Finite Group Databasebeta

← #19139543

Subgroups — #19139543

Order 5504.

676 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 171 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×#13063324C211yesmaximal, characteristic, complemented
2C2×#13063303C212yesmaximal, complemented
3C2×#13063302C212yesmaximal, complemented
4C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic
5#14582836C211yesmaximal, characteristic, complemented
6#14582835C211yesmaximal, characteristic, complemented
7#14582834C211yesmaximal, characteristic, complemented
8#14582799C212yesmaximal
9#14582768C212yesmaximal, complemented
10#14582750C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C22×Dic86C2212yes—
13C22×C22⋊D43C2211yescharacteristic
14C23×Dic43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16#13063324—24no—
17#13063303—28no—
18#13063302—28no—
19(C22⋊D43)⋊C4—24no—
20C2×C4⋊Dic43C2211yescharacteristic
21C2×C4⋊Dic43C2212yes—
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C2×Dic43⋊C4C2212yes—
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2212yes—
27C2×C22⋊Dic43C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
29C2×(C2×D43)⋊C4C2212yes—
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×C4×Dic43C2212yes—
32C2×C4×Dic43C2211yescharacteristic
33C43⋊#95C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C4⋊C4×C43C2212yes—
36C2×C22⋊C4×C43C2212yes—
37C2×C22⋊C4×C43C2211yescharacteristic
38#95×C43C2211yescharacteristic
39C24×C43C2311yescharacteristic
40C23×D43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2312yes—
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43Q814yescomplemented
48C22×Dic43—22no—
49C22×Dic43—24no—
50C22×Dic43C2312yes—
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2312yes—
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2311yescharacteristic
55C2×C4×D43—22no—
56C2×C4×D43—24no—
57C2×Dic86—24no—
58C2×Dic86—24no—
59C2×Dic86—24no—
60C4⋊C4×C43—24no—
61C4⋊C4×C43—22no—
62C22⋊C4×C43—22no—
63C22⋊C4×C43—24no—
64C22⋊Dic43—24no—
65(C2×D43)⋊C4—22no—
66(C2×D43)⋊C4—24no—
67(C2×D43)⋊C4—24no—
68C4⋊Dic43—24no—
69C4⋊Dic43—22no—
70Dic43⋊C4—22no—
71Dic43⋊C4—24no—
72Dic43⋊C4—24no—
73Dic43⋊C4—24no—
74Dic43⋊C4D418yescomplemented
75C4×Dic43—24no—
76C4×Dic43D414yes—
77C23×C43—22no—
78C23×C43—21no—
79C23×C43—21no—
80C23×C43—22no—
81C23×C43C2×Q812yes—
82C23×C43C2411yescharacteristic
83C22×D43—22no—
84C22×D43—21no—
85C22×D43—21no—
86C22×D43—22no—
87C22×D43C2×Q812yes—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2×D414yes—
98C22⋊D43—28no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—22no—
106C2×Dic43—44no—
107C2×Dic43C2×D414yes—
108C2×Dic43C2×D412yes—
109C2×Dic43C2×D412yes—
110C2×Dic43C2×D414yes—
111C2×Dic43C2×Q812yes—
112C2×Dic43#4112yes—
113C4×D43—44no—
114Dic86—48no—
115C22×C43—22no—
116C22×C43—24no—
117C22×C43—41no—
118C22×C43—41no—
119C22×C43—42no—
120C22×C43C22×D411yescharacteristic
121C22×C43C22×D412yes—
122C22×C43C22×Q811yescharacteristic
123C22×C43C2×#4111yescharacteristic
124C22×C432−1+412yes—
125C2×D43—22no—
126C2×D43—24no—
127C2×D43—41no—
128C2×D43—41no—
129C2×D43—42no—
130C4×C43—22no—
131C4×C43—24no—
132C4×C43—42no—
133C4×C43—41no—
134Dic43—24no—
135Dic43—42no—
136Dic43—41no—
137Dic43C22⋊Q814yescomplemented
138Dic43#12714yes—
139#2542—431nomaximal, Sylow
140C2×C43—42no—
141C2×C43C2×C22⋊Q811yescharacteristic
142C2×C43C2×#12711yescharacteristic
143C2×C43#53611yescharacteristic
144C2×C43#54712yes—
145C2×C43D4×Q812yes—
146D43—42no—
147C2×C4⋊Q8—431no—
148C2×C22⋊Q8—432no—
149C2×C22⋊Q8—432no—
150C2×C4×D4—431no—
151#399—431no—
152#399—431no—
153#399—431no—
154#399D4311yescharacteristic, complemented
155#390—432no—
156#384—432no—
157C4×C4⋊C4—431no—
158C43#254211yescharacteristic, complemented, Sylow
159C22×Q8—432no—
160C22×D4—431no—
161C23×C4—431no—
162C23×C4—431no—
163C4⋊Q8—864no—
164C22⋊Q8—868no—
165C22⋊Q8—868no—
166C4×D4—864no—
167C2×C4⋊C4—432no—
168C2×C4⋊C4—431no—
169C2×C4⋊C4—432no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—432no—
172C2×C4⋊C4—432no—
173C2×C4⋊C4—431no—
174C2×C4⋊C4C2×D4312yes—
175C2×C4⋊C4C2×D4311yescharacteristic
176C2×C22⋊C4—432no—
177C2×C22⋊C4—431no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4C2×D4311yescharacteristic
181C2×C22⋊C4C2×D4312yes—
182C2×C42—431no—
183C2×C42—432no—
184#95—431no—
185#95C2×D4311yescharacteristic
186C24—431no—
187C24C22×D4311yescharacteristic
188C2×Q8—864no—
189C2×Q8—864no—
190C2×Q8—864no—
191C2×D4—434no—
192C2×D4—862no—
193C2×D4—862no—
194C22×C4—431no—
195C22×C4—431no—
196C22×C4—432no—
197C22×C4—432no—
198C22×C4—431no—
199C22×C4—862no—
200C22×C4—864no—
201C22×C4—862no—
202C22×C4—864no—
203C22×C4C22×D4312yes—
204C22×C4C22×D4311yescharacteristic
205C22×C4C22×D4311yescharacteristic
206C22×C4C22×D4312yes—
207C4⋊C4—24no—
208C4⋊C4—22no—
209C4⋊C4—438no—
210C4⋊C4—862no—
211C4⋊C4—864no—
212C4⋊C4—864no—
213C4⋊C4—864no—
214C4⋊C4—864no—
215C4⋊C4—862no—
216C22⋊C4—22no—
217C22⋊C4—24no—
218C22⋊C4—864no—
219C22⋊C4—864no—
220C22⋊C4—862no—
221C22⋊C4—864no—
222C42—434no—
223C42—864no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—22no—
228C23—432no—
229C23—862no—
230C23—861no—
231C23—861no—
232C23—862no—
233C23Q8×D4312yes—
234C23C23×D4311yescharacteristic
235Q8—1728no—
236D4—868no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—432no—
246C2×C4—432no—
247C2×C4—434no—
248C2×C4—432no—
249C2×C4—432no—
250C2×C4—434no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—861no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—862no—
257C2×C4—862no—
258C2×C4—1724no—
259C2×C4—1724no—
260C2×C4D4×D4312yes—
261C2×C4D4×D4314yes—
262C22—24no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—42no—
267C22—864no—
268C22—862no—
269C22—1721no—
270C22—1721no—
271C22—1722no—
272C22C2×D4×D4312yes—
273C22C2×D4×D4311yescharacteristic
274C22C2×Q8×D4311yescharacteristic
275C22#41×D4311yescharacteristic
276C22#1306337212yes—
277C4—22no—
278C4—24no—
279C4—41no—
280C4—42no—
281C4—434no—
282C4—434no—
283C4—864no—
284C4—1721no—
285C4—1722no—
286C2—42no—
287C2—1722no—
288C2C22⋊Q8×D4311yescharacteristic
289C2#127×D4311yescharacteristic
290C2#1458347111yescharacteristic
291C2#1458354712yes—
292C2#1458356212yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2542
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063324C2semidirect
2. C2×#13063303C2semidirect
3. C2×#13063302C2semidirect
5. #14582836C2semidirect
6. #14582835C2semidirect
7. #14582834C2semidirect
9. #14582768C2semidirect
10. #14582750C2semidirect
11. C43×#399C2semidirect
47. C2×C22⋊D43Q8semidirect
74. Dic43⋊C4D4semidirect
137. Dic43C22⋊Q8semidirect
154. #399D43semidirect
158. C43#2542semidirect