Finite Group Databasebeta

← #49123245

Subgroups — #49123245

Order 36224.

354 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 45 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#31826651C212yesmaximal, complemented
2#31826632C211yesmaximal, characteristic, complemented
3#31826258C211yesmaximal, characteristic, complemented
4#31826252C212yesmaximal, complemented
5D42×C283C211yesmaximal, characteristic, complemented
6#22583655C2211yescharacteristic, complemented
7#22583636—21no—
8#22583579—22no—
9#22583538—21no—
10#22583527C2211yescharacteristic, complemented
11#22583525C2212yescomplemented
12#22583524—22no—
13C22×D4×C283—22no—
14#127×C283C2211yescharacteristic
15#121×C283—22no—
16#120×C283—21no—
17#120×C283C2212yes—
18C4×D4×C283—21no—
19#17985392—21no—
20#17985391—41no—
21C2×C22⋊D283—22no—
22C2×C22⋊D283—42no—
23D4×D283—41no—
24#17985380—41no—
25#17985377—41no—
26#17985376—21no—
27C22⋊Dic283—22no—
28C22⋊Dic283—42no—
29C24×C283—21no—
30C24×C283D412yescomplemented
31C2×D4×C283—21no—
32C2×D4×C283—22no—
33C2×D4×C283—22no—
34C2×D4×C283—22no—
35C2×D4×C283—48no—
36C2×D4×C283D411yescharacteristic, complemented
37C2×D4×C283C2311yescharacteristic
38C22×C4×C283—22no—
39C4⋊C4×C283—21no—
40C22⋊C4×C283—21no—
41C22⋊C4×C283—22no—
42C22⋊C4×C283D412yescomplemented
43C42×C283D411yescharacteristic, complemented
44C22×D283—22no—
45Dic566—21no—
46D1132—21no—
47C22⋊D283—42no—
48C22⋊D283—41no—
49C22⋊D283—84no—
50C2×Dic283—22no—
51C2×Dic283—42no—
52C4×D283—41no—
53C283⋊C8—41no—
54C23×C283—22no—
55C23×C283—21no—
56C23×C283—44no—
57C23×C283—42no—
58C23×C283—44no—
59C23×C283—81no—
60C23×C283C2×D412yes—
61D4×C283—24no—
62D4×C283—41no—
63D4×C283—41no—
64D4×C283—44no—
65D4×C283—44no—
66D4×C283—44no—
67C2×C4×C283—21no—
68C2×C4×C283—22no—
69C2×C4×C283—44no—
70C2×C4×C283C2×D411yescharacteristic
71C22×C283—24no—
72C22×C283—22no—
73C22×C283—42no—
74C22×C283—42no—
75C22×C283—42no—
76C22×C283—44no—
77C22×C283—42no—
78C22×C283—41no—
79C22×C283—82no—
80C22×C283—84no—
81C22×C283#12011yescharacteristic
82C2×D283—41no—
83C2×D283—82no—
84C4×C283—22no—
85C4×C283—21no—
86C4×C283—42no—
87Dic283—41no—
88Dic283—82no—
89C2×C283—21no—
90C2×C283—42no—
91C2×C283—44no—
92C2×C283—81no—
93C2×C283B(4,𝔽2)11yescharacteristic
94D283—81no—
95C283#219611yescharacteristic, complemented, Sylow
96#2196—2831nomaximal, Sylow
97D42D28311yescharacteristic, complemented
98B(4,𝔽2)—2832no—
99#453—2831no—
100#353—2831no—
101AΣL(1,𝔽16)—2832no—
102H(5,𝔽2)—2831no—
103C22×D4—22no—
104AGL(1,ℤ/8)—5661no—
105#127C2×D28311yescharacteristic
106#121—22no—
107#120—21no—
108#120—5662no—
109#120C2×D28312yes—
110C4×D4—21no—
111#104—5661no—
112#100—2831no—
113#99—2832no—
114#99—5662no—
115C24—21no—
116C24C22⋊D28312yescomplemented
117#41—5661no—
118#41—11321no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—5662no—
125C2×D4—11321no—
126C2×D4—11322no—
127C2×D4C22⋊D28311yescharacteristic, complemented
128C2×D4C22×D28311yescharacteristic
129C22×C4—22no—
130SD16—11321no—
131D8—11321no—
132M16—5661no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—5662no—
137C22⋊C4—11322no—
138C22⋊C4C22⋊D28312yescomplemented
139C42C22⋊D28311yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—5662no—
147C23C2×C22⋊D28312yes—
148Q8—5661no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—5661no—
156D4—11322no—
157D4—11321no—
158D4—22644no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—5662no—
163C2×C4—11321no—
164C2×C4—11322no—
165C2×C4C2×C22⋊D28311yescharacteristic
166C8—11321no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—11321no—
178C22—22642no—
179C22#2258357911yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—11321no—
184C4—22642no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—22641no—
190C2#3182665211yescharacteristic
subgroupG/H
centerC2#31826652
commutator, cosocleC2×D4×C283C23
FrattiniC2×D4C22×D283
FittingD42×C283C2
socleC2×C283B(4,𝔽2)
hypercenterD42D283
hypocenterC283#2196
LCSG ▷ C2×D4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #31826651C2semidirect
2. #31826632C2semidirect
3. #31826258C2semidirect
4. #31826252C2semidirect
5. D42×C283C2semidirect
6. #22583655C22semidirect
10. #22583527C22semidirect
11. #22583525C22semidirect
30. C24×C283D4semidirect
36. C2×D4×C283D4semidirect
42. C22⋊C4×C283D4semidirect
43. C42×C283D4semidirect
95. C283#2196semidirect
97. D42D283semidirect
116. C24C22⋊D283semidirect
127. C2×D4C22⋊D283semidirect
138. C22⋊C4C22⋊D283semidirect
139. C42C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318266512
#318266322
#318262582
#318262522
D42×C2832
#2196283