Finite Group Databasebeta

← #49097318

Subgroups — #49097318

Order 35968.

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

normal subgroups only

This group has 226 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#31824213C211yesmaximal, characteristic, complemented
2#31823654C212yesmaximal
3#31823640C211yesmaximal, characteristic
4#31823252C212yesmaximal, complemented
5#354×C281C211yesmaximal, characteristic, complemented
6#22582924C2211yescharacteristic
7#22582910—21no—
8#22582877—21no—
9#22582872—22no—
10#22582871—21no—
11#22582863—22no—
12#22582860C2212yes—
13#22582856—22no—
14#22582807—21no—
15#22582796C2211yescharacteristic
16#22582793—22no—
17#124×C281C2211yescharacteristic
18#99×C281C2212yes—
19#17985138—21no—
20#17985137—41no—
21C2×Dic562—21no—
22C2×C22⋊D281—22no—
23D4×D281—41no—
24C22×Dic281D412yes—
25#17985128—41no—
26#17985125—41no—
27#17985122—21no—
28C4⋊Dic281—21no—
29C4⋊Dic281—21no—
30C4⋊Dic281—42no—
31#17985117—22no—
32#17985117—22no—
33#17985117—22no—
34C22⋊Dic281—22no—
35C22⋊Dic281D412yes—
36#17985115—42no—
37C4×Dic281—21no—
38C2×Q8×C281D411yescharacteristic
39C2×D4×C281C2311yescharacteristic
40C22⋊C4×C281—22no—
41C22⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43C22×D281—22no—
44Dic562—21no—
45Dic562—81no—
46D1124—21no—
47C22⋊D281—42no—
48C22⋊D281—41no—
49C2×Dic281—22no—
50C2×Dic281—22no—
51C2×Dic281—22no—
52C2×Dic281—42no—
53C4×D281—41no—
54#14555886—41no—
55C23×C281C2×D412yes—
56Q8×C281—41no—
57D4×C281—41no—
58C2×C4×C281—21no—
59C2×C4×C281—21no—
60C2×C4×C281—42no—
61C2×C4×C281C2×D411yescharacteristic
62C22×C281—22no—
63C22×C281—42no—
64C22×C281#12011yescharacteristic
65C2×D281—41no—
66C2×D281—82no—
67C4×C281—21no—
68C4×C281—41no—
69C4×C281—41no—
70C4×C281—82no—
71Dic281—42no—
72Dic281—41no—
73Dic281—42no—
74C2×C281—21no—
75C2×C281—42no—
76C2×C281B(4,𝔽2)11yescharacteristic
77D281—81no—
78C281#220111yescharacteristic, complemented, Sylow
79#2201—2811nomaximal, Sylow
80#563—2811no—
81#458—2812no—
82#455—2811no—
83#354D28111yescharacteristic, complemented
84#352—2812no—
85H(5,𝔽2)—2811no—
86#137—5621no—
87C4⋊Q8—5621no—
88#126—5622no—
89#125—5621no—
90#124C2×D28111yescharacteristic
91#123—2812no—
92#123—5622no—
93C22⋊Q8—5622no—
94#104—5621no—
95#100—2811no—
96#99—5622no—
97#99C2×D28112yes—
98#41—5621no—
99#41—11241no—
100C2×Q8—5621no—
101C2×Q8D112411yescharacteristic
102C2×D4—5622no—
103C2×D4—11241no—
104C2×D4C22×D28111yescharacteristic
105C22×C4—2812no—
106Q16—11241no—
107SD16—11241no—
108M16—5621no—
109C4⋊C4—5622no—
110C4⋊C4—5622no—
111C4⋊C4—5621no—
112C4⋊C4—5621no—
113C4⋊C4—5622no—
114C4⋊C4—11242no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—2812no—
118C22⋊C4—5622no—
119C22⋊C4—11242no—
120C42—5621no—
121C42D112411yescharacteristic
122C23—5622no—
123C23D4×D28112yes—
124Q8—41no—
125Q8—5621no—
126Q8—22481no—
127D4—41no—
128D4—5621no—
129D4—11242no—
130D4—11241no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—42no—
134C2×C4—5622no—
135C2×C4—5622no—
136C2×C4—5622no—
137C2×C4—11241no—
138C2×C4—11242no—
139C2×C4C2×D112411yescharacteristic
140C8—11241no—
141C22—22no—
142C22—42no—
143C22—11241no—
144C22—22482no—
145C22#2258284911yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—82no—
150C4—11242no—
151C4—11241no—
152C4—11242no—
153C2—21no—
154C2—42no—
155C2—22481no—
156C2#3182365111yescharacteristic
subgroupG/H
centerC2#31823651
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting#354×C281C2
socleC2×C281B(4,𝔽2)
prime radical#22582924C22
hypercenter#354D281
hypocenterC281#2201
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
1. #31824213C2semidirect
4. #31823252C2semidirect
5. #354×C281C2semidirect
78. C281#2201semidirect
83. #354D281semidirect

Maximal subgroups

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

subgroupindex
#318242132
#318236542
#318236402
#318232522
#354×C2812
#2201281