Finite Group Databasebeta

← #19140225

Subgroups — #19140225

Order 5504.

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

normal subgroups only

This group has 582 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×#13063287C211yesmaximal, characteristic, complemented
3#14582830C211yesmaximal, characteristic, complemented
4#14582817C211yesmaximal, characteristic, complemented
5#14582808C211yesmaximal, characteristic
6#14582799C212yesmaximal, complemented
7#14582788C212yesmaximal, complemented
8#14582775C212yesmaximal, complemented
9#14582773C212yesmaximal, complemented
10#14582744C211yesmaximal, characteristic, complemented
11C43×#397C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C22×C4×D43C2212yes—
15#13063318—24no—
16#13063287—24no—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×C22⋊Dic43C2211yescharacteristic
22C2×C22⋊Dic43C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2212yes—
28C2×C4×Dic43C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C2×C22⋊D43—24no—
44C2×C22⋊D43—24no—
45C2×C22⋊D43—42no—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C22×Dic43C2312yes—
51C2×D172—22no—
52C2×D172—24no—
53C2×C4×D43—24no—
54C2×C4×D43—42no—
55C2×C4×D43—42no—
56C4⋊C4×C43—22no—
57C22⋊C4×C43—22no—
58C22⋊C4×C43—42no—
59C22⋊Dic43—22no—
60C22⋊Dic43—22no—
61(C2×D43)⋊C4—24no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—24no—
64(C2×D43)⋊C4—42no—
65C4⋊Dic43—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4—42no—
69C4×Dic43—24no—
70C4×Dic43D414yescomplemented
71C23×C43—21no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43C2411yescharacteristic
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43#4114yes—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43C2×D412yes—
94C22⋊D43—48no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—22no—
103C2×Dic43—21no—
104C2×Dic43—21no—
105C2×Dic43C2×D412yes—
106C2×Dic43C2×D412yes—
107C2×Dic43#4114yes—
108D172—28no—
109C4×D43—48no—
110C22×C43—41no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43—42no—
114C22×C43—42no—
115C22×C43C22×D411yescharacteristic
116C22×C43C2×#4112yes—
117C22×C43C2×#4112yes—
118C22×C43H(5,𝔽2)11yescharacteristic
119C22×C43H(5,𝔽2)11yescharacteristic
120C2×D43—24no—
121C2×D43—24no—
122C2×D43—24no—
123C2×D43—42no—
124C2×D43—42no—
125C2×D43—42no—
126C2×D43—42no—
127C4×C43—22no—
128C4×C43—41no—
129C4×C43—42no—
130C4×C43—42no—
131Dic43—22no—
132Dic43—22no—
133Dic43—24no—
134Dic43—41no—
135Dic43—41no—
136#2603—431nomaximal, Sylow
137C2×C43—81no—
138C2×C43#52511yescharacteristic
139C2×C43#53211yescharacteristic
140C2×C43#53511yescharacteristic
141C2×C43#55112yes—
142C2×C43#55312yes—
143D43—44no—
144C2×#126—431no—
145C2×C4×D4—431no—
146#398—431no—
147#397D4311yescharacteristic, complemented
148#394—431no—
149#392—431no—
150#390—432no—
151#388—432no—
152#386—432no—
153#385—432no—
154#376—431no—
155C43#260311yescharacteristic, complemented, Sylow
156C22×D4—432no—
157C22×D4—431no—
158C23×C4—432no—
159#126—864no—
160C4×D4—864no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—431no—
163C2×C4⋊C4—431no—
164C2×C4⋊C4—432no—
165C2×C4⋊C4C2×D4311yescharacteristic
166C2×C22⋊C4—431no—
167C2×C22⋊C4—431no—
168C2×C22⋊C4—432no—
169C2×C22⋊C4—432no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4C2×D4311yescharacteristic
173C2×C22⋊C4C2×D4312yes—
174C2×C42—431no—
175C2×C42—432no—
176#95—432no—
177#95—431no—
178#95—432no—
179#95C2×D4311yescharacteristic
180#95C2×D4312yes—
181C24—432no—
182C24C22×D4311yescharacteristic
183C2×D4—864no—
184C2×D4—864no—
185C2×D4—864no—
186C2×D4—862no—
187C2×D4—1722no—
188C22×C4—432no—
189C22×C4—431no—
190C22×C4—431no—
191C22×C4—431no—
192C22×C4—431no—
193C22×C4—864no—
194C22×C4—1722no—
195C22×C4—1722no—
196C22×C4C22×D4312yes—
197C22×C4C22×D4312yes—
198C22×C4C22×D4311yescharacteristic
199C22×C4C22×D4311yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—862no—
202C4⋊C4—862no—
203C4⋊C4—862no—
204C4⋊C4—1722no—
205C22⋊C4—22no—
206C22⋊C4—42no—
207C22⋊C4—864no—
208C22⋊C4—864no—
209C22⋊C4—864no—
210C22⋊C4—862no—
211C22⋊C4—862no—
212C22⋊C4—1722no—
213C42—434no—
214C42—864no—
215C23—21no—
216C23—22no—
217C23—22no—
218C23—21no—
219C23—21no—
220C23—434no—
221C23—862no—
222C23—862no—
223C23—862no—
224C23—862no—
225C23—862no—
226C23—862no—
227C23C23×D4311yescharacteristic
228D4—868no—
229D4—1728no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—432no—
240C2×C4—432no—
241C2×C4—434no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—861no—
245C2×C4—862no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—861no—
249C2×C4—862no—
250C2×C4—861no—
251C2×C4—861no—
252C2×C4—1728no—
253C2×C4D4×D4312yes—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—864no—
260C22—864no—
261C22—864no—
262C22—1722no—
263C22—1722no—
264C22—1722no—
265C22—1722no—
266C22C2×D4×D4311yescharacteristic
267C22#41×D4312yes—
268C22#41×D4312yes—
269C22#1306337011yescharacteristic
270C22#1306337111yescharacteristic
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—864no—
276C4—862no—
277C4—862no—
278C4—1721no—
279C4—1721no—
280C2—81no—
281C2—1724no—
282C2#1458340711yescharacteristic
283C2#1458344811yescharacteristic
284C2#1458346511yescharacteristic
285C2#1458357412yes—
286C2#1458359412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2603
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13063318C2semidirect
2. C2×#13063287C2semidirect
3. #14582830C2semidirect
4. #14582817C2semidirect
6. #14582799C2semidirect
7. #14582788C2semidirect
8. #14582775C2semidirect
9. #14582773C2semidirect
10. #14582744C2semidirect
11. C43×#397C2semidirect
70. C4×Dic43D4semidirect
147. #397D43semidirect
155. C43#2603semidirect