Finite Group Databasebeta

← #19137758

Subgroups — #19137758

Order 5504.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13063304C211yesmaximal, characteristic
2#14582803C212yesmaximal, complemented
3#14582794C212yesmaximal, complemented
4#14582793C212yesmaximal
5#14582787C212yesmaximal
6#14582782C212yesmaximal, complemented
7#14582780C212yesmaximal, complemented
8#14582762C211yesmaximal, characteristic
9C43×#380C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11#13063304C418yescomplemented
12C2×C4⋊Dic43C2211yescharacteristic
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×C22⋊Dic43C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C4×Dic43C2212yes—
19C2×C4×Dic43C2212yes—
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2211yescharacteristic
27C23×C4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2212yes—
29C2×C22⋊C4×C43C2211yescharacteristic
30C2×C22⋊C4×C43C2211yescharacteristic
31#95×C43C2212yes—
32C24×C43C2311yescharacteristic
33C22×C4×C43—42no—
34C22×C4×C43C2×C414yes—
35C22×C4×C43C2312yes—
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C2×Dic86—42no—
44C2×Dic86C2×C414yes—
45C4⋊C4×C43—42no—
46C22⋊C4×C43—41no—
47C22⋊C4×C43—41no—
48C22⋊Dic43—42no—
49C22⋊Dic43C2×C418yes—
50C4⋊Dic43C2×C414yes—
51Dic43⋊C4—42no—
52Dic43⋊C4—42no—
53Dic43⋊C4C2×C418yes—
54C4×Dic43—42no—
55C4×Dic43—42no—
56C23×C43—22no—
57C23×C43—21no—
58C23×C43—22no—
59C23×C43—21no—
60C23×C43C22×C412yes—
61C23×C43C2411yescharacteristic
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—44no—
71C2×C4×C43C22×C412yes—
72C2×C4×C43C22×C412yes—
73C2×Dic43—22no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43C22×C414yes—
84C2×Dic43C22×C414yes—
85Dic86—44no—
86C22×C43—22no—
87C22×C43—22no—
88C22×C43—22no—
89C22×C43—42no—
90C22×C43—42no—
91C22×C43C23×C411yescharacteristic
92C22×C43H(5,𝔽2)12yes—
93C22×C43H(5,𝔽2)11yescharacteristic
94C22×C432−1+412yes—
95C22×C432−1+411yescharacteristic
96C4×C43—22no—
97C4×C43—22no—
98C4×C43—42no—
99C4×C43—42no—
100Dic43—24no—
101Dic43—24no—
102Dic43—42no—
103Dic43—42no—
104#2378—431nomaximal, Sylow
105C2×C43—42no—
106C2×C43#51811yescharacteristic
107C2×C43#51911yescharacteristic
108C2×C43#52011yescharacteristic
109C2×C43#56212yes—
110C2×C43#56312yes—
111C2×C22⋊Q8—431no—
112#391—432no—
113#389—432no—
114#388—432no—
115#388—432no—
116#387—432no—
117#387—432no—
118#381—431no—
119#380D4311yescharacteristic
120C43#237811yescharacteristic, complemented, Sylow
121C22×Q8—431no—
122C23×C4C2×D4311yescharacteristic
123C22⋊Q8—438no—
124C2×C4⋊C4—432no—
125C2×C4⋊C4—431no—
126C2×C4⋊C4—432no—
127C2×C4⋊C4—432no—
128C2×C4⋊C4C2×D4312yes—
129C2×C22⋊C4—432no—
130C2×C22⋊C4—432no—
131C2×C22⋊C4C2×D4311yescharacteristic
132C2×C22⋊C4C2×D4311yescharacteristic
133C2×C42—432no—
134C2×C42—432no—
135#95—431no—
136#95—432no—
137#95—431no—
138#95—432no—
139#95—432no—
140#95—432no—
141#95—432no—
142#95C2×D4312yes—
143C24C22×D4311yescharacteristic
144C2×Q8—434no—
145C2×Q8—1722no—
146C22×C4—42no—
147C22×C4—432no—
148C22×C4—432no—
149C22×C4—432no—
150C22×C4—432no—
151C22×C4C4×D4314yes—
152C22×C4C22×D4312yes—
153C22×C4C22×D4312yes—
154C22×C4C22×D4311yescharacteristic
155C22×C4C22×D4311yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—438no—
158C4⋊C4—434no—
159C4⋊C4—1722no—
160C4⋊C4—1722no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—438no—
164C22⋊C4—1722no—
165C42—1722no—
166C42—1722no—
167C23—21no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23C2×C4×D4312yes—
172C23C23×D4311yescharacteristic
173Q8—1724no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—434no—
184C2×C4—434no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4C2×C4×D4312yes—
196C2×C4C2×C4×D4312yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D4311yescharacteristic
203C22#1306337012yes—
204C22#1306337011yescharacteristic
205C22#1306337212yes—
206C22#1306337311yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—864no—
212C4—864no—
213C4—1722no—
214C4—1722no—
215C2—42no—
216C2#1458337211yescharacteristic
217C2#1458337611yescharacteristic
218C2#1458338011yescharacteristic
219C2#1458364412yes—
220C2#1458365012yes—
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#380C2
socleC23×C43C24
hypercenter#380D43
hypocenterC43#2378
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #14582803C2semidirect
3. #14582794C2semidirect
6. #14582782C2semidirect
7. #14582780C2semidirect
11. #13063304C4semidirect
120. C43#2378semidirect