Finite Group Databasebeta

← #19138896

Subgroups — #19138896

Order 5504.

624 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 151 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×#13063307C212yesmaximal
2C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic
3C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#14582831C211yesmaximal, characteristic, complemented
5#14582830C211yesmaximal, characteristic, complemented
6#14582824C211yesmaximal, characteristic, complemented
7#14582796C212yesmaximal, complemented
8#14582761C212yesmaximal, complemented
9#14582758C211yesmaximal, characteristic, complemented
10#14582757C212yesmaximal, complemented
11C43×#397C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C22×C4×D43C2212yes—
15C22×C4×D43C2211yescharacteristic
16#13063307—28no—
17(C22⋊D43)⋊C4—24no—
18C2×C4⋊Dic43C2212yes—
19C2×C4⋊Dic43C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2211yescharacteristic
24C4⋊C4×D43—24no—
25C2×C22⋊Dic43C2212yes—
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2212yes—
28C2×C4×Dic43C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C43⋊#95C2212yes—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2212yes—
37#95×C43C2211yescharacteristic
38C24×C43C2311yescharacteristic
39C23×D43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—22no—
45C2×C22⋊D43—22no—
46C2×C22⋊D43D414yes—
47C22×Dic43—22no—
48C22×Dic43—24no—
49C22×Dic43C2311yescharacteristic
50C22×Dic43C2312yes—
51C22×Dic43C2312yes—
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2311yescharacteristic
54C2×C4×D43—24no—
55C2×C4×D43—24no—
56C2×C4×D43—24no—
57C2×C4×D43—24no—
58C2×C4×D43D414yes—
59C4⋊C4×C43—22no—
60C22⋊C4×C43—22no—
61C22⋊C4×C43—24no—
62C22⋊Dic43—24no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—24no—
65C4⋊Dic43—22no—
66C4⋊Dic43—24no—
67Dic43⋊C4—22no—
68Dic43⋊C4—24no—
69Dic43⋊C4—24no—
70Dic43⋊C4—24no—
71C4×Dic43—22no—
72C23×C43—21no—
73C23×C43—22no—
74C23×C43—21no—
75C23×C43—22no—
76C23×C43C2×D412yes—
77C23×C43C2411yescharacteristic
78C22×D43—22no—
79C22×D43—22no—
80C22×D43C2×D412yes—
81C22×D43C2×D412yes—
82C22×D43#4112yes—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43C2×D412yes—
93C22⋊D43—28no—
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—21no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—44no—
105C2×Dic43C2×D412yes—
106C2×Dic43C2×D412yes—
107C2×Dic43#4114yes—
108C4×D43—28no—
109C4×D43—48no—
110C22×C43—22no—
111C22×C43—24no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—42no—
115C22×C43C22×D411yescharacteristic
116C22×C43C22×D411yescharacteristic
117C22×C43C2×#4111yescharacteristic
118C22×C43C2×#4112yes—
119C22×C432−1+412yes—
120C2×D43—22no—
121C2×D43—22no—
122C2×D43—24no—
123C2×D43—24no—
124C2×D43#12114yes—
125C4×C43—22no—
126C4×C43—42no—
127C4×C43—41no—
128C4×C43—42no—
129Dic43—22no—
130Dic43—42no—
131Dic43—41no—
132Dic43—42no—
133Dic43#12314yescomplemented
134#2486—431nomaximal, Sylow
135C2×C43—42no—
136C2×C43C2×#12111yescharacteristic
137C2×C43C2×#12311yescharacteristic
138C2×C43#53611yescharacteristic
139C2×C43#54712yes—
140C2×C43#55212yes—
141D43—24no—
142C2×#123—432no—
143C2×C4×D4—431no—
144C22×C4⋊C4—431no—
145#398—431no—
146#398—431no—
147#397—431no—
148#397D4311yescharacteristic, complemented
149#389—432no—
150#381—432no—
151#380—432no—
152#380—431no—
153C43#248611yescharacteristic, complemented, Sylow
154C22×D4—431no—
155C23×C4—431no—
156C23×C4—431no—
157C23×C4—432no—
158#123—868no—
159C4×D4—864no—
160C2×C4⋊C4—432no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—431no—
163C2×C4⋊C4—432no—
164C2×C4⋊C4—432no—
165C2×C4⋊C4—432no—
166C2×C4⋊C4—864no—
167C2×C4⋊C4C2×D4311yescharacteristic
168C2×C22⋊C4—432no—
169C2×C22⋊C4—431no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4C2×D4311yescharacteristic
172C2×C22⋊C4C2×D4312yes—
173C2×C42—431no—
174#95—432no—
175#95—432no—
176#95—431no—
177#95—432no—
178#95C2×D4311yescharacteristic
179#95C2×D4312yes—
180C24—431no—
181C24C22×D4311yescharacteristic
182C2×D4—434no—
183C2×D4—862no—
184C2×D4—862no—
185C22×C4—431no—
186C22×C4—431no—
187C22×C4—434no—
188C22×C4—431no—
189C22×C4—432no—
190C22×C4—432no—
191C22×C4—864no—
192C22×C4—864no—
193C22×C4—864no—
194C22×C4—864no—
195C22×C4—862no—
196C22×C4—864no—
197C22×C4C22×D4311yescharacteristic
198C22×C4C22×D4312yes—
199C22×C4C22×D4312yes—
200C22×C4C22×D4311yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—864no—
203C4⋊C4—864no—
204C4⋊C4—864no—
205C4⋊C4—864no—
206C4⋊C4—862no—
207C4⋊C4—862no—
208C22⋊C4—24no—
209C22⋊C4—22no—
210C22⋊C4—862no—
211C22⋊C4—864no—
212C22⋊C4—864no—
213C42—862no—
214C23—21no—
215C23—22no—
216C23—21no—
217C23—22no—
218C23—432no—
219C23—432no—
220C23—432no—
221C23—862no—
222C23—862no—
223C23D4×D4312yes—
224C23C23×D4311yescharacteristic
225D4—868no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—432no—
236C2×C4—434no—
237C2×C4—432no—
238C2×C4—868no—
239C2×C4—861no—
240C2×C4—861no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4—861no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—862no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—1728no—
250C2×C4—1724no—
251C2×C4D4×D4312yes—
252C22—22no—
253C22—24no—
254C22—42no—
255C22—41no—
256C22—41no—
257C22—434no—
258C22—864no—
259C22—862no—
260C22—862no—
261C22—864no—
262C22C2×D4×D4311yescharacteristic
263C22C2×D4×D4311yescharacteristic
264C22#41×D4311yescharacteristic
265C22#41×D4312yes—
266C22#1306337212yes—
267C4—22no—
268C4—42no—
269C4—41no—
270C4—42no—
271C4—434no—
272C4—862no—
273C4—1722no—
274C4—1721no—
275C4—1722no—
276C2—42no—
277C2—864no—
278C2#121×D4311yescharacteristic
279C2#123×D4311yescharacteristic
280C2#1458346911yescharacteristic
281C2#1458354712yes—
282C2#1458358512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2486
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D43C2semidirect
4. #14582831C2semidirect
5. #14582830C2semidirect
6. #14582824C2semidirect
7. #14582796C2semidirect
8. #14582761C2semidirect
9. #14582758C2semidirect
10. #14582757C2semidirect
11. C43×#397C2semidirect
133. Dic43#123semidirect
148. #397D43semidirect
153. C43#2486semidirect