Finite Group Databasebeta

← #35291997

Subgroups — #35291997

Order 21248.

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

normal subgroups only

This group has 206 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#24908624C211yesmaximal, characteristic
2#24905289C211yesmaximal, characteristic
3C83×#1394C211yesmaximal, characteristic
4#19128332C411yescharacteristic
5#19127710—21no—
6#19127470C411yescharacteristic
7#19127461—21no—
8#19127456—21no—
9C2×#101×C83—21no—
10#391×C83C2211yescharacteristic
11C2×#13050574—21no—
12C22×C83⋊C8—41no—
13#14581791—41no—
14#14581783—41no—
15#14581771—41no—
16#14581751—21no—
17#14581716—41no—
18#14581716—41no—
19C22×Q8×C83D411yescharacteristic
20C2×M16×C83—41no—
21C2×C4⋊C4×C83C2×C411yescharacteristic
22C2×C42×C83D411yescharacteristic
23#101×C83—22no—
24#101×C83—41no—
25#95×C83—41no—
26C2×Dic166—41no—
27#13050574—41no—
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—
39C2×Q8×C83—21no—
40C2×Q8×C83—41no—
41C2×Q8×C83—41no—
42C2×Q8×C83SD1611yescharacteristic
43C2×Q8×C83Q1611yescharacteristic
44C22×C4×C83—21no—
45C22×C4×C83—21no—
46C22×C4×C83—21no—
47C22×C4×C83C22⋊C411yescharacteristic
48M16×C83—42no—
49M16×C83—81no—
50C2×C8×C83—81no—
51C4⋊C4×C83—41no—
52C42×C83—41no—
53C23×C83#9911yescharacteristic
54Q8×C83—41no—
55Q8×C83—41no—
56Q8×C83—81no—
57C2×C4×C83—21no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—21no—
62C2×C4×C83—21no—
63C2×C4×C83—41no—
64C2×C4×C83—41no—
65C2×C4×C83—41no—
66C2×C4×C83—41no—
67C2×C4×C83—41no—
68C2×C4×C83—81no—
69C2×C4×C83#10311yescharacteristic
70C2×C4×C83#10411yescharacteristic
71C2×Dic83—41no—
72C2×Dic83—41no—
73Dic166—161no—
74C8×C83—82no—
75C83⋊C8—81no—
76C83⋊C8—82no—
77C22×C83—21no—
78C22×C83—21no—
79C22×C83#32811yescharacteristic
80C22×C83AΣL(1,𝔽16)11yescharacteristic
81C22×C83#35411yescharacteristic
82C4×C83—21no—
83C4×C83—21no—
84C4×C83—41no—
85C4×C83—41no—
86C4×C83—41no—
87C4×C83—41no—
88C4×C83—81no—
89Dic83—81no—
90Dic83—81no—
91#7431—831nomaximal, Sylow
92C2×C83—21no—
93C2×C83—21no—
94C2×C83#135111yescharacteristic
95C2×C83#140311yescharacteristic
96C2×C83#140511yescharacteristic
97#2028—831no—
98#1394D8311yescharacteristic
99#1272—831no—
100C83#743111yescharacteristic, complemented, Sylow
101#544—831no—
102#419—1661no—
103C2×#101—21no—
104#391C2×D8311yescharacteristic
105#343—831no—
106#339—1661no—
107#336—1661no—
108C22×Q8C22⋊D8311yescharacteristic
109C2×M16—41no—
110C2×M16—1661no—
111C22×C8—3321no—
112C4⋊Q8—3321no—
113#125—3321no—
114C22⋊Q8—3321no—
115#117—1661no—
116C2×C4⋊C4C4×D8311yescharacteristic
117C2×C42D33211yescharacteristic
118#103—3321no—
119#103—3321no—
120#101—22no—
121#101—41no—
122#95—41no—
123C2×Q8—21no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—3321no—
127C2×Q8#1305057811yescharacteristic
128C2×Q8#1305058011yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4(C2×D83)⋊C411yescharacteristic
133M16—42no—
134M16—81no—
135M16—3321no—
136M16—3321no—
137C2×C8—81no—
138C2×C8—3321no—
139C2×C8—3322no—
140C2×C8—6641no—
141C2×C8—6641no—
142C4⋊C4—41no—
143C4⋊C4—3321no—
144C4⋊C4—3322no—
145C4⋊C4—1661no—
146C4⋊C4—1661no—
147C22⋊C4—3321no—
148C42—41no—
149C42—3321no—
150C23#1458170611yescharacteristic
151Q8—41no—
152Q8—41no—
153Q8—81no—
154Q8—13281no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—3321no—
168C2×C4—3321no—
169C2×C4#1458171511yescharacteristic
170C2×C4#1458172011yescharacteristic
171C8—82no—
172C8—6641no—
173C8—6642no—
174C22—21no—
175C22—21no—
176C22#1912743711yescharacteristic
177C22#1912748711yescharacteristic
178C22#1912749511yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—6641no—
187C4—6641no—
188C2—21no—
189C2—21no—
190C2#2490548311yescharacteristic
191C2#2490561011yescharacteristic
192C2#2490561611yescharacteristic
subgroupG/H
centerC22#19127487
commutatorC2×C4⋊C4×C83C2×C4
Frattini#391C2×D83
FittingC83×#1394C2
socleC22×C83AΣL(1,𝔽16)
prime radicalC23×C83#99
cosocle#391×C83C22
hypercenter#1394D83
hypocenterC83#7431
LCSG ▷ C2×C4⋊C4×C83 ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1394

Complements

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

NH ≅ G/Ntype
100. C83#7431semidirect

Maximal subgroups

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

subgroupindex
#249086242
#249052892
C83×#13942
#743183