Finite Group Databasebeta

← #19140537

Subgroups — #19140537

Order 5504.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063321C211yesmaximal, characteristic
2C2×#13063315C211yesmaximal, characteristic, complemented
3#14582817C211yesmaximal, characteristic, complemented
4#14582816C211yesmaximal, characteristic, complemented
5#14582815C212yesmaximal, complemented
6#14582814C212yesmaximal, complemented
7#14582813C211yesmaximal, characteristic, complemented
8#14582799C212yesmaximal, complemented
9#14582799C212yesmaximal, complemented
10#14582744C211yesmaximal, characteristic, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C22×C22⋊D43C2212yes—
15#13063321—24no—
16#13063315—24no—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×C22⋊Dic43C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×C4×Dic43C2212yes—
29C2×C4×Dic43C2211yescharacteristic
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C22×D4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2312yes—
38C23×D43C2312yes—
39C2×D4×C43—22no—
40C2×D4×C43—42no—
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—24no—
46C2×C22⋊D43—24no—
47C2×C22⋊D43—24no—
48C2×C22⋊D43—24no—
49C2×C22⋊D43—42no—
50C2×C22⋊D43—42no—
51C22×Dic43C2312yes—
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2311yescharacteristic
55C22×Dic43C2311yescharacteristic
56C2×D172—22no—
57C2×D172—42no—
58C4⋊C4×C43—22no—
59C22⋊C4×C43—42no—
60C22⋊C4×C43—42no—
61C22⋊Dic43—42no—
62C22⋊Dic43—42no—
63(C2×D43)⋊C4—42no—
64(C2×D43)⋊C4—42no—
65(C2×D43)⋊C4—42no—
66(C2×D43)⋊C4—42no—
67C4⋊Dic43—22no—
68Dic43⋊C4—22no—
69Dic43⋊C4—22no—
70Dic43⋊C4—22no—
71Dic43⋊C4—22no—
72C4×Dic43—24no—
73C4×Dic43D414yes—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43C2411yescharacteristic
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89D4×C43—44no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43C2×D412yes—
100C22⋊D43—48no—
101C22⋊D43—48no—
102C2×Dic43—21no—
103C2×Dic43—21no—
104C2×Dic43—21no—
105C2×Dic43—21no—
106C2×Dic43—22no—
107C2×Dic43—21no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—21no—
112C2×Dic43C2×D412yes—
113C2×Dic43C2×D412yes—
114C2×Dic43#4114yes—
115D172—44no—
116C22×C43—42no—
117C22×C43—42no—
118C22×C43—42no—
119C22×C43—42no—
120C22×C43—42no—
121C22×C43—42no—
122C22×C43—42no—
123C22×C43C22×D411yescharacteristic
124C22×C43C2×#4112yes—
125C22×C43H(5,𝔽2)12yes—
126C22×C43H(5,𝔽2)11yescharacteristic
127C22×C43H(5,𝔽2)11yescharacteristic
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—42no—
135C4×C43—22no—
136C4×C43—41no—
137C4×C43—41no—
138C4×C43—42no—
139Dic43—22no—
140Dic43—41no—
141Dic43—41no—
142Dic43—42no—
143Dic43#12414yes—
144#2641—431nomaximal, Sylow
145C2×C43—82no—
146C2×C43C2×#12411yescharacteristic
147C2×C43#53511yescharacteristic
148C2×C43#53511yescharacteristic
149C2×C43#54012yes—
150C2×C43#54012yes—
151D43—82no—
152C2×#127—431no—
153C2×#125—431no—
154#394—431no—
155#394—431no—
156#394—432no—
157#394—432no—
158#394—431no—
159#394D4311yescharacteristic, complemented
160#390—432no—
161#390—432no—
162#376—431no—
163C43#264111yescharacteristic, complemented, Sylow
164C22×D4—432no—
165C22×D4—432no—
166C22×D4—431no—
167C22×D4C2×D4311yescharacteristic
168#127—864no—
169#125—864no—
170C2×C4⋊C4—431no—
171C2×C4⋊C4—431no—
172C2×C4⋊C4—431no—
173C2×C4⋊C4—431no—
174C2×C4⋊C4—431no—
175C2×C4⋊C4C2×D4311yescharacteristic
176C2×C22⋊C4—432no—
177C2×C22⋊C4—432no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4—432no—
181C2×C22⋊C4—432no—
182C2×C22⋊C4C2×D4312yes—
183C2×C22⋊C4C2×D4312yes—
184C2×C42—431no—
185C2×C42—432no—
186#95—432no—
187#95—431no—
188#95C2×D4311yescharacteristic
189C24—432no—
190C24C22×D4312yes—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—864no—
194C2×D4—864no—
195C2×D4—864no—
196C2×D4—864no—
197C2×D4—862no—
198C2×D4—1722no—
199C2×D4—1722no—
200C2×D4—1722no—
201C22×C4—431no—
202C22×C4—431no—
203C22×C4—432no—
204C22×C4—431no—
205C22×C4—431no—
206C22×C4C22×D4312yes—
207C22×C4C22×D4311yescharacteristic
208C22×C4C22×D4311yescharacteristic
209C22×C4C22×D4311yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—862no—
212C4⋊C4—862no—
213C4⋊C4—862no—
214C4⋊C4—862no—
215C4⋊C4—862no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—1722no—
219C22⋊C4—1722no—
220C22⋊C4—1722no—
221C22⋊C4—1722no—
222C22⋊C4—1722no—
223C22⋊C4—1722no—
224C42—434no—
225C42—864no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—862no—
234C23—862no—
235C23—862no—
236C23—862no—
237C23—862no—
238C23—862no—
239C23—862no—
240C23C23×D4311yescharacteristic
241D4—44no—
242D4—1724no—
243D4—1728no—
244D4—1728no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—432no—
255C2×C4—434no—
256C2×C4—432no—
257C2×C4—861no—
258C2×C4—861no—
259C2×C4—861no—
260C2×C4—861no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—861no—
264C2×C4—862no—
265C2×C4—861no—
266C2×C4—862no—
267C2×C4D4×D4312yes—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—1722no—
276C22—1722no—
277C22—1722no—
278C22—1722no—
279C22—1722no—
280C22—1722no—
281C22—1722no—
282C22C2×D4×D4311yescharacteristic
283C22#41×D4312yes—
284C22#1306337012yes—
285C22#1306337011yescharacteristic
286C22#1306337111yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—434no—
292C4—862no—
293C4—1721no—
294C4—1721no—
295C4—1722no—
296C2—82no—
297C2—3442no—
298C2#124×D4311yescharacteristic
299C2#1458346411yescharacteristic
300C2#1458346511yescharacteristic
301C2#1458349912yes—
302C2#1458350112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2641
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13063315C2semidirect
3. #14582817C2semidirect
4. #14582816C2semidirect
5. #14582815C2semidirect
6. #14582814C2semidirect
7. #14582813C2semidirect
8. #14582799C2semidirect
9. #14582799C2semidirect
10. #14582744C2semidirect
11. C43×#394C2semidirect
159. #394D43semidirect
163. C43#2641semidirect