Finite Group Databasebeta

← #49120474

Subgroups — #49120474

Order 36224.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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#31827172C211yesmaximal, characteristic
2#31826817C211yesmaximal, characteristic, complemented
3#31826672C211yesmaximal, characteristic, complemented
4#31826213C211yesmaximal, characteristic, complemented
5#31826195C211yesmaximal, characteristic, complemented
6D4⋊(C283⋊C8)C211yesmaximal, characteristic
7#474×C283C211yesmaximal, characteristic
8C2×#17985382—21no—
9#22583610C2211yescharacteristic
10#22583601—21no—
11#22583589—21no—
12#22583587—22no—
13C4×Dic566C2211yescharacteristic
14D4×Dic283—21no—
15C2×C4⋊Dic283—21no—
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583534—21no—
18#22583533—22no—
19C4×C283⋊C8C2211yescharacteristic
20C4⋊Q8×C283C2211yescharacteristic
21C4×D4×C283C2211yescharacteristic
22#107×C283—21no—
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566D411yescharacteristic
26C2×Dic566D412yes—
27C22×Dic283—22no—
28#17985382—42no—
29C2×C283⋊C8—21no—
30C2×C283⋊C8—21no—
31C4⋊Dic283—22no—
32C4⋊Dic283—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283D411yescharacteristic
35Dic283⋊C4—22no—
36Dic283⋊C4—21no—
37C22⋊Dic283—22no—
38C4×Dic283—21no—
39C2×Q8×C283—21no—
40C2×D4×C283D411yescharacteristic
41C22×C4×C283—21no—
42C2×C8×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D411yescharacteristic
46C22⋊C4×C283—21no—
47C42×C283C2311yescharacteristic
48Dic566—21no—
49Dic566—21no—
50Dic566—42no—
51C2×Dic283—21no—
52C2×Dic283—21no—
53C2×Dic283—22no—
54C2×Dic283—82no—
55C283⋊C8—41no—
56C283⋊C8—41no—
57C23×C283—21no—
58Q8×C283—41no—
59Q8×C283—41no—
60D4×C283—21no—
61D4×C283Q1612yescomplemented
62C2×C4×C283—21no—
63C2×C4×C283—41no—
64C2×C4×C283—41no—
65C2×C4×C283—41no—
66C2×C4×C283C2×D411yescharacteristic
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C8×C283—41no—
70C22×C283—22no—
71C22×C283—41no—
72C22×C283—41no—
73C22×C283#12011yescharacteristic
74C4×C283—21no—
75C4×C283—41no—
76C4×C283—81no—
77C4×C283C2×Q1611yescharacteristic
78C4×C283#13511yescharacteristic
79C4×C283AGL(1,ℤ/8)11yescharacteristic
80C4×C283#13711yescharacteristic
81Dic283—41no—
82Dic283—41no—
83Dic283—42no—
84C2×C283—42no—
85C2×C283#44911yescharacteristic
86C2×C283#45111yescharacteristic
87C2×C283#45511yescharacteristic
88C283#164411yescharacteristic, complemented, Sylow
89#1644—2831nomaximal, Sylow
90#554—2831no—
91#487—2831no—
92#474D28311yescharacteristic
93#462—2831no—
94#333—2831no—
95Q8⋊C8—2831no—
96D4⋊C8—2831no—
97C2×Q16—5661no—
98C4⋊Q8—2831no—
99C4⋊Q8C2×D28311yescharacteristic
100#125—5661no—
101C22⋊Q8—5662no—
102C22⋊Q8—5661no—
103C4×Q8—2831no—
104C4×D4—5661no—
105C4×D4C2×D28311yescharacteristic
106C2×C4⋊C4—5661no—
107#107—21no—
108C4⋊C8—2831no—
109C4⋊C8C2×D28311yescharacteristic
110#103—5662no—
111#103—5661no—
112#102—21no—
113C4×C8—2831no—
114C2×Q8—21no—
115C2×Q8—2831no—
116C2×Q8—2832no—
117C2×D4C22⋊D28311yescharacteristic
118C22×C4—21no—
119C22×C4—5662no—
120Q16—11322no—
121C2×C8—21no—
122C2×C8—5661no—
123C2×C8—5661no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2831no—
127C4⋊C4—5662no—
128C4⋊C4—5662no—
129C4⋊C4—5661no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C4⋊C4C22⋊D28311yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—5662no—
135C42—5661no—
136C42C22×D28311yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—5661no—
141Q8—5661no—
142Q8—11322no—
143D4—21no—
144D4#1798538212yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—5661no—
150C2×C4—5661no—
151C2×C4—5662no—
152C2×C4—22642no—
153C2×C4D4×D28311yescharacteristic
154C2×C4D4×D28311yescharacteristic
155C2×C4C2×C22⋊D28311yescharacteristic
156C8—41no—
157C8—11321no—
158C8—11321no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#2258357811yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—11321no—
167C4—11321no—
168C4—11322no—
169C4C2×#1798538211yescharacteristic
170C4#2258362911yescharacteristic
171C4#2258363411yescharacteristic
172C4#2258364011yescharacteristic
173C2—42no—
174C2#3182660711yescharacteristic
175C2#3182662011yescharacteristic
176C2#3182664111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#474×C283C2
socleC22×C283#120
prime radicalC2×D4×C283D4
hypercenter#474D283
hypocenterC283#1644
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #31826817C2semidirect
3. #31826672C2semidirect
4. #31826213C2semidirect
5. #31826195C2semidirect
61. D4×C283Q16semidirect
88. C283#1644semidirect
144. D4#17985382semidirect

Maximal subgroups

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

subgroupindex
#318271722
#318268172
#318266722
#318262132
#318261952
D4⋊(C283⋊C8)2
#474×C2832
#1644283