Finite Group Databasebeta

← #19142621

Subgroups — #19142621

Order 5504.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13063301C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic
3#14582836C211yesmaximal, characteristic, complemented
4#14582835C211yesmaximal, characteristic, complemented
5#14582833C212yesmaximal, complemented
6#14582817C212yesmaximal, complemented
7#14582815C212yesmaximal, complemented
8#14582814C212yesmaximal, complemented
9#14582810C211yesmaximal, characteristic, complemented
10#14582761C211yesmaximal, characteristic, complemented
11C43×#393C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C22×C22⋊D43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16#13063301—24no—
17#13063298—24no—
18C2×C4⋊Dic43C2211yescharacteristic
19C2×C4⋊Dic43C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C22×Q8×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C23×D43C2311yescharacteristic
40C2×Q8×C43—22no—
41C2×Q8×C43—42no—
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2312yes—
45C22×C4×C43C2311yescharacteristic
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—42no—
49C2×C22⋊D43—42no—
50C22×Dic43C2312yes—
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2312yes—
53C22×Dic43C2311yescharacteristic
54C2×D172—22no—
55C2×D172—42no—
56C2×C4×D43—42no—
57C2×C4×D43D414yes—
58C22⋊C4×C43—22no—
59C22⋊C4×C43—42no—
60C22⋊Dic43—42no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—42no—
64(C2×D43)⋊C4—42no—
65(C2×D43)⋊C4—42no—
66C4⋊Dic43—22no—
67C4⋊Dic43—42no—
68Dic43⋊C4—22no—
69Dic43⋊C4—24no—
70Dic43⋊C4—42no—
71C23×C43—21no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43C2411yescharacteristic
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—21no—
80C22×D43—21no—
81C22×D43—21no—
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—21no—
85C22×D43—21no—
86C22×D43C2×D412yes—
87Q8×C43—44no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43C2×D412yes—
98C22⋊D43—44no—
99C22⋊D43—44no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43C2×D412yes—
110D172—44no—
111C4×D43—44no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—41no—
115C22×C43—42no—
116C22×C43—42no—
117C22×C43C22×D411yescharacteristic
118C22×C43H(5,𝔽2)12yes—
119C22×C43H(5,𝔽2)12yes—
120C22×C432−1+411yescharacteristic
121C22×C432−1+411yescharacteristic
122C2×D43—22no—
123C2×D43—22no—
124C2×D43—22no—
125C2×D43—42no—
126C2×D43—42no—
127C2×D43—41no—
128C2×D43—41no—
129C2×D43—41no—
130C2×D43—42no—
131C2×D43—42no—
132C4×C43—22no—
133C4×C43—42no—
134C4×C43—41no—
135C4×C43—42no—
136Dic43—22no—
137Dic43—42no—
138Dic43—41no—
139Dic43—42no—
140#2816—431nomaximal, Sylow
141C2×C43—81no—
142C2×C43#53411yescharacteristic
143C2×C43#53511yescharacteristic
144C2×C43#53611yescharacteristic
145C2×C43#56212yes—
146C2×C43#56212yes—
147D43—42no—
148D43—81no—
149C2×C22⋊Q8—431no—
150C2×#121—431no—
151#399—431no—
152#399—431no—
153#398—432no—
154#394—432no—
155#394—432no—
156#394—432no—
157#393—431no—
158#393D4311yescharacteristic, complemented
159#381—431no—
160C43#281611yescharacteristic, complemented, Sylow
161C22×Q8C2×D4311yescharacteristic
162C22×D4—431no—
163C22×D4—431no—
164C22×D4—431no—
165C23×C4—431no—
166C22⋊Q8—864no—
167#121—864no—
168C2×C4⋊C4—431no—
169C2×C4⋊C4—432no—
170C2×C4⋊C4—431no—
171C2×C4⋊C4—432no—
172C2×C4⋊C4—432no—
173C2×C22⋊C4—431no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4—432no—
176C2×C22⋊C4—432no—
177C2×C22⋊C4—432no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4C2×D4311yescharacteristic
180C2×C22⋊C4C2×D4312yes—
181#95—431no—
182#95—432no—
183#95—432no—
184#95C2×D4311yescharacteristic
185#95C2×D4312yes—
186C24—431no—
187C24—431no—
188C24C22×D4311yescharacteristic
189C2×Q8—22no—
190C2×Q8—42no—
191C2×D4—862no—
192C2×D4—862no—
193C2×D4—862no—
194C2×D4—1722no—
195C2×D4—1722no—
196C2×D4—1722no—
197C22×C4—431no—
198C22×C4—434no—
199C22×C4—432no—
200C22×C4—431no—
201C22×C4—432no—
202C22×C4—1722no—
203C22×C4C22×D4312yes—
204C22×C4C22×D4312yes—
205C22×C4C22×D4311yescharacteristic
206C22×C4C22×D4311yescharacteristic
207C4⋊C4—862no—
208C4⋊C4—864no—
209C4⋊C4—862no—
210C4⋊C4—1722no—
211C4⋊C4—1722no—
212C22⋊C4—22no—
213C22⋊C4—42no—
214C22⋊C4—864no—
215C22⋊C4—862no—
216C22⋊C4—1722no—
217C22⋊C4—1722no—
218C22⋊C4—1722no—
219C22⋊C4—1722no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—432no—
226C23—862no—
227C23—862no—
228C23—861no—
229C23—861no—
230C23—861no—
231C23—862no—
232C23—862no—
233C23—861no—
234C23—861no—
235C23C23×D4311yescharacteristic
236Q8—44no—
237D4—1724no—
238D4—1724no—
239D4—1724no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—432no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—861no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—862no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—1724no—
260C2×C4D4×D4312yes—
261C22—42no—
262C22—42no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—862no—
267C22—862no—
268C22—862no—
269C22—1722no—
270C22—1722no—
271C22—1721no—
272C22—1721no—
273C22—1721no—
274C22—1722no—
275C22—1722no—
276C22C2×D4×D4311yescharacteristic
277C22#1306337012yes—
278C22#1306337112yes—
279C22#1306337211yescharacteristic
280C22#1306337311yescharacteristic
281C4—22no—
282C4—42no—
283C4—42no—
284C4—41no—
285C4—862no—
286C4—1722no—
287C4—1721no—
288C4—1722no—
289C2—81no—
290C2—3441no—
291C2—1722no—
292C2#1458345911yescharacteristic
293C2#1458346711yescharacteristic
294C2#1458347211yescharacteristic
295C2#1458364312yes—
296C2#1458364512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#393C2
hypercenter#393D43
hypocenterC43#2816
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13063301C2semidirect
3. #14582836C2semidirect
4. #14582835C2semidirect
5. #14582833C2semidirect
6. #14582817C2semidirect
7. #14582815C2semidirect
8. #14582814C2semidirect
9. #14582810C2semidirect
10. #14582761C2semidirect
11. C43×#393C2semidirect
158. #393D43semidirect
160. C43#2816semidirect