Finite Group Databasebeta

← #49094607

Subgroups — #49094607

Order 35968.

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

normal subgroups only

This group has 228 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#31824205C211yesmaximal, characteristic
2#31823825C212yesmaximal, complemented
3#31823203C211yesmaximal, characteristic, complemented
4#31823202C212yesmaximal, complemented
5#497×C281C211yesmaximal, characteristic, complemented
6#22582868—21no—
7#22582867C2212yes—
8#22582865—22no—
9#22582849—22no—
10#22582847—21no—
11#22582802—22no—
12#22582799—22no—
13#22582790C2212yescomplemented
14C2×Q16×C281—21no—
15C2×SD16×C281—21no—
16C4⋊Q8×C281C2211yescharacteristic, complemented
17#124×C281C2211yescharacteristic
18#97×C281C2211yescharacteristic, complemented
19C23×D281—21no—
20C2×Dic562D412yes—
21C2×D1124—21no—
22C2×D1124D412yes—
23C2×C22⋊D281—22no—
24C2×#14555886—22no—
25C22⋊Dic281—21no—
26#17985115—22no—
27#17985115—22no—
28#17985115—22no—
29C4×Dic281—21no—
30C2×Q8×C281—21no—
31C2×Q8×C281D411yescharacteristic
32C2×D4×C281D411yescharacteristic
33Q16×C281—42no—
34SD16×C281—42no—
35C2×C8×C281—21no—
36C4⋊C4×C281—22no—
37C22⋊C4×C281—22no—
38C42×C281C2311yescharacteristic
39C22×D281—22no—
40C22×D281—81no—
41C22×D281—82no—
42Dic562—42no—
43D1124—42no—
44D1124—81no—
45C22⋊D281—82no—
46C2×Dic281—22no—
47#14555886—42no—
48C23×C281—21no—
49Q8×C281—41no—
50Q8×C281—41no—
51Q8×C281—41no—
52D4×C281—41no—
53C2×C4×C281—21no—
54C2×C4×C281—41no—
55C2×C4×C281C2×D412yes—
56C2×C4×C281C2×D411yescharacteristic
57C8×C281—22no—
58C22×C281—41no—
59C22×C281—42no—
60C22×C281#12011yescharacteristic
61C2×D281—42no—
62C2×D281—42no—
63C2×D281—42no—
64C2×D281—84no—
65C4×C281—21no—
66C4×C281—22no—
67C4×C281—41no—
68C4×C281—81no—
69Dic281—42no—
70C2×C281—81no—
71C2×C281#45311yescharacteristic
72C2×C281#45512yes—
73D281—82no—
74C281#165911yescharacteristic, complemented, Sylow
75#1659—2811nomaximal, Sylow
76H(3,𝔽4)—2811no—
77#497D28111yescharacteristic, complemented
78#489—2812no—
79#329—2811no—
80#329—2812no—
81C2×Q16—21no—
82C2×SD16—21no—
83C4⋊Q8C2×D28111yescharacteristic, complemented
84#124—2812no—
85#124—5622no—
86#124—5621no—
87#124C2×D28111yescharacteristic
88#120—5622no—
89#120—5621no—
90#103—5622no—
91#102—5622no—
92#97—2812no—
93#97C2×D28111yescharacteristic, complemented
94C24—5621no—
95C2×Q8—21no—
96C2×Q8—2812no—
97C2×Q8C22⋊D28111yescharacteristic
98C2×D4—2812no—
99C2×D4—5621no—
100C2×D4—5622no—
101C2×D4C22⋊D28111yescharacteristic
102Q16—42no—
103SD16—42no—
104C2×C8—21no—
105C2×C8—5622no—
106C4⋊C4—22no—
107C22⋊C4—22no—
108C22⋊C4—5622no—
109C22⋊C4—5621no—
110C22⋊C4—5622no—
111C22⋊C4—5622no—
112C42—5621no—
113C42C22×D28111yescharacteristic
114C23—21no—
115C23—5622no—
116C23—22481no—
117C23—22482no—
118Q8—41no—
119Q8—41no—
120Q8—41no—
121Q8—11242no—
122D4—41no—
123D4—11242no—
124D4—22481no—
125D4—22482no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—5622no—
129C2×C4D4×D28112yes—
130C2×C4C2×C22⋊D28111yescharacteristic
131C8—22no—
132C8—11242no—
133C22—41no—
134C22—42no—
135C22—11242no—
136C22—11242no—
137C22—11242no—
138C22—22484no—
139C22#2258284711yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—81no—
144C4—11242no—
145C2—81no—
146C2—22482no—
147C2#3182363011yescharacteristic
148C2#3182363912yes—
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#497×C281C2
socleC22×C281#120
prime radical#31824205C2
hypercenter#497D281
hypocenterC281#1659
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #31823825C2semidirect
3. #31823203C2semidirect
4. #31823202C2semidirect
5. #497×C281C2semidirect
13. #22582790C22semidirect
16. C4⋊Q8×C281C22semidirect
18. #97×C281C22semidirect
74. C281#1659semidirect
77. #497D281semidirect
83. C4⋊Q8C2×D281semidirect
93. #97C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242052
#318238252
#318232032
#318232022
#497×C2812
#1659281