Finite Group Databasebeta

← C3×#71896 #11793127

Subgroups — C3×#71896 #11793127

Order 1152.

677 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 677 conjugacy classes of subgroups — too many to draw. Only its 134 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, complemented
2C2×C3×#806C213yesmaximal
3C3×#4527C213yesmaximal, complemented
4C3×#2032—31nomaximal
5#71896C311yesmaximal, characteristic, direct product factor
6C22×C3×#67C2211yescharacteristic
7C32×C22⋊Q8—26no—
8C2×C32×C22⋊C4C2213yes—
9C2×C3×#217C2213yes—
10C3×#806—26no—
11C3×#543—21no—
12C3×#543D311yescharacteristic, complemented
13C3×#543C2×C311yescharacteristic, complemented
14C2×C3×#99—33no—
15C2×#806C2×C313yes—
16C3×#342—33no—
17#4527C2×C313yescomplemented
18C24×C32C2311yescharacteristic
19C23×C3×D3Q811yescharacteristic, complemented
20C2×C32×Q8—22no—
21C22×C32×C4—23no—
22C2×C3×#67—23no—
23C2×C3×#67—23no—
24C22×C3×Dic3—23no—
25C22×C3×Dic3Q811yescharacteristic, complemented
26C32×C4⋊C4—26no—
27C32×C22⋊C4—23no—
28C32×C22⋊C4D416yes—
29C3×#217—23no—
30C3×#217—23no—
31#2032—31noSylow
32C22×C3×D4—31no—
33C22×#67C22×C311yescharacteristic
34C3×C22⋊Q8—212no—
35C3×C22⋊Q8—26no—
36C3×C22⋊Q8—26no—
37C2×C3×C22⋊C4—23no—
38C2×C3×C22⋊C4—33no—
39C2×C3×C22⋊C4C2×D313yes—
40C2×C3×C22⋊C4C22×C313yes—
41C2×#217C22×C313yes—
42C3×#99—66no—
43#806—26no—
44C23×C32—81no—
45C23×C32C2×D413yes—
46C23×C32C2×Q811yescharacteristic
47C23×C32#4113yes—
48C22×C3×D3—23no—
49C22×C3×D3—81no—
50C32×Q8—82no—
51C2×C32×C4—26no—
52C2×C32×C4—83no—
53C3×#67—41no—
54C3×#67—43no—
55C2×C3×Dic3—23no—
56C2×C3×Dic3—43no—
57C2×C3×Dic3—83no—
58#543C3×D311yescharacteristic, complemented
59C2×#99—33no—
60#342—33no—
61C24×C3—21no—
62C24×C3—31no—
63C24×C3C22×D311yescharacteristic
64C24×C3C23×C311yescharacteristic
65C23×D3C3×Q811yescharacteristic, complemented
66C2×C3×Q8—24no—
67C2×C3×Q8—22no—
68C2×C3×Q8—22no—
69C2×C3×D4—63no—
70C2×C3×D4—63no—
71C22×C3×C4—26no—
72C22×C3×C4—23no—
73C22×C3×C4—23no—
74C22×C3×C4—31no—
75C22×C3×C4—63no—
76C2×#67—23no—
77C2×#67—23no—
78C22×Dic3—23no—
79C22×Dic3C3×Q811yescharacteristic, complemented
80C3×C4⋊C4—212no—
81C3×C4⋊C4—26no—
82C3×C4⋊C4—26no—
83C3×C22⋊C4—26no—
84C3×C22⋊C4—23no—
85C3×C22⋊C4—23no—
86C3×C22⋊C4—26no—
87C3×C22⋊C4—63no—
88C3×C22⋊C4—63no—
89C3×C22⋊C4#6716yes—
90C3×C22⋊C4C3×D416yes—
91#217—23no—
92#217—23no—
93C22×C32—43no—
94C22×C32—43no—
95C22×C32—41no—
96C22×C32#12011yescharacteristic
97C22×C32C22⋊Q813yes—
98C22×C32#12413yes—
99C2×C3×D3—41no—
100C2×C3×D3—83no—
101C32×C4—46no—
102C3×Dic3—41no—
103C3×Dic3—83no—
104C22×D4—31no—
105C22⋊Q8—26no—
106C2×C22⋊C4—33no—
107C2×C22⋊C4C2×C3×D313yes—
108#99—66no—
109C23×C3—21no—
110C23×C3—23no—
111C23×C3—23no—
112C23×C3—63no—
113C23×C3—81no—
114C23×C3—81no—
115C23×C3—82no—
116C23×C3—241no—
117C23×C3D3×Q811yescharacteristic
118C23×C3#23913yes—
119C23×C3C2×#6713yes—
120C23×C3C2×C3×D413yes—
121C23×C3C2×C3×Q811yescharacteristic
122C23×C3C3×#4113yes—
123C22×D3—23no—
124C22×D3—81no—
125C3×Q8—84no—
126C3×Q8—82no—
127C3×Q8—82no—
128C3×D4—123no—
129C3×D4—121no—
130C2×C3×C4—212no—
131C2×C3×C4—26no—
132C2×C3×C4—26no—
133C2×C3×C4—63no—
134C2×C3×C4—83no—
135C2×C3×C4—83no—
136C2×C3×C4—86no—
137C2×C3×C4—123no—
138C2×C3×C4—243no—
139#67—41no—
140#67—43no—
141C2×Dic3—23no—
142C2×Dic3—43no—
143C2×Dic3—83no—
144C2×C32—21no—
145C2×C32—23no—
146C2×C32—23no—
147C2×C32#39311yescharacteristic
148C3×D3—81no—
149C24—31no—
150C24C22×C3×D311yescharacteristic
151C2×Q8—22no—
152C2×D4—63no—
153C2×D4—63no—
154C22×C4—23no—
155C22×C4—31no—
156C22×C4—63no—
157C4⋊C4—26no—
158C22⋊C4—23no—
159C22⋊C4—63no—
160C22⋊C4—63no—
161C22⋊C4C3×#6716yes—
162C22×C3—23no—
163C22×C3—23no—
164C22×C3—21no—
165C22×C3—43no—
166C22×C3—43no—
167C22×C3—43no—
168C22×C3—43no—
169C22×C3—41no—
170C22×C3—41no—
171C22×C3—46no—
172C22×C3—83no—
173C22×C3—81no—
174C22×C3—121no—
175C22×C3—243no—
176C22×C3#94613yes—
177C22×C3#94713yes—
178C22×C3#95311yescharacteristic
179C22×C3C3×#12011yescharacteristic
180C22×C3C3×C22⋊Q813yes—
181C22×C3C3×#12413yes—
182C2×D3—41no—
183C2×D3—83no—
184C3×C4—412no—
185C3×C4—46no—
186C3×C4—46no—
187C3×C4—121no—
188C3×C4—243no—
189Dic3—41no—
190Dic3—83no—
191C32#203211yescharacteristic, complemented, Sylow
192C23—63no—
193C23—81no—
194C23—241no—
195C23C3×D3×Q811yescharacteristic
196C23C3×#23913yes—
197C23C2×C3×#6713yes—
198Q8—82no—
199D4—123no—
200D4—121no—
201C2×C4—26no—
202C2×C4—63no—
203C2×C4—83no—
204C2×C4—123no—
205C2×C4—243no—
206C2×C3—22no—
207C2×C3—23no—
208C2×C3—21no—
209C2×C3—23no—
210C2×C3—21no—
211C2×C3—23no—
212C2×C3—23no—
213C2×C3—21no—
214C2×C3—43no—
215C2×C3—43no—
216C2×C3—241no—
217C2×C3#523111yescharacteristic
218C2×C3C3×#39311yescharacteristic
219D3—81no—
220C22—43no—
221C22—43no—
222C22—41no—
223C22—121no—
224C22—243no—
225C22C3×#94613yes—
226C22C3×#94713yes—
227C22C3×#95311yescharacteristic
228C4—46no—
229C4—121no—
230C4—243no—
231C3—21no—
232C3#7189611yescharacteristic, direct product factor
233C3C3×#203211yescharacteristic, complemented
234C2—21no—
235C2—23no—
236C2—23no—
237C2—241no—
238C2C3×#523111yescharacteristic
subgroupG/H
centerC2×C3#5231
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC32×#543C2
socleC2×C32#393
prime radicalC22×C3×#67C22
hypercenterC3×#543D3
hypocenterC3C3×#2032
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C24×C3 ◁ C3×#543

Complements

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

NH ≅ G/Ntype
1. C32×#543C2semidirect
3. C3×#4527C2semidirect
5. #71896C3direct (N × H)
12. C3×#543D3semidirect
13. C3×#543C2×C3semidirect
17. #4527C2×C3semidirect
19. C23×C3×D3Q8semidirect
25. C22×C3×Dic3Q8semidirect
58. #543C3×D3semidirect
65. C23×D3C3×Q8semidirect
79. C22×Dic3C3×Q8semidirect
191. C32#2032semidirect
232. C3#71896direct (N × H)
233. C3C3×#2032semidirect

Maximal subgroups

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

subgroupindex
C32×#5432
C2×C3×#8062
C3×#45272
C3×#20323
#718963