Finite Group Databasebeta

← C2×C3⋊#4625 #11921036

Subgroups — C2×C3⋊#4625 #11921036

Order 1152.

334 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C2×C3×#120⋊C3C211yesmaximal, characteristic
2C3⋊#4625C212yesmaximal, direct product factor
3C2×#4625—33nomaximal
4C2×#4536—31nomaximal
5C2×C3×C22⋊A4C411yescharacteristic, complemented
6C2×C3⋊SL(2,ℤ/4)—41nomaximal
7C3×#120⋊C3C411yescharacteristic, complemented
8C3×#120⋊C3C2211yescharacteristic
9C2×C3×#120D311yescharacteristic
10C2×#120⋊C3D313yes—
11C2×#834—31no—
12C2×#833—31no—
13#4625—36no—
14#4536—32no—
15#4536—32no—
16C3×C22⋊A4C2×C411yescharacteristic, complemented
17C22×C3×A4—41no—
18C3⋊SL(2,ℤ/4)—42no—
19C2×AΣL(1,𝔽16)—91noSylow
20C25×C3Dic311yescharacteristic, complemented
21C2×C22⋊A4Dic313yescomplemented
22C22×C3×D4—31no—
23C2×SL(2,ℤ/4)—123no—
24C3×#120—31no—
25C3×#120—31no—
26C3×#120Dic311yescharacteristic, complemented
27C3×#120C2×D311yescharacteristic
28C2×C3×C22⋊C4—31no—
29C2×#217—61no—
30C2×#208—61no—
31#120⋊C3Dic313yescomplemented
32#120⋊C3C2×D313yes—
33#834—32no—
34#834—61no—
35#833—32no—
36#833—61no—
37C2×C3×A4—41no—
38C2×C3×A4—41no—
39C2×C3×A4—41no—
40C2×C3×A4—161no—
41C2×C3⋊Dic3—161no—
42C2×#120C3⋊D311yescharacteristic
43C2×#100—91no—
44C2×#99—91no—
45AΣL(1,𝔽16)—92no—
46AΣL(1,𝔽16)—92no—
47C24×C3—31no—
48C24×C3—31no—
49C24×C3—121no—
50C24×C3—121no—
51C24×C3C2×Dic311yescharacteristic, complemented
52C24×C3S411yescharacteristic
53C22⋊A4C2×Dic313yescomplemented
54C22×A4—43no—
55C2×C3×D4—31no—
56C2×C3×D4—31no—
57C2×C3×D4—31no—
58C2×C3×D4—31no—
59C2×C3×D4—121no—
60C2×C3×D4—121no—
61C22×C3×C4—31no—
62C22×Dic3—121no—
63SL(2,ℤ/4)—126no—
64C3×C22⋊C4—31no—
65C3×C22⋊C4—31no—
66C3×C22⋊C4—61no—
67#217—62no—
68#217—121no—
69#208—62no—
70#208—121no—
71C2×C3⋊C8—121no—
72C22×C32—161no—
73C3×A4—41no—
74C3×A4—161no—
75C3⋊Dic3—162no—
76C25C3⋊Dic311yescharacteristic, complemented
77C22×D4—31no—
78C2×M16—181no—
79#120—31no—
80#120—31no—
81#120C3⋊Dic311yescharacteristic, complemented
82#120C2×C3⋊D311yescharacteristic
83C2×C22⋊C4—31no—
84C2×C22⋊C4—181no—
85#100—92no—
86#100—181no—
87#99—92no—
88#99—181no—
89C23×C3—31no—
90C23×C3—31no—
91C23×C3—41no—
92C23×C3—61no—
93C23×C3—61no—
94C23×C3—61no—
95C23×C3—61no—
96C23×C3—121no—
97C23×C3—121no—
98C23×C3—121no—
99C23×C3—121no—
100C23×C3—122no—
101C23×C3—121no—
102C23×C3—121no—
103C23×C3—121no—
104C23×C3—122no—
105C23×C3SL(2,ℤ/4)11yescharacteristic
106C23×C3SL(2,ℤ/4)11yescharacteristic
107C23×C3C2×S411yescharacteristic
108C2×A4—43no—
109C2×A4—43no—
110C2×A4—43no—
111C2×A4—163no—
112C3×D4—121no—
113C3×D4—121no—
114C3×D4—121no—
115C3×D4—121no—
116C2×C3×C4—31no—
117C2×C3×C4—31no—
118C2×C3×C4—61no—
119C2×C3×C4—61no—
120C2×Dic3—122no—
121C2×Dic3—241no—
122C2×Dic3—241no—
123C2×Dic3—483no—
124C3⋊C8—122no—
125C2×C32—161no—
126C2×C32—161no—
127C2×C32—161no—
128C24—31no—
129C24—31no—
130C24—121no—
131C24—121no—
132C24C2×C3⋊Dic311yescharacteristic, complemented
133C24C3⋊S411yescharacteristic
134C2×D4—31no—
135C2×D4—31no—
136C2×D4—31no—
137C2×D4—31no—
138C2×D4—121no—
139C2×D4—121no—
140C22×C4—31no—
141C22×C4—361no—
142M16—182no—
143M16—361no—
144C2×C8—361no—
145C22⋊C4—31no—
146C22⋊C4—31no—
147C22⋊C4—61no—
148C22⋊C4—182no—
149C22⋊C4—361no—
150C22×C3—31no—
151C22×C3—31no—
152C22×C3—41no—
153C22×C3—41no—
154C22×C3—61no—
155C22×C3—61no—
156C22×C3—61no—
157C22×C3—61no—
158C22×C3—121no—
159C22×C3—121no—
160C22×C3—121no—
161C22×C3—122no—
162C22×C3—121no—
163C22×C3—121no—
164C22×C3—121no—
165C22×C3—121no—
166C22×C3—122no—
167C22×C3—121no—
168C22×C3—163no—
169C22×C3C2×SL(2,ℤ/4)11yescharacteristic
170A4—43no—
171A4—163no—
172C3×C4—61no—
173C3×C4—61no—
174Dic3—242no—
175Dic3—486no—
176C32—161noSylow
177C23—31no—
178C23—31no—
179C23—41no—
180C23—61no—
181C23—61no—
182C23—61no—
183C23—61no—
184C23—121no—
185C23—121no—
186C23—121no—
187C23—121no—
188C23—122no—
189C23—121no—
190C23—121no—
191C23—121no—
192C23—122no—
193C23C3⋊SL(2,ℤ/4)11yescharacteristic
194C23C3⋊SL(2,ℤ/4)11yescharacteristic
195C23C2×C3⋊S411yescharacteristic
196D4—121no—
197D4—121no—
198D4—121no—
199D4—121no—
200C2×C4—31no—
201C2×C4—31no—
202C2×C4—61no—
203C2×C4—61no—
204C2×C4—362no—
205C2×C4—721no—
206C2×C4—721no—
207C8—362no—
208C2×C3—31no—
209C2×C3—31no—
210C2×C3—41no—
211C2×C3—41no—
212C2×C3—121no—
213C2×C3—121no—
214C2×C3—163no—
215C2×C3—163no—
216C2×C3—163no—
217C2×C3#462511yescharacteristic, complemented
218C22—31no—
219C22—31no—
220C22—41no—
221C22—41no—
222C22—61no—
223C22—61no—
224C22—61no—
225C22—61no—
226C22—121no—
227C22—121no—
228C22—121no—
229C22—122no—
230C22—121no—
231C22—121no—
232C22—121no—
233C22—121no—
234C22—122no—
235C22—121no—
236C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
237C4—61no—
238C4—61no—
239C4—722no—
240C3—163no—
241C3C2×#462511yescharacteristic, complemented
242C2—31no—
243C2—31no—
244C2—41no—
245C2—41no—
246C2—121no—
247C2—121no—
248C2C3⋊#462511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#4625
commutator, hypocenterC3×C22⋊A4C2×C4
FrattiniC23C2×C3⋊S4
FittingC2×C3×#120D3
socleC23×C3SL(2,ℤ/4)
prime radicalC2×C3×#120⋊C3C2
cosocleC3×#120⋊C3C22
LCSG ▷ C3×C22⋊A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#4625C2direct (N × H)
5. C2×C3×C22⋊A4C4semidirect
7. C3×#120⋊C3C4semidirect
16. C3×C22⋊A4C2×C4semidirect
20. C25×C3Dic3semidirect
21. C2×C22⋊A4Dic3semidirect
26. C3×#120Dic3semidirect
31. #120⋊C3Dic3semidirect
51. C24×C3C2×Dic3semidirect
53. C22⋊A4C2×Dic3semidirect
76. C25C3⋊Dic3semidirect
81. #120C3⋊Dic3semidirect
132. C24C2×C3⋊Dic3semidirect
217. C2×C3#4625semidirect
241. C3C2×#4625semidirect
248. C2C3⋊#4625direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#120⋊C32
C3⋊#46252
C2×#46253
C2×#45363
C2×C3⋊SL(2,ℤ/4)4