Finite Group Databasebeta

← C2×C3⋊(#395⋊C3) #11921363

Subgroups — C2×C3⋊(#395⋊C3) #11921363

Order 1152.

406 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 37 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×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic
2C3⋊(#395⋊C3)C212yesmaximal, direct product factor
3C2×#5230C311yesmaximal, characteristic, complemented
4C2×#395⋊C3—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6C2×Dic3×A4—41nomaximal
7C23×C3×Q8C2×C311yescharacteristic
8C2×C22⋊SL(2,𝔽3)—21no—
9C2×C22⋊SL(2,𝔽3)D311yescharacteristic
10C22×Dic3⋊C4—31no—
11#5230—32no—
12#5230C2×C312yescomplemented
13C2×C3⋊#95—31no—
14#395⋊C3—32no—
15C22×C3×A4—41no—
16C2×C3×SL(2,𝔽3)—82no—
17Dic3×A4—42no—
18C2×#395—31noSylow
19C22×C3×Q8—31no—
20C22×C3×Q8—62no—
21C22×C3×Q8—62no—
22C22×C3×Q8C22×C311yescharacteristic
23C23×C3×C4—31no—
24C23×Dic3—31no—
25C23×Dic3A411yescharacteristic
26C22⋊SL(2,𝔽3)—21no—
27C22⋊SL(2,𝔽3)C2×D311yescharacteristic
28C2×C4×A4—121no—
29C2×Dic3⋊C4—32no—
30C2×Dic3⋊C4—32no—
31C2×Dic3⋊C4—62no—
32C2×Dic3⋊C4—62no—
33C3⋊#95—32no—
34C3⋊#95—32no—
35C2×C3×A4—42no—
36C2×C3×A4—41no—
37C2×C3×Dic3—161no—
38C3×SL(2,𝔽3)—82no—
39C23×Q8C3×D311yescharacteristic
40C22×C4⋊C4—91no—
41#395—32no—
42#395—92no—
43C2×#95—91no—
44C24×C3C2×A411yescharacteristic
45C22×A4—41no—
46C22×A4—81no—
47C2×C3×Q8—22no—
48C2×C3×Q8—62no—
49C2×C3×Q8—62no—
50C2×C3×Q8—64no—
51C2×C3×Q8—62no—
52C2×C3×Q8—62no—
53C2×C3×Q8—64no—
54C2×C3×Q8—62no—
55C22×C3×C4—32no—
56C22×C3×C4—32no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—62no—
60C22×C3×C4—62no—
61C22×Dic3—34no—
62C22×Dic3—32no—
63C22×Dic3—61no—
64C22×Dic3—61no—
65C22×Dic3—61no—
66C22×Dic3—62no—
67C22×Dic3—61no—
68C22×Dic3C2×A412yes—
69C2×SL(2,𝔽3)—82no—
70C2×SL(2,𝔽3)—84no—
71C4×A4—122no—
72Dic3⋊C4—64no—
73Dic3⋊C4—64no—
74C22×C32—161no—
75C3×A4—41no—
76C3×Dic3—162no—
77C22×Q8—31no—
78C22×Q8—62no—
79C22×Q8—62no—
80C22×Q8C2×C3×D311yescharacteristic
81C23×C4—31no—
82C23×C4—31no—
83C23×C4—91no—
84C2×C4⋊C4—92no—
85C2×C4⋊C4—92no—
86C2×C4⋊C4—182no—
87C2×C4⋊C4—182no—
88#95—92no—
89#95—92no—
90C23×C3—32no—
91C23×C3—31no—
92C23×C3—31no—
93C23×C3#41⋊C312yes—
94C23×C3C22×A411yescharacteristic
95C2×A4—41no—
96C2×A4—42no—
97C2×A4—81no—
98C2×A4—82no—
99C3×Q8—22no—
100C3×Q8—62no—
101C3×Q8—62no—
102C3×Q8—62no—
103C3×Q8—64no—
104C2×C3×C4—32no—
105C2×C3×C4—32no—
106C2×C3×C4—62no—
107C2×C3×C4—64no—
108C2×C3×C4—62no—
109C2×C3×C4—62no—
110C2×C3×C4—62no—
111C2×C3×C4—481no—
112C2×Dic3—34no—
113C2×Dic3—41no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—64no—
117C2×Dic3—64no—
118C2×Dic3—62no—
119C2×Dic3—121no—
120SL(2,𝔽3)—82no—
121SL(2,𝔽3)—84no—
122C2×C32—162no—
123C2×C32—161no—
124C24D3×A411yescharacteristic
125C2×Q8—22no—
126C2×Q8—62no—
127C2×Q8—62no—
128C2×Q8—64no—
129C2×Q8—62no—
130C2×Q8—62no—
131C2×Q8—64no—
132C2×Q8—62no—
133C22×C4—32no—
134C22×C4—32no—
135C22×C4—31no—
136C22×C4—31no—
137C22×C4—32no—
138C22×C4—62no—
139C22×C4—62no—
140C22×C4—94no—
141C22×C4—92no—
142C22×C4—181no—
143C22×C4—181no—
144C22×C4—181no—
145C22×C4—182no—
146C22×C4—181no—
147C4⋊C4—184no—
148C4⋊C4—184no—
149C22×C3—31no—
150C22×C3—32no—
151C22×C3—32no—
152C22×C3—32no—
153C22×C3—32no—
154C22×C3—31no—
155C22×C3—31no—
156C22×C3—161no—
157C22×C3—321no—
158C22×C3#120⋊C311yescharacteristic
159C22×C3C2×#41⋊C311yescharacteristic
160A4—41no—
161A4—81no—
162C3×C4—62no—
163C3×C4—62no—
164C3×C4—482no—
165Dic3—42no—
166Dic3—64no—
167C32—161noSylow
168C23—31no—
169C23—32no—
170C23—31no—
171C23C3⋊(#41⋊C3)12yes—
172C23C2×D3×A411yescharacteristic
173Q8—22no—
174Q8—62no—
175Q8—62no—
176Q8—62no—
177Q8—64no—
178C2×C4—32no—
179C2×C4—32no—
180C2×C4—62no—
181C2×C4—64no—
182C2×C4—62no—
183C2×C4—62no—
184C2×C4—62no—
185C2×C4—94no—
186C2×C4—121no—
187C2×C4—182no—
188C2×C4—182no—
189C2×C4—184no—
190C2×C4—184no—
191C2×C4—182no—
192C2×C4—361no—
193C2×C3—31no—
194C2×C3—31no—
195C2×C3—32no—
196C2×C3—162no—
197C2×C3—161no—
198C2×C3—322no—
199C2×C3—321no—
200C2×C3#395⋊C312yescomplemented
201C2×C3C2×#120⋊C311yescharacteristic
202C22—31no—
203C22—32no—
204C22—32no—
205C22—32no—
206C22—32no—
207C22—31no—
208C22—31no—
209C22C3⋊(#120⋊C3)11yescharacteristic
210C22C2×C3⋊(#41⋊C3)11yescharacteristic
211C4—62no—
212C4—62no—
213C4—122no—
214C4—184no—
215C3—161no—
216C3—321no—
217C3C2×#395⋊C311yescharacteristic, complemented
218C2—31no—
219C2—31no—
220C2—32no—
221C2C3⋊(#395⋊C3)12yesdirect product factor
222C2C2×C3⋊(#120⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊(#120⋊C3)
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC23×C3×Q8C2×C3
socleC24×C3C2×A4
prime radicalC2×C3×C22⋊SL(2,𝔽3)C2
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C3⋊(#395⋊C3)C2direct (N × H)
3. C2×#5230C3semidirect
12. #5230C2×C3semidirect
200. C2×C3#395⋊C3semidirect
217. C3C2×#395⋊C3semidirect
221. C2C3⋊(#395⋊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×C22⋊SL(2,𝔽3)2
C3⋊(#395⋊C3)2
C2×#52303
C2×#395⋊C33
C2×Dic3×A44