Finite Group Databasebeta

← C3×#3549⋊C3 #11919846

Subgroups — C3×#3549⋊C3 #11919846

Order 1152.

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

normal subgroups only

This group has 526 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×#3549C311yesmaximal, characteristic, complemented
3#3549⋊C3C313yesmaximal, direct product factor
4C3×#127⋊C3—42nomaximal
5C3×#120⋊C3—42nomaximal
6C2×C3×C42⋊C3—41nomaximal
7C3×H(3,𝔽4)—31no—
8C3×H(3,𝔽4)C2×C311yescharacteristic, complemented
9C3×#555—32no—
10C3×D42—32no—
11C3×#535—32no—
12C3×#535—32no—
13C3×#532—31no—
14#5464C2×C313yescomplemented
15C3×C22⋊A4—42no—
16C3×C42⋊C3—41no—
17C3×C42⋊C3—42no—
18#3549C3211yescharacteristic, complemented, Sylow
19C2×C3×#41—31no—
20C2×C3×#41—31no—
21C22×C3×D4—32no—
22C22×C3×D4—32no—
23C3×C4⋊Q8—31no—
24C3×#127—31no—
25C3×#127—32no—
26C3×#127A412yescomplemented
27C3×#124—32no—
28C3×#124—34no—
29C3×#124—31no—
30C3×#124—31no—
31C3×#124—32no—
32C3×#121—34no—
33C3×#121—34no—
34C3×#121—34no—
35C3×#120—34no—
36C3×#120—32no—
37C3×#120—32no—
38C3×#120—32no—
39C3×#120A412yescomplemented
40C3×C4×D4—34no—
41C3×#117—32no—
42C3×#117—32no—
43C2×C3×C42A411yescharacteristic, complemented
44#127⋊C3—46no—
45#120⋊C3—46no—
46C2×C42⋊C3—43no—
47C2×C3×A4—161no—
48H(3,𝔽4)—31no—
49H(3,𝔽4)C2×C3211yescharacteristic, complemented
50#555—32no—
51D42—32no—
52#535—32no—
53#535—32no—
54#532—31no—
55C24×C3—32no—
56C24×C3C2×A412yes—
57C22⋊A4—46no—
58C3×#41—122no—
59C3×#41—122no—
60C2×C3×Q8—31no—
61C2×C3×Q8—31no—
62C2×C3×D4—34no—
63C2×C3×D4—32no—
64C2×C3×D4—31no—
65C2×C3×D4—31no—
66C2×C3×D4—34no—
67C2×C3×D4—32no—
68C2×C3×D4—32no—
69C2×C3×D4—32no—
70C2×C3×D4—124no—
71C2×C3×D4—124no—
72C22×C3×C4—32no—
73C22×C3×C4—32no—
74C22×C3×C4—31no—
75C3×C4⋊C4—34no—
76C3×C22⋊C4—34no—
77C3×C22⋊C4—32no—
78C3×C22⋊C4—34no—
79C3×C22⋊C4—34no—
80C3×C22⋊C4—32no—
81C3×C42—31no—
82C3×C42—32no—
83C3×C42C2×A411yescharacteristic
84C3×C42C2×A412yes—
85C42⋊C3—43no—
86C42⋊C3—46no—
87C3×A4—161no—
88C3×A4—324no—
89C2×#41—31no—
90C2×#41—31no—
91C22×D4—32no—
92C22×D4—32no—
93C4⋊Q8—31no—
94#127—31no—
95#127—32no—
96#127C3×A412yescomplemented
97#124—32no—
98#124—34no—
99#124—31no—
100#124—31no—
101#124—32no—
102#121—34no—
103#121—34no—
104#121—34no—
105#120—32no—
106#120—34no—
107#120—32no—
108#120—32no—
109#120C3×A412yescomplemented
110C4×D4—34no—
111#117—32no—
112#117—32no—
113C2×C42C3×A411yescharacteristic, complemented
114C23×C3—32no—
115C23×C3—32no—
116C23×C3—122no—
117C23×C3—122no—
118C23×C3—124no—
119C23×C3C22⋊A411yescharacteristic
120C2×A4—163no—
121C3×Q8—121no—
122C3×Q8—121no—
123C3×D4—68no—
124C3×D4—122no—
125C3×D4—124no—
126C3×D4—122no—
127C3×D4—122no—
128C3×D4—122no—
129C3×D4—121no—
130C3×D4—121no—
131C2×C3×C4—31no—
132C2×C3×C4—32no—
133C2×C3×C4—31no—
134C2×C3×C4—32no—
135C2×C3×C4—64no—
136C2×C3×C4—64no—
137C2×C3×C4—62no—
138C2×C32—641no—
139C24—32no—
140C24C2×C3×A412yes—
141#41—122no—
142#41—122no—
143C2×Q8—31no—
144C2×Q8—31no—
145C2×D4—34no—
146C2×D4—32no—
147C2×D4—31no—
148C2×D4—31no—
149C2×D4—34no—
150C2×D4—32no—
151C2×D4—32no—
152C2×D4—32no—
153C2×D4—124no—
154C2×D4—124no—
155C22×C4—32no—
156C22×C4—32no—
157C22×C4—31no—
158C4⋊C4—34no—
159C22⋊C4—34no—
160C22⋊C4—32no—
161C22⋊C4—34no—
162C22⋊C4—34no—
163C22⋊C4—32no—
164C42—31no—
165C42—32no—
166C42C2×C3×A411yescharacteristic
167C42C2×C3×A412yes—
168C22×C3—61no—
169C22×C3—62no—
170C22×C3—62no—
171C22×C3—64no—
172C22×C3—64no—
173C22×C3—84no—
174C22×C3—244no—
175C22×C3C2×C22⋊A411yescharacteristic
176A4—163no—
177A4—3212no—
178C3×C4—32no—
179C3×C4—62no—
180C3×C4—62no—
181C3×C4—61no—
182C32—641noSylow
183C23—32no—
184C23—32no—
185C23—122no—
186C23—122no—
187C23—124no—
188C23C3×C22⋊A411yescharacteristic
189Q8—121no—
190Q8—121no—
191D4—68no—
192D4—122no—
193D4—124no—
194D4—122no—
195D4—122no—
196D4—122no—
197D4—121no—
198D4—121no—
199C2×C4—31no—
200C2×C4—32no—
201C2×C4—31no—
202C2×C4—32no—
203C2×C4—64no—
204C2×C4—64no—
205C2×C4—62no—
206C2×C3—31no—
207C2×C3—41no—
208C2×C3—122no—
209C2×C3—122no—
210C2×C3—643no—
211C22—61no—
212C22—62no—
213C22—62no—
214C22—64no—
215C22—64no—
216C22—84no—
217C22—244no—
218C22C2×C3×C22⋊A411yescharacteristic
219C4—32no—
220C4—62no—
221C4—62no—
222C4—61no—
223C3—643no—
224C3#3549⋊C311yescharacteristic, direct product factor
225C2—31no—
226C2—41no—
227C2—122no—
228C2—122no—
subgroupG/H
center, hypercenterC3#3549⋊C3
commutator, cosocle, hypocenterH(3,𝔽4)C2×C32
FrattiniC22C2×C3×C22⋊A4
FittingC3×#3549C3
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×#3549C3semidirect
3. #3549⋊C3C3direct (N × H)
8. C3×H(3,𝔽4)C2×C3semidirect
14. #5464C2×C3semidirect
18. #3549C32semidirect
26. C3×#127A4semidirect
39. C3×#120A4semidirect
43. C2×C3×C42A4semidirect
49. H(3,𝔽4)C2×C32semidirect
96. #127C3×A4semidirect
109. #120C3×A4semidirect
113. C2×C42C3×A4semidirect
224. C3#3549⋊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×#35493
#3549⋊C33
C3×#127⋊C34
C3×#120⋊C34
C2×C3×C42⋊C34