Finite Group Databasebeta

← #49094635

Subgroups — #49094635

Order 35968.

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

normal subgroups only

This group has 184 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#31824217C211yesmaximal, characteristic
2#31823831C211yesmaximal, characteristic, complemented
3#31823825C211yesmaximal, characteristic
4#31823205C211yesmaximal, characteristic, complemented
5#31823204C211yesmaximal, characteristic, complemented
6#31823202C211yesmaximal, characteristic
7#501×C281C211yesmaximal, characteristic, complemented
8#22582878—21no—
9#22582874—21no—
10#22582874—21no—
11#22582871C2211yescharacteristic
12#22582867C2211yescharacteristic
13#22582864—21no—
14#22582859—21no—
15#22582857—21no—
16#22582803—21no—
17#22582803—21no—
18#22582802—21no—
19#22582799—21no—
20#22582790C2211yescharacteristic
21#22582790C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#125×C281C2211yescharacteristic
24#107×C281—21no—
25#106×C281—21no—
26#97×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562D411yescharacteristic
29C2×D1124D411yescharacteristic
30C2×C4×D281—21no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281D411yescharacteristic
35C4⋊Dic281D411yescharacteristic
36#17985117—21no—
37#17985117—21no—
38#17985117—21no—
39#17985115—21no—
40#17985115—21no—
41#17985115—21no—
42#17985115—21no—
43#17985115—21no—
44C4×Dic281—21no—
45C2×Q8×C281—21no—
46C2×C8×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281—21no—
49C4⋊C4×C281—21no—
50C4⋊C4×C281—21no—
51C4⋊C4×C281D411yescharacteristic
52C4⋊C4×C281D411yescharacteristic
53C42×C281C2311yescharacteristic
54C22×D281—21no—
55Dic562—41no—
56Dic562—81no—
57D1124—41no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C4×D281—81no—
62#14555886—41no—
63#14555886—41no—
64Q8×C281—42no—
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—22no—
72C22×C281#12011yescharacteristic
73C2×D281—41no—
74C2×D281—41no—
75C2×D281—41no—
76C4×C281—21no—
77C4×C281—21no—
78C4×C281—21no—
79C4×C281—41no—
80C4×C281—41no—
81C4×C281—81no—
82Dic281—41no—
83Dic281—41no—
84Dic281—41no—
85C2×C281#45411yescharacteristic
86C2×C281#45511yescharacteristic
87C2×C281#45611yescharacteristic
88D281—81no—
89C281#166411yescharacteristic, complemented, Sylow
90#1664—2811nomaximal, Sylow
91#563—2811no—
92#501D28111yescharacteristic, complemented
93#491—2811no—
94#489—2811no—
95#330—2811no—
96#330—2811no—
97#329—2811no—
98C4⋊Q8—5621no—
99C4⋊Q8C2×D28111yescharacteristic
100#126—5621no—
101#126—5621no—
102#125—2811no—
103#125C2×D28111yescharacteristic
104#124—2811no—
105#123—5621no—
106C22⋊Q8—5621no—
107C22⋊Q8—5621no—
108#107—21no—
109#106—21no—
110#103—5621no—
111#103—5621no—
112#103—5621no—
113#102—5621no—
114#97—2811no—
115#97—2811no—
116#97C2×D28111yescharacteristic
117C2×Q8—21no—
118C2×Q8—2811no—
119C2×Q8—5621no—
120C2×D4—2811no—
121C22×C4—5621no—
122C2×C8—21no—
123C2×C8—5621no—
124C2×C8—5621no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2811no—
130C4⋊C4—2811no—
131C4⋊C4—5621no—
132C4⋊C4—5621no—
133C4⋊C4—5621no—
134C4⋊C4—5621no—
135C4⋊C4C22⋊D28111yescharacteristic
136C4⋊C4C22⋊D28111yescharacteristic
137C22⋊C4—5621no—
138C22⋊C4—5621no—
139C22⋊C4—5621no—
140C22⋊C4—5621no—
141C22⋊C4—5621no—
142C42—5621no—
143C42C22×D28111yescharacteristic
144C23—5621no—
145Q8—42no—
146Q8—11241no—
147Q8—22481no—
148D4—11241no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—5621no—
153C2×C4—5621no—
154C2×C4—5621no—
155C2×C4—22481no—
156C2×C4D4×D28111yescharacteristic
157C2×C4D4×D28111yescharacteristic
158C2×C4C2×C22⋊D28111yescharacteristic
159C8—22no—
160C8—11241no—
161C8—11241no—
162C22—11241no—
163C22—11241no—
164C22—11241no—
165C22#2258284711yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—11241no—
173C4—11241no—
174C4—11241no—
175C2—22481no—
176C2#3182363411yescharacteristic
177C2#3182363911yescharacteristic
178C2#3182364511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#501×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#501D281
hypocenterC281#1664
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #31823831C2semidirect
4. #31823205C2semidirect
5. #31823204C2semidirect
7. #501×C281C2semidirect
89. C281#1664semidirect
92. #501D281semidirect

Maximal subgroups

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

subgroupindex
#318242172
#318238312
#318238252
#318232052
#318232042
#318232022
#501×C2812
#1664281