Finite Group Databasebeta

← #19139974

Subgroups — #19139974

Order 5504.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×#13063302C211yesmaximal, characteristic
2C22×Dic43⋊C4C211yesmaximal, characteristic
3#14582833C212yesmaximal, complemented
4#14582819C212yesmaximal, complemented
5#14582796C212yesmaximal, complemented
6#14582795C212yesmaximal, complemented
7#14582774C211yesmaximal, characteristic
8#14582772C211yesmaximal, characteristic
9#14582771C211yesmaximal, characteristic
10C22⋊C4×Dic43C211yesmaximal, characteristic
11C43×#385C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C23×Dic43C2211yescharacteristic
15#13063302—24no—
16C2×C4⋊Dic43C2212yes—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4—24no—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2212yes—
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×C4×Dic43C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C23×C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36#95×C43C2212yes—
37C24×C43C2311yescharacteristic
38C22×C4×C43—22no—
39C22×C4×C43—42no—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×Dic43—24no—
45C22×Dic43—22no—
46C22×Dic43—42no—
47C22×Dic43D414yes—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2312yes—
53C22×Dic43C2312yes—
54C2×Dic86—22no—
55C2×Dic86—42no—
56C4⋊C4×C43—42no—
57C22⋊C4×C43—22no—
58C22⋊C4×C43Q814yescomplemented
59C22⋊Dic43—22no—
60C22⋊Dic43Q814yescomplemented
61C4⋊Dic43—22no—
62C4⋊Dic43—24no—
63Dic43⋊C4—24no—
64Dic43⋊C4—24no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4—24no—
68Dic43⋊C4—42no—
69C4×Dic43—42no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43C2×D412yes—
73C23×C43C2×Q812yes—
74C23×C43C2×Q812yes—
75C23×C43C2411yescharacteristic
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—44no—
86C2×C4×C43C2×Q814yes—
87C2×Dic43—28no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—44no—
99C2×Dic43C2×D412yes—
100C2×Dic43C2×D412yes—
101C2×Dic43C2×Q814yes—
102C2×Dic43#4114yes—
103Dic86—44no—
104C22×C43—22no—
105C22×C43—22no—
106C22×C43—24no—
107C22×C43—24no—
108C22×C43C4⋊Q814yes—
109C22×C43C22×D411yescharacteristic
110C22×C43C22×Q811yescharacteristic
111C22×C43C22×Q811yescharacteristic
112C22×C43C2×#4112yes—
113C22×C43H(5,𝔽2)12yes—
114C4×C43—24no—
115C4×C43—41no—
116C4×C43—41no—
117C4×C43—42no—
118Dic43—24no—
119Dic43—22no—
120Dic43—22no—
121Dic43—24no—
122Dic43—41no—
123Dic43—41no—
124#2583—431nomaximal, Sylow
125C2×C43—24no—
126C2×C43#52511yescharacteristic
127C2×C43C2×C4⋊Q811yescharacteristic
128C2×C43#53411yescharacteristic
129C2×C43#55412yes—
130C2×C43#55412yes—
131C2×C22⋊Q8—431no—
132C22×C4⋊C4—431no—
133#398—432no—
134#395—432no—
135#389—432no—
136#389—432no—
137#385—431no—
138#385—431no—
139#385—431no—
140#385D4311yescharacteristic
141C4×C22⋊C4—431no—
142C43#258311yescharacteristic, complemented, Sylow
143C22×Q8—431no—
144C23×C4—431no—
145C23×C4—431no—
146C23×C4C2×D4311yescharacteristic
147C22⋊Q8—864no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4—432no—
150C2×C4⋊C4—431no—
151C2×C4⋊C4—431no—
152C2×C4⋊C4—431no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—432no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—864no—
157C2×C4⋊C4C2×D4312yes—
158C2×C22⋊C4—431no—
159C2×C22⋊C4—431no—
160C2×C22⋊C4C2×D4311yescharacteristic
161C2×C22⋊C4C2×D4311yescharacteristic
162C2×C42—432no—
163#95—432no—
164#95—432no—
165#95—432no—
166#95—432no—
167#95C2×D4312yes—
168C24C22×D4311yescharacteristic
169C2×Q8—862no—
170C2×Q8—1722no—
171C22×C4—22no—
172C22×C4—42no—
173C22×C4—432no—
174C22×C4—432no—
175C22×C4—431no—
176C22×C4—431no—
177C22×C4—434no—
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—864no—
181C22×C4—862no—
182C22×C4—1722no—
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4312yes—
185C22×C4C22×D4311yescharacteristic
186C22×C4C22×D4312yes—
187C4⋊C4—42no—
188C4⋊C4—864no—
189C4⋊C4—864no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—864no—
194C4⋊C4—864no—
195C4⋊C4—1722no—
196C22⋊C4—22no—
197C22⋊C4—434no—
198C22⋊C4—862no—
199C22⋊C4Dic8614yescomplemented
200C42—1722no—
201C23—22no—
202C23—22no—
203C23C2×Dic8612yes—
204C23D4×D4312yes—
205C23Q8×D4312yes—
206C23C23×D4311yescharacteristic
207Q8—1724no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—44no—
218C2×C4—432no—
219C2×C4—432no—
220C2×C4—434no—
221C2×C4—434no—
222C2×C4—868no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—861no—
230C2×C4—861no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—1724no—
234C2×C4C2×Dic8614yes—
235C22—24no—
236C22—24no—
237C22—22no—
238C22—22no—
239C22#1306332414yes—
240C22C2×D4×D4311yescharacteristic
241C22C2×Q8×D4311yescharacteristic
242C22C22×Dic8611yescharacteristic
243C22#41×D4312yes—
244C22#1306337012yes—
245C4—24no—
246C4—41no—
247C4—42no—
248C4—41no—
249C4—864no—
250C4—864no—
251C4—862no—
252C4—862no—
253C4—1721no—
254C4—1721no—
255C2—24no—
256C2#1458340711yescharacteristic
257C2C2×#1306332411yescharacteristic
258C2#1458345911yescharacteristic
259C2#1458360312yes—
260C2#1458360812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#385C2
hypercenter#385D43
hypocenterC43#2583
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #14582833C2semidirect
4. #14582819C2semidirect
5. #14582796C2semidirect
6. #14582795C2semidirect
58. C22⋊C4×C43Q8semidirect
60. C22⋊Dic43Q8semidirect
142. C43#2583semidirect
199. C22⋊C4Dic86semidirect