Finite Group Databasebeta

← #11786132

Subgroups — #11786132

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C42×C3⋊Dic3C211yesmaximal, characteristic
2C3×#4524C212yesmaximal
3#10589156C212yesmaximal
4#10589156C212yesmaximal
5#68607—32nomaximal
6C2×C32×C42C2211yescharacteristic
7C2×C4×C3⋊Dic3C411yescharacteristic
8C2×C4×C3⋊Dic3C411yescharacteristic
9C2×C4×C3⋊Dic3C411yescharacteristic
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊C8C2214yes—
14C42×Dic3—32no—
15C42×Dic3—61no—
16C3×#336—32no—
17#4550—34no—
18#4550—34no—
19#4524D312yes—
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2311yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C32×C42—22no—
28C4×C3⋊Dic3—22no—
29C4×C3⋊Dic3—22no—
30C4×C3⋊Dic3—22no—
31C4×C3⋊Dic3—22no—
32C4×C3⋊Dic3—22no—
33C4×C3⋊Dic3C814yescomplemented
34C2×C3×C3⋊C8—24no—
35C2×C3×C3⋊C8—24no—
36C2×C3×C3⋊C8—24no—
37#1839—91noSylow
38C22×C3×C8—34no—
39C2×C3×C42—21no—
40C2×C3×C42C2×D312yes—
41C2×C4×Dic3—32no—
42C2×C4×Dic3—32no—
43C2×C4×Dic3—32no—
44C2×C4×Dic3—32no—
45C2×C4×Dic3—32no—
46C2×C4×Dic3—32no—
47C2×C4×Dic3—61no—
48C2×C4×Dic3—61no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52C2×C4×Dic3—61no—
53C22×C3⋊C8C2×D314yes—
54C23×C32C22×C411yescharacteristic
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4C2×C812yes—
60C2×C32×C4M1612yes—
61C2×C32×C4#4112yes—
62C2×C32×C4#4112yes—
63C2×C32×C4#4112yes—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3C2×C812yes—
73C2×C3⋊Dic3C2×C812yes—
74C2×C3⋊Dic3M1612yes—
75C2×C3⋊Dic3M1612yes—
76C3×C3⋊C8—44no—
77C43—91no—
78#336—32no—
79#336—92no—
80#336—92no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×C3×C4C4×D312yes—
85C22×C3×C4C4×D312yes—
86C22×C3×C4C22×D312yes—
87C22×Dic3—32no—
88C22×Dic3—32no—
89C22×Dic3—32no—
90C22×Dic3—32no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C2×C3×C8—64no—
96C2×C3×C8—64no—
97C2×C3×C8—64no—
98C3×C42—24no—
99C3×C42—24no—
100C4×Dic3—38no—
101C4×Dic3—64no—
102C4×Dic3—64no—
103C4×Dic3—64no—
104C4×Dic3—64no—
105C4×Dic3—64no—
106C4×Dic3—64no—
107C4×Dic3—64no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C4×Dic3—64no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C2×C3⋊C8—24no—
114C2×C3⋊C8—24no—
115C2×C3⋊C8—24no—
116C22×C32#11711yescharacteristic
117C22×C32#11711yescharacteristic
118C22×C32#11711yescharacteristic
119C22×C32C22×C811yescharacteristic
120C22×C32C2×M1611yescharacteristic
121C22×C32C2×M1611yescharacteristic
122C22×C32C2×M1611yescharacteristic
123C32×C4—22no—
124C32×C4—22no—
125C32×C4#12614yes—
126C3⋊Dic3—22no—
127C3⋊Dic3—22no—
128C3⋊Dic3—22no—
129C3⋊Dic3—22no—
130C22×C8—34no—
131C2×C42—91no—
132C2×C42—91no—
133C2×C42—91no—
134C2×C42—91no—
135C2×C42—91no—
136C2×C42—91no—
137C2×C42D3211yescharacteristic
138C23×C3—21no—
139C23×C3C2×C4×D312yes—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4D3×C814yes—
154C2×C3×C4ΓL(1,𝔽25)14yes—
155C2×C3×C4#23514yes—
156C2×C3×C4#23712yes—
157C2×C3×C4#23714yes—
158C2×C3×C4#23912yes—
159C2×Dic3—34no—
160C2×Dic3—34no—
161C2×Dic3—34no—
162C2×Dic3—34no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C3×C8—124no—
184C3⋊C8—44no—
185C2×C32#38311yescharacteristic
186C2×C32#43111yescharacteristic
187C2×C32#43111yescharacteristic
188C2×C32#43111yescharacteristic
189C2×C32#43211yescharacteristic
190C2×C32#43211yescharacteristic
191C2×C32#43211yescharacteristic
192C22×C4—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4#62411yescharacteristic
197C22×C4#62411yescharacteristic
198C22×C4C2×D3211yescharacteristic
199C2×C8—64no—
200C2×C8—64no—
201C2×C8—64no—
202C42—22no—
203C42—94no—
204C42—182no—
205C42—182no—
206C42—182no—
207C42—182no—
208C42—182no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3#87212yes—
217C22×C3#87712yes—
218C22×C3#89212yes—
219C22×C3C2×D3×C812yes—
220C22×C3C2×ΓL(1,𝔽25)12yes—
221C22×C3D3×M1612yes—
222C22×C3D3×M1612yes—
223C3×C4—24no—
224C3×C4—24no—
225C3×C4—24no—
226C3×C4—24no—
227C3×C4—24no—
228C3×C4#87914yes—
229C3×C4#89814yes—
230Dic3—64no—
231Dic3—64no—
232Dic3—64no—
233Dic3—64no—
234Dic3—64no—
235Dic3—64no—
236Dic3—64no—
237Dic3—64no—
238C32#183911yescharacteristic, complemented, Sylow
239C23C2×#62411yescharacteristic
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—92no—
248C2×C4—181no—
249C2×C4—181no—
250C2×C4—181no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4—181no—
254C2×C4—181no—
255C2×C4—181no—
256C2×C4#371012yes—
257C2×C4#371212yes—
258C2×C4#379612yes—
259C2×C4#379812yes—
260C2×C4#380512yes—
261C8—124no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3#465112yes—
270C2×C3#468512yes—
271C2×C3#470512yes—
272C2×C3#471812yes—
273C2×C3#471912yes—
274C2×C3#483312yes—
275C2×C3#483512yes—
276C22C2×#371011yescharacteristic
277C22#6381811yescharacteristic
278C22#6381811yescharacteristic
279C22C2×#371211yescharacteristic
280C22#6384911yescharacteristic
281C22#6387411yescharacteristic
282C22#6395711yescharacteristic
283C4—22no—
284C4—22no—
285C4—182no—
286C4—182no—
287C4—182no—
288C4—182no—
289C4#6386214yes—
290C3—21no—
291C3#6860712yescomplemented
292C2#1059025611yescharacteristic
293C2#1059026011yescharacteristic
294C2#1059029711yescharacteristic
295C2#1059029911yescharacteristic
296C2#1059106111yescharacteristic
297C2#1059106611yescharacteristic
298C2#1059122911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC2×C32×C42C22
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1839
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
33. C4×C3⋊Dic3C8semidirect
238. C32#1839semidirect
291. C3#68607semidirect

Maximal subgroups

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

subgroupindex
C42×C3⋊Dic32
C3×#45242
#105891562
#686073