Finite Group Databasebeta

← C3×#2889⋊C3 #11919538

Subgroups — C3×#2889⋊C3 #11919538

Order 1152.

448 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 90 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×C3×2−1+4⋊C3C211yesmaximal, characteristic
2C3×#568⋊C3C212yesmaximal, complemented
3C3×#2889C311yesmaximal, characteristic, complemented
4#2889⋊C3C313yesmaximal, direct product factor
5C3×2−1+4⋊C3—22no—
6C2×C3×#41⋊C3C2211yescharacteristic
7C22×C3×SL(2,𝔽3)C412yes—
8C3×#131⋊C3—22no—
9C32×#100—41nomaximal
10C2×C3×2−1+4C2×C311yescharacteristic
11C2×2−1+4⋊C3C2×C313yes—
12C3×#568C2×C312yescomplemented
13#568⋊C3C2×C316yescomplemented
14C3×#413—31no—
15C3×#413—31no—
16C2×C3×#101—32no—
17C2×C32×D4—41no—
18C3×#41⋊C3D412yes—
19C2×C3×SL(2,𝔽3)—22no—
20C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
21C32×M16—42no—
22#2889C3211yescharacteristic, complemented, Sylow
23C3×2−1+4—22no—
24C3×2−1+4—62no—
25C2×C3×#41—31no—
26C2×C3×#41—32no—
27C2×C3×#41C22×C311yescharacteristic
28C22×C3×Q8—31no—
29C22×C3×Q8C3×C412yes—
302−1+4⋊C3—26no—
31C2×#41⋊C3C22×C313yes—
32C22×SL(2,𝔽3)C3×C416yes—
33C3×#131—22no—
34C3×#131—62no—
35C2×C3×M16—32no—
36C2×C3×M16—32no—
37#131⋊C3—26no—
38C3×#101—32no—
39C3×#101—32no—
40C3×#100—31no—
41C3×#100—43no—
42C3×#100A411yescharacteristic
43C23×C32—42no—
44C32×D4—82no—
45C2×C32×C4—41no—
46C3×SL(2,𝔽3)C22⋊C411yescharacteristic
47C32×C8—82no—
48C2×2−1+4C2×C3211yescharacteristic
49#568C2×C3212yescomplemented
50#413—31no—
51#413—31no—
52C2×#101—32no—
53C3×#41—32no—
54C3×#41—62no—
55C3×#41—62no—
56C3×#41—64no—
57C3×#41—64no—
58C3×#41C3×D412yes—
59C2×C3×Q8—22no—
60C2×C3×Q8—31no—
61C2×C3×Q8—32no—
62C2×C3×Q8—62no—
63C2×C3×Q8—62no—
64C2×C3×Q8—62no—
65C2×C3×Q8C2×C3×C411yescharacteristic
66C2×C3×D4—31no—
67C2×C3×D4—32no—
68C2×C3×D4—43no—
69C2×C3×D4C2×A411yescharacteristic
70C22×C3×C4—31no—
71C22×C3×C4—32no—
72C22×C3×C4—32no—
73#41⋊C3C3×D416yes—
74C2×SL(2,𝔽3)—26no—
75C2×SL(2,𝔽3)C2×C3×C413yes—
76C3×M16—32no—
77C3×M16—46no—
78C3×M16—62no—
79C3×M16—62no—
80C3×M16C2×A412yes—
81C2×C3×C8—62no—
82C2×C3×C8—62no—
83C22×C32—41no—
84C22×C32—82no—
85C22×C32—162no—
86C32×C4—42no—
872−1+4—22no—
882−1+4—62no—
89C2×#41—31no—
90C2×#41—32no—
91C2×#41C22×C3211yescharacteristic
92C22×Q8—31no—
93C22×Q8C32×C412yes—
94#131—22no—
95#131—62no—
96C2×M16—32no—
97C2×M16—32no—
98#101—32no—
99#101—32no—
100#100—31no—
101#100C3×A411yescharacteristic
102C23×C3—31no—
103C23×C3—46no—
104C23×C3C4×A412yes—
105C3×Q8—31no—
106C3×Q8—62no—
107C3×Q8—62no—
108C3×Q8—62no—
109C3×Q8C3×C22⋊C411yescharacteristic
110C3×D4—22no—
111C3×D4—32no—
112C3×D4—32no—
113C3×D4—64no—
114C3×D4—86no—
115C2×C3×C4—31no—
116C2×C3×C4—32no—
117C2×C3×C4—32no—
118C2×C3×C4—32no—
119C2×C3×C4—43no—
120C2×C3×C4—62no—
121C2×C3×C4—62no—
122C2×C3×C4—64no—
123C2×C3×C4C22×A411yescharacteristic
124SL(2,𝔽3)C3×C22⋊C413yes—
125C3×C8—22no—
126C3×C8—62no—
127C3×C8—86no—
128C2×C32—41no—
129C2×C32—81no—
130C2×C32—162no—
131#41—32no—
132#41—62no—
133#41—62no—
134#41—64no—
135#41—64no—
136#41C32×D412yes—
137C2×Q8—22no—
138C2×Q8—31no—
139C2×Q8—32no—
140C2×Q8—62no—
141C2×Q8—62no—
142C2×Q8—62no—
143C2×Q8C2×C32×C411yescharacteristic
144C2×D4—31no—
145C2×D4—32no—
146C2×D4C2×C3×A411yescharacteristic
147C22×C4—31no—
148C22×C4—32no—
149C22×C4—32no—
150M16—32no—
151M16—62no—
152M16—62no—
153M16C2×C3×A412yes—
154C2×C8—62no—
155C2×C8—62no—
156C22×C3—22no—
157C22×C3—32no—
158C22×C3—42no—
159C22×C3—43no—
160C22×C3—86no—
161C22×C3—121no—
162C22×C3—166no—
163C22×C3C2×C4×A411yescharacteristic
164C3×C4—31no—
165C3×C4—31no—
166C3×C4—46no—
167C3×C4—62no—
168C3×C4D4×A412yes—
169C32—41noSylow
170C23—31no—
171C23C3×C4×A412yes—
172Q8—31no—
173Q8—62no—
174Q8—62no—
175Q8—62no—
176Q8C32×C22⋊C411yescharacteristic
177D4—22no—
178D4—32no—
179D4—32no—
180D4—64no—
181C2×C4—31no—
182C2×C4—32no—
183C2×C4—32no—
184C2×C4—32no—
185C2×C4—62no—
186C2×C4—62no—
187C2×C4—64no—
188C2×C4C22×C3×A411yescharacteristic
189C8—22no—
190C8—62no—
191C2×C3—21no—
192C2×C3—42no—
193C2×C3—43no—
194C2×C3—62no—
195C2×C3—83no—
196C2×C3—166no—
197C2×C3A4×C22⋊C411yescharacteristic
198C22—22no—
199C22—32no—
200C22—42no—
201C22—121no—
202C22C2×C3×C4×A411yescharacteristic
203C4—31no—
204C4—31no—
205C4—62no—
206C4C3×D4×A412yes—
207C3—43no—
208C3#2889⋊C311yescharacteristic, direct product factor
209C2—21no—
210C2—42no—
211C2—62no—
212C2C3×A4×C22⋊C411yescharacteristic
subgroupG/H
center, socleC2×C3A4×C22⋊C4
commutatorC2×Q8C2×C32×C4
FrattiniC2×C4C22×C3×A4
FittingC3×#2889C3
prime radicalC2×C3×2−1+4⋊C3C2
cosocleC2×#41C22×C32
hypercenterC3×#100A4
hypocenterQ8C32×C22⋊C4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#100

Complements

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

NH ≅ G/Ntype
2. C3×#568⋊C3C2semidirect
3. C3×#2889C3semidirect
4. #2889⋊C3C3direct (N × H)
12. C3×#568C2×C3semidirect
13. #568⋊C3C2×C3semidirect
22. #2889C32semidirect
49. #568C2×C32semidirect
208. C3#2889⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×2−1+4⋊C32
C3×#568⋊C32
C3×#28893
#2889⋊C33
C32×#1004