Finite Group Databasebeta

← C3×#71895 #11794300

Subgroups — C3×#71895 #11794300

Order 1152.

749 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 749 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C32×#543C211yesmaximal, characteristic
2C3×#4946C213yesmaximal
3C3×#4526C213yesmaximal
4C3×#2062—31nomaximal
5#71895C311yesmaximal, characteristic, direct product factor
6C23×C3×Dic3C2211yescharacteristic
7C32×C22⋊Q8—23no—
8C32×C22⋊Q8—23no—
9C2×C32×C22⋊C4C2213yes—
10C2×C3×#217C2213yes—
11C2×C3×Dic3⋊C4—23no—
12C3×C3⋊#95—23no—
13C3×#543—21no—
14C3×#543D311yescharacteristic
15C3×#543C2×C311yescharacteristic
16C3×#385—33no—
17#4946C2×C313yes—
18C3×#342—33no—
19#4526C2×C313yes—
20C24×C32C2311yescharacteristic
21C2×C32×Q8—21no—
22C2×C32×Q8—21no—
23C22×C32×C4D413yes—
24C22×C32×C4D413yes—
25C22×C3×Dic3—23no—
26C22×C3×Dic3—23no—
27C22×C3×Dic3—42no—
28C32×C4⋊C4—23no—
29C32×C4⋊C4—23no—
30C32×C22⋊C4—26no—
31C3×#217—23no—
32C3×#217Q816yescomplemented
33C3×Dic3⋊C4—46no—
34#2062—31noSylow
35C23×C3×C4—31no—
36C23×Dic3C22×C311yescharacteristic
37C3×C22⋊Q8—26no—
38C3×C22⋊Q8—26no—
39C3×C22⋊Q8—23no—
40C3×C22⋊Q8—23no—
41C3×C22⋊Q8—23no—
42C3×C22⋊Q8—23no—
43C2×C3×C4⋊C4—63no—
44C2×C3×C22⋊C4—23no—
45C2×C3×C22⋊C4—33no—
46C2×C3×C22⋊C4C2×D313yes—
47C2×C3×C22⋊C4C22×C313yes—
48C2×#217C22×C313yes—
49C2×Dic3⋊C4—23no—
50C3×#95—63no—
51C3⋊#95—23no—
52C23×C32—41no—
53C23×C32—41no—
54C23×C32C2×D413yes—
55C23×C32C2×Q813yes—
56C23×C32#4111yescharacteristic
57C32×Q8—81no—
58C32×Q8—81no—
59C2×C32×C4—23no—
60C2×C32×C4—23no—
61C2×C32×C4—43no—
62C2×C32×C4—43no—
63C2×C3×Dic3—26no—
64C2×C3×Dic3—26no—
65C2×C3×Dic3—43no—
66C2×C3×Dic3—43no—
67C2×C3×Dic3—43no—
68C2×C3×Dic3—41no—
69#543C3×D311yescharacteristic
70#385—33no—
71#342—33no—
72C24×C3—21no—
73C24×C3C22×D311yescharacteristic
74C24×C3C23×C311yescharacteristic
75C2×C3×Q8—22no—
76C2×C3×Q8—22no—
77C2×C3×Q8—21no—
78C2×C3×Q8—21no—
79C2×C3×Q8—21no—
80C2×C3×Q8—21no—
81C22×C3×C4—23no—
82C22×C3×C4—23no—
83C22×C3×C4—63no—
84C22×C3×C4—63no—
85C22×C3×C4—122no—
86C22×C3×C4#6713yes—
87C22×C3×C4#6713yes—
88C22×C3×C4C3×D413yes—
89C22×C3×C4C3×D413yes—
90C22×Dic3—23no—
91C22×Dic3—23no—
92C22×Dic3—42no—
93C3×C4⋊C4—26no—
94C3×C4⋊C4—26no—
95C3×C4⋊C4—23no—
96C3×C4⋊C4—23no—
97C3×C4⋊C4—23no—
98C3×C4⋊C4—23no—
99C3×C4⋊C4—126no—
100C3×C22⋊C4—212no—
101C3×C22⋊C4—26no—
102C3×C22⋊C4—26no—
103C3×C22⋊C4—36no—
104C3×C22⋊C4—63no—
105#217—23no—
106#217C3×Q816yescomplemented
107Dic3⋊C4—46no—
108C22×C32—23no—
109C22×C32—23no—
110C22×C32—43no—
111C22×C32—41no—
112C22×C32#12011yescharacteristic
113C22×C32C22⋊Q813yes—
114C22×C32C4⋊Q813yes—
115C32×C4—43no—
116C32×C4—43no—
117C3×Dic3—46no—
118C3×Dic3—42no—
119C23×C4—31no—
120C22⋊Q8—23no—
121C22⋊Q8—23no—
122C2×C4⋊C4—63no—
123C2×C22⋊C4—33no—
124C2×C22⋊C4C2×C3×D313yes—
125#95—63no—
126C23×C3—23no—
127C23×C3—21no—
128C23×C3—23no—
129C23×C3—41no—
130C23×C3—41no—
131C23×C3—41no—
132C23×C3—41no—
133C23×C3—81no—
134C23×C3—81no—
135C23×C3D3×Q813yes—
136C23×C3#23911yescharacteristic
137C23×C3C2×#6713yes—
138C23×C3C2×C3×D413yes—
139C23×C3C2×C3×Q813yes—
140C23×C3C3×#4111yescharacteristic
141C3×Q8—82no—
142C3×Q8—82no—
143C3×Q8—81no—
144C3×Q8—81no—
145C3×Q8—81no—
146C3×Q8—81no—
147C2×C3×C4—26no—
148C2×C3×C4—26no—
149C2×C3×C4—23no—
150C2×C3×C4—23no—
151C2×C3×C4—23no—
152C2×C3×C4—23no—
153C2×C3×C4—43no—
154C2×C3×C4—43no—
155C2×C3×C4—43no—
156C2×C3×C4—43no—
157C2×C3×C4—66no—
158C2×C3×C4—66no—
159C2×C3×C4—83no—
160C2×C3×C4—83no—
161C2×C3×C4—123no—
162C2×C3×C4—123no—
163C2×C3×C4—123no—
164C2×C3×C4—121no—
165C2×Dic3—26no—
166C2×Dic3—26no—
167C2×Dic3—43no—
168C2×Dic3—43no—
169C2×Dic3—43no—
170C2×Dic3—41no—
171C2×C32—23no—
172C2×C32—23no—
173C2×C32#39511yescharacteristic
174C2×C32B(4,𝔽2)11yescharacteristic
175C2×C32#45811yescharacteristic
176C24C22×C3×D311yescharacteristic
177C2×Q8—21no—
178C2×Q8—21no—
179C22×C4—63no—
180C22×C4—63no—
181C22×C4—122no—
182C22×C4C3×#6713yes—
183C22×C4C3×#6713yes—
184C4⋊C4—23no—
185C4⋊C4—23no—
186C4⋊C4—126no—
187C22⋊C4—26no—
188C22⋊C4—36no—
189C22⋊C4—63no—
190C22×C3—23no—
191C22×C3—23no—
192C22×C3—23no—
193C22×C3—23no—
194C22×C3—23no—
195C22×C3—23no—
196C22×C3—21no—
197C22×C3—43no—
198C22×C3—43no—
199C22×C3—43no—
200C22×C3—41no—
201C22×C3—43no—
202C22×C3—41no—
203C22×C3—83no—
204C22×C3—81no—
205C22×C3#94413yes—
206C22×C3#94613yes—
207C22×C3#95311yescharacteristic
208C22×C3C3×#12011yescharacteristic
209C22×C3C3×C22⋊Q813yes—
210C22×C3C3×C4⋊Q813yes—
211C3×C4—46no—
212C3×C4—46no—
213C3×C4—43no—
214C3×C4—43no—
215C3×C4—43no—
216C3×C4—43no—
217C3×C4—126no—
218C3×C4—122no—
219Dic3—46no—
220Dic3—42no—
221C32#206211yescharacteristic, complemented, Sylow
222C23—41no—
223C23—41no—
224C23C3×D3×Q813yes—
225C23C3×#23911yescharacteristic
226C23C2×C3×#6713yes—
227Q8—81no—
228Q8—81no—
229C2×C4—23no—
230C2×C4—23no—
231C2×C4—43no—
232C2×C4—43no—
233C2×C4—66no—
234C2×C4—66no—
235C2×C4—123no—
236C2×C4—123no—
237C2×C4—123no—
238C2×C4—121no—
239C2×C3—23no—
240C2×C3—23no—
241C2×C3—23no—
242C2×C3—23no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—43no—
247C2×C3—43no—
248C2×C3#523011yescharacteristic
249C2×C3#524311yescharacteristic
250C2×C3#524411yescharacteristic
251C2×C3C3×#39511yescharacteristic
252C2×C3C3×B(4,𝔽2)11yescharacteristic
253C2×C3C3×#45811yescharacteristic
254C22—23no—
255C22—23no—
256C22—43no—
257C22—41no—
258C22C3×#94413yes—
259C22C3×#94613yes—
260C22C3×#95311yescharacteristic
261C4—43no—
262C4—43no—
263C4—126no—
264C4—122no—
265C3—21no—
266C3#7189511yescharacteristic, direct product factor
267C3C3×#206211yescharacteristic, complemented
268C2—23no—
269C2—23no—
270C2C3×#523011yescharacteristic
271C2C3×#524311yescharacteristic
272C2C3×#524411yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC32×#543C2
socleC22×C32#120
prime radicalC24×C32C23
hypercenterC3×#543D3
hypocenterC3C3×#2062
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#543

Complements

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

NH ≅ G/Ntype
5. #71895C3direct (N × H)
32. C3×#217Q8semidirect
106. #217C3×Q8semidirect
221. C32#2062semidirect
266. C3#71895direct (N × H)
267. C3C3×#2062semidirect

Maximal subgroups

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

subgroupindex
C32×#5432
C3×#49462
C3×#45262
C3×#20623
#718953