Finite Group Databasebeta

← #19139501

Subgroups — #19139501

Order 5504.

604 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13063303C212yesmaximal, complemented
2C2×#13063290C211yesmaximal, characteristic, complemented
3C2×#13063287C211yesmaximal, characteristic
4#14582830C211yesmaximal, characteristic, complemented
5#14582817C211yesmaximal, characteristic
6#14582816C211yesmaximal, characteristic
7#14582789C212yesmaximal, complemented
8#14582788C212yesmaximal, complemented
9#14582763C211yesmaximal, characteristic, complemented
10#14582758C212yesmaximal, complemented
11C43×#398C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C22×C4×D43C2212yes—
15#13063303—28no—
16#13063290—24no—
17#13063287—24no—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C2×C4×Dic43C2211yescharacteristic
29C2×C4×Dic43C2211yescharacteristic
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C43⋊#95C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C4⋊C4×C43C2211yescharacteristic
36#95×C43C2212yes—
37#95×C43C2211yescharacteristic
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
48C22×Dic43C2311yescharacteristic
49C2×D172—22no—
50C2×D172—24no—
51C2×C4×D43—24no—
52C2×C4×D43—24no—
53C2×C4×D43—24no—
54C2×Dic86—22no—
55C2×Dic86—22no—
56C2×Dic86D414yescomplemented
57C4⋊C4×C43—22no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—24no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—24no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—24no—
64(C2×D43)⋊C4—24no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4—24no—
68Dic43⋊C4—24no—
69C4×Dic43—22no—
70C4×Dic43—22no—
71C4×Dic43D414yes—
72C23×C43C2411yescharacteristic
73C22×D43—22no—
74C22×D43—22no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43#4114yes—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43C2×D412yes—
92C2×C4×C43C2×D412yes—
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—21no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43C2×D412yes—
102C2×Dic43C2×D412yes—
103C2×Dic43C2×D412yes—
104C2×Dic43C2×D412yes—
105C2×Dic43#4112yes—
106D172—28no—
107C4×D43—48no—
108Dic86—28no—
109C22×C43C22×D411yescharacteristic
110C22×C43C22×D411yescharacteristic
111C22×C43C2×#4111yescharacteristic
112C22×C43C2×#4112yes—
113C22×C432−1+412yes—
114C2×D43—24no—
115C2×D43—24no—
116C2×D43—24no—
117C2×D43—42no—
118C2×D43—42no—
119C2×D43—42no—
120C2×D43—42no—
121C4×C43—22no—
122C4×C43—22no—
123C4×C43—42no—
124C4×C43—41no—
125C4×C43—42no—
126Dic43—22no—
127Dic43—22no—
128Dic43—41no—
129Dic43—42no—
130Dic43#12114yes—
131#2536—431nomaximal, Sylow
132C2×C43C2×#12111yescharacteristic
133C2×C43#52511yescharacteristic
134C2×C43#53611yescharacteristic
135C2×C43#54812yes—
136C2×C43#55212yes—
137D43—44no—
138C2×C22⋊Q8—432no—
139C2×C4×Q8—431no—
140C2×C4×D4—431no—
141#398—431no—
142#398D4311yescharacteristic, complemented
143#394—431no—
144#394—431no—
145#388—432no—
146#388—432no—
147#382—431no—
148#380—432no—
149C43#253611yescharacteristic, complemented, Sylow
150C22×Q8—431no—
151C22×D4—431no—
152C23×C4—432no—
153C22⋊Q8—868no—
154C4×Q8—864no—
155C4×D4—864no—
156C2×C4⋊C4—431no—
157C2×C4⋊C4—431no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4—432no—
160C2×C4⋊C4C2×D4311yescharacteristic
161C2×C4⋊C4C2×D4311yescharacteristic
162C2×C4⋊C4C2×D4312yes—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4—432no—
166C2×C22⋊C4—432no—
167C2×C22⋊C4—432no—
168C2×C42—431no—
169C2×C42—431no—
170C2×C42—431no—
171#95—432no—
172#95—432no—
173#95—431no—
174#95C2×D4312yes—
175#95C2×D4311yescharacteristic
176C24—432no—
177C2×Q8—434no—
178C2×Q8—862no—
179C2×Q8—862no—
180C2×D4—864no—
181C2×D4—862no—
182C22×C4—431no—
183C22×C4—431no—
184C22×C4—431no—
185C22×C4—432no—
186C22×C4—431no—
187C22×C4—864no—
188C22×C4—864no—
189C22×C4—864no—
190C22×C4C22×D4312yes—
191C22×C4C22×D4312yes—
192C22×C4C22×D4311yescharacteristic
193C22×C4C22×D4311yescharacteristic
194C22×C4C22×D4311yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—862no—
199C4⋊C4—864no—
200C4⋊C4—864no—
201C4⋊C4—862no—
202C22⋊C4—864no—
203C22⋊C4—864no—
204C22⋊C4—864no—
205C22⋊C4—864no—
206C22⋊C4—864no—
207C42—434no—
208C42—862no—
209C42—862no—
210C23—434no—
211C23—862no—
212C23—862no—
213C23—862no—
214C23—862no—
215C23—862no—
216C23—862no—
217C23C23×D4311yescharacteristic
218Q8—868no—
219D4—868no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—432no—
232C2×C4—432no—
233C2×C4—432no—
234C2×C4—432no—
235C2×C4—432no—
236C2×C4—861no—
237C2×C4—861no—
238C2×C4—862no—
239C2×C4—861no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—1728no—
245C2×C4D4×D4312yes—
246C2×C4D4×D4312yes—
247C22—864no—
248C22—864no—
249C22—864no—
250C22—1722no—
251C22—1722no—
252C22—1722no—
253C22—1722no—
254C22C2×D4×D4311yescharacteristic
255C22C2×D4×D4311yescharacteristic
256C22#41×D4312yes—
257C22#41×D4311yescharacteristic
258C22#1306337312yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—42no—
263C4—41no—
264C4—434no—
265C4—862no—
266C4—862no—
267C4—1722no—
268C4—1721no—
269C2—1724no—
270C2#121×D4311yescharacteristic
271C2#1458340711yescharacteristic
272C2#1458347411yescharacteristic
273C2#1458355912yes—
274C2#1458358112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2536
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13063303C2semidirect
2. C2×#13063290C2semidirect
4. #14582830C2semidirect
7. #14582789C2semidirect
8. #14582788C2semidirect
9. #14582763C2semidirect
10. #14582758C2semidirect
11. C43×#398C2semidirect
56. C2×Dic86D4semidirect
142. #398D43semidirect
149. C43#2536semidirect