Finite Group Databasebeta

← #19140489

Subgroups — #19140489

Order 5504.

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

normal subgroups only

This group has 562 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×#13063318C211yesmaximal, characteristic, complemented
2C2×D4×Dic43C211yesmaximal, characteristic, complemented
3#14582839C211yesmaximal, characteristic, complemented
4#14582835C211yesmaximal, characteristic, complemented
5#14582822C212yesmaximal, complemented
6#14582813C211yesmaximal, characteristic, complemented
7#14582813C212yesmaximal, complemented
8#14582779C212yesmaximal, complemented
9#14582771C212yesmaximal, complemented
10#14582763C211yesmaximal, characteristic, complemented
11C43×#392C211yesmaximal, characteristic
12C23×Dic43C2212yes—
13#13063318—24no—
14D4×Dic43—24no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×C22⋊Dic43C2211yescharacteristic
22C2×C22⋊Dic43C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×C22⋊Dic43C2211yescharacteristic
25C2×C22⋊Dic43C2212yes—
26C2×C22⋊Dic43C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×D4×C43C2211yescharacteristic
33C22×D4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C24×C43C2312yes—
39C2×D4×C43—22no—
40C2×D4×C43—24no—
41C2×D4×C43—24no—
42C2×D4×C43—42no—
43C2×D4×C43—42no—
44C22×C4×C43C2312yes—
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C22×Dic43—24no—
48C22×Dic43—42no—
49C22×Dic43—42no—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2312yes—
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2312yes—
54C22×Dic43C2311yescharacteristic
55C22×Dic43C2311yescharacteristic
56C22⋊C4×C43—22no—
57C22⋊C4×C43—42no—
58C22⋊Dic43—24no—
59C22⋊Dic43—22no—
60C22⋊Dic43—22no—
61C22⋊Dic43—24no—
62C22⋊Dic43—42no—
63C22⋊Dic43—42no—
64C4⋊Dic43—22no—
65C4⋊Dic43—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4—42no—
69Dic43⋊C4—42no—
70C4×Dic43D414yescomplemented
71C23×C43—22no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43—21no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—21no—
81C23×C43—21no—
82C23×C43#4114yes—
83C23×C43C2411yescharacteristic
84D4×C43—28no—
85D4×C43—48no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43C2×D412yes—
93C2×Dic43—21no—
94C2×Dic43—22no—
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43—21no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—22no—
106C2×Dic43—21no—
107C2×Dic43—48no—
108C2×Dic43C2×D412yes—
109C2×Dic43C2×D412yes—
110C22×C43—24no—
111C22×C43—24no—
112C22×C43—24no—
113C22×C43—42no—
114C22×C43—42no—
115C22×C43—42no—
116C22×C43—42no—
117C22×C43—41no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43—42no—
121C22×C43—42no—
122C22×C43C22×D411yescharacteristic
123C22×C43C2×#4112yes—
124C22×C43H(5,𝔽2)12yes—
125C22×C43H(5,𝔽2)11yescharacteristic
126C22×C432−1+411yescharacteristic
127C4×C43—22no—
128C4×C43—41no—
129C4×C43—42no—
130Dic43—22no—
131Dic43—22no—
132Dic43—41no—
133Dic43—42no—
134Dic43—41no—
135Dic43—42no—
136#2636—431nomaximal, Sylow
137C2×C43—44no—
138C2×C43—81no—
139C2×C43#52511yescharacteristic
140C2×C43#53511yescharacteristic
141C2×C43#53711yescharacteristic
142C2×C43#53812yes—
143C2×C43#53912yes—
144C2×#126—431no—
145C2×C4×D4—431no—
146#400—431no—
147#399—431no—
148#396—432no—
149#394—431no—
150#394—432no—
151#392D4311yescharacteristic
152#386—432no—
153#385—432no—
154#382—431no—
155C43#263611yescharacteristic, complemented, Sylow
156C22×D4C2×D4311yescharacteristic
157C22×D4C2×D4312yes—
158C23×C4—432no—
159#126—864no—
160C4×D4—864no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—431no—
163C2×C4⋊C4—431no—
164C2×C4⋊C4—431no—
165C2×C4⋊C4—432no—
166C2×C4⋊C4—432no—
167C2×C22⋊C4—432no—
168C2×C22⋊C4—431no—
169C2×C22⋊C4—431no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4C2×D4311yescharacteristic
174C2×C22⋊C4C2×D4312yes—
175C2×C42—431no—
176#95—432no—
177#95—431no—
178#95—432no—
179#95—432no—
180#95C2×D4311yescharacteristic
181C24C22×D4311yescharacteristic
182C24C22×D4312yes—
183C2×D4—24no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—42no—
188C22×C4—431no—
189C22×C4—431no—
190C22×C4—431no—
191C22×C4—431no—
192C22×C4—432no—
193C22×C4—432no—
194C22×C4—864no—
195C22×C4—1722no—
196C22×C4—1722no—
197C22×C4C22×D4312yes—
198C22×C4C22×D4311yescharacteristic
199C22×C4C22×D4311yescharacteristic
200C4⋊C4—862no—
201C4⋊C4—862no—
202C4⋊C4—862no—
203C4⋊C4—862no—
204C4⋊C4—1722no—
205C4⋊C4—1722no—
206C22⋊C4—22no—
207C22⋊C4—42no—
208C22⋊C4—864no—
209C22⋊C4—862no—
210C22⋊C4—862no—
211C22⋊C4—864no—
212C22⋊C4—1722no—
213C22⋊C4—1722no—
214C42—434no—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23#1062190014yes—
227C23C23×D4311yescharacteristic
228D4—28no—
229D4—48no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—432no—
237C2×C4—432no—
238C2×C4—861no—
239C2×C4—862no—
240C2×C4—861no—
241C2×C4—861no—
242C2×C4—861no—
243C2×C4—862no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—861no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—861no—
252C2×C4—1728no—
253C2×C4D4×D4312yes—
254C22—24no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22C2×D4×D4311yescharacteristic
267C22C2×#1062190012yes—
268C22#1306337012yes—
269C22#1306337011yescharacteristic
270C22#1306337211yescharacteristic
271C4—22no—
272C4—41no—
273C4—42no—
274C4—862no—
275C4—862no—
276C4—1721no—
277C4—1722no—
278C4—1721no—
279C4—1722no—
280C2—44no—
281C2—81no—
282C2#1458340511yescharacteristic
283C2#1458346211yescharacteristic
284C2#1458347811yescharacteristic
285C2#1458348412yes—
286C2#1458349412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2636
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13063318C2semidirect
2. C2×D4×Dic43C2semidirect
3. #14582839C2semidirect
4. #14582835C2semidirect
5. #14582822C2semidirect
6. #14582813C2semidirect
7. #14582813C2semidirect
8. #14582779C2semidirect
9. #14582771C2semidirect
10. #14582763C2semidirect
70. C4×Dic43D4semidirect
155. C43#2636semidirect