Finite Group Databasebeta

← #49120467

Subgroups — #49120467

Order 36224.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827175C211yesmaximal, characteristic
2#31826817C211yesmaximal, characteristic, complemented
3#31826667C211yesmaximal, characteristic
4#31826213C211yesmaximal, characteristic, complemented
5Q8⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic
7#475×C283C211yesmaximal, characteristic, complemented
8C2×#17985379—21no—
9#22583610C2211yescharacteristic
10#22583602—21no—
11#22583588—22no—
12#22583586—21no—
13C4×D1132—21no—
14C4×D1132C2211yescharacteristic
15C4⋊C4×D283—21no—
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583534—21no—
18#22583533—22no—
19C4×C283⋊C8C2211yescharacteristic
20C4⋊Q8×C283C2211yescharacteristic
21C4×Q8×C283C2211yescharacteristic
22#106×C283—21no—
23C4⋊C8×C283C2211yescharacteristic
24#103×C283—21no—
25C2×Dic566D412yes—
26C2×D1132D411yescharacteristic
27C2×C4×D283—22no—
28C2×C4×D283—21no—
29#17985379—42no—
30C2×C283⋊C8—21no—
31C2×C283⋊C8—21no—
32C4⋊Dic283—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283D411yescharacteristic
35Dic283⋊C4—22no—
36Dic283⋊C4—22no—
37(C2×D283)⋊C4—22no—
38(C2×D283)⋊C4—21no—
39C2×Q8×C283—21no—
40C2×Q8×C283D411yescharacteristic
41C2×C8×C283—21no—
42C4⋊C4×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D411yescharacteristic
46C42×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49Dic566—42no—
50D1132—21no—
51D1132SD1612yes—
52C2×Dic283—21no—
53C2×Dic283—22no—
54C4×D283—41no—
55C4×D283—41no—
56C4×D283—82no—
57C283⋊C8—41no—
58C283⋊C8—41no—
59Q8×C283—21no—
60Q8×C283—21no—
61Q8×C283—41no—
62Q8×C283—41no—
63C2×C4×C283—21no—
64C2×C4×C283—21no—
65C2×C4×C283—41no—
66C2×C4×C283C2×D411yescharacteristic
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C8×C283—41no—
70C22×C283#12011yescharacteristic
71C2×D283—22no—
72C2×D283—41no—
73C2×D283—41no—
74C4×C283—21no—
75C4×C283—41no—
76C4×C283—41no—
77C4×C283—81no—
78C4×C283C2×SD1611yescharacteristic
79C4×C283#13511yescharacteristic
80C4×C283#13711yescharacteristic
81C4×C283#13711yescharacteristic
82Dic283—41no—
83Dic283—42no—
84C2×C283#44811yescharacteristic
85C2×C283#45211yescharacteristic
86C2×C283#45511yescharacteristic
87D283—42no—
88C283#164311yescharacteristic, complemented, Sylow
89#1643—2831nomaximal, Sylow
90#554—2831no—
91#487—2831no—
92#475D28311yescharacteristic, complemented
93#461—2831no—
94#333—2831no—
95Q8⋊C8—2831no—
96D4⋊C8—2831no—
97C2×SD16—5661no—
98C4⋊Q8—2831no—
99C4⋊Q8C2×D28311yescharacteristic
100#125—5661no—
101C22⋊Q8—5662no—
102C22⋊Q8—5661no—
103C4×Q8C2×D28311yescharacteristic
104C4×D4—2831no—
105C4×D4—5661no—
106C2×C4⋊C4—5661no—
107#106—21no—
108C4⋊C8—2831no—
109C4⋊C8C2×D28311yescharacteristic
110#103—21no—
111#103—5662no—
112#103—5661no—
113C4×C8—2831no—
114C2×Q8—21no—
115C2×Q8—2832no—
116C2×Q8C22⋊D28311yescharacteristic
117C2×D4—2831no—
118C22×C4—5662no—
119C22×C4—5661no—
120SD16—11322no—
121C2×C8—21no—
122C2×C8—5661no—
123C2×C8—5661no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2831no—
128C4⋊C4—5662no—
129C4⋊C4—5662no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C4⋊C4C22⋊D28311yescharacteristic
133C22⋊C4—5662no—
134C22⋊C4—5661no—
135C42—21no—
136C42C22×D28311yescharacteristic
137C23—5661no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—11322no—
143D4—2832no—
144D4—5661no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—5661no—
149C2×C4—5662no—
150C2×C4—11321no—
151C2×C4—11321no—
152C2×C4—22642no—
153C2×C4D4×D28311yescharacteristic
154C2×C4D4×D28311yescharacteristic
155C2×C4C2×C22⋊D28311yescharacteristic
156C8—41no—
157C8—11321no—
158C8—11321no—
159C22—5662no—
160C22—11321no—
161C22—11321no—
162C22#2258357811yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—11321no—
168C4—11322no—
169C4SD16×D28311yescharacteristic
170C4#2258363011yescharacteristic
171C4#2258363911yescharacteristic
172C4#2258364111yescharacteristic
173C2—11322no—
174C2#3182660211yescharacteristic
175C2#3182662511yescharacteristic
176C2#3182664111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#475×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#475D283
hypocenterC283#1643
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #31826817C2semidirect
4. #31826213C2semidirect
5. Q8⋊(C283⋊C8)C2semidirect
7. #475×C283C2semidirect
88. C283#1643semidirect
92. #475D283semidirect

Maximal subgroups

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

subgroupindex
#318271752
#318268172
#318266672
#318262132
Q8⋊(C283⋊C8)2
#318261922
#475×C2832
#1643283