Finite Group Databasebeta

← #11787860

Subgroups — #11787860

Order 1152.

1332 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 1332 conjugacy classes of subgroups — too many to draw. Only its 221 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×#64149C211yesmaximal, characteristic
2#10596269C211yesmaximal, characteristic, complemented
3C2×C32×#100C211yesmaximal, characteristic, complemented
4#10592830C212yesmaximal, complemented
5#10589421C212yesmaximal, complemented
6#70070—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638—22no—
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C2×C32×M16C2212yes—
11C2×#3757—22no—
12#64149—22no—
13#64149C414yescomplemented
14D4×C3⋊Dic3—24no—
15#64135C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C32×#100—22no—
18#63648—24no—
19C2×#940—34no—
20#5798—34no—
21C2×C3×#100D314yescomplemented
22#5131—38no—
23#4555—38no—
24C24×C32D412yes—
25C23×C3⋊D3—21no—
26C2×C32×D4—22no—
27C2×C32×D4—22no—
28C2×C32×D4C2×C412yes—
29C2×C32×D4D412yes—
30C22×C32×C4C2311yescharacteristic
31C2×#638—28no—
32C2×#638—48no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—24no—
35C2×C4⋊(C3⋊D3)—22no—
36C2×C4⋊(C3⋊D3)—22no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)C2×C412yescomplemented
39C32×M16—22no—
40C32×M16—22no—
41C2×C32×C8—22no—
42#3757—24no—
43#3757—22no—
44C4⋊(C3⋊Dic3)D414yescomplemented
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—22no—
47C4×C3⋊Dic3C2×C412yescomplemented
48#1887—91noSylow
49C22×C3×D4C2×D314yes—
50C22×#67—68no—
51C22×D12—34no—
52C2×C3×M16C2×D318yes—
53C2×#217—68no—
54#940—316no—
55#940—68no—
56D4×Dic3—616no—
57#926—38no—
58C2×C4×Dic3—34no—
59C3×#100—28no—
60#821—616no—
61C23×C32—22no—
62C23×C32—22no—
63C23×C32—44no—
64C23×C32C22⋊C414yes—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—44no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3—41no—
70C32×D4—24no—
71C32×D4—24no—
72C2×C32×C4C22×C411yescharacteristic
73C2×C32×C4C2×D412yes—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4#4112yes—
76#638—416no—
77C2×C3⋊Dic3—24no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—24no—
80C2×C3⋊Dic3—84no—
81C4⋊(C3⋊D3)—24no—
82C4⋊(C3⋊D3)—42no—
83C32×C8—42no—
84C2×#127—91no—
85#518—91no—
86#418—92no—
87C2×#100C3⋊D311yescharacteristic, complemented
88#339—92no—
89C24×C3D1218yes—
90C23×D3—64no—
91C2×C3×D4—28no—
92C2×C3×D4—28no—
93C2×C3×D4C4×D318yes—
94C2×C3×D4#6718yes—
95C22×C3×C4C22×D314yes—
96C2×#67—632no—
97C2×#67—1232no—
98C22×Dic3—64no—
99C22×Dic3—616no—
100C2×D12—38no—
101C2×D12—68no—
102C2×D12—68no—
103C2×D12—64no—
104C3×M16—28no—
105C3×M16—28no—
106C2×C3×C8—28no—
107#217—616no—
108#217—68no—
109C4⋊Dic3—316no—
110C4×Dic3—38no—
111C4×Dic3—68no—
112C4×Dic3—64no—
113C22×C32—22no—
114C22×C32—24no—
115C22×C32—44no—
116C22×C32—44no—
117C22×C32—82no—
118C22×C32C2×C22⋊C411yescharacteristic
119C22×C32#12011yescharacteristic
120C22×C32#12311yescharacteristic
121C2×C3⋊D3—44no—
122C2×C3⋊D3—42no—
123C2×C3⋊D3—82no—
124C2×C3⋊D3—82no—
125C32×C4C4×D412yes—
126C32×C4#12112yes—
127C3⋊Dic3—24no—
128C3⋊Dic3—44no—
129C22×D4—91no—
130C22×D4—182no—
131C22×D4C2×C3⋊D311yescharacteristic
132C2×M16C2×C3⋊D312yes—
133#127—94no—
134#127—182no—
135C4×D4—184no—
136#117—92no—
137C2×C22⋊C4—182no—
138C2×C42—91no—
139#102—184no—
140#100—22no—
141C23×C3—28no—
142C23×C3—28no—
143C23×C3—416no—
144C23×C3(C2×D3)⋊C4116yes—
145C23×C3C2×D1214yes—
146C22×D3—68no—
147C22×D3—1216no—
148C22×D3—124no—
149C22×D3—124no—
150C3×D4—216no—
151C3×D4—216no—
152C2×C3×C4C2×C4×D314yes—
153C2×C3×C4D3×D418yes—
154C2×C3×C4#23718yes—
155C2×C3×C4C2×#6714yes—
156#67—1264no—
157C2×Dic3—616no—
158C2×Dic3—68no—
159C2×Dic3—616no—
160C2×Dic3—2416no—
161D12—616no—
162D12—128no—
163C3×C8—48no—
164C2×C32—21no—
165C2×C32—21no—
166C2×C32—44no—
167C2×C32#38611yescharacteristic
168C2×C32#45312yes—
169C3⋊D3—82no—
170C24—181no—
171C24C4⋊(C3⋊D3)12yes—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—92no—
175C2×D4—188no—
176C2×D4—182no—
177C2×D4—182no—
178C2×D4—181no—
179C2×D4—368no—
180C2×D4C4×C3⋊D312yes—
181C2×D4#63812yes—
182C22×C4—181no—
183C22×C4—184no—
184C22×C4C22×C3⋊D311yescharacteristic
185M16—22no—
186M16—22no—
187C2×C8—22no—
188C4⋊C4—94no—
189C22⋊C4—184no—
190C22⋊C4—182no—
191C42—92no—
192C42—182no—
193C42—181no—
194C22×C3—28no—
195C22×C3—216no—
196C22×C3—416no—
197C22×C3—416no—
198C22×C3—88no—
199C22×C3#88214yes—
200C22×C3#88614yes—
201C22×C3C2×(C2×D3)⋊C414yes—
202C2×D3—1216no—
203C2×D3—128no—
204C2×D3—248no—
205C2×D3—248no—
206C3×C4#67⋊C418yes—
207C3×C4#93918yes—
208Dic3—616no—
209Dic3—1216no—
210C32#188711yescharacteristic, complemented, Sylow
211C23—22no—
212C23—22no—
213C23—44no—
214C23—182no—
215C23—364no—
216C23—361no—
217C23—361no—
218C23#375214yes—
219C23C2×C4⋊(C3⋊D3)11yescharacteristic
220D4—24no—
221D4—24no—
222D4—184no—
223D4—3616no—
224D4—362no—
225C2×C4—184no—
226C2×C4—182no—
227C2×C4—184no—
228C2×C4—724no—
229C2×C4C2×C4×C3⋊D311yescharacteristic
230C2×C4D4×C3⋊D312yes—
231C2×C4#383012yes—
232C2×C4C2×#63811yescharacteristic
233C8—42no—
234C2×C3—24no—
235C2×C3—24no—
236C2×C3—416no—
237C2×C3#474718yes—
238C2×C3#495814yes—
239D3—248no—
240C22—22no—
241C22—24no—
242C22—44no—
243C22—44no—
244C22—82no—
245C22—364no—
246C22—362no—
247C22—722no—
248C22—722no—
249C22#6409111yescharacteristic
250C22#6409511yescharacteristic
251C22C2×#375211yescharacteristic
252C4—184no—
253C4—364no—
254C4#6409012yes—
255C4#6414812yes—
256C3#7007014yescomplemented
257C2—21no—
258C2—21no—
259C2—44no—
260C2—722no—
261C2#1059244612yes—
262C2#1059265711yescharacteristic
subgroupG/H
centerC22#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#100C2
socleC22×C32#120
prime radicalC2×#64149C2
cosocleC22×C32×C4C23
hypercenterC2×#100C3⋊D3
hypocenterC32#1887
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #10596269C2semidirect
3. C2×C32×#100C2semidirect
4. #10592830C2semidirect
5. #10589421C2semidirect
13. #64149C4semidirect
21. C2×C3×#100D3semidirect
38. C2×C4⋊(C3⋊D3)C2×C4semidirect
44. C4⋊(C3⋊Dic3)D4semidirect
47. C4×C3⋊Dic3C2×C4semidirect
87. C2×#100C3⋊D3semidirect
210. C32#1887semidirect
256. C3#70070semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
#105962692
C2×C32×#1002
#105928302
#105894212
#700703