Finite Group Databasebeta

← #19139947

Subgroups — #19139947

Order 5504.

584 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 153 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×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×Dic43⋊C4C211yesmaximal, characteristic, complemented
3#14582830C212yesmaximal, complemented
4#14582823C212yesmaximal, complemented
5#14582781C212yesmaximal, complemented
6#14582778C211yesmaximal, characteristic
7#14582776C211yesmaximal, characteristic
8#14582771C211yesmaximal, characteristic, complemented
9#14582770C212yesmaximal, complemented
10#14582757C211yesmaximal, characteristic, complemented
11C43×#385C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C23×Dic43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16(C22⋊D43)⋊C4—24no—
17C2×Dic43⋊C4—24no—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C23×C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36#95×C43C2212yes—
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43—22no—
40C22×C4×C43—42no—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43Q814yes—
48C22×Dic43—24no—
49C22×Dic43—22no—
50C22×Dic43—42no—
51C22×Dic43D414yes—
52C22×Dic43C2312yes—
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2311yescharacteristic
55C22×Dic43C2311yescharacteristic
56C22×Dic43C2312yes—
57C2×C4×D43—22no—
58C2×C4×D43—42no—
59C4⋊C4×C43—42no—
60C22⋊C4×C43—22no—
61C22⋊C4×C43—22no—
62C22⋊Dic43—22no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—42no—
66Dic43⋊C4—24no—
67Dic43⋊C4—24no—
68Dic43⋊C4—22no—
69Dic43⋊C4—24no—
70Dic43⋊C4—42no—
71C4×Dic43—22no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43C2×D412yes—
75C23×C43C2×Q812yes—
76C23×C43#4112yes—
77C23×C43C2411yescharacteristic
78C22×D43—21no—
79C22×D43—22no—
80C22×D43—21no—
81C22×D43—22no—
82C22×D43C2×Q812yes—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
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—44no—
94C22⋊D43—28no—
95C2×Dic43—28no—
96C2×Dic43—21no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—44no—
106C2×Dic43C2×D412yes—
107C2×Dic43C2×D412yes—
108C2×Dic43C2×Q812yes—
109C2×Dic43#4114yes—
110C4×D43—44no—
111C22×C43—22no—
112C22×C43—22no—
113C22×C43—24no—
114C22×C43—24no—
115C22×C43C22⋊Q814yes—
116C22×C43C22×D411yescharacteristic
117C22×C43C22×Q811yescharacteristic
118C22×C43C2×#4112yes—
119C22×C43C2×#4111yescharacteristic
120C22×C43H(5,𝔽2)12yes—
121C2×D43—22no—
122C2×D43—24no—
123C2×D43—41no—
124C2×D43—41no—
125C2×D43—42no—
126C4×C43—41no—
127C4×C43—41no—
128C4×C43—42no—
129C4×C43—42no—
130Dic43—22no—
131Dic43—24no—
132Dic43—22no—
133Dic43—22no—
134Dic43—42no—
135#2579—431nomaximal, Sylow
136C2×C43—24no—
137C2×C43C2×C22⋊Q811yescharacteristic
138C2×C43#52511yescharacteristic
139C2×C43#53411yescharacteristic
140C2×C43#55312yes—
141C2×C43#55412yes—
142D43—42no—
143C2×C4×D4—431no—
144C22×C4⋊C4—431no—
145#398—432no—
146#396—432no—
147#387—432no—
148#386—431no—
149#386—431no—
150#385—432no—
151#385—431no—
152#385D4311yescharacteristic, complemented
153#380—431no—
154C43#257911yescharacteristic, complemented, Sylow
155C22×D4—431no—
156C23×C4—431no—
157C23×C4—431no—
158C23×C4—431no—
159C23×C4C2×D4311yescharacteristic
160C4×D4—864no—
161C2×C4⋊C4—432no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—431no—
164C2×C4⋊C4—432no—
165C2×C4⋊C4—432no—
166C2×C4⋊C4—864no—
167C2×C4⋊C4C2×D4312yes—
168C2×C22⋊C4—431no—
169C2×C22⋊C4—431no—
170C2×C22⋊C4—432no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4C2×D4311yescharacteristic
173C2×C22⋊C4C2×D4311yescharacteristic
174C2×C42—431no—
175#95—432no—
176#95—432no—
177#95—432no—
178#95—432no—
179#95C2×D4312yes—
180C24—431no—
181C24C22×D4311yescharacteristic
182C2×D4—434no—
183C2×D4—862no—
184C2×D4—862no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—431no—
188C22×C4—431no—
189C22×C4—432no—
190C22×C4—431no—
191C22×C4—434no—
192C22×C4—432no—
193C22×C4—862no—
194C22×C4—864no—
195C22×C4—862no—
196C22×C4—1722no—
197C22×C4—1722no—
198C22×C4C22×D4312yes—
199C22×C4C22×D4311yescharacteristic
200C22×C4C22×D4312yes—
201C22×C4C22×D4311yescharacteristic
202C4⋊C4—42no—
203C4⋊C4—864no—
204C4⋊C4—864no—
205C4⋊C4—862no—
206C4⋊C4—864no—
207C4⋊C4—1722no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—862no—
211C22⋊C4—864no—
212C22⋊C4—862no—
213C22⋊C4—1722no—
214C42—862no—
215C23—22no—
216C23—22no—
217C23—432no—
218C23—861no—
219C23—862no—
220C23—861no—
221C23—862no—
222C23#1062189812yes—
223C23D4×D4312yes—
224C23Q8×D4312yes—
225C23C23×D4311yescharacteristic
226D4—868no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—432no—
239C2×C4—432no—
240C2×C4—432no—
241C2×C4—434no—
242C2×C4—868no—
243C2×C4—861no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—861no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—1724no—
253C2×C4—1724no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—22no—
258C22—864no—
259C22—862no—
260C22—1722no—
261C22—1721no—
262C22—1721no—
263C22#1306330314yes—
264C22C2×D4×D4311yescharacteristic
265C22C2×Q8×D4311yescharacteristic
266C22#41×D4312yes—
267C22C2×#1062189811yescharacteristic
268C22#1306337012yes—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—862no—
274C4—864no—
275C4—862no—
276C4—862no—
277C4—1722no—
278C2—24no—
279C2—1722no—
280C2C2×#1306330311yescharacteristic
281C2#1458340711yescharacteristic
282C2#1458345911yescharacteristic
283C2#1458359812yes—
284C2#1458360312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#385C2
hypercenter#385D43
hypocenterC43#2579
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×Dic43⋊C4C2semidirect
3. #14582830C2semidirect
4. #14582823C2semidirect
5. #14582781C2semidirect
8. #14582771C2semidirect
9. #14582770C2semidirect
10. #14582757C2semidirect
11. C43×#385C2semidirect
152. #385D43semidirect
154. C43#2579semidirect