Finite Group Databasebeta

← #49120571

Subgroups — #49120571

Order 36224.

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#31827219C211yesmaximal, characteristic
2#31826871C211yesmaximal, characteristic, complemented
3#31826857C211yesmaximal, characteristic
4#31826207C211yesmaximal, characteristic, complemented
5#31826206C211yesmaximal, characteristic, complemented
6#31826204C211yesmaximal, characteristic
7#501×C283C211yesmaximal, characteristic, complemented
8C2×#17985382—21no—
9C2×#17985379—21no—
10#22583609—21no—
11#22583605—21no—
12#22583605—21no—
13#22583602C2211yescharacteristic
14#22583598C2211yescharacteristic
15#22583595—21no—
16#22583590—21no—
17#22583588—21no—
18#22583543—21no—
19#22583541—21no—
20#22583521C2211yescharacteristic
21#22583521C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23#125×C283C2211yescharacteristic
24#107×C283—21no—
25#106×C283—21no—
26#97×C283C2211yescharacteristic
27C2×Dic566—21no—
28C2×Dic566D411yescharacteristic
29C2×D1132D411yescharacteristic
30C2×C4×D283—21no—
31#17985382—42no—
32#17985379—42no—
33C2×C283⋊C8—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37C4⋊Dic283D411yescharacteristic
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41(C2×D283)⋊C4—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—21no—
45(C2×D283)⋊C4—21no—
46C4×Dic283—21no—
47C2×Q8×C283—21no—
48C2×C8×C283—21no—
49C4⋊C4×C283—21no—
50C4⋊C4×C283—21no—
51C4⋊C4×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283D411yescharacteristic
54C4⋊C4×C283D411yescharacteristic
55C42×C283C2311yescharacteristic
56C22×D283—21no—
57Dic566—41no—
58Dic566—81no—
59D1132—41no—
60C2×Dic283—21no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C4×D283—81no—
64C283⋊C8—22no—
65C283⋊C8—22no—
66Q8×C283—41no—
67Q8×C283—41no—
68C2×C4×C283—21no—
69C2×C4×C283—21no—
70C2×C4×C283—41no—
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C2×C4×C283C2×D411yescharacteristic
74C8×C283—22no—
75C22×C283#12011yescharacteristic
76C2×D283—41no—
77C2×D283—41no—
78C2×D283—41no—
79C4×C283—21no—
80C4×C283—21no—
81C4×C283—21no—
82C4×C283—41no—
83C4×C283—41no—
84C4×C283—81no—
85Dic283—41no—
86Dic283—41no—
87Dic283—41no—
88C2×C283#45311yescharacteristic
89C2×C283#45611yescharacteristic
90C2×C283#45611yescharacteristic
91D283—81no—
92C283#166011yescharacteristic, complemented, Sylow
93#1660—2831nomaximal, Sylow
94#563—2831no—
95#501—2831no—
96#501D28311yescharacteristic, complemented
97#497—2831no—
98#330—2831no—
99#330—2831no—
100#329—2831no—
101C2×Q16—5661no—
102C2×SD16—5661no—
103C4⋊Q8—5661no—
104C4⋊Q8C2×D28311yescharacteristic
105#126—5661no—
106#126—5661no—
107#125—2831no—
108#125C2×D28311yescharacteristic
109#124—2831no—
110#123—5661no—
111C22⋊Q8—5661no—
112C22⋊Q8—5661no—
113#107—21no—
114#107—5661no—
115#106—21no—
116#106—5661no—
117#97—2831no—
118#97—2831no—
119#97C2×D28311yescharacteristic
120C2×Q8—21no—
121C2×Q8—2831no—
122C2×Q8—5661no—
123C2×D4—2831no—
124C22×C4—5661no—
125Q16—11322no—
126SD16—11322no—
127C2×C8—21no—
128C2×C8—5661no—
129C2×C8—5661no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2831no—
135C4⋊C4—2831no—
136C4⋊C4—5661no—
137C4⋊C4—5661no—
138C4⋊C4—5661no—
139C4⋊C4—5661no—
140C4⋊C4C22⋊D28311yescharacteristic
141C4⋊C4C22⋊D28311yescharacteristic
142C22⋊C4—5661no—
143C22⋊C4—5661no—
144C22⋊C4—5661no—
145C22⋊C4—5661no—
146C22⋊C4—5661no—
147C42—5661no—
148C42C22×D28311yescharacteristic
149C23—5661no—
150Q8—41no—
151Q8—41no—
152Q8—11321no—
153Q8—22641no—
154D4—11321no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—5661no—
159C2×C4—5661no—
160C2×C4—5661no—
161C2×C4—22641no—
162C2×C4D4×D28311yescharacteristic
163C2×C4D4×D28311yescharacteristic
164C2×C4C2×C22⋊D28311yescharacteristic
165C8—22no—
166C8—5662no—
167C8—5662no—
168C22—11321no—
169C22—11321no—
170C22—11321no—
171C22#2258357811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—11321no—
179C4—11321no—
180C4—11321no—
181C2—22641no—
182C2#3182663111yescharacteristic
183C2#3182664611yescharacteristic
184C2#3182664711yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#501×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#501D283
hypocenterC283#1660
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #31826871C2semidirect
4. #31826207C2semidirect
5. #31826206C2semidirect
7. #501×C283C2semidirect
92. C283#1660semidirect
96. #501D283semidirect

Maximal subgroups

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

subgroupindex
#318272192
#318268712
#318268572
#318262072
#318262062
#318262042
#501×C2832
#1660283