Finite Group Databasebeta

← #19138897

Subgroups — #19138897

Order 5504.

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

normal subgroups only

This group has 624 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×#13063308C212yesmaximal
2C2×C4×C22⋊D43C211yesmaximal, characteristic
3#14582830C212yesmaximal, complemented
4#14582825C212yesmaximal, complemented
5#14582795C212yesmaximal, complemented
6#14582762C212yesmaximal, complemented
7#14582759C211yesmaximal, characteristic, complemented
8#14582756C212yesmaximal, complemented
9C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
10C22×C22⋊D43C2211yescharacteristic
11C22×C4×D43C2211yescharacteristic
12#13063308—28no—
13C4×C22⋊D43—24no—
14C2×C4⋊Dic43C2212yes—
15C2×Dic43⋊C4C2214yes—
16C2×Dic43⋊C4C2211yescharacteristic
17C2×C22⋊Dic43C2211yescharacteristic
18C2×C22⋊Dic43C2212yes—
19C2×(C2×D43)⋊C4C2211yescharacteristic
20C2×(C2×D43)⋊C4C2214yes—
21C2×C4×Dic43C2211yescharacteristic
22C43⋊#95C2214yes—
23C43⋊#95C2212yes—
24C43⋊#95C2214yes—
25C23×C4×C43C2212yes—
26C23×C4×C43C2211yescharacteristic
27C2×C4⋊C4×C43—24no—
28C2×C4⋊C4×C43C2212yes—
29C2×C4⋊C4×C43C2212yes—
30C24×C43C2311yescharacteristic
31C23×D43C2311yescharacteristic
32C22×C4×C43—24no—
33C22×C4×C43—24no—
34C22×C4×C43—24no—
35C22×C4×C43—24no—
36C22×C4×C43D414yes—
37C22×C4×C43C2314yes—
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C2×C22⋊D43—22no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43D414yes—
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2314yes—
46C22×Dic43C2311yescharacteristic
47C2×C4×D43—22no—
48C2×C4×D43—24no—
49C4⋊C4×C43—24no—
50C4⋊C4×C43—24no—
51C22⋊Dic43—22no—
52C22⋊Dic43—24no—
53(C2×D43)⋊C4—22no—
54(C2×D43)⋊C4—28no—
55C4⋊Dic43—24no—
56Dic43⋊C4—22no—
57Dic43⋊C4—28no—
58C4×Dic43—22no—
59C23×C43—22no—
60C23×C43—22no—
61C23×C43C2×D412yes—
62C23×C43C2×D412yes—
63C23×C43#4112yes—
64C23×C43C2411yescharacteristic
65C22×D43—21no—
66C22×D43—22no—
67C22×D43—21no—
68C22×D43—22no—
69C22×D43C2×D412yes—
70C2×C4×C43—22no—
71C2×C4×C43—28no—
72C2×C4×C43—24no—
73C2×C4×C43—24no—
74C2×C4×C43—24no—
75C2×C4×C43—48no—
76C2×C4×C43C2×D412yes—
77C2×C4×C43C2×D412yes—
78C2×C4×C43#4114yes—
79C22⋊D43—28no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—24no—
84C2×Dic43—21no—
85C2×Dic43—24no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—24no—
89C2×Dic43C2×D412yes—
90C4×D43—44no—
91C22×C43—22no—
92C22×C43—22no—
93C22×C43—24no—
94C22×C43—24no—
95C22×C43#12114yes—
96C22×C43C22×D411yescharacteristic
97C22×C43C22×D411yescharacteristic
98C22×C43C2×#4111yescharacteristic
99C22×C43C2×#4112yes—
100C22×C432−1+412yes—
101C2×D43—22no—
102C2×D43—24no—
103C2×D43—41no—
104C2×D43—41no—
105C2×D43—42no—
106C4×C43—22no—
107C4×C43—44no—
108C4×C43#12314yescomplemented
109Dic43—22no—
110Dic43—41no—
111Dic43—41no—
112Dic43—44no—
113#2486—431nomaximal, Sylow
114C2×C43—24no—
115C2×C43C2×#12111yescharacteristic
116C2×C43C2×#12311yescharacteristic
117C2×C43#53611yescharacteristic
118C2×C43#54712yes—
119C2×C43#55212yes—
120D43—42no—
121C2×#123—432no—
122C2×C4×D4—431no—
123C22×C4⋊C4D4311yescharacteristic, complemented
124#398—432no—
125#397—432no—
126#389—432no—
127#381—432no—
128#380—431no—
129#380—432no—
130C43#248611yescharacteristic, complemented, Sylow
131C22×D4—431no—
132C23×C4—431no—
133C23×C4C2×D4312yes—
134C23×C4C2×D4311yescharacteristic
135#123—868no—
136C4×D4—864no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—431no—
139C2×C4⋊C4—434no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4C2×D4312yes—
142C2×C4⋊C4C2×D4312yes—
143C2×C22⋊C4—431no—
144C2×C22⋊C4—432no—
145C2×C22⋊C4—431no—
146C2×C22⋊C4—434no—
147C2×C42—431no—
148#95—434no—
149#95—432no—
150#95—434no—
151C24—431no—
152C24C22×D4311yescharacteristic
153C2×D4—434no—
154C2×D4—862no—
155C2×D4—862no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—431no—
161C22×C4—431no—
162C22×C4—431no—
163C22×C4—434no—
164C22×C4—864no—
165C22×C4—862no—
166C22×C4C22⋊D4314yes—
167C22×C4C22×D4314yes—
168C22×C4C22×D4311yescharacteristic
169C22×C4C22×D4311yescharacteristic
170C4⋊C4—24no—
171C4⋊C4—24no—
172C4⋊C4—868no—
173C4⋊C4—864no—
174C4⋊C4—862no—
175C22⋊C4—868no—
176C22⋊C4—864no—
177C22⋊C4—862no—
178C22⋊C4—862no—
179C42—862no—
180C23—22no—
181C23—22no—
182C23—432no—
183C23—861no—
184C23—861no—
185C23—862no—
186C23—862no—
187C23D4×D4312yes—
188C23#1062190012yes—
189C23C2×C22⋊D4312yes—
190C23C23×D4311yescharacteristic
191D4—868no—
192C2×C4—22no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—48no—
198C2×C4—432no—
199C2×C4—861no—
200C2×C4—861no—
201C2×C4—864no—
202C2×C4—861no—
203C2×C4—861no—
204C2×C4—864no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—864no—
208C2×C4—1724no—
209C2×C4#1062189814yes—
210C2×C4C2×C22⋊D4312yes—
211C2×C4C2×C22⋊D4312yes—
212C22—24no—
213C22—22no—
214C22—22no—
215C22—24no—
216C22—862no—
217C22—864no—
218C22—1722no—
219C22—1721no—
220C22—1721no—
221C22#1306329614yes—
222C22C2×D4×D4311yescharacteristic
223C22C22×C22⋊D4311yescharacteristic
224C22C2×#1062190011yescharacteristic
225C22C2×#1062189812yes—
226C22#1306337312yes—
227C4—22no—
228C4—44no—
229C4—862no—
230C4—1721no—
231C4—1721no—
232C4—1724no—
233C4#1306330814yescomplemented
234C2—24no—
235C2—1722no—
236C2C2×#1306329611yescharacteristic
237C2C2×#1306330811yescharacteristic
238C2#1458347311yescharacteristic
239C2#1458355012yes—
240C2#1458358412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC22×C4⋊C4×C43C2
hypercenterC22×C4⋊C4D43
hypocenterC43#2486
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14582830C2semidirect
4. #14582825C2semidirect
5. #14582795C2semidirect
6. #14582762C2semidirect
7. #14582759C2semidirect
8. #14582756C2semidirect
9. C22×C4⋊C4×C43C2semidirect
108. C4×C43#123semidirect
123. C22×C4⋊C4D43semidirect
130. C43#2486semidirect
233. C4#13063308semidirect