Finite Group Databasebeta

← #73846⋊C3 #11921141

Subgroups — #73846⋊C3 #11921141

Order 1152.

449 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 449 conjugacy classes of subgroups — too many to draw. Only its 32 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
1Dic3×C22⋊A4C211yesmaximal, characteristic
2C3×#379⋊C3C211yesmaximal, characteristic
3C3⋊(#379⋊C3)C211yesmaximal, characteristic
4#73846C311yesmaximal, characteristic, complemented
5#2848⋊C3—31nomaximal
6C2×C3×C22⋊A4C2211yescharacteristic
7A4×Dic6—41nomaximal
8C24×Dic3C2×C311yescharacteristic
9C4×C22⋊A4—31no—
10C2×#878—31no—
11C3×#379C2×C311yescharacteristic
12#5247C2×C311yescharacteristic
13#4950—31no—
14#4946—31no—
15#4942—31no—
16#379⋊C3—21no—
17#379⋊C3—31no—
18#379⋊C3D311yescharacteristic
19C3×C22⋊A4Q811yescharacteristic, complemented
20C3×C4×A4—41no—
21Dic3×A4—41no—
22Dic3×A4—41no—
23Dic3×A4—82no—
24#2848—31noSylow
25C25×C3C22×C311yescharacteristic
26C2×C22⋊A4—21no—
27C2×C22⋊A4C2×D311yescharacteristic
28C23×Dic3—31no—
29C23×Dic3—31no—
30C23×Dic3—62no—
31C23×Dic3—62no—
32C22×Dic6A411yescharacteristic, complemented
33Q8×A4—121no—
34C2×C3×C22⋊C4—31no—
35C2×C3×C22⋊C4—31no—
36C2×#217—31no—
37C2×#217—31no—
38C2×C4⋊Dic3—31no—
39C2×Dic3⋊C4—31no—
40C2×Dic3⋊C4—31no—
41#878—62no—
42#878—62no—
43C3⋊#95—32no—
44C2×C3×A4—41no—
45C2×C3×A4—82no—
46C3×Dic6—161no—
47C24×C4—31no—
48C2×C22⋊Q8—91no—
49#385—91no—
50#385—91no—
51#380—91no—
52#379—31no—
53#379C3×D311yescharacteristic
54C24×C3—31no—
55C24×C3—31no—
56C24×C3—62no—
57C24×C3—62no—
58C24×C3C3×Q811yescharacteristic, complemented
59C22⋊A4—21no—
60C22⋊A4Dic611yescharacteristic, complemented
61C22×C3×C4—31no—
62C22×C3×C4C2×A411yescharacteristic
63C22×Dic3—22no—
64C22×Dic3—32no—
65C22×Dic3—32no—
66C22×Dic3—31no—
67C22×Dic3—31no—
68C22×Dic3—62no—
69C22×Dic3—62no—
70C22×Dic3—64no—
71C22×Dic3—62no—
72C22×Dic3—62no—
73C22×Dic3—64no—
74C22×Dic3—62no—
75C22×Dic3—62no—
76C22×Dic3C2×A411yescharacteristic
77C22×Dic3C2×A411yescharacteristic
78C2×Dic6—61no—
79C2×Dic6—61no—
80C4×A4—41no—
81C4×A4—81no—
82C4×A4—121no—
83C4×A4—121no—
84C4×A4—242no—
85C3×C22⋊C4—62no—
86C3×C22⋊C4—62no—
87#217—62no—
88#217—62no—
89C4⋊Dic3—62no—
90Dic3⋊C4—61no—
91Dic3⋊C4—61no—
92Dic3⋊C4—62no—
93C3×A4—41no—
94C3×A4—82no—
95C32×C4—161no—
96C3×Dic3—161no—
97C3×Dic3—161no—
98C25C2×C3×D311yescharacteristic
99C22×Q8—31no—
100C23×C4—91no—
101C23×C4—91no—
102C23×C4—182no—
103C23×C4—182no—
104C22⋊Q8—182no—
105C22⋊Q8—182no—
106C2×C4⋊C4—91no—
107C2×C4⋊C4—91no—
108C2×C4⋊C4—91no—
109C2×C22⋊C4—31no—
110C2×C22⋊C4—31no—
111C2×C22⋊C4—91no—
112C2×C22⋊C4—91no—
113#95—92no—
114C23×C3—22no—
115C23×C3—32no—
116C23×C3—32no—
117C23×C3—31no—
118C23×C3—31no—
119C23×C3—62no—
120C23×C3—62no—
121C23×C3—62no—
122C23×C3—62no—
123C23×C3—62no—
124C23×C3—64no—
125C23×C3—62no—
126C23×C3—62no—
127C23×C3—64no—
128C23×C3C22×A411yescharacteristic
129C2×A4—41no—
130C2×A4—82no—
131C2×A4—81no—
132C2×A4—162no—
133C3×Q8—481no—
134C2×C3×C4—61no—
135C2×C3×C4—61no—
136C2×C3×C4—62no—
137C2×Dic3—31no—
138C2×Dic3—31no—
139C2×Dic3—32no—
140C2×Dic3—62no—
141C2×Dic3—64no—
142C2×Dic3—61no—
143C2×Dic3—62no—
144C2×Dic3—64no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—61no—
149C2×Dic3—62no—
150Dic6—41no—
151Dic6—121no—
152C2×C32—161no—
153C24—31no—
154C24—31no—
155C24—62no—
156C24—62no—
157C24C3×Dic611yescharacteristic, complemented
158C2×Q8—181no—
159C2×Q8—181no—
160C22×C4—31no—
161C22×C4—31no—
162C22×C4—31no—
163C22×C4—62no—
164C22×C4—92no—
165C22×C4—92no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—182no—
169C22×C4—182no—
170C22×C4—184no—
171C22×C4—182no—
172C22×C4—182no—
173C22×C4—184no—
174C22×C4—182no—
175C22×C4—182no—
176C22×C4D3×A411yescharacteristic
177C4⋊C4—182no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C4⋊C4—182no—
181C22⋊C4—62no—
182C22⋊C4—62no—
183C22⋊C4—182no—
184C22⋊C4—182no—
185C22×C3—22no—
186C22×C3—31no—
187C22×C3—31no—
188C22×C3—32no—
189C22×C3—32no—
190C22×C3—62no—
191C22×C3—64no—
192C22×C3—62no—
193C22×C3—62no—
194C22×C3—62no—
195C22×C3—62no—
196C22×C3—62no—
197C22×C3—64no—
198C22×C3—62no—
199C22×C3Q8×A411yescharacteristic
200A4—41no—
201A4—82no—
202A4—81no—
203A4—162no—
204C3×C4—41no—
205C3×C4—121no—
206C3×C4—161no—
207C3×C4—321no—
208C3×C4—481no—
209C3×C4—481no—
210Dic3—31no—
211Dic3—41no—
212Dic3—62no—
213Dic3—121no—
214Dic3#120⋊C311yescharacteristic
215C32—161noSylow
216C23—22no—
217C23—32no—
218C23—32no—
219C23—31no—
220C23—31no—
221C23—62no—
222C23—62no—
223C23—62no—
224C23—62no—
225C23—62no—
226C23—64no—
227C23—62no—
228C23—62no—
229C23—64no—
230C23C2×D3×A411yescharacteristic
231Q8—121no—
232Q8—361no—
233C2×C4—61no—
234C2×C4—61no—
235C2×C4—62no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—92no—
239C2×C4—182no—
240C2×C4—182no—
241C2×C4—184no—
242C2×C4—181no—
243C2×C4—182no—
244C2×C4—184no—
245C2×C4—182no—
246C2×C4—182no—
247C2×C4—181no—
248C2×C4—182no—
249C2×C3—31no—
250C2×C3—31no—
251C2×C3—62no—
252C2×C3—62no—
253C2×C3—161no—
254C2×C3—321no—
255C2×C3C2×#120⋊C311yescharacteristic
256C22—22no—
257C22—31no—
258C22—31no—
259C22—32no—
260C22—32no—
261C22—62no—
262C22—64no—
263C22—62no—
264C22—62no—
265C22—62no—
266C22—62no—
267C22—62no—
268C22—64no—
269C22—62no—
270C22A4×Dic611yescharacteristic
271C4—31no—
272C4—41no—
273C4—91no—
274C4—121no—
275C4—121no—
276C4—182no—
277C4—361no—
278C3—161no—
279C3—321no—
280C3#2848⋊C311yescharacteristic, complemented
281C2—31no—
282C2—31no—
283C2—62no—
284C2—62no—
285C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
commutator, cosocleC25×C3C22×C3
FrattiniC23C2×D3×A4
FittingC3×#379C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C22⋊A4C22
hypocenterC24×C3C3×Q8
LCSG ▷ C25×C3 ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. #73846C3semidirect
19. C3×C22⋊A4Q8semidirect
32. C22×Dic6A4semidirect
58. C24×C3C3×Q8semidirect
60. C22⋊A4Dic6semidirect
157. C24C3×Dic6semidirect
280. C3#2848⋊C3semidirect

Maximal subgroups

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

subgroupindex
Dic3×C22⋊A42
C3×#379⋊C32
C3⋊(#379⋊C3)2
#738463
#2848⋊C33
A4×Dic64