Finite Group Databasebeta

← #49094487

Subgroups — #49094487

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#31824198C211yesmaximal, characteristic
2#31823811C211yesmaximal, characteristic
3#31823745C211yesmaximal, characteristic, complemented
4#31823206C211yesmaximal, characteristic
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6#31823193C211yesmaximal, characteristic, complemented
7#462×C281C211yesmaximal, characteristic, complemented
8#22582876C2211yescharacteristic
9#22582868—21no—
10#22582867—21no—
11#22582864—22no—
12C4×Dic562C2211yescharacteristic
13C4×D1124—21no—
14#22582841—21no—
15#22582810—21no—
16C4⋊#14555886C2211yescharacteristic
17#22582802—21no—
18#22582799—22no—
19C4×#14555886C2211yescharacteristic
20C2×Q16×C281—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4×Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24#103×C281—21no—
25C2×Dic562D411yescharacteristic
26C2×D1124—21no—
27C2×D1124—21no—
28C2×D1124D412yes—
29C2×C4×D281—22no—
30C2×#14555886—21no—
31C2×#14555886—21no—
32C4⋊Dic281D411yescharacteristic
33#17985117—21no—
34#17985115—22no—
35#17985115—22no—
36#17985115—22no—
37C4×Dic281—21no—
38C2×Q8×C281—21no—
39C2×Q8×C281D411yescharacteristic
40Q16×C281—42no—
41C2×C8×C281—21no—
42C4⋊C4×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281D411yescharacteristic
46C42×C281—21no—
47C42×C281C2311yescharacteristic
48C22×D281—22no—
49Dic562—21no—
50Dic562—21no—
51D1124—42no—
52D1124—41no—
53D1124—41no—
54D1124—41no—
55D1124—41no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C4×D281—82no—
59#14555886—41no—
60#14555886—41no—
61Q8×C281—21no—
62Q8×C281—21no—
63Q8×C281—41no—
64Q8×C281—41no—
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281—41no—
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C8×C281—41no—
72C22×C281#12011yescharacteristic
73C2×D281—42no—
74C2×D281—42no—
75C2×D281—42no—
76C4×C281—21no—
77C4×C281—41no—
78C4×C281—41no—
79C4×C281—81no—
80C4×C281#13511yescharacteristic
81C4×C281#13511yescharacteristic
82C4×C281AGL(1,ℤ/8)11yescharacteristic
83C4×C281#13711yescharacteristic
84Dic281—41no—
85Dic281—41no—
86C2×C281#44911yescharacteristic
87C2×C281#45211yescharacteristic
88C2×C281#45511yescharacteristic
89D281—82no—
90C281#164011yescharacteristic, complemented, Sylow
91#1640—2811nomaximal, Sylow
92#559—2811no—
93#486—2811no—
94#475—2811no—
95#462D28111yescharacteristic, complemented
96#331—2811no—
97Q8⋊C8—2811no—
98Q8⋊C8—2811no—
99C2×Q16—21no—
100C4⋊Q8C2×D28111yescharacteristic
101#127—2811no—
102#124—5621no—
103#124—5621no—
104#123—5622no—
105C4×Q8—2811no—
106C4×Q8C2×D28111yescharacteristic
107C4×D4—5621no—
108C4×D4—5621no—
109#106—5621no—
110C4⋊C8—2811no—
111C4⋊C8C2×D28111yescharacteristic
112#103—21no—
113#103—5621no—
114#102—5622no—
115C4×C8—2811no—
116C2×Q8—21no—
117C2×Q8—2811no—
118C2×Q8C22⋊D28111yescharacteristic
119C2×D4—2812no—
120C2×D4—5621no—
121C2×D4—5621no—
122C22×C4—5622no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—5621no—
126C2×C8—5621no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2811no—
131C4⋊C4—5621no—
132C4⋊C4C22⋊D28111yescharacteristic
133C22⋊C4—5622no—
134C22⋊C4—5622no—
135C22⋊C4—5622no—
136C42—21no—
137C42—5621no—
138C42C22×D28111yescharacteristic
139C23—5622no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—5621no—
145Q8—5621no—
146D4—11242no—
147D4—11241no—
148D4—11241no—
149D4—11241no—
150D4—11241no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
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—11242no—
164C22—11242no—
165C22—11242no—
166C22#2258284711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—11241no—
172C4—11241no—
173C4#2258289911yescharacteristic
174C4#2258290211yescharacteristic
175C4#2258290511yescharacteristic
176C4#2258291111yescharacteristic
177C2—22482no—
178C2#3182360611yescharacteristic
179C2#3182362411yescharacteristic
180C2#3182363911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#462×C281C2
socleC22×C281#120
prime radical#22582876C22
hypercenter#462D281
hypocenterC281#1640
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #31823745C2semidirect
5. Q8⋊#14555886C2semidirect
6. #31823193C2semidirect
7. #462×C281C2semidirect
90. C281#1640semidirect
95. #462D281semidirect

Maximal subgroups

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

subgroupindex
#318241982
#318238112
#318237452
#318232062
Q8⋊#145558862
#318231932
#462×C2812
#1640281