Finite Group Databasebeta

← #19137832

Subgroups — #19137832

Order 5504.

696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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×(C22⋊D43)⋊C4C212yesmaximal, complemented
3C2×#13063281C211yesmaximal, characteristic, complemented
4#14582830C211yesmaximal, characteristic, complemented
5#14582823C212yesmaximal, complemented
6#14582817C211yesmaximal, characteristic, complemented
7#14582814C212yesmaximal, complemented
8#14582808C211yesmaximal, characteristic
9#14582750C211yesmaximal, characteristic, complemented
10#14582746C212yesmaximal, complemented
11C43×#397C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C23×Dic43C2211yescharacteristic
15C22×C4×D43C2212yes—
16#13063287—24no—
17(C22⋊D43)⋊C4—28no—
18#13063281—24no—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×C4×Dic43C2211yescharacteristic
29C2×C4×Dic43C2212yes—
30C2×C4×Dic43C2211yescharacteristic
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37#95×C43C2212yes—
38C24×C43C2311yescharacteristic
39C23×D43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—24no—
45C2×C22⋊D43—24no—
46C2×C22⋊D43—24no—
47C22×Dic43—22no—
48C22×Dic43—22no—
49C22×Dic43D414yescomplemented
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2312yes—
54C22×Dic43C2311yescharacteristic
55C2×D172—22no—
56C2×D172—24no—
57C2×C4×D43—24no—
58C2×C4×D43—24no—
59C2×C4×D43—24no—
60C4⋊C4×C43—22no—
61C22⋊C4×C43—22no—
62C22⋊C4×C43—24no—
63C22⋊Dic43—22no—
64(C2×D43)⋊C4—24no—
65(C2×D43)⋊C4—24no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—24no—
68Dic43⋊C4—22no—
69Dic43⋊C4—22no—
70Dic43⋊C4—24no—
71Dic43⋊C4—24no—
72C4×Dic43—22no—
73C4×Dic43—24no—
74C4×Dic43D414yescomplemented
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43C2×D412yes—
80C23×C43C2411yescharacteristic
81C22×D43—22no—
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—22no—
87C22×D43#4114yes—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
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×C43—22no—
97C2×C4×C43C2×D412yes—
98C22⋊D43—216no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—28no—
105C2×Dic43—21no—
106C2×Dic43—22no—
107C2×Dic43C2×D412yes—
108C2×Dic43C2×D412yes—
109C2×Dic43C2×D412yes—
110C2×Dic43C2×D412yes—
111C2×Dic43#4114yes—
112C2×Dic43#4112yes—
113D172—28no—
114C4×D43—48no—
115C22×C43—22no—
116C22×C43—24no—
117C22×C43—41no—
118C22×C43—42no—
119C22×C43—41no—
120C22×C43C22×D411yescharacteristic
121C22×C43C22×D411yescharacteristic
122C22×C43C2×#4111yescharacteristic
123C22×C43C2×#4112yes—
124C22×C43C2×#4112yes—
125C2×D43—24no—
126C2×D43—24no—
127C2×D43—24no—
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—42no—
132C4×C43—22no—
133C4×C43—42no—
134C4×C43—42no—
135C4×C43—41no—
136Dic43—22no—
137Dic43—24no—
138Dic43—22no—
139Dic43—41no—
140Dic43#12114yes—
141#2392—431nomaximal, Sylow
142C2×C43—42no—
143C2×C43C2×#12111yescharacteristic
144C2×C43#52512yes—
145C2×C43#52511yescharacteristic
146C2×C43#52912yes—
147C2×C43#53211yescharacteristic
148D43—44no—
149C2×C4×D4—431no—
150C2×C4×D4—432no—
151C2×#117—431no—
152#398—431no—
153#397D4311yescharacteristic, complemented
154#396—432no—
155#394—432no—
156#394—431no—
157#392—431no—
158C4×C4⋊C4—431no—
159C4×C22⋊C4—432no—
160C43#239211yescharacteristic, complemented, Sylow
161C22×D4—432no—
162C22×D4—431no—
163C23×C4—431no—
164C23×C4—432no—
165C4×D4—864no—
166C4×D4—868no—
167#117—864no—
168C2×C4⋊C4—431no—
169C2×C4⋊C4—431no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—432no—
172C2×C4⋊C4C2×D4311yescharacteristic
173C2×C22⋊C4—431no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4—432no—
176C2×C22⋊C4—432no—
177C2×C22⋊C4—432no—
178C2×C22⋊C4C2×D4311yescharacteristic
179C2×C22⋊C4C2×D4312yes—
180C2×C42—431no—
181C2×C42—431no—
182C2×C42—432no—
183#95—432no—
184#95—431no—
185#95C2×D4312yes—
186#95C2×D4311yescharacteristic
187C24—432no—
188C24C22×D4311yescharacteristic
189C2×D4—864no—
190C2×D4—864no—
191C2×D4—864no—
192C2×D4—864no—
193C2×D4—862no—
194C22×C4—431no—
195C22×C4—434no—
196C22×C4—432no—
197C22×C4—431no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—864no—
201C22×C4—864no—
202C22×C4—864no—
203C22×C4—862no—
204C22×C4—862no—
205C22×C4C22×D4312yes—
206C22×C4C22×D4312yes—
207C22×C4C22×D4311yescharacteristic
208C22×C4C22×D4311yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—862no—
211C4⋊C4—864no—
212C4⋊C4—864no—
213C4⋊C4—862no—
214C22⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—864no—
217C22⋊C4—864no—
218C22⋊C4—864no—
219C22⋊C4—864no—
220C22⋊C4—862no—
221C42—434no—
222C42—862no—
223C42—864no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23—22no—
228C23—434no—
229C23—862no—
230C23—862no—
231C23—862no—
232C23—862no—
233C23—862no—
234C23—862no—
235C23D4×D4312yes—
236C23C23×D4311yescharacteristic
237D4—868no—
238D4—8616no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—432no—
249C2×C4—432no—
250C2×C4—432no—
251C2×C4—432no—
252C2×C4—432no—
253C2×C4—434no—
254C2×C4—868no—
255C2×C4—862no—
256C2×C4—861no—
257C2×C4—862no—
258C2×C4—861no—
259C2×C4—862no—
260C2×C4—861no—
261C2×C4—862no—
262C2×C4—1728no—
263C2×C4D4×D4312yes—
264C22—22no—
265C22—24no—
266C22—41no—
267C22—42no—
268C22—41no—
269C22—864no—
270C22—864no—
271C22—864no—
272C22—1722no—
273C22—1722no—
274C22—1722no—
275C22—1722no—
276C22C2×D4×D4311yescharacteristic
277C22C2×D4×D4311yescharacteristic
278C22#41×D4311yescharacteristic
279C22#41×D4312yes—
280C22#41×D4312yes—
281C4—22no—
282C4—42no—
283C4—42no—
284C4—41no—
285C4—434no—
286C4—862no—
287C4—864no—
288C4—862no—
289C4—1721no—
290C2—42no—
291C2—1724no—
292C2#121×D4311yescharacteristic
293C2#1458340711yescharacteristic
294C2#1458340712yes—
295C2#1458343212yes—
296C2#1458344811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2392
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13063287C2semidirect
2. C2×(C22⋊D43)⋊C4C2semidirect
3. C2×#13063281C2semidirect
4. #14582830C2semidirect
5. #14582823C2semidirect
6. #14582817C2semidirect
7. #14582814C2semidirect
9. #14582750C2semidirect
10. #14582746C2semidirect
11. C43×#397C2semidirect
49. C22×Dic43D4semidirect
74. C4×Dic43D4semidirect
153. #397D43semidirect
160. C43#2392semidirect