Finite Group Databasebeta

← #19137852

Subgroups — #19137852

Order 5504.

560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×C22⋊D43C211yesmaximal, characteristic
2#14582837C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic, complemented
4#14582830C211yesmaximal, characteristic, complemented
5#14582827C212yesmaximal, complemented
6#14582825C211yesmaximal, characteristic, complemented
7#14582814C212yesmaximal
8C4×Dic43⋊C4C212yesmaximal, complemented
9C4×(C2×D43)⋊C4C212yesmaximal, complemented
10C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
11C2×#117×C43C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C4×C22⋊D43—24no—
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2211yescharacteristic
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2211yescharacteristic
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×C4×Dic43C2211yescharacteristic
24C2×C4×Dic43C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C23×C4×C43C2211yescharacteristic
32#117×C43—24no—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36C2×C42×C43C2212yes—
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43—24no—
40C22×C4×C43D414yes—
41C22×C4×C43C2312yes—
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48C22×Dic43C2312yes—
49C22×Dic43C2311yescharacteristic
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2312yes—
52C22×Dic43C2311yescharacteristic
53C2×C4×D43—22no—
54C2×C4×D43—24no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C22⋊C4×C43—24no—
58C42×C43—24no—
59C22⋊Dic43—24no—
60C22⋊Dic43—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—24no—
64Dic43⋊C4—22no—
65Dic43⋊C4—24no—
66Dic43⋊C4—24no—
67C4×Dic43—22no—
68C4×Dic43—24no—
69C23×C43—22no—
70C23×C43—21no—
71C23×C43—21no—
72C23×C43—22no—
73C23×C43C2×D412yes—
74C23×C43C2411yescharacteristic
75C22×D43—21no—
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—21no—
79C22×D43#4112yes—
80C2×C4×C43—22no—
81C2×C4×C43—28no—
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—
89C2×C4×C43C2×D412yes—
90C2×C4×C43#4114yes—
91C22⋊D43—28no—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43—21no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43#4112yes—
104C2×Dic43#4114yes—
105C4×D43—44no—
106C22×C43—22no—
107C22×C43—22no—
108C22×C43—22no—
109C22×C43—42no—
110C22×C43—42no—
111C22×C43C22×D411yescharacteristic
112C22×C43C2×#4111yescharacteristic
113C22×C43C2×#4111yescharacteristic
114C22×C43C2×#4112yes—
115C22×C43C2×#4112yes—
116C2×D43—22no—
117C2×D43—24no—
118C2×D43—41no—
119C2×D43—42no—
120C2×D43—41no—
121C4×C43—22no—
122C4×C43—42no—
123C4×C43—42no—
124C4×C43#12314yes—
125Dic43—22no—
126Dic43—24no—
127Dic43—41no—
128Dic43—42no—
129Dic43—41no—
130#2395—431nomaximal, Sylow
131C2×C43—42no—
132C2×C43C2×#12311yescharacteristic
133C2×C43#52511yescharacteristic
134C2×C43#52912yes—
135C2×C43#52912yes—
136C2×C43#53211yescharacteristic
137D43—42no—
138C2×C4×D4—431no—
139C2×#117D4311yescharacteristic, complemented
140#400—431no—
141#399—431no—
142#398—431no—
143#397—431no—
144#397—432no—
145#394—432no—
146C4×C4⋊C4—432no—
147C4×C22⋊C4—431no—
148C4×C22⋊C4—432no—
149C43#239511yescharacteristic, complemented, Sylow
150C22×D4—431no—
151C23×C4—431no—
152C23×C4C2×D4311yescharacteristic
153C4×D4—864no—
154#117—24no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4C2×D4311yescharacteristic
159C2×C4⋊C4C2×D4311yescharacteristic
160C2×C22⋊C4—431no—
161C2×C22⋊C4—432no—
162C2×C22⋊C4—431no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4C2×D4312yes—
166C2×C42—431no—
167C2×C42—432no—
168C2×C42C2×D4312yes—
169#95—432no—
170#95—431no—
171#95—432no—
172#95—431no—
173#95—432no—
174#95—432no—
175C24—431no—
176C24C22×D4311yescharacteristic
177C2×D4—862no—
178C2×D4—862no—
179C2×D4—862no—
180C22×C4—24no—
181C22×C4—432no—
182C22×C4—431no—
183C22×C4—432no—
184C22×C4—431no—
185C22×C4—431no—
186C22×C4—864no—
187C22×C4—862no—
188C22×C4C22⋊D4314yes—
189C22×C4C22×D4312yes—
190C22×C4C22×D4312yes—
191C22×C4C22×D4311yescharacteristic
192C22×C4C22×D4311yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—864no—
196C4⋊C4—864no—
197C4⋊C4—862no—
198C22⋊C4—24no—
199C22⋊C4—864no—
200C22⋊C4—864no—
201C22⋊C4—864no—
202C22⋊C4—862no—
203C22⋊C4—862no—
204C42—24no—
205C42—864no—
206C42—862no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—432no—
212C23—861no—
213C23—862no—
214C23—861no—
215C23—862no—
216C23C2×C22⋊D4312yes—
217C23C23×D4311yescharacteristic
218D4—868no—
219C2×C4—22no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—434no—
228C2×C4—432no—
229C2×C4—861no—
230C2×C4—862no—
231C2×C4—861no—
232C2×C4—862no—
233C2×C4—861no—
234C2×C4—861no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—1724no—
241C2×C4#1062189814yes—
242C2×C4C2×C22⋊D4312yes—
243C2×C4C2×C22⋊D4312yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—862no—
250C22—864no—
251C22—1721no—
252C22—1722no—
253C22—1721no—
254C22C22×C22⋊D4311yescharacteristic
255C22#41×D4311yescharacteristic
256C22#41×D4311yescharacteristic
257C22#41×D4312yes—
258C22C2×#1062189812yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—862no—
263C4—864no—
264C4—1721no—
265C4—1722no—
266C4—1721no—
267C4#1306330814yes—
268C2—42no—
269C2—1722no—
270C2C2×#1306330811yescharacteristic
271C2#1458340611yescharacteristic
272C2#1458342712yes—
273C2#1458342712yes—
274C2#1458344511yescharacteristic
subgroupG/H
centerC22×C4C22×D43
commutator, socleC23×C43C24
FrattiniC23C23×D43
FittingC2×#117×C43C2
hypercenterC2×#117D43
hypocenterC43#2395
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14582837C2semidirect
3. #14582834C2semidirect
4. #14582830C2semidirect
5. #14582827C2semidirect
6. #14582825C2semidirect
8. C4×Dic43⋊C4C2semidirect
9. C4×(C2×D43)⋊C4C2semidirect
10. C4×C22⋊Dic43C2semidirect
11. C2×#117×C43C2semidirect
139. C2×#117D43semidirect
149. C43#2395semidirect