Finite Group Databasebeta

← #35318685

Subgroups — #35318685

Order 21248.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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#24909371C211yesmaximal, characteristic, complemented
2#24906830C211yesmaximal, characteristic, complemented
3#24906820C211yesmaximal, characteristic
4#24905535C211yesmaximal, characteristic, complemented
5#24905512C211yesmaximal, characteristic, complemented
6#24905509C211yesmaximal, characteristic
7C83×#2248C211yesmaximal, characteristic
8#19127983—21no—
9#19127898—21no—
10C8×Dic166C2211yescharacteristic
11C4⋊(C83⋊C16)C2211yescharacteristic
12Dic83⋊C16—21no—
13#19127476—21no—
14#19127454C2211yescharacteristic
15#19127454C2211yescharacteristic
16#19127447—21no—
17#19127445—21no—
18C2×SD32×C83—21no—
19C2×SD32×C83—21no—
20#494×C83C2211yescharacteristic
21#493×C83C2211yescharacteristic
22C4×C16×C83C2211yescharacteristic
23C2×#13050578—41no—
24C4×Dic166D411yescharacteristic
25C2×C83⋊C16—21no—
26#14581723—41no—
27C4⋊(C83⋊C8)—21no—
28C4⋊(C83⋊C8)—21no—
29C4⋊(C83⋊C8)D411yescharacteristic
30Dic83⋊C8—21no—
31#14581715—41no—
32#14581713—41no—
33C8×Dic83—21no—
34C2×Q16×C83—21no—
35C2×Q16×C83—21no—
36C2×D8×C83—21no—
37C2×D8×C83—21no—
38C4⋊Q8×C83—21no—
39#127×C83—21no—
40SD32×C83—42no—
41SD32×C83—42no—
42C2×C16×C83D411yescharacteristic
43C2×C16×C83D411yescharacteristic
44C4×C8×C83C2311yescharacteristic
45C2×Dic166D811yescharacteristic
46#13050578—82no—
47C2×C83⋊C8—21no—
48C2×C83⋊C8—41no—
49C2×C83⋊C8—41no—
50C4⋊Dic83D811yescharacteristic
51Dic83⋊C4—21no—
52C4×Dic83—21no—
53C83⋊C16—41no—
54C2×Q8×C83—41no—
55C2×D4×C83—41no—
56C2×D4×C83—41no—
57C2×D4×C83—41no—
58Q16×C83—41no—
59Q16×C83—41no—
60Q16×C83—81no—
61D8×C83—41no—
62D8×C83—41no—
63D8×C83—81no—
64C2×C8×C83C2×D411yescharacteristic
65C2×C8×C83#4111yescharacteristic
66C4⋊C4×C83—41no—
67C4⋊C4×C83—41no—
68C42×C83C2×D411yescharacteristic
69C16×C83—21no—
70C16×C83SD1612yescomplemented
71C23×C83—81no—
72Q8×C83—81no—
73Q8×C83—81no—
74D4×C83—81no—
75D4×C83—81no—
76D4×C83—81no—
77D4×C83—81no—
78D4×C83—161no—
79C2×C4×C83—81no—
80C2×C4×C83#12111yescharacteristic
81C2×C4×C83C2×D811yescharacteristic
82C2×C4×C83#13511yescharacteristic
83C2×Dic83—21no—
84C2×Dic83—21no—
85Dic166—21no—
86Dic166—21no—
87C8×C83—21no—
88C8×C83C2×SD1611yescharacteristic
89C8×C83AGL(1,ℤ/8)11yescharacteristic
90C83⋊C8—41no—
91C83⋊C8—81no—
92C83⋊C8—81no—
93C22×C83—161no—
94C22×C83—161no—
95C22×C83—161no—
96C22×C83#46611yescharacteristic
97C4×C83—21no—
98C4×C83—161no—
99C4×C83#46011yescharacteristic
100C4×C83#47211yescharacteristic
101C4×C83#50911yescharacteristic
102C4×C83#51011yescharacteristic
103Dic83—41no—
104Dic83—41no—
105#12444—831nomaximal, Sylow
106C2×C83—321no—
107C2×C83#166811yescharacteristic
108C2×C83#222011yescharacteristic
109C2×C83#222311yescharacteristic
110#2248D8311yescharacteristic
111#2183—831no—
112#1670—831no—
113#1668—831no—
114#1371—831no—
115#1362—831no—
116#1361—831no—
117C83#1244411yescharacteristic, complemented, Sylow
118C2×SD32—21no—
119C2×SD32—21no—
120#494C2×D8311yescharacteristic
121#493C2×D8311yescharacteristic
122#475—1661no—
123#460—1661no—
124C8×Q8—831no—
125C4⋊C16—831no—
126C4⋊C16—1661no—
127#346—1661no—
128C4×C16C2×D8311yescharacteristic
129#335—831no—
130#335—831no—
131#332—1661no—
132#331—1661no—
133C2×Q16—21no—
134C2×Q16—21no—
135C2×SD16—3321no—
136C2×D8—21no—
137C2×D8—21no—
138C4⋊Q8—21no—
139#127—21no—
140C4×Q8—831no—
141SD32—42no—
142SD32—42no—
143C2×C16—1661no—
144C2×C16C22⋊D8311yescharacteristic
145C2×C16C22⋊D8311yescharacteristic
146#106—3321no—
147C4⋊C8—831no—
148C4⋊C8—1661no—
149C4⋊C8—1661no—
150C4⋊C8—1661no—
151#103—3321no—
152#102—3321no—
153C4×C8—1661no—
154C4×C8C22×D8311yescharacteristic
155C2×Q8—41no—
156C2×Q8—831no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—41no—
161Q16—41no—
162Q16—81no—
163SD16—6642no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—3321no—
168C2×C8—3321no—
169C2×C8—1661no—
170C2×C8C2×C22⋊D8311yescharacteristic
171C2×C8#1305058911yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—831no—
175C4⋊C4—1661no—
176C42—1661no—
177C42D4×D8311yescharacteristic
178C16—21no—
179C16—3321no—
180C16#1305057812yescomplemented
181C23—81no—
182Q8—81no—
183Q8—81no—
184Q8—1661no—
185Q8—1661no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—81no—
192C2×C4—1661no—
193C2×C4—1661no—
194C2×C4#1458176311yescharacteristic
195C2×C4D8×D8311yescharacteristic
196C2×C4#1458181111yescharacteristic
197C8—21no—
198C8—3321no—
199C8—6641no—
200C8—6641no—
201C8C2×#1305057811yescharacteristic
202C8#1458181811yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1912793411yescharacteristic
207C4—21no—
208C4—161no—
209C4—3321no—
210C4—3321no—
211C4#1912789811yescharacteristic
212C4#1912796811yescharacteristic
213C4#1912813811yescharacteristic
214C4#1912814011yescharacteristic
215C2—321no—
216C2#2490682011yescharacteristic
217C2#2490957311yescharacteristic
218C2#2490959011yescharacteristic
subgroupG/H
centerC22#19127934
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#2248C2
socleC22×C83#466
prime radical#493×C83C22
hypercenter#2248D83
hypocenterC83#12444
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #24909371C2semidirect
2. #24906830C2semidirect
4. #24905535C2semidirect
5. #24905512C2semidirect
70. C16×C83SD16semidirect
117. C83#12444semidirect
180. C16#13050578semidirect

Maximal subgroups

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

subgroupindex
#249093712
#249068302
#249068202
#249055352
#249055122
#249055092
C83×#22482
#1244483