Finite Group Databasebeta

← C3×#3028⋊C3 #11919594

Subgroups — C3×#3028⋊C3 #11919594

Order 1152.

356 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 46 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×#5950C211yesmaximal, characteristic
2C3×#458⋊C3C212yesmaximal, complemented
3C3×#3028C311yesmaximal, characteristic, complemented
4#3028⋊C3C313yesmaximal, direct product factor
5C3×#997C2211yescharacteristic
6C3×Q8×A4—41nomaximal
7C3×#585C2×C311yescharacteristic
8#5950C2×C313yes—
9C3×#536—31no—
10C3×#458—32no—
11C3×#458C2×C312yes—
12C3×#410—31no—
13#458⋊C3C2×C316yescomplemented
14C3×#41⋊C3—81no—
15C3×C4×A4—41no—
16C3×C4×A4—42no—
17C3×C4×A4—81no—
18#3028C3211yescharacteristic, complemented, Sylow
19C3×2−1+4—61no—
20C3×H(5,𝔽2)—31no—
21C3×H(5,𝔽2)—61no—
22C3×H(5,𝔽2)C22×C311yescharacteristic
23C2×C3×#41—31no—
24C2×C3×#41—61no—
25C2×C3×#41—61no—
26C22×C3×Q8A411yescharacteristic, complemented
27#997C22×C313yes—
28Q8×A4—43no—
29C3×C4⋊Q8—61no—
30C3×#124—61no—
31C3×#123—32no—
32C3×#123—32no—
33C3×C22⋊Q8—61no—
34C3×C22⋊Q8—61no—
35C3×#117—31no—
36C3×#99—32no—
37C3×#99—32no—
38C2×C3×A4—41no—
39C2×C3×A4—81no—
40C32×Q8—161no—
41C3×SL(2,𝔽3)—81no—
42#585C2×C3211yescharacteristic
43#536—31no—
44#458—32no—
45#458C2×C3212yes—
46#410—31no—
47C3×#41—21no—
48C3×#41—62no—
49C3×#41—62no—
50C3×#41—61no—
51C3×#41—62no—
52C3×#41—61no—
53C3×#41—62no—
54C3×#41—62no—
55C3×#41—61no—
56C2×C3×Q8—31no—
57C2×C3×Q8—61no—
58C2×C3×Q8—61no—
59C2×C3×Q8—61no—
60C2×C3×Q8—61no—
61C2×C3×D4—31no—
62C2×C3×D4—31no—
63C2×C3×D4—31no—
64C2×C3×D4—61no—
65C2×C3×D4—62no—
66C2×C3×D4—61no—
67C2×C3×D4—61no—
68C2×C3×D4—61no—
69C22×C3×C4—21no—
70C22×C3×C4—31no—
71C22×C3×C4—31no—
72C22×C3×C4—61no—
73C22×C3×C4C2×A411yescharacteristic
74C22×C3×C4C2×A412yes—
75#41⋊C3—83no—
76C4×A4—46no—
77C4×A4—43no—
78C4×A4—83no—
79C3×C4⋊C4—61no—
80C3×C4⋊C4—62no—
81C3×C4⋊C4—62no—
82C3×C22⋊C4—32no—
83C3×C22⋊C4—62no—
84C3×C22⋊C4—62no—
85C3×C42—61no—
86C3×A4—41no—
87C3×A4—81no—
88C32×C4—162no—
89C32×C4—161no—
902−1+4—61no—
91H(5,𝔽2)—31no—
92H(5,𝔽2)—61no—
93H(5,𝔽2)C22×C3211yescharacteristic
94C2×#41—31no—
95C2×#41—61no—
96C2×#41—61no—
97C22×Q8C3×A411yescharacteristic, complemented
98C4⋊Q8—61no—
99#124—61no—
100#123—32no—
101#123—32no—
102C22⋊Q8—61no—
103C22⋊Q8—61no—
104#117—31no—
105#99—32no—
106#99—32no—
107C23×C3—21no—
108C23×C3—31no—
109C23×C3—31no—
110C23×C3—61no—
111C23×C3C22×A411yescharacteristic
112C2×A4—43no—
113C2×A4—83no—
114C3×Q8—21no—
115C3×Q8—41no—
116C3×Q8—62no—
117C3×Q8—61no—
118C3×Q8—121no—
119C3×Q8—163no—
120C3×D4—62no—
121C3×D4—62no—
122C3×D4—62no—
123C3×D4—61no—
124C3×D4—61no—
125C3×D4—62no—
126C2×C3×C4—31no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—61no—
131C2×C3×C4—61no—
132C2×C3×C4—62no—
133C2×C3×C4—62no—
134C2×C3×C4—61no—
135C2×C3×C4—61no—
136C2×C3×C4—61no—
137C2×C3×C4—61no—
138C2×C3×C4—62no—
139SL(2,𝔽3)—83no—
140C2×C32—161no—
141#41—21no—
142#41—62no—
143#41—62no—
144#41—61no—
145#41—62no—
146#41—61no—
147#41—62no—
148#41—62no—
149#41—61no—
150C2×Q8—31no—
151C2×Q8—61no—
152C2×Q8—61no—
153C2×Q8—61no—
154C2×Q8—61no—
155C2×D4—31no—
156C2×D4—31no—
157C2×D4—31no—
158C2×D4—61no—
159C2×D4—62no—
160C2×D4—61no—
161C2×D4—61no—
162C2×D4—61no—
163C22×C4—21no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—61no—
167C22×C4C2×C3×A411yescharacteristic
168C22×C4C2×C3×A412yes—
169C4⋊C4—61no—
170C4⋊C4—62no—
171C4⋊C4—62no—
172C22⋊C4—32no—
173C22⋊C4—62no—
174C22⋊C4—62no—
175C42—61no—
176C22×C3—31no—
177C22×C3—41no—
178C22×C3—61no—
179C22×C3—61no—
180C22×C3—81no—
181C22×C3—121no—
182C22×C3—121no—
183C22×C3—241no—
184A4—43no—
185A4—83no—
186C3×C4—31no—
187C3×C4—42no—
188C3×C4—61no—
189C3×C4—61no—
190C3×C4—122no—
191C3×C4—166no—
192C3×C4—163no—
193C3×C4#120⋊C311yescharacteristic
194C32—161noSylow
195C23—21no—
196C23—31no—
197C23—31no—
198C23—61no—
199C23C22×C3×A411yescharacteristic
200Q8—21no—
201Q8—41no—
202Q8—62no—
203Q8—61no—
204Q8—121no—
205D4—62no—
206D4—62no—
207D4—62no—
208D4—61no—
209D4—61no—
210D4—62no—
211C2×C4—31no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—61no—
216C2×C4—61no—
217C2×C4—62no—
218C2×C4—62no—
219C2×C4—61no—
220C2×C4—61no—
221C2×C4—61no—
222C2×C4—61no—
223C2×C4—62no—
224C2×C3—61no—
225C2×C3—121no—
226C2×C3—121no—
227C2×C3—163no—
228C2×C3C2×#120⋊C311yescharacteristic
229C22—31no—
230C22—41no—
231C22—61no—
232C22—61no—
233C22—81no—
234C22—121no—
235C22—121no—
236C22—241no—
237C4—31no—
238C4—42no—
239C4—61no—
240C4—61no—
241C4—122no—
242C4C3×#120⋊C311yescharacteristic
243C3—163no—
244C3#3028⋊C311yescharacteristic, direct product factor
245C2—61no—
246C2—121no—
247C2—121no—
248C2C2×C3×#120⋊C311yescharacteristic
subgroupG/H
center, socleC2×C3C2×#120⋊C3
commutator, cosocle, hypocenterH(5,𝔽2)C22×C32
FrattiniC23C22×C3×A4
FittingC3×#3028C3
prime radicalC3×#5950C2
hypercenterC3×C4#120⋊C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×#458⋊C3C2semidirect
3. C3×#3028C3semidirect
4. #3028⋊C3C3direct (N × H)
13. #458⋊C3C2×C3semidirect
18. #3028C32semidirect
26. C22×C3×Q8A4semidirect
97. C22×Q8C3×A4semidirect
244. C3#3028⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#59502
C3×#458⋊C32
C3×#30283
#3028⋊C33
C3×Q8×A44