Finite Group Databasebeta

← #49097304

Subgroups — #49097304

Order 35968.

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

normal subgroups only

This group has 270 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#31823649C212yesmaximal, complemented
2#31823640C211yesmaximal, characteristic, complemented
3#31823258C211yesmaximal, characteristic, complemented
4#31823250C212yesmaximal, complemented
5H(3,𝔽4)×C281C211yesmaximal, characteristic, complemented
6#22582924C2211yescharacteristic
7#22582910—21no—
8#22582848—22no—
9#22582807—21no—
10#22582796C2211yescharacteristic
11#22582794C2212yes—
12#22582793—22no—
13#124×C281—21no—
14#124×C281—22no—
15#124×C281—21no—
16#124×C281C2211yescharacteristic
17#120×C281—22no—
18#120×C281C2212yes—
19#17985138—21no—
20#17985137—41no—
21C2×C22⋊D281—22no—
22C2×C22⋊D281—42no—
23D4×D281—41no—
24#17985128—41no—
25#17985125—41no—
26#17985122—21no—
27C22⋊Dic281—22no—
28C22⋊Dic281—42no—
29C24×C281D412yescomplemented
30C2×Q8×C281—21no—
31C2×Q8×C281D411yescharacteristic, complemented
32C2×D4×C281—21no—
33C2×D4×C281—21no—
34C2×D4×C281—22no—
35C2×D4×C281C2311yescharacteristic
36C22⋊C4×C281—22no—
37C22⋊C4×C281—22no—
38C22⋊C4×C281—22no—
39C22⋊C4×C281—22no—
40C22⋊C4×C281D412yescomplemented
41C42×C281—21no—
42C42×C281D411yescharacteristic, complemented
43C22×D281—22no—
44Dic562—21no—
45D1124—21no—
46C22⋊D281—42no—
47C22⋊D281—41no—
48C22⋊D281—84no—
49C2×Dic281—22no—
50C2×Dic281—42no—
51C4×D281—41no—
52#14555886—41no—
53C23×C281—22no—
54C23×C281—42no—
55C23×C281—82no—
56C23×C281C2×D412yes—
57Q8×C281—41no—
58Q8×C281—81no—
59D4×C281—41no—
60D4×C281—82no—
61D4×C281—81no—
62D4×C281—81no—
63C2×C4×C281—21no—
64C2×C4×C281—22no—
65C2×C4×C281—21no—
66C2×C4×C281C2×D411yescharacteristic
67C22×C281—22no—
68C22×C281—42no—
69C22×C281—42no—
70C22×C281—42no—
71C22×C281—44no—
72C22×C281—42no—
73C22×C281—82no—
74C22×C281#12011yescharacteristic
75C2×D281—41no—
76C2×D281—82no—
77C4×C281—21no—
78C4×C281—42no—
79C4×C281—41no—
80C4×C281—41no—
81Dic281—41no—
82Dic281—82no—
83C2×C281—21no—
84C2×C281—42no—
85C2×C281—82no—
86C2×C281B(4,𝔽2)11yescharacteristic
87D281—81no—
88C281#219911yescharacteristic, complemented, Sylow
89#2199—2811nomaximal, Sylow
90H(3,𝔽4)D28111yescharacteristic, complemented
91B(4,𝔽2)—2812no—
92#455—2811no—
93#354—2811no—
94AΣL(1,𝔽16)—2812no—
95H(5,𝔽2)—2811no—
96#137—5621no—
97#124—21no—
98#124—22no—
99#124—21no—
100#124C2×D28111yescharacteristic
101#120—22no—
102#120—5622no—
103#120C2×D28112yes—
104#104—5621no—
105#100—2811no—
106#99—2812no—
107#99—5622no—
108C24C22⋊D28112yescomplemented
109#41—5621no—
110#41—11241no—
111C2×Q8—21no—
112C2×Q8C22⋊D28111yescharacteristic, complemented
113C2×D4—21no—
114C2×D4—21no—
115C2×D4—22no—
116C2×D4—5622no—
117C2×D4—11241no—
118C2×D4—11242no—
119C2×D4C22×D28111yescharacteristic
120Q16—11241no—
121SD16—11241no—
122M16—5621no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C22⋊C4—5622no—
128C22⋊C4—11242no—
129C22⋊C4C22⋊D28112yescomplemented
130C42—21no—
131C42C22⋊D28111yescharacteristic, complemented
132C23—22no—
133C23—42no—
134C23—82no—
135C23—5622no—
136C23C2×C22⋊D28112yes—
137Q8—41no—
138Q8—81no—
139Q8—5621no—
140D4—41no—
141D4—82no—
142D4—81no—
143D4—81no—
144D4—5621no—
145D4—11242no—
146D4—11241no—
147D4—22484no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—5622no—
152C2×C4—11241no—
153C2×C4—11242no—
154C2×C4C2×C22⋊D28111yescharacteristic
155C8—11241no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22—44no—
161C22—42no—
162C22—82no—
163C22—11241no—
164C22—22482no—
165C22#2258284811yescharacteristic
166C4—21no—
167C4—42no—
168C4—41no—
169C4—41no—
170C4—11241no—
171C4—22482no—
172C2—21no—
173C2—42no—
174C2—82no—
175C2—22481no—
176C2#3182365011yescharacteristic
subgroupG/H
centerC2#31823650
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
FittingH(3,𝔽4)×C281C2
socleC2×C281B(4,𝔽2)
hypercenterH(3,𝔽4)D281
hypocenterC281#2199
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #31823649C2semidirect
2. #31823640C2semidirect
3. #31823258C2semidirect
4. #31823250C2semidirect
5. H(3,𝔽4)×C281C2semidirect
29. C24×C281D4semidirect
31. C2×Q8×C281D4semidirect
40. C22⋊C4×C281D4semidirect
42. C42×C281D4semidirect
88. C281#2199semidirect
90. H(3,𝔽4)D281semidirect
108. C24C22⋊D281semidirect
112. C2×Q8C22⋊D281semidirect
129. C22⋊C4C22⋊D281semidirect
131. C42C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318236492
#318236402
#318232582
#318232502
H(3,𝔽4)×C2812
#2199281