Finite Group Databasebeta

← #49094602

Subgroups — #49094602

Order 35968.

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

normal subgroups only

This group has 206 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#31824213C211yesmaximal, characteristic, complemented
2#31823853C211yesmaximal, characteristic
3#31823828C212yesmaximal, complemented
4#31823204C212yesmaximal, complemented
5#329×C281C211yesmaximal, characteristic, complemented
6C2×#17985125—21no—
7C2×#17985123—21no—
8#22582877—21no—
9#22582876C2211yescharacteristic
10#22582872—22no—
11#22582871C2212yes—
12#22582860—21no—
13#22582856—22no—
14#22582801—22no—
15#22582801—22no—
16#22582790C2211yescharacteristic
17#124×C281C2211yescharacteristic
18#97×C281C2212yes—
19C2×Dic562—21no—
20C2×D1124—22no—
21C2×D1124—21no—
22C22×Dic281—21no—
23#17985125—42no—
24#17985123—42no—
25C2×#14555886—21no—
26C4⋊Dic281D412yes—
27C4⋊Dic281D412yes—
28#17985117—22no—
29#17985117—22no—
30#17985117—22no—
31C22⋊Dic281—22no—
32C22⋊Dic281—21no—
33C4×Dic281—21no—
34C2×Q8×C281D411yescharacteristic
35C2×D4×C281D411yescharacteristic
36C2×C8×C281—22no—
37C22⋊C4×C281—22no—
38C42×C281C2311yescharacteristic
39C22×D281—41no—
40Dic562—81no—
41D1124—41no—
42D1124—41no—
43D1124—44no—
44C2×Dic281—22no—
45C2×Dic281—22no—
46C2×Dic281—81no—
47#14555886—22no—
48C23×C281—21no—
49Q8×C281—41no—
50D4×C281—41no—
51C2×C4×C281—21no—
52C2×C4×C281C2×D412yes—
53C2×C4×C281C2×D411yescharacteristic
54C8×C281—42no—
55C22×C281—41no—
56C22×C281—42no—
57C22×C281#12011yescharacteristic
58C2×D281—81no—
59C2×D281—82no—
60C4×C281—21no—
61C4×C281—22no—
62C4×C281—41no—
63Dic281—42no—
64Dic281—42no—
65C2×C281—81no—
66C2×C281#45311yescharacteristic
67C2×C281#45412yes—
68D281—161no—
69C281#165711yescharacteristic, complemented, Sylow
70#1657—2811nomaximal, Sylow
71#563—2811no—
72#496—2811no—
73#490—2812no—
74#330—2812no—
75#329D28111yescharacteristic, complemented
76C2×SD16—5621no—
77C2×D8—5621no—
78C4⋊Q8—5621no—
79#127—2811no—
80#126—5622no—
81#125—2812no—
82#124C2×D28111yescharacteristic
83#123—5621no—
84C22⋊Q8—5622no—
85#102—5622no—
86#102—5622no—
87#97—2811no—
88#97C2×D28112yes—
89C2×Q8—5621no—
90C2×Q8D112411yescharacteristic
91C2×D4—5622no—
92C2×D4—5621no—
93C2×D4D112411yescharacteristic
94C22×C4—5621no—
95SD16—11242no—
96D8—11242no—
97C2×C8—22no—
98C2×C8—5621no—
99C4⋊C4—2812no—
100C4⋊C4—2812no—
101C4⋊C4—5622no—
102C4⋊C4—5622no—
103C4⋊C4—5622no—
104C22⋊C4—22no—
105C22⋊C4—5622no—
106C22⋊C4—5621no—
107C42—5621no—
108C42C22×D28111yescharacteristic
109C23—21no—
110C23—11241no—
111Q8—41no—
112Q8—22481no—
113D4—41no—
114D4—11241no—
115D4—11241no—
116D4—11244no—
117C2×C4—21no—
118C2×C4—5622no—
119C2×C4—5622no—
120C2×C4—22481no—
121C2×C4D4×D28112yes—
122C2×C4C2×D112411yescharacteristic
123C8—42no—
124C8—5622no—
125C22—41no—
126C22—42no—
127C22—22481no—
128C22—22482no—
129C22#2258284911yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—11242no—
134C4—11242no—
135C2—81no—
136C2—44961no—
137C2#3182363311yescharacteristic
138C2#3182363712yes—
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281#120
prime radical#31823853C2
hypercenter#329D281
hypocenterC281#1657
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #31824213C2semidirect
3. #31823828C2semidirect
4. #31823204C2semidirect
5. #329×C281C2semidirect
69. C281#1657semidirect
75. #329D281semidirect

Maximal subgroups

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

subgroupindex
#318242132
#318238532
#318238282
#318232042
#329×C2812
#1657281