Finite Group Databasebeta

← #19142639

Subgroups — #19142639

Order 5504.

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

normal subgroups only

This group has 580 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×#13063311C212yesmaximal, complemented
2#14582816C211yesmaximal, characteristic, complemented
3#14582815C212yesmaximal, complemented
4#14582812C212yesmaximal, complemented
5#14582811C212yesmaximal, complemented
6#14582808C212yesmaximal, complemented
7#14582807C212yesmaximal, complemented
8#14582764C211yesmaximal, characteristic, complemented
9C43×#394C211yesmaximal, characteristic, complemented
10C22×Dic86C2212yes—
11C22×D172C2211yescharacteristic
12C22×C22⋊D43C2212yes—
13C22×C22⋊D43C2212yes—
14#13063311—28no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C22⋊Dic43C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×C4×Dic43C2211yescharacteristic
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2211yescharacteristic
26C43⋊#95C2212yes—
27C22×D4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2211yescharacteristic
29C2×C22⋊C4×C43C2212yes—
30C2×C22⋊C4×C43C2212yes—
31#95×C43C2211yescharacteristic
32C24×C43C2312yes—
33C23×D43C2312yes—
34C2×D4×C43—42no—
35C2×D4×C43—41no—
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C2×C22⋊D43—24no—
41C2×C22⋊D43—42no—
42C2×C22⋊D43—42no—
43C2×C22⋊D43—42no—
44C2×C22⋊D43—42no—
45C2×C22⋊D43—42no—
46C22×Dic43C2312yes—
47C22×Dic43C2312yes—
48C22×Dic43C2312yes—
49C2×D172—42no—
50C2×D172—41no—
51C2×Dic86—24no—
52C2×Dic86—42no—
53C2×Dic86—42no—
54C4⋊C4×C43—41no—
55C22⋊C4×C43—24no—
56C22⋊C4×C43—42no—
57C22⋊Dic43—24no—
58C22⋊Dic43—42no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—42no—
62(C2×D43)⋊C4—42no—
63C4⋊Dic43—41no—
64C4×Dic43D414yescomplemented
65C23×C43—22no—
66C23×C43—22no—
67C23×C43—22no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43C2411yescharacteristic
73C22×D43—22no—
74C22×D43—22no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80D4×C43—44no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43C2×D412yes—
91C22⋊D43—48no—
92C22⋊D43—48no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43C2×D414yes—
102D172—44no—
103Dic86—48no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43—42no—
107C22×C43—42no—
108C22×C43—42no—
109C22×C43—42no—
110C22×C43—42no—
111C22×C43C22×D411yescharacteristic
112C22×C43H(5,𝔽2)12yes—
113C22×C43H(5,𝔽2)11yescharacteristic
114C22×C43H(5,𝔽2)12yes—
115C22×C432−1+411yescharacteristic
116C2×D43—42no—
117C2×D43—42no—
118C2×D43—42no—
119C2×D43—42no—
120C2×D43—42no—
121C2×D43—42no—
122C2×D43—42no—
123C4×C43—22no—
124C4×C43—42no—
125C4×C43—41no—
126C4×C43—41no—
127Dic43—24no—
128Dic43—42no—
129Dic43—42no—
130#2819—431nomaximal, Sylow
131C2×C43—82no—
132C2×C43#53512yes—
133C2×C43#53711yescharacteristic
134C2×C43H(3,𝔽4)11yescharacteristic
135C2×C43H(3,𝔽4)11yescharacteristic
136C2×C43#56212yes—
137D43—82no—
138C2×#124—432no—
139#394—431no—
140#394—432no—
141#394D4311yescharacteristic, complemented
142#393—432no—
143#393—432no—
144#392—432no—
145#392—432no—
146#382—431no—
147C43#281911yescharacteristic, complemented, Sylow
148C22×Q8—432no—
149C22×D4—432no—
150C22×D4—432no—
151C22×D4—431no—
152C22×D4C2×D4311yescharacteristic
153#124—868no—
154C2×C4⋊C4—431no—
155C2×C4⋊C4C2×D4311yescharacteristic
156C2×C22⋊C4—432no—
157C2×C22⋊C4—432no—
158C2×C22⋊C4—432no—
159C2×C22⋊C4—432no—
160C2×C22⋊C4—432no—
161C2×C22⋊C4—432no—
162C2×C22⋊C4C2×D4312yes—
163C2×C22⋊C4C2×D4312yes—
164C2×C42—431no—
165#95—432no—
166#95—432no—
167#95—432no—
168#95—431no—
169#95C2×D4311yescharacteristic
170C24—432no—
171C24C22×D4312yes—
172C2×Q8—864no—
173C2×Q8—1722no—
174C2×Q8—1722no—
175C2×D4—42no—
176C2×D4—41no—
177C2×D4—864no—
178C2×D4—1722no—
179C2×D4—1721no—
180C2×D4—1722no—
181C2×D4—1722no—
182C2×D4—1722no—
183C2×D4—1722no—
184C2×D4—1722no—
185C22×C4—432no—
186C22×C4—432no—
187C22×C4—432no—
188C22×C4C22×D4311yescharacteristic
189C22×C4C22×D4311yescharacteristic
190C22×C4C22×D4312yes—
191C22×C4C22×D4311yescharacteristic
192C4⋊C4—41no—
193C4⋊C4—1721no—
194C22⋊C4—24no—
195C22⋊C4—42no—
196C22⋊C4—864no—
197C22⋊C4—864no—
198C22⋊C4—864no—
199C22⋊C4—1722no—
200C22⋊C4—1722no—
201C22⋊C4—1722no—
202C42—434no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—862no—
211C23—862no—
212C23—862no—
213C23—862no—
214C23—862no—
215C23—862no—
216C23—862no—
217C23C23×D4311yescharacteristic
218Q8—1728no—
219D4—44no—
220D4—1724no—
221D4—1728no—
222D4—1728no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—434no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4D4×D4312yes—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—1722no—
250C22—1722no—
251C22—1722no—
252C22—1722no—
253C22—1722no—
254C22—1722no—
255C22—1722no—
256C22C2×D4×D4311yescharacteristic
257C22#1306337011yescharacteristic
258C22#1306337012yes—
259C22#1306337112yes—
260C22#1306337211yescharacteristic
261C4—22no—
262C4—41no—
263C4—41no—
264C4—42no—
265C4—864no—
266C4—1722no—
267C4—1722no—
268C2—82no—
269C2—3442no—
270C2#1458346512yes—
271C2#1458347611yescharacteristic
272C2#1458364111yescharacteristic
273C2#1458364211yescharacteristic
274C2#1458364612yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2819
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063311C2semidirect
2. #14582816C2semidirect
3. #14582815C2semidirect
4. #14582812C2semidirect
5. #14582811C2semidirect
6. #14582808C2semidirect
7. #14582807C2semidirect
8. #14582764C2semidirect
9. C43×#394C2semidirect
64. C4×Dic43D4semidirect
141. #394D43semidirect
147. C43#2819semidirect