Finite Group Databasebeta

← #19139061

Subgroups — #19139061

Order 5504.

708 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13063310C212yesmaximal, complemented
2C2×#13063307C212yesmaximal, complemented
3C2×#13063298C211yesmaximal, characteristic
4C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
5#14582836C211yesmaximal, characteristic, complemented
6#14582835C211yesmaximal, characteristic, complemented
7#14582834C211yesmaximal, characteristic, complemented
8#14582799C212yesmaximal, complemented
9#14582768C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic, complemented
11C43×#399C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C22×C22⋊D43C2211yescharacteristic
15C22×C4×D43C2212yes—
16C22×C4×D43C2211yescharacteristic
17#13063310—28no—
18#13063307—28no—
19#13063298—24no—
20C2×C4⋊Dic43C2211yescharacteristic
21C2×C4⋊Dic43C2212yes—
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C2×Dic43⋊C4C2212yes—
25C2×Dic43⋊C4C2211yescharacteristic
26C4⋊C4×D43—24no—
27C2×C22⋊Dic43C2212yes—
28C2×(C2×D43)⋊C4C2212yes—
29C2×(C2×D43)⋊C4C2212yes—
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2212yes—
32C2×C4×Dic43C2212yes—
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
41C23×D43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2312yes—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—24no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—24no—
50C22×Dic43C2312yes—
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2312yes—
53C22×Dic43C2311yescharacteristic
54C2×D172—22no—
55C2×D172—24no—
56C2×C4×D43—24no—
57C2×C4×D43—24no—
58C2×C4×D43—24no—
59C2×C4×D43—24no—
60C2×C4×D43D414yes—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—24no—
63C22⋊C4×C43—22no—
64C22⋊C4×C43—24no—
65C22⋊Dic43—24no—
66(C2×D43)⋊C4—22no—
67(C2×D43)⋊C4—24no—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4D418yescomplemented
70C4⋊Dic43—22no—
71C4⋊Dic43—24no—
72Dic43⋊C4—24no—
73Dic43⋊C4—22no—
74Dic43⋊C4—24no—
75Dic43⋊C4—24no—
76C4×Dic43—24no—
77C23×C43—22no—
78C23×C43—21no—
79C23×C43—22no—
80C23×C43—21no—
81C23×C43—21no—
82C23×C43C2411yescharacteristic
83C22×D43—22no—
84C22×D43—21no—
85C22×D43—21no—
86C22×D43—22no—
87C22×D43—21no—
88C22×D43—22no—
89C22×D43—21no—
90C22×D43—21no—
91C22×D43C2×D414yes—
92C22×D43C2×D412yes—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43C2×D414yes—
102C2×C4×C43C2×D412yes—
103C22⋊D43—44no—
104C22⋊D43—44no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—21no—
111C2×Dic43—22no—
112C2×Dic43C2×D414yes—
113C2×Dic43C2×D412yes—
114C2×Dic43#4114yes—
115D172—44no—
116C4×D43—28no—
117C4×D43—48no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43—41no—
121C22×C43—42no—
122C22×C43—42no—
123C22×C43C22×D411yescharacteristic
124C22×C43C22×D412yes—
125C22×C43C2×#4112yes—
126C22×C432−1+411yescharacteristic
127C22×C432−1+411yescharacteristic
128C2×D43—22no—
129C2×D43—22no—
130C2×D43—24no—
131C2×D43—24no—
132C2×D43—41no—
133C2×D43—41no—
134C2×D43—41no—
135C2×D43—42no—
136C2×D43—42no—
137C2×D43#12714yes—
138C4×C43—22no—
139C4×C43—24no—
140C4×C43—42no—
141C4×C43—41no—
142Dic43—24no—
143Dic43—42no—
144Dic43—41no—
145Dic43#12314yescomplemented
146#2501—431nomaximal, Sylow
147C2×C43—81no—
148C2×C43C2×#12311yescharacteristic
149C2×C43C2×#12711yescharacteristic
150C2×C43#53611yescharacteristic
151C2×C43#54712yes—
152C2×C43#54712yes—
153D43—24no—
154D43—81no—
155C2×#123—432no—
156C2×#123—432no—
157C2×#121—431no—
158C22×C4⋊C4—431no—
159#399—431no—
160#399—431no—
161#399—431no—
162#399D4311yescharacteristic, complemented
163#390—432no—
164#384—432no—
165C4×C22⋊C4—431no—
166C43#250111yescharacteristic, complemented, Sylow
167C22×D4—431no—
168C22×D4—431no—
169C22×D4—431no—
170C23×C4—431no—
171C23×C4—432no—
172#123—868no—
173#123—868no—
174#121—864no—
175C2×C4⋊C4—432no—
176C2×C4⋊C4—431no—
177C2×C4⋊C4—431no—
178C2×C4⋊C4—432no—
179C2×C4⋊C4—432no—
180C2×C4⋊C4—432no—
181C2×C4⋊C4—864no—
182C2×C4⋊C4C2×D4311yescharacteristic
183C2×C4⋊C4C2×D4312yes—
184C2×C22⋊C4—432no—
185C2×C22⋊C4—432no—
186C2×C22⋊C4—431no—
187C2×C22⋊C4—432no—
188C2×C22⋊C4—432no—
189C2×C22⋊C4C2×D4311yescharacteristic
190C2×C22⋊C4C2×D4312yes—
191C2×C42—432no—
192#95—431no—
193#95C2×D4311yescharacteristic
194C24—431no—
195C24—431no—
196C24C22×D4311yescharacteristic
197C2×D4—862no—
198C2×D4—864no—
199C2×D4—862no—
200C2×D4—864no—
201C2×D4—862no—
202C2×D4—864no—
203C22×C4—431no—
204C22×C4—432no—
205C22×C4—434no—
206C22×C4—432no—
207C22×C4—431no—
208C22×C4—864no—
209C22×C4—864no—
210C22×C4—864no—
211C22×C4—864no—
212C22×C4C22×D4312yes—
213C22×C4C22×D4311yescharacteristic
214C22×C4C22×D4311yescharacteristic
215C22×C4C22×D4312yes—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4—864no—
219C4⋊C4—862no—
220C4⋊C4—864no—
221C4⋊C4—864no—
222C4⋊C4—862no—
223C4⋊C4—864no—
224C22⋊C4—22no—
225C22⋊C4—24no—
226C22⋊C4—438no—
227C22⋊C4—864no—
228C22⋊C4—864no—
229C22⋊C4—862no—
230C22⋊C4—864no—
231C42—864no—
232C23—22no—
233C23—21no—
234C23—22no—
235C23—21no—
236C23—21no—
237C23—434no—
238C23—432no—
239C23—862no—
240C23—861no—
241C23—861no—
242C23—862no—
243C23—861no—
244C23—862no—
245C23—861no—
246C23—861no—
247C23C23×D4311yescharacteristic
248D4—1724no—
249D4—1724no—
250D4—1724no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—432no—
260C2×C4—434no—
261C2×C4—434no—
262C2×C4—868no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—862no—
266C2×C4—862no—
267C2×C4—861no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—1728no—
271C2×C4D4×D4314yes—
272C2×C4D4×D4312yes—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—434no—
279C22—862no—
280C22—862no—
281C22—864no—
282C22—864no—
283C22—1721no—
284C22—1721no—
285C22—1721no—
286C22—1722no—
287C22—1722no—
288C22C2×D4×D4311yescharacteristic
289C22C2×D4×D4312yes—
290C22#41×D4312yes—
291C22#1306337211yescharacteristic
292C22#1306337311yescharacteristic
293C4—22no—
294C4—24no—
295C4—42no—
296C4—41no—
297C4—434no—
298C4—864no—
299C4—1722no—
300C4—1721no—
301C2—81no—
302C2—864no—
303C2—3441no—
304C2#123×D4311yescharacteristic
305C2#127×D4311yescharacteristic
306C2#1458347211yescharacteristic
307C2#1458354712yes—
308C2#1458355112yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2501
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063310C2semidirect
2. C2×#13063307C2semidirect
4. C2×C4⋊C4×D43C2semidirect
5. #14582836C2semidirect
6. #14582835C2semidirect
7. #14582834C2semidirect
8. #14582799C2semidirect
9. #14582768C2semidirect
10. #14582746C2semidirect
11. C43×#399C2semidirect
69. (C2×D43)⋊C4D4semidirect
145. Dic43#123semidirect
162. #399D43semidirect
166. C43#2501semidirect