Finite Group Databasebeta

← #49094486

Subgroups — #49094486

Order 35968.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824199C211yesmaximal, characteristic
2#31823745C211yesmaximal, characteristic, complemented
3#31823670C211yesmaximal, characteristic, complemented
4#31823207C211yesmaximal, characteristic
5#31823195C211yesmaximal, characteristic, complemented
6#31823195C211yesmaximal, characteristic, complemented
7#486×C281C211yesmaximal, characteristic
8C2×#17985128—21no—
9#22582866—21no—
10#22582866—21no—
11#22582860—22no—
12C4×Dic562C2211yescharacteristic
13C4×Dic562C2211yescharacteristic
14D4×Dic281—21no—
15D4×Dic281—21no—
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582803—21no—
20#22582802—21no—
21C4⋊Q8×C281C2211yescharacteristic
22#127×C281C2211yescharacteristic
23#102×C281—22no—
24C4×C8×C281C2211yescharacteristic
25C2×Dic562D411yescharacteristic
26C2×Dic562D411yescharacteristic
27C22×Dic281—22no—
28#17985128—42no—
29C2×#14555886—21no—
30C2×#14555886—21no—
31C4⋊Dic281D411yescharacteristic
32C4⋊Dic281D411yescharacteristic
33#17985117—21no—
34#17985117—21no—
35C22⋊Dic281—22no—
36C22⋊Dic281—22no—
37C22⋊Dic281—22no—
38C4×Dic281—21no—
39C4×Dic281—21no—
40C2×Q8×C281—21no—
41C2×D4×C281—21no—
42C2×D4×C281—21no—
43C2×D4×C281D412yes—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C42×C281C2311yescharacteristic
48Dic562—21no—
49Dic562—21no—
50Dic562—21no—
51Dic562—21no—
52C2×Dic281—21no—
53C2×Dic281—21no—
54C2×Dic281—21no—
55C2×Dic281—21no—
56C2×Dic281—82no—
57#14555886—41no—
58#14555886—41no—
59C23×C281—22no—
60Q8×C281—41no—
61Q8×C281—41no—
62D4×C281—42no—
63D4×C281—41no—
64D4×C281—41no—
65D4×C281—41no—
66D4×C281—41no—
67C2×C4×C281—41no—
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C8×C281—41no—
72C22×C281—42no—
73C22×C281—42no—
74C22×C281—42no—
75C22×C281#12011yescharacteristic
76C4×C281—21no—
77C4×C281—81no—
78C4×C281#13511yescharacteristic
79C4×C281#13511yescharacteristic
80C4×C281AGL(1,ℤ/8)11yescharacteristic
81C4×C281#13711yescharacteristic
82Dic281—41no—
83Dic281—41no—
84Dic281—41no—
85Dic281—41no—
86C2×C281—82no—
87C2×C281#44911yescharacteristic
88C2×C281#45211yescharacteristic
89C2×C281#45511yescharacteristic
90C281#164011yescharacteristic, complemented, Sylow
91#1640—2811nomaximal, Sylow
92#559—2811no—
93#486D28111yescharacteristic
94#475—2811no—
95#462—2811no—
96#331—2811no—
97Q8⋊C8—2811no—
98Q8⋊C8—2811no—
99C2×Q16—5621no—
100C4⋊Q8C2×D28111yescharacteristic
101#127C2×D28111yescharacteristic
102#124—5621no—
103#124—5621no—
104#123—5622no—
105C4×Q8—2811no—
106C4×Q8—2811no—
107C4×D4—5621no—
108C4×D4—5621no—
109#106—5621no—
110C4⋊C8—2811no—
111C4⋊C8—2811no—
112#103—5621no—
113#103—5621no—
114#102—22no—
115C4×C8C2×D28111yescharacteristic
116C2×Q8—21no—
117C2×Q8—2811no—
118C2×Q8—2811no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D28112yes—
122C22×C4—5622no—
123Q16—11242no—
124C2×C8—21no—
125C2×C8—5621no—
126C2×C8—5621no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2811no—
130C4⋊C4—2811no—
131C4⋊C4—5621no—
132C4⋊C4—5621no—
133C22⋊C4—5622no—
134C22⋊C4—5622no—
135C22⋊C4—5622no—
136C42—5621no—
137C42—5621no—
138C42C22×D28111yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—5621no—
143Q8—5621no—
144Q8—5621no—
145Q8—5621no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—5621no—
153C2×C4—5621no—
154C2×C4—5621no—
155C2×C4—5621no—
156C2×C4—22482no—
157C2×C4D4×D28111yescharacteristic
158C2×C4D4×D28111yescharacteristic
159C2×C4C2×C22⋊D28111yescharacteristic
160C8—41no—
161C8—11241no—
162C8—11241no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#2258284711yescharacteristic
167C4—21no—
168C4—81no—
169C4—11241no—
170C4—11241no—
171C4—11241no—
172C4—11241no—
173C4#2258289811yescharacteristic
174C4#2258290011yescharacteristic
175C4#2258290311yescharacteristic
176C4#2258290811yescharacteristic
177C2—82no—
178C2#3182360511yescharacteristic
179C2#3182362211yescharacteristic
180C2#3182364011yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#486×C281C2
socleC22×C281#120
prime radical#127×C281C22
hypercenter#486D281
hypocenterC281#1640
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #31823745C2semidirect
3. #31823670C2semidirect
5. #31823195C2semidirect
6. #31823195C2semidirect
90. C281#1640semidirect

Maximal subgroups

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

subgroupindex
#318241992
#318237452
#318236702
#318232072
#318231952
#486×C2812
#1640281