Finite Group Databasebeta

← #35318554

Subgroups — #35318554

Order 21248.

218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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#24909616C211yesmaximal, characteristic
2#24909510C211yesmaximal, characteristic
3#24907057C211yesmaximal, characteristic
4#24906269C211yesmaximal, characteristic
5#24905526C211yesmaximal, characteristic
6#24905522C211yesmaximal, characteristic
7C83×#1362C211yesmaximal, characteristic
8C2×#14581738—21no—
9#19128106C2211yescharacteristic
10#19128097—21no—
11#19128053—21no—
12#19127825—21no—
13C4×Dic332C2211yescharacteristic
14#19127527—21no—
15C4⋊(C83⋊C16)C2211yescharacteristic
16#19127506—21no—
17#19127505—21no—
18#19127431—21no—
19C8×C83⋊C8C2211yescharacteristic
20#494×C83C2211yescharacteristic
21C4⋊C16×C83C2211yescharacteristic
22#335×C83C2211yescharacteristic
23C2×Dic332D411yescharacteristic
24#14581792—21no—
25C4×Dic166—21no—
26#14581738—42no—
27C2×C83⋊C16—21no—
28#14581726—21no—
29#14581726—21no—
30#14581726D411yescharacteristic
31#14581723—41no—
32#14581723—41no—
33Dic83⋊C8—41no—
34#14581717—21no—
35#14581715—42no—
36C4×C83⋊C8D411yescharacteristic
37C4×C83⋊C8D411yescharacteristic
38C8×Dic83—41no—
39C2×Q16×C83—21no—
40C2×Q16×C83—21no—
41C4⋊Q8×C83—21no—
42C2×C16×C83—21no—
43C4⋊C8×C83—21no—
44C4×C8×C83C2311yescharacteristic
45C2×Dic166—21no—
46C2×Dic166—41no—
47Dic332—21no—
48Dic332SD1612yes—
49C2×C83⋊C8—21no—
50C2×C83⋊C8D811yescharacteristic
51C2×C83⋊C8D811yescharacteristic
52C4⋊Dic83—21no—
53C4⋊Dic83—41no—
54C4⋊Dic83—41no—
55Dic83⋊C4—41no—
56C4×Dic83—41no—
57C83⋊C16—41no—
58C2×Q8×C83—41no—
59Q16×C83—41no—
60Q16×C83—41no—
61Q16×C83—81no—
62C2×C8×C83—41no—
63C2×C8×C83C2×D411yescharacteristic
64C2×C8×C83#4111yescharacteristic
65C4⋊C4×C83—41no—
66C4⋊C4×C83—41no—
67C42×C83C2×D411yescharacteristic
68C16×C83—41no—
69Q8×C83—81no—
70Q8×C83—81no—
71C2×C4×C83—81no—
72C2×C4×C83#12111yescharacteristic
73C2×C4×C83C2×D811yescharacteristic
74C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
75C2×Dic83—41no—
76C2×Dic83—41no—
77C2×Dic83—81no—
78Dic166—22no—
79Dic166—41no—
80Dic166—82no—
81C8×C83—21no—
82C8×C83—81no—
83C8×C83C2×SD1611yescharacteristic
84C8×C83#13511yescharacteristic
85C83⋊C8—21no—
86C83⋊C8—41no—
87C83⋊C8Q3212yescomplemented
88C22×C83#45911yescharacteristic
89C4×C83—21no—
90C4×C83—161no—
91C4×C83#46511yescharacteristic
92C4×C83#47111yescharacteristic
93C4×C83C2×Q3211yescharacteristic
94C4×C83#51011yescharacteristic
95Dic83—42no—
96Dic83—81no—
97Dic83—161no—
98#12421—831nomaximal, Sylow
99C2×C83#166511yescharacteristic
100C2×C83#220911yescharacteristic
101C2×C83#221211yescharacteristic
102#2227—831no—
103#2209—831no—
104#1707—831no—
105C8×Q16—831no—
106#1367—831no—
107#1365—831no—
108#1362D8311yescharacteristic
109C83#1242111yescharacteristic, complemented, Sylow
110C2×Q32—1661no—
111#500—831no—
112#498—1661no—
113#494C2×D8311yescharacteristic
114#487—1661no—
115C8×Q8—1661no—
116C4×Q16—831no—
117#366—1661no—
118C4⋊C16—831no—
119C4⋊C16C2×D8311yescharacteristic
120#358—1661no—
121#358—1661no—
122#335C2×D8311yescharacteristic
123Q8⋊C8—1661no—
124C82—831no—
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16—831no—
128C4⋊Q8—21no—
129C4⋊Q8—1661no—
130C4×Q8—1661no—
131Q32—3322no—
132C2×C16—21no—
133C2×C16—1661no—
134#107—831no—
135#107—1661no—
136#107—1661no—
137#106—3321no—
138#106—3321no—
139C4⋊C8—21no—
140C4⋊C8—3321no—
141#103—3322no—
142#103—1661no—
143C4×C8—3321no—
144C4×C8—831no—
145C4×C8—831no—
146C4×C8C22×D8311yescharacteristic
147C2×Q8—41no—
148C2×Q8—3321no—
149C2×Q8—1661no—
150Q16—41no—
151Q16—41no—
152Q16—81no—
153Q16—832no—
154Q16—1661no—
155C2×C8—41no—
156C2×C8—831no—
157C2×C8—831no—
158C2×C8—1661no—
159C2×C8D4×D8311yescharacteristic
160C2×C8#1305059011yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—3321no—
164C4⋊C4—3321no—
165C4⋊C4—3321no—
166C4⋊C4—1661no—
167C42—3321no—
168C42D4×D8311yescharacteristic
169C16—41no—
170C16—3321no—
171Q8—81no—
172Q8—81no—
173Q8—3321no—
174Q8—6642no—
175Q8—1662no—
176C2×C4—81no—
177C2×C4—3321no—
178C2×C4—3321no—
179C2×C4—6641no—
180C2×C4#1458176511yescharacteristic
181C2×C4D8×D8311yescharacteristic
182C2×C4#1458181911yescharacteristic
183C8—21no—
184C8—81no—
185C8—3321no—
186C8—832no—
187C8—1661no—
188C8SD16×D8311yescharacteristic
189C8#1458181111yescharacteristic
190C22#1912789511yescharacteristic
191C4—21no—
192C4—161no—
193C4—13281no—
194C4—3322no—
195C4—6641no—
196C4#1912792911yescharacteristic
197C4#1912796311yescharacteristic
198C4Q32×D8311yescharacteristic
199C4#1912814011yescharacteristic
200C2#2490680311yescharacteristic
201C2#2490951211yescharacteristic
202C2#2490953511yescharacteristic
subgroupG/H
centerC22#19127895
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#1362C2
socle, prime radicalC22×C83#459
hypercenter#1362D83
hypocenterC83#12421
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
87. C83⋊C8Q32semidirect
109. C83#12421semidirect

Maximal subgroups

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

subgroupindex
#249096162
#249095102
#249070572
#249062692
#249055262
#249055222
C83×#13622
#1242183