Finite Group Databasebeta

← #49094613

Subgroups — #49094613

Order 35968.

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

normal subgroups only

This group has 196 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#31823869C211yesmaximal, characteristic, complemented
3#31823855C211yesmaximal, characteristic
4#31823205C211yesmaximal, characteristic, complemented
5#31823204C211yesmaximal, characteristic, complemented
6#31823202C211yesmaximal, characteristic
7#501×C281C211yesmaximal, characteristic, complemented
8C2×#17985128—21no—
9C2×#17985125—21no—
10#22582878—21no—
11#22582874—21no—
12#22582874—21no—
13#22582871C2211yescharacteristic
14#22582867C2211yescharacteristic
15#22582864—21no—
16#22582859—21no—
17#22582857—21no—
18#22582812—21no—
19#22582810—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—
31#17985128—42no—
32#17985125—42no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281D411yescharacteristic
37C4⋊Dic281D411yescharacteristic
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985115—21no—
42#17985115—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46C4×Dic281—21no—
47C2×Q8×C281—21no—
48C2×C8×C281—21no—
49C4⋊C4×C281—21no—
50C4⋊C4×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281—21no—
53C4⋊C4×C281D411yescharacteristic
54C4⋊C4×C281D411yescharacteristic
55C42×C281C2311yescharacteristic
56C22×D281—21no—
57Dic562—41no—
58Dic562—81no—
59D1124—41no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63C4×D281—81no—
64#14555886—22no—
65#14555886—22no—
66Q8×C281—41no—
67Q8×C281—41no—
68C2×C4×C281—21no—
69C2×C4×C281—21no—
70C2×C4×C281—41no—
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C8×C281—22no—
75C22×C281#12011yescharacteristic
76C2×D281—41no—
77C2×D281—41no—
78C2×D281—41no—
79C4×C281—21no—
80C4×C281—21no—
81C4×C281—21no—
82C4×C281—41no—
83C4×C281—41no—
84C4×C281—81no—
85Dic281—41no—
86Dic281—41no—
87Dic281—41no—
88C2×C281#45311yescharacteristic
89C2×C281#45611yescharacteristic
90C2×C281#45611yescharacteristic
91D281—81no—
92C281#166011yescharacteristic, complemented, Sylow
93#1660—2811nomaximal, Sylow
94#563—2811no—
95#501—2811no—
96#501D28111yescharacteristic, complemented
97#497—2811no—
98#330—2811no—
99#330—2811no—
100#329—2811no—
101C2×Q16—5621no—
102C2×SD16—5621no—
103C4⋊Q8—5621no—
104C4⋊Q8C2×D28111yescharacteristic
105#126—5621no—
106#126—5621no—
107#125—2811no—
108#125C2×D28111yescharacteristic
109#124—2811no—
110#123—5621no—
111C22⋊Q8—5621no—
112C22⋊Q8—5621no—
113#107—21no—
114#107—5621no—
115#106—21no—
116#106—5621no—
117#97—2811no—
118#97—2811no—
119#97C2×D28111yescharacteristic
120C2×Q8—21no—
121C2×Q8—2811no—
122C2×Q8—5621no—
123C2×D4—2811no—
124C22×C4—5621no—
125Q16—11242no—
126SD16—11242no—
127C2×C8—21no—
128C2×C8—5621no—
129C2×C8—5621no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2811no—
135C4⋊C4—2811no—
136C4⋊C4—5621no—
137C4⋊C4—5621no—
138C4⋊C4—5621no—
139C4⋊C4—5621no—
140C4⋊C4C22⋊D28111yescharacteristic
141C4⋊C4C22⋊D28111yescharacteristic
142C22⋊C4—5621no—
143C22⋊C4—5621no—
144C22⋊C4—5621no—
145C22⋊C4—5621no—
146C22⋊C4—5621no—
147C42—5621no—
148C42C22×D28111yescharacteristic
149C23—5621no—
150Q8—41no—
151Q8—41no—
152Q8—11241no—
153Q8—22481no—
154D4—11241no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—5621no—
159C2×C4—5621no—
160C2×C4—5621no—
161C2×C4—22481no—
162C2×C4D4×D28111yescharacteristic
163C2×C4D4×D28111yescharacteristic
164C2×C4C2×C22⋊D28111yescharacteristic
165C8—22no—
166C8—5622no—
167C8—5622no—
168C22—11241no—
169C22—11241no—
170C22—11241no—
171C22#2258284711yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—11241no—
179C4—11241no—
180C4—11241no—
181C2—22481no—
182C2#3182362911yescharacteristic
183C2#3182364411yescharacteristic
184C2#3182364511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#501×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#501D281
hypocenterC281#1660
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. #31823869C2semidirect
4. #31823205C2semidirect
5. #31823204C2semidirect
7. #501×C281C2semidirect
92. C281#1660semidirect
96. #501D281semidirect

Maximal subgroups

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

subgroupindex
#318242172
#318238692
#318238552
#318232052
#318232042
#318232022
#501×C2812
#1660281