Finite Group Databasebeta

← #35308576

Subgroups — #35308576

Order 21248.

402 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 83 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#24906196C212yesmaximal, complemented
3#24905915C212yesmaximal, complemented
4C83⋊#1309C211yesmaximal, characteristic, complemented
5C83×#1848C211yesmaximal, characteristic, complemented
6#19128251C2212yes—
7#19127992—22no—
8#19127954—22no—
9#19127897—22no—
10#19127725C2212yes—
11#19127449—22no—
12#19127444—22no—
13#19127430—24no—
14C2×#108×C83—22no—
15#423×C83C2211yescharacteristic
16#423×C83C2211yescharacteristic
17C2×C4×C8×C83C2211yescharacteristic
18C2×#13050590—22no—
19C2×D664—22no—
20C2×#13050574—22no—
21#14581792D412yes—
22#14581789D412yes—
23#14581780—22no—
24#14581766—22no—
25#14581766—22no—
26C4×D332—22no—
27C4×D332—22no—
28#14581724—22no—
29C4⋊(C83⋊C8)—22no—
30C4⋊(C83⋊C8)—22no—
31#14581714—24no—
32C2×M16×C83—21no—
33C2×M16×C83D412yes—
34C22×C8×C83—21no—
35C2×C42×C83C2311yescharacteristic
36#108×C83—44no—
37C4⋊C8×C83—22no—
38C4⋊C8×C83—22no—
39C4×C8×C83—21no—
40C4×C8×C83D412yes—
41#13050590—82no—
42#13050590—82no—
43C2×Dic166—22no—
44C2×D332—22no—
45C2×D332—22no—
46C2×D332—22no—
47C2×C22⋊D83—42no—
48C2×C4×D83—42no—
49D664—82no—
50#13050574—82no—
51C2×C83⋊C8—42no—
52C4⋊Dic83—22no—
53C4⋊Dic83—22no—
54(C2×D83)⋊C4—42no—
55(C2×D83)⋊C4—42no—
56C22×C4×C83C2×D411yescharacteristic
57C22×C4×C83#4112yes—
58M16×C83—42no—
59M16×C83—42no—
60C2×C8×C83—22no—
61C2×C8×C83—22no—
62C2×C8×C83—22no—
63C2×C8×C83—22no—
64C2×C8×C83—41no—
65C42×C83C2×D412yes—
66C42×C83C2×D411yescharacteristic
67C42×C83#4111yescharacteristic
68C23×C83#12411yescharacteristic
69C22×D83—42no—
70C2×C4×C83—21no—
71C2×C4×C83—21no—
72C2×C4×C83—22no—
73C2×C4×C83—22no—
74C2×C4×C83#12011yescharacteristic
75C2×C4×C83#12111yescharacteristic
76C2×C4×C83#12112yes—
77C2×C4×C83#12312yes—
78C22⋊D83—84no—
79C2×Dic83—42no—
80D332—42no—
81D332—42no—
82D332—42no—
83D332—42no—
84D332—82no—
85C4×D83—82no—
86C4×D83—82no—
87Dic166—82no—
88C8×C83—24no—
89C8×C83—42no—
90C8×C83—81no—
91C83⋊C8—82no—
92C22×C83—22no—
93C22×C83—21no—
94C22×C83#39411yescharacteristic
95C2×D83—82no—
96C2×D83—82no—
97C2×D83—82no—
98C4×C83—22no—
99C4×C83—21no—
100C4×C83#45311yescharacteristic
101C4×C83#45611yescharacteristic
102C4×C83#47112yes—
103C4×C83#47212yes—
104Dic83—82no—
105#10530—831nomaximal, Sylow
106C2×C83—41no—
107C2×C83#203911yescharacteristic
108C2×C83#205112yes—
109D83—162no—
110#3253—831no—
111#1848D8311yescharacteristic, complemented
112#1560—832no—
113#1492—832no—
114#1309—831no—
115C83#1053011yescharacteristic, complemented, Sylow
116#532—832no—
117#476—1662no—
118#469—1662no—
119#459—1662no—
120C2×#108—22no—
121#423—832no—
122#423C2×D8311yescharacteristic
123#423C2×D8311yescharacteristic
124C2×C4×C8C2×D8311yescharacteristic
125#333—1662no—
126#331—1662no—
127D4⋊C8—1664no—
128C2×#41—1662no—
129C2×D8—1662no—
130C2×M16—21no—
131C2×M16—1662no—
132C2×M16C22⋊D8312yes—
133C22×C8—21no—
134C4⋊Q8—832no—
135#127—832no—
136#124—1662no—
137#121—1662no—
138#121—1662no—
139C4×D4—1662no—
140C4×D4—1662no—
141C2×C42C22×D8311yescharacteristic
142#108—44no—
143#106—1662no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—1662no—
147C4⋊C8—1662no—
148#102—1664no—
149C4×C8—21no—
150C4×C8D33212yes—
151#41—6642no—
152#41—6642no—
153C2×Q8—1662no—
154C2×D4—3322no—
155C2×D4—1662no—
156C2×D4—1662no—
157C2×D4—1662no—
158C22×C4—3322no—
159C22×C4C2×C22⋊D8311yescharacteristic
160C22×C4#1305059112yes—
161D8—6642no—
162M16—42no—
163M16—42no—
164M16—6642no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—3322no—
171C4⋊C4—1662no—
172C4⋊C4—1662no—
173C22⋊C4—3322no—
174C22⋊C4—3322no—
175C42D4×D8312yes—
176C42C2×D33211yescharacteristic
177C42#1305059011yescharacteristic
178C23—3322no—
179C23#1458178111yescharacteristic
180Q8—6642no—
181D4—3322no—
182D4—3322no—
183D4—3322no—
184D4—3322no—
185D4—6642no—
186D4—6644no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—3322no—
192C2×C4—6642no—
193C2×C4—6642no—
194C2×C4#1458176011yescharacteristic
195C2×C4#1458176611yescharacteristic
196C2×C4#1458176712yes—
197C2×C4#1458177712yes—
198C8—24no—
199C8—42no—
200C8—81no—
201C8—6642no—
202C22—21no—
203C22—22no—
204C22—6642no—
205C22—6642no—
206C22—6642no—
207C22#1912761811yescharacteristic
208C4—21no—
209C4—22no—
210C4—6642no—
211C4#1912786811yescharacteristic
212C4#1912788311yescharacteristic
213C4#1912796512yes—
214C4#1912797212yes—
215C2—41no—
216C2—13282no—
217C2#2490868711yescharacteristic
218C2#2490875712yes—
subgroupG/H
centerC22#19127618
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1848C2
socleC22×C83#394
prime radical#24918844C2
hypercenter#1848D83
hypocenterC83#10530
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1848

Complements

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

NH ≅ G/Ntype
2. #24906196C2semidirect
3. #24905915C2semidirect
4. C83⋊#1309C2semidirect
5. C83×#1848C2semidirect
111. #1848D83semidirect
115. C83#10530semidirect

Maximal subgroups

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

subgroupindex
#249188442
#249061962
#249059152
C83⋊#13092
C83×#18482
#1053083