Finite Group Databasebeta

← #19140449

Subgroups — #19140449

Order 5504.

628 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13063311C211yesmaximal, characteristic, complemented
2C2×#13063287C211yesmaximal, characteristic, complemented
3#14582825C211yesmaximal, characteristic, complemented
4#14582812C212yesmaximal, complemented
5#14582809C211yesmaximal, characteristic, complemented
6#14582808C211yesmaximal, characteristic, complemented
7#14582808C212yesmaximal, complemented
8#14582777C212yesmaximal, complemented
9#14582775C212yesmaximal, complemented
10#14582766C211yesmaximal, characteristic, complemented
11C43×#397C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C22×D172C2212yes—
15C22×C22⋊D43C2211yescharacteristic
16C22×C22⋊D43C2212yes—
17C22×C4×D43C2212yes—
18#13063311—24no—
19#13063287—24no—
20C2×C22⋊Dic43C2211yescharacteristic
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C23×D43C2312yes—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—22no—
45C2×C22⋊D43—24no—
46C2×C22⋊D43—42no—
47C2×C22⋊D43—42no—
48C2×C22⋊D43—42no—
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C2×D172—22no—
54C2×D172—24no—
55C2×D172—24no—
56C2×D172—42no—
57C2×D172—42no—
58C2×C4×D43—24no—
59C2×C4×D43—42no—
60C2×C4×D43—42no—
61C2×Dic86—22no—
62C2×Dic86—42no—
63C4⋊C4×C43—22no—
64C22⋊C4×C43—22no—
65C22⋊C4×C43—42no—
66C22⋊Dic43—22no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4—22no—
70(C2×D43)⋊C4—42no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—42no—
73C4×Dic43D414yescomplemented
74C23×C43—21no—
75C23×C43—22no—
76C23×C43—21no—
77C23×C43—21no—
78C23×C43—22no—
79C23×C43C2411yescharacteristic
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—21no—
87C22×D43—22no—
88C22×D43—21no—
89C22×D43—21no—
90C22×D43—22no—
91C22×D43#4114yes—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43C2×D412yes—
102C22⋊D43—44no—
103C22⋊D43—48no—
104C2×Dic43—22no—
105C2×Dic43—21no—
106C2×Dic43—21no—
107C2×Dic43—21no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43C2×D412yes—
113C2×Dic43C2×D412yes—
114D172—28no—
115D172—48no—
116C4×D43—48no—
117Dic86—44no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43—41no—
121C22×C43—42no—
122C22×C43—42no—
123C22×C43C22×D411yescharacteristic
124C22×C43C2×#4112yes—
125C22×C43H(5,𝔽2)11yescharacteristic
126C22×C43H(5,𝔽2)11yescharacteristic
127C22×C43H(5,𝔽2)12yes—
128C2×D43—24no—
129C2×D43—24no—
130C2×D43—24no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—42no—
135C2×D43—41no—
136C2×D43—41no—
137C2×D43—41no—
138C2×D43—42no—
139C2×D43—42no—
140C4×C43—22no—
141C4×C43—41no—
142C4×C43—42no—
143C4×C43—42no—
144Dic43—22no—
145Dic43—22no—
146Dic43—41no—
147Dic43—42no—
148#2631—431nomaximal, Sylow
149C2×C43—81no—
150C2×C43#52511yescharacteristic
151C2×C43#53511yescharacteristic
152C2×C43#53511yescharacteristic
153C2×C43#53812yes—
154C2×C43#53812yes—
155D43—44no—
156D43—81no—
157C2×#124—431no—
158C2×C4×D4—431no—
159#397—431no—
160#397D4311yescharacteristic, complemented
161#393—432no—
162#392—432no—
163#392—431no—
164#392—431no—
165#386—432no—
166#386—432no—
167#383—431no—
168C43#263111yescharacteristic, complemented, Sylow
169C22×Q8—431no—
170C22×D4—431no—
171C22×D4—432no—
172C22×D4—431no—
173C22×D4—432no—
174C23×C4—432no—
175#124—864no—
176C4×D4—864no—
177C2×C4⋊C4C2×D4311yescharacteristic
178C2×C22⋊C4—431no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4—431no—
181C2×C22⋊C4—431no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—432no—
184C2×C22⋊C4—432no—
185C2×C22⋊C4C2×D4311yescharacteristic
186C2×C22⋊C4C2×D4312yes—
187C2×C42—431no—
188#95—432no—
189#95—432no—
190#95—431no—
191#95—432no—
192#95C2×D4311yescharacteristic
193#95C2×D4312yes—
194C24—432no—
195C24—431no—
196C24C22×D4311yescharacteristic
197C2×Q8—862no—
198C2×Q8—1722no—
199C2×D4—864no—
200C2×D4—864no—
201C2×D4—862no—
202C2×D4—864no—
203C2×D4—862no—
204C2×D4—1722no—
205C2×D4—1722no—
206C2×D4—1722no—
207C2×D4—1722no—
208C2×D4—1722no—
209C22×C4—431no—
210C22×C4—431no—
211C22×C4—432no—
212C22×C4—431no—
213C22×C4—864no—
214C22×C4—1722no—
215C22×C4—1722no—
216C22×C4C22×D4312yes—
217C22×C4C22×D4312yes—
218C22×C4C22×D4311yescharacteristic
219C22×C4C22×D4311yescharacteristic
220C4⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—42no—
223C22⋊C4—864no—
224C22⋊C4—862no—
225C22⋊C4—862no—
226C22⋊C4—862no—
227C22⋊C4—1722no—
228C22⋊C4—1722no—
229C22⋊C4—1722no—
230C42—434no—
231C23—21no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—434no—
237C23—862no—
238C23—862no—
239C23—862no—
240C23—862no—
241C23—862no—
242C23—862no—
243C23—861no—
244C23—862no—
245C23—861no—
246C23—861no—
247C23—862no—
248C23C23×D4311yescharacteristic
249Q8—1724no—
250D4—868no—
251D4—1728no—
252D4—1724no—
253D4—1728no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—432no—
264C2×C4—432no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—862no—
268C2×C4—861no—
269C2×C4—862no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—1728no—
274C2×C4D4×D4312yes—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—864no—
281C22—864no—
282C22—864no—
283C22—1721no—
284C22—1721no—
285C22—1721no—
286C22—1722no—
287C22—1722no—
288C22—1722no—
289C22—1722no—
290C22—1722no—
291C22—1722no—
292C22C2×D4×D4311yescharacteristic
293C22#41×D4312yes—
294C22#1306337011yescharacteristic
295C22#1306337111yescharacteristic
296C22#1306337112yes—
297C4—22no—
298C4—42no—
299C4—41no—
300C4—42no—
301C4—862no—
302C4—862no—
303C4—1721no—
304C4—1722no—
305C2—81no—
306C2—3441no—
307C2—1724no—
308C2#1458340711yescharacteristic
309C2#1458346511yescharacteristic
310C2#1458346711yescharacteristic
311C2#1458348512yes—
312C2#1458348812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2631
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13063311C2semidirect
2. C2×#13063287C2semidirect
3. #14582825C2semidirect
4. #14582812C2semidirect
5. #14582809C2semidirect
6. #14582808C2semidirect
7. #14582808C2semidirect
8. #14582777C2semidirect
9. #14582775C2semidirect
10. #14582766C2semidirect
11. C43×#397C2semidirect
73. C4×Dic43D4semidirect
160. #397D43semidirect
168. C43#2631semidirect