Finite Group Databasebeta

← #19139068

Subgroups — #19139068

Order 5504.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13063303C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic
3#14582831C211yesmaximal, characteristic, complemented
4#14582830C211yesmaximal, characteristic, complemented
5#14582829C211yesmaximal, characteristic, complemented
6#14582803C212yesmaximal, complemented
7#14582773C212yesmaximal
8#14582770C212yesmaximal
9#14582768C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic
11C43×#398C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2212yes—
15#13063303—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2212yes—
23C4⋊C4×D43—24no—
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C2×C4×D43—24no—
49C2×C4×D43—24no—
50C2×C4×D43—42no—
51C2×C4×D43—42no—
52C2×C4×D43D414yes—
53C2×Dic86—22no—
54C2×Dic86—24no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—42no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4Q818yescomplemented
61C4⋊Dic43—22no—
62C4⋊Dic43—42no—
63Dic43⋊C4—22no—
64Dic43⋊C4—24no—
65Dic43⋊C4—22no—
66Dic43⋊C4—42no—
67Dic43⋊C4—42no—
68C4×Dic43—24no—
69C23×C43C2411yescharacteristic
70C22×D43—22no—
71C22×D43—21no—
72C22×D43—21no—
73C22×D43C2×D412yes—
74C22×D43C2×Q814yes—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43C2×D412yes—
87C2×C4×C43C2×Q814yes—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—21no—
97C2×Dic43—22no—
98C2×Dic43C2×D412yes—
99C2×Dic43C2×Q814yes—
100C2×Dic43#4114yes—
101C4×D43—28no—
102C4×D43—48no—
103Dic86—44no—
104C22×C43C22×D411yescharacteristic
105C22×C43C22×Q812yes—
106C22×C43C2×#4112yes—
107C22×C43H(5,𝔽2)11yescharacteristic
108C22×C43H(5,𝔽2)11yescharacteristic
109C2×D43—22no—
110C2×D43—22no—
111C2×D43—24no—
112C2×D43—24no—
113C2×D43C4⋊Q814yes—
114C4×C43—22no—
115C4×C43—24no—
116C4×C43—41no—
117C4×C43—42no—
118C4×C43—41no—
119Dic43—24no—
120Dic43—41no—
121Dic43—42no—
122Dic43—41no—
123Dic43#12314yes—
124#2502—431nomaximal, Sylow
125C2×C43C2×#12311yescharacteristic
126C2×C43C2×C4⋊Q811yescharacteristic
127C2×C43#53511yescharacteristic
128C2×C43#55412yes—
129C2×C43#55412yes—
130D43—24no—
131C2×C22⋊Q8—431no—
132C22×C4⋊C4—431no—
133#398—431no—
134#398—431no—
135#398—431no—
136#398D4311yescharacteristic, complemented
137#391—432no—
138#385—432no—
139#385—432no—
140#384—432no—
141C4×C22⋊C4—431no—
142C43#250211yescharacteristic, complemented, Sylow
143C22×Q8—431no—
144C23×C4—431no—
145C23×C4—432no—
146C22⋊Q8—864no—
147C2×C4⋊C4—432no—
148C2×C4⋊C4—431no—
149C2×C4⋊C4—431no—
150C2×C4⋊C4—431no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—864no—
155C2×C4⋊C4C2×D4311yescharacteristic
156C2×C4⋊C4C2×D4311yescharacteristic
157C2×C4⋊C4C2×D4312yes—
158C2×C22⋊C4—432no—
159C2×C22⋊C4—431no—
160C2×C22⋊C4—431no—
161C2×C42—432no—
162#95—431no—
163#95—432no—
164#95—432no—
165#95—432no—
166#95C2×D4311yescharacteristic
167#95C2×D4312yes—
168C24—431no—
169C2×Q8—862no—
170C2×Q8—864no—
171C22×C4—431no—
172C22×C4—432no—
173C22×C4—434no—
174C22×C4—431no—
175C22×C4—432no—
176C22×C4—431no—
177C22×C4—864no—
178C22×C4—864no—
179C22×C4—1722no—
180C22×C4—1722no—
181C22×C4C22×D4311yescharacteristic
182C22×C4C22×D4312yes—
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4311yescharacteristic
185C22×C4C22×D4312yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—864no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C4⋊C4—1722no—
196C22⋊C4—438no—
197C22⋊C4—862no—
198C22⋊C4—862no—
199C42—864no—
200C23—432no—
201C23—434no—
202C23—862no—
203C23—861no—
204C23—861no—
205C23C23×D4311yescharacteristic
206Q8—1724no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—432no—
219C2×C4—434no—
220C2×C4—434no—
221C2×C4—868no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—861no—
225C2×C4—861no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—861no—
229C2×C4—862no—
230C2×C4—861no—
231C2×C4—862no—
232C2×C4—1728no—
233C2×C4D4×D4312yes—
234C2×C4Q8×D4314yes—
235C22—434no—
236C22—864no—
237C22—864no—
238C22—862no—
239C22—862no—
240C22C2×D4×D4311yescharacteristic
241C22C2×Q8×D4312yes—
242C22#41×D4312yes—
243C22#1306337011yescharacteristic
244C22#1306337111yescharacteristic
245C4—24no—
246C4—22no—
247C4—41no—
248C4—42no—
249C4—41no—
250C4—434no—
251C4—864no—
252C4—1721no—
253C4—1722no—
254C4—1721no—
255C2—864no—
256C2#123×D4311yescharacteristic
257C2C4⋊Q8×D4311yescharacteristic
258C2#1458346511yescharacteristic
259C2#1458360312yes—
260C2#1458360512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2502
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #14582831C2semidirect
4. #14582830C2semidirect
5. #14582829C2semidirect
6. #14582803C2semidirect
9. #14582768C2semidirect
11. C43×#398C2semidirect
60. (C2×D43)⋊C4Q8semidirect
136. #398D43semidirect
142. C43#2502semidirect