Finite Group Databasebeta

← C4⋊(C3⋊#857) #11920938

Subgroups — C4⋊(C3⋊#857) #11920938

Order 1152.

376 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 33 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⋊#857C212yesmaximal, complemented
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C4⋊#857—33nomaximal
4#69395—31nomaximal
5C4⋊(C3⋊S4)—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3⋊#857—22no—
8#5477—31no—
9C2×#857—36no—
10C3×C43D311yescharacteristic, complemented
11C2×#805—32no—
12C2×#805—32no—
13#4924—31no—
14C4×C42⋊C3D313yescomplemented
15C2×C3⋊S4—42no—
16C3×C4×A4—41no—
17C3×C42⋊C3D411yescharacteristic, complemented
18#1962—91noSylow
19C2×#235—32no—
20C4⋊S4—123no—
21C2×C3×C42—31no—
22C2×C3×C42—31no—
23C2×C3×C42C2×D311yescharacteristic
24#930—61no—
25#930—61no—
26C2×#208—32no—
27#875—32no—
28#874—31no—
29C4×D12—61no—
30C4×D12—61no—
31#869—31no—
32C2×C42⋊C3C2×D313yes—
33#857—66no—
34#805—62no—
35#805—64no—
36#805—62no—
37C4⋊(C3⋊C8)—61no—
38C4⋊(C3⋊C8)—61no—
39C2×C3×A4—41no—
40C3⋊S4—82no—
41C4⋊(C3⋊D3)—161no—
42#532—91no—
43#423—91no—
44C2×#104—92no—
45C2×#104—92no—
46C43C3⋊D311yescharacteristic, complemented
47C2×S4—126no—
48C22×C3×C4—31no—
49C22×C3×C4—31no—
50C22×C3×C4S411yescharacteristic
51C2×#67—62no—
52#235—62no—
53#235—62no—
54#235—62no—
55#235—62no—
56C2×D12—32no—
57C2×D12—61no—
58C2×D12—61no—
59C2×C4×D3—62no—
60C2×Dic6—32no—
61C4×A4—43no—
62C3×C42—31no—
63C3×C42—31no—
64C3×C42—31no—
65C3×C42—31no—
66C3×C42—31no—
67C3×C42—32no—
68C3×C42—61no—
69C3×C42D1211yescharacteristic, complemented
70(C2×D3)⋊C4—62no—
71(C2×D3)⋊C4—62no—
72C4⋊Dic3—61no—
73C4⋊Dic3—61no—
74#208—62no—
75#208—62no—
76C2×C3⋊C8—62no—
77C42⋊C3D1213yescomplemented
78C2×C3⋊D3—162no—
79C3×A4—41no—
80C32×C4—161no—
81C2×#41—92no—
82C2×M16—92no—
83C4⋊Q8—91no—
84#127—91no—
85#124—92no—
86#121—181no—
87#121—181no—
88C4×D4—181no—
89C4×D4—181no—
90C2×C42—31no—
91C2×C42—31no—
92C2×C42C2×C3⋊D311yescharacteristic
93C4⋊C8—181no—
94C4⋊C8—181no—
95#104—182no—
96#104—184no—
97#104—182no—
98C23×C3C2×S411yescharacteristic
99C22×D3—62no—
100C2×A4—43no—
101S4—246no—
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—31no—
112C2×C3×C4—62no—
113#67—122no—
114#67—122no—
115C2×Dic3—62no—
116D12—62no—
117D12—62no—
118D12—122no—
119D12—121no—
120D12—121no—
121D12—483no—
122C4×D3—122no—
123C4×D3—122no—
124Dic6—62no—
125Dic6—62no—
126C3⋊C8—122no—
127C2×C32—161no—
128C3⋊D3—322no—
129#41—182no—
130#41—182no—
131#41—182no—
132#41—182no—
133C2×Q8—92no—
134C2×D4—92no—
135C2×D4—181no—
136C2×D4—181no—
137C2×D4—182no—
138C22×C4—31no—
139C22×C4—31no—
140C22×C4—182no—
141C22×C4C3⋊S411yescharacteristic
142M16—182no—
143M16—182no—
144C2×C8—182no—
145C4⋊C4—181no—
146C4⋊C4—181no—
147C22⋊C4—182no—
148C22⋊C4—182no—
149C42—31no—
150C42—31no—
151C42—31no—
152C42—31no—
153C42—31no—
154C42—32no—
155C42—61no—
156C42C4⋊(C3⋊D3)11yescharacteristic, complemented
157C22×C3—31no—
158C22×C3—31no—
159C22×C3C4⋊S411yescharacteristic
160C2×D3—122no—
161C2×D3—122no—
162C2×D3—122no—
163C2×D3—486no—
164A4—43no—
165C3×C4—31no—
166C3×C4—31no—
167C3×C4—31no—
168C3×C4—31no—
169C3×C4—32no—
170C3×C4—31no—
171C3×C4—61no—
172C3×C4—163no—
173C3×C4#85711yescharacteristic, complemented
174Dic3—122no—
175C32—161noSylow
176C23—182no—
177C23C2×C3⋊S411yescharacteristic
178Q8—182no—
179Q8—182no—
180D4—182no—
181D4—182no—
182D4—362no—
183D4—361no—
184D4—362no—
185D4—362no—
186D4—361no—
187C2×C4—31no—
188C2×C4—31no—
189C2×C4—31no—
190C2×C4—31no—
191C2×C4—31no—
192C2×C4—31no—
193C2×C4—31no—
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—62no—
198C2×C4—182no—
199C2×C4—362no—
200C2×C4—362no—
201C8—362no—
202C2×C3—31no—
203C2×C3—31no—
204C2×C3—163no—
205C2×C3C2×#85711yescharacteristic
206D3—242no—
207D3—966no—
208C22—31no—
209C22—31no—
210C22—362no—
211C22—362no—
212C22—362no—
213C22C4⋊(C3⋊S4)11yescharacteristic
214C4—31no—
215C4—31no—
216C4—31no—
217C4—31no—
218C4—32no—
219C4—31no—
220C4—61no—
221C4—362no—
222C4C3⋊#85711yescharacteristic, complemented
223C3—163no—
224C3C4⋊#85711yescharacteristic, complemented
225C2—31no—
226C2—31no—
227C2—722no—
228C2C2×C3⋊#85711yescharacteristic
subgroupG/H
centerC2C2×C3⋊#857
commutator, cosocleC2×C3×C42⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×C43D3
socleC23×C3C2×S4
hypercenterC4C3⋊#857
hypocenterC3×C42⋊C3D4
LCSG ▷ C2×C3×C42⋊C3 ▷ C3×C42⋊C3
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#857C2semidirect
2. C3×C4×C42⋊C3C2semidirect
10. C3×C43D3semidirect
14. C4×C42⋊C3D3semidirect
17. C3×C42⋊C3D4semidirect
46. C43C3⋊D3semidirect
69. C3×C42D12semidirect
77. C42⋊C3D12semidirect
156. C42C4⋊(C3⋊D3)semidirect
173. C3×C4#857semidirect
222. C4C3⋊#857semidirect
224. C3C4⋊#857semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#8572
C3×C4×C42⋊C32
C4⋊#8573
#693953
C4⋊(C3⋊S4)4