Finite Group Databasebeta

← #19142649

Subgroups — #19142649

Order 5504.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13063316C211yesmaximal, characteristic, complemented
2C2×#13063311C211yesmaximal, characteristic
3#14582834C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic, complemented
5#14582824C211yesmaximal, characteristic, complemented
6#14582822C212yesmaximal, complemented
7#14582821C212yesmaximal, complemented
8#14582819C212yesmaximal, complemented
9#14582814C212yesmaximal
10#14582763C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14#13063316—24no—
15#13063311—24no—
16C2×C4⋊Dic43C2212yes—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×C22⋊Dic43C2211yescharacteristic
22C2×C22⋊Dic43C2212yes—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C2×C22⋊D43—22no—
44C2×C22⋊D43—42no—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2312yes—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C2×Dic86—22no—
51C2×Dic86—42no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—42no—
54C22⋊C4×C43—22no—
55C22⋊C4×C43—42no—
56C22⋊Dic43—22no—
57C22⋊Dic43—42no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—42no—
61(C2×D43)⋊C4—42no—
62C4⋊Dic43—22no—
63C4⋊Dic43—24no—
64Dic43⋊C4—24no—
65Dic43⋊C4—42no—
66Dic43⋊C4—42no—
67C4×Dic43D414yes—
68C23×C43—21no—
69C23×C43—21no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43—21no—
73C23×C43C2411yescharacteristic
74C22×D43—21no—
75C22×D43—21no—
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43C2×D412yes—
89C22⋊D43—44no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43C2×D412yes—
102C2×Dic43C2×D412yes—
103Dic86—44no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43—42no—
108C22×C43—42no—
109C22×C43C22×D411yescharacteristic
110C22×C43H(5,𝔽2)12yes—
111C22×C43H(5,𝔽2)11yescharacteristic
112C22×C432−1+412yes—
113C22×C432−1+411yescharacteristic
114C2×D43—41no—
115C2×D43—41no—
116C2×D43—41no—
117C2×D43—42no—
118C2×D43—42no—
119C4×C43—22no—
120C4×C43—41no—
121C4×C43—42no—
122C4×C43—42no—
123Dic43—22no—
124Dic43—22no—
125Dic43—41no—
126Dic43—42no—
127Dic43—42no—
128#2820—431nomaximal, Sylow
129C2×C43—81no—
130C2×C43#53511yescharacteristic
131C2×C43#53611yescharacteristic
132C2×C43#53711yescharacteristic
133C2×C43#56212yes—
134C2×C43#56312yes—
135D43—81no—
136C2×#125—431no—
137C2×#124—431no—
138#399—431no—
139#399D4311yescharacteristic, complemented
140#397—431no—
141#397—431no—
142#396—432no—
143#396—432no—
144#395—432no—
145#394—432no—
146#382—431no—
147C43#282011yescharacteristic, complemented, Sylow
148C22×Q8—431no—
149C22×D4—431no—
150#125—864no—
151#124—864no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—431no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4C2×D4311yescharacteristic
158C2×C4⋊C4C2×D4312yes—
159C2×C22⋊C4—431no—
160C2×C22⋊C4—431no—
161C2×C22⋊C4—431no—
162C2×C22⋊C4—432no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4C2×D4311yescharacteristic
166C2×C22⋊C4C2×D4312yes—
167C2×C42—431no—
168#95—432no—
169#95—431no—
170#95—432no—
171#95—432no—
172#95C2×D4311yescharacteristic
173C24—431no—
174C24C22×D4311yescharacteristic
175C2×Q8—862no—
176C2×Q8—1722no—
177C2×D4—862no—
178C2×D4—1722no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—432no—
182C22×C4—432no—
183C22×C4—431no—
184C22×C4C22×D4312yes—
185C22×C4C22×D4311yescharacteristic
186C22×C4C22×D4312yes—
187C22×C4C22×D4311yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—864no—
191C4⋊C4—864no—
192C4⋊C4—862no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—862no—
198C22⋊C4—862no—
199C22⋊C4—862no—
200C22⋊C4—1722no—
201C22⋊C4—1722no—
202C22⋊C4—1722no—
203C42—434no—
204C23—21no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23—21no—
209C23—861no—
210C23—862no—
211C23—861no—
212C23—862no—
213C23—861no—
214C23C23×D4311yescharacteristic
215Q8—1724no—
216D4—1724no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—432no—
227C2×C4—432no—
228C2×C4—862no—
229C2×C4—861no—
230C2×C4—861no—
231C2×C4—861no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4D4×D4312yes—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—1722no—
246C22—1722no—
247C22—1721no—
248C22—1721no—
249C22—1721no—
250C22C2×D4×D4311yescharacteristic
251C22#1306337012yes—
252C22#1306337111yescharacteristic
253C22#1306337212yes—
254C22#1306337311yescharacteristic
255C4—22no—
256C4—42no—
257C4—41no—
258C4—42no—
259C4—862no—
260C4—862no—
261C4—1722no—
262C4—1721no—
263C4—1722no—
264C2—81no—
265C2—3441no—
266C2#1458346211yescharacteristic
267C2#1458347111yescharacteristic
268C2#1458347911yescharacteristic
269C2#1458364612yes—
270C2#1458365012yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2820
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063316C2semidirect
3. #14582834C2semidirect
4. #14582826C2semidirect
5. #14582824C2semidirect
6. #14582822C2semidirect
7. #14582821C2semidirect
8. #14582819C2semidirect
10. #14582763C2semidirect
11. C43×#399C2semidirect
139. #399D43semidirect
147. C43#2820semidirect