Finite Group Databasebeta

← #35291024

Subgroups — #35291024

Order 21248.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#24907529C211yesmaximal, characteristic
2#24905387C211yesmaximal, characteristic
3C83×#1314C211yesmaximal, characteristic
4C22×C4×Dic83C411yescharacteristic
5C2×C22⋊(C83⋊C8)C411yescharacteristic
6C22⋊(C83⋊C16)—21no—
7#19127455—21no—
8#19127455—21no—
9C2×C22⋊C8×C83C2211yescharacteristic
10C22⋊C16×C83—21no—
11C23×Dic83C811yescharacteristic
12C23×Dic83C811yescharacteristic
13C22×C83⋊C8—21no—
14C2×C4×Dic83—21no—
15C2×C4×Dic83—21no—
16C2×C4×Dic83—41no—
17C2×C4×Dic83—41no—
18C2×C83⋊C16—41no—
19C22⋊(C83⋊C8)—41no—
20C23×C4×C83C2×C411yescharacteristic
21C22×C8×C83D411yescharacteristic
22C22×C8×C83D411yescharacteristic
23C2×C16×C83—41no—
24C22⋊C8×C83—41no—
25C22×Dic83—21no—
26C22×Dic83—21no—
27C22×Dic83—21no—
28C22×Dic83—42no—
29C22×Dic83—41no—
30C22×Dic83—41no—
31C22×Dic83—41no—
32C22×Dic83C1612yescomplemented
33C2×C83⋊C8—41no—
34C2×C83⋊C8—41no—
35C2×C83⋊C8—41no—
36C4×Dic83—42no—
37C4×Dic83—41no—
38C4×Dic83—41no—
39C83⋊C16—81no—
40C24×C83C2×C811yescharacteristic
41C22×C4×C83—21no—
42C22×C4×C83—21no—
43C22×C4×C83—41no—
44C22×C4×C83—41no—
45C22×C4×C83C22⋊C411yescharacteristic
46C22×C4×C83M1611yescharacteristic
47C2×C8×C83—21no—
48C2×C8×C83—21no—
49C2×C8×C83—41no—
50C2×C8×C83—41no—
51C16×C83—81no—
52C23×C83—21no—
53C23×C83—21no—
54C23×C83—41no—
55C23×C83—41no—
56C23×C83C22⋊C811yescharacteristic
57C23×C83C2×C1611yescharacteristic
58C23×C83M3211yescharacteristic
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—21no—
62C2×C4×C83—42no—
63C2×C4×C83—41no—
64C2×C4×C83—41no—
65C2×C4×C83—41no—
66C2×C4×C83#9911yescharacteristic
67C2×C4×C83#10011yescharacteristic
68C2×Dic83—22no—
69C2×Dic83—22no—
70C2×Dic83—42no—
71C2×Dic83—41no—
72C2×Dic83—42no—
73C2×Dic83—41no—
74C2×Dic83—41no—
75C2×Dic83—41no—
76C2×Dic83—42no—
77C2×Dic83—42no—
78C8×C83—41no—
79C8×C83—41no—
80C83⋊C8—81no—
81C22×C83—21no—
82C22×C83—21no—
83C22×C83—21no—
84C22×C83—21no—
85C22×C83—41no—
86C22×C83—41no—
87C22×C83—42no—
88C22×C83—41no—
89C22×C83—41no—
90C22×C83#32311yescharacteristic
91C22×C83C22⋊C1611yescharacteristic
92C22×C83#34911yescharacteristic
93C4×C83—21no—
94C4×C83—41no—
95C4×C83#35211yescharacteristic
96C4×C83#35211yescharacteristic
97Dic83—42no—
98Dic83—42no—
99#7055—831nomaximal, Sylow
100C2×C83—21no—
101C2×C83—21no—
102C2×C83—41no—
103C2×C83—41no—
104C2×C83#131411yescharacteristic
105C2×C83#131711yescharacteristic
106C2×C83#132011yescharacteristic
107#1817—831no—
108#1314—831no—
109#1314D8311yescharacteristic
110C83#705511yescharacteristic, complemented, Sylow
111C22×C42—831no—
112C2×C22⋊C8—831no—
113C2×C22⋊C8C2×D8311yescharacteristic
114C22⋊C16—21no—
115C22⋊C16—1661no—
116#336—1661no—
117#336—1661no—
118C23×C4—831no—
119C23×C4—831no—
120C23×C4C4×D8311yescharacteristic
121C22×C8—1661no—
122C22×C8D33211yescharacteristic
123C22×C8C22⋊D8311yescharacteristic
124C2×C42—3321no—
125C2×C42—3321no—
126C2×C42—1661no—
127C2×C42—1661no—
128C2×C16—41no—
129C2×C16—3321no—
130C22⋊C8—41no—
131C22⋊C8—3321no—
132C24C8×D8311yescharacteristic
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4—3321no—
138C22×C4—3321no—
139C22×C4—3321no—
140C22×C4—3322no—
141C22×C4—832no—
142C22×C4—1661no—
143C22×C4—1661no—
144C22×C4—1661no—
145C22×C4(C2×D83)⋊C411yescharacteristic
146C22×C4#1305057311yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—3321no—
152C2×C8—3321no—
153C2×C8—3321no—
154C42—3322no—
155C42—3321no—
156C42—3321no—
157C16—81no—
158C16—6641no—
159C23—21no—
160C23—21no—
161C23—41no—
162C23—41no—
163C23(C2×D83)⋊C811yescharacteristic
164C23C16×D8311yescharacteristic
165C23#1458173111yescharacteristic
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3322no—
174C2×C4—3321no—
175C2×C4—3322no—
176C2×C4—3321no—
177C2×C4—3321no—
178C2×C4—3321no—
179C2×C4—3322no—
180C2×C4—3322no—
181C2×C4—1662no—
182C2×C4—1662no—
183C2×C4#1458170611yescharacteristic
184C2×C4#1458170811yescharacteristic
185C8—41no—
186C8—41no—
187C8—6641no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—41no—
197C22#1912742411yescharacteristic
198C22(C2×D83)⋊C1611yescharacteristic
199C22#1912748211yescharacteristic
200C4—21no—
201C4—41no—
202C4—3322no—
203C4—3322no—
204C4#1912749011yescharacteristic
205C4#1912749211yescharacteristic
206C2—21no—
207C2—21no—
208C2—41no—
209C2—41no—
210C2#2490538611yescharacteristic
211C2#2490539211yescharacteristic
212C2#2490539811yescharacteristic
subgroupG/H
centerC2×C4#14581706
commutatorC23×C83C2×C16
FrattiniC2×C22⋊C8C2×D83
FittingC83×#1314C2
socleC22×C83#323
prime radicalC24×C83C2×C8
cosocleC2×C22⋊C8×C83C22
hypercenter#1314D83
hypocenterC83#7055
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
32. C22×Dic83C16semidirect
110. C83#7055semidirect

Maximal subgroups

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

subgroupindex
#249075292
#249053872
C83×#13142
#705583