Finite Group Databasebeta

← #49097319

Subgroups — #49097319

Order 35968.

248 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 41 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#31824205C211yesmaximal, characteristic, complemented
2#31823636C212yesmaximal, complemented
3#31823260C211yesmaximal, characteristic, complemented
4#31823259C212yesmaximal, complemented
5#454×C281C211yesmaximal, characteristic, complemented
6#22582904—22no—
7#22582868C2212yes—
8#22582867—21no—
9#22582865—22no—
10#22582849—22no—
11#22582847—21no—
12#22582806—22no—
13#22582798C2212yescomplemented
142−1+4×C281C2211yescharacteristic, complemented
15AGL(1,ℤ/8)×C281—21no—
16#124×C281C2211yescharacteristic
17#104×C281—21no—
18#101×C281C2211yescharacteristic, complemented
19C23×D281—21no—
20C2×Dic562—21no—
21C2×D1124—21no—
22C2×D1124D412yes—
23C2×C22⋊D281—22no—
24#17985125—42no—
25#17985123—42no—
26#17985122—22no—
27C22⋊Dic281—21no—
28#17985115—22no—
29#17985115—22no—
30#17985115—22no—
31C4×Dic281D412yes—
32#41×C281—22no—
33#41×C281—21no—
34#41×C281—41no—
35C2×Q8×C281—41no—
36C2×Q8×C281C2311yescharacteristic
37C2×D4×C281D411yescharacteristic
38SD16×C281—41no—
39D8×C281—41no—
40M16×C281—21no—
41C22⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43C22×D281—22no—
44C22×D281—82no—
45C22×D281—81no—
46Dic562—81no—
47D1124—42no—
48D1124—81no—
49C22⋊D281—82no—
50C2×Dic281—22no—
51#14555886—42no—
52C23×C281—21no—
53Q8×C281—21no—
54Q8×C281—22no—
55Q8×C281—41no—
56D4×C281—21no—
57D4×C281—22no—
58D4×C281—41no—
59D4×C281—41no—
60C2×C4×C281—21no—
61C2×C4×C281—41no—
62C2×C4×C281—42no—
63C2×C4×C281C2×D412yes—
64C2×C4×C281C2×D411yescharacteristic
65C8×C281—41no—
66C22×C281—42no—
67C22×C281—41no—
68C22×C281—41no—
69C22×C281#12011yescharacteristic
70C2×D281—42no—
71C2×D281—42no—
72C2×D281—42no—
73C2×D281—84no—
74C4×C281—21no—
75C4×C281—22no—
76C4×C281—41no—
77C4×C281—41no—
78Dic281—42no—
79C2×C281—21no—
80C2×C281—81no—
81C2×C281—81no—
82C2×C281B(4,𝔽2)11yescharacteristic
83D281—82no—
84C281#220211yescharacteristic, complemented, Sylow
85#2202—2811nomaximal, Sylow
86H(3,𝔽4)—2811no—
87#454—2812no—
88#454D28111yescharacteristic, complemented
89#355—2811no—
90#355—2812no—
912−1+4C2×D28111yescharacteristic, complemented
92AGL(1,ℤ/8)—21no—
93AGL(1,ℤ/8)—5622no—
94#124—2812no—
95#124—5622no—
96#124—5621no—
97#124C2×D28111yescharacteristic
98#120—5622no—
99#120—5621no—
100#104—21no—
101#104—5622no—
102#101—2812no—
103#101C2×D28111yescharacteristic, complemented
104C24—5621no—
105#41—22no—
106#41—21no—
107#41—41no—
108C2×Q8—41no—
109C2×Q8—5621no—
110C2×Q8C22×D28111yescharacteristic
111C2×D4—2812no—
112C2×D4—5621no—
113C2×D4—5622no—
114C2×D4C22⋊D28111yescharacteristic
115SD16—41no—
116SD16—11242no—
117D8—41no—
118D8—11242no—
119M16—21no—
120M16—5622no—
121C22⋊C4—22no—
122C22⋊C4—5622no—
123C22⋊C4—5621no—
124C22⋊C4—5622no—
125C22⋊C4—5622no—
126C42—2812no—
127C42C22⋊D28111yescharacteristic
128C23—21no—
129C23—5622no—
130C23—22482no—
131C23—22481no—
132Q8—21no—
133Q8—22no—
134Q8—41no—
135Q8—22481no—
136D4—21no—
137D4—22no—
138D4—41no—
139D4—41no—
140D4—11242no—
141D4—22481no—
142D4—22482no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—5622no—
147C2×C4D4×D28112yes—
148C2×C4C2×C22⋊D28111yescharacteristic
149C8—41no—
150C8—11242no—
151C22—42no—
152C22—41no—
153C22—41no—
154C22—11242no—
155C22—11242no—
156C22—11242no—
157C22—22484no—
158C22#2258284711yescharacteristic
159C4—21no—
160C4—22no—
161C4—41no—
162C4—41no—
163C4—11242no—
164C2—21no—
165C2—81no—
166C2—81no—
167C2—22482no—
168C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#454×C281C2
socleC2×C281B(4,𝔽2)
hypercenter#454D281
hypocenterC281#2202
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #31824205C2semidirect
2. #31823636C2semidirect
3. #31823260C2semidirect
4. #31823259C2semidirect
5. #454×C281C2semidirect
13. #22582798C22semidirect
14. 2−1+4×C281C22semidirect
18. #101×C281C22semidirect
84. C281#2202semidirect
88. #454D281semidirect
91. 2−1+4C2×D281semidirect
103. #101C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242052
#318236362
#318232602
#318232592
#454×C2812
#2202281