Finite Group Databasebeta

← #19140512

Subgroups — #19140512

Order 5504.

520 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063304C211yesmaximal, characteristic, complemented
2#14582829C211yesmaximal, characteristic, complemented
3#14582827C212yesmaximal, complemented
4#14582824C211yesmaximal, characteristic, complemented
5#14582819C211yesmaximal, characteristic, complemented
6#14582813C212yesmaximal
7#14582811C211yesmaximal, characteristic, complemented
8#14582783C212yesmaximal, complemented
9#14582772C212yesmaximal, complemented
10#14582762C211yesmaximal, characteristic, complemented
11C2×C4×D4×C43C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13#13063304—24no—
14C2×C4⋊Dic43C2211yescharacteristic
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2212yes—
21C2×C22⋊Dic43C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2211yescharacteristic
24C43⋊#95C2212yes—
25C43⋊#95C2211yescharacteristic
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C22×D4×C43C2211yescharacteristic
30C23×C4×C43C2211yescharacteristic
31C23×C4×C43C2211yescharacteristic
32C4×D4×C43—24no—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36C2×C42×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C24×C43C2311yescharacteristic
39C2×D4×C43—22no—
40C2×D4×C43—22no—
41C2×D4×C43—22no—
42C22×C4×C43—22no—
43C22×C4×C43—42no—
44C22×C4×C43—42no—
45C22×C4×C43D414yes—
46C22×C4×C43C2311yescharacteristic
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2311yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C22×Dic43C2312yes—
52C22×Dic43C2312yes—
53C22×Dic43C2312yes—
54C22×Dic43C2312yes—
55C2×Dic86—22no—
56C2×Dic86—42no—
57C4⋊C4×C43—22no—
58C22⋊C4×C43—22no—
59C22⋊C4×C43—22no—
60C42×C43—22no—
61C22⋊Dic43—24no—
62C22⋊Dic43—24no—
63C22⋊Dic43—42no—
64C22⋊Dic43—42no—
65C4⋊Dic43—22no—
66Dic43⋊C4—24no—
67Dic43⋊C4—24no—
68Dic43⋊C4—42no—
69C23×C43—21no—
70C23×C43—21no—
71C23×C43—21no—
72C23×C43—21no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43C2×D412yes—
78C23×C43#4112yes—
79C23×C43C2411yescharacteristic
80D4×C43—28no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—44no—
90C2×C4×C43—44no—
91C2×C4×C43C2×D412yes—
92C2×C4×C43C2×D412yes—
93C2×C4×C43#4112yes—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106Dic86—44no—
107C22×C43—22no—
108C22×C43—22no—
109C22×C43—22no—
110C22×C43—22no—
111C22×C43—24no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—42no—
115C22×C43—42no—
116C22×C43—42no—
117C22×C43C22×D411yescharacteristic
118C22×C43C2×#4111yescharacteristic
119C22×C43C2×#4111yescharacteristic
120C22×C43H(5,𝔽2)12yes—
121C22×C432−1+412yes—
122C4×C43—22no—
123C4×C43—22no—
124C4×C43—22no—
125C4×C43—41no—
126C4×C43—41no—
127Dic43—42no—
128Dic43—42no—
129Dic43—42no—
130Dic43—42no—
131#2638—431nomaximal, Sylow
132C2×C43—42no—
133C2×C43—42no—
134C2×C43#52511yescharacteristic
135C2×C43#53411yescharacteristic
136C2×C43#53611yescharacteristic
137C2×C43#53912yes—
138C2×C43#54212yes—
139C2×C22⋊Q8—431no—
140C2×C4×D4D4311yescharacteristic
141#398—431no—
142#397—431no—
143#397—432no—
144#395—431no—
145#394—432no—
146#393—431no—
147#387—432no—
148#385—432no—
149#381—431no—
150C43#263811yescharacteristic, complemented, Sylow
151C22×Q8—431no—
152C22×D4C2×D4311yescharacteristic
153C23×C4C2×D4311yescharacteristic
154C23×C4C2×D4311yescharacteristic
155C22⋊Q8—864no—
156C4×D4—24no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—431no—
159C2×C4⋊C4—432no—
160C2×C4⋊C4—432no—
161C2×C4⋊C4C2×D4311yescharacteristic
162C2×C22⋊C4—432no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4—432no—
166C2×C22⋊C4C2×D4311yescharacteristic
167C2×C22⋊C4C2×D4311yescharacteristic
168C2×C42C2×D4311yescharacteristic
169#95—432no—
170#95—431no—
171#95—431no—
172#95—432no—
173#95—432no—
174#95—432no—
175#95—432no—
176C24C22×D4311yescharacteristic
177C24C22×D4311yescharacteristic
178C2×Q8—862no—
179C2×Q8—1722no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—432no—
187C22×C4—432no—
188C22×C4—432no—
189C22×C4—432no—
190C22×C4C22⋊D4314yes—
191C22×C4C22×D4311yescharacteristic
192C22×C4C22×D4311yescharacteristic
193C22×C4C22×D4311yescharacteristic
194C22×C4C22×D4311yescharacteristic
195C22×C4C22×D4311yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—864no—
198C4⋊C4—864no—
199C4⋊C4—862no—
200C4⋊C4—1722no—
201C22⋊C4—22no—
202C22⋊C4—22no—
203C22⋊C4—864no—
204C22⋊C4—864no—
205C22⋊C4—1722no—
206C22⋊C4—1722no—
207C42—22no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23#1062189812yes—
217C23C2×C22⋊D4312yes—
218C23C23×D4311yescharacteristic
219Q8—1724no—
220D4—28no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4#1062189812yes—
244C2×C4C2×C22⋊D4312yes—
245C2×C4C2×C22⋊D4312yes—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—24no—
251C22—41no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22C22×C22⋊D4311yescharacteristic
257C22C2×#1062189811yescharacteristic
258C22C2×#1062189811yescharacteristic
259C22#1306337012yes—
260C22#1306337212yes—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—1722no—
267C4—1722no—
268C4—1722no—
269C4—1722no—
270C2—42no—
271C2—42no—
272C2#1458341011yescharacteristic
273C2#1458345811yescharacteristic
274C2#1458347011yescharacteristic
275C2#1458349112yes—
276C2#1458351412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×C4×D4×C43C2
hypercenterC2×C4×D4D43
hypocenterC43#2638
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13063304C2semidirect
2. #14582829C2semidirect
3. #14582827C2semidirect
4. #14582824C2semidirect
5. #14582819C2semidirect
7. #14582811C2semidirect
8. #14582783C2semidirect
9. #14582772C2semidirect
10. #14582762C2semidirect
150. C43#2638semidirect