Finite Group Databasebeta

← #35308582

Subgroups — #35308582

Order 21248.

386 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 81 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#24907600C211yesmaximal, characteristic, complemented
3#24906196C212yesmaximal, complemented
4#24905913C212yesmaximal, complemented
5C83×#1309C211yesmaximal, characteristic, complemented
6#19128251C2212yes—
7#19127992—22no—
8#19127954—22no—
9#19127897—22no—
10#19127725C2211yescharacteristic
11C2×C4×C83⋊C8C2211yescharacteristic
12#19127465—22no—
13#19127449—22no—
14#19127444—22no—
15#19127428—24no—
16#423×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—
32C4×C83⋊C8—21no—
33C4×C83⋊C8D412yes—
34C2×M16×C83—22no—
35C2×M16×C83D412yes—
36C2×C42×C83C2311yescharacteristic
37C4⋊C8×C83—22no—
38C4⋊C8×C83—22no—
39C4⋊C8×C83—22no—
40#13050590—82no—
41#13050590—82no—
42C2×Dic166—22no—
43C2×D332—22no—
44C2×D332—22no—
45C2×D332—22no—
46C2×C22⋊D83—42no—
47C2×C4×D83—42no—
48D664—82no—
49#13050574—42no—
50C2×C83⋊C8—22no—
51C2×C83⋊C8—41no—
52C2×C83⋊C8—41no—
53C2×C83⋊C8—41no—
54C4⋊Dic83—22no—
55C4⋊Dic83—22no—
56(C2×D83)⋊C4—42no—
57(C2×D83)⋊C4—42no—
58C22×C4×C83C2×D411yescharacteristic
59C22×C4×C83#4112yes—
60M16×C83—42no—
61M16×C83—82no—
62C2×C8×C83—22no—
63C2×C8×C83—42no—
64C42×C83C2×D412yes—
65C42×C83C2×D411yescharacteristic
66C42×C83#4111yescharacteristic
67C23×C83#12411yescharacteristic
68C22×D83—42no—
69C2×C4×C83—21no—
70C2×C4×C83—21no—
71C2×C4×C83—22no—
72C2×C4×C83—22no—
73C2×C4×C83#12011yescharacteristic
74C2×C4×C83#12112yes—
75C2×C4×C83#12111yescharacteristic
76C2×C4×C83#12312yes—
77C22⋊D83—84no—
78C2×Dic83—42no—
79D332—42no—
80D332—42no—
81D332—42no—
82D332—42no—
83D332—82no—
84C4×D83—82no—
85C4×D83—82no—
86Dic166—82no—
87C8×C83—42no—
88C8×C83—82no—
89C83⋊C8—42no—
90C83⋊C8—81no—
91C22×C83—22no—
92C22×C83—21no—
93C22×C83#39411yescharacteristic
94C2×D83—82no—
95C2×D83—82no—
96C2×D83—82no—
97C4×C83—22no—
98C4×C83—21no—
99C4×C83#45411yescharacteristic
100C4×C83#45511yescharacteristic
101C4×C83#47112yes—
102C4×C83#47212yes—
103Dic83—82no—
104#10531—831nomaximal, Sylow
105C2×C83—41no—
106C2×C83#204011yescharacteristic
107C2×C83#205112yes—
108D83—162no—
109#3253—831no—
110#1837—831no—
111#1560—832no—
112#1492—832no—
113#1309D8311yescharacteristic, complemented
114C83#1053111yescharacteristic, complemented, Sylow
115#532—832no—
116#476—1662no—
117#469—1662no—
118#459—1662no—
119#423—831no—
120#423C2×D8312yes—
121#423C2×D8311yescharacteristic
122C2×C4×C8—831no—
123#341—1662no—
124#333—1662no—
125#331—1662no—
126D4⋊C8—1664no—
127C2×#41—1662no—
128C2×D8—1662no—
129C2×M16—22no—
130C2×M16—1661no—
131C2×M16D33212yes—
132C22×C8—1661no—
133C4⋊Q8—832no—
134#127—832no—
135#124—1662no—
136#121—1662no—
137#121—1662no—
138C4×D4—1662no—
139C4×D4—1662no—
140C2×C42C22×D8311yescharacteristic
141#106—1662no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—1662no—
146#102—1664no—
147C4×C8—832no—
148C4×C8—1661no—
149#41—6642no—
150#41—6642no—
151C2×Q8—1662no—
152C2×D4—3322no—
153C2×D4—1662no—
154C2×D4—1662no—
155C2×D4—1662no—
156C22×C4—3322no—
157C22×C4C2×D33211yescharacteristic
158C22×C4#1305059012yes—
159D8—6642no—
160M16—42no—
161M16—82no—
162M16—3322no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—3321no—
166C2×C8—3321no—
167C2×C8—3321no—
168C2×C8—1662no—
169C4⋊C4—1662no—
170C4⋊C4—1662no—
171C22⋊C4—3322no—
172C22⋊C4—3322no—
173C42D4×D8312yes—
174C42D4×D8311yescharacteristic
175C42#1305059111yescharacteristic
176C23—3322no—
177C23#1458178011yescharacteristic
178Q8—6642no—
179D4—3322no—
180D4—3322no—
181D4—3322no—
182D4—3322no—
183D4—6642no—
184D4—6644no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—3322no—
190C2×C4—6642no—
191C2×C4—6642no—
192C2×C4#1458176211yescharacteristic
193C2×C4#1458176512yes—
194C2×C4#1458176711yescharacteristic
195C2×C4#1458177712yes—
196C8—42no—
197C8—82no—
198C8—3322no—
199C8—6641no—
200C22—21no—
201C22—22no—
202C22—6642no—
203C22—6642no—
204C22—6642no—
205C22#1912761911yescharacteristic
206C4—21no—
207C4—22no—
208C4—6642no—
209C4#1912787611yescharacteristic
210C4#1912788111yescharacteristic
211C4#1912796712yes—
212C4#1912797012yes—
213C2—41no—
214C2—13282no—
215C2#2490869311yescharacteristic
216C2#2490875812yes—
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1309C2
socleC22×C83#394
prime radical#24918844C2
hypercenter#1309D83
hypocenterC83#10531
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
2. #24907600C2semidirect
3. #24906196C2semidirect
4. #24905913C2semidirect
5. C83×#1309C2semidirect
113. #1309D83semidirect
114. C83#10531semidirect

Maximal subgroups

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

subgroupindex
#249188442
#249076002
#249061962
#249059132
C83×#13092
#1053183