Finite Group Databasebeta

← #19140164

Subgroups — #19140164

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×#13063283C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic, complemented
4#14582816C211yesmaximal, characteristic, complemented
5#14582809C211yesmaximal, characteristic
6#14582788C212yesmaximal, complemented
7#14582777C212yesmaximal, complemented
8#14582777C212yesmaximal, complemented
9#14582773C212yesmaximal, complemented
10#14582766C211yesmaximal, characteristic, complemented
11C43×#400C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×D172C2212yes—
14C22×C4×D43C2211yescharacteristic
15C22×C4×D43C2212yes—
16#13063287—24no—
17#13063283—24no—
18C2×C4⋊Dic43C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C2×C4×Dic43C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2311yescharacteristic
38C23×D43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×D172—22no—
49C2×D172—24no—
50C2×D172—24no—
51C2×D172—24no—
52C2×D172—42no—
53C2×C4×D43—22no—
54C2×C4×D43—22no—
55C2×C4×D43—24no—
56C2×C4×D43—22no—
57C2×C4×D43—42no—
58C2×C4×D43—42no—
59C4⋊C4×C43—22no—
60C4⋊C4×C43—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—42no—
67(C2×D43)⋊C4—42no—
68C4⋊Dic43—22no—
69Dic43⋊C4—42no—
70C4×Dic43—22no—
71C4×Dic43D414yescomplemented
72C23×C43C2411yescharacteristic
73C22×D43—21no—
74C22×D43—22no—
75C22×D43—22no—
76C22×D43—21no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43#4114yes—
84C22×D43#4112yes—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43C2×D412yes—
97C2×C4×C43#4112yes—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43C2×D412yes—
107C2×Dic43C2×D412yes—
108D172—28no—
109D172—48no—
110C4×D43—28no—
111C4×D43—48no—
112C22×C43C22×D411yescharacteristic
113C22×C43C2×#4111yescharacteristic
114C22×C43C2×#4112yes—
115C22×C43C2×#4111yescharacteristic
116C22×C43H(5,𝔽2)12yes—
117C2×D43—22no—
118C2×D43—24no—
119C2×D43—24no—
120C2×D43—24no—
121C2×D43—24no—
122C2×D43—41no—
123C2×D43—42no—
124C2×D43—41no—
125C2×D43—42no—
126C2×D43—42no—
127C2×D43—42no—
128C2×D43—42no—
129C4×C43—22no—
130C4×C43—22no—
131C4×C43—41no—
132C4×C43—42no—
133C4×C43—42no—
134Dic43—22no—
135Dic43—22no—
136Dic43—41no—
137Dic43—42no—
138#2598—431nomaximal, Sylow
139C2×C43#52511yescharacteristic
140C2×C43#52511yescharacteristic
141C2×C43#53511yescharacteristic
142C2×C43#55112yes—
143C2×C43#55312yes—
144D43—42no—
145D43—44no—
146C2×C4×D4—431no—
147C2×#117—431no—
148#400D4311yescharacteristic, complemented
149#399—431no—
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—431no—
159C22×D4—432no—
160C23×C4—431no—
161C23×C4—432no—
162C4×D4—864no—
163#117—864no—
164C2×C4⋊C4—431no—
165C2×C4⋊C4—432no—
166C2×C4⋊C4C2×D4311yescharacteristic
167C2×C4⋊C4C2×D4311yescharacteristic
168C2×C22⋊C4—431no—
169C2×C22⋊C4—431no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4—432no—
174C2×C22⋊C4—432no—
175C2×C42—431no—
176C2×C42—431no—
177#95—432no—
178#95—432no—
179#95—431no—
180#95C2×D4311yescharacteristic
181#95C2×D4312yes—
182#95C2×D4312yes—
183C24—432no—
184C24—431no—
185C2×D4—864no—
186C2×D4—864no—
187C2×D4—864no—
188C2×D4—862no—
189C2×D4—1722no—
190C22×C4—431no—
191C22×C4—431no—
192C22×C4—432no—
193C22×C4—431no—
194C22×C4—862no—
195C22×C4—864no—
196C22×C4—862no—
197C22×C4—862no—
198C22×C4—1722no—
199C22×C4—1722no—
200C22×C4C22×D4312yes—
201C22×C4C22×D4311yescharacteristic
202C22×C4C22×D4312yes—
203C22×C4C22×D4311yescharacteristic
204C22×C4C22×D4311yescharacteristic
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—862no—
208C4⋊C4—1722no—
209C22⋊C4—862no—
210C22⋊C4—864no—
211C22⋊C4—864no—
212C22⋊C4—862no—
213C22⋊C4—864no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—434no—
217C42—862no—
218C23—434no—
219C23—432no—
220C23—861no—
221C23—862no—
222C23—862no—
223C23—862no—
224C23—862no—
225C23—862no—
226C23—861no—
227C23—862no—
228C23—862no—
229C23—862no—
230C23C23×D4311yescharacteristic
231D4—868no—
232D4—1728no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—432no—
245C2×C4—432no—
246C2×C4—868no—
247C2×C4—861no—
248C2×C4—861no—
249C2×C4—862no—
250C2×C4—861no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—1728no—
256C2×C4D4×D4312yes—
257C2×C4#1062190212yes—
258C22—864no—
259C22—864no—
260C22—864no—
261C22—864no—
262C22—862no—
263C22—1722no—
264C22—1722no—
265C22—1722no—
266C22—1721no—
267C22—1722no—
268C22—1722no—
269C22—1721no—
270C22C2×D4×D4311yescharacteristic
271C22#41×D4311yescharacteristic
272C22#41×D4312yes—
273C22C2×#1062190211yescharacteristic
274C22#1306337112yes—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—41no—
279C4—42no—
280C4—862no—
281C4—862no—
282C4—1722no—
283C4—1721no—
284C2—1722no—
285C2—1724no—
286C2#1458340711yescharacteristic
287C2#1458341211yescharacteristic
288C2#1458346711yescharacteristic
289C2#1458357412yes—
290C2#1458360212yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2598
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#13063287C2semidirect
2. C2×#13063283C2semidirect
3. #14582834C2semidirect
4. #14582816C2semidirect
6. #14582788C2semidirect
7. #14582777C2semidirect
8. #14582777C2semidirect
9. #14582773C2semidirect
10. #14582766C2semidirect
11. C43×#400C2semidirect
71. C4×Dic43D4semidirect
148. #400D43semidirect
157. C43#2598semidirect