Finite Group Databasebeta

← #35318682

Subgroups — #35318682

Order 21248.

212 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 63 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#24909715C211yesmaximal, characteristic
2#24909368C211yesmaximal, characteristic
3#24906834C211yesmaximal, characteristic
4#24906830C211yesmaximal, characteristic
5#24905536C211yesmaximal, characteristic
6#24905513C211yesmaximal, characteristic
7C83×#1362C211yesmaximal, characteristic
8C2×#14581738—21no—
9C2×#14581738—21no—
10#19128081C2211yescharacteristic
11#19127987—21no—
12#19127983—21no—
13C8×Dic166C2211yescharacteristic
14Dic83⋊C16—21no—
15#19127476—21no—
16C4×C83⋊C16C2211yescharacteristic
17#19127454C2211yescharacteristic
18#19127447—21no—
19#19127446—21no—
20#494×C83C2211yescharacteristic
21C4⋊C16×C83C2211yescharacteristic
22#335×C83C2211yescharacteristic
23C2×Dic332—21no—
24C2×Dic332—21no—
25#14581792—21no—
26C4×Dic166D411yescharacteristic
27#14581738—42no—
28#14581738—42no—
29C2×C83⋊C16D411yescharacteristic
30C2×C83⋊C16D411yescharacteristic
31#14581724—41no—
32#14581723—41no—
33C4⋊(C83⋊C8)—21no—
34C4⋊(C83⋊C8)D411yescharacteristic
35Dic83⋊C8—21no—
36#14581717—41no—
37#14581715—41no—
38C8×Dic83—21no—
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—41no—
46C2×Dic166D811yescharacteristic
47Dic332—41no—
48Dic332—41no—
49Dic332—81no—
50C2×C83⋊C8—21no—
51C2×C83⋊C8—41no—
52C4⋊Dic83—41no—
53C4⋊Dic83—41no—
54C4⋊Dic83D811yescharacteristic
55Dic83⋊C4—21no—
56C4×Dic83—21no—
57C83⋊C16—21no—
58C83⋊C16SD1612yes—
59C2×Q8×C83—41no—
60Q16×C83—41no—
61Q16×C83—41no—
62Q16×C83—81no—
63C2×C8×C83—41no—
64C2×C8×C83C2×D411yescharacteristic
65C2×C8×C83#4111yescharacteristic
66C4⋊C4×C83—41no—
67C4⋊C4×C83—41no—
68C42×C83C2×D411yescharacteristic
69C16×C83—41no—
70Q8×C83—81no—
71Q8×C83—81no—
72C2×C4×C83—81no—
73C2×C4×C83#12111yescharacteristic
74C2×C4×C83C2×D811yescharacteristic
75C2×C4×C83#13511yescharacteristic
76C2×Dic83—21no—
77C2×Dic83—21no—
78C2×Dic83—81no—
79Dic166—21no—
80Dic166—21no—
81Dic166—81no—
82Dic166—81no—
83C8×C83—21no—
84C8×C83—81no—
85C8×C83C2×SD1611yescharacteristic
86C8×C83AGL(1,ℤ/8)11yescharacteristic
87C83⋊C8—41no—
88C83⋊C8—81no—
89C22×C83#46611yescharacteristic
90C4×C83—21no—
91C4×C83—161no—
92C4×C83#46011yescharacteristic
93C4×C83#47211yescharacteristic
94C4×C83#51011yescharacteristic
95C4×C83#51011yescharacteristic
96Dic83—41no—
97Dic83—41no—
98Dic83—161no—
99#12443—831nomaximal, Sylow
100C2×C83#166811yescharacteristic
101C2×C83#221911yescharacteristic
102C2×C83#222211yescharacteristic
103#2247—831no—
104#2183—831no—
105#1670—831no—
106#1670—831no—
107#1372—831no—
108#1362—831no—
109#1362D8311yescharacteristic
110C83#1244311yescharacteristic, complemented, Sylow
111C2×Q32—1661no—
112C2×Q32—1661no—
113#494—831no—
114#494C2×D8311yescharacteristic
115#475—1661no—
116#475—1661no—
117C8×Q8—831no—
118C4⋊C16—1661no—
119C4⋊C16C2×D8311yescharacteristic
120#346—1661no—
121C4×C16—831no—
122#335—831no—
123#335C2×D8311yescharacteristic
124#332—1661no—
125#332—1661no—
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16—1661no—
129C2×Q16—1661no—
130C4⋊Q8—21no—
131C4⋊Q8—1661no—
132C4×Q8—831no—
133Q32—3322no—
134Q32—3322no—
135C2×C16—21no—
136C2×C16—831no—
137C2×C16—831no—
138#106—3321no—
139#106—3321no—
140C4⋊C8—21no—
141C4⋊C8—831no—
142C4⋊C8—1661no—
143C4⋊C8—1661no—
144#103—3321no—
145#103—3321no—
146C4×C8—1661no—
147C4×C8C22×D8311yescharacteristic
148C2×Q8—41no—
149C2×Q8—3321no—
150C2×Q8—831no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—3321no—
155Q16—3321no—
156Q16—6641no—
157C2×C8—41no—
158C2×C8—3321no—
159C2×C8—1661no—
160C2×C8D4×D8311yescharacteristic
161C2×C8#1305059011yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—3321no—
165C4⋊C4—3321no—
166C4⋊C4—831no—
167C4⋊C4—1661no—
168C42—1661no—
169C42D4×D8311yescharacteristic
170C16—41no—
171C16—832no—
172C16—1661no—
173Q8—81no—
174Q8—81no—
175Q8—6641no—
176Q8—6641no—
177Q8—1661no—
178Q8—1661no—
179C2×C4—81no—
180C2×C4—6641no—
181C2×C4—1661no—
182C2×C4—1661no—
183C2×C4#1458176511yescharacteristic
184C2×C4D8×D8311yescharacteristic
185C2×C4#1458181311yescharacteristic
186C8—21no—
187C8—81no—
188C8—3321no—
189C8—6641no—
190C8SD16×D8311yescharacteristic
191C8#1458181611yescharacteristic
192C22#1912793611yescharacteristic
193C4—21no—
194C4—161no—
195C4—13281no—
196C4—3321no—
197C4—3321no—
198C4#1912790011yescharacteristic
199C4#1912797011yescharacteristic
200C4#1912814011yescharacteristic
201C4#1912814311yescharacteristic
202C2#2490682211yescharacteristic
203C2#2490957011yescharacteristic
204C2#2490958711yescharacteristic
subgroupG/H
centerC22#19127936
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#1362C2
socle, prime radicalC22×C83#466
hypercenter#1362D83
hypocenterC83#12443
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
110. C83#12443semidirect

Maximal subgroups

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

subgroupindex
#249097152
#249093682
#249068342
#249068302
#249055362
#249055132
C83×#13622
#1244383