Finite Group Databasebeta

← #11808753

Subgroups — #11808753

Order 1152.

1769 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 1769 conjugacy classes of subgroups — too many to draw. Only its 268 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×C4×D12C212yesmaximal, complemented
2C2×C4×#625C214yesmaximal, complemented
3#10592631C211yesmaximal, characteristic, complemented
4#10591389C214yesmaximal, complemented
5#10591324C214yesmaximal, complemented
6#82347—32nomaximal
7C22×C3×D12C2212yes—
8C22×C3×C4×D3C2214yes—
9C22×#625C2214yes—
10C2×C32×C42C2211yescharacteristic
11C2×C4×C3⋊Dic3C2212yes—
12C2×C3×(C2×D3)⋊C4C2214yes—
13C2×C3×C4⋊Dic3C2212yes—
14C3×C4×D12—28no—
15C2×#3724C2214yes—
16C2×(C2×D3)⋊Dic3C2218yes—
17C4×#625—216no—
18#63658C2214yes—
19C2×C3×C4×D4—32no—
20C2×C4×#67—38no—
21C2×C4×D12D312yescomplemented
22#5223—34no—
23#4993—34no—
24#4960—34no—
25#4949—34no—
26#4932—32no—
27#4932—61no—
28C23×C3×D3C2314yes—
29C22×C32×C4C2312yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2314yes—
32C22×C3×Dic3C2314yes—
33C2×C3×D12—28no—
34C2×C3×D12—24no—
35C2×C3×C4×D3—216no—
36C2×C3×C4×D3—28no—
37C2×#625—216no—
38C2×#625—28no—
39C32×C42D414yescomplemented
40C4×C3⋊Dic3D418yescomplemented
41C3×(C2×D3)⋊C4—28no—
42C3×C4⋊Dic3—24no—
43#3724—28no—
44(C2×D3)⋊Dic3—216no—
45#2397—91noSylow
46C22×C3×D4—32no—
47C23×C3×C4—34no—
48C22×#67—38no—
49C22×D12C2×D312yes—
50C22×C4×D3C2×D314yes—
51C3×C4×D4—68no—
52C2×C3×C4⋊C4—32no—
53C2×C3×C22⋊C4—34no—
54C2×C3×C42—21no—
55C2×C3×C42C2×D312yes—
56C2×#217—38no—
57C4×#67—632no—
58C2×(C2×D3)⋊C4—38no—
59C2×(C2×D3)⋊C4C2×D314yes—
60C2×C4⋊Dic3C2×D312yes—
61C2×Dic3⋊C4—38no—
62C2×C4×Dic3—34no—
63C2×C4×Dic3—62no—
64C4×D12—28no—
65C3⋊#95—34no—
66C3⋊#95—34no—
67C3⋊#95—64no—
68C23×C32C2411yescharacteristic
69C22×C3×D3—28no—
70C22×C3×D3—24no—
71C22×C3×D3—28no—
72C22×C3×D3—24no—
73C22×C3×D3#4118yes—
74C2×C32×C4—24no—
75C2×C32×C4C2×D414yes—
76C2×C32×C4C2×D414yes—
77C2×C32×C4C2×D412yes—
78C2×C3⋊Dic3—28no—
79C2×C3⋊Dic3C2×D418yes—
80C2×C3×Dic3—28no—
81C2×C3×Dic3—24no—
82C3×D12—216no—
83C3×C4×D3—416no—
84#625—232no—
85C2×C4×D4—32no—
86C2×C4×D4—94no—
87#399—94no—
88#392—94no—
89#376—91no—
90C24×C3—34no—
91C23×D3C22×D314yes—
92C2×C3×D4—68no—
93C2×C3×D4—64no—
94C22×C3×C4—22no—
95C22×C3×C4—21no—
96C22×C3×C4—34no—
97C22×C3×C4—616no—
98C22×C3×C4—68no—
99C22×C3×C4C22×D312yes—
100C22×C3×C4C22×D312yes—
101C22×C3×C4C22×D312yes—
102C2×#67—616no—
103C2×#67—616no—
104C2×#67—616no—
105C22×Dic3—38no—
106C22×Dic3—64no—
107C22×Dic3C22×D314yes—
108C2×D12—28no—
109C2×D12—24no—
110C2×C4×D3—216no—
111C2×C4×D3—28no—
112C3×C4⋊C4—64no—
113C3×C22⋊C4—68no—
114C3×C42—24no—
115C3×C42#6718yescomplemented
116#217—616no—
117(C2×D3)⋊C4—28no—
118(C2×D3)⋊C4—616no—
119C4⋊Dic3—24no—
120Dic3⋊C4—616no—
121C4×Dic3—316no—
122C4×Dic3—68no—
123C22×C32C22×D412yes—
124C22×C32C22×D411yescharacteristic
125C22×C32C2×#4114yes—
126C2×C3×D3—216no—
127C2×C3×D3—28no—
128C2×C3×D3—48no—
129C2×C3×D3—44no—
130C2×C3×D3—44no—
131C32×C4—24no—
132C32×C4#12714yes—
133C3⋊Dic3—28no—
134C3×Dic3—44no—
135C22×D4—32no—
136C22×D4—94no—
137C23×C4—34no—
138C4×D4—68no—
139C4×D4—1816no—
140C2×C4⋊C4—32no—
141C2×C4⋊C4—94no—
142C2×C22⋊C4—34no—
143C2×C22⋊C4—98no—
144C2×C42—92no—
145C2×C42D3211yescharacteristic
146#95—94no—
147C23×C3—21no—
148C23×C3—38no—
149C23×C3—68no—
150C23×C3—68no—
151C23×C3—64no—
152C23×C3—64no—
153C23×C3C23×D312yes—
154C22×D3—24no—
155C22×D3—28no—
156C22×D3—28no—
157C22×D3—24no—
158C22×D3#23518yes—
159C3×D4—616no—
160C2×C3×C4—24no—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—22no—
164C2×C3×C4—24no—
165C2×C3×C4—44no—
166C2×C3×C4—68no—
167C2×C3×C4—64no—
168C2×C3×C4—1216no—
169C2×C3×C4D3×D418yes—
170C2×C3×C4C2×#6714yes—
171C2×C3×C4C2×#6714yes—
172C2×C3×C4C2×#6714yes—
173#67—664no—
174C2×Dic3—28no—
175C2×Dic3—24no—
176C2×Dic3—316no—
177C2×Dic3—68no—
178C2×Dic3—68no—
179C2×Dic3—68no—
180C2×Dic3—128no—
181D12—216no—
182C4×D3—416no—
183C2×C32#52512yes—
184C2×C32#52514yes—
185C2×C32C2×#12711yescharacteristic
186C3×D3—48no—
187C24—34no—
188C2×D4—68no—
189C2×D4—64no—
190C2×D4—188no—
191C2×D4—1816no—
192C22×C4—34no—
193C22×C4—616no—
194C22×C4—68no—
195C22×C4—94no—
196C22×C4C2×D3212yes—
197C22×C4C2×D3211yescharacteristic
198C4⋊C4—64no—
199C4⋊C4—188no—
200C22⋊C4—68no—
201C22⋊C4—1816no—
202C42—98no—
203C42#62514yescomplemented
204C22×C3—22no—
205C22×C3—24no—
206C22×C3—21no—
207C22×C3—616no—
208C22×C3—68no—
209C22×C3—124no—
210C22×C3—128no—
211C22×C3—124no—
212C22×C3C2×#23514yes—
213C22×C3C2×D3×D414yes—
214C22×C3D3×#4114yes—
215C22×C3C22×#6712yes—
216C2×D3—28no—
217C2×D3—216no—
218C2×D3—48no—
219C2×D3—44no—
220C2×D3—44no—
221C3×C4—24no—
222C3×C4—24no—
223C3×C4—24no—
224C3×C4—44no—
225C3×C4—124no—
226C3×C4#94018yes—
227Dic3—44no—
228Dic3—616no—
229Dic3—128no—
230C32#239711yescharacteristic, complemented, Sylow
231C23—38no—
232C23—68no—
233C23—64no—
234C23—68no—
235C23—64no—
236C23C22×D3211yescharacteristic
237D4—616no—
238D4—1832no—
239C2×C4—24no—
240C2×C4—68no—
241C2×C4—64no—
242C2×C4—98no—
243C2×C4—1216no—
244C2×C4—188no—
245C2×C4#380214yes—
246C2×C4C2×#62514yes—
247C2×C4C2×#62512yes—
248C2×C3—21no—
249C2×C3—22no—
250C2×C3—24no—
251C2×C3—128no—
252C2×C3#554718yes—
253C2×C3#579112yes—
254C2×C3C2×#94012yes—
255C2×C3#582812yes—
256D3—48no—
257C22—68no—
258C22—616no—
259C22—124no—
260C22—124no—
261C22—128no—
262C22C2×#380212yes—
263C22D3×#23514yes—
264C22C22×#62511yescharacteristic
265C4—24no—
266C4—124no—
267C4—188no—
268C4#6391414yes—
269C3—21no—
270C3#8234712yescomplemented
271C2—128no—
272C2#1059400614yes—
273C2C2×#6391411yescharacteristic
274C2#1059502212yes—
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D12C2semidirect
2. C2×C4×#625C2semidirect
3. #10592631C2semidirect
4. #10591389C2semidirect
5. #10591324C2semidirect
21. C2×C4×D12D3semidirect
39. C32×C42D4semidirect
40. C4×C3⋊Dic3D4semidirect
115. C3×C42#67semidirect
203. C42#625semidirect
230. C32#2397semidirect
270. C3#82347semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×C4×#6252
#105926312
#105913892
#105913242
#823473