Finite Group Databasebeta

← #19142628

Subgroups — #19142628

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×#13063303C211yesmaximal, characteristic, complemented
2C2×#13063300C211yesmaximal, characteristic
3#14582834C212yesmaximal, complemented
4#14582830C211yesmaximal, characteristic, complemented
5#14582817C212yesmaximal, complemented
6#14582817C211yesmaximal, characteristic, complemented
7#14582816C211yesmaximal, characteristic, complemented
8#14582816C212yesmaximal, complemented
9#14582812C212yesmaximal, complemented
10#14582761C211yesmaximal, characteristic, complemented
11C43×#398C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C22×D172C2212yes—
15C22×C4×D43C2211yescharacteristic
16#13063303—24no—
17#13063300—24no—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
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×D43C2312yes—
38C23×D43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×D172—22no—
49C2×D172—24no—
50C2×D172—42no—
51C2×D172—42no—
52C2×D172—42no—
53C2×C4×D43—42no—
54C2×C4×D43D414yes—
55C2×Dic86—22no—
56C2×Dic86—42no—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—42no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—42no—
64(C2×D43)⋊C4—42no—
65(C2×D43)⋊C4—42no—
66(C2×D43)⋊C4—42no—
67(C2×D43)⋊C4—42no—
68Dic43⋊C4—22no—
69Dic43⋊C4—22no—
70Dic43⋊C4—42no—
71C23×C43C2411yescharacteristic
72C22×D43—22no—
73C22×D43—21no—
74C22×D43—21no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43C2×D412yes—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43C2×D412yes—
97C2×Dic43—22no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43C2×D412yes—
107D172—44no—
108D172—48no—
109C4×D43—44no—
110Dic86—44no—
111C22×C43C22×D411yescharacteristic
112C22×C43H(5,𝔽2)11yescharacteristic
113C22×C43H(5,𝔽2)12yes—
114C22×C43H(5,𝔽2)11yescharacteristic
115C22×C432−1+412yes—
116C2×D43—22no—
117C2×D43—22no—
118C2×D43—22no—
119C2×D43—42no—
120C2×D43—42no—
121C2×D43—42no—
122C2×D43—42no—
123C2×D43—42no—
124C2×D43—42no—
125C2×D43—42no—
126C2×D43—42no—
127C2×D43—42no—
128C4×C43—22no—
129C4×C43—41no—
130C4×C43—42no—
131C4×C43—41no—
132C4×C43—42no—
133Dic43—22no—
134Dic43—41no—
135Dic43—41no—
136Dic43—42no—
137#2816—431nomaximal, Sylow
138C2×C43#53411yescharacteristic
139C2×C43#53511yescharacteristic
140C2×C43#53611yescharacteristic
141C2×C43#56212yes—
142C2×C43#56212yes—
143D43—42no—
144D43—82no—
145C2×C22⋊Q8—431no—
146C2×#121—431no—
147#399—432no—
148#398—431no—
149#398D4311yescharacteristic, complemented
150#394—431no—
151#394—432no—
152#394—431no—
153#394—432no—
154#393—432no—
155#381—431no—
156C43#281611yescharacteristic, complemented, Sylow
157C22×Q8—431no—
158C22×D4—432no—
159C22×D4—431no—
160C23×C4—431no—
161C22⋊Q8—864no—
162#121—864no—
163C2×C4⋊C4—431no—
164C2×C4⋊C4—431no—
165C2×C4⋊C4—432no—
166C2×C4⋊C4C2×D4311yescharacteristic
167C2×C4⋊C4C2×D4311yescharacteristic
168C2×C4⋊C4C2×D4312yes—
169C2×C22⋊C4—432no—
170C2×C22⋊C4—431no—
171C2×C22⋊C4—431no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4—432no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4—432no—
176C2×C22⋊C4—432no—
177#95—432no—
178#95—431no—
179#95—432no—
180#95C2×D4311yescharacteristic
181#95C2×D4312yes—
182C24—431no—
183C24—432no—
184C2×Q8—862no—
185C2×Q8—1722no—
186C2×D4—864no—
187C2×D4—862no—
188C2×D4—1722no—
189C2×D4—1722no—
190C2×D4—1722no—
191C22×C4—431no—
192C22×C4—434no—
193C22×C4—432no—
194C22×C4—431no—
195C22×C4—431no—
196C22×C4—1722no—
197C22×C4C22×D4312yes—
198C22×C4C22×D4312yes—
199C22×C4C22×D4311yescharacteristic
200C22×C4C22×D4311yescharacteristic
201C22×C4C22×D4311yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—862no—
206C4⋊C4—862no—
207C4⋊C4—1722no—
208C22⋊C4—864no—
209C22⋊C4—862no—
210C22⋊C4—862no—
211C22⋊C4—1722no—
212C22⋊C4—1722no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C23—432no—
217C23—861no—
218C23—862no—
219C23—861no—
220C23—862no—
221C23—862no—
222C23—862no—
223C23—862no—
224C23—862no—
225C23—862no—
226C23—862no—
227C23—862no—
228C23C23×D4311yescharacteristic
229Q8—1724no—
230D4—1724no—
231D4—1728no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—432no—
245C2×C4—862no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—861no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—861no—
253C2×C4—862no—
254C2×C4—1724no—
255C2×C4D4×D4312yes—
256C22—862no—
257C22—862no—
258C22—862no—
259C22—1722no—
260C22—1722no—
261C22—1722no—
262C22—1722no—
263C22—1722no—
264C22—1722no—
265C22—1722no—
266C22—1722no—
267C22—1722no—
268C22C2×D4×D4311yescharacteristic
269C22#1306337011yescharacteristic
270C22#1306337112yes—
271C22#1306337111yescharacteristic
272C22#1306337312yes—
273C4—22no—
274C4—42no—
275C4—41no—
276C4—42no—
277C4—41no—
278C4—862no—
279C4—1722no—
280C4—1721no—
281C4—1721no—
282C2—3442no—
283C2—1722no—
284C2#1458346011yescharacteristic
285C2#1458346511yescharacteristic
286C2#1458347411yescharacteristic
287C2#1458364512yes—
288C2#1458364712yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2816
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13063303C2semidirect
3. #14582834C2semidirect
4. #14582830C2semidirect
5. #14582817C2semidirect
6. #14582817C2semidirect
7. #14582816C2semidirect
8. #14582816C2semidirect
9. #14582812C2semidirect
10. #14582761C2semidirect
11. C43×#398C2semidirect
149. #398D43semidirect
156. C43#2816semidirect