Finite Group Databasebeta

← #49094400

Subgroups — #49094400

Order 35968.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824188C211yesmaximal, characteristic, complemented
2#31823811C211yesmaximal, characteristic
3#31823664C211yesmaximal, characteristic
4#31823664C211yesmaximal, characteristic
5#31823193C211yesmaximal, characteristic, complemented
6#31823193C211yesmaximal, characteristic, complemented
7#332×C281C211yesmaximal, characteristic, complemented
8C2×#17985127—21no—
9C2×#17985127—21no—
10#22582877—21no—
11#22582876C2211yescharacteristic
12#22582870—21no—
13#22582869—22no—
14Q8×Dic281—21no—
15C4×Dic562C2211yescharacteristic
16C4×Dic562C2211yescharacteristic
17#22582844—21no—
18#22582801—21no—
19#22582801—21no—
20#22582799—22no—
21C4×#14555886C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25C2×Dic562D411yescharacteristic
26C2×Dic562D411yescharacteristic
27C2×D1124—21no—
28C2×D1124—21no—
29C2×D1124—21no—
30#17985127—42no—
31#17985127—42no—
32C2×#14555886—21no—
33C4⋊Dic281—22no—
34C4⋊Dic281D411yescharacteristic
35C4⋊Dic281D411yescharacteristic
36#17985117—22no—
37#17985117—22no—
38#17985117—21no—
39#17985117—21no—
40C4×Dic281—22no—
41C4×Dic281—21no—
42C4×Dic281—21no—
43C2×Q8×C281—21no—
44C2×C8×C281—21no—
45C2×C8×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D412yes—
48C42×C281C2311yescharacteristic
49C22×D281—41no—
50Dic562—21no—
51Dic562—21no—
52Dic562—21no—
53Dic562SD1612yescomplemented
54D1124—42no—
55D1124—41no—
56D1124—41no—
57D1124—41no—
58D1124—41no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63#14555886—41no—
64Q8×C281—41no—
65Q8×C281—41no—
66C2×C4×C281—22no—
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C8×C281—41no—
71C8×C281—41no—
72C22×C281#12011yescharacteristic
73C2×D281—81no—
74C2×D281—81no—
75C2×D281—81no—
76C4×C281—21no—
77C4×C281—42no—
78C4×C281C2×SD1611yescharacteristic
79C4×C281#13511yescharacteristic
80C4×C281AGL(1,ℤ/8)11yescharacteristic
81C4×C281#13711yescharacteristic
82Dic281—22no—
83Dic281—41no—
84Dic281—41no—
85Dic281—41no—
86C2×C281#44811yescharacteristic
87C2×C281#44911yescharacteristic
88C2×C281#45411yescharacteristic
89D281—161no—
90C281#162611yescharacteristic, complemented, Sylow
91#1626—2811nomaximal, Sylow
92#557—2811no—
93#486—2811no—
94#460—2811no—
95#460—2811no—
96#332D28111yescharacteristic, complemented
97Q8⋊C8—2811no—
98Q8⋊C8—2811no—
99C2×SD16—5621no—
100C2×SD16—5621no—
101C4⋊Q8—5621no—
102C4⋊Q8C2×D28111yescharacteristic
103#127—2811no—
104#125—5621no—
105#125—5622no—
106C4×Q8—2811no—
107C4×Q8—2811no—
108C4×Q8—5621no—
109C4×Q8—5621no—
110C4⋊C8C2×D28111yescharacteristic
111C4⋊C8C2×D28111yescharacteristic
112#102—5621no—
113#102—5621no—
114#102—5622no—
115C4×C8—2811no—
116C2×Q8—21no—
117C2×Q8—2811no—
118C2×Q8—2811no—
119C2×D4—5621no—
120C2×D4—5621no—
121C2×D4—5621no—
122SD16—11242no—
123SD16—11242no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—5621no—
127C4⋊C4—21no—
128C4⋊C4—2811no—
129C4⋊C4—2811no—
130C4⋊C4—5622no—
131C4⋊C4—5622no—
132C4⋊C4—5622no—
133C4⋊C4—5621no—
134C4⋊C4—5621no—
135C4⋊C4D112412yes—
136C42—5622no—
137C42—5621no—
138C42—5621no—
139C42C22×D28111yescharacteristic
140C23—11241no—
141Q8—41no—
142Q8—41no—
143Q8—2812no—
144Q8—5621no—
145Q8—5621no—
146Q8—5621no—
147D4—11242no—
148D4—11241no—
149D4—11241no—
150D4—11241no—
151D4—11241no—
152C2×C4—22no—
153C2×C4—5621no—
154C2×C4—5621no—
155C2×C4—5621no—
156C2×C4—5621no—
157C2×C4D4×D28111yescharacteristic
158C2×C4D4×D28111yescharacteristic
159C2×C4C2×D112411yescharacteristic
160C8—41no—
161C8—41no—
162C8—11241no—
163C22—22481no—
164C22—22481no—
165C22—22481no—
166C22#2258284911yescharacteristic
167C4—21no—
168C4—42no—
169C4—5622no—
170C4—11241no—
171C4—11241no—
172C4—11241no—
173C4SD16×D28111yescharacteristic
174C4#2258290011yescharacteristic
175C4#2258290311yescharacteristic
176C4#2258291111yescharacteristic
177C2—44961no—
178C2#3182360311yescharacteristic
179C2#3182360911yescharacteristic
180C2#3182363811yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#332×C281C2
socleC22×C281#120
prime radical#22582876C22
hypercenter#332D281
hypocenterC281#1626
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #31824188C2semidirect
5. #31823193C2semidirect
6. #31823193C2semidirect
7. #332×C281C2semidirect
53. Dic562SD16semidirect
90. C281#1626semidirect
96. #332D281semidirect

Maximal subgroups

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

subgroupindex
#318241882
#318238112
#318236642
#318231932
#332×C2812
#1626281