Finite Group Databasebeta

← #35318795

Subgroups — #35318795

Order 21248.

172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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#24909739C211yesmaximal, characteristic, complemented
2#24909639C211yesmaximal, characteristic
3#24909300C211yesmaximal, characteristic
4#24905538C211yesmaximal, characteristic, complemented
5#24905524C211yesmaximal, characteristic, complemented
6#24905523C211yesmaximal, characteristic, complemented
7C83×#2231C211yesmaximal, characteristic
8#19128118—21no—
9#19128103C2211yescharacteristic
10#19127528—21no—
11#19127526—21no—
12#19127525—21no—
13#19127522C2211yescharacteristic
14#19127522C2211yescharacteristic
15#19127511—21no—
16#19127485—21no—
17C4×C83⋊C16C2211yescharacteristic
18#499×C83C2211yescharacteristic
19#443×C83C2211yescharacteristic
20#365×C83—21no—
21#364×C83C2211yescharacteristic
22#360×C83—21no—
23#14581784—21no—
24#14581732—21no—
25#14581732—21no—
26#14581732—41no—
27C2×C83⋊C16—41no—
28C2×C83⋊C16D411yescharacteristic
29C2×C83⋊C16D411yescharacteristic
30#14581726—21no—
31#14581724—21no—
32#135×C83D411yescharacteristic
33#131×C83—21no—
34#125×C83—21no—
35M32×C83—21no—
36#108×C83D411yescharacteristic
37#107×C83—21no—
38#106×C83—21no—
39#104×C83—21no—
40C4×C8×C83C2311yescharacteristic
41C4⋊Dic83—41no—
42Dic83⋊C4—81no—
43C83⋊C16—21no—
44C83⋊C16—41no—
45C83⋊C16—41no—
46C83⋊C16SD1611yescharacteristic
47C83⋊C16SD1611yescharacteristic
48#41×C83—21no—
49Q16×C83Q1611yescharacteristic
50SD16×C83—21no—
51D8×C83Q1611yescharacteristic
52M16×C83—21no—
53M16×C83—41no—
54C2×C8×C83—41no—
55C2×C8×C83C2×D411yescharacteristic
56C2×C8×C83C2×D411yescharacteristic
57C4⋊C4×C83—41no—
58C4⋊C4×C83—81no—
59C42×C83#4111yescharacteristic
60C16×C83—41no—
61Q8×C83—21no—
62D4×C83—21no—
63D4×C83—41no—
64C2×C4×C83—21no—
65C2×C4×C83—41no—
66C2×C4×C83—81no—
67C2×C4×C83#12111yescharacteristic
68C2×Dic83—81no—
69C8×C83—41no—
70C8×C83C2×SD1611yescharacteristic
71C8×C83C2×Q1611yescharacteristic
72C8×C83#13511yescharacteristic
73C8×C83#13711yescharacteristic
74C22×C83—41no—
75C22×C83#47211yescharacteristic
76C4×C83—41no—
77C4×C83—41no—
78C4×C83—161no—
79C4×C83#46111yescharacteristic
80C4×C83#46711yescharacteristic
81Dic83—161no—
82#12463—831nomaximal, Sylow
83C2×C83—21no—
84C2×C83—81no—
85C2×C83#167511yescharacteristic
86#2253—831no—
87#2231—831no—
88#2231D8311yescharacteristic
89#2170—831no—
90#1373—831no—
91#1366—831no—
92#1366—831no—
93C83#1246311yescharacteristic, complemented, Sylow
94#504—1661no—
95#499—831no—
96#499C2×D8311yescharacteristic
97#443C2×D8311yescharacteristic
98#367—1661no—
99#366—1661no—
100#365—21no—
101#365—1661no—
102#364—831no—
103#364—831no—
104#364C2×D8311yescharacteristic
105#360—21no—
106#360—1661no—
107#350—1661no—
108C4×C16—831no—
109#135C22⋊D8311yescharacteristic
110#131—21no—
111#125—21no—
112#125—1661no—
113M32—21no—
114M32—3321no—
115M32—1661no—
116M32—1661no—
117C2×C16—3321no—
118C2×C16—831no—
119C2×C16—831no—
120#108C22⋊D8311yescharacteristic
121#107—21no—
122#107—1661no—
123#106—21no—
124#106—1661no—
125#104—21no—
126C4×C8C22×D8311yescharacteristic
127#41—21no—
128Q16#1305058011yescharacteristic
129SD16—21no—
130D8#1305058011yescharacteristic
131M16—21no—
132M16—41no—
133C2×C8—41no—
134C2×C8D4×D8311yescharacteristic
135C2×C8C2×C22⋊D8311yescharacteristic
136C4⋊C4—41no—
137C4⋊C4—81no—
138C4⋊C4—3321no—
139C4⋊C4—6641no—
140C42#1305058911yescharacteristic
141C16—41no—
142C16—3321no—
143C16—3321no—
144C16—831no—
145C16—831no—
146C16—1661no—
147Q8—21no—
148D4—21no—
149D4—41no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—6641no—
154C2×C4#1458176411yescharacteristic
155C8—41no—
156C8SD16×D8311yescharacteristic
157C8C2×#1305058011yescharacteristic
158C8#1458181211yescharacteristic
159C8#1458182111yescharacteristic
160C22—41no—
161C22#1912796911yescharacteristic
162C4—41no—
163C4—41no—
164C4—161no—
165C4—13281no—
166C4#1912790411yescharacteristic
167C4#1912794011yescharacteristic
168C2—21no—
169C2—81no—
170C2#2490686011yescharacteristic
subgroupG/H
centerC2#24906860
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#2231C2
socleC2×C83#1675
prime radical#135×C83D4
hypercenter#2231D83
hypocenterC83#12463
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2231

Complements

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

NH ≅ G/Ntype
1. #24909739C2semidirect
4. #24905538C2semidirect
5. #24905524C2semidirect
6. #24905523C2semidirect
93. C83#12463semidirect

Maximal subgroups

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

subgroupindex
#249097392
#249096392
#249093002
#249055382
#249055242
#249055232
C83×#22312
#1246383