Finite Group Databasebeta

← #35308547

Subgroups — #35308547

Order 21248.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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#24906183C212yesmaximal, complemented
3#24906073C212yesmaximal, complemented
4#24905374C211yesmaximal, characteristic, complemented
5C83×#1838C211yesmaximal, characteristic, complemented
6#19128251C2212yes—
7#19127992—22no—
8#19127954—22no—
9#19127897—22no—
10#19127758C2212yes—
11#19127446—22no—
12#19127444—22no—
13#19127440—24no—
14#423×C83C2211yescharacteristic
15#423×C83C2211yescharacteristic
16C2×#97×C83C2211yescharacteristic
17#341×C83—22no—
18C2×#13050590—22no—
19C2×D664—22no—
20#14581792D412yes—
21#14581789D412yes—
22#14581780—22no—
23#14581766—22no—
24#14581766—22no—
25C4×D332—22no—
26C4×D332—22no—
27#14581724—22no—
28C4⋊(C83⋊C8)—22no—
29#14581714—24no—
30C22⋊(C83⋊C8)—22no—
31#14581703—22no—
32C2×M16×C83—21no—
33C2×M16×C83D412yes—
34C22×C8×C83—21no—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38#97×C83—21no—
39#97×C83D412yes—
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—
48C2×C83⋊C8—42no—
49C4⋊Dic83—22no—
50C4⋊Dic83—22no—
51(C2×D83)⋊C4—42no—
52(C2×D83)⋊C4—42no—
53C22×C4×C83C2×D411yescharacteristic
54C22×C4×C83#4112yes—
55M16×C83—42no—
56M16×C83—42no—
57C2×C8×C83—22no—
58C2×C8×C83—22no—
59C2×C8×C83—41no—
60C2×C8×C83—41no—
61C2×C8×C83—41no—
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#12111yescharacteristic
72C2×C4×C83#12112yes—
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—42no—
84C8×C83—81no—
85C83⋊C8—82no—
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#1838D8311yescharacteristic, complemented
105#1557—832no—
106#1530—832no—
107#1307—831no—
108C83#1052511yescharacteristic, complemented, Sylow
109#532—832no—
110#476—1662no—
111#469—1662no—
112#459—1662no—
113#432—832no—
114#423C2×D8311yescharacteristic
115#423C2×D8311yescharacteristic
116C2×#97C2×D8311yescharacteristic
117#341—22no—
118#332—1662no—
119#331—1662no—
120#329—1664no—
121C2×#41—1662no—
122C2×D8—1662no—
123C2×M16—21no—
124C2×M16C22⋊D8312yes—
125C22×C8—21no—
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—1662no—
140#97—21no—
141#97—1662no—
142#97D33212yes—
143#41—6644no—
144C2×Q8—1662no—
145C2×D4—3322no—
146C2×D4—1662no—
147C2×D4—1662no—
148C2×D4—1662no—
149C22×C4—3322no—
150C22×C4C2×C22⋊D8311yescharacteristic
151C22×C4#1305059112yes—
152D8—6642no—
153M16—42no—
154M16—42no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—3322no—
161C4⋊C4—1662no—
162C4⋊C4—1662no—
163C22⋊C4—3322no—
164C22⋊C4—3322no—
165C42D4×D8312yes—
166C42C2×D33211yescharacteristic
167C42#1305059011yescharacteristic
168C23—3322no—
169C23#1458178111yescharacteristic
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#1458176011yescharacteristic
182C2×C4#1458176611yescharacteristic
183C2×C4#1458176712yes—
184C2×C4#1458177712yes—
185C8—42no—
186C8—42no—
187C8—81no—
188C8—6642no—
189C22—21no—
190C22—22no—
191C22—6642no—
192C22—6642no—
193C22—6642no—
194C22#1912761811yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—6642no—
199C4#1912787311yescharacteristic
200C4#1912787811yescharacteristic
201C2—41no—
202C2—13282no—
203C2#2490869211yescharacteristic
204C2#2490873812yes—
subgroupG/H
centerC22#19127618
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1838C2
socleC22×C83#394
prime radical#24918844C2
hypercenter#1838D83
hypocenterC83#10525
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
2. #24906183C2semidirect
3. #24906073C2semidirect
4. #24905374C2semidirect
5. C83×#1838C2semidirect
104. #1838D83semidirect
108. C83#10525semidirect

Maximal subgroups

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

subgroupindex
#249188442
#249061832
#249060732
#249053742
C83×#18382
#1052583