Finite Group Databasebeta

← C2×#10593654 #11923052

Subgroups — C2×#10593654 #11923052

Order 1152.

896 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 896 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C23×C3×SL(2,𝔽3)C211yesmaximal, characteristic
2#10593654C214yesmaximal, direct product factor
3C2×C3⋊#859C212yesmaximal, complemented
4C2×#5420—33nomaximal
5C2×#5225—31nomaximal
6C22×C3×SL(2,𝔽3)C414yescomplemented
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C22×C3×SL(2,𝔽3)C2212yes—
9C2×#3757—41nomaximal
10C3⋊#859C2214yescomplemented
11C23×C3×Q8D311yescharacteristic
12C23×SL(2,𝔽3)D313yes—
13C2×#926—31no—
14C22×#208—31no—
15#5420—312no—
16C2×#859—36no—
17#5225—34no—
18#5225—34no—
19C2×#835—32no—
20C2×#835—32no—
21C24×C32—41no—
22C22×C3⋊Dic3—42no—
23C2×C3×SL(2,𝔽3)C2×C412yes—
24C2×C3×SL(2,𝔽3)C2×C414yescomplemented
25C2×C3×SL(2,𝔽3)C2311yescharacteristic
26#3757—44no—
27C2×#419—91noSylow
28C22×C3×Q8—34no—
29C22×C3×Q8—31no—
30C22×C3×Q8—32no—
31C22×C3×Q8Dic314yescomplemented
32C22×C3×Q8C2×D311yescharacteristic
33C22×C3×Q8C2×D312yes—
34C23×C3×C4—31no—
35C22×SL(2,𝔽3)Dic3112yescomplemented
36C22×SL(2,𝔽3)C2×D313yes—
37C22×SL(2,𝔽3)C2×D316yes—
38C2×#217—61no—
39C2×#217—123no—
40#926—34no—
41#926—62no—
42C2×C4⋊Dic3—32no—
43C2×C4×Dic3—61no—
44C2×#208—34no—
45C2×#208—64no—
46C22×C3⋊C8—32no—
47#859—312no—
48#835—38no—
49#835—34no—
50#835—34no—
51C23×C32—44no—
52C23×C32—41no—
53C23×C32—42no—
54C23×C32—84no—
55C2×C3⋊Dic3—44no—
56C2×C3⋊Dic3—84no—
57C3×SL(2,𝔽3)C22×C411yescharacteristic
58C23×Q8C3⋊D311yescharacteristic
59C22×M16—91no—
60C2×#117—91no—
61#419—94no—
62#419—94no—
63C2×#103—92no—
64C2×#103—92no—
65C24×C3—43no—
66C24×C3S411yescharacteristic
67C2×C3×Q8—32no—
68C2×C3×Q8—31no—
69C2×C3×Q8—34no—
70C2×C3×Q8—38no—
71C2×C3×Q8—32no—
72C2×C3×Q8—34no—
73C2×C3×Q8—62no—
74C2×C3×Q8—64no—
75C2×C3×Q8—61no—
76C2×C3×Q8C2×Dic312yes—
77C2×C3×Q8C2×Dic314yescomplemented
78C2×C3×Q8C22×D311yescharacteristic
79C22×C3×C4—34no—
80C22×C3×C4—34no—
81C22×C3×C4—31no—
82C22×C3×C4—32no—
83C22×C3×C4—31no—
84C22×C3×C4—32no—
85C22×Dic3—62no—
86C22×Dic3—126no—
87C2×SL(2,𝔽3)C2×Dic316yes—
88C2×SL(2,𝔽3)C2×Dic3112yescomplemented
89C2×SL(2,𝔽3)C22×D313yes—
90#217—64no—
91#217—1212no—
92C4⋊Dic3—34no—
93C4⋊Dic3—62no—
94C4×Dic3—64no—
95#208—68no—
96C2×C3⋊C8—34no—
97C2×C3⋊C8—64no—
98C22×C32—44no—
99C22×C32—42no—
100C22×C32—44no—
101C22×C32—41no—
102C22×C32—84no—
103C22×C32—88no—
104C3⋊Dic3—84no—
105C22×Q8—31no—
106C22×Q8—32no—
107C22×Q8—34no—
108C22×Q8C3⋊Dic314yescomplemented
109C22×Q8C2×C3⋊D311yescharacteristic
110C22×Q8C2×C3⋊D312yes—
111C23×C4—31no—
112C2×M16—94no—
113C2×M16—184no—
114C22×C8—92no—
115#117—94no—
116#117—182no—
117C2×C4⋊C4—92no—
118C2×C22⋊C4—181no—
119C2×C42—181no—
120#103—98no—
121#103—94no—
122#103—94no—
123C23×C3—24no—
124C23×C3—46no—
125C23×C3—43no—
126C23×C3—412no—
127C23×C3—812no—
128C23×C3SL(2,ℤ/4)14yes—
129C23×C3C2×S412yes—
130C23×C3C2×S411yescharacteristic
131C3×Q8—32no—
132C3×Q8—34no—
133C3×Q8—31no—
134C3×Q8—61no—
135C3×Q8—62no—
136C3×Q8—64no—
137C3×Q8C22×Dic311yescharacteristic
138C2×C3×C4—32no—
139C2×C3×C4—34no—
140C2×C3×C4—32no—
141C2×C3×C4—34no—
142C2×C3×C4—38no—
143C2×C3×C4—34no—
144C2×C3×C4—31no—
145C2×C3×C4—32no—
146C2×C3×C4—31no—
147C2×Dic3—64no—
148C2×Dic3—1212no—
149C2×Dic3—124no—
150C2×Dic3—2412no—
151SL(2,𝔽3)C22×Dic313yes—
152C3⋊C8—64no—
153C2×C32—42no—
154C2×C32—41no—
155C2×C32—44no—
156C2×C32—84no—
157C24C3⋊S411yescharacteristic
158C2×Q8—32no—
159C2×Q8—31no—
160C2×Q8—34no—
161C2×Q8—38no—
162C2×Q8—32no—
163C2×Q8—34no—
164C2×Q8—62no—
165C2×Q8—64no—
166C2×Q8—61no—
167C2×Q8C2×C3⋊Dic312yes—
168C2×Q8C2×C3⋊Dic314yescomplemented
169C2×Q8C22×C3⋊D311yescharacteristic
170C22×C4—32no—
171C22×C4—32no—
172C22×C4—31no—
173C22×C4—31no—
174C22×C4—34no—
175C22×C4—34no—
176C22×C4—182no—
177M16—188no—
178C2×C8—94no—
179C2×C8—184no—
180C4⋊C4—94no—
181C4⋊C4—182no—
182C22⋊C4—184no—
183C42—184no—
184C22×C3—24no—
185C22×C3—28no—
186C22×C3—412no—
187C22×C3—46no—
188C22×C3—412no—
189C22×C3—43no—
190C22×C3—824no—
191C22×C3—812no—
192C22×C3#98314yes—
193C22×C3C2×SL(2,ℤ/4)14yes—
194C22×C3C2×SL(2,ℤ/4)12yes—
195C22×C3C22×S411yescharacteristic
196C3×C4—31no—
197C3×C4—31no—
198C3×C4—32no—
199C3×C4—34no—
200Dic3—124no—
201Dic3—2412no—
202C32—41noSylow
203C23—24no—
204C23C3⋊SL(2,ℤ/4)14yes—
205C23C2×C3⋊S412yes—
206C23C2×C3⋊S411yescharacteristic
207Q8—32no—
208Q8—34no—
209Q8—31no—
210Q8—61no—
211Q8—62no—
212Q8—64no—
213Q8C22×C3⋊Dic311yescharacteristic
214C2×C4—32no—
215C2×C4—34no—
216C2×C4—32no—
217C2×C4—34no—
218C2×C4—38no—
219C2×C4—34no—
220C2×C4—32no—
221C2×C4—31no—
222C2×C4—31no—
223C2×C4—184no—
224C2×C4—364no—
225C8—184no—
226C2×C3—24no—
227C2×C3—412no—
228C2×C3—46no—
229C2×C3—43no—
230C2×C3—812no—
231C2×C3#542014yescomplemented
232C2×C3C2×#98312yes—
233C2×C3C22×SL(2,ℤ/4)11yescharacteristic
234C22—28no—
235C22—24no—
236C22#6426414yes—
237C22C2×C3⋊SL(2,ℤ/4)14yes—
238C22C2×C3⋊SL(2,ℤ/4)12yes—
239C22C22×C3⋊S411yescharacteristic
240C4—31no—
241C4—31no—
242C4—32no—
243C4—34no—
244C4—364no—
245C3—43no—
246C3C2×#542011yescharacteristic, complemented
247C2—24no—
248C2#1059365414yesdirect product factor
249C2C2×#6426412yes—
250C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C22×C3⋊S4
FittingC23×C3×Q8D3
socleC23×C3C2×S4
prime radicalC23×C3×SL(2,𝔽3)C2
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC24C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. #10593654C2direct (N × H)
3. C2×C3⋊#859C2semidirect
6. C22×C3×SL(2,𝔽3)C4semidirect
10. C3⋊#859C22semidirect
24. C2×C3×SL(2,𝔽3)C2×C4semidirect
31. C22×C3×Q8Dic3semidirect
35. C22×SL(2,𝔽3)Dic3semidirect
77. C2×C3×Q8C2×Dic3semidirect
88. C2×SL(2,𝔽3)C2×Dic3semidirect
108. C22×Q8C3⋊Dic3semidirect
168. C2×Q8C2×C3⋊Dic3semidirect
231. C2×C3#5420semidirect
246. C3C2×#5420semidirect
248. C2#10593654direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×SL(2,𝔽3)2
#105936542
C2×C3⋊#8592
C2×#54203
C2×#52253
C2×#37574