Finite Group Databasebeta

← #19141561

Subgroups — #19141561

Order 5504.

512 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063302C212yesmaximal, complemented
2#14582841C212yesmaximal, complemented
3#14582829C211yesmaximal, characteristic, complemented
4#14582827C212yesmaximal, complemented
5#14582804C211yesmaximal, characteristic, complemented
6#14582793C212yesmaximal, complemented
7#14582779C212yesmaximal
8#14582774C212yesmaximal, complemented
9C43×#394C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11C23×Dic43C2212yes—
12#13063302—28no—
13C2×C4⋊Dic43C2212yes—
14C2×C4⋊Dic43C2211yescharacteristic
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C4×Dic43C2211yescharacteristic
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2211yescharacteristic
26C43⋊#95C2212yes—
27C22×D4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2211yescharacteristic
29C2×C22⋊C4×C43C2212yes—
30C2×C22⋊C4×C43C2212yes—
31#95×C43C2211yescharacteristic
32C24×C43C2312yes—
33C2×D4×C43—24no—
34C2×D4×C43—41no—
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43—24no—
40C22×Dic43—42no—
41C22×Dic43—42no—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C2×Dic86—41no—
47C2×Dic86—41no—
48C2×Dic86D414yescomplemented
49C4⋊C4×C43—41no—
50C22⋊C4×C43—24no—
51C22⋊C4×C43—24no—
52C22⋊Dic43—24no—
53C22⋊Dic43—24no—
54C22⋊Dic43—42no—
55C4⋊Dic43—24no—
56C4⋊Dic43—41no—
57Dic43⋊C4—24no—
58Dic43⋊C4—24no—
59C4×Dic43—41no—
60C23×C43—22no—
61C23×C43—22no—
62C23×C43—22no—
63C23×C43—22no—
64C23×C43—22no—
65C23×C43—22no—
66C23×C43#4114yes—
67C23×C43C2411yescharacteristic
68D4×C43—44no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43C2×D412yes—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—48no—
91C2×Dic43C2×D414yes—
92Dic86—44no—
93C22×C43—24no—
94C22×C43—24no—
95C22×C43—24no—
96C22×C43—42no—
97C22×C43—42no—
98C22×C43—42no—
99C22×C43—42no—
100C22×C43C22×D411yescharacteristic
101C22×C43C2×#4112yes—
102C22×C43H(5,𝔽2)11yescharacteristic
103C22×C43H(5,𝔽2)11yescharacteristic
104C22×C432−1+412yes—
105C4×C43—22no—
106C4×C43—42no—
107C4×C43—41no—
108C4×C43—41no—
109Dic43—24no—
110Dic43—42no—
111Dic43—42no—
112Dic43—42no—
113#2728—431nomaximal, Sylow
114C2×C43—44no—
115C2×C43#53411yescharacteristic
116C2×C43#53912yes—
117C2×C43#54812yes—
118C2×C43#55111yescharacteristic
119C2×C43#56311yescharacteristic
120C2×C22⋊Q8—432no—
121#400—432no—
122#398—431no—
123#397—432no—
124#394D4311yescharacteristic
125#391—431no—
126#388—432no—
127#386—432no—
128#385—432no—
129C43#272811yescharacteristic, complemented, Sylow
130C22×Q8—431no—
131C22×D4C2×D4311yescharacteristic
132C23×C4—432no—
133C22⋊Q8—868no—
134C2×C4⋊C4—432no—
135C2×C4⋊C4—432no—
136C2×C4⋊C4—432no—
137C2×C4⋊C4—431no—
138C2×C4⋊C4C2×D4311yescharacteristic
139C2×C22⋊C4—432no—
140C2×C22⋊C4—432no—
141C2×C22⋊C4—432no—
142C2×C22⋊C4C2×D4312yes—
143C2×C22⋊C4C2×D4312yes—
144C2×C42—431no—
145#95—432no—
146#95—432no—
147#95—432no—
148#95—432no—
149#95—432no—
150#95—431no—
151#95C2×D4311yescharacteristic
152C24C22×D4312yes—
153C2×Q8—434no—
154C2×Q8—1721no—
155C2×Q8—1721no—
156C2×D4—24no—
157C2×D4—41no—
158C22×C4—432no—
159C22×C4—432no—
160C22×C4—432no—
161C22×C4—432no—
162C22×C4—864no—
163C22×C4—1722no—
164C22×C4—1722no—
165C22×C4C22×D4311yescharacteristic
166C22×C4C22×D4311yescharacteristic
167C22×C4C22×D4312yes—
168C22×C4C22×D4311yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—864no—
171C4⋊C4—864no—
172C4⋊C4—864no—
173C4⋊C4—1721no—
174C22⋊C4—24no—
175C22⋊C4—24no—
176C22⋊C4—864no—
177C22⋊C4—864no—
178C22⋊C4—1722no—
179C42—1721no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23—22no—
185C23—22no—
186C23#1062190014yes—
187C23C23×D4311yescharacteristic
188Q8—1724no—
189D4—44no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—434no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—1728no—
212C2×C4D4×D4312yes—
213C22—24no—
214C22—24no—
215C22—24no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22C2×D4×D4311yescharacteristic
221C22C2×#1062190012yes—
222C22#1306337011yescharacteristic
223C22#1306337111yescharacteristic
224C22#1306337212yes—
225C4—22no—
226C4—42no—
227C4—41no—
228C4—41no—
229C4—864no—
230C4—1722no—
231C4—1722no—
232C4—1722no—
233C2—44no—
234C2#1458345711yescharacteristic
235C2#1458349312yes—
236C2#1458355512yes—
237C2#1458358011yescharacteristic
238C2#1458364911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2728
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063302C2semidirect
2. #14582841C2semidirect
3. #14582829C2semidirect
4. #14582827C2semidirect
5. #14582804C2semidirect
6. #14582793C2semidirect
8. #14582774C2semidirect
48. C2×Dic86D4semidirect
129. C43#2728semidirect