Finite Group Databasebeta

← #19138002

Subgroups — #19138002

Order 5504.

610 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063308C211yesmaximal, characteristic
2C2×#13063308C211yesmaximal, characteristic
3C2×#13063284C211yesmaximal, characteristic, complemented
4#14582832C212yesmaximal, complemented
5#14582821C212yesmaximal, complemented
6#14582794C212yesmaximal, complemented
7#14582789C212yesmaximal, complemented
8#14582778C211yesmaximal, characteristic
9#14582772C211yesmaximal, characteristic, complemented
10#14582762C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13#13063308—24no—
14#13063308—24no—
15#13063284—24no—
16C2×C4⋊Dic43C2212yes—
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×C22⋊Dic43C2211yescharacteristic
22C2×C22⋊Dic43C2211yescharacteristic
23C2×C22⋊Dic43C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×C4×Dic43C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C43⋊#95C2212yes—
33C23×C4×C43C2211yescharacteristic
34C23×C4×C43C2211yescharacteristic
35C23×C4×C43C2211yescharacteristic
36C2×C4⋊C4×C43—24no—
37C2×C4⋊C4×C43C2212yes—
38C2×C4⋊C4×C43C2212yes—
39C24×C43C2311yescharacteristic
40C23×D43C2311yescharacteristic
41C22×C4×C43—24no—
42C22×C4×C43—22no—
43C22×C4×C43—22no—
44C22×C4×C43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—22no—
47C22×C4×C43—22no—
48C22×C4×C43D414yes—
49C22×C4×C43C2312yes—
50C22×C4×C43C2311yescharacteristic
51C22×C4×C43C2311yescharacteristic
52C22×C4×C43C2312yes—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—22no—
56C22×Dic43C2311yescharacteristic
57C22×Dic43C2312yes—
58C22×Dic43C2311yescharacteristic
59C22×Dic43C2311yescharacteristic
60C22×Dic43C2312yes—
61C4⋊C4×C43—24no—
62C4⋊C4×C43—24no—
63C22⋊Dic43—22no—
64C22⋊Dic43—22no—
65C22⋊Dic43D414yes—
66(C2×D43)⋊C4—22no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4—24no—
70C4⋊Dic43—24no—
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73Dic43⋊C4—24no—
74Dic43⋊C4—24no—
75C4×Dic43—24no—
76C23×C43—22no—
77C23×C43—22no—
78C23×C43C2×D412yes—
79C23×C43C2×D412yes—
80C23×C43#4112yes—
81C23×C43C2411yescharacteristic
82C22×D43—21no—
83C22×D43—21no—
84C22×D43—22no—
85C22×D43—21no—
86C22×D43—22no—
87C2×C4×C43—28no—
88C2×C4×C43—28no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—44no—
99C2×C4×C43C2×D412yes—
100C2×C4×C43C2×D412yes—
101C2×C4×C43#4114yes—
102C22⋊D43—44no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—21no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—21no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43C2×D414yes—
116C22×C43—22no—
117C22×C43—22no—
118C22×C43—24no—
119C22×C43—24no—
120C22×C43#12114yes—
121C22×C43C22×D411yescharacteristic
122C22×C43C22×D411yescharacteristic
123C22×C43C2×#4111yescharacteristic
124C22×C43C2×#4112yes—
125C22×C432−1+412yes—
126C2×D43—41no—
127C2×D43—41no—
128C2×D43—41no—
129C2×D43—42no—
130C2×D43—42no—
131C4×C43—22no—
132C4×C43—22no—
133C4×C43—24no—
134C4×C43—42no—
135Dic43—24no—
136Dic43—41no—
137Dic43—41no—
138Dic43—41no—
139Dic43—42no—
140#2413—431nomaximal, Sylow
141C2×C43—24no—
142C2×C43C2×#12111yescharacteristic
143C2×C43#52511yescharacteristic
144C2×C43#53611yescharacteristic
145C2×C43#54712yes—
146C2×C43#55212yes—
147D43—81no—
148C2×#123—431no—
149C2×#123—431no—
150C2×#117—431no—
151C22×C4⋊C4D4311yescharacteristic, complemented
152#398—432no—
153#396—432no—
154#389—432no—
155#388—432no—
156#386—431no—
157#385—431no—
158#381—431no—
159C43#241311yescharacteristic, complemented, Sylow
160C22×D4—431no—
161C23×C4C2×D4311yescharacteristic
162C23×C4C2×D4311yescharacteristic
163C23×C4C2×D4311yescharacteristic
164#123—864no—
165#123—864no—
166#117—864no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—432no—
169C2×C4⋊C4—431no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—431no—
172C2×C4⋊C4—432no—
173C2×C4⋊C4C2×D4312yes—
174C2×C4⋊C4C2×D4312yes—
175C2×C22⋊C4—431no—
176C2×C22⋊C4—431no—
177C2×C22⋊C4—431no—
178C2×C22⋊C4—431no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4—431no—
181C2×C22⋊C4—432no—
182C2×C42—432no—
183#95—432no—
184#95—432no—
185#95—432no—
186#95—432no—
187C24—431no—
188C24C22×D4311yescharacteristic
189C2×D4—862no—
190C2×D4—862no—
191C2×D4—862no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—432no—
200C22×C4—431no—
201C22×C4—432no—
202C22×C4—431no—
203C22×C4—431no—
204C22×C4C22⋊D4314yes—
205C22×C4C22×D4312yes—
206C22×C4C22×D4312yes—
207C22×C4C22×D4311yescharacteristic
208C22×C4C22×D4311yescharacteristic
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—864no—
212C4⋊C4—864no—
213C4⋊C4—864no—
214C4⋊C4—862no—
215C4⋊C4—862no—
216C22⋊C4—434no—
217C22⋊C4—864no—
218C22⋊C4—862no—
219C22⋊C4—862no—
220C22⋊C4—864no—
221C22⋊C4—862no—
222C22⋊C4—862no—
223C42—864no—
224C23—22no—
225C23—22no—
226C23—861no—
227C23—861no—
228C23—861no—
229C23—862no—
230C23—862no—
231C23D4×D4312yes—
232C23#1062190012yes—
233C23C2×C22⋊D4312yes—
234C23C23×D4311yescharacteristic
235D4—1724no—
236C2×C4—28no—
237C2×C4—28no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—44no—
248C2×C4—434no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—861no—
253C2×C4—861no—
254C2×C4—861no—
255C2×C4—861no—
256C2×C4—861no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—862no—
260C2×C4—862no—
261C2×C4#1062189814yes—
262C2×C4C2×C22⋊D4312yes—
263C2×C4C2×C22⋊D4312yes—
264C22—24no—
265C22—22no—
266C22—22no—
267C22—24no—
268C22—1722no—
269C22—1721no—
270C22—1721no—
271C22—1721no—
272C22—1722no—
273C22#1306329714yes—
274C22C2×D4×D4311yescharacteristic
275C22C22×C22⋊D4311yescharacteristic
276C22C2×#1062190011yescharacteristic
277C22C2×#1062189812yes—
278C22#1306337312yes—
279C4—22no—
280C4—22no—
281C4—24no—
282C4—42no—
283C4—864no—
284C4—1721no—
285C4—1721no—
286C4—1721no—
287C4—1722no—
288C2—24no—
289C2—3441no—
290C2C2×#1306329711yescharacteristic
291C2#1458341011yescharacteristic
292C2#1458347311yescharacteristic
293C2#1458355012yes—
294C2#1458358412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC22×C4⋊C4×C43C2
hypercenterC22×C4⋊C4D43
hypocenterC43#2413
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#13063284C2semidirect
4. #14582832C2semidirect
5. #14582821C2semidirect
6. #14582794C2semidirect
7. #14582789C2semidirect
9. #14582772C2semidirect
10. #14582762C2semidirect
11. C22×C4⋊C4×C43C2semidirect
151. C22×C4⋊C4D43semidirect
159. C43#2413semidirect