212C32#132511yescharacteristic, complemented, Sylow
213C23C3×(C2×D3)⋊C411yescharacteristic
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—62no—
221C2×C4—62no—
222C2×C4—62no—
223C2×C4—121no—
224C2×C4—121no—
225C2×C4—121no—
226C2×C4C3×D3×C811yescharacteristic
227C2×C4C3×ΓL(1,𝔽25)11yescharacteristic
228C8—81no—
229C8—241no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—41no—
238C2×C3—41no—
239C2×C3#446911yescharacteristic
240C2×C3#447411yescharacteristic
241C2×C3#447811yescharacteristic
242C2×C3C3×#32411yescharacteristic
243C2×C3C3×#35311yescharacteristic
244C2×C3C3×#35611yescharacteristic
245C22—21no—
246C22—21no—
247C22C3×#80611yescharacteristic
248C22C3×(C2×D3)⋊C811yescharacteristic
249C22C3×#82411yescharacteristic
250C4—21no—
251C4—21no—
252C4—41no—
253C4—41no—
254C4—64no—
255C4—241no—
256C3—21no—
257C3#6745311yescharacteristic, direct product factor
258C3C3×#132511yescharacteristic, complemented
259C2—21no—
260C2—21no—
261C2C3×#446911yescharacteristic
262C2C3×#447411yescharacteristic
263C2C3×#447811yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC2×C3×C4C2×C3×C8
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#324C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#324D3
hypocenterC3C3×#1325
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
5. #67453C3direct (N × H)
31. C3×C4×Dic3C8semidirect
99. C4×Dic3C3×C8semidirect
212. C32#1325semidirect
257. C3#67453direct (N × H)
258. C3C3×#1325semidirect

Maximal subgroups

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

subgroupindex
C3×#49752
C32×#3242
C3×#45282
C3×#13253
#674533