Finite Group Databasebeta

← #19145826

Subgroups — #19145826

Order 5504.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2#14583434C211yesmaximal, characteristic
3#14583309C211yesmaximal, characteristic, complemented
4#14583261C211yesmaximal, characteristic, complemented
5#14583259C211yesmaximal, characteristic, complemented
6#14583236C212yesmaximal, complemented
7#14583219C212yesmaximal
8#14583183C212yesmaximal, complemented
9#14583178C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#501C211yesmaximal, characteristic, complemented
12C2×Q8×D43—21no—
13#13063325C2211yescharacteristic
14#13063324—21no—
15#13063324C2212yes—
16#13063323—21no—
17#13063320—21no—
18#13063313C2211yescharacteristic
19#13063310—21no—
20#13063305C2211yescharacteristic
21#13063300C2211yescharacteristic
22#13063290C2211yescharacteristic
23#13063287—21no—
24#13063287C2211yescharacteristic
25#13063283—21no—
26C4⋊C4×D43—21no—
27C4⋊C4×D43C2212yes—
28C42×D43C2211yescharacteristic
29#13063258C2212yes—
30#13063256C2212yes—
31Dic43⋊C8C2212yes—
32#13063250C2212yes—
33#13063248C2212yes—
34#13063247C2212yes—
35#13063245C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic
38C4⋊Q8×C43C2211yescharacteristic
39#125×C43C2211yescharacteristic
40#107×C43C2212yes—
41#106×C43C2212yes—
42#97×C43C2211yescharacteristic
43C2×Q8×C43—21no—
44Q8×D43—44no—
45C2×D172—21no—
46C2×D172C2311yescharacteristic
47C2×C4×D43—21no—
48C2×C4×D43—22no—
49C2×C4×D43D411yescharacteristic
50C2×C4×D43D411yescharacteristic
51C2×C4×D43C2311yescharacteristic
52C2×Dic86—21no—
53C2×Dic86—22no—
54C2×Dic86C2311yescharacteristic
55C2×C8×C43C2312yes—
56C4⋊C4×C43—21no—
57C4⋊C4×C43—21no—
58C4⋊C4×C43—21no—
59C4⋊C4×C43C2311yescharacteristic
60C4⋊C4×C43C2312yes—
61C4⋊C4×C43C2311yescharacteristic
62C42×C43C2311yescharacteristic
63(C2×D43)⋊C4—21no—
64(C2×D43)⋊C4—21no—
65(C2×D43)⋊C4—21no—
66(C2×D43)⋊C4—21no—
67(C2×D43)⋊C4—21no—
68C4⋊Dic43—21no—
69C4⋊Dic43—21no—
70C4⋊Dic43C2312yes—
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73Dic43⋊C4—21no—
74C4×Dic43—21no—
75C4×Dic43D411yescharacteristic
76C4×Dic43D411yescharacteristic
77C4×Dic43C2311yescharacteristic
78C2×C43⋊C8C2312yes—
79C22×D43—21no—
80C22×D43C2×D411yescharacteristic
81Q8×C43—42no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2411yescharacteristic
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43C2×D411yescharacteristic
91C2×Dic43C2×D411yescharacteristic
92C2×Dic43C2×D411yescharacteristic
93D172—22no—
94D172—42no—
95C4×D43—22no—
96C4×D43—22no—
97C4×D43—22no—
98C4×D43—44no—
99C4×D43—42no—
100Dic86—22no—
101Dic86—42no—
102Dic86—44no—
103C8×C43—22no—
104C43⋊C8—22no—
105C22×C43C22×D411yescharacteristic
106C2×D43—21no—
107C2×D43—21no—
108C2×D43—41no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43#13712yes—
112C4×C43—21no—
113C4×C43—21no—
114C4×C43—42no—
115C4×C43—41no—
116C4×C43—41no—
117C4×C432−1+412yes—
118Dic43—21no—
119Dic43—21no—
120Dic43—41no—
121Dic43—42no—
122Dic43AGL(1,ℤ/8)12yes—
123#3239—431nomaximal, Sylow
124C2×C43#53611yescharacteristic
125C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C43C2×#13711yescharacteristic
127D43—22no—
128D43—81no—
129C2×C4⋊Q8—431no—
130#529—431no—
131#501—431no—
132#501D4311yescharacteristic, complemented
133#489—431no—
134#489—431no—
135#484—432no—
136#481—432no—
137#475—432no—
138#474—432no—
139#432—431no—
140C43#323911yescharacteristic, complemented, Sylow
141C22×Q8—861no—
142C4⋊Q8—432no—
143C4⋊Q8—431no—
144C4⋊Q8—861no—
145C4⋊Q8—861no—
146C4⋊Q8C2×D4311yescharacteristic
147#126—861no—
148#125C2×D4311yescharacteristic
149#124—431no—
150#123—861no—
151C22⋊Q8—431no—
152#121—431no—
153C4×Q8—431no—
154C4×D4—431no—
155C4×D4—861no—
156#117—861no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—861no—
159C2×C42—431no—
160#107—432no—
161#107C2×D4312yes—
162#106—432no—
163#106C2×D4312yes—
164C4⋊C8—432no—
165#103—432no—
166#103—432no—
167#102—432no—
168#102—432no—
169C22⋊C8—432no—
170#97—431no—
171#97C2×D4311yescharacteristic
172C2×Q8—21no—
173C2×Q8—431no—
174C2×Q8—862no—
175C2×Q8—861no—
176C2×Q8—1724no—
177C2×D4—431no—
178C2×D4—861no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—431no—
182C22×C4—861no—
183C22×C4—862no—
184C2×C8—432no—
185C2×C8C22×D4312yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—432no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—861no—
193C4⋊C4—861no—
194C4⋊C4—861no—
195C4⋊C4C22×D4312yes—
196C4⋊C4C22×D4311yescharacteristic
197C4⋊C4C22×D4311yescharacteristic
198C22⋊C4—861no—
199C22⋊C4—861no—
200C22⋊C4—861no—
201C22⋊C4—861no—
202C22⋊C4—861no—
203C42—431no—
204C42—431no—
205C42—431no—
206C42—861no—
207C42C22×D4311yescharacteristic
208C23—431no—
209C23—861no—
210Q8—42no—
211Q8—862no—
212Q8—1722no—
213Q8—1724no—
214D4—862no—
215D4—1722no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—431no—
220C2×C4—431no—
221C2×C4—431no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—861no—
226C2×C4—862no—
227C2×C4—1722no—
228C2×C4—1724no—
229C2×C4D4×D4311yescharacteristic
230C2×C4D4×D4311yescharacteristic
231C2×C4C23×D4311yescharacteristic
232C8—22no—
233C8—862no—
234C22—432no—
235C22—861no—
236C22—861no—
237C22—1721no—
238C22—1721no—
239C22—1721no—
240C22C2×D4×D4311yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—432no—
247C4—861no—
248C4—861no—
249C4—1722no—
250C4—1721no—
251C4#1306337312yes—
252C2—862no—
253C2—3441no—
254C2#1458347411yescharacteristic
255C2AGL(1,ℤ/8)×D4311yescharacteristic
256C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3239
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D43C2semidirect
3. #14583309C2semidirect
4. #14583261C2semidirect
5. #14583259C2semidirect
6. #14583236C2semidirect
8. #14583183C2semidirect
9. #14583178C2semidirect
10. #14582954C2semidirect
11. C43×#501C2semidirect
132. #501D43semidirect
140. C43#3239semidirect