Finite Group Databasebeta

← C2×C3⋊(#458⋊C3) #11921375

Subgroups — C2×C3⋊(#458⋊C3) #11921375

Order 1152.

384 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 31 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×#997C211yesmaximal, characteristic
2C3⋊(#458⋊C3)C212yesmaximal, direct product factor
3C2×#5243C311yesmaximal, characteristic, complemented
4C2×#458⋊C3—31nomaximal
5C3×#997C2211yescharacteristic
6C2×Dic3×A4—41nomaximal
7C2×C3×H(5,𝔽2)C2×C311yescharacteristic
8C2×#997—21no—
9C2×#997D311yescharacteristic
10C2×#935—31no—
11#5243—32no—
12#5243C2×C312yescomplemented
13C2×#834—31no—
14#458⋊C3—32no—
15C22×C3×A4—41no—
16C22×C3×A4—81no—
17C2×C3×SL(2,𝔽3)—81no—
18Dic3×A4—42no—
19C2×#458—31noSylow
20C3×H(5,𝔽2)—31no—
21C3×H(5,𝔽2)—61no—
22C3×H(5,𝔽2)—61no—
23C3×H(5,𝔽2)C22×C311yescharacteristic
24C2×C3×#41—61no—
25C22×C3×D4—31no—
26C22×C3×D4—61no—
27C23×Dic3A411yescharacteristic, complemented
28#997—21no—
29#997C2×D311yescharacteristic
30C2×C4×A4—121no—
31C2×#217—31no—
32C2×#217—61no—
33#935—32no—
34#935—32no—
35#935—61no—
36#935—61no—
37C2×Dic3⋊C4—61no—
38#834—32no—
39#834—32no—
40C2×C3×A4—42no—
41C2×C3×A4—41no—
42C2×C3×A4—81no—
43C2×C3×A4—82no—
44C2×C3×Dic3—161no—
45C3×SL(2,𝔽3)—81no—
46C2×H(5,𝔽2)C3×D311yescharacteristic
47C2×#123—91no—
48#458—32no—
49#458—92no—
50C2×#99—91no—
51C24×C3—21no—
52C24×C3—31no—
53C24×C3C2×A411yescharacteristic
54C22×A4—41no—
55C22×A4—81no—
56C22×A4—82no—
57C22×A4—81no—
58C3×#41—61no—
59C3×#41—62no—
60C3×#41—61no—
61C3×#41—61no—
62C3×#41—62no—
63C3×#41—61no—
64C2×C3×Q8—21no—
65C2×C3×D4—31no—
66C2×C3×D4—31no—
67C2×C3×D4—31no—
68C2×C3×D4—31no—
69C2×C3×D4—61no—
70C2×C3×D4—62no—
71C2×C3×D4—62no—
72C2×C3×D4—62no—
73C2×C3×D4—61no—
74C2×C3×D4—61no—
75C2×C3×D4—62no—
76C2×C3×D4—61no—
77C2×C3×D4—61no—
78C22×C3×C4—31no—
79C22×C3×C4—61no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C22×Dic3C2×A412yescomplemented
84C2×SL(2,𝔽3)—81no—
85C2×SL(2,𝔽3)—82no—
86C4×A4—122no—
87#217—32no—
88#217—62no—
89#217—62no—
90#217—61no—
91Dic3⋊C4—62no—
92Dic3⋊C4—62no—
93C22×C32—161no—
94C3×A4—41no—
95C3×A4—81no—
96C3×Dic3—162no—
97H(5,𝔽2)—31no—
98H(5,𝔽2)—61no—
99H(5,𝔽2)—61no—
100H(5,𝔽2)C2×C3×D311yescharacteristic
101C2×#41—61no—
102C22×D4—31no—
103C22×D4—61no—
104C23×C4—31no—
105#123—92no—
106#123—92no—
107#123—181no—
108#123—181no—
109C2×C4⋊C4—181no—
110C2×C22⋊C4—91no—
111C2×C22⋊C4—181no—
112#99—92no—
113#99—92no—
114C23×C3—21no—
115C23×C3—31no—
116C23×C3—31no—
117C23×C3—31no—
118C23×C3—31no—
119C23×C3—42no—
120C23×C3—61no—
121C23×C3—61no—
122C23×C3—61no—
123C23×C3—82no—
124C23×C3—122no—
125C23×C3C22×A411yescharacteristic
126C2×A4—42no—
127C2×A4—41no—
128C2×A4—81no—
129C2×A4—82no—
130C2×A4—82no—
131C2×A4—82no—
132C2×A4—84no—
133C2×A4—81no—
134C3×Q8—21no—
135C3×Q8—61no—
136C3×D4—62no—
137C3×D4—62no—
138C3×D4—62no—
139C3×D4—62no—
140C3×D4—61no—
141C3×D4—61no—
142C3×D4—62no—
143C2×C3×C4—31no—
144C2×C3×C4—31no—
145C2×C3×C4—61no—
146C2×C3×C4—62no—
147C2×C3×C4—61no—
148C2×C3×C4—61no—
149C2×C3×C4—61no—
150C2×C3×C4—481no—
151C2×Dic3—41no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—121no—
155C2×Dic3—122no—
156SL(2,𝔽3)—81no—
157SL(2,𝔽3)—82no—
158C2×C32—162no—
159C2×C32—161no—
160C24—21no—
161C24—31no—
162C24D3×A411yescharacteristic
163#41—61no—
164#41—62no—
165#41—61no—
166#41—61no—
167#41—62no—
168#41—61no—
169C2×Q8—21no—
170C2×D4—31no—
171C2×D4—31no—
172C2×D4—31no—
173C2×D4—31no—
174C2×D4—61no—
175C2×D4—62no—
176C2×D4—62no—
177C2×D4—62no—
178C2×D4—61no—
179C2×D4—61no—
180C2×D4—62no—
181C2×D4—61no—
182C2×D4—61no—
183C22×C4—31no—
184C22×C4—32no—
185C22×C4—61no—
186C22×C4—181no—
187C22×C4—181no—
188C22×C4—181no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C22⋊C4—92no—
192C22⋊C4—181no—
193C22⋊C4—182no—
194C22⋊C4—182no—
195C22×C3—31no—
196C22×C3—31no—
197C22×C3—41no—
198C22×C3—62no—
199C22×C3—61no—
200C22×C3—61no—
201C22×C3—81no—
202C22×C3—121no—
203C22×C3—121no—
204C22×C3—121no—
205C22×C3—122no—
206C22×C3—161no—
207C22×C3—241no—
208C22×C3—241no—
209C22×C3—321no—
210C22×C3#120⋊C311yescharacteristic
211A4—41no—
212A4—81no—
213A4—81no—
214A4—82no—
215C3×C4—61no—
216C3×C4—61no—
217C3×C4—482no—
218Dic3—42no—
219Dic3—122no—
220C32—161noSylow
221C23—21no—
222C23—31no—
223C23—31no—
224C23—31no—
225C23—31no—
226C23—42no—
227C23—61no—
228C23—61no—
229C23—61no—
230C23—82no—
231C23—122no—
232C23C2×D3×A411yescharacteristic
233Q8—21no—
234Q8—61no—
235D4—62no—
236D4—62no—
237D4—62no—
238D4—62no—
239D4—61no—
240D4—61no—
241D4—62no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—61no—
245C2×C4—62no—
246C2×C4—61no—
247C2×C4—61no—
248C2×C4—61no—
249C2×C4—121no—
250C2×C4—182no—
251C2×C4—182no—
252C2×C4—361no—
253C2×C4—362no—
254C2×C3—61no—
255C2×C3—61no—
256C2×C3—121no—
257C2×C3—121no—
258C2×C3—162no—
259C2×C3—161no—
260C2×C3—322no—
261C2×C3—321no—
262C2×C3#458⋊C312yescomplemented
263C2×C3C2×#120⋊C311yescharacteristic
264C22—31no—
265C22—31no—
266C22—41no—
267C22—62no—
268C22—61no—
269C22—61no—
270C22—81no—
271C22—121no—
272C22—121no—
273C22—121no—
274C22—122no—
275C22—241no—
276C22—241no—
277C22C3⋊(#120⋊C3)11yescharacteristic
278C4—61no—
279C4—61no—
280C4—122no—
281C4—362no—
282C3—161no—
283C3—321no—
284C3C2×#458⋊C311yescharacteristic, complemented
285C2—61no—
286C2—61no—
287C2—121no—
288C2—121no—
289C2C3⋊(#458⋊C3)12yesdirect product factor
290C2C2×C3⋊(#120⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊(#120⋊C3)
commutator, cosocle, hypocenterC3×H(5,𝔽2)C22×C3
FrattiniC23C2×D3×A4
FittingC2×C3×H(5,𝔽2)C2×C3
socleC22×C3#120⋊C3
prime radicalC2×C3×#997C2
LCSG ▷ C3×H(5,𝔽2)
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C3⋊(#458⋊C3)C2direct (N × H)
3. C2×#5243C3semidirect
12. #5243C2×C3semidirect
27. C23×Dic3A4semidirect
83. C22×Dic3C2×A4semidirect
262. C2×C3#458⋊C3semidirect
284. C3C2×#458⋊C3semidirect
289. C2C3⋊(#458⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9972
C3⋊(#458⋊C3)2
C2×#52433
C2×#458⋊C33
C2×Dic3×A44