Finite Group Databasebeta

← #49131727

Subgroups — #49131727

Order 36224.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#22583643C212yesmaximal, complemented
2C2×#22583638C212yesmaximal, complemented
3#31827015C211yesmaximal, characteristic, complemented
4C2×#22583598C211yesmaximal, characteristic, complemented
5#31826859C212yesmaximal, complemented
6#31826854C212yesmaximal, complemented
7#31826849C214yesmaximal, complemented
8C4×M16×C283C211yesmaximal, characteristic, complemented
9C2×#17985392C2212yes—
10C22×Dic566C2211yescharacteristic
11C22×D1132C2211yescharacteristic
12#22583643—28no—
13#22583638—28no—
14C2×Dic1132C2214yescomplemented
15C2×#17985381C2214yes—
16C2×#17985381C2214yescomplemented
17C2×D2264C2214yes—
18#22583610C2211yescharacteristic, complemented
19#22583607C2211yescharacteristic, complemented
20#22583598—22no—
21#22583598C2212yes—
22#22583598C2212yes—
23#22583598C2212yescomplemented
24#22583584—22no—
25C4×D1132—22no—
26C2×(C2×D283)⋊C4—22no—
27C2×M16×C283C2212yes—
28C2×C42×C283C2211yescharacteristic
29#97×C283C2212yescomplemented
30C4×C8×C283C2212yescomplemented
31C23×D283—21no—
32#17985392—24no—
33#17985392—24no—
34C2×Dic566—21no—
35C2×Dic566—24no—
36C2×Dic566C2312yes—
37C2×Dic566C2312yes—
38C2×D1132—24no—
39C2×D1132—22no—
40C2×D1132—21no—
41C2×D1132C2312yes—
42C2×D1132C2312yes—
43C2×C22⋊D283—22no—
44C22×Dic283—21no—
45C2×C4×D283—22no—
46Dic1132—28no—
47#17985381—28no—
48#17985381—28no—
49D2264—28no—
50C4⋊Dic283—22no—
51(C2×D283)⋊C4—24no—
52(C2×D283)⋊C4—24no—
53(C2×D283)⋊C4—24no—
54C22×C4×C283D412yes—
55C22×C4×C283C2311yescharacteristic
56M16×C283D418yescomplemented
57C2×C8×C283C2314yes—
58C42×C283D412yes—
59C42×C283C2311yescharacteristic
60C42×C283C2311yescharacteristic
61C22×D283—22no—
62C22×D283—22no—
63C22×D283—44no—
64C22×D283—42no—
65Dic566—22no—
66Dic566—24no—
67Dic566—22no—
68Dic566—42no—
69D1132—22no—
70D1132—24no—
71D1132—22no—
72D1132—44no—
73D1132—42no—
74C22⋊D283—44no—
75C2×Dic283—22no—
76C2×Dic283—22no—
77C2×Dic283—42no—
78C4×D283—44no—
79C23×C283C2×D411yescharacteristic
80C2×C4×C283—42no—
81C2×C4×C283C2×D412yes—
82C2×C4×C283C2×D412yes—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D414yes—
85C2×C4×C283C2411yescharacteristic
86C8×C283C2×D418yes—
87C22×C283—22no—
88C22×C283#12712yes—
89C22×C283C22×D411yescharacteristic
90C2×D283—42no—
91C2×D283—42no—
92C2×D283—44no—
93C2×D283—44no—
94C2×D283—84no—
95C4×C283—22no—
96C4×C283—22no—
97C4×C283#12712yes—
98C4×C283C22×D412yes—
99Dic283—42no—
100Dic283—42no—
101C2×C283—22no—
102C2×C283C2×#12711yescharacteristic
103C2×C283#57512yes—
104D283—82no—
105D283—82no—
106C283#315311yescharacteristic, complemented, Sylow
107#3153—2831nomaximal, Sylow
108C2×#137—2832no—
109C2×AGL(1,ℤ/8)—2832no—
110#532—2831no—
111C2×#124—2831no—
112#497—2832no—
113#496—2832no—
114#495—2834no—
115C4×M16D28311yescharacteristic, complemented
116C2×#41—2832no—
117C22×Q8—2831no—
118C22×D4—2831no—
119#137—5668no—
120AGL(1,ℤ/8)—5668no—
121C2×Q16—2834no—
122C2×SD16—2834no—
123C2×SD16—2834no—
124C2×D8—2834no—
125C2×M16C2×D28312yes—
126C4⋊Q8—2831no—
127#127—2831no—
128#124—2832no—
129#124—2832no—
130#124—2832no—
131#124—5662no—
132#121—5662no—
133C4×D4—5662no—
134C2×C22⋊C4—5662no—
135C2×C42C2×D28311yescharacteristic
136#97C2×D28312yescomplemented
137C4×C8C2×D28312yescomplemented
138C24—5661no—
139#41—5664no—
140#41—5664no—
141C2×Q8—2832no—
142C2×Q8—2832no—
143C2×Q8—5661no—
144C2×Q8—5664no—
145C2×D4—2832no—
146C2×D4—2832no—
147C2×D4—5662no—
148C2×D4—5664no—
149C2×D4—5662no—
150C2×D4—5661no—
151C22×C4—5661no—
152C22×C4—5662no—
153C22×C4D113212yes—
154C22×C4C22×D28311yescharacteristic
155Q16—5668no—
156SD16—5668no—
157SD16—5668no—
158D8—5668no—
159M16D113218yescomplemented
160C2×C8C22×D28314yes—
161C4⋊C4—5662no—
162C22⋊C4—5664no—
163C22⋊C4—5664no—
164C22⋊C4—5664no—
165C42D113212yes—
166C42C22×D28311yescharacteristic
167C42C22×D28311yescharacteristic
168C23—5662no—
169C23—5662no—
170C23—11324no—
171C23—11322no—
172C23C2×D113211yescharacteristic
173Q8—5662no—
174Q8—5664no—
175Q8—5662no—
176Q8—11322no—
177D4—5662no—
178D4—5664no—
179D4—5662no—
180D4—11324no—
181D4—11324no—
182D4—11322no—
183C2×C4—42no—
184C2×C4—5662no—
185C2×C4—5662no—
186C2×C4—11322no—
187C2×C4—11324no—
188C2×C4C2×D113212yes—
189C2×C4C2×D113212yes—
190C2×C4C2×D113211yescharacteristic
191C2×C4C2×D113214yes—
192C2×C4C23×D28311yescharacteristic
193C8C2×D113218yes—
194C22—22no—
195C22—11322no—
196C22—11322no—
197C22—11324no—
198C22—11324no—
199C22—22644no—
200C22#2258360712yes—
201C22C22×D113211yescharacteristic
202C4—22no—
203C4—22no—
204C4—11322no—
205C4—11322no—
206C4#2258360712yes—
207C4C22×D113212yes—
208C2—22no—
209C2—22642no—
210C2—22642no—
211C2C2×#2258360711yescharacteristic
212C2#3182726512yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×M16×C283C2
socleC22×C283C22×D4
hypercenterC4×M16D283
hypocenterC283#3153
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#22583643C2semidirect
2. C2×#22583638C2semidirect
3. #31827015C2semidirect
4. C2×#22583598C2semidirect
5. #31826859C2semidirect
6. #31826854C2semidirect
7. #31826849C2semidirect
8. C4×M16×C283C2semidirect
14. C2×Dic1132C22semidirect
16. C2×#17985381C22semidirect
18. #22583610C22semidirect
19. #22583607C22semidirect
23. #22583598C22semidirect
29. #97×C283C22semidirect
30. C4×C8×C283C22semidirect
56. M16×C283D4semidirect
106. C283#3153semidirect
115. C4×M16D283semidirect
136. #97C2×D283semidirect
137. C4×C8C2×D283semidirect
159. M16D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C2×#225836382
#318270152
C2×#225835982
#318268592
#318268542
#318268492
C4×M16×C2832
#3153283