Finite Group Databasebeta

← #49094593

Subgroups — #49094593

Order 35968.

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

normal subgroups only

This group has 262 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, complemented
2#31823853C211yesmaximal, characteristic, complemented
3#31823852C212yesmaximal, complemented
4#31823202C212yesmaximal, complemented
5#329×C281C211yesmaximal, characteristic, complemented
6C2×#17985127—22no—
7C2×#17985125—21no—
8C2×D2248—22no—
9C2×#17985123—21no—
10#22582876C2211yescharacteristic, complemented
11#22582868—21no—
12#22582867C2212yes—
13#22582865—22no—
14#22582849—22no—
15#22582847—21no—
16#22582790C2211yescharacteristic, complemented
17#124×C281C2211yescharacteristic
18#97×C281C2212yescomplemented
19C23×D281—21no—
20C2×Dic562D412yes—
21C2×D1124—21no—
22C2×D1124—21no—
23C2×D1124—22no—
24C2×D1124D412yes—
25C2×C22⋊D281—22no—
26#17985127—44no—
27#17985125—42no—
28D2248—44no—
29#17985123—42no—
30C2×#14555886—21no—
31C22⋊Dic281—21no—
32#17985115—22no—
33#17985115—22no—
34#17985115—22no—
35C4×Dic281—21no—
36C2×Q8×C281D411yescharacteristic
37C2×D4×C281D411yescharacteristic
38C2×C8×C281—22no—
39C22⋊C4×C281—22no—
40C42×C281C2311yescharacteristic
41C22×D281—22no—
42C22×D281—41no—
43C22×D281—82no—
44C22×D281—81no—
45Dic562—42no—
46D1124—42no—
47D1124—41no—
48D1124—42no—
49D1124—41no—
50D1124—42no—
51D1124—81no—
52C22⋊D281—82no—
53C2×Dic281—22no—
54#14555886—22no—
55C23×C281—21no—
56Q8×C281—41no—
57D4×C281—41no—
58C2×C4×C281—21no—
59C2×C4×C281C2×D412yes—
60C2×C4×C281C2×D411yescharacteristic
61C8×C281—24no—
62C22×C281—41no—
63C22×C281—42no—
64C22×C281#12011yescharacteristic
65C2×D281—42no—
66C2×D281—42no—
67C2×D281—42no—
68C2×D281—84no—
69C2×D281—82no—
70C2×D281—81no—
71C4×C281—22no—
72C4×C281—21no—
73C4×C281—41no—
74Dic281—42no—
75C2×C281—81no—
76C2×C281#45312yes—
77C2×C281#45311yescharacteristic
78D281—82no—
79D281—161no—
80C281#165511yescharacteristic, complemented, Sylow
81#1655—2811nomaximal, Sylow
82H(3,𝔽4)—2811no—
83#496—2811no—
84#496—2812no—
85#329—2812no—
86#329D28111yescharacteristic, complemented
87C2×SD16—5622no—
88C2×SD16—5621no—
89C2×D8—5622no—
90C2×D8—5621no—
91#127—2811no—
92#124—2812no—
93#124—5622no—
94#124—5621no—
95#124C2×D28111yescharacteristic
96#120—5622no—
97#120—5621no—
98#97—2811no—
99#97C2×D28112yescomplemented
100C24—5621no—
101C2×Q8—2812no—
102C2×Q8D112411yescharacteristic
103C2×D4—2812no—
104C2×D4—5621no—
105C2×D4—5622no—
106C2×D4—5622no—
107C2×D4—5621no—
108C2×D4D112411yescharacteristic
109SD16—11244no—
110SD16—11242no—
111D8—11244no—
112D8—11242no—
113C2×C8—22no—
114C2×C8—5621no—
115C22⋊C4—22no—
116C22⋊C4—5622no—
117C22⋊C4—5621no—
118C22⋊C4—5622no—
119C22⋊C4—5622no—
120C42—5621no—
121C42C22×D28111yescharacteristic
122C23—21no—
123C23—5622no—
124C23—11241no—
125C23—22482no—
126C23—22481no—
127Q8—41no—
128Q8—11242no—
129D4—41no—
130D4—11242no—
131D4—11242no—
132D4—11241no—
133D4—11242no—
134D4—11241no—
135D4—22481no—
136D4—22482no—
137C2×C4—21no—
138C2×C4—5622no—
139C2×C4D4×D28112yes—
140C2×C4C2×D112411yescharacteristic
141C8—24no—
142C8—5622no—
143C22—42no—
144C22—41no—
145C22—11242no—
146C22—11242no—
147C22—11242no—
148C22—22484no—
149C22—22482no—
150C22—22481no—
151C22#2258284911yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—11242no—
156C2—81no—
157C2—44961no—
158C2—22482no—
159C2#3182363212yes—
160C2#3182363311yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281#120
hypercenter#329D281
hypocenterC281#1655
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. #31824205C2semidirect
2. #31823853C2semidirect
3. #31823852C2semidirect
4. #31823202C2semidirect
5. #329×C281C2semidirect
10. #22582876C22semidirect
16. #22582790C22semidirect
18. #97×C281C22semidirect
80. C281#1655semidirect
86. #329D281semidirect
99. #97C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242052
#318238532
#318238522
#318232022
#329×C2812
#1655281