Finite Group Databasebeta

← C22×C3⋊#857 #11922834

Subgroups — C22×C3⋊#857 #11922834

Order 1152.

892 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 892 conjugacy classes of subgroups — too many to draw. Only its 61 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×C42⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊#857C216yesmaximal, direct product factor
3C22×#857—33nomaximal
4C22×#805—31nomaximal
5C22×C3⋊S4—41nomaximal
6C2×C3×C42⋊C3C2213yescomplemented
7C3⋊#857C2214yesdirect product factor
8C22×#235—31no—
9C22×C3×C42D311yescharacteristic, complemented
10C22×#208—31no—
11C22×C42⋊C3D313yescomplemented
12C2×#857—318no—
13C2×#805—36no—
14C2×#805—36no—
15C22×C3×A4—41no—
16C2×C3⋊S4—46no—
17C3×C42⋊C3C2311yescharacteristic, complemented
18C22×#104—91noSylow
19C22×S4—123no—
20C23×C3×C4—31no—
21C22×#67—61no—
22C2×#235—36no—
23C2×#235—36no—
24C2×#235—63no—
25C2×#235—63no—
26C22×D12—31no—
27C22×C4×D3—61no—
28C22×Dic6—31no—
29C2×C3×C42—33no—
30C2×C3×C42C2×D313yescomplemented
31C2×#208—36no—
32C2×#208—63no—
33C22×C3⋊C8—61no—
34C2×C42⋊C3C2×D319yescomplemented
35#857—312no—
36#805—312no—
37#805—34no—
38C22×C3⋊D3—161no—
39C2×C3×A4—43no—
40C3⋊S4—44no—
41C22×#41—91no—
42C22×M16—91no—
43C22×C42C3⋊D311yescharacteristic, complemented
44C2×#104—96no—
45C2×#104—96no—
46C24×C3S411yescharacteristic
47C23×D3—61no—
48C22×A4—43no—
49C2×S4—1218no—
50C22×C3×C4—31no—
51C22×C3×C4—33no—
52C22×C3×C4—31no—
53C22×C3×C4—33no—
54C22×C3×C4—33no—
55C22×C3×C4—33no—
56C2×#67—66no—
57C2×#67—66no—
58C22×Dic3—61no—
59#235—34no—
60#235—312no—
61#235—66no—
62#235—612no—
63#235—66no—
64C2×D12—36no—
65C2×D12—63no—
66C2×C4×D3—66no—
67C2×C4×D3—66no—
68C2×Dic6—36no—
69C2×Dic6—63no—
70C3×C42—33no—
71C3×C42—61no—
72C3×C42C22×D311yescharacteristic, complemented
73#208—34no—
74#208—66no—
75C2×C3⋊C8—66no—
76C42⋊C3C22×D313yescomplemented
77C22×C32—161no—
78C2×C3⋊D3—166no—
79C3×A4—41no—
80C2×#41—96no—
81C2×#41—96no—
82C2×#41—183no—
83C2×#41—183no—
84C22×Q8—91no—
85C22×D4—91no—
86C22×D4—181no—
87C23×C4—31no—
88C23×C4—181no—
89C2×M16—96no—
90C2×M16—183no—
91C22×C8—181no—
92C2×C42—33no—
93C2×C42C2×C3⋊D313yescomplemented
94#104—912no—
95#104—94no—
96C23×C3—31no—
97C23×C3—33no—
98C23×C3C2×S413yes—
99C22×D3—66no—
100C22×D3—123no—
101C22×D3—121no—
102C22×D3—483no—
103C2×A4—49no—
104S4—1212no—
105C2×C3×C4—33no—
106C2×C3×C4—33no—
107C2×C3×C4—33no—
108C2×C3×C4—33no—
109C2×C3×C4—33no—
110C2×C3×C4—33no—
111C2×C3×C4—36no—
112C2×C3×C4—31no—
113C2×C3×C4—33no—
114#67—612no—
115#67—64no—
116C2×Dic3—66no—
117D12—34no—
118D12—66no—
119C4×D3—64no—
120C4×D3—612no—
121Dic6—34no—
122Dic6—66no—
123C3⋊C8—64no—
124C2×C32—163no—
125C3⋊D3—164no—
126C24—181no—
127C24C3⋊S411yescharacteristic
128#41—94no—
129#41—912no—
130#41—186no—
131#41—1812no—
132#41—186no—
133C2×Q8—96no—
134C2×Q8—183no—
135C2×D4—96no—
136C2×D4—183no—
137C2×D4—186no—
138C2×D4—186no—
139C22×C4—31no—
140C22×C4—33no—
141C22×C4—31no—
142C22×C4—33no—
143C22×C4—33no—
144C22×C4—33no—
145C22×C4—186no—
146C22×C4—186no—
147C22×C4—181no—
148M16—94no—
149M16—186no—
150C2×C8—186no—
151C42—33no—
152C42—61no—
153C42C22×C3⋊D311yescharacteristic, complemented
154C22×C3—33no—
155C22×C3—33no—
156C22×C3—33no—
157C22×C3—61no—
158C22×C3—163no—
159C22×C3#85711yescharacteristic, complemented
160C22×C3C22×S411yescharacteristic
161C2×D3—64no—
162C2×D3—126no—
163C2×D3—126no—
164C2×D3—4818no—
165A4—43no—
166C3×C4—31no—
167C3×C4—31no—
168C3×C4—33no—
169C3×C4—33no—
170Dic3—64no—
171C32—161noSylow
172C23—31no—
173C23—33no—
174C23—186no—
175C23—363no—
176C23—361no—
177C23C2×C3⋊S413yes—
178Q8—94no—
179Q8—186no—
180D4—94no—
181D4—186no—
182D4—1812no—
183D4—184no—
184C2×C4—33no—
185C2×C4—33no—
186C2×C4—33no—
187C2×C4—33no—
188C2×C4—33no—
189C2×C4—33no—
190C2×C4—36no—
191C2×C4—31no—
192C2×C4—33no—
193C2×C4—184no—
194C2×C4—1812no—
195C2×C4—186no—
196C8—184no—
197C2×C3—31no—
198C2×C3—33no—
199C2×C3—169no—
200C2×C3C2×#85713yescomplemented
201D3—124no—
202D3—4812no—
203C22—33no—
204C22—33no—
205C22—33no—
206C22—61no—
207C22—184no—
208C22—366no—
209C22—366no—
210C22C3⋊#85711yescharacteristic, direct product factor
211C22C22×C3⋊S411yescharacteristic
212C4—31no—
213C4—33no—
214C4—31no—
215C4—33no—
216C4—184no—
217C3—163no—
218C3C22×#85711yescharacteristic, complemented
219C2—31no—
220C2—33no—
221C2—364no—
222C2C2×C3⋊#85713yesdirect product factor
subgroupG/H
center, hypercenterC22C3⋊#857
commutator, cosocle, hypocenterC3×C42⋊C3C23
FrattiniC22C22×C3⋊S4
FittingC22×C3×C42D3
socleC24×C3S4
LCSG ▷ C3×C42⋊C3
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×C42⋊C3C2semidirect
2. C2×C3⋊#857C2direct (N × H)
6. C2×C3×C42⋊C3C22semidirect
7. C3⋊#857C22direct (N × H)
9. C22×C3×C42D3semidirect
11. C22×C42⋊C3D3semidirect
17. C3×C42⋊C3C23semidirect
30. C2×C3×C42C2×D3semidirect
34. C2×C42⋊C3C2×D3semidirect
43. C22×C42C3⋊D3semidirect
72. C3×C42C22×D3semidirect
76. C42⋊C3C22×D3semidirect
93. C2×C42C2×C3⋊D3semidirect
153. C42C22×C3⋊D3semidirect
159. C22×C3#857semidirect
200. C2×C3C2×#857semidirect
210. C22C3⋊#857direct (N × H)
218. C3C22×#857semidirect
222. C2C2×C3⋊#857direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C42⋊C32
C2×C3⋊#8572
C22×#8573
C22×#8053
C22×C3⋊S44