Finite Group Databasebeta

← #19138471

Subgroups — #19138471

Order 5504.

660 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063306C212yesmaximal, complemented
2C2×D4×Dic43C212yesmaximal, complemented
3#14582835C211yesmaximal, characteristic, complemented
4#14582813C212yesmaximal, complemented
5#14582796C212yesmaximal, complemented
6#14582793C212yesmaximal, complemented
7#14582774C212yesmaximal, complemented
8#14582771C211yesmaximal, characteristic, complemented
9C43×#392C211yesmaximal, characteristic
10C23×Dic43C2211yescharacteristic
11C23×Dic43C2212yes—
12#13063306—28no—
13D4×Dic43—28no—
14C2×C4⋊Dic43C2212yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2211yescharacteristic
21C2×C22⋊Dic43C2212yes—
22C2×C22⋊Dic43C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×C4×Dic43C2212yes—
25C43⋊#95C2211yescharacteristic
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C22×D4×C43C2212yes—
29C22×D4×C43C2211yescharacteristic
30C2×C22⋊C4×C43C2212yes—
31C2×C22⋊C4×C43C2211yescharacteristic
32#95×C43C2211yescharacteristic
33C24×C43C2312yes—
34C24×C43C2311yescharacteristic
35C2×D4×C43—24no—
36C2×D4×C43—24no—
37C2×D4×C43—24no—
38C2×D4×C43—24no—
39C2×D4×C43—41no—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×Dic43—24no—
44C22×Dic43—24no—
45C22×Dic43—24no—
46C22×Dic43—41no—
47C22×Dic43—42no—
48C22×Dic43C2312yes—
49C22×Dic43C2312yes—
50C22×Dic43C2312yes—
51C22×Dic43C2312yes—
52C22⋊C4×C43—24no—
53C22⋊C4×C43—41no—
54C22⋊Dic43—24no—
55C22⋊Dic43—24no—
56C22⋊Dic43—24no—
57C22⋊Dic43—22no—
58C22⋊Dic43D418yescomplemented
59C4⋊Dic43—24no—
60C4⋊Dic43—41no—
61Dic43⋊C4—24no—
62Dic43⋊C4—24no—
63Dic43⋊C4—24no—
64C4×Dic43—24no—
65C23×C43—22no—
66C23×C43—22no—
67C23×C43—22no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43—21no—
72C23×C43—22no—
73C23×C43—21no—
74C23×C43—22no—
75C23×C43C2×D414yes—
76C23×C43#4112yes—
77C23×C43C2411yescharacteristic
78D4×C43—216no—
79D4×C43—44no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43#4114yes—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—44no—
98C2×Dic43—48no—
99C2×Dic43C2×D414yes—
100C2×Dic43C2×D414yes—
101C22×C43—24no—
102C22×C43—24no—
103C22×C43—22no—
104C22×C43—24no—
105C22×C43—24no—
106C22×C43—42no—
107C22×C43—42no—
108C22×C43—41no—
109C22×C43—42no—
110C22×C43—42no—
111C22×C43—42no—
112C22×C43—41no—
113C22×C43C22×D412yes—
114C22×C43C2×#4111yescharacteristic
115C22×C43C2×#4112yes—
116C22×C43H(5,𝔽2)11yescharacteristic
117C22×C432−1+411yescharacteristic
118C4×C43—24no—
119C4×C43—41no—
120C4×C43—41no—
121Dic43—24no—
122Dic43—24no—
123Dic43—42no—
124Dic43—42no—
125#2455—431nomaximal, Sylow
126C2×C43—44no—
127C2×C43—42no—
128C2×C43#52512yes—
129C2×C43#53911yescharacteristic
130C2×C43D4211yescharacteristic
131C2×C43#54712yes—
132C2×C43#55911yescharacteristic
133C2×#123—432no—
134C2×C4×D4—432no—
135#399—431no—
136#394—432no—
137#392D4311yescharacteristic
138#389—432no—
139#388—432no—
140#385—431no—
141#385—432no—
142C43#245511yescharacteristic, complemented, Sylow
143C22×D4C2×D4312yes—
144C22×D4C2×D4311yescharacteristic
145C23×C4—431no—
146C23×C4—432no—
147#123—868no—
148C4×D4—868no—
149C2×C4⋊C4—432no—
150C2×C4⋊C4—432no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—431no—
154C2×C22⋊C4—432no—
155C2×C22⋊C4—432no—
156C2×C22⋊C4—432no—
157C2×C22⋊C4—432no—
158C2×C22⋊C4—431no—
159C2×C22⋊C4C2×D4312yes—
160C2×C22⋊C4C2×D4311yescharacteristic
161C2×C42—432no—
162#95—432no—
163#95—432no—
164#95—431no—
165#95C2×D4311yescharacteristic
166C24C22×D4312yes—
167C24C22×D4311yescharacteristic
168C2×D4—24no—
169C2×D4—24no—
170C2×D4—24no—
171C2×D4—24no—
172C2×D4—41no—
173C22×C4—432no—
174C22×C4—432no—
175C22×C4—432no—
176C22×C4—432no—
177C22×C4—864no—
178C22×C4—864no—
179C22×C4—864no—
180C22×C4—1721no—
181C22×C4—1722no—
182C22×C4C22×D4311yescharacteristic
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4312yes—
185C4⋊C4—864no—
186C4⋊C4—864no—
187C4⋊C4—864no—
188C4⋊C4—864no—
189C4⋊C4—1721no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—438no—
193C22⋊C4—864no—
194C22⋊C4—864no—
195C22⋊C4—864no—
196C22⋊C4—862no—
197C42—864no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—21no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23D4×D4314yes—
209C23#1062190012yes—
210C23C23×D4311yescharacteristic
211D4—216no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—434no—
220C2×C4—434no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—862no—
231C2×C4—1724no—
232C2×C4—1728no—
233C2×C4#1062190014yes—
234C22—24no—
235C22—24no—
236C22—22no—
237C22—24no—
238C22—24no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—42no—
243C22—41no—
244C22—42no—
245C22—42no—
246C22C2×D4×D4312yes—
247C22C2×#1062190012yes—
248C22C2×#1062190011yescharacteristic
249C22#1306337011yescharacteristic
250C22#1306337211yescharacteristic
251C4—24no—
252C4—41no—
253C4—41no—
254C4—864no—
255C4—864no—
256C4—1722no—
257C4—1722no—
258C2—44no—
259C2—42no—
260C2#1458340512yes—
261C2#1458349411yescharacteristic
262C2#1458353111yescharacteristic
263C2#1458354912yes—
264C2#1458363511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2455
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13063306C2semidirect
2. C2×D4×Dic43C2semidirect
3. #14582835C2semidirect
4. #14582813C2semidirect
5. #14582796C2semidirect
6. #14582793C2semidirect
7. #14582774C2semidirect
8. #14582771C2semidirect
58. C22⋊Dic43D4semidirect
142. C43#2455semidirect