Finite Group Databasebeta

← #19140492

Subgroups — #19140492

Order 5504.

562 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×D172C211yesmaximal, characteristic, complemented
2#14582838C211yesmaximal, characteristic, complemented
3#14582835C211yesmaximal, characteristic, complemented
4#14582821C212yesmaximal, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582815C212yesmaximal, complemented
7#14582808C211yesmaximal, characteristic
8#14582775C212yesmaximal, complemented
9#14582770C212yesmaximal, complemented
10#14582765C211yesmaximal, characteristic, complemented
11C2×#126×C43C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C22×C4×D43C2212yes—
15C4×D172—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29#126×C43—24no—
30C2×C4⋊C4×C43C2211yescharacteristic
31C2×C4⋊C4×C43C2211yescharacteristic
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36C2×C42×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—24no—
46C2×C22⋊D43—42no—
47C2×C22⋊D43—42no—
48C22×Dic43C2312yes—
49C22×Dic43C2312yes—
50C22×Dic43C2312yes—
51C2×D172—22no—
52C2×D172—24no—
53C2×C4×D43—24no—
54C2×C4×D43—42no—
55C2×C4×D43—42no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—22no—
59C22⋊C4×C43—22no—
60C22⋊C4×C43—22no—
61C22⋊C4×C43—22no—
62C42×C43D414yescomplemented
63C22⋊Dic43—42no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—42no—
67(C2×D43)⋊C4—42no—
68C4⋊Dic43—22no—
69C4⋊Dic43—42no—
70Dic43⋊C4—42no—
71C23×C43—21no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43C2411yescharacteristic
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43#4114yes—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43C2×D412yes—
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2×D412yes—
98C22⋊D43—48no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108D172—28no—
109C4×D43—48no—
110C22×C43—41no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43—42no—
114C22×C43—42no—
115C22×C43C22×D411yescharacteristic
116C22×C43C2×#4112yes—
117C22×C43H(5,𝔽2)12yes—
118C22×C43H(5,𝔽2)11yescharacteristic
119C22×C432−1+411yescharacteristic
120C2×D43—24no—
121C2×D43—24no—
122C2×D43—24no—
123C2×D43—42no—
124C2×D43—42no—
125C2×D43—42no—
126C2×D43—42no—
127C4×C43—22no—
128C4×C43—22no—
129C4×C43—22no—
130C4×C43—41no—
131C4×C43—41no—
132C4×C43—41no—
133Dic43—42no—
134Dic43—42no—
135Dic43—42no—
136#2636—431nomaximal, Sylow
137C2×C43—81no—
138C2×C43#52511yescharacteristic
139C2×C43#53511yescharacteristic
140C2×C43#53711yescharacteristic
141C2×C43#53812yes—
142C2×C43#53912yes—
143D43—44no—
144C2×#126D4311yescharacteristic, complemented
145C2×C4×D4—431no—
146#400—431no—
147#399—431no—
148#396—432no—
149#394—431no—
150#394—432no—
151#392—431no—
152#386—432no—
153#385—432no—
154#382—431no—
155C43#263611yescharacteristic, complemented, Sylow
156C22×D4—432no—
157C22×D4—431no—
158C23×C4—432no—
159#126—24no—
160C4×D4—864no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—432no—
164C2×C4⋊C4C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic
173C2×C22⋊C4C2×D4311yescharacteristic
174C2×C22⋊C4C2×D4311yescharacteristic
175C2×C42C2×D4311yescharacteristic
176#95—432no—
177#95—431no—
178#95—431no—
179#95—432no—
180#95—432no—
181C24—432no—
182C24C22×D4311yescharacteristic
183C2×D4—864no—
184C2×D4—864no—
185C2×D4—862no—
186C2×D4—1722no—
187C2×D4—1722no—
188C22×C4—432no—
189C22×C4—432no—
190C22×C4—432no—
191C22×C4—864no—
192C22×C4—1722no—
193C22×C4—1722no—
194C22×C4C22×D4311yescharacteristic
195C22×C4C22×D4311yescharacteristic
196C22×C4C22×D4311yescharacteristic
197C22×C4C22×D4311yescharacteristic
198C22×C4C22×D4311yescharacteristic
199C22×C4C22×D4311yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—862no—
204C4⋊C4—1722no—
205C4⋊C4—1722no—
206C22⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—864no—
210C22⋊C4—864no—
211C22⋊C4—1722no—
212C22⋊C4—1722no—
213C22⋊C4—1722no—
214C42C22⋊D4314yescomplemented
215C23—21no—
216C23—22no—
217C23—22no—
218C23—21no—
219C23—21no—
220C23—434no—
221C23—862no—
222C23—862no—
223C23—862no—
224C23—862no—
225C23—862no—
226C23—862no—
227C23C23×D4311yescharacteristic
228D4—868no—
229D4—1728no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—862no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—1728no—
251C2×C4C2×C22⋊D4312yes—
252C2×C4C2×C22⋊D4312yes—
253C2×C4C2×C22⋊D4312yes—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—864no—
260C22—864no—
261C22—864no—
262C22—1722no—
263C22—1722no—
264C22—1722no—
265C22—1722no—
266C22C22×C22⋊D4311yescharacteristic
267C22#41×D4312yes—
268C22#1306337112yes—
269C22#1306337111yescharacteristic
270C22#1306337211yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—1722no—
278C4—1722no—
279C4—1722no—
280C2—81no—
281C2—1724no—
282C2#1458340611yescharacteristic
283C2#1458346311yescharacteristic
284C2#1458347711yescharacteristic
285C2#1458348812yes—
286C2#1458349012yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#126×C43C2
hypercenterC2×#126D43
hypocenterC43#2636
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C4×D172C2semidirect
2. #14582838C2semidirect
3. #14582835C2semidirect
4. #14582821C2semidirect
5. #14582816C2semidirect
6. #14582815C2semidirect
8. #14582775C2semidirect
9. #14582770C2semidirect
10. #14582765C2semidirect
11. C2×#126×C43C2semidirect
62. C42×C43D4semidirect
144. C2×#126D43semidirect
155. C43#2636semidirect
214. C42C22⋊D43semidirect