Finite Group Databasebeta

← D53⋊#354 #20290984

Subgroups — D53⋊#354 #20290984

Order 6784.

284 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D53⋊#99C212yesmaximal
2#16811530C212yesmaximal, complemented
3#16811529C212yesmaximal, complemented
4#124×D53C211yesmaximal, characteristic
5C2×C22⋊#6157—22no—
6#13133276C2214yes—
7#13133275—22no—
8C2×Q8×D53C411yescharacteristic, complemented
9C2×D4×D53C2211yescharacteristic
10#13133206C2211yescharacteristic
11#13133205C2211yescharacteristic
12#13133204C411yescharacteristic, complemented
13#13133203—22no—
14C22⋊C4×D53—22no—
15C42×D53C411yescharacteristic, complemented
16#124×C53C411yescharacteristic, complemented
17C23×D53D412yes—
18C22×#6157—42no—
19C2×Q8×C53C2×C411yescharacteristic, complemented
20C2×D4×C53C2×C411yescharacteristic
21C2×C22⋊D53D412yes—
22Q8×D53—41no—
23Q8×D53—41no—
24D4×D53—41no—
25D4×D53—41no—
26C2×D212C2311yescharacteristic
27C2×C4×D53—21no—
28C2×C4×D53—21no—
29C2×C4×D53C2×C411yescharacteristic
30C2×Dic106—21no—
31C2×Dic106C2×C411yescharacteristic, complemented
32C22⋊#6157—24no—
33C22⋊#6157—42no—
34C22⋊C4×C53—22no—
35C42×C53C2×C411yescharacteristic, complemented
36C22⋊Dic53—22no—
37#11719921—22no—
38#11719921—22no—
39C4×Dic53—21no—
40C4×Dic53C2×C411yescharacteristic, complemented
41C23×C53C22⋊C412yes—
42C22×D53—22no—
43C22×D53—22no—
44C22×D53—44no—
45C22×D53C22⋊C411yescharacteristic
46C22×D53C2×D412yes—
47C2×#6157—44no—
48C2×#6157—84no—
49Q8×C53—41no—
50D4×C53—41no—
51C2×C4×C53—21no—
52C2×C4×C53—21no—
53C2×C4×C53C22×C411yescharacteristic
54C22⋊D53—42no—
55C2×Dic53—21no—
56C2×Dic53—21no—
57C2×Dic53C22⋊C411yescharacteristic
58D212—41no—
59C4×D53—21no—
60C4×D53—21no—
61C4×D53—42no—
62C4×D53—41no—
63C4×D53—41no—
64Dic106—42no—
65Dic106—41no—
66C22×C53—22no—
67C22×C53—42no—
68C22×C53C2×C22⋊C411yescharacteristic
69C2×D53—22no—
70C2×D53—22no—
71C2×D53—44no—
72C2×D53—42no—
73C2×D53—82no—
74C2×D53#9911yescharacteristic
75C2×D53#9911yescharacteristic
76#6157—84no—
77C4×C53—21no—
78C4×C53—41no—
79C4×C53—41no—
80Dic53—21no—
81Dic53—41no—
82Dic53—41no—
83C2×#354—531nomaximal, Sylow
84C2×C53—21no—
85C2×C53—42no—
86C2×C53C2×#9911yescharacteristic
87D53—21no—
88D53—42no—
89D53#35412yescomplemented
90C2×#124—531no—
91C2×#99—532no—
92#354—532no—
93#354—532no—
94C53C2×#35411yescharacteristic, complemented, Sylow
95C22×Q8—531no—
96C22×D4—531no—
97#124—531no—
98#124—531no—
99#124—531no—
100#124—1062no—
101#124#615711yescharacteristic, complemented
102C2×C22⋊C4—1062no—
103C2×C22⋊C4—1062no—
104C2×C42—531no—
105#99—534no—
106#99—1062no—
107C24—532no—
108C2×Q8—531no—
109C2×Q8—1061no—
110C2×Q8—2121no—
111C2×Q8—2121no—
112C2×Q8C2×#615711yescharacteristic, complemented
113C2×D4—532no—
114C2×D4—531no—
115C2×D4—2121no—
116C2×D4—2121no—
117C2×D4C2×#615711yescharacteristic
118C22×C4—531no—
119C22×C4—1061no—
120C22×C4—1061no—
121C22×C4—2122no—
122C22⋊C4—22no—
123C22⋊C4—1062no—
124C22⋊C4—1062no—
125C22⋊C4—1062no—
126C22⋊C4—1064no—
127C22⋊C4—2122no—
128C42—531no—
129C42—1061no—
130C42C2×#615711yescharacteristic, complemented
131C23—531no—
132C23—532no—
133C23—1062no—
134C23—1062no—
135C23—2124no—
136C23C22⋊#615712yes—
137Q8—41no—
138Q8—2121no—
139Q8—2122no—
140D4—41no—
141D4—2121no—
142D4—2122no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—531no—
146C2×C4—1061no—
147C2×C4—1061no—
148C2×C4—1061no—
149C2×C4—1061no—
150C2×C4—4244no—
151C2×C4—2121no—
152C2×C4—2121no—
153C2×C4—2122no—
154C2×C4—2124no—
155C2×C4C22×#615711yescharacteristic
156C22—22no—
157C22—42no—
158C22—531no—
159C22—531no—
160C22—1062no—
161C22—1062no—
162C22—4242no—
163C22—2122no—
164C22—2124no—
165C22C2×C22⋊#615711yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—1061no—
170C4—4244no—
171C4—2121no—
172C4—2121no—
173C2—21no—
174C2—42no—
175C2—532no—
176C2—1061no—
177C2—2122no—
178C2D53⋊#9911yescharacteristic
subgroupG/H
centerC2D53⋊#99
commutatorC2×C4×C53C22×C4
FrattiniC2×C4C22×#6157
Fitting#124×C53C4
socleC2×C53C2×#99
hypercenter#124#6157
hypocenterC53C2×#354
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #16811530C2semidirect
3. #16811529C2semidirect
8. C2×Q8×D53C4semidirect
12. #13133204C4semidirect
15. C42×D53C4semidirect
16. #124×C53C4semidirect
19. C2×Q8×C53C2×C4semidirect
31. C2×Dic106C2×C4semidirect
35. C42×C53C2×C4semidirect
40. C4×Dic53C2×C4semidirect
89. D53#354semidirect
94. C53C2×#354semidirect
101. #124#6157semidirect
112. C2×Q8C2×#6157semidirect
130. C42C2×#6157semidirect