Finite Group Databasebeta

← #35292035

Subgroups — #35292035

Order 21248.

198 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 41 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#24908808C211yesmaximal, characteristic
2#24905346C211yesmaximal, characteristic
3C83×#1325C211yesmaximal, characteristic
4#19128332C411yescharacteristic
5#19127741—21no—
6C2×C4⋊(C83⋊C8)—21no—
7#19127470C411yescharacteristic
8#19127461—21no—
9#384×C83C2211yescharacteristic
10#324×C83—21no—
11C2×#13050574—21no—
12C22×C83⋊C8—41no—
13#14581791—41no—
14#14581783—41no—
15#14581771—41no—
16#14581751—21no—
17#14581725—41no—
18#14581723—41no—
19C4⋊(C83⋊C8)—22no—
20C4⋊(C83⋊C8)—41no—
21C2×C4⋊C4×C83—41no—
22C2×C4⋊C4×C83C2×C411yescharacteristic
23C2×C4⋊C4×C83D411yescharacteristic
24C2×C42×C83D411yescharacteristic
25C22⋊C8×C83—41no—
26C2×Dic166—41no—
27#13050574—22no—
28#13050574—41no—
29C2×C83⋊C8—41no—
30C2×C83⋊C8—42no—
31C2×C83⋊C8—81no—
32C2×C83⋊C8—81no—
33C4⋊Dic83—21no—
34C4⋊Dic83—21no—
35C4⋊Dic83—41no—
36Dic83⋊C4—42no—
37C22⋊Dic83—41no—
38C4×Dic83—41no—
39C22×C4×C83—21no—
40C22×C4×C83—21no—
41C22×C4×C83—21no—
42C22×C4×C83C22⋊C411yescharacteristic
43C2×C8×C83—81no—
44C4⋊C4×C83—41no—
45C4⋊C4×C83—41no—
46C4⋊C4×C83—81no—
47C4⋊C4×C83—81no—
48C42×C83—21no—
49C42×C83SD1611yescharacteristic
50C42×C83Q1611yescharacteristic
51C23×C83#9911yescharacteristic
52C2×C4×C83—21no—
53C2×C4×C83—21no—
54C2×C4×C83—21no—
55C2×C4×C83—21no—
56C2×C4×C83—21no—
57C2×C4×C83—21no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—41no—
61C2×C4×C83—41no—
62C2×C4×C83—81no—
63C2×C4×C83—81no—
64C2×C4×C83#10311yescharacteristic
65C2×C4×C83#10411yescharacteristic
66C2×Dic83—41no—
67C2×Dic83—41no—
68Dic166—161no—
69C8×C83—161no—
70C83⋊C8—42no—
71C83⋊C8—82no—
72C22×C83—21no—
73C22×C83—21no—
74C22×C83#32811yescharacteristic
75C22×C83AΣL(1,𝔽16)11yescharacteristic
76C22×C83#35611yescharacteristic
77C4×C83—21no—
78C4×C83—21no—
79C4×C83—21no—
80C4×C83—21no—
81C4×C83—21no—
82C4×C83—21no—
83C4×C83—81no—
84C4×C83—81no—
85Dic83—81no—
86Dic83—81no—
87#7443—831nomaximal, Sylow
88C2×C83—21no—
89C2×C83—21no—
90C2×C83#135411yescharacteristic
91C2×C83#140211yescharacteristic
92C2×C83#140511yescharacteristic
93#2060—831no—
94#1325D8311yescharacteristic
95#1296—831no—
96C83#744311yescharacteristic, complemented, Sylow
97#544—831no—
98#428—1661no—
99C2×C4⋊C8—1661no—
100#384C2×D8311yescharacteristic
101#343—831no—
102#339—1661no—
103#324—21no—
104C2×M16—1661no—
105C22×C8—3321no—
106C4⋊Q8—3321no—
107#125—3321no—
108C22⋊Q8—3321no—
109#117—1661no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4C4×D8311yescharacteristic
112C2×C4⋊C4C22⋊D8311yescharacteristic
113C2×C42D33211yescharacteristic
114#107—3321no—
115#106—3321no—
116C4⋊C8—3321no—
117C4⋊C8—1662no—
118C22⋊C8—41no—
119C2×Q8—3321no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4(C2×D83)⋊C411yescharacteristic
124M16—3321no—
125M16—1662no—
126C2×C8—81no—
127C2×C8—3321no—
128C2×C8—3322no—
129C2×C8—6641no—
130C2×C8—6641no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—81no—
134C4⋊C4—81no—
135C4⋊C4—3321no—
136C4⋊C4—3322no—
137C4⋊C4—1661no—
138C4⋊C4—1661no—
139C22⋊C4—3321no—
140C42—21no—
141C42—3321no—
142C42#1305057911yescharacteristic
143C42Dic33211yescharacteristic
144C23#1458170611yescharacteristic
145Q8—13281no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—3321no—
159C2×C4—3321no—
160C2×C4#1458171711yescharacteristic
161C2×C4#1458171811yescharacteristic
162C8—161no—
163C8—3322no—
164C8—6642no—
165C22—21no—
166C22—21no—
167C22#1912743911yescharacteristic
168C22#1912748711yescharacteristic
169C22#1912749911yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—6641no—
179C4—6641no—
180C2—21no—
181C2—21no—
182C2#2490549411yescharacteristic
183C2#2490560711yescharacteristic
184C2#2490561611yescharacteristic
subgroupG/H
centerC22#19127487
commutatorC2×C4⋊C4×C83C2×C4
Frattini#384C2×D83
FittingC83×#1325C2
socleC22×C83AΣL(1,𝔽16)
prime radicalC23×C83#99
cosocle#384×C83C22
hypercenter#1325D83
hypocenterC83#7443
LCSG ▷ C2×C4⋊C4×C83 ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
96. C83#7443semidirect

Maximal subgroups

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

subgroupindex
#249088082
#249053462
C83×#13252
#744383