Finite Group Databasebeta

← C2×#10593660 #11923067

Subgroups — C2×#10593660 #11923067

Order 1152.

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

normal subgroups only

This group has 840 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#10593660C214yesmaximal, direct product factor
3C2×C3⋊#859C212yesmaximal, complemented
4C2×#5426—33nomaximal
5C2×#5232—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—
13C22×C4⋊Dic3—31no—
14C22×#208—31no—
15#5426—312no—
16C2×#859—36no—
17#5232—34no—
18#5232—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×C412yescomplemented
25C2×C3×SL(2,𝔽3)C2311yescharacteristic
26C4⋊(C3⋊Dic3)—44no—
27C2×#417—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—
35C23×Dic3—61no—
36C2×#41⋊C3Dic3112yescomplemented
37C2×#41⋊C3C2×D316yes—
38C22×SL(2,𝔽3)C2×D313yes—
39C2×C4⋊Dic3—32no—
40C2×C4⋊Dic3—34no—
41C2×C4⋊Dic3—62no—
42C2×C4⋊Dic3—61no—
43C2×C4⋊Dic3—123no—
44C2×#208—34no—
45C2×#208—64no—
46C22×C3⋊C8—32no—
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—84no—
56C3×SL(2,𝔽3)C22×C411yescharacteristic, complemented
57C22×#41C3⋊D311yescharacteristic
58C22×M16—91no—
59C22×C4⋊C4—91no—
60#417—94no—
61#417—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—64no—
85C22×Dic3—62no—
86C22×Dic3—126no—
87C22×Dic3—124no—
88#41⋊C3C2×Dic3112yescomplemented
89C2×SL(2,𝔽3)C2×Dic316yescomplemented
90C2×SL(2,𝔽3)C22×D313yes—
91C4⋊Dic3—34no—
92C4⋊Dic3—62no—
93C4⋊Dic3—64no—
94C4⋊Dic3—1212no—
95#208—68no—
96C2×C3⋊C8—34no—
97C2×C3⋊C8—64no—
98C22×C32—42no—
99C22×C32—42no—
100C22×C32—42no—
101C22×C32—41no—
102C32×C4—44no—
103C3⋊Dic3—84no—
104C2×#41—32no—
105C2×#41—34no—
106C2×#41C3⋊Dic314yescomplemented
107C2×#41C2×C3⋊D312yes—
108C22×Q8C2×C3⋊D311yescharacteristic
109C22×D4—31no—
110C23×C4—31no—
111C23×C4—181no—
112C2×M16—94no—
113C2×M16—184no—
114C22×C8—92no—
115C2×C4⋊C4—92no—
116C2×C4⋊C4—94no—
117C2×C4⋊C4—182no—
118C2×C4⋊C4—181no—
119#103—94no—
120#103—94no—
121#102—98no—
122C23×C3—34no—
123C23×C3—32no—
124C23×C3—43no—
125C23×C3—62no—
126C23×C3—62no—
127C23×C3C2×S411yescharacteristic
128C3×Q8—32no—
129C3×Q8—31no—
130C3×Q8—61no—
131C3×Q8C22×Dic311yescharacteristic
132C3×D4—34no—
133C3×D4—62no—
134C3×D4—64no—
135C2×C3×C4—32no—
136C2×C3×C4—32no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—34no—
140C2×C3×C4—34no—
141C2×C3×C4—38no—
142C2×C3×C4—46no—
143C2×C3×C4—412no—
144C2×C3×C4SL(2,ℤ/4)14yes—
145C2×C3×C4C2×S412yes—
146C2×Dic3—64no—
147C2×Dic3—1212no—
148C2×Dic3—128no—
149C2×Dic3—124no—
150C2×Dic3—2412no—
151SL(2,𝔽3)C22×Dic313yescomplemented
152C3⋊C8—64no—
153C2×C32—41no—
154C2×C32—41no—
155C2×C32—41no—
156C2×C32—44no—
157C24—31no—
158#41—38no—
159#41—34no—
160#41—64no—
161#41C2×C3⋊Dic314yescomplemented
162C2×Q8—31no—
163C2×Q8—32no—
164C2×Q8C2×C3⋊Dic312yes—
165C2×Q8C22×C3⋊D311yescharacteristic
166C2×D4—32no—
167C2×D4—34no—
168C2×D4—62no—
169C2×D4—61no—
170C22×C4—31no—
171C22×C4—32no—
172C22×C4—32no—
173C22×C4—34no—
174C22×C4—34no—
175C22×C4—184no—
176C22×C4—182no—
177C22×C4—364no—
178C22×C4C3⋊S411yescharacteristic
179M16—188no—
180C2×C8—94no—
181C2×C8—184no—
182C4⋊C4—94no—
183C4⋊C4—182no—
184C4⋊C4—184no—
185C22×C3—34no—
186C22×C3—46no—
187C22×C3—46no—
188C22×C3—46no—
189C22×C3—43no—
190C22×C3—62no—
191C22×C3—62no—
192C22×C3—68no—
193C22×C3#98412yes—
194C22×C3#98612yes—
195C22×C3C2×SL(2,ℤ/4)12yes—
196C22×C3C22×S411yescharacteristic
197C3×C4—31no—
198C3×C4—31no—
199C3×C4—32no—
200C3×C4—412no—
201C3×C4C2×SL(2,ℤ/4)14yes—
202Dic3—124no—
203Dic3—2412no—
204C32—41noSylow
205C23—34no—
206C23—32no—
207C23—62no—
208C23—62no—
209C23C2×C3⋊S411yescharacteristic
210Q8—32no—
211Q8—31no—
212Q8—61no—
213Q8C22×C3⋊Dic311yescharacteristic
214D4—34no—
215D4—62no—
216D4—64no—
217C2×C4—32no—
218C2×C4—32no—
219C2×C4—31no—
220C2×C4—31no—
221C2×C4—34no—
222C2×C4—34no—
223C2×C4—38no—
224C2×C4—184no—
225C2×C4—368no—
226C2×C4—364no—
227C2×C4C3⋊SL(2,ℤ/4)14yes—
228C2×C4C2×C3⋊S412yes—
229C8—184no—
230C2×C3—412no—
231C2×C3—43no—
232C2×C3—43no—
233C2×C3—43no—
234C2×C3—64no—
235C2×C3#542614yescomplemented
236C2×C3C2×#98411yescharacteristic
237C2×C3C2×#98611yescharacteristic
238C2×C3C22×SL(2,ℤ/4)11yescharacteristic
239C22—34no—
240C22—68no—
241C22—62no—
242C22—62no—
243C22#6426512yes—
244C22#6426712yes—
245C22C2×C3⋊SL(2,ℤ/4)12yes—
246C22C22×C3⋊S411yescharacteristic
247C4—31no—
248C4—31no—
249C4—32no—
250C4—364no—
251C4C2×C3⋊SL(2,ℤ/4)14yes—
252C3—43no—
253C3C2×#542611yescharacteristic, complemented
254C2—64no—
255C2#1059366014yesdirect product factor
256C2C2×#6426511yescharacteristic
257C2C2×#6426711yescharacteristic
258C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC23C2×C3⋊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
hypercenterC22×C4C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593660C2direct (N × H)
3. C2×C3⋊#859C2semidirect
6. C2×C3×#41⋊C3C4semidirect
10. C3⋊#859C22semidirect
23. C3×#41⋊C3C2×C4semidirect
24. C2×C3×SL(2,𝔽3)C2×C4semidirect
30. C2×C3×#41Dic3semidirect
36. C2×#41⋊C3Dic3semidirect
56. C3×SL(2,𝔽3)C22×C4semidirect
68. C3×#41C2×Dic3semidirect
88. #41⋊C3C2×Dic3semidirect
89. C2×SL(2,𝔽3)C2×Dic3semidirect
106. C2×#41C3⋊Dic3semidirect
151. SL(2,𝔽3)C22×Dic3semidirect
161. #41C2×C3⋊Dic3semidirect
235. C2×C3#5426semidirect
253. C3C2×#5426semidirect
255. C2#10593660direct (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
#105936602
C2×C3⋊#8592
C2×#54263
C2×#52323
C2×C4⋊(C3⋊Dic3)4