Finite Group Databasebeta

← C2×#10593658 #11923064

Subgroups — C2×#10593658 #11923064

Order 1152.

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

normal subgroups only

This group has 848 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
1C22×C3×#41⋊C3C211yesmaximal, characteristic
2#10593658C214yesmaximal, direct product factor
3C2×C3⋊#859C212yesmaximal, complemented
4C2×#5424—33nomaximal
5C2×#5233—31nomaximal
6C2×C3×#41⋊C3C414yescomplemented
7C2×C3×#41⋊C3C2212yes—
8C22×C3×SL(2,𝔽3)C2211yescharacteristic
9C2×C4×C3⋊Dic3—41nomaximal
10C3⋊#859C2214yescomplemented
11C22×C3×#41D311yescharacteristic
12C22×#41⋊C3D313yes—
13C2×#926—31no—
14C23×C3⋊C8—31no—
15#5424—312no—
16C2×#859—36no—
17#5233—34no—
18#5233—34no—
19C2×#835—32no—
20C2×#832—32no—
21C22×C32×C4—41no—
22C22×C3⋊Dic3—42no—
23C3×#41⋊C3C2×C414yescomplemented
24C2×C3×SL(2,𝔽3)C2×C412yes—
25C2×C3×SL(2,𝔽3)C2311yescharacteristic
26C4×C3⋊Dic3—44no—
27C2×#416—91noSylow
28C2×C3×#41—34no—
29C2×C3×#41—32no—
30C2×C3×#41Dic314yescomplemented
31C2×C3×#41C2×D312yes—
32C22×C3×Q8C2×D311yescharacteristic
33C22×C3×D4—31no—
34C23×C3×C4—31no—
35C2×#41⋊C3Dic3112yescomplemented
36C2×#41⋊C3C2×D316yes—
37C22×SL(2,𝔽3)C2×D313yes—
38C2×#217—61no—
39#926—34no—
40#926—62no—
41C2×C4⋊Dic3—32no—
42C2×C4×Dic3—61no—
43C2×C4×Dic3—123no—
44C22×C3⋊C8—32no—
45C22×C3⋊C8—34no—
46C22×C3⋊C8—64no—
47#859—312no—
48#835—34no—
49#835—34no—
50#832—38no—
51C23×C32—41no—
52C2×C32×C4—44no—
53C2×C32×C4—42no—
54C2×C3⋊Dic3—44no—
55C2×C3⋊Dic3—48no—
56C3×SL(2,𝔽3)C22×C411yescharacteristic
57C22×#41C3⋊D311yescharacteristic
58C23×C8—91no—
59C2×#117—91no—
60#416—94no—
61#416—94no—
62C2×#103—92no—
63C2×#102—92no—
64C24×C3—31no—
65C3×#41—38no—
66C3×#41—34no—
67C3×#41—64no—
68C3×#41C2×Dic314yescomplemented
69C2×C3×Q8—31no—
70C2×C3×Q8—32no—
71C2×C3×Q8C2×Dic312yes—
72C2×C3×Q8C22×D311yescharacteristic
73C2×C3×D4—32no—
74C2×C3×D4—34no—
75C2×C3×D4—62no—
76C2×C3×D4—61no—
77C22×C3×C4—31no—
78C22×C3×C4—34no—
79C22×C3×C4—34no—
80C22×C3×C4—32no—
81C22×C3×C4—32no—
82C22×C3×C4—43no—
83C22×C3×C4S411yescharacteristic
84C22×Dic3—62no—
85C22×Dic3—126no—
86#41⋊C3C2×Dic3112yescomplemented
87C2×SL(2,𝔽3)C2×Dic316yes—
88C2×SL(2,𝔽3)C22×D313yes—
89#217—64no—
90C4⋊Dic3—34no—
91C4⋊Dic3—62no—
92C4×Dic3—64no—
93C4×Dic3—1212no—
94C2×C3⋊C8—34no—
95C2×C3⋊C8—64no—
96C2×C3⋊C8—68no—
97C22×C32—44no—
98C22×C32—42no—
99C22×C32—41no—
100C32×C4—44no—
101C3⋊Dic3—48no—
102C2×#41—32no—
103C2×#41—34no—
104C2×#41C3⋊Dic314yescomplemented
105C2×#41C2×C3⋊D312yes—
106C22×Q8C2×C3⋊D311yescharacteristic
107C22×D4—31no—
108C23×C4—31no—
109C22×C8—92no—
110C22×C8—94no—
111C22×C8—184no—
112#117—94no—
113#117—182no—
114C2×C4⋊C4—92no—
115C2×C22⋊C4—181no—
116C2×C42—181no—
117#103—94no—
118#103—94no—
119#102—98no—
120C23×C3—34no—
121C23×C3—32no—
122C23×C3—43no—
123C23×C3—64no—
124C23×C3C2×S411yescharacteristic
125C3×Q8—32no—
126C3×Q8—31no—
127C3×Q8—61no—
128C3×Q8C22×Dic311yescharacteristic
129C3×D4—34no—
130C3×D4—62no—
131C3×D4—64no—
132C2×C3×C4—32no—
133C2×C3×C4—32no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—34no—
137C2×C3×C4—34no—
138C2×C3×C4—38no—
139C2×C3×C4—46no—
140C2×C3×C4—412no—
141C2×C3×C4SL(2,ℤ/4)14yes—
142C2×C3×C4C2×S412yes—
143C2×Dic3—64no—
144C2×Dic3—1212no—
145C2×Dic3—1224no—
146C2×Dic3—124no—
147SL(2,𝔽3)C22×Dic313yes—
148C3⋊C8—64no—
149C2×C32—42no—
150C2×C32—41no—
151C2×C32—44no—
152C24—31no—
153#41—38no—
154#41—34no—
155#41—64no—
156#41C2×C3⋊Dic314yescomplemented
157C2×Q8—31no—
158C2×Q8—32no—
159C2×Q8C2×C3⋊Dic312yes—
160C2×Q8C22×C3⋊D311yescharacteristic
161C2×D4—32no—
162C2×D4—34no—
163C2×D4—62no—
164C2×D4—61no—
165C22×C4—31no—
166C22×C4—32no—
167C22×C4—32no—
168C22×C4—34no—
169C22×C4—34no—
170C22×C4—182no—
171C22×C4C3⋊S411yescharacteristic
172C2×C8—94no—
173C2×C8—184no—
174C2×C8—188no—
175C4⋊C4—94no—
176C4⋊C4—182no—
177C22⋊C4—184no—
178C42—184no—
179C22×C3—34no—
180C22×C3—412no—
181C22×C3—46no—
182C22×C3—43no—
183C22×C3—64no—
184C22×C3—68no—
185C22×C3#98514yes—
186C22×C3C2×SL(2,ℤ/4)12yes—
187C22×C3C22×S411yescharacteristic
188C3×C4—31no—
189C3×C4—31no—
190C3×C4—32no—
191C3×C4—412no—
192C3×C4C2×SL(2,ℤ/4)14yes—
193Dic3—1224no—
194Dic3—124no—
195C32—41noSylow
196C23—34no—
197C23—32no—
198C23—64no—
199C23C2×C3⋊S411yescharacteristic
200Q8—32no—
201Q8—31no—
202Q8—61no—
203Q8C22×C3⋊Dic311yescharacteristic
204D4—34no—
205D4—62no—
206D4—64no—
207C2×C4—32no—
208C2×C4—32no—
209C2×C4—31no—
210C2×C4—31no—
211C2×C4—34no—
212C2×C4—34no—
213C2×C4—38no—
214C2×C4—184no—
215C2×C4—364no—
216C2×C4C3⋊SL(2,ℤ/4)14yes—
217C2×C4C2×C3⋊S412yes—
218C8—184no—
219C2×C3—412no—
220C2×C3—46no—
221C2×C3—43no—
222C2×C3—64no—
223C2×C3#542414yescomplemented
224C2×C3C2×#98512yes—
225C2×C3C22×SL(2,ℤ/4)11yescharacteristic
226C22—34no—
227C22—68no—
228C22—64no—
229C22#6426614yes—
230C22C2×C3⋊SL(2,ℤ/4)12yes—
231C22C22×C3⋊S411yescharacteristic
232C4—31no—
233C4—31no—
234C4—32no—
235C4—364no—
236C4C2×C3⋊SL(2,ℤ/4)14yes—
237C3—43no—
238C3C2×#542411yescharacteristic, complemented
239C2—64no—
240C2#1059365814yesdirect product factor
241C2C2×#6426612yes—
242C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC22×C4C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C22×C3⋊S4
FittingC22×C3×#41D3
socleC23×C3C2×S4
prime radicalC22×C3×#41⋊C3C2
cosocleC2×C3×SL(2,𝔽3)C23
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593658C2direct (N × H)
3. C2×C3⋊#859C2semidirect
6. C2×C3×#41⋊C3C4semidirect
10. C3⋊#859C22semidirect
23. C3×#41⋊C3C2×C4semidirect
30. C2×C3×#41Dic3semidirect
35. C2×#41⋊C3Dic3semidirect
68. C3×#41C2×Dic3semidirect
86. #41⋊C3C2×Dic3semidirect
104. C2×#41C3⋊Dic3semidirect
156. #41C2×C3⋊Dic3semidirect
223. C2×C3#5424semidirect
238. C3C2×#5424semidirect
240. C2#10593658direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#41⋊C32
#105936582
C2×C3⋊#8592
C2×#54243
C2×#52333
C2×C4×C3⋊Dic34