Finite Group Databasebeta

← #83191⋊C3 #11921298

Subgroups — #83191⋊C3 #11921298

Order 1152.

305 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 305 conjugacy classes of subgroups — too many to draw. Only its 31 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×#127⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊(#126⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#383⋊C3)C211yesmaximal, characteristic, complemented
4#83191C311yesmaximal, characteristic, complemented
5#2818⋊C3—31nomaximal
6A4×#67—41nomaximal
7C3×#127⋊C3—21no—
8C2×C3×C42⋊C3C2211yescharacteristic
9C3⋊(#126⋊C3)—21no—
10C2×C3×#127C2×C311yescharacteristic, complemented
11C2×#876C2×C311yescharacteristic, complemented
12C2×#127⋊C3—21no—
13C2×#127⋊C3D311yescharacteristic, complemented
14C2×#126⋊C3—31no—
15#5223—31no—
16#5223—31no—
17#5222—31no—
18#5222—31no—
19#4937C2×C311yescharacteristic, complemented
20#383⋊C3—31no—
21C22×C3×A4—41no—
22C2×D3×A4—41no—
23Dic3×A4—41no—
24C3×C42⋊C3D411yescharacteristic, complemented
25#2818—31noSylow
26C22×C3×D4—31no—
27C22×C3×D4—31no—
28C22×#67—31no—
29C22×#67A411yescharacteristic
30D4×A4—121no—
31C3×#127—21no—
32C3×#127—61no—
33C2×C3×C42C22×C311yescharacteristic
34C2×#217—31no—
35C2×#217—31no—
36C2×#217—31no—
37C2×#217—31no—
38C2×(C2×D3)⋊C4—31no—
39C2×Dic3⋊C4—31no—
40#876—21no—
41#876—61no—
42#127⋊C3—22no—
43#127⋊C3—21no—
44#126⋊C3—61no—
45C2×C42⋊C3—21no—
46C2×C42⋊C3C2×D311yescharacteristic
47C3⋊#95—31no—
48C3⋊#95—31no—
49C2×C3×A4—41no—
50C2×C3×A4—81no—
51D3×A4—81no—
52C3×#67—161no—
53C2×#127C3×D311yescharacteristic, complemented
54C2×#126—31no—
55#394—91no—
56#394—91no—
57#392—91no—
58#392—91no—
59#383—31no—
60C24×C3—31no—
61C24×C3C2×A411yescharacteristic
62C23×D3C2×A411yescharacteristic
63C22×A4—41no—
64C22×A4—81no—
65C22×A4—121no—
66C2×C3×D4—61no—
67C2×C3×D4—61no—
68C2×C3×D4—61no—
69C2×C3×D4—61no—
70C2×C3×D4—121no—
71C2×C3×D4—121no—
72C2×C3×D4—121no—
73C2×C3×D4—121no—
74C22×C3×C4—31no—
75C2×#67—121no—
76C2×#67—121no—
77C2×#67—121no—
78C2×#67—121no—
79C22×Dic3—31no—
80C22×Dic3—31no—
81C22×Dic3C2×A411yescharacteristic
82C4×A4—121no—
83C3×C42—31no—
84C3×C42C3×D411yescharacteristic, complemented
85#217—121no—
86#217—121no—
87#217—121no—
88#217—121no—
89(C2×D3)⋊C4—61no—
90(C2×D3)⋊C4—61no—
91Dic3⋊C4—61no—
92Dic3⋊C4—61no—
93C42⋊C3—21no—
94C42⋊C3#6711yescharacteristic, complemented
95C22×C32—161no—
96C2×C3×D3—161no—
97C3×A4—41no—
98C3×Dic3—161no—
99C22×D4—31no—
100C22×D4—31no—
101C22×D4—31no—
102C22×D4—91no—
103#127—21no—
104#127—61no—
105#126—61no—
106#126—181no—
107C2×C4⋊C4—91no—
108C2×C22⋊C4—91no—
109C2×C22⋊C4—91no—
110C2×C22⋊C4—91no—
111C2×C22⋊C4—91no—
112C2×C22⋊C4—91no—
113C2×C42C2×C3×D311yescharacteristic
114#95—91no—
115#95—91no—
116C23×C3—21no—
117C23×C3—61no—
118C23×C3—61no—
119C23×C3—61no—
120C23×C3—61no—
121C23×C3—61no—
122C23×C3—61no—
123C23×C3—61no—
124C23×C3—61no—
125C23×C3—61no—
126C23×C3C22×A411yescharacteristic
127C22×D3—21no—
128C22×D3—61no—
129C22×D3—61no—
130C2×A4—41no—
131C2×A4—81no—
132C2×A4—82no—
133C2×A4—81no—
134C2×A4—241no—
135C3×D4—122no—
136C3×D4—122no—
137C3×D4—122no—
138C3×D4—122no—
139C3×D4—481no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—61no—
143C2×C3×C4—61no—
144#67—41no—
145#67—121no—
146#67—124no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×C32—161no—
155C2×C32—321no—
156C3×D3—321no—
157C24—31no—
158C24—31no—
159C24D3×A411yescharacteristic
160C2×D4—61no—
161C2×D4—61no—
162C2×D4—61no—
163C2×D4—61no—
164C2×D4—121no—
165C2×D4—121no—
166C2×D4—121no—
167C2×D4—121no—
168C2×D4—361no—
169C2×D4—361no—
170C2×D4—361no—
171C2×D4—361no—
172C22×C4—31no—
173C22×C4—31no—
174C22×C4—91no—
175C22×C4—91no—
176C4⋊C4—181no—
177C4⋊C4—181no—
178C22⋊C4—181no—
179C22⋊C4—181no—
180C22⋊C4—361no—
181C22⋊C4—361no—
182C22⋊C4—361no—
183C22⋊C4—361no—
184C42—31no—
185C42C3×#6711yescharacteristic, complemented
186C22×C3—31no—
187C22×C3—31no—
188C22×C3—41no—
189C22×C3—121no—
190C22×C3—121no—
191C22×C3—121no—
192C22×C3—121no—
193C22×C3—121no—
194C22×C3—121no—
195C22×C3—121no—
196C22×C3—121no—
197C22×C3—121no—
198C22×C3—161no—
199C22×C3—321no—
200C22×C3—481no—
201C22×C3D4×A411yescharacteristic
202C2×D3—41no—
203C2×D3—121no—
204C2×D3—121no—
205A4—41no—
206A4—81no—
207C3×C4—61no—
208C3×C4—61no—
209C3×C4—481no—
210Dic3—41no—
211Dic3—121no—
212Dic3—121no—
213C32—161noSylow
214C23—21no—
215C23—61no—
216C23—61no—
217C23—61no—
218C23—61no—
219C23—61no—
220C23—61no—
221C23—61no—
222C23—61no—
223C23—61no—
224C23—61no—
225C23—181no—
226C23—181no—
227C23C2×D3×A411yescharacteristic
228D4—122no—
229D4—122no—
230D4—122no—
231D4—122no—
232D4—121no—
233D4—361no—
234D4—364no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—61no—
238C2×C4—61no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—181no—
243C2×C4—181no—
244C2×C4—181no—
245C2×C4—181no—
246C2×C3—31no—
247C2×C3—31no—
248C2×C3—81no—
249C2×C3—161no—
250C2×C3—241no—
251C2×C3—321no—
252C2×C3—322no—
253C2×C3—321no—
254C2×C3—961no—
255C2×C3#560⋊C311yescharacteristic
256D3—81no—
257C22—31no—
258C22—31no—
259C22—41no—
260C22—121no—
261C22—121no—
262C22—121no—
263C22—121no—
264C22—121no—
265C22—121no—
266C22—121no—
267C22—121no—
268C22—121no—
269C22—121no—
270C22—361no—
271C22—361no—
272C22A4×#6711yescharacteristic
273C4—61no—
274C4—61no—
275C4—121no—
276C4—361no—
277C4—361no—
278C3—161no—
279C3—321no—
280C3#2818⋊C311yescharacteristic, complemented
281C2—31no—
282C2—31no—
283C2—81no—
284C2—241no—
285C2—241no—
286C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC2×C3×#127C2×C3
socleC23×C3C22×A4
hypocenterC3×C42C3×D4
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#127⋊C3C2semidirect
2. C2×C3⋊(#126⋊C3)C2semidirect
3. C3⋊(#383⋊C3)C2semidirect
4. #83191C3semidirect
10. C2×C3×#127C2×C3semidirect
11. C2×#876C2×C3semidirect
13. C2×#127⋊C3D3semidirect
19. #4937C2×C3semidirect
24. C3×C42⋊C3D4semidirect
53. C2×#127C3×D3semidirect
84. C3×C42C3×D4semidirect
94. C42⋊C3#67semidirect
185. C42C3×#67semidirect
280. C3#2818⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
C2×C3⋊(#126⋊C3)2
C3⋊(#383⋊C3)2
#831913
#2818⋊C33
A4×#674