Finite Group Databasebeta

← #49097259

Subgroups — #49097259

Order 35968.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#31824264C211yesmaximal, characteristic, complemented
2#31823899C211yesmaximal, characteristic, complemented
3#31823730C211yesmaximal, characteristic, complemented
4#31823276C211yesmaximal, characteristic, complemented
5#31823271C211yesmaximal, characteristic, complemented
6#31823246C211yesmaximal, characteristic, complemented
7C2×D16×C281C211yesmaximal, characteristic, complemented
8#22582924—21no—
9#22582905—21no—
10#22582905—21no—
11#22582903—22no—
12#22582901C2211yescharacteristic
13#22582898—21no—
14D8×D281—21no—
15#22582885C2211yescharacteristic
16#22582823—21no—
17#22582820—21no—
18#22582819C2211yescharacteristic, complemented
19#22582815C2211yescharacteristic, complemented
20#22582796—21no—
21C2×D8×C281C2211yescharacteristic
22C2×D8×C281C2211yescharacteristic, complemented
23D16×C281—22no—
24C2×C16×C281C2211yescharacteristic, complemented
25#17985138—21no—
26#17985138D411yescharacteristic
27#17985137—22no—
28#17985137—41no—
29C2×C22⋊D281—42no—
30D4×D281—22no—
31D4×D281—41no—
32Dic1124D411yescharacteristic
33#17985127—21no—
34#17985126—22no—
35#17985126—41no—
36D2248D411yescharacteristic
37#17985123—22no—
38#17985123—41no—
39#17985122—21no—
40#17985122D411yescharacteristic
41#17985121—21no—
42C8×D281—21no—
43#17985113—21no—
44C2×D4×C281—21no—
45C2×D4×C281—21no—
46D8×C281—21no—
47D8×C281—21no—
48D8×C281—21no—
49D8×C281D412yes—
50C2×C8×C281C2311yescharacteristic
51C16×C281—21no—
52C22×D281—42no—
53Dic562—21no—
54Dic562D811yescharacteristic
55D1124—21no—
56D1124D811yescharacteristic
57C22⋊D281—21no—
58C22⋊D281—42no—
59C22⋊D281—42no—
60C22⋊D281—41no—
61C2×Dic281—42no—
62C4×D281—21no—
63C4×D281—41no—
64#14555886—21no—
65#14555886—41no—
66C23×C281—41no—
67C23×C281—41no—
68D4×C281—22no—
69D4×C281—41no—
70D4×C281—41no—
71D4×C281—41no—
72C2×C4×C281C2×D411yescharacteristic
73C8×C281C2×D411yescharacteristic
74C8×C281C2×D411yescharacteristic
75C22×C281—42no—
76C22×C281—81no—
77C22×C281—161no—
78C22×C281—161no—
79C22×C281AGL(1,ℤ/8)11yescharacteristic
80C2×D281—21no—
81C2×D281—41no—
82C2×D281—162no—
83C4×C281#12011yescharacteristic
84C4×C281C2×D811yescharacteristic
85Dic281—21no—
86Dic281—41no—
87C2×C281—21no—
88C2×C281—82no—
89C2×C281—161no—
90C2×C281#44711yescharacteristic
91D281—41no—
92D281—81no—
93C281#219211yescharacteristic, complemented, Sylow
94#2192—2811nomaximal, Sylow
95#576—2811no—
96#509—2811no—
97C2×D16D28111yescharacteristic, complemented
98#472—2811no—
99#361—2811no—
100#359—2811no—
101#350—2811no—
102H(5,𝔽2)—5621no—
103AGL(1,ℤ/8)—5621no—
104AGL(1,ℤ/8)—5622no—
105AGL(1,ℤ/8)—5621no—
106#135—2811no—
107#135—5621no—
108C2×D8—5621no—
109C2×D8C2×D28111yescharacteristic
110C2×D8C2×D28111yescharacteristic, complemented
111#131—2811no—
112SD32—5621no—
113D16—22no—
114D16—5621no—
115M32—2811no—
116C2×C16C2×D28111yescharacteristic, complemented
117#108—2811no—
118#100—5621no—
119#41—2811no—
120#41—5622no—
121#41—5621no—
122#41—11241no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—5622no—
126C2×D4—11241no—
127C2×D4—11242no—
128Q16—2811no—
129SD16—5622no—
130SD16—5621no—
131SD16—11241no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—2811no—
136D8—5622no—
137D8—11241no—
138D8C22⋊D28112yes—
139M16—2811no—
140M16—5621no—
141M16—5621no—
142C2×C8—5621no—
143C2×C8C22×D28111yescharacteristic
144C16—21no—
145C16—5621no—
146C23—41no—
147C23—41no—
148C23—11242no—
149Q8—2811no—
150Q8—5621no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—2811no—
156D4—5621no—
157D4—5621no—
158D4—11242no—
159D4—11242no—
160D4—11241no—
161C2×C4—5621no—
162C2×C4—11242no—
163C2×C4—11241no—
164C2×C4D4×D28111yescharacteristic
165C8—5621no—
166C8—11241no—
167C8D4×D28111yescharacteristic
168C8C2×C22⋊D28111yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—5621no—
174C22—11241no—
175C22—44962no—
176C22#2258290311yescharacteristic
177C4—5621no—
178C4—11241no—
179C4#2258284711yescharacteristic
180C4D8×D28111yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—11241no—
185C2—22481no—
186C2#3182359511yescharacteristic
subgroupG/H
centerC2#31823595
commutator, cosocleC2×C8×C281C23
FrattiniC2×C8C22×D281
FittingC2×D16×C281C2
socleC2×C281#447
hypercenterC2×D16D281
hypocenterC281#2192
LCSG ▷ C2×C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #31824264C2semidirect
2. #31823899C2semidirect
3. #31823730C2semidirect
4. #31823276C2semidirect
5. #31823271C2semidirect
6. #31823246C2semidirect
7. C2×D16×C281C2semidirect
18. #22582819C22semidirect
19. #22582815C22semidirect
22. C2×D8×C281C22semidirect
24. C2×C16×C281C22semidirect
93. C281#2192semidirect
97. C2×D16D281semidirect
110. C2×D8C2×D281semidirect
116. C2×C16C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242642
#318238992
#318237302
#318232762
#318232712
#318232462
C2×D16×C2812
#2192281