Finite Group Databasebeta

← #84031⋊C3 #11921354

Subgroups — #84031⋊C3 #11921354

Order 1152.

457 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 457 conjugacy classes of subgroups — too many to draw. Only its 33 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⋊C3)C212yesmaximal
3#84031C311yesmaximal, characteristic, complemented
4#2848⋊C3—31nomaximal
5C2×C3×C22⋊A4C2211yescharacteristic
6A4×Dic6—41nomaximal
7C24×C3×C4C2×C311yescharacteristic
8C4×C22⋊A4—21no—
9C4×C22⋊A4D311yescharacteristic
10C2×#924—31no—
11#5247C2×C312yes—
12#5212—31no—
13#5210—32no—
14#379⋊C3—32no—
15C3×C22⋊A4Q811yescharacteristic, complemented
16C3×C4×A4—41no—
17C3×C4×A4—82no—
18Dic3×A4—42no—
19#2848—31noSylow
20C25×C3C22×C311yescharacteristic
21C2×C22⋊A4—21no—
22C2×C22⋊A4C2×D311yescharacteristic
23C23×C3×C4—31no—
24C23×C3×C4—31no—
25C23×C3×C4—62no—
26C23×C3×C4—62no—
27C22×Dic6A411yescharacteristic, complemented
28Q8×A4—121no—
29C2×#217—32no—
30C2×#217—32no—
31C2×C4⋊Dic3—31no—
32#924—62no—
33#924—62no—
34C2×Dic3⋊C4—32no—
35C3⋊#95—32no—
36C2×C3×A4—41no—
37C2×C3×A4—82no—
38C3×Dic6—161no—
39C24×C4C3×D311yescharacteristic
40C2×C22⋊Q8—91no—
41#385—92no—
42#380—91no—
43#379—32no—
44C24×C3—31no—
45C24×C3—31no—
46C24×C3—62no—
47C24×C3—62no—
48C24×C3C3×Q811yescharacteristic, complemented
49C22⋊A4—21no—
50C22⋊A4Dic611yescharacteristic, complemented
51C22×C3×C4—22no—
52C22×C3×C4—32no—
53C22×C3×C4—32no—
54C22×C3×C4—31no—
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×Dic3—32no—
65C22×Dic3C2×A412yes—
66C2×Dic6—61no—
67C2×Dic6—61no—
68C4×A4—41no—
69C4×A4—82no—
70C4×A4—84no—
71C4×A4—81no—
72C4×A4—122no—
73#217—64no—
74#217—64no—
75C4⋊Dic3—61no—
76C4⋊Dic3—61no—
77Dic3⋊C4—64no—
78C3×A4—41no—
79C3×A4—82no—
80C32×C4—161no—
81C3×Dic3—162no—
82C25C2×C3×D311yescharacteristic
83C22×Q8—31no—
84C23×C4—31no—
85C23×C4—31no—
86C23×C4—62no—
87C23×C4—62no—
88C22⋊Q8—182no—
89C22⋊Q8—182no—
90C2×C4⋊C4—92no—
91C2×C4⋊C4—91no—
92C2×C22⋊C4—92no—
93C2×C22⋊C4—92no—
94#95—92no—
95C23×C3—22no—
96C23×C3—32no—
97C23×C3—32no—
98C23×C3—31no—
99C23×C3—31no—
100C23×C3—62no—
101C23×C3—62no—
102C23×C3—62no—
103C23×C3—62no—
104C23×C3—62no—
105C23×C3—64no—
106C23×C3—62no—
107C23×C3—62no—
108C23×C3—64no—
109C23×C3C22×A411yescharacteristic
110C2×A4—41no—
111C2×A4—82no—
112C2×A4—84no—
113C2×A4—81no—
114C3×Q8—481no—
115C2×C3×C4—31no—
116C2×C3×C4—31no—
117C2×C3×C4—32no—
118C2×C3×C4—62no—
119C2×C3×C4—64no—
120C2×C3×C4—62no—
121C2×C3×C4—64no—
122C2×C3×C4—62no—
123C2×C3×C4—62no—
124C2×C3×C4—62no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C2×Dic3—64no—
128Dic6—41no—
129Dic6—121no—
130C2×C32—161no—
131C24—31no—
132C24—31no—
133C24—62no—
134C24—62no—
135C24C3×Dic611yescharacteristic, complemented
136C2×Q8—181no—
137C2×Q8—181no—
138C22×C4—22no—
139C22×C4—32no—
140C22×C4—32no—
141C22×C4—31no—
142C22×C4—32no—
143C22×C4—62no—
144C22×C4—62no—
145C22×C4—64no—
146C22×C4—62no—
147C22×C4—62no—
148C22×C4—64no—
149C22×C4—62no—
150C22×C4—62no—
151C22×C4—92no—
152C22×C4D3×A411yescharacteristic
153C4⋊C4—184no—
154C4⋊C4—181no—
155C4⋊C4—181no—
156C22⋊C4—184no—
157C22⋊C4—184no—
158C22×C3—22no—
159C22×C3—31no—
160C22×C3—31no—
161C22×C3—32no—
162C22×C3—32no—
163C22×C3—62no—
164C22×C3—64no—
165C22×C3—62no—
166C22×C3—62no—
167C22×C3—62no—
168C22×C3—62no—
169C22×C3—62no—
170C22×C3—64no—
171C22×C3—62no—
172C22×C3Q8×A411yescharacteristic
173A4—41no—
174A4—82no—
175A4—84no—
176A4—81no—
177C3×C4—31no—
178C3×C4—62no—
179C3×C4—161no—
180C3×C4—321no—
181C3×C4—482no—
182C3×C4#120⋊C311yescharacteristic
183Dic3—42no—
184Dic3—122no—
185C32—161noSylow
186C23—22no—
187C23—32no—
188C23—32no—
189C23—31no—
190C23—31no—
191C23—62no—
192C23—62no—
193C23—62no—
194C23—62no—
195C23—62no—
196C23—64no—
197C23—62no—
198C23—62no—
199C23—64no—
200C23C2×D3×A411yescharacteristic
201Q8—121no—
202Q8—361no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—32no—
206C2×C4—62no—
207C2×C4—64no—
208C2×C4—62no—
209C2×C4—64no—
210C2×C4—62no—
211C2×C4—62no—
212C2×C4—62no—
213C2×C4—182no—
214C2×C4—182no—
215C2×C4—184no—
216C2×C3—31no—
217C2×C3—31no—
218C2×C3—62no—
219C2×C3—62no—
220C2×C3—161no—
221C2×C3—321no—
222C2×C3C2×#120⋊C311yescharacteristic
223C22—22no—
224C22—31no—
225C22—31no—
226C22—32no—
227C22—32no—
228C22—62no—
229C22—64no—
230C22—62no—
231C22—62no—
232C22—62no—
233C22—62no—
234C22—62no—
235C22—64no—
236C22—62no—
237C22A4×Dic611yescharacteristic
238C4—31no—
239C4—62no—
240C4—122no—
241C4—362no—
242C4C3⋊(#120⋊C3)11yescharacteristic
243C3—161no—
244C3—321no—
245C3#2848⋊C311yescharacteristic, complemented
246C2—31no—
247C2—31no—
248C2—62no—
249C2—62no—
250C2C2×C3⋊(#120⋊C3)11yescharacteristic
subgroupG/H
centerC2C2×C3⋊(#120⋊C3)
commutator, cosocleC25×C3C22×C3
FrattiniC23C2×D3×A4
FittingC24×C3×C4C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C22⋊A4C22
hypercenterC4C3⋊(#120⋊C3)
hypocenterC24×C3C3×Q8
LCSG ▷ C25×C3 ▷ C24×C3
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
3. #84031C3semidirect
15. C3×C22⋊A4Q8semidirect
27. C22×Dic6A4semidirect
48. C24×C3C3×Q8semidirect
50. C22⋊A4Dic6semidirect
135. C24C3×Dic6semidirect
245. C3#2848⋊C3semidirect

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⋊C3)2
#840313
#2848⋊C33
A4×Dic64