Finite Group Databasebeta

← #19139558

Subgroups — #19139558

Order 5504.

724 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13063298C212yesmaximal, complemented
2C2×#13063296C211yesmaximal, characteristic, complemented
3C2×#13063287C211yesmaximal, characteristic, complemented
4#14582829C211yesmaximal, characteristic, complemented
5#14582826C211yesmaximal, characteristic, complemented
6#14582807C211yesmaximal, characteristic, complemented
7#14582793C212yesmaximal, complemented
8#14582775C212yesmaximal, complemented
9#14582775C212yesmaximal, complemented
10#95×D43C211yesmaximal, characteristic, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2212yes—
14C22×C22⋊D43C2212yes—
15C22×C4×D43C2212yes—
16C22×C4×D43C2211yescharacteristic
17C22×C4×D43C2211yescharacteristic
18#13063298—28no—
19#13063296—24no—
20#13063287—24no—
21C2×C4⋊Dic43C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×C22⋊Dic43C2212yes—
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×C4×Dic43C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C22×D4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36C2×C22⋊C4×C43C2212yes—
37#95×C43C2211yescharacteristic
38C24×C43C2312yes—
39C23×D43C2311yescharacteristic
40C23×D43C2311yescharacteristic
41C2×D4×C43—22no—
42C2×D4×C43—42no—
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—24no—
48C2×C22⋊D43—24no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43—24no—
51C2×C22⋊D43—24no—
52C2×C22⋊D43—42no—
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2312yes—
55C22×Dic43C2311yescharacteristic
56C22×Dic43C2312yes—
57C2×D172—22no—
58C2×D172—22no—
59C2×D172D414yescomplemented
60C2×C4×D43—22no—
61C2×C4×D43—24no—
62C2×C4×D43—24no—
63C2×C4×D43—42no—
64C2×C4×D43—42no—
65C2×C4×D43—42no—
66C2×C4×D43D414yescomplemented
67C4⋊C4×C43—22no—
68C22⋊C4×C43—24no—
69C22⋊C4×C43—42no—
70C22⋊Dic43—24no—
71C22⋊Dic43—24no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—24no—
75C4⋊Dic43—22no—
76Dic43⋊C4—24no—
77C4×Dic43—22no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43C2411yescharacteristic
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—21no—
89C22×D43—21no—
90C22×D43—22no—
91C22×D43—22no—
92C22×D43C2×D412yes—
93C22×D43C2×D412yes—
94C22×D43C2×D412yes—
95C22×D43#4112yes—
96D4×C43—44no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43C2×D412yes—
106C2×C4×C43C2×D412yes—
107C22⋊D43—48no—
108C22⋊D43—48no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—21no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43C2×D412yes—
118C2×Dic43#4114yes—
119D172—28no—
120C4×D43—44no—
121C4×D43—48no—
122C4×D43—44no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43C22×D411yescharacteristic
131C22×C43C22×D411yescharacteristic
132C22×C43C2×#4111yescharacteristic
133C22×C43C2×#4112yes—
134C22×C43H(5,𝔽2)12yes—
135C2×D43—22no—
136C2×D43—22no—
137C2×D43—24no—
138C2×D43—24no—
139C2×D43—22no—
140C2×D43—24no—
141C2×D43—41no—
142C2×D43—41no—
143C2×D43—42no—
144C2×D43#12114yes—
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—41no—
148C4×C43—42no—
149Dic43—22no—
150Dic43—24no—
151Dic43—42no—
152Dic43—41no—
153#2543—431nomaximal, Sylow
154C2×C43—82no—
155C2×C43C2×#12111yescharacteristic
156C2×C43#53211yescharacteristic
157C2×C43#53411yescharacteristic
158C2×C43#54612yes—
159C2×C43#55312yes—
160D43—24no—
161D43—42no—
162C2×#121—431no—
163C2×#121—432no—
164C2×C4×D4—431no—
165#398—431no—
166#397—431no—
167#394D4311yescharacteristic, complemented
168#392—431no—
169#388—432no—
170#386—432no—
171#386—432no—
172C2×#95—431no—
173C43#254311yescharacteristic, complemented, Sylow
174C22×D4—432no—
175C22×D4—432no—
176C22×D4—431no—
177C22×D4C2×D4311yescharacteristic
178C23×C4—431no—
179C23×C4—432no—
180C23×C4—431no—
181#121—868no—
182#121—864no—
183C4×D4—864no—
184C2×C4⋊C4—432no—
185C2×C4⋊C4—431no—
186C2×C4⋊C4C2×D4311yescharacteristic
187C2×C22⋊C4—432no—
188C2×C22⋊C4—432no—
189C2×C22⋊C4—431no—
190C2×C22⋊C4—431no—
191C2×C22⋊C4—432no—
192C2×C22⋊C4C2×D4312yes—
193C2×C22⋊C4C2×D4312yes—
194C2×C42—431no—
195#95—432no—
196#95—431no—
197#95—432no—
198#95—432no—
199#95C2×D4311yescharacteristic
200C24—431no—
201C24—431no—
202C24C22×D4312yes—
203C2×D4—22no—
204C2×D4—42no—
205C2×D4—434no—
206C2×D4—862no—
207C2×D4—862no—
208C2×D4—864no—
209C2×D4—864no—
210C2×D4—864no—
211C2×D4—864no—
212C2×D4—864no—
213C2×D4—1722no—
214C22×C4—432no—
215C22×C4—431no—
216C22×C4—434no—
217C22×C4—431no—
218C22×C4—432no—
219C22×C4—862no—
220C22×C4—864no—
221C22×C4—864no—
222C22×C4—1722no—
223C22×C4—1722no—
224C22×C4—1722no—
225C22×C4C22×D4312yes—
226C22×C4C22×D4311yescharacteristic
227C22×C4C22×D4311yescharacteristic
228C22×C4C22×D4311yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—864no—
231C4⋊C4—862no—
232C22⋊C4—24no—
233C22⋊C4—42no—
234C22⋊C4—862no—
235C22⋊C4—864no—
236C22⋊C4—864no—
237C22⋊C4—864no—
238C22⋊C4—862no—
239C42—862no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—432no—
248C23—432no—
249C23—432no—
250C23—432no—
251C23—862no—
252C23—862no—
253C23—861no—
254C23—861no—
255C23—862no—
256C23—862no—
257C23C23×D4311yescharacteristic
258D4—44no—
259D4—868no—
260D4—1728no—
261D4—1728no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—432no—
271C2×C4—434no—
272C2×C4—862no—
273C2×C4—862no—
274C2×C4—862no—
275C2×C4—861no—
276C2×C4—862no—
277C2×C4—862no—
278C2×C4—862no—
279C2×C4—862no—
280C2×C4—1724no—
281C2×C4—1728no—
282C2×C4—1724no—
283C2×C4D4×D4312yes—
284C2×C4D4×D4312yes—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—434no—
293C22—864no—
294C22—862no—
295C22—862no—
296C22—864no—
297C22—862no—
298C22—864no—
299C22—1722no—
300C22—1721no—
301C22—1721no—
302C22C2×D4×D4311yescharacteristic
303C22C2×D4×D4311yescharacteristic
304C22#41×D4311yescharacteristic
305C22#41×D4312yes—
306C22#1306337012yes—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—42no—
311C4—862no—
312C4—864no—
313C4—1722no—
314C4—1721no—
315C2—82no—
316C2—864no—
317C2—1722no—
318C2#121×D4311yescharacteristic
319C2#1458344811yescharacteristic
320C2#1458345911yescharacteristic
321C2#1458354612yes—
322C2#1458359412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2543
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063298C2semidirect
2. C2×#13063296C2semidirect
3. C2×#13063287C2semidirect
4. #14582829C2semidirect
5. #14582826C2semidirect
6. #14582807C2semidirect
7. #14582793C2semidirect
8. #14582775C2semidirect
9. #14582775C2semidirect
10. #95×D43C2semidirect
11. C43×#394C2semidirect
59. C2×D172D4semidirect
66. C2×C4×D43D4semidirect
167. #394D43semidirect
173. C43#2543semidirect