Finite Group Databasebeta

← #20273277

Subgroups — #20273277

Order 6784.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#16811175C211yesmaximal, characteristic
2#16810673C211yesmaximal, characteristic
3#16810487C211yesmaximal, characteristic
4#16810361C211yesmaximal, characteristic
5#16810360C211yesmaximal, characteristic
6#16810359C211yesmaximal, characteristic
7C53×#328C211yesmaximal, characteristic
8#13133216C411yescharacteristic, complemented
9#13133215C411yescharacteristic, complemented
10#13133207—21no—
11#13133196C2211yescharacteristic
12#13133194—21no—
13Q8×Dic53C411yescharacteristic, complemented
14#13133182—21no—
15#13133182C411yescharacteristic, complemented
16#13133173—21no—
17C2×#11719919—21no—
18C2×C4×Dic53C2211yescharacteristic
19#13133146—21no—
20C22⋊#88322C2211yescharacteristic
21C8×Dic53—21no—
22#13133124—21no—
23#13133124C2211yescharacteristic
24C22⋊Q8×C53C2211yescharacteristic
25C22⋊C8×C53C2211yescharacteristic
26#95×C53C2211yescharacteristic
27C2×Q8×C53C2×C411yescharacteristic
28C22×C4×C53—21no—
29C22×C4×C53C2311yescharacteristic
30C22×Dic53—21no—
31C22×Dic53D411yescharacteristic
32C22×Dic53D411yescharacteristic
33C2×Dic106—21no—
34C2×Dic106C2×C411yescharacteristic
35C2×C8×C53—21no—
36C4⋊C4×C53—21no—
37C4⋊C4×C53C2×C411yescharacteristic
38C22⋊C4×C53—21no—
39C22⋊Dic53—21no—
40C4⋊Dic53—21no—
41C4⋊Dic53C2×C411yescharacteristic
42#11719919—21no—
43#11719919—21no—
44#11719919—21no—
45#11719919—21no—
46#11719919—21no—
47#11719919—42no—
48C4×Dic53—21no—
49C4×Dic53—21no—
50C4×Dic53C2×C411yescharacteristic
51C4×Dic53C2×C411yescharacteristic
52C4×Dic53D411yescharacteristic
53C4×Dic53D411yescharacteristic
54C2×#88322—21no—
55C23×C53C2×D411yescharacteristic
56Q8×C53—41no—
57C2×C4×C53—21no—
58C2×C4×C53—21no—
59C2×C4×C53—41no—
60C2×C4×C53—41no—
61C2×C4×C53—41no—
62C2×C4×C53—41no—
63C2×C4×C53C22×C411yescharacteristic
64C2×C4×C53C2×D411yescharacteristic
65C2×Dic53—21no—
66C2×Dic53—21no—
67C2×Dic53—41no—
68C2×Dic53—41no—
69C2×Dic53—41no—
70C2×Dic53—41no—
71C2×Dic53C22⋊C411yescharacteristic
72C2×Dic53C22⋊C411yescharacteristic
73C2×Dic53C22⋊C411yescharacteristic
74C2×Dic53C22⋊C411yescharacteristic
75C2×Dic53SD1612yes—
76C2×Dic53Q1612yes—
77Dic106—42no—
78Dic106—41no—
79C8×C53—41no—
80#88322—41no—
81C22×C53—21no—
82C22×C53—21no—
83C22×C53C2×C22⋊C411yescharacteristic
84C22×C53C2×SD1611yescharacteristic
85C22×C53C2×Q1611yescharacteristic
86C4×C53—21no—
87C4×C53—21no—
88C4×C53—41no—
89C4×C53—41no—
90C4×C53—81no—
91Dic53—21no—
92Dic53—21no—
93Dic53—41no—
94Dic53—41no—
95Dic53—81no—
96Dic53#10312yes—
97Dic53#10312yes—
98#1518—531nomaximal, Sylow
99C2×C53—21no—
100C2×C53—21no—
101C2×C53#41011yescharacteristic
102C2×C53C2×#10311yescharacteristic
103C2×C53#42111yescharacteristic
104#533—531no—
105#431—531no—
106#382—531no—
107#328—531no—
108#328—531no—
109#328—531no—
110#328D5311yescharacteristic
111C53#151811yescharacteristic, complemented, Sylow
112C4⋊Q8—531no—
113C4⋊Q8—531no—
114#125—1061no—
115C22⋊Q8—531no—
116C22⋊Q8—1061no—
117C22⋊Q8C2×D5311yescharacteristic
118C4×Q8—531no—
119C4×Q8—531no—
120C4×Q8—1061no—
121#117—1061no—
122C2×C4⋊C4—1061no—
123C2×C42—531no—
124C4⋊C8—1061no—
125C22⋊C8—531no—
126C22⋊C8C2×D5311yescharacteristic
127C4×C8—1061no—
128#95—531no—
129#95—1061no—
130#95C2×D5311yescharacteristic
131C2×Q8—531no—
132C2×Q8—1061no—
133C2×Q8C4×D5311yescharacteristic
134C22×C4—21no—
135C22×C4—531no—
136C22×C4—531no—
137C22×C4—1061no—
138C22×C4C22×D5311yescharacteristic
139C2×C8—21no—
140C2×C8—1061no—
141C4⋊C4—21no—
142C4⋊C4—531no—
143C4⋊C4—1061no—
144C4⋊C4—1061no—
145C4⋊C4—1061no—
146C4⋊C4—1061no—
147C4⋊C4—1061no—
148C4⋊C4—1061no—
149C4⋊C4—2122no—
150C4⋊C4C4×D5311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1061no—
153C42—531no—
154C42—531no—
155C42—531no—
156C42—531no—
157C42—1061no—
158C42—1061no—
159C23D4×D5311yescharacteristic
160Q8—41no—
161Q8—2121no—
162Q8—2122no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—531no—
170C2×C4—531no—
171C2×C4—532no—
172C2×C4—532no—
173C2×C4—531no—
174C2×C4—531no—
175C2×C4—1061no—
176C2×C4—1061no—
177C2×C4—2121no—
178C2×C4—2121no—
179C2×C4—2121no—
180C2×C4—2121no—
181C2×C4C2×C4×D5311yescharacteristic
182C2×C4D4×D5311yescharacteristic
183C8—41no—
184C8—2121no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D5311yescharacteristic
188C22SD16×D5311yescharacteristic
189C22Q16×D5311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—532no—
196C4—532no—
197C4—1061no—
198C4—1061no—
199C4—4241no—
200C4—2121no—
201C4—2121no—
202C2—21no—
203C2—21no—
204C2#1681059511yescharacteristic
205C2#103×D5311yescharacteristic
206C2#1681063811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D53
commutatorC2×C4×C53C22×C4
FrattiniC22×C4C22×D53
FittingC53×#328C2
socleC22×C53C2×C22⋊C4
hypercenter#328D53
hypocenterC53#1518
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #13133216C4semidirect
9. #13133215C4semidirect
13. Q8×Dic53C4semidirect
15. #13133182C4semidirect
111. C53#1518semidirect