Finite Group Databasebeta

← #19140739

Subgroups — #19140739

Order 5504.

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

normal subgroups only

This group has 534 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×#13063320C211yesmaximal, characteristic, complemented
2C2×#13063314C211yesmaximal, characteristic, complemented
3#14582821C212yesmaximal, complemented
4#14582817C212yesmaximal, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582810C211yesmaximal, characteristic, complemented
7#14582809C211yesmaximal, characteristic
8#14582800C212yesmaximal, complemented
9#14582788C212yesmaximal, complemented
10#14582750C211yesmaximal, characteristic, complemented
11C43×#395C211yesmaximal, characteristic, complemented
12C22×D172C2212yes—
13C22×D172C2211yescharacteristic
14#13063320—24no—
15#13063314—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×C4×Dic43C2212yes—
29C2×C4×Dic43C2211yescharacteristic
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C23×D43C2312yes—
39C2×Q8×C43—22no—
40C2×Q8×C43—42no—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2312yes—
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C2×D172—22no—
51C2×D172—24no—
52C2×D172—42no—
53C2×D172—42no—
54C2×D172—42no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—42no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—24no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—42no—
64(C2×D43)⋊C4—42no—
65(C2×D43)⋊C4—42no—
66C4⋊Dic43—22no—
67Dic43⋊C4—24no—
68Dic43⋊C4—22no—
69C4×Dic43—42no—
70C4×Dic43D414yescomplemented
71C23×C43C2411yescharacteristic
72C22×D43—21no—
73C22×D43—22no—
74C22×D43—22no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43—22no—
81C22×D43—21no—
82C22×D43—21no—
83C22×D43—22no—
84Q8×C43—44no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
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×C4×C43#4114yes—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43C2×D412yes—
107C2×Dic43C2×D412yes—
108D172—44no—
109D172—48no—
110C22×C43C22×D411yescharacteristic
111C22×C43C2×#4112yes—
112C22×C43H(5,𝔽2)12yes—
113C22×C43H(5,𝔽2)11yescharacteristic
114C22×C432−1+411yescharacteristic
115C2×D43—41no—
116C2×D43—42no—
117C2×D43—41no—
118C2×D43—42no—
119C2×D43—41no—
120C2×D43—42no—
121C2×D43—42no—
122C2×D43—42no—
123C2×D43—42no—
124C2×D43—42no—
125C2×D43—42no—
126C2×D43—42no—
127C4×C43—22no—
128C4×C43—24no—
129C4×C43—41no—
130C4×C43—42no—
131C4×C43—41no—
132Dic43—22no—
133Dic43—22no—
134Dic43—41no—
135Dic43—42no—
136#2662—431nomaximal, Sylow
137C2×C43#53211yescharacteristic
138C2×C43#53511yescharacteristic
139C2×C43#53711yescharacteristic
140C2×C43#53812yes—
141C2×C43#54212yes—
142D43—81no—
143D43—82no—
144C2×#126—431no—
145C2×#124—431no—
146#396—432no—
147#395D4311yescharacteristic, complemented
148#394—431no—
149#394—432no—
150#393—431no—
151#392—431no—
152#390—432no—
153#388—432no—
154C4×C4⋊C4—431no—
155C43#266211yescharacteristic, complemented, Sylow
156C22×Q8C2×D4311yescharacteristic
157C22×D4—431no—
158C22×D4—432no—
159#126—864no—
160#124—864no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—431no—
163C2×C4⋊C4—432no—
164C2×C4⋊C4C2×D4311yescharacteristic
165C2×C4⋊C4C2×D4312yes—
166C2×C22⋊C4—432no—
167C2×C22⋊C4—432no—
168C2×C22⋊C4—431no—
169C2×C22⋊C4—431no—
170C2×C22⋊C4—431no—
171C2×C22⋊C4—432no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4—432no—
174C2×C22⋊C4—432no—
175C2×C42—431no—
176C2×C42—432no—
177#95—431no—
178#95—432no—
179#95C2×D4311yescharacteristic
180#95C2×D4312yes—
181C24—431no—
182C24—432no—
183C2×Q8—22no—
184C2×Q8—42no—
185C2×D4—862no—
186C2×D4—864no—
187C2×D4—1722no—
188C2×D4—1722no—
189C2×D4—1722no—
190C22×C4—431no—
191C22×C4—431no—
192C22×C4—432no—
193C22×C4—431no—
194C22×C4C22×D4312yes—
195C22×C4C22×D4311yescharacteristic
196C22×C4C22×D4311yescharacteristic
197C22×C4C22×D4311yescharacteristic
198C22×C4C22×D4312yes—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—862no—
202C4⋊C4—862no—
203C4⋊C4—864no—
204C22⋊C4—864no—
205C22⋊C4—864no—
206C22⋊C4—862no—
207C22⋊C4—862no—
208C22⋊C4—862no—
209C22⋊C4—864no—
210C22⋊C4—1722no—
211C22⋊C4—1722no—
212C22⋊C4—1722no—
213C42—434no—
214C42—1722no—
215C23—861no—
216C23—862no—
217C23—862no—
218C23—862no—
219C23—862no—
220C23—862no—
221C23—862no—
222C23—862no—
223C23—862no—
224C23—861no—
225C23—861no—
226C23—862no—
227C23C23×D4311yescharacteristic
228Q8—44no—
229D4—1724no—
230D4—1728no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—432no—
243C2×C4—432no—
244C2×C4—862no—
245C2×C4—861no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4D4×D4312yes—
253C2×C4#1062190214yes—
254C22—1721no—
255C22—1722no—
256C22—1722no—
257C22—1721no—
258C22—1721no—
259C22—1722no—
260C22—1722no—
261C22—1722no—
262C22—1722no—
263C22—1722no—
264C22—1722no—
265C22—1722no—
266C22C2×D4×D4311yescharacteristic
267C22C2×#1062190212yes—
268C22#1306337012yes—
269C22#1306337111yescharacteristic
270C22#1306337311yescharacteristic
271C4—22no—
272C4—24no—
273C4—42no—
274C4—41no—
275C4—41no—
276C4—862no—
277C4—862no—
278C4—1721no—
279C4—1722no—
280C2—3442no—
281C2—3441no—
282C2#1458345011yescharacteristic
283C2#1458346411yescharacteristic
284C2#1458347911yescharacteristic
285C2#1458348912yes—
286C2#1458352312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2662
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#13063320C2semidirect
2. C2×#13063314C2semidirect
3. #14582821C2semidirect
4. #14582817C2semidirect
5. #14582816C2semidirect
6. #14582810C2semidirect
8. #14582800C2semidirect
9. #14582788C2semidirect
10. #14582750C2semidirect
11. C43×#395C2semidirect
70. C4×Dic43D4semidirect
147. #395D43semidirect
155. C43#2662semidirect