Finite Group Databasebeta

← #19140527

Subgroups — #19140527

Order 5504.

576 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063303C211yesmaximal, characteristic, complemented
2C2×#13063300C211yesmaximal, characteristic
3#14582837C211yesmaximal, characteristic, complemented
4#14582828C212yesmaximal, complemented
5#14582817C211yesmaximal, characteristic, complemented
6#14582816C211yesmaximal, characteristic, complemented
7#14582812C212yesmaximal, complemented
8#14582777C212yesmaximal, complemented
9#14582777C212yesmaximal, complemented
10#95×D43C211yesmaximal, characteristic, complemented
11C43×#400C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×D172C2212yes—
14C22×D172C2211yescharacteristic
15C22×C4×D43C2212yes—
16C22×C4×D43C2211yescharacteristic
17#13063303—24no—
18#13063300—24no—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
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×(C2×D43)⋊C4C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2312yes—
38C23×D43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×D172—22no—
49C2×D172—24no—
50C2×D172—24no—
51C2×D172—24no—
52C2×D172—42no—
53C2×C4×D43—24no—
54C2×C4×D43—42no—
55C2×C4×D43—42no—
56C2×C4×D43—42no—
57C2×C4×D43D414yes—
58C2×Dic86—22no—
59C2×Dic86—42no—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—22no—
64(C2×D43)⋊C4—22no—
65(C2×D43)⋊C4—42no—
66(C2×D43)⋊C4—42no—
67(C2×D43)⋊C4—42no—
68(C2×D43)⋊C4—42no—
69Dic43⋊C4—22no—
70Dic43⋊C4—22no—
71C23×C43C2411yescharacteristic
72C22×D43—22no—
73C22×D43—21no—
74C22×D43—21no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—22no—
82C22×D43C2×D412yes—
83C22×D43#4114yes—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43C2×D412yes—
97C2×Dic43—22no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—21no—
106C2×Dic43C2×D412yes—
107D172—44no—
108D172—48no—
109C4×D43—44no—
110C4×D43—48no—
111Dic86—44no—
112C22×C43C22×D411yescharacteristic
113C22×C43C2×#4112yes—
114C22×C43H(5,𝔽2)12yes—
115C22×C43H(5,𝔽2)11yescharacteristic
116C22×C432−1+411yescharacteristic
117C2×D43—22no—
118C2×D43—22no—
119C2×D43—24no—
120C2×D43—24no—
121C2×D43—42no—
122C2×D43—42no—
123C2×D43—42no—
124C2×D43—42no—
125C2×D43—42no—
126C2×D43—42no—
127C2×D43—42no—
128C2×D43#12414yes—
129C4×C43—22no—
130C4×C43—42no—
131C4×C43—41no—
132C4×C43—41no—
133C4×C43—42no—
134Dic43—22no—
135Dic43—41no—
136Dic43—41no—
137Dic43—42no—
138#2639—431nomaximal, Sylow
139C2×C43C2×#12411yescharacteristic
140C2×C43#53411yescharacteristic
141C2×C43#53711yescharacteristic
142C2×C43#53812yes—
143C2×C43#53912yes—
144D43—24no—
145D43—82no—
146C2×C22⋊Q8—431no—
147C2×#121—431no—
148#400—431no—
149#400D4311yescharacteristic, complemented
150#397—432no—
151#394—431no—
152#394—431no—
153#393—432no—
154#386—432no—
155#386—432no—
156C2×#95—431no—
157C43#263911yescharacteristic, complemented, Sylow
158C22×Q8—431no—
159C22×D4—432no—
160C22×D4—431no—
161C23×C4—431no—
162C23×C4—432no—
163C22⋊Q8—864no—
164#121—864no—
165C2×C4⋊C4—431no—
166C2×C4⋊C4—431no—
167C2×C4⋊C4C2×D4311yescharacteristic
168C2×C4⋊C4C2×D4311yescharacteristic
169C2×C22⋊C4—432no—
170C2×C22⋊C4—431no—
171C2×C22⋊C4—431no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4—432no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4—432no—
176#95—432no—
177#95—431no—
178#95—432no—
179#95—432no—
180#95C2×D4311yescharacteristic
181#95C2×D4312yes—
182#95C2×D4312yes—
183C24—431no—
184C24—432no—
185C2×Q8—862no—
186C2×Q8—1722no—
187C2×D4—864no—
188C2×D4—864no—
189C2×D4—864no—
190C2×D4—862no—
191C2×D4—1722no—
192C22×C4—431no—
193C22×C4—434no—
194C22×C4—432no—
195C22×C4—431no—
196C22×C4—431no—
197C22×C4—864no—
198C22×C4—1722no—
199C22×C4—1722no—
200C22×C4—1722no—
201C22×C4C22×D4312yes—
202C22×C4C22×D4312yes—
203C22×C4C22×D4311yescharacteristic
204C22×C4C22×D4311yescharacteristic
205C22×C4C22×D4311yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—862no—
209C4⋊C4—862no—
210C22⋊C4—864no—
211C22⋊C4—862no—
212C22⋊C4—862no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C22⋊C4—1722no—
217C23—432no—
218C23—434no—
219C23—862no—
220C23—861no—
221C23—861no—
222C23—862no—
223C23—862no—
224C23—862no—
225C23—862no—
226C23—862no—
227C23—862no—
228C23—862no—
229C23C23×D4311yescharacteristic
230Q8—1724no—
231D4—1724no—
232D4—1728no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—432no—
246C2×C4—862no—
247C2×C4—861no—
248C2×C4—861no—
249C2×C4—862no—
250C2×C4—861no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—861no—
255C2×C4—1724no—
256C2×C4—1728no—
257C2×C4D4×D4312yes—
258C22—434no—
259C22—862no—
260C22—862no—
261C22—864no—
262C22—864no—
263C22—1722no—
264C22—1722no—
265C22—1722no—
266C22—1722no—
267C22—1722no—
268C22—1722no—
269C22—1722no—
270C22C2×D4×D4311yescharacteristic
271C22#41×D4312yes—
272C22#1306337112yes—
273C22#1306337111yescharacteristic
274C22#1306337311yescharacteristic
275C4—22no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—42no—
280C4—862no—
281C4—1721no—
282C4—1721no—
283C4—1722no—
284C2—864no—
285C2—3442no—
286C2#124×D4311yescharacteristic
287C2#1458346011yescharacteristic
288C2#1458347911yescharacteristic
289C2#1458348812yes—
290C2#1458349712yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2639
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#13063303C2semidirect
3. #14582837C2semidirect
4. #14582828C2semidirect
5. #14582817C2semidirect
6. #14582816C2semidirect
7. #14582812C2semidirect
8. #14582777C2semidirect
9. #14582777C2semidirect
10. #95×D43C2semidirect
11. C43×#400C2semidirect
149. #400D43semidirect
157. C43#2639semidirect