Finite Group Databasebeta

← #19140282

Subgroups — #19140282

Order 5504.

576 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13063313C211yesmaximal, characteristic, complemented
2#14582819C211yesmaximal, characteristic, complemented
3#14582816C211yesmaximal, characteristic, complemented
4#14582811C211yesmaximal, characteristic, complemented
5#14582808C211yesmaximal, characteristic
6#14582799C212yesmaximal, complemented
7#14582790C212yesmaximal, complemented
8#14582789C212yesmaximal, complemented
9#14582778C212yesmaximal, complemented
10#14582745C211yesmaximal, characteristic, complemented
11C2×#117×C43C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C22×C22⋊D43C2212yes—
15#13063313—24no—
16C2×Dic43⋊C4C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×C4×Dic43C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2211yescharacteristic
29C23×C4×C43C2211yescharacteristic
30#117×C43—24no—
31C2×C4⋊C4×C43C2211yescharacteristic
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C42×C43C2211yescharacteristic
36C2×C42×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2312yes—
39C22×C4×C43—22no—
40C22×C4×C43—22no—
41C22×C4×C43—22no—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—24no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43—42no—
51C22×Dic43C2312yes—
52C22×Dic43C2312yes—
53C22×Dic43C2312yes—
54C2×D172—22no—
55C2×D172—42no—
56C2×Dic86—22no—
57C2×Dic86—42no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—22no—
60C22⋊C4×C43—22no—
61C22⋊C4×C43—22no—
62C42×C43—22no—
63C42×C43D414yescomplemented
64C22⋊Dic43—42no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—24no—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4—42no—
70Dic43⋊C4—42no—
71C4×Dic43—24no—
72C23×C43—21no—
73C23×C43—22no—
74C23×C43—21no—
75C23×C43—22no—
76C23×C43#4112yes—
77C23×C43C2411yescharacteristic
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—22no—
85C2×C4×C43—28no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2×D412yes—
98C2×C4×C43C2×D412yes—
99C2×C4×C43#4112yes—
100C22⋊D43—48no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43#4114yes—
110D172—44no—
111Dic86—44no—
112C22×C43—22no—
113C22×C43—24no—
114C22×C43—41no—
115C22×C43—41no—
116C22×C43—42no—
117C22×C43C22×D411yescharacteristic
118C22×C43C2×#4112yes—
119C22×C43C2×#4111yescharacteristic
120C22×C43C2×#4111yescharacteristic
121C22×C43H(5,𝔽2)12yes—
122C2×D43—42no—
123C2×D43—42no—
124C2×D43—42no—
125C2×D43—42no—
126C2×D43—42no—
127C2×D43—42no—
128C2×D43—42no—
129C4×C43—22no—
130C4×C43—22no—
131C4×C43—22no—
132C4×C43—22no—
133C4×C43—41no—
134C4×C43—41no—
135Dic43—24no—
136Dic43—42no—
137Dic43—42no—
138#2610—431nomaximal, Sylow
139C2×C43—42no—
140C2×C43#52511yescharacteristic
141C2×C43#53211yescharacteristic
142C2×C43#53511yescharacteristic
143C2×C43#55112yes—
144C2×C43#55512yes—
145D43—82no—
146C2×#124—431no—
147C2×#117D4311yescharacteristic, complemented
148#395—431no—
149#394—431no—
150#393—431no—
151#392—431no—
152#390—432no—
153#388—432no—
154#388—432no—
155#386—432no—
156#376—431no—
157C43#261011yescharacteristic, complemented, Sylow
158C22×Q8—431no—
159C22×D4—432no—
160C22×D4—431no—
161C23×C4C2×D4311yescharacteristic
162#124—864no—
163#117—24no—
164C2×C4⋊C4—432no—
165C2×C4⋊C4C2×D4311yescharacteristic
166C2×C4⋊C4C2×D4311yescharacteristic
167C2×C22⋊C4—432no—
168C2×C22⋊C4—432no—
169C2×C22⋊C4—432no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4C2×D4311yescharacteristic
174C2×C22⋊C4C2×D4311yescharacteristic
175C2×C42—432no—
176C2×C42C2×D4311yescharacteristic
177C2×C42C2×D4311yescharacteristic
178#95—432no—
179#95—431no—
180#95—431no—
181#95—432no—
182#95—432no—
183C24—432no—
184C24C22×D4311yescharacteristic
185C2×Q8—862no—
186C2×Q8—1722no—
187C2×D4—864no—
188C2×D4—864no—
189C2×D4—862no—
190C2×D4—1722no—
191C2×D4—1722no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—432no—
196C22×C4—432no—
197C22×C4—432no—
198C22×C4C22×D4311yescharacteristic
199C22×C4C22×D4311yescharacteristic
200C22×C4C22×D4311yescharacteristic
201C22×C4C22×D4311yescharacteristic
202C22×C4C22×D4311yescharacteristic
203C22×C4C22×D4311yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—1722no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—864no—
210C22⋊C4—864no—
211C22⋊C4—864no—
212C22⋊C4—864no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C42—22no—
216C42—864no—
217C42C22⋊D4314yescomplemented
218C23—21no—
219C23—22no—
220C23—21no—
221C23—22no—
222C23—862no—
223C23—862no—
224C23—862no—
225C23—862no—
226C23—862no—
227C23—862no—
228C23—862no—
229C23#1062189812yes—
230C23C23×D4311yescharacteristic
231Q8—1724no—
232D4—1724no—
233D4—1728no—
234C2×C4—28no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—434no—
246C2×C4—862no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4#1062189812yes—
255C2×C4C2×C22⋊D4312yes—
256C2×C4C2×C22⋊D4312yes—
257C2×C4C2×C22⋊D4312yes—
258C22—24no—
259C22—22no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—1722no—
264C22—1722no—
265C22—1722no—
266C22—1722no—
267C22—1722no—
268C22—1722no—
269C22—1722no—
270C22C22×C22⋊D4311yescharacteristic
271C22#41×D4312yes—
272C22C2×#1062189811yescharacteristic
273C22C2×#1062189811yescharacteristic
274C22#1306337112yes—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—41no—
281C4—864no—
282C4—1722no—
283C4—1722no—
284C2—42no—
285C2—3442no—
286C2#1458341011yescharacteristic
287C2#1458344511yescharacteristic
288C2#1458346311yescharacteristic
289C2#1458357312yes—
290C2#1458361212yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#117×C43C2
hypercenterC2×#117D43
hypocenterC43#2610
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#13063313C2semidirect
2. #14582819C2semidirect
3. #14582816C2semidirect
4. #14582811C2semidirect
6. #14582799C2semidirect
7. #14582790C2semidirect
8. #14582789C2semidirect
9. #14582778C2semidirect
10. #14582745C2semidirect
11. C2×#117×C43C2semidirect
63. C42×C43D4semidirect
147. C2×#117D43semidirect
157. C43#2610semidirect
217. C42C22⋊D43semidirect