Finite Group Databasebeta

← #19139075

Subgroups — #19139075

Order 5504.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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#14582839C211yesmaximal, characteristic, complemented
4#14582838C211yesmaximal, characteristic, complemented
5#14582837C211yesmaximal, characteristic, complemented
6#14582803C212yesmaximal, complemented
7#14582763C212yesmaximal, complemented
8#14582761C212yesmaximal
9#14582761C212yesmaximal
10#14582746C211yesmaximal, characteristic
11C43×#400C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×C4×D43C2212yes—
14C22×C4×D43C2211yescharacteristic
15#13063303—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C4⋊C4×D43—24no—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×C4×Dic43C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×Dic43C2312yes—
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C2×C4×D43—24no—
49C2×C4×D43—24no—
50C2×C4×D43—28no—
51C2×C4×D43D414yes—
52C2×Dic86—22no—
53C2×Dic86—24no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—24no—
59C4⋊Dic43—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4—24no—
62Dic43⋊C4—22no—
63C4×Dic43—24no—
64C23×C43C2411yescharacteristic
65C22×D43—22no—
66C22×D43—21no—
67C22×D43—21no—
68C22×D43C2×D412yes—
69C22×D43#4114yes—
70C2×C4×C43—22no—
71C2×C4×C43—21no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—24no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43C2×D412yes—
82C2×Dic43—21no—
83C2×Dic43—22no—
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—24no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43C2×D412yes—
93C2×Dic43#4114yes—
94C4×D43—28no—
95C4×D43—48no—
96Dic86—44no—
97C22×C43C22×D411yescharacteristic
98C22×C43C2×#4112yes—
99C22×C43C2×#4112yes—
100C22×C432−1+411yescharacteristic
101C22×C432−1+411yescharacteristic
102C2×D43—22no—
103C2×D43—22no—
104C2×D43—24no—
105C2×D43—24no—
106C2×D43#12414yes—
107C4×C43—22no—
108C4×C43—41no—
109C4×C43—42no—
110C4×C43—41no—
111C4×C43—42no—
112Dic43—41no—
113Dic43—42no—
114Dic43—41no—
115Dic43—42no—
116Dic43#12314yes—
117#2503—431nomaximal, Sylow
118C2×C43C2×#12311yescharacteristic
119C2×C43C2×#12411yescharacteristic
120C2×C43#53611yescharacteristic
121C2×C43#55212yes—
122C2×C43#55212yes—
123D43—24no—
124C2×C22⋊Q8—431no—
125C22×C4⋊C4—431no—
126#400—431no—
127#400—431no—
128#400—431no—
129#400D4311yescharacteristic, complemented
130#391—432no—
131#382—432no—
132#381—432no—
133#381—432no—
134C4×C22⋊C4—431no—
135C43#250311yescharacteristic, complemented, Sylow
136C22×Q8—431no—
137C23×C4—431no—
138C23×C4—432no—
139C22⋊Q8—864no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—864no—
145C2×C4⋊C4C2×D4311yescharacteristic
146C2×C4⋊C4C2×D4311yescharacteristic
147C2×C22⋊C4—431no—
148C2×C22⋊C4—431no—
149C2×C22⋊C4—432no—
150C2×C42—432no—
151#95—431no—
152#95—432no—
153#95—432no—
154#95—432no—
155#95—432no—
156#95—432no—
157#95—432no—
158#95C2×D4311yescharacteristic
159#95C2×D4312yes—
160#95C2×D4312yes—
161C24—431no—
162C2×Q8—862no—
163C2×Q8—864no—
164C22×C4—431no—
165C22×C4—434no—
166C22×C4—432no—
167C22×C4—431no—
168C22×C4—431no—
169C22×C4—432no—
170C22×C4—864no—
171C22×C4—864no—
172C22×C4—868no—
173C22×C4C22×D4312yes—
174C22×C4C22×D4311yescharacteristic
175C22×C4C22×D4311yescharacteristic
176C22×C4C22×D4312yes—
177C22×C4C22×D4311yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—864no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C22⋊C4—864no—
187C42—864no—
188C23—432no—
189C23—434no—
190C23—862no—
191C23—861no—
192C23—861no—
193C23C23×D4311yescharacteristic
194Q8—1724no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—432no—
207C2×C4—434no—
208C2×C4—868no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—862no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—864no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—861no—
219C2×C4—1728no—
220C2×C4D4×D4312yes—
221C22—434no—
222C22—864no—
223C22—864no—
224C22—862no—
225C22—862no—
226C22C2×D4×D4311yescharacteristic
227C22#41×D4312yes—
228C22#41×D4312yes—
229C22#1306337211yescharacteristic
230C22#1306337311yescharacteristic
231C4—22no—
232C4—42no—
233C4—41no—
234C4—42no—
235C4—41no—
236C4—434no—
237C4—1722no—
238C4—1721no—
239C4—1722no—
240C4—1721no—
241C2—864no—
242C2#123×D4311yescharacteristic
243C2#124×D4311yescharacteristic
244C2#1458347211yescharacteristic
245C2#1458358112yes—
246C2#1458358512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2503
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #14582839C2semidirect
4. #14582838C2semidirect
5. #14582837C2semidirect
6. #14582803C2semidirect
7. #14582763C2semidirect
11. C43×#400C2semidirect
129. #400D43semidirect
135. C43#2503semidirect