Finite Group Databasebeta

← #19140338

Subgroups — #19140338

Order 5504.

632 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13063310C212yesmaximal, complemented
2C2×#13063300C211yesmaximal, characteristic
3C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#14582830C211yesmaximal, characteristic, complemented
5#14582823C212yesmaximal, complemented
6#14582821C212yesmaximal, complemented
7#14582817C211yesmaximal, characteristic, complemented
8#14582816C211yesmaximal, characteristic, complemented
9#14582777C212yesmaximal, complemented
10#14582758C211yesmaximal, characteristic, complemented
11C43×#398C211yesmaximal, characteristic, complemented
12C22×D172C2212yes—
13C22×D172C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16C22×C4×D43C2211yescharacteristic
17#13063310—28no—
18#13063300—24no—
19C2×C4⋊Dic43C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C4⋊C4×D43—24no—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
29C2×(C2×D43)⋊C4C2212yes—
30C2×(C2×D43)⋊C4C2212yes—
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35C2×C4⋊C4×C43C2211yescharacteristic
36#95×C43C2211yescharacteristic
37#95×C43C2212yes—
38C23×D43C2312yes—
39C23×D43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2311yescharacteristic
49C2×D172—22no—
50C2×D172—24no—
51C2×D172—24no—
52C2×D172—24no—
53C2×D172—42no—
54C2×C4×D43—22no—
55C2×C4×D43—22no—
56C2×C4×D43—22no—
57C2×C4×D43—42no—
58C2×C4×D43—42no—
59C2×C4×D43D414yes—
60C2×C4×D43D414yescomplemented
61C4⋊C4×C43—22no—
62C4⋊C4×C43—22no—
63C4⋊C4×C43—24no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—24no—
68(C2×D43)⋊C4—42no—
69(C2×D43)⋊C4—42no—
70C4⋊Dic43—22no—
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73Dic43⋊C4—24no—
74Dic43⋊C4—42no—
75C23×C43C2411yescharacteristic
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43C2×D412yes—
86C22×D43C2×D412yes—
87C22×D43#4112yes—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43C2×D412yes—
100C2×C4×C43C2×D412yes—
101C2×Dic43—21no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43C2×D412yes—
110C2×Dic43C2×D412yes—
111D172—44no—
112D172—48no—
113C4×D43—28no—
114C4×D43—44no—
115C4×D43—44no—
116C22×C43C22×D411yescharacteristic
117C22×C43C22×D411yescharacteristic
118C22×C43C2×#4111yescharacteristic
119C22×C43H(5,𝔽2)12yes—
120C22×C432−1+412yes—
121C2×D43—22no—
122C2×D43—22no—
123C2×D43—24no—
124C2×D43—24no—
125C2×D43—42no—
126C2×D43—42no—
127C2×D43—42no—
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43#12114yes—
133C4×C43—22no—
134C4×C43—22no—
135C4×C43—42no—
136C4×C43—41no—
137C4×C43—42no—
138Dic43—22no—
139Dic43—22no—
140Dic43—41no—
141Dic43—42no—
142#2618—431nomaximal, Sylow
143C2×C43C2×#12111yescharacteristic
144C2×C43#53411yescharacteristic
145C2×C43#53611yescharacteristic
146C2×C43#53712yes—
147C2×C43#53912yes—
148D43—24no—
149D43—82no—
150C2×#123—432no—
151C2×#121—431no—
152C22×C4⋊C4—431no—
153#398—431no—
154#398D4311yescharacteristic, complemented
155#396—432no—
156#396—432no—
157#394—431no—
158#394—431no—
159#386—432no—
160#380—431no—
161C43#261811yescharacteristic, complemented, Sylow
162C22×D4—432no—
163C22×D4—431no—
164C23×C4—431no—
165C23×C4—431no—
166C23×C4—431no—
167#123—868no—
168#121—864no—
169C2×C4⋊C4—431no—
170C2×C4⋊C4—431no—
171C2×C4⋊C4—431no—
172C2×C4⋊C4—432no—
173C2×C4⋊C4—432no—
174C2×C4⋊C4—864no—
175C2×C4⋊C4C2×D4311yescharacteristic
176C2×C4⋊C4C2×D4311yescharacteristic
177C2×C4⋊C4C2×D4312yes—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4—432no—
181C2×C22⋊C4—432no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—432no—
184#95—431no—
185#95—432no—
186#95C2×D4311yescharacteristic
187#95C2×D4312yes—
188C24—431no—
189C24—432no—
190C2×D4—864no—
191C2×D4—864no—
192C2×D4—864no—
193C2×D4—862no—
194C2×D4—1722no—
195C22×C4—431no—
196C22×C4—431no—
197C22×C4—434no—
198C22×C4—434no—
199C22×C4—432no—
200C22×C4—431no—
201C22×C4—862no—
202C22×C4—862no—
203C22×C4—862no—
204C22×C4—1722no—
205C22×C4—1722no—
206C22×C4C22×D4312yes—
207C22×C4C22×D4312yes—
208C22×C4C22×D4311yescharacteristic
209C22×C4C22×D4311yescharacteristic
210C22×C4C22×D4311yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—24no—
214C4⋊C4—862no—
215C4⋊C4—862no—
216C4⋊C4—864no—
217C4⋊C4—862no—
218C4⋊C4—1722no—
219C22⋊C4—864no—
220C22⋊C4—864no—
221C22⋊C4—864no—
222C22⋊C4—864no—
223C22⋊C4—1722no—
224C22⋊C4—1722no—
225C23—432no—
226C23—432no—
227C23—432no—
228C23—862no—
229C23—862no—
230C23—862no—
231C23—862no—
232C23—862no—
233C23—862no—
234C23—862no—
235C23—862no—
236C23—862no—
237C23C23×D4311yescharacteristic
238D4—1724no—
239D4—1728no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—432no—
252C2×C4—432no—
253C2×C4—868no—
254C2×C4—861no—
255C2×C4—861no—
256C2×C4—862no—
257C2×C4—862no—
258C2×C4—861no—
259C2×C4—862no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—1724no—
263C2×C4—1724no—
264C2×C4D4×D4312yes—
265C2×C4D4×D4312yes—
266C22—434no—
267C22—862no—
268C22—862no—
269C22—864no—
270C22—864no—
271C22—1722no—
272C22—1722no—
273C22—1722no—
274C22—1722no—
275C22—1722no—
276C22—1722no—
277C22—1722no—
278C22C2×D4×D4311yescharacteristic
279C22C2×D4×D4311yescharacteristic
280C22#41×D4311yescharacteristic
281C22#1306337112yes—
282C22#1306337312yes—
283C4—22no—
284C4—22no—
285C4—42no—
286C4—41no—
287C4—42no—
288C4—862no—
289C4—862no—
290C4—1721no—
291C4—1722no—
292C2—864no—
293C2—3442no—
294C2#121×D4311yescharacteristic
295C2#1458346011yescharacteristic
296C2#1458347411yescharacteristic
297C2#1458347912yes—
298C2#1458349712yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2618
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13063310C2semidirect
3. C2×C4⋊C4×D43C2semidirect
4. #14582830C2semidirect
5. #14582823C2semidirect
6. #14582821C2semidirect
7. #14582817C2semidirect
8. #14582816C2semidirect
9. #14582777C2semidirect
10. #14582758C2semidirect
11. C43×#398C2semidirect
60. C2×C4×D43D4semidirect
154. #398D43semidirect
161. C43#2618semidirect