Finite Group Databasebeta

← #19140162

Subgroups — #19140162

Order 5504.

604 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 135 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×#13063287C211yesmaximal, characteristic, complemented
2C2×#13063281C211yesmaximal, characteristic, complemented
3#14582837C211yesmaximal, characteristic, complemented
4#14582817C211yesmaximal, characteristic, complemented
5#14582808C211yesmaximal, characteristic
6#14582789C212yesmaximal, complemented
7#14582776C212yesmaximal, complemented
8#14582775C212yesmaximal, complemented
9#14582770C212yesmaximal, complemented
10#14582766C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C23×Dic43C2211yescharacteristic
15C22×C4×D43C2212yes—
16#13063287—24no—
17#13063281—24no—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×C22⋊Dic43C2211yescharacteristic
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C2×C4×Dic43C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C2×C22⋊D43—24no—
44C2×C22⋊D43—24no—
45C2×C22⋊D43—42no—
46C22×Dic43—22no—
47C22×Dic43—22no—
48C22×Dic43—22no—
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2311yescharacteristic
54C2×D172—22no—
55C2×D172—24no—
56C2×C4×D43—24no—
57C2×C4×D43—42no—
58C2×C4×D43—42no—
59C4⋊C4×C43—22no—
60C4⋊C4×C43—42no—
61C22⋊C4×C43—22no—
62C22⋊C4×C43—42no—
63C22⋊Dic43—22no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—42no—
68Dic43⋊C4—22no—
69Dic43⋊C4—22no—
70C4×Dic43—22no—
71C4×Dic43D414yescomplemented
72C23×C43—21no—
73C23×C43—21no—
74C23×C43—22no—
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#4114yes—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43C2×D412yes—
95C22⋊D43—48no—
96C2×Dic43—28no—
97C2×Dic43—21no—
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×Dic43—22no—
107C2×Dic43C2×D412yes—
108C2×Dic43C2×D412yes—
109C2×Dic43#4112yes—
110D172—28no—
111C4×D43—48no—
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—24no—
123C2×D43—24no—
124C2×D43—24no—
125C2×D43—42no—
126C2×D43—42no—
127C2×D43—42no—
128C2×D43—42no—
129C4×C43—22no—
130C4×C43—42no—
131C4×C43—41no—
132C4×C43—42no—
133Dic43—22no—
134Dic43—22no—
135Dic43—22no—
136Dic43—41no—
137Dic43—42no—
138#2598—431nomaximal, Sylow
139C2×C43—42no—
140C2×C43#52511yescharacteristic
141C2×C43#52511yescharacteristic
142C2×C43#53511yescharacteristic
143C2×C43#55112yes—
144C2×C43#55312yes—
145D43—44no—
146C2×C4×D4—431no—
147C2×#117—431no—
148#400—431no—
149#399D4311yescharacteristic, complemented
150#394—431no—
151#392—431no—
152#388—432no—
153#386—432no—
154#386—432no—
155#385—432no—
156#383—431no—
157C43#259811yescharacteristic, complemented, Sylow
158C22×D4—432no—
159C22×D4—431no—
160C23×C4—431no—
161C23×C4—432no—
162C4×D4—864no—
163#117—864no—
164C2×C4⋊C4—431no—
165C2×C4⋊C4—431no—
166C2×C4⋊C4C2×D4311yescharacteristic
167C2×C4⋊C4C2×D4312yes—
168C2×C22⋊C4—431no—
169C2×C22⋊C4—432no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4C2×D4311yescharacteristic
174C2×C22⋊C4C2×D4312yes—
175C2×C42—431no—
176C2×C42—431no—
177#95—432no—
178#95—432no—
179#95—431no—
180#95—432no—
181#95—432no—
182#95C2×D4311yescharacteristic
183C24—432no—
184C24C22×D4311yescharacteristic
185C2×D4—864no—
186C2×D4—864no—
187C2×D4—864no—
188C2×D4—862no—
189C2×D4—1722no—
190C22×C4—431no—
191C22×C4—431no—
192C22×C4—431no—
193C22×C4—432no—
194C22×C4—431no—
195C22×C4—864no—
196C22×C4—862no—
197C22×C4—862no—
198C22×C4—862no—
199C22×C4—1722no—
200C22×C4—1722no—
201C22×C4C22×D4312yes—
202C22×C4C22×D4312yes—
203C22×C4C22×D4311yescharacteristic
204C22×C4C22×D4311yescharacteristic
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—862no—
208C4⋊C4—862no—
209C22⋊C4—22no—
210C22⋊C4—42no—
211C22⋊C4—864no—
212C22⋊C4—864no—
213C22⋊C4—864no—
214C22⋊C4—862no—
215C22⋊C4—1722no—
216C42—434no—
217C42—862no—
218C23—21no—
219C23—21no—
220C23—22no—
221C23—22no—
222C23—434no—
223C23—862no—
224C23—862no—
225C23—862no—
226C23—862no—
227C23—862no—
228C23—862no—
229C23#1062190212yes—
230C23C23×D4311yescharacteristic
231D4—868no—
232D4—1728no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—432no—
243C2×C4—432no—
244C2×C4—432no—
245C2×C4—868no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—861no—
249C2×C4—861no—
250C2×C4—862no—
251C2×C4—861no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—1728no—
257C2×C4D4×D4312yes—
258C22—24no—
259C22—22no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—864no—
264C22—864no—
265C22—864no—
266C22—1722no—
267C22—1722no—
268C22—1722no—
269C22—1722no—
270C22C2×D4×D4311yescharacteristic
271C22#41×D4312yes—
272C22#41×D4311yescharacteristic
273C22C2×#1062190211yescharacteristic
274C22#1306337012yes—
275C4—22no—
276C4—42no—
277C4—42no—
278C4—41no—
279C4—862no—
280C4—862no—
281C4—862no—
282C4—1722no—
283C4—1721no—
284C2—42no—
285C2—1724no—
286C2#1458340711yescharacteristic
287C2#1458341211yescharacteristic
288C2#1458346211yescharacteristic
289C2#1458357612yes—
290C2#1458359412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2598
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063287C2semidirect
2. C2×#13063281C2semidirect
3. #14582837C2semidirect
4. #14582817C2semidirect
6. #14582789C2semidirect
7. #14582776C2semidirect
8. #14582775C2semidirect
9. #14582770C2semidirect
10. #14582766C2semidirect
11. C43×#399C2semidirect
71. C4×Dic43D4semidirect
149. #399D43semidirect
157. C43#2598semidirect