Finite Group Databasebeta

← #35308474

Subgroups — #35308474

Order 21248.

408 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 79 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#24918773C211yesmaximal, characteristic
2#24906156C212yesmaximal, complemented
3#24905970C212yesmaximal, complemented
4#24905333C211yesmaximal, characteristic, complemented
5C83×#1843C211yesmaximal, characteristic, complemented
6#19128251C2212yes—
7#19127982—22no—
8#19127937—22no—
9#19127897—22no—
10#19127758C2212yes—
11#19127449—22no—
12#19127444—22no—
13#19127434—24no—
14C2×C4⋊C8×C83—22no—
15C2×C4⋊C8×C83C2211yescharacteristic
16C2×C4⋊C8×C83C2211yescharacteristic
17#376×C83C2211yescharacteristic
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#14581726—22no—
28C4⋊(C83⋊C8)—22no—
29#14581714—24no—
30C22⋊(C83⋊C8)—22no—
31#14581703—22no—
32C22×C8×C83—21no—
33C22×C8×C83D412yes—
34C2×C42×C83—21no—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38C4⋊C8×C83—44no—
39#95×C83—21no—
40#95×C83D412yes—
41#13050590—84no—
42C2×Dic166—22no—
43C2×D332—22no—
44C2×D332—22no—
45C2×D332—22no—
46C2×C22⋊D83—42no—
47C2×C4×D83—42no—
48D664—82no—
49C2×C83⋊C8—42no—
50C4⋊Dic83—22no—
51C4⋊Dic83—22no—
52(C2×D83)⋊C4—42no—
53(C2×D83)⋊C4—42no—
54C22×C4×C83—22no—
55C22×C4×C83C2×D411yescharacteristic
56C22×C4×C83C2×D411yescharacteristic
57C22×C4×C83#4111yescharacteristic
58C2×C8×C83—22no—
59C2×C8×C83—42no—
60C2×C8×C83—42no—
61C2×C8×C83—41no—
62C42×C83—22no—
63C42×C83—22no—
64C42×C83C2×D412yes—
65C42×C83#4112yes—
66C23×C83#12111yescharacteristic
67C22×D83—42no—
68C2×C4×C83—22no—
69C2×C4×C83—21no—
70C2×C4×C83—21no—
71C2×C4×C83—24no—
72C2×C4×C83—41no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83#12011yescharacteristic
76C2×C4×C83#12112yes—
77C2×C4×C83#12312yes—
78C2×C4×C83#12411yescharacteristic
79C22⋊D83—84no—
80C2×Dic83—42no—
81D332—42no—
82D332—42no—
83D332—82no—
84D332—82no—
85C4×D83—84no—
86Dic166—82no—
87C8×C83—42no—
88C8×C83—81no—
89C83⋊C8—82no—
90C22×C83—21no—
91C22×C83—21no—
92C22×C83#39411yescharacteristic
93C22×C83#47212yes—
94C2×D83—82no—
95C2×D83—82no—
96C2×D83—82no—
97C4×C83—22no—
98C4×C83—21no—
99C4×C83—22no—
100C4×C83—44no—
101C4×C83#45311yescharacteristic
102C4×C83#45611yescharacteristic
103Dic83—82no—
104#10512—831nomaximal, Sylow
105C2×C83—22no—
106C2×C83#203911yescharacteristic
107C2×C83#204511yescharacteristic
108C2×C83#205311yescharacteristic
109D83—162no—
110#3245—831no—
111#1843D8311yescharacteristic, complemented
112#1551—832no—
113#1505—832no—
114#1290—831no—
115C83#1051211yescharacteristic, complemented, Sylow
116#532—832no—
117#474—1662no—
118#466—1662no—
119#459—1662no—
120#432—832no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8C2×D8311yescharacteristic
123C2×C4⋊C8C2×D8311yescharacteristic
124#376C2×D8311yescharacteristic
125#333—1662no—
126#331—1662no—
127#327—1664no—
128C2×#41—1662no—
129C2×D8—1662no—
130C22×C8—21no—
131C22×C8C22⋊D8312yes—
132C4⋊Q8—832no—
133#127—832no—
134#124—1662no—
135#121—1662no—
136#121—1662no—
137C4×D4—1662no—
138C4×D4—1662no—
139C2×C42—21no—
140C2×C42C22×D8311yescharacteristic
141#107—1662no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—44no—
145C4⋊C8—1662no—
146#102—1664no—
147C22⋊C8—1662no—
148#97—1662no—
149#95—21no—
150#95D33212yes—
151#41—6644no—
152C2×Q8—1662no—
153C2×D4—3322no—
154C2×D4—1662no—
155C2×D4—1662no—
156C2×D4—1662no—
157C22×C4—22no—
158C22×C4—3322no—
159C22×C4C2×C22⋊D8311yescharacteristic
160C22×C4C2×D33211yescharacteristic
161C22×C4#1305059011yescharacteristic
162D8—6642no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—41no—
167C2×C8—3322no—
168C4⋊C4—1662no—
169C4⋊C4—1662no—
170C22⋊C4—3322no—
171C22⋊C4—3322no—
172C42—22no—
173C42—22no—
174C42D4×D8312yes—
175C42#1305059112yes—
176C23—3322no—
177C23#1458176611yescharacteristic
178Q8—6642no—
179D4—3322no—
180D4—3322no—
181D4—6642no—
182D4—6642no—
183D4—6644no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—3322no—
192C2×C4—6644no—
193C2×C4#1458176011yescharacteristic
194C2×C4#1458176712yes—
195C2×C4#1458177712yes—
196C2×C4#1458178111yescharacteristic
197C8—42no—
198C8—81no—
199C8—6642no—
200C22—21no—
201C22—21no—
202C22—6642no—
203C22—6642no—
204C22—6642no—
205C22#1912761811yescharacteristic
206C22#1912797112yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—44no—
211C4—6642no—
212C4#1912786811yescharacteristic
213C4#1912788311yescharacteristic
214C2—22no—
215C2—13282no—
216C2#2490868711yescharacteristic
217C2#2490871911yescharacteristic
218C2#2490876911yescharacteristic
subgroupG/H
centerC22#19127618
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1843C2
socleC22×C83#394
prime radical#24918773C2
hypercenter#1843D83
hypocenterC83#10512
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
2. #24906156C2semidirect
3. #24905970C2semidirect
4. #24905333C2semidirect
5. C83×#1843C2semidirect
111. #1843D83semidirect
115. C83#10512semidirect

Maximal subgroups

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

subgroupindex
#249187732
#249061562
#249059702
#249053332
C83×#18432
#1051283