Finite Group Databasebeta

← #49131725

Subgroups — #49131725

Order 36224.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583641C212yesmaximal, complemented
2C2×#22583636C212yesmaximal, complemented
3#31827015C211yesmaximal, characteristic, complemented
4#31826860C212yesmaximal, complemented
5#31826855C212yesmaximal, complemented
6#31826847C214yesmaximal, complemented
7C4×#17985376C211yesmaximal, characteristic, complemented
8C2×#124×C283C211yesmaximal, characteristic, complemented
9C2×#17985392C2212yes—
10#22583641—28no—
11#22583636—28no—
12C2×#17985382C2214yescomplemented
13C2×#17985380C2214yes—
14C2×#17985379C2214yescomplemented
15C2×#17985377C2214yes—
16C2×#17985376C2212yes—
17#22583610C2211yescharacteristic, complemented
18#22583607C2211yescharacteristic, complemented
19#22583598C2212yescomplemented
20#22583584—22no—
21C4×D1132—22no—
22#22583521C2212yescomplemented
23C4×C283⋊C8C2212yescomplemented
24C22×Q8×C283C2211yescharacteristic
25C22×D4×C283C2211yescharacteristic
26#124×C283—22no—
27#124×C283C2212yes—
28#124×C283C2212yes—
29C2×C22⋊C4×C283—22no—
30C2×C42×C283C2211yescharacteristic
31#17985392—24no—
32#17985392—24no—
33C2×Dic566C2312yes—
34C2×D1132—22no—
35C2×D1132C2312yes—
36C2×C22⋊D283—22no—
37C2×C4×D283—22no—
38#17985382—28no—
39#17985380—28no—
40#17985379—28no—
41#17985377—28no—
42#17985376D418yescomplemented
43C2×C283⋊C8C2314yes—
44C4⋊Dic283—22no—
45(C2×D283)⋊C4—24no—
46C24×C283—21no—
47C2×Q8×C283—21no—
48C2×Q8×C283—24no—
49C2×Q8×C283C2312yes—
50C2×D4×C283—24no—
51C2×D4×C283—21no—
52C2×D4×C283C2312yes—
53C22×C4×C283—21no—
54C22×C4×C283D412yes—
55C22×C4×C283C2311yescharacteristic
56C22⋊C4×C283—24no—
57C22⋊C4×C283—24no—
58C42×C283D412yes—
59C42×C283C2311yescharacteristic
60C42×C283C2311yescharacteristic
61C22×D283—22no—
62Dic566—22no—
63Dic566—22no—
64D1132—22no—
65D1132—22no—
66D1132—44no—
67C22⋊D283—44no—
68C2×Dic283—22no—
69C4×D283—44no—
70C283⋊C8C2×D418yes—
71C23×C283—22no—
72C23×C283—44no—
73C23×C283—42no—
74C23×C283C2×D411yescharacteristic
75Q8×C283—24no—
76Q8×C283—42no—
77D4×C283—24no—
78D4×C283—42no—
79C2×C4×C283—22no—
80C2×C4×C283—42no—
81C2×C4×C283—42no—
82C2×C4×C283C2×D414yes—
83C2×C4×C283C2×D412yes—
84C2×C4×C283C2×D412yes—
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283C2411yescharacteristic
87C22×C283—22no—
88C22×C283—42no—
89C22×C283—44no—
90C22×C283—84no—
91C22×C283#12712yes—
92C22×C283C22×D411yescharacteristic
93C2×D283—42no—
94C2×D283—44no—
95C4×C283—22no—
96C4×C283—22no—
97C4×C283—42no—
98C4×C283#12712yes—
99C4×C283C22×D412yes—
100Dic283—42no—
101C2×C283—22no—
102C2×C283—82no—
103C2×C283C2×#12711yescharacteristic
104C2×C283#57512yes—
105D283—82no—
106C283#315311yescharacteristic, complemented, Sylow
107#3153—2831nomaximal, Sylow
108C2×#137—2832no—
109C2×AGL(1,ℤ/8)—2832no—
110#532—2831no—
111C2×#124D28311yescharacteristic, complemented
112#497—2832no—
113#496—2832no—
114#495—2834no—
115C4×M16—2831no—
116C2×#41—2832no—
117C22×Q8C2×D28311yescharacteristic
118C22×D4C2×D28311yescharacteristic
119#137—5668no—
120AGL(1,ℤ/8)—5668no—
121C2×Q16—2834no—
122C2×SD16—2834no—
123C2×SD16—2834no—
124C2×D8—2834no—
125C2×M16—2832no—
126C4⋊Q8—2831no—
127#127—2831no—
128#124—22no—
129#124—2832no—
130#124C2×D28312yes—
131#124C2×D28312yes—
132#121—5662no—
133C4×D4—5662no—
134C2×C22⋊C4—22no—
135C2×C42C2×D28311yescharacteristic
136#97—2832no—
137C4×C8—2832no—
138C24—21no—
139#41—5664no—
140#41—5664no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—2832no—
144C2×Q8C22×D28312yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—2832no—
148C2×D4—5662no—
149C2×D4—5662no—
150C2×D4C22×D28312yes—
151C22×C4—21no—
152C22×C4—5662no—
153C22×C4C22⋊D28312yes—
154C22×C4C22×D28311yescharacteristic
155Q16—5668no—
156SD16—5668no—
157SD16—5668no—
158D8—5668no—
159M16—2838no—
160C2×C8—2834no—
161C4⋊C4—5662no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—5664no—
165C42C22⋊D28312yes—
166C42C22×D28311yescharacteristic
167C42C22×D28311yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—5662no—
172C23C2×C22⋊D28311yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—5662no—
176Q8—5662no—
177D4—24no—
178D4—42no—
179D4—5662no—
180D4—5662no—
181D4—11324no—
182D4—11324no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—5662no—
187C2×C4—11324no—
188C2×C4D4×D28314yes—
189C2×C4C2×C22⋊D28312yes—
190C2×C4C2×C22⋊D28312yes—
191C2×C4C2×C22⋊D28311yescharacteristic
192C2×C4C23×D28311yescharacteristic
193C8—2838no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—11322no—
199C22—11324no—
200C22#2258360612yes—
201C22C22×C22⋊D28311yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—11322no—
206C4#2258360612yes—
207C4C2×D4×D28312yes—
208C2—22no—
209C2—82no—
210C2—22642no—
211C2C2×#2258360611yescharacteristic
212C2#3182726312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#124×C283C2
socleC22×C283C22×D4
hypercenterC2×#124D283
hypocenterC283#3153
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#22583641C2semidirect
2. C2×#22583636C2semidirect
3. #31827015C2semidirect
4. #31826860C2semidirect
5. #31826855C2semidirect
6. #31826847C2semidirect
7. C4×#17985376C2semidirect
8. C2×#124×C283C2semidirect
12. C2×#17985382C22semidirect
14. C2×#17985379C22semidirect
17. #22583610C22semidirect
18. #22583607C22semidirect
19. #22583598C22semidirect
22. #22583521C22semidirect
23. C4×C283⋊C8C22semidirect
42. #17985376D4semidirect
106. C283#3153semidirect
111. C2×#124D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836412
C2×#225836362
#318270152
#318268602
#318268552
#318268472
C4×#179853762
C2×#124×C2832
#3153283