Finite Group Databasebeta

← #35308548

Subgroups — #35308548

Order 21248.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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#24918844C211yesmaximal, characteristic
2#24907603C211yesmaximal, characteristic, complemented
3#24906186C212yesmaximal, complemented
4#24906075C212yesmaximal, complemented
5C83×#1307C211yesmaximal, characteristic, complemented
6#19128251C2212yes—
7#19127992—22no—
8#19127954—22no—
9#19127897—22no—
10#19127725C2211yescharacteristic
11C2×#14581703C2211yescharacteristic
12#19127465—22no—
13#19127448—22no—
14#19127444—22no—
15#19127440—24no—
16#432×C83C2212yes—
17#423×C83C2211yescharacteristic
18C2×#13050590—22no—
19C2×D664—22no—
20C2×#13050574—21no—
21C22×C83⋊C8—21no—
22#14581792D412yes—
23#14581789D412yes—
24#14581780—22no—
25#14581766—22no—
26#14581766—22no—
27C4×D332—22no—
28C4×D332—22no—
29#14581724—22no—
30C4⋊(C83⋊C8)—22no—
31#14581714—24no—
32#14581703—21no—
33#14581703D412yes—
34C2×M16×C83D412yes—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38C22⋊C8×C83—22no—
39#97×C83—22no—
40#13050590—84no—
41C2×Dic166—22no—
42C2×D332—22no—
43C2×D332—22no—
44C2×D332—22no—
45C2×C22⋊D83—42no—
46C2×C4×D83—42no—
47D664—82no—
48#13050574—42no—
49C2×C83⋊C8—22no—
50C2×C83⋊C8—41no—
51C2×C83⋊C8—41no—
52C2×C83⋊C8—41no—
53C4⋊Dic83—22no—
54C4⋊Dic83—22no—
55(C2×D83)⋊C4—42no—
56(C2×D83)⋊C4—42no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83#4112yes—
59M16×C83—42no—
60C2×C8×C83—22no—
61C2×C8×C83—42no—
62C42×C83C2×D412yes—
63C42×C83C2×D411yescharacteristic
64C42×C83#4111yescharacteristic
65C23×C83#12411yescharacteristic
66C22×D83—42no—
67C2×C4×C83—21no—
68C2×C4×C83—21no—
69C2×C4×C83—42no—
70C2×C4×C83#12011yescharacteristic
71C2×C4×C83#12112yes—
72C2×C4×C83#12111yescharacteristic
73C2×C4×C83#12312yes—
74C22⋊D83—84no—
75C2×Dic83—42no—
76D332—42no—
77D332—42no—
78D332—82no—
79D332—82no—
80C4×D83—84no—
81Dic166—82no—
82C8×C83—42no—
83C8×C83—82no—
84C83⋊C8—42no—
85C83⋊C8—81no—
86C22×C83—22no—
87C22×C83—21no—
88C22×C83#39411yescharacteristic
89C2×D83—82no—
90C2×D83—82no—
91C2×D83—82no—
92C4×C83—22no—
93C4×C83—22no—
94C4×C83—21no—
95C4×C83#45411yescharacteristic
96C4×C83#45511yescharacteristic
97Dic83—82no—
98#10525—831nomaximal, Sylow
99C2×C83—41no—
100C2×C83#204011yescharacteristic
101C2×C83#204812yes—
102D83—162no—
103#3253—831no—
104#1838—831no—
105#1557—832no—
106#1530—832no—
107#1307D8311yescharacteristic, complemented
108C83#1052511yescharacteristic, complemented, Sylow
109#532—832no—
110#476—1662no—
111#469—1662no—
112#459—1662no—
113#432C2×D8312yes—
114#423—831no—
115#423C2×D8311yescharacteristic
116C2×#97—831no—
117#341—1662no—
118#332—1662no—
119#331—1662no—
120#329—1664no—
121C2×#41—1662no—
122C2×D8—1662no—
123C2×M16—1661no—
124C2×M16D33212yes—
125C22×C8—1661no—
126C4⋊Q8—832no—
127#127—832no—
128#124—1662no—
129#121—1662no—
130#121—1662no—
131C4×D4—1662no—
132C4×D4—1662no—
133C2×C42C22×D8311yescharacteristic
134#106—1662no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—1662no—
138#102—1664no—
139C22⋊C8—22no—
140#97—22no—
141#97—832no—
142#97—1661no—
143#41—6644no—
144C2×Q8—1662no—
145C2×D4—3322no—
146C2×D4—1662no—
147C2×D4—1662no—
148C2×D4—1662no—
149C22×C4—3322no—
150C22×C4C2×D33211yescharacteristic
151C22×C4#1305059012yes—
152D8—6642no—
153M16—42no—
154M16—3322no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—3321no—
158C2×C8—3321no—
159C2×C8—3321no—
160C2×C8—1662no—
161C4⋊C4—1662no—
162C4⋊C4—1662no—
163C22⋊C4—3322no—
164C22⋊C4—3322no—
165C42D4×D8312yes—
166C42D4×D8311yescharacteristic
167C42#1305059111yescharacteristic
168C23—3322no—
169C23#1458178011yescharacteristic
170Q8—6642no—
171D4—3322no—
172D4—3322no—
173D4—6642no—
174D4—6642no—
175D4—6644no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—3322no—
180C2×C4—6644no—
181C2×C4#1458176211yescharacteristic
182C2×C4#1458176512yes—
183C2×C4#1458176711yescharacteristic
184C2×C4#1458177712yes—
185C8—42no—
186C8—82no—
187C8—3322no—
188C8—6641no—
189C22—21no—
190C22—22no—
191C22—6642no—
192C22—6642no—
193C22—6642no—
194C22#1912761911yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—6642no—
199C4#1912787611yescharacteristic
200C4#1912788111yescharacteristic
201C2—41no—
202C2—13282no—
203C2#2490869311yescharacteristic
204C2#2490873912yes—
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1307C2
socleC22×C83#394
prime radical#24918844C2
hypercenter#1307D83
hypocenterC83#10525
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #24907603C2semidirect
3. #24906186C2semidirect
4. #24906075C2semidirect
5. C83×#1307C2semidirect
107. #1307D83semidirect
108. C83#10525semidirect

Maximal subgroups

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

subgroupindex
#249188442
#249076032
#249061862
#249060752
C83×#13072
#1052583