Finite Group Databasebeta

← #487×D53 #20285023

Subgroups — #487×D53 #20285023

Order 6784.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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×D53C211yesmaximal, characteristic
2C4⋊Q8×D53C211yesmaximal, characteristic
3#16810975C211yesmaximal, characteristic, complemented
4#16810974C211yesmaximal, characteristic, complemented
5#16810973C211yesmaximal, characteristic, complemented
6#16810972C214yesmaximal, complemented
7#103×D53C214yesmaximal
8C4×C8×D53C211yesmaximal, characteristic
9C53×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D53—21no—
11C2×Q8×D53C2212yes—
12C2×C8×D53C2212yes—
13#13133217C2211yescharacteristic
14#13133217C2211yescharacteristic
15#13133216—21no—
16#13133216—21no—
17#13133216—21no—
18#13133216C2212yes—
19#13133215—21no—
20#13133215C2212yes—
21C4⋊C4×D53—21no—
22C4⋊C4×D53—21no—
23C4⋊C4×D53—21no—
24C4⋊C4×D53C2212yes—
25C42×D53C2211yescharacteristic
26#13133142C2214yes—
27#13133141C2214yes—
28#13133140C2214yes—
29C4×#88322C2211yescharacteristic
30C8×Dic53C2212yes—
31C4⋊Q8×C53C2211yescharacteristic
32C4⋊Q8×C53C2211yescharacteristic
33#103×C53C2214yes—
34C4×C8×C53C2211yescharacteristic
35C2×Q8×C53—21no—
36C2×Q8×C53C2312yes—
37Q8×D53—28no—
38Q8×D53—44no—
39C2×C4×D53—22no—
40C2×C4×D53—22no—
41C2×C4×D53D411yescharacteristic
42C2×C4×D53D411yescharacteristic
43C2×C4×D53C2311yescharacteristic
44C2×Dic106—21no—
45C2×Dic106—22no—
46C2×Dic106—22no—
47C2×Dic106C2312yes—
48C2×C8×C53C2312yes—
49C4⋊C4×C53—21no—
50C4⋊C4×C53—21no—
51C4⋊C4×C53—21no—
52C4⋊C4×C53C2312yes—
53C42×C53C2311yescharacteristic
54C4⋊Dic53—21no—
55C4⋊Dic53—21no—
56C4⋊Dic53—21no—
57C4⋊Dic53C2312yes—
58#11719919—22no—
59#11719919—22no—
60#11719919—22no—
61#11719919—22no—
62C4×Dic53D411yescharacteristic
63C4×Dic53D411yescharacteristic
64C4×Dic53C2311yescharacteristic
65C2×#88322C2312yes—
66C8×D53—24no—
67C22×D53C2×D411yescharacteristic
68Q8×C53—24no—
69Q8×C53—42no—
70C2×C4×C53—22no—
71C2×C4×C53—22no—
72C2×C4×C53C2×D411yescharacteristic
73C2×C4×C53C2×D411yescharacteristic
74C2×C4×C53C2411yescharacteristic
75C2×Dic53—22no—
76C2×Dic53—22no—
77C2×Dic53C2×D411yescharacteristic
78C2×Dic53C2×D411yescharacteristic
79C2×Dic53C2×D411yescharacteristic
80C4×D53—44no—
81C4×D53—44no—
82C4×D53SD1614yes—
83C4×D53Q1614yes—
84C4×D53#4114yes—
85Dic106—24no—
86Dic106—42no—
87Dic106—44no—
88Dic106—44no—
89C8×C53—22no—
90#88322—22no—
91C22×C53C22×D411yescharacteristic
92C2×D53#12412yes—
93C2×D53C2×SD1612yes—
94C2×D53C2×Q1612yes—
95C4×C53—42no—
96C4×C53—42no—
97C4×C53C2×SD1612yes—
98C4×C53C2×Q1612yes—
99C4×C53C2×#4112yes—
100Dic53—42no—
101Dic53—42no—
102Dic53#12412yes—
103Dic53C2×SD1612yes—
104Dic53C2×Q1612yes—
105C2×#487—531nomaximal, Sylow
106C2×C53C2×#12411yescharacteristic
107C2×C53C22×SD1611yescharacteristic
108C2×C53C22×Q1611yescharacteristic
109D53#48714yesdirect product factor
110C2×C4⋊Q8—531no—
111C2×C4⋊Q8—531no—
112#487—531no—
113#487—531no—
114#487—534no—
115#487—531no—
116#487D5311yescharacteristic, direct product factor
117C2×#103—534no—
118C2×C4×C8—531no—
119C53C2×#48711yescharacteristic, complemented, Sylow
120C22×Q8—532no—
121C22×Q8—1061no—
122C22×C8—532no—
123C4⋊Q8—532no—
124C4⋊Q8—532no—
125C4⋊Q8—531no—
126C4⋊Q8—531no—
127C4⋊Q8—1061no—
128C4⋊Q8—1061no—
129C4⋊Q8—1061no—
130C4⋊Q8—1061no—
131C4⋊Q8C2×D5311yescharacteristic
132C4⋊Q8C2×D5311yescharacteristic
133C2×C4⋊C4—532no—
134C2×C4⋊C4—1061no—
135C2×C4⋊C4—1061no—
136C2×C4⋊C4—1061no—
137C2×C42—531no—
138#103—534no—
139#103—534no—
140#103—534no—
141#103C2×D5314yes—
142C4×C8—532no—
143C4×C8—531no—
144C4×C8C2×D5311yescharacteristic
145C2×Q8—21no—
146C2×Q8—532no—
147C2×Q8—1062no—
148C2×Q8—1062no—
149C2×Q8—1068no—
150C2×Q8—1061no—
151C2×Q8—2124no—
152C2×Q8C22×D5312yes—
153C22×C4—531no—
154C22×C4—531no—
155C22×C4—531no—
156C22×C4—1062no—
157C22×C4—1062no—
158C2×C8—532no—
159C2×C8—1064no—
160C2×C8C22×D5312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—532no—
165C4⋊C4—1062no—
166C4⋊C4—1062no—
167C4⋊C4—1062no—
168C4⋊C4—1062no—
169C4⋊C4—1061no—
170C4⋊C4—1061no—
171C4⋊C4—1061no—
172C4⋊C4C22×D5312yes—
173C42—531no—
174C42—531no—
175C42—531no—
176C42C22×D5311yescharacteristic
177C23—531no—
178Q8—24no—
179Q8—42no—
180Q8—1064no—
181Q8—2124no—
182Q8—2124no—
183Q8—2122no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—531no—
187C2×C4—531no—
188C2×C4—531no—
189C2×C4—534no—
190C2×C4—534no—
191C2×C4—534no—
192C2×C4—1062no—
193C2×C4—1062no—
194C2×C4—2124no—
195C2×C4—2124no—
196C2×C4D4×D5311yescharacteristic
197C2×C4D4×D5311yescharacteristic
198C2×C4C23×D5311yescharacteristic
199C8—22no—
200C8—1062no—
201C22—532no—
202C22—532no—
203C22—532no—
204C22C2×D4×D5311yescharacteristic
205C4—42no—
206C4—42no—
207C4—532no—
208C4—532no—
209C4—532no—
210C4—2122no—
211C4—2122no—
212C4SD16×D5312yes—
213C4Q16×D5312yes—
214C4#41×D5312yes—
215C2—534no—
216C2#124×D5311yescharacteristic
217C2C2×SD16×D5311yescharacteristic
218C2C2×Q16×D5311yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC2×C4×C53C24
FrattiniC2×C4C23×D53
FittingC53×#487C2
socleC22×C53C22×D4
hypercenter#487D53
hypocenterC53C2×#487
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16810975C2semidirect
4. #16810974C2semidirect
5. #16810973C2semidirect
6. #16810972C2semidirect
9. C53×#487C2semidirect
109. D53#487direct (N × H)
116. #487D53direct (N × H)
119. C53C2×#487semidirect