Finite Group Databasebeta

← #135×Dic283 #49130034

Subgroups — #135×Dic283 #49130034

Order 36224.

500 conjugacy classes of subgroups; only the 225 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 225 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#41×Dic283C212yesmaximal, complemented
2Q16×Dic283C212yesmaximal, complemented
3SD16×Dic283C214yesmaximal, complemented
4D8×Dic283C212yesmaximal, complemented
5#31826503C211yesmaximal, characteristic, complemented
6#31826461C212yesmaximal, complemented
7C2×C8×Dic283C211yesmaximal, characteristic, complemented
8C2×#135×C283C211yesmaximal, characteristic
9C22×C283⋊C8C2211yescharacteristic
10Q8×Dic283C2214yes—
11D4×Dic283—24no—
12D4×Dic283C2214yes—
13#22583569—22no—
14#22583569C2212yes—
15C2×C4×Dic283—22no—
16C2×C4×Dic283C2211yescharacteristic
17#22583544C2212yes—
18#22583542C2212yes—
19#22583534C2214yes—
20#22583531C2214yes—
21C8×Dic283C2212yes—
22C8×Dic283C2212yes—
23C2×#41×C283C2212yes—
24#135×C283C418yescomplemented
25C2×Q16×C283C2211yescharacteristic
26C2×SD16×C283C2212yes—
27C2×D8×C283C2211yescharacteristic
28C22×C8×C283C2211yescharacteristic
29C22×Dic283—24no—
30C22×Dic283D412yes—
31C2×C283⋊C8—22no—
32C2×C283⋊C8C2312yes—
33C4⋊Dic283—24no—
34C4⋊Dic283C2314yes—
35C22⋊Dic283—24no—
36C22⋊Dic283—22no—
37C4×Dic283—24no—
38C4×Dic283—22no—
39C4×Dic283D411yescharacteristic
40C4×Dic283D411yescharacteristic
41C4×Dic283C2312yes—
42#41×C283—24no—
43#41×C283C2×C418yescomplemented
44C2×Q8×C283C2312yes—
45C2×D4×C283—22no—
46C2×D4×C283C2312yes—
47C22×C4×C283—22no—
48C22×C4×C283C2311yescharacteristic
49Q16×C283C2×C414yescomplemented
50SD16×C283C2×C418yescomplemented
51D8×C283C2×C414yescomplemented
52C2×C8×C283C2×C414yescomplemented
53C2×C8×C283C2311yescharacteristic
54C2×C8×C283C2311yescharacteristic
55C2×Dic283—24no—
56C2×Dic283—24no—
57C2×Dic283—48no—
58C2×Dic283C2×D412yes—
59C2×Dic283C2×D412yes—
60C283⋊C8—22no—
61C23×C283—22no—
62C23×C283C2×D411yescharacteristic
63Q8×C283—22no—
64Q8×C283C22×C414yes—
65D4×C283—28no—
66D4×C283—22no—
67D4×C283C22×C414yes—
68C2×C4×C283—22no—
69C2×C4×C283—28no—
70C2×C4×C283C22×C412yes—
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283#4112yes—
73C2×C4×C283C2411yescharacteristic
74C8×C283C22×C412yes—
75C8×C283C22×C412yes—
76C22×C283—22no—
77C22×C283—24no—
78C22×C283—44no—
79C22×C283C4×D412yes—
80C22×C283C22×D411yescharacteristic
81C4×C283—24no—
82C4×C283C4×D412yes—
83C4×C283C23×C411yescharacteristic
84C4×C283C2×#4111yescharacteristic
85Dic283—22no—
86Dic283—44no—
87Dic283#13514yesdirect product factor
88C2×C283—22no—
89C2×C283—44no—
90C2×C283C2×C4×D411yescharacteristic
91C2×C283C2×#13512yes—
92C283C4×#13511yescharacteristic, complemented, Sylow
93C4×#135—2831nomaximal, Sylow
94C2×#135D28311yescharacteristic
95C4×#41—2832no—
96C4×Q16—2832no—
97C4×SD16—2834no—
98C4×D8—2832no—
99#427—2831no—
100#416—2832no—
101C2×C4×C8—2831no—
102C2×#41C2×D28312yes—
103#135Dic28318yesdirect product factor
104C2×Q16C2×D28311yescharacteristic
105C2×SD16C2×D28312yes—
106C2×D8C2×D28311yescharacteristic
107C22×C8—2831no—
108C22×C8C2×D28311yescharacteristic
109C4×Q8—2834no—
110C4×D4—2834no—
111C4×D4—5664no—
112#117—2832no—
113#117—5662no—
114C2×C42—2831no—
115C2×C42—5662no—
116#107—2832no—
117#106—2832no—
118#103—2834no—
119#102—2834no—
120C4×C8—2832no—
121C4×C8—2832no—
122#41—24no—
123#41C2×Dic28318yescomplemented
124C2×Q8C22×D28312yes—
125C2×D4—22no—
126C2×D4C22×D28312yes—
127C22×C4—22no—
128C22×C4—2832no—
129C22×C4—5664no—
130C22×C4C22×D28311yescharacteristic
131Q16C2×Dic28314yescomplemented
132SD16C2×Dic28318yescomplemented
133D8C2×Dic28314yescomplemented
134C2×C8—2832no—
135C2×C8—5662no—
136C2×C8C2×Dic28314yescomplemented
137C2×C8C22×D28311yescharacteristic
138C2×C8C22×D28311yescharacteristic
139C4⋊C4—2834no—
140C4⋊C4—5664no—
141C22⋊C4—5664no—
142C22⋊C4—5662no—
143C42—2831no—
144C42—2831no—
145C42—2832no—
146C42—5664no—
147C42—5662no—
148C23—22no—
149C23D4×D28311yescharacteristic
150Q8—22no—
151Q8C22×Dic28314yes—
152D4—28no—
153D4—22no—
154D4C22×Dic28314yes—
155C2×C4—22no—
156C2×C4—28no—
157C2×C4—2832no—
158C2×C4—2832no—
159C2×C4—5664no—
160C2×C4—5664no—
161C2×C4—11328no—
162C2×C4C22×Dic28312yes—
163C2×C4D4×D28311yescharacteristic
164C2×C4#1798539112yes—
165C2×C4C23×D28311yescharacteristic
166C8—5662no—
167C8C22×Dic28312yes—
168C8C22×Dic28312yes—
169C22—22no—
170C22—24no—
171C22—44no—
172C22D4×Dic28312yes—
173C22C2×D4×D28311yescharacteristic
174C4—24no—
175C4—2834no—
176C4—5662no—
177C4—11324no—
178C4D4×Dic28312yes—
179C4C23×Dic28311yescharacteristic
180C4C2×#1798539111yescharacteristic
181C2—22no—
182C2—44no—
183C2C2×D4×Dic28311yescharacteristic
184C2#135×D28312yes—
subgroupG/H
centerC2×C4D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting, prime radicalC2×#135×C283C2
socleC22×C283C22×D4
cosocleC2×C4×C283C24
hypercenterC2×#135D283
hypocenterC283C4×#135
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. #41×Dic283C2semidirect
2. Q16×Dic283C2semidirect
3. SD16×Dic283C2semidirect
4. D8×Dic283C2semidirect
5. #31826503C2semidirect
6. #31826461C2semidirect
7. C2×C8×Dic283C2semidirect
24. #135×C283C4semidirect
43. #41×C283C2×C4semidirect
49. Q16×C283C2×C4semidirect
50. SD16×C283C2×C4semidirect
51. D8×C283C2×C4semidirect
52. C2×C8×C283C2×C4semidirect
87. Dic283#135direct (N × H)
92. C283C4×#135semidirect
103. #135Dic283direct (N × H)
123. #41C2×Dic283semidirect
131. Q16C2×Dic283semidirect
132. SD16C2×Dic283semidirect
133. D8C2×Dic283semidirect
136. C2×C8C2×Dic283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#41×Dic2832
Q16×Dic2832
SD16×Dic2832
D8×Dic2832
#318265032
#318264612
C2×C8×Dic2832
C2×#135×C2832
C4×#135283