Finite Group Databasebeta

← C2×#10593641 #11922999

Subgroups — C2×#10593641 #11922999

Order 1152.

672 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 81 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×#64267C212yesmaximal, complemented
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3#10593641C214yesmaximal, direct product factor
4C2×#5407—33nomaximal
5C2×#5142—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64267—22no—
8#64267C2214yescomplemented
9C2×C3⋊GL(2,𝔽3)—22no—
10C2×#3745—41nomaximal
11C3×#131⋊C3C2212yescomplemented
12C2×#986—36no—
13C2×C3×#131D311yescharacteristic, complemented
14C2×#949—32no—
15C22×D24—31no—
16C2×#131⋊C3D313yescomplemented
17#5407—312no—
18#5142—34no—
19#5142—34no—
20C2×#823—32no—
21C2×#819—31no—
22C2×C4⋊(C3⋊D3)—42no—
23C3×#41⋊C3D411yescharacteristic
24C3×#41⋊C3C2311yescharacteristic
25C2×C3×SL(2,𝔽3)D411yescharacteristic
26C3⋊GL(2,𝔽3)—24no—
27C2×C32×C8—41no—
28#3745—44no—
29C2×#472—91noSylow
30C2×C3×#41C2×D311yescharacteristic
31C22×D12—32no—
32C2×#41⋊C3C2×D313yes—
33#986—312no—
34#986—66no—
35C2×GL(2,𝔽3)—66no—
36C3×#131—32no—
37C3×#131C2×D312yescomplemented
38C2×C3×M16—31no—
39C22×C3×C8—31no—
40#949—34no—
41#949—34no—
42#949—62no—
43#949—62no—
44C2×#215—62no—
45C2×#213—62no—
46C2×#208—32no—
47C2×D24—34no—
48C2×D24—61no—
49C2×D24—62no—
50C2×D24—61no—
51C2×D24—123no—
52#131⋊C3C2×D316yescomplemented
53#823—38no—
54#819—34no—
55C22×C3⋊D3—82no—
56C2×C32×C4—41no—
57C4⋊(C3⋊D3)—44no—
58C4⋊(C3⋊D3)—82no—
59C3×SL(2,𝔽3)C2×D411yescharacteristic
60C32×C8—42no—
61C2×AGL(1,ℤ/8)—92no—
62C22×D8—91no—
63C2×#131C3⋊D311yescharacteristic, complemented
64#472—94no—
65#472—94no—
66C2×#108—91no—
67C2×#100—92no—
68C23×D3—62no—
69C3×#41—31no—
70C3×#41—31no—
71C3×#41D1211yescharacteristic
72C3×#41C22×D311yescharacteristic
73C2×C3×Q8D1211yescharacteristic
74C2×C3×D4—31no—
75C22×C3×C4—31no—
76C2×D12—34no—
77C2×D12—62no—
78C2×D12—62no—
79C2×D12—62no—
80C2×D12—62no—
81C2×D12—62no—
82C2×D12—126no—
83#41⋊C3D1213yes—
84#41⋊C3C22×D313yes—
85C2×SL(2,𝔽3)D1213yes—
86GL(2,𝔽3)—612no—
87C3×M16—32no—
88C3×M16—61no—
89C2×C3×C8—31no—
90C2×C3×C8—32no—
91C2×C3×C8—32no—
92C2×C3×C8—43no—
93C2×C3×C8S411yescharacteristic
94#215—64no—
95#215—64no—
96#213—64no—
97#213—64no—
98#208—34no—
99#208—62no—
100C2×C3⋊C8—62no—
101D24—64no—
102D24—64no—
103D24—1212no—
104C22×C32—41no—
105C2×C3⋊D3—84no—
106C2×C3⋊D3—164no—
107C32×C4—41no—
108C32×C4—41no—
109C2×#41C2×C3⋊D311yescharacteristic
110C22×D4—92no—
111AGL(1,ℤ/8)—94no—
112AGL(1,ℤ/8)—94no—
113AGL(1,ℤ/8)—182no—
114AGL(1,ℤ/8)—182no—
115C2×SD16—182no—
116C2×D8—94no—
117C2×D8—181no—
118C2×D8—182no—
119C2×D8—182no—
120C2×D8—181no—
121#131—32no—
122#131C2×C3⋊D312yescomplemented
123C2×M16—31no—
124C2×M16—92no—
125C22×C8—31no—
126#108—94no—
127#100—98no—
128C23×C3—31no—
129C22×D3—64no—
130C22×D3—122no—
131C22×D3—122no—
132C22×D3—246no—
133C22×D3—244no—
134C3×Q8—31no—
135C3×Q8C2×D1211yescharacteristic
136C3×D4—31no—
137C3×D4—31no—
138C3×D4—61no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—31no—
143C2×C3×C4—31no—
144C2×C3×C4—43no—
145C2×C3×C4C2×S411yescharacteristic
146D12—64no—
147D12—64no—
148D12—1212no—
149D12—122no—
150D12—122no—
151D12—246no—
152SL(2,𝔽3)C2×D1213yes—
153C3×C8—32no—
154C3×C8—46no—
155C3×C8C2×S412yes—
156C3⋊C8—64no—
157C2×C32—41no—
158C2×C32—42no—
159C3⋊D3—164no—
160C24—182no—
161#41—31no—
162#41—31no—
163#41C4⋊(C3⋊D3)11yescharacteristic
164#41C22×C3⋊D311yescharacteristic
165C2×Q8C4⋊(C3⋊D3)11yescharacteristic
166C2×D4—31no—
167C2×D4—94no—
168C2×D4—182no—
169C2×D4—182no—
170C2×D4—182no—
171C2×D4—182no—
172C2×D4—182no—
173C22×C4—31no—
174SD16—184no—
175SD16—184no—
176D8—184no—
177D8—184no—
178D8—184no—
179D8—184no—
180M16—32no—
181M16—61no—
182M16—94no—
183M16—182no—
184C2×C8—31no—
185C2×C8—32no—
186C2×C8—32no—
187C2×C8—182no—
188C2×C8C3⋊S411yescharacteristic
189C22×C3—31no—
190C22×C3—31no—
191C22×C3—43no—
192C22×C3—62no—
193C22×C3C4⋊S411yescharacteristic
194C2×D3—124no—
195C2×D3—2412no—
196C2×D3—244no—
197C2×D3—244no—
198C2×D3—244no—
199C2×D3—4812no—
200C3×C4—31no—
201C3×C4—31no—
202C3×C4—43no—
203C3×C4—43no—
204C3×C4C4⋊S411yescharacteristic
205C3×C4C22×S411yescharacteristic
206C32—41noSylow
207C23—31no—
208C23—184no—
209C23—362no—
210C23—362no—
211C23—724no—
212Q8—31no—
213Q8C2×C4⋊(C3⋊D3)11yescharacteristic
214D4—31no—
215D4—31no—
216D4—61no—
217D4—184no—
218D4—184no—
219D4—362no—
220D4—362no—
221C2×C4—31no—
222C2×C4—31no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4C2×C3⋊S411yescharacteristic
227C8—32no—
228C8—184no—
229C8C2×C3⋊S412yes—
230C2×C3—46no—
231C2×C3—43no—
232C2×C3—61no—
233C2×C3—61no—
234C2×C3#540712yescomplemented
235C2×C3C2×C4⋊S411yescharacteristic
236D3—244no—
237D3—4812no—
238C22—31no—
239C22—31no—
240C22—62no—
241C22—364no—
242C22—724no—
243C22—724no—
244C22—724no—
245C22C4⋊(C3⋊S4)11yescharacteristic
246C4—31no—
247C4—31no—
248C4C4⋊(C3⋊S4)11yescharacteristic
249C4C22×C3⋊S411yescharacteristic
250C3—43no—
251C3C2×#540711yescharacteristic, complemented
252C2—61no—
253C2—61no—
254C2—724no—
255C2#1059364112yesdirect product factor
256C2C2×C4⋊(C3⋊S4)11yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C22×C3⋊S4
FittingC2×C3×#131D3
socleC22×C3C4⋊S4
hypercenterC2×C8C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64267C2semidirect
2. C2×C3×#131⋊C3C2semidirect
3. #10593641C2direct (N × H)
8. #64267C22semidirect
11. C3×#131⋊C3C22semidirect
13. C2×C3×#131D3semidirect
16. C2×#131⋊C3D3semidirect
37. C3×#131C2×D3semidirect
52. #131⋊C3C2×D3semidirect
63. C2×#131C3⋊D3semidirect
122. #131C2×C3⋊D3semidirect
234. C2×C3#5407semidirect
251. C3C2×#5407semidirect
255. C2#10593641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642672
C2×C3×#131⋊C32
#105936412
C2×#54073
C2×#51423
C2×#37454