Finite Group Databasebeta

← C3×#3568⋊C3 #11919852

Subgroups — C3×#3568⋊C3 #11919852

Order 1152.

426 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 38 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
1C3×#5464C211yesmaximal, characteristic, complemented
2C3×#3568C311yesmaximal, characteristic, complemented
3#3568⋊C3C313yesmaximal, direct product factor
4C3×#126⋊C3—42nomaximal
5C3×#120⋊C3—42nomaximal
6C2×C3×C42⋊C3—41nomaximal
7C3×#563—31no—
8C3×H(3,𝔽4)C2×C311yescharacteristic, complemented
9C3×#556—32no—
10C3×#551—32no—
11C3×#542—32no—
12C3×#538—32no—
13C3×#529—31no—
14#5464C2×C313yescomplemented
15C3×C22⋊A4—42no—
16C3×C42⋊C3—41no—
17C3×C42⋊C3—42no—
18#3568C3211yescharacteristic, complemented, Sylow
19C3×C4⋊Q8—32no—
20C3×#126—32no—
21C3×#126—32no—
22C3×#126—32no—
23C3×#126—32no—
24C3×#126A412yescomplemented
25C3×#125—31no—
26C3×#124—32no—
27C3×#124—32no—
28C3×#124—31no—
29C3×#124—32no—
30C3×#123—32no—
31C3×#123—32no—
32C3×#123—32no—
33C3×C22⋊Q8—32no—
34C3×C22⋊Q8—32no—
35C3×C22⋊Q8—31no—
36C3×C22⋊Q8—32no—
37C3×#121—31no—
38C3×#121—32no—
39C3×#120—32no—
40C3×#120A412yescomplemented
41C3×C4×Q8—31no—
42C3×C4×Q8—32no—
43C3×C4×D4—32no—
44C3×C4×D4—31no—
45C3×C4×D4—32no—
46C3×#117—32no—
47C3×#117—32no—
48C2×C3×C22⋊C4—32no—
49C2×C3×C42A411yescharacteristic, complemented
50#126⋊C3—46no—
51#120⋊C3—46no—
52C2×C42⋊C3—43no—
53C2×C3×A4—161no—
54#563—31no—
55H(3,𝔽4)C2×C3211yescharacteristic, complemented
56#556—32no—
57#551—32no—
58#542—32no—
59#538—32no—
60#529—31no—
61C24×C3C2×A412yes—
62C22⋊A4—46no—
63C2×C3×Q8—32no—
64C2×C3×Q8—31no—
65C2×C3×D4—31no—
66C2×C3×D4—32no—
67C2×C3×D4—32no—
68C22×C3×C4—32no—
69C22×C3×C4—32no—
70C22×C3×C4—31no—
71C3×C4⋊C4—32no—
72C3×C4⋊C4—32no—
73C3×C4⋊C4—32no—
74C3×C4⋊C4—32no—
75C3×C4⋊C4—31no—
76C3×C4⋊C4—32no—
77C3×C4⋊C4—31no—
78C3×C4⋊C4—32no—
79C3×C22⋊C4—32no—
80C3×C22⋊C4—32no—
81C3×C22⋊C4—32no—
82C3×C22⋊C4—32no—
83C3×C22⋊C4—32no—
84C3×C22⋊C4—32no—
85C3×C22⋊C4—32no—
86C3×C22⋊C4—32no—
87C3×C22⋊C4—32no—
88C3×C42—31no—
89C3×C42—32no—
90C3×C42—32no—
91C3×C42C2×A411yescharacteristic
92C3×C42C2×A412yes—
93C42⋊C3—43no—
94C42⋊C3—46no—
95C3×A4—161no—
96C3×A4—324no—
97C4⋊Q8—32no—
98#126—32no—
99#126—32no—
100#126—32no—
101#126—32no—
102#126C3×A412yescomplemented
103#125—31no—
104#124—32no—
105#124—32no—
106#124—31no—
107#124—32no—
108#123—32no—
109#123—32no—
110#123—32no—
111C22⋊Q8—31no—
112C22⋊Q8—32no—
113C22⋊Q8—32no—
114C22⋊Q8—32no—
115#121—31no—
116#121—32no—
117#120—32no—
118#120C3×A412yescomplemented
119C4×Q8—31no—
120C4×Q8—32no—
121C4×D4—32no—
122C4×D4—31no—
123C4×D4—32no—
124#117—32no—
125#117—32no—
126C2×C22⋊C4—32no—
127C2×C42C3×A411yescharacteristic, complemented
128C23×C3—32no—
129C23×C3—122no—
130C23×C3C22⋊A411yescharacteristic
131C2×A4—163no—
132C3×Q8—122no—
133C3×Q8—121no—
134C3×D4—122no—
135C3×D4—121no—
136C3×D4—122no—
137C2×C3×C4—31no—
138C2×C3×C4—32no—
139C2×C3×C4—32no—
140C2×C3×C4—31no—
141C2×C3×C4—32no—
142C2×C3×C4—122no—
143C2×C3×C4—121no—
144C2×C3×C4—122no—
145C2×C32—641no—
146C24C2×C3×A412yes—
147C2×Q8—32no—
148C2×Q8—31no—
149C2×D4—31no—
150C2×D4—32no—
151C2×D4—32no—
152C22×C4—32no—
153C22×C4—32no—
154C22×C4—31no—
155C4⋊C4—32no—
156C4⋊C4—32no—
157C4⋊C4—32no—
158C4⋊C4—32no—
159C4⋊C4—31no—
160C4⋊C4—32no—
161C4⋊C4—31no—
162C4⋊C4—32no—
163C22⋊C4—32no—
164C22⋊C4—32no—
165C22⋊C4—32no—
166C22⋊C4—32no—
167C22⋊C4—32no—
168C22⋊C4—32no—
169C22⋊C4—32no—
170C22⋊C4—32no—
171C22⋊C4—32no—
172C42—31no—
173C42—32no—
174C42—32no—
175C42C2×C3×A411yescharacteristic
176C42C2×C3×A412yes—
177C22×C3—61no—
178C22×C3—62no—
179C22×C3—62no—
180C22×C3—62no—
181C22×C3—84no—
182C22×C3C2×C22⋊A411yescharacteristic
183A4—163no—
184A4—3212no—
185C3×C4—61no—
186C3×C4—62no—
187C3×C4—62no—
188C3×C4—61no—
189C3×C4—62no—
190C32—641noSylow
191C23—32no—
192C23—122no—
193C23C3×C22⋊A411yescharacteristic
194Q8—122no—
195Q8—121no—
196D4—122no—
197D4—121no—
198D4—122no—
199C2×C4—31no—
200C2×C4—32no—
201C2×C4—32no—
202C2×C4—31no—
203C2×C4—32no—
204C2×C4—122no—
205C2×C4—121no—
206C2×C4—122no—
207C2×C3—31no—
208C2×C3—41no—
209C2×C3—122no—
210C2×C3—643no—
211C22—61no—
212C22—62no—
213C22—62no—
214C22—62no—
215C22—84no—
216C22C2×C3×C22⋊A411yescharacteristic
217C4—61no—
218C4—62no—
219C4—62no—
220C4—61no—
221C4—62no—
222C3—643no—
223C3#3568⋊C311yescharacteristic, direct product factor
224C2—31no—
225C2—41no—
226C2—122no—
subgroupG/H
center, hypercenterC3#3568⋊C3
commutator, cosocle, hypocenterH(3,𝔽4)C2×C32
FrattiniC22C2×C3×C22⋊A4
FittingC3×#3568C3
socleC22×C3C2×C22⋊A4
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#5464C2semidirect
2. C3×#3568C3semidirect
3. #3568⋊C3C3direct (N × H)
8. C3×H(3,𝔽4)C2×C3semidirect
14. #5464C2×C3semidirect
18. #3568C32semidirect
24. C3×#126A4semidirect
40. C3×#120A4semidirect
49. C2×C3×C42A4semidirect
55. H(3,𝔽4)C2×C32semidirect
102. #126C3×A4semidirect
118. #120C3×A4semidirect
127. C2×C42C3×A4semidirect
223. C3#3568⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#54642
C3×#35683
#3568⋊C33
C3×#126⋊C34
C3×#120⋊C34
C2×C3×C42⋊C34