Finite Group Databasebeta

← C3×#2848⋊C3 #11919502

Subgroups — C3×#2848⋊C3 #11919502

Order 1152.

484 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 54 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×C4×C22⋊A4C211yesmaximal, characteristic
2C3×#379⋊C3C212yesmaximal
3C3×#2848C311yesmaximal, characteristic, complemented
4#2848⋊C3C313yesmaximal, direct product factor
5C2×C3×C22⋊A4C2211yescharacteristic
6C3×Q8×A4—41nomaximal
7C24×C3×C4C2×C311yescharacteristic
8C4×C22⋊A4C2×C313yes—
9C2×C3×C22⋊Q8—31no—
10C3×#385—32no—
11C3×#380—31no—
12C3×#379C2×C312yes—
13#379⋊C3C2×C316yes—
14C3×C22⋊A4Q811yescharacteristic, complemented
15C3×C4×A4—41no—
16C3×C4×A4—42no—
17C3×C4×A4—82no—
18#2848C3211yescharacteristic, complemented, Sylow
19C25×C3C22×C311yescharacteristic
20C2×C22⋊A4C22×C313yes—
21C22×C3×Q8A411yescharacteristic, complemented
22C23×C3×C4—31no—
23C23×C3×C4—31no—
24C23×C3×C4—62no—
25C23×C3×C4—62no—
26Q8×A4—43no—
27C3×C22⋊Q8—62no—
28C3×C22⋊Q8—62no—
29C2×C3×C4⋊C4—31no—
30C2×C3×C4⋊C4—32no—
31C2×C3×C22⋊C4—32no—
32C2×C3×C22⋊C4—32no—
33C3×#95—32no—
34C2×C3×A4—41no—
35C2×C3×A4—82no—
36C32×Q8—161no—
37C24×C4C2×C3211yescharacteristic
38C2×C22⋊Q8—31no—
39#385—32no—
40#380—31no—
41#379C2×C3212yes—
42C24×C3—31no—
43C24×C3—31no—
44C24×C3—62no—
45C24×C3—62no—
46C24×C3C3×Q811yescharacteristic, complemented
47C22⋊A4C3×Q813yescomplemented
48C2×C3×Q8—61no—
49C2×C3×Q8—61no—
50C22×C3×C4—22no—
51C22×C3×C4—32no—
52C22×C3×C4—32no—
53C22×C3×C4—31no—
54C22×C3×C4—32no—
55C22×C3×C4—62no—
56C22×C3×C4—62no—
57C22×C3×C4—64no—
58C22×C3×C4—62no—
59C22×C3×C4—62no—
60C22×C3×C4—64no—
61C22×C3×C4—62no—
62C22×C3×C4—62no—
63C22×C3×C4C2×A411yescharacteristic
64C22×C3×C4C2×A412yes—
65C4×A4—46no—
66C4×A4—43no—
67C4×A4—86no—
68C3×C4⋊C4—61no—
69C3×C4⋊C4—61no—
70C3×C4⋊C4—64no—
71C3×C22⋊C4—64no—
72C3×C22⋊C4—64no—
73C3×A4—41no—
74C3×A4—82no—
75C32×C4—162no—
76C32×C4—161no—
77C25C22×C3211yescharacteristic
78C22×Q8C3×A411yescharacteristic, complemented
79C23×C4—31no—
80C23×C4—31no—
81C23×C4—62no—
82C23×C4—62no—
83C22⋊Q8—62no—
84C22⋊Q8—62no—
85C2×C4⋊C4—31no—
86C2×C4⋊C4—32no—
87C2×C22⋊C4—32no—
88C2×C22⋊C4—32no—
89#95—32no—
90C23×C3—22no—
91C23×C3—32no—
92C23×C3—32no—
93C23×C3—31no—
94C23×C3—31no—
95C23×C3—62no—
96C23×C3—62no—
97C23×C3—62no—
98C23×C3—62no—
99C23×C3—62no—
100C23×C3—64no—
101C23×C3—62no—
102C23×C3—62no—
103C23×C3—64no—
104C23×C3C22×A411yescharacteristic
105C2×A4—43no—
106C2×A4—86no—
107C3×Q8—41no—
108C3×Q8—121no—
109C3×Q8—163no—
110C2×C3×C4—31no—
111C2×C3×C4—31no—
112C2×C3×C4—32no—
113C2×C3×C4—62no—
114C2×C3×C4—64no—
115C2×C3×C4—62no—
116C2×C3×C4—62no—
117C2×C3×C4—64no—
118C2×C3×C4—62no—
119C2×C3×C4—62no—
120C2×C3×C4—62no—
121C2×C3×C4—62no—
122C2×C3×C4—64no—
123C2×C32—161no—
124C24—31no—
125C24—31no—
126C24—62no—
127C24—62no—
128C24C32×Q811yescharacteristic, complemented
129C2×Q8—61no—
130C2×Q8—61no—
131C22×C4—22no—
132C22×C4—32no—
133C22×C4—32no—
134C22×C4—31no—
135C22×C4—32no—
136C22×C4—62no—
137C22×C4—62no—
138C22×C4—64no—
139C22×C4—62no—
140C22×C4—62no—
141C22×C4—64no—
142C22×C4—62no—
143C22×C4—62no—
144C22×C4C2×C3×A411yescharacteristic
145C22×C4C2×C3×A412yes—
146C4⋊C4—61no—
147C4⋊C4—61no—
148C4⋊C4—64no—
149C22⋊C4—64no—
150C22⋊C4—64no—
151C22×C3—22no—
152C22×C3—31no—
153C22×C3—31no—
154C22×C3—32no—
155C22×C3—32no—
156C22×C3—62no—
157C22×C3—64no—
158C22×C3—62no—
159C22×C3—62no—
160C22×C3—62no—
161C22×C3—62no—
162C22×C3—62no—
163C22×C3—64no—
164C22×C3—62no—
165C22×C3Q8×A411yescharacteristic
166A4—43no—
167A4—86no—
168C3×C4—31no—
169C3×C4—42no—
170C3×C4—62no—
171C3×C4—122no—
172C3×C4—166no—
173C3×C4—163no—
174C3×C4#120⋊C311yescharacteristic
175C32—161noSylow
176C23—22no—
177C23—32no—
178C23—32no—
179C23—31no—
180C23—31no—
181C23—62no—
182C23—62no—
183C23—62no—
184C23—62no—
185C23—62no—
186C23—64no—
187C23—62no—
188C23—62no—
189C23—64no—
190C23C22×C3×A411yescharacteristic
191Q8—41no—
192Q8—121no—
193C2×C4—31no—
194C2×C4—31no—
195C2×C4—32no—
196C2×C4—62no—
197C2×C4—64no—
198C2×C4—62no—
199C2×C4—62no—
200C2×C4—64no—
201C2×C4—62no—
202C2×C4—62no—
203C2×C4—62no—
204C2×C4—62no—
205C2×C4—64no—
206C2×C3—31no—
207C2×C3—31no—
208C2×C3—62no—
209C2×C3—62no—
210C2×C3—163no—
211C2×C3C2×#120⋊C311yescharacteristic
212C22—22no—
213C22—31no—
214C22—31no—
215C22—32no—
216C22—32no—
217C22—62no—
218C22—64no—
219C22—62no—
220C22—62no—
221C22—62no—
222C22—62no—
223C22—62no—
224C22—64no—
225C22—62no—
226C22C3×Q8×A411yescharacteristic
227C4—31no—
228C4—42no—
229C4—62no—
230C4—122no—
231C4C3×#120⋊C311yescharacteristic
232C3—163no—
233C3#2848⋊C311yescharacteristic, direct product factor
234C2—31no—
235C2—31no—
236C2—62no—
237C2—62no—
238C2C2×C3×#120⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×#120⋊C3
commutator, cosocleC25C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2848C3
socleC23×C3C22×A4
prime radicalC2×C3×C22⋊A4C22
hypercenterC3×C4#120⋊C3
hypocenterC24C32×Q8
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
3. C3×#2848C3semidirect
4. #2848⋊C3C3direct (N × H)
14. C3×C22⋊A4Q8semidirect
18. #2848C32semidirect
21. C22×C3×Q8A4semidirect
46. C24×C3C3×Q8semidirect
47. C22⋊A4C3×Q8semidirect
78. C22×Q8C3×A4semidirect
128. C24C32×Q8semidirect
233. C3#2848⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C22⋊A42
C3×#379⋊C32
C3×#28483
#2848⋊C33
C3×Q8×A44