Finite Group Databasebeta

← #20276284

Subgroups — #20276284

Order 6784.

198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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#16810521C211yesmaximal, characteristic
2#16810489C211yesmaximal, characteristic
3#16810386C211yesmaximal, characteristic
4#16810386C211yesmaximal, characteristic
5#16810386C211yesmaximal, characteristic
6#16810386C211yesmaximal, characteristic
7C53×#336C211yesmaximal, characteristic
8C2×C4⋊Dic53C2211yescharacteristic
9C2×C4⋊Dic53C2211yescharacteristic
10C2×C4⋊Dic53C2211yescharacteristic
11C2×C4⋊Dic53C2211yescharacteristic
12C2×#11719919—21no—
13#13133124—21no—
14#13133124—21no—
15#13133124—21no—
16C22×C8×C53C2211yescharacteristic
17C22×C8×C53C2211yescharacteristic
18C2×C42×C53C2211yescharacteristic
19C22×C4×C53D411yescharacteristic
20C22×C4×C53D411yescharacteristic
21C22×C4×C53C2311yescharacteristic
22C22×Dic53—21no—
23C22×Dic53—21no—
24C22×Dic53—21no—
25C22×Dic53—21no—
26C2×C8×C53—21no—
27C2×C8×C53—21no—
28C2×C8×C53—21no—
29C2×C8×C53—21no—
30C2×C8×C53—21no—
31C2×C8×C53—21no—
32C42×C53—21no—
33C42×C53—21no—
34C4⋊Dic53—21no—
35C4⋊Dic53—21no—
36C4⋊Dic53—21no—
37C4⋊Dic53—21no—
38C4⋊Dic53—21no—
39C4⋊Dic53—21no—
40C4⋊Dic53—21no—
41C4⋊Dic53Q812yes—
42#11719919—42no—
43C23×C53C2×D411yescharacteristic
44C2×C4×C53—21no—
45C2×C4×C53—21no—
46C2×C4×C53—21no—
47C2×C4×C53—21no—
48C2×C4×C53—21no—
49C2×C4×C53—21no—
50C2×C4×C53C2×Q811yescharacteristic
51C2×C4×C53#4111yescharacteristic
52C2×C4×C53#4111yescharacteristic
53C2×C4×C53#4111yescharacteristic
54C2×C4×C53#4111yescharacteristic
55C2×C4×C53#4111yescharacteristic
56C2×Dic53—22no—
57C2×Dic53—41no—
58C2×Dic53—41no—
59C2×Dic53—41no—
60C2×Dic53—41no—
61C2×Dic53—41no—
62C2×Dic53—41no—
63C2×Dic53—41no—
64C2×Dic53—41no—
65C2×Dic53—41no—
66C2×Dic53—41no—
67C2×Dic53—41no—
68C8×C53—41no—
69C8×C53—41no—
70C22×C53C22⋊Q811yescharacteristic
71C22×C53#12311yescharacteristic
72C22×C53#12411yescharacteristic
73C22×C53#13511yescharacteristic
74C22×C53#13511yescharacteristic
75C22×C53AGL(1,ℤ/8)11yescharacteristic
76C22×C53#13711yescharacteristic
77C4×C53—41no—
78C4×C53—41no—
79C4×C53#12511yescharacteristic
80C4×C53#12511yescharacteristic
81C4×C53#12611yescharacteristic
82C4×C53#12611yescharacteristic
83Dic53—42no—
84Dic53—81no—
85Dic53—81no—
86Dic53—81no—
87#2101—531nomaximal, Sylow
88C2×C53#40011yescharacteristic
89C2×C53#47811yescharacteristic
90C2×C53#47911yescharacteristic
91C2×C53#48211yescharacteristic
92C2×C53#48511yescharacteristic
93C2×C53#48811yescharacteristic
94C2×C53#48911yescharacteristic
95#389—531no—
96#382—531no—
97#340—531no—
98#340—531no—
99#340—531no—
100#340—531no—
101#336D5311yescharacteristic
102C53#210111yescharacteristic, complemented, Sylow
103C22×C8C2×D5311yescharacteristic
104C22×C8C2×D5311yescharacteristic
105C2×C4⋊C4—531no—
106C2×C4⋊C4—531no—
107C2×C4⋊C4—531no—
108C2×C4⋊C4—531no—
109C2×C4⋊C4—1061no—
110C2×C42C2×D5311yescharacteristic
111#95—1061no—
112#95—1061no—
113#95—1061no—
114C22×C4—1061no—
115C22×C4—1061no—
116C22×C4—1061no—
117C22×C4—1061no—
118C22×C4D21211yescharacteristic
119C22×C4D21211yescharacteristic
120C22×C4C22×D5311yescharacteristic
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C4⋊C4—532no—
128C4⋊C4—1061no—
129C4⋊C4—1061no—
130C4⋊C4—1061no—
131C4⋊C4—1061no—
132C4⋊C4—1061no—
133C4⋊C4—1061no—
134C4⋊C4—1061no—
135C4⋊C4—2122no—
136C42—21no—
137C42—21no—
138C23C2×D21211yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—1062no—
146C2×C4—2121no—
147C2×C4—2121no—
148C2×C4—2121no—
149C2×C4—2121no—
150C2×C4—2121no—
151C2×C4—2121no—
152C2×C4—2121no—
153C2×C4—2121no—
154C2×C4—2121no—
155C2×C4—2121no—
156C2×C4—2121no—
157C2×C4#1171994511yescharacteristic
158C2×C4#1171994511yescharacteristic
159C2×C4#1171994711yescharacteristic
160C2×C4#1171994711yescharacteristic
161C2×C4#1171994711yescharacteristic
162C2×C4Q8×D5311yescharacteristic
163C8—41no—
164C8—41no—
165C22#1313319711yescharacteristic
166C22#1313320111yescharacteristic
167C22#1313320511yescharacteristic
168C22#1313323911yescharacteristic
169C22#1313323911yescharacteristic
170C22#1313324511yescharacteristic
171C22#1313325011yescharacteristic
172C4—41no—
173C4—41no—
174C4—4241no—
175C4—4241no—
176C4—4241no—
177C4—2122no—
178C4#1313320711yescharacteristic
179C4#1313320711yescharacteristic
180C4#1313321011yescharacteristic
181C4#1313321011yescharacteristic
182C2#1681056311yescharacteristic
183C2#1681092411yescharacteristic
184C2#1681093111yescharacteristic
185C2#1681094811yescharacteristic
186C2#1681096511yescharacteristic
187C2#1681097811yescharacteristic
188C2#1681098311yescharacteristic
subgroupG/H
centerC23C2×D212
commutatorC22×C4×C53C23
FrattiniC22×C4C22×D53
FittingC53×#336C2
socleC23×C53C2×D4
hypercenter#336D53
hypocenterC53#2101
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
102. C53#2101semidirect