Finite Group Databasebeta

← #73851⋊C3 #11921145

Subgroups — #73851⋊C3 #11921145

Order 1152.

329 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 37 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
1C2×C3⋊(#120⋊C3)C211yesmaximal, characteristic
2C3×#379⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#379⋊C3)C211yesmaximal, characteristic, complemented
4#73851C311yesmaximal, characteristic, complemented
5#2375⋊C3—31nomaximal
6C2×C3×C22⋊A4C2211yescharacteristic
7C4×D3×A4—41nomaximal
8C3⋊(#120⋊C3)C412yescomplemented
9C2×#953C2×C311yescharacteristic
10C2×#120⋊C3—31no—
11C3×#379C2×C311yescharacteristic, complemented
12#5247C2×C311yescharacteristic, complemented
13#4957—31no—
14#4956—31no—
15#4945—31no—
16#4944—31no—
17#379⋊C3—21no—
18#379⋊C3—31no—
19#379⋊C3D311yescharacteristic, complemented
20C3×C22⋊A4C2×C411yescharacteristic, complemented
21C2×D3×A4—41no—
22C3×C4×A4—41no—
23Dic3×A4—41no—
24#2375—31noSylow
25C25×C3C22×C311yescharacteristic
26C2×C22⋊A4—21no—
27C2×C22⋊A4C2×D311yescharacteristic
28C22×#67—31no—
29C22×C4×D3A411yescharacteristic, complemented
30C2×C4×A4—121no—
31C2×C3×C22⋊C4—31no—
32C2×C3×C22⋊C4—31no—
33#953—32no—
34#953C3×C412yescomplemented
35C2×#217—31no—
36C2×#217—31no—
37C2×#217—31no—
38C2×(C2×D3)⋊C4—31no—
39C2×Dic3⋊C4—31no—
40C2×C4×Dic3—31no—
41#120⋊C3—32no—
42C3⋊#95—31no—
43C3⋊#95—31no—
44C2×C3×A4—41no—
45C2×C3×A4—161no—
46D3×A4—42no—
47C3×C4×D3—161no—
48C2×#120—31no—
49#390—91no—
50#388—91no—
51#388—91no—
52#386—91no—
53#379—31no—
54#379C3×D311yescharacteristic, complemented
55C24×C3—31no—
56C24×C3—31no—
57C24×C3—121no—
58C24×C3—121no—
59C24×C3C2×C3×C411yescharacteristic, complemented
60C23×D3C2×A411yescharacteristic
61C22⋊A4—21no—
62C22⋊A4C4×D311yescharacteristic, complemented
63C22×A4—121no—
64C22×C3×C4—31no—
65C22×C3×C4C2×A411yescharacteristic
66C2×#67—32no—
67C2×#67—32no—
68C2×#67—121no—
69C2×#67—121no—
70C22×Dic3—31no—
71C22×Dic3—31no—
72C22×Dic3C2×A411yescharacteristic
73C2×C4×D3—121no—
74C4×A4—41no—
75C4×A4—81no—
76C4×A4—121no—
77C3×C22⋊C4—121no—
78C3×C22⋊C4—121no—
79#217—32no—
80#217—32no—
81#217—121no—
82#217—121no—
83(C2×D3)⋊C4—121no—
84Dic3⋊C4—121no—
85C4×Dic3—121no—
86C2×C3×D3—161no—
87C3×A4—41no—
88C3×A4—161no—
89C32×C4—161no—
90C3×Dic3—161no—
91C25C2×C3×D311yescharacteristic
92C22×D4—91no—
93C23×C4—31no—
94#120—32no—
95#120—92no—
96C2×C4⋊C4—91no—
97C2×C22⋊C4—31no—
98C2×C22⋊C4—31no—
99C2×C22⋊C4—91no—
100C2×C22⋊C4—91no—
101C2×C22⋊C4—91no—
102C2×C22⋊C4—91no—
103C2×C42—91no—
104#95—91no—
105#95—91no—
106C23×C3—31no—
107C23×C3—31no—
108C23×C3—41no—
109C23×C3—61no—
110C23×C3—61no—
111C23×C3—61no—
112C23×C3—61no—
113C23×C3—61no—
114C23×C3—61no—
115C23×C3—121no—
116C23×C3—121no—
117C23×C3—121no—
118C23×C3—121no—
119C23×C3—121no—
120C23×C3—121no—
121C23×C3—123no—
122C23×C3C22×A411yescharacteristic
123C22×D3—61no—
124C22×D3—61no—
125C22×D3C4×A412yes—
126C2×A4—41no—
127C2×A4—81no—
128C2×A4—122no—
129C2×A4—161no—
130C2×A4—162no—
131C2×C3×C4—61no—
132C2×C3×C4—61no—
133C2×C3×C4—61no—
134C2×C3×C4—61no—
135C2×C3×C4—481no—
136#67—122no—
137#67—122no—
138C2×Dic3—32no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C4×D3—41no—
146C4×D3—121no—
147C2×C32—161no—
148C3×D3—162no—
149C24—31no—
150C24—31no—
151C24—31no—
152C24—121no—
153C24—121no—
154C24C3×C4×D311yescharacteristic, complemented
155C2×D4—92no—
156C2×D4—92no—
157C2×D4—361no—
158C2×D4—361no—
159C22×C4—31no—
160C22×C4—31no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—361no—
164C22×C4D3×A411yescharacteristic
165C4⋊C4—361no—
166C22⋊C4—92no—
167C22⋊C4—92no—
168C22⋊C4—121no—
169C22⋊C4—121no—
170C22⋊C4—361no—
171C22⋊C4—361no—
172C22⋊C4—361no—
173C42—361no—
174C22×C3—31no—
175C22×C3—31no—
176C22×C3—41no—
177C22×C3—61no—
178C22×C3—61no—
179C22×C3—61no—
180C22×C3—61no—
181C22×C3—61no—
182C22×C3—61no—
183C22×C3—121no—
184C22×C3—121no—
185C22×C3—121no—
186C22×C3—121no—
187C22×C3—121no—
188C22×C3—123no—
189C22×C3—121no—
190C22×C3—481no—
191C22×C3C2×C4×A411yescharacteristic
192C2×D3—41no—
193C2×D3—62no—
194C2×D3—121no—
195A4—41no—
196A4—81no—
197A4—161no—
198A4—162no—
199C3×C4—41no—
200C3×C4—121no—
201C3×C4—161no—
202C3×C4—321no—
203C3×C4—481no—
204Dic3—41no—
205Dic3—62no—
206Dic3—121no—
207C32—161noSylow
208C23—31no—
209C23—31no—
210C23—32no—
211C23—41no—
212C23—61no—
213C23—61no—
214C23—61no—
215C23—61no—
216C23—61no—
217C23—61no—
218C23—121no—
219C23—121no—
220C23—121no—
221C23—121no—
222C23—121no—
223C23—121no—
224C23—123no—
225C23—181no—
226C23—181no—
227C23C2×D3×A411yescharacteristic
228D4—362no—
229D4—362no—
230C2×C4—61no—
231C2×C4—61no—
232C2×C4—61no—
233C2×C4—61no—
234C2×C4—92no—
235C2×C4—121no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—361no—
243C2×C3—31no—
244C2×C3—31no—
245C2×C3—121no—
246C2×C3—121no—
247C2×C3—161no—
248C2×C3—321no—
249C2×C3—482no—
250C2×C3#545011yescharacteristic
251D3—42no—
252C22—31no—
253C22—31no—
254C22—41no—
255C22—61no—
256C22—61no—
257C22—61no—
258C22—61no—
259C22—61no—
260C22—61no—
261C22—121no—
262C22—121no—
263C22—121no—
264C22—121no—
265C22—121no—
266C22—123no—
267C22—121no—
268C22—121no—
269C22—182no—
270C22—361no—
271C22C4×D3×A411yescharacteristic
272C4—41no—
273C4—121no—
274C4—121no—
275C4—182no—
276C4—361no—
277C3—161no—
278C3—321no—
279C3#2375⋊C311yescharacteristic, complemented
280C2—31no—
281C2—31no—
282C2—121no—
283C2—121no—
284C2—122no—
285C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, hypocenterC24×C3C2×C3×C4
FrattiniC23C2×D3×A4
FittingC3×#379C2×C3
socleC23×C3C22×A4
prime radicalC2×C3⋊(#120⋊C3)C2
cosocleC25×C3C22×C3
LCSG ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×#379⋊C3C2semidirect
3. C3⋊(#379⋊C3)C2semidirect
4. #73851C3semidirect
8. C3⋊(#120⋊C3)C4semidirect
11. C3×#379C2×C3semidirect
12. #5247C2×C3semidirect
19. #379⋊C3D3semidirect
20. C3×C22⋊A4C2×C4semidirect
29. C22×C4×D3A4semidirect
34. #953C3×C4semidirect
54. #379C3×D3semidirect
59. C24×C3C2×C3×C4semidirect
62. C22⋊A4C4×D3semidirect
154. C24C3×C4×D3semidirect
279. C3#2375⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(#120⋊C3)2
C3×#379⋊C32
C3⋊(#379⋊C3)2
#738513
#2375⋊C33
C4×D3×A44