Finite Group Databasebeta

← #35297395

Subgroups — #35297395

Order 21248.

388 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 93 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#24916174C211yesmaximal, characteristic
2#24906224C212yesmaximal, complemented
3#24906097C212yesmaximal
4#24905374C211yesmaximal, characteristic, complemented
5C83×#1307C211yesmaximal, characteristic, complemented
6C2×#14581800C412yes—
7#19128251C2211yescharacteristic
8#19127778—22no—
9#19127766—22no—
10#19127758C2212yes—
11#19127669C412yes—
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127453—22no—
14#19127451—22no—
15#19127440—24no—
16#432×C83C2212yes—
17#423×C83C2211yescharacteristic
18C2×#13050590C2×C412yes—
19#14581800—44no—
20C2×#13050573—22no—
21C22×C83⋊C8C2×C411yescharacteristic
22C22×C83⋊C8C2×C411yescharacteristic
23C2×C8×D83—22no—
24#14581792Q811yescharacteristic
25#14581789Q811yescharacteristic
26#14581780D412yes—
27#14581766—22no—
28C4×D332—22no—
29C4⋊(C83⋊C8)—22no—
30C22⋊(C83⋊C8)—22no—
31(C2×D83)⋊C8—24no—
32#14581703—22no—
33C4×C83⋊C8D412yes—
34C4×C83⋊C8D412yes—
35C2×M16×C83C2×C412yes—
36C2×C42×C83C2311yescharacteristic
37C4⋊C8×C83—22no—
38C4⋊C8×C83—22no—
39C22⋊C8×C83—22no—
40#97×C83—22no—
41#13050590—42no—
42#13050590—42no—
43C2×Dic166C4⋊C412yes—
44C2×D332—22no—
45C2×D332C4⋊C412yes—
46C2×C22⋊D83—22no—
47C2×C4×D83—22no—
48#13050573—44no—
49C2×C83⋊C8—22no—
50C2×C83⋊C8—41no—
51C2×C83⋊C8—42no—
52C2×C83⋊C8C22⋊C411yescharacteristic
53C2×C83⋊C8C22⋊C412yes—
54C2×C83⋊C8C22⋊C411yescharacteristic
55C8×D83—44no—
56C4⋊Dic83—22no—
57(C2×D83)⋊C4—24no—
58C22×C4×C83C22×C411yescharacteristic
59C22×C4×C83#4112yes—
60M16×C83—42no—
61C2×C8×C83—22no—
62C2×C8×C83—42no—
63C42×C83C2×D412yes—
64C42×C83C2×D411yescharacteristic
65C42×C83C2×Q811yescharacteristic
66C23×C83#11711yescharacteristic
67C22×D83—22no—
68C2×C4×C83—21no—
69C2×C4×C83—21no—
70C2×C4×C83—42no—
71C2×C4×C83C2×C22⋊C411yescharacteristic
72C2×C4×C83C2×C4⋊C411yescharacteristic
73C2×C4×C83#12112yes—
74C2×C4×C83C22⋊Q812yes—
75C22⋊D83—44no—
76C2×Dic83—22no—
77D332—42no—
78D332—44no—
79C4×D83—42no—
80C4×D83—42no—
81Dic166—42no—
82C8×C83—42no—
83C8×C83—82no—
84C83⋊C8—21no—
85C83⋊C8—22no—
86C83⋊C8—82no—
87C83⋊C8#10012yes—
88C22×C83—21no—
89C22×C83—22no—
90C22×C83#38011yescharacteristic
91C2×D83—42no—
92C2×D83—44no—
93C4×C83—21no—
94C4×C83—22no—
95C4×C83—22no—
96C4×C83C2×#10011yescharacteristic
97C4×C83#41311yescharacteristic
98Dic83—42no—
99#8630—831nomaximal, Sylow
100C2×C83—41no—
101C2×C83#180011yescharacteristic
102C2×C83#181412yes—
103D83—82no—
104#2931—831no—
105#1568—832no—
106#1536—832no—
107#1307—831no—
108#1307D8311yescharacteristic, complemented
109C83#863011yescharacteristic, complemented, Sylow
110C2×#131—832no—
111#532—831no—
112#436—1662no—
113C8×D4—1662no—
114#432—832no—
115#432C2×D8312yes—
116#423C2×D8311yescharacteristic
117#408—832no—
118C2×C4×C8—831no—
119#335—1662no—
120#334—1662no—
121#329—1664no—
122C2×#41—832no—
123#131—3324no—
124C2×M16—1662no—
125C2×M16C4×D8312yes—
126C22×C8—831no—
127C22×C8—831no—
128C22×C8—1662no—
129C4⋊Q8—831no—
130#127—831no—
131#124—832no—
132#121—1662no—
133C4×D4—1662no—
134C2×C42C22×D8311yescharacteristic
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—1662no—
138C22⋊C8—22no—
139C22⋊C8—1664no—
140C22⋊C8—1662no—
141#97—22no—
142#97—1662no—
143C4×C8—832no—
144C4×C8—832no—
145#41—3322no—
146#41—3322no—
147C2×Q8—832no—
148C2×D4—832no—
149C2×D4—1662no—
150C2×D4—1662no—
151C22×C4—1662no—
152C22×C4C2×C4×D8311yescharacteristic
153C22×C4#1305059012yes—
154M16—42no—
155M16—3324no—
156C2×C8—22no—
157C2×C8—42no—
158C2×C8—3324no—
159C2×C8—3322no—
160C2×C8—3321no—
161C2×C8—831no—
162C2×C8—832no—
163C2×C8—831no—
164C2×C8—1662no—
165C4⋊C4—1662no—
166C22⋊C4—1664no—
167C42D4×D8311yescharacteristic
168C42D4×D8312yes—
169C42Q8×D8311yescharacteristic
170C23—1662no—
171C23#1458174911yescharacteristic
172Q8—3322no—
173D4—3322no—
174D4—3324no—
175D4—3324no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—3322no—
180C2×C4—3322no—
181C2×C4—1662no—
182C2×C4C22⋊C4×D8311yescharacteristic
183C2×C4C4⋊C4×D8311yescharacteristic
184C2×C4#1458176512yes—
185C2×C4#1458177012yes—
186C8—42no—
187C8—82no—
188C8—832no—
189C8—6642no—
190C8—1661no—
191C8—1662no—
192C22—21no—
193C22—22no—
194C22—3322no—
195C22—3324no—
196C22#1912756011yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—3322no—
201C4#100×D8311yescharacteristic
202C4#1912768411yescharacteristic
203C2—41no—
204C2—6642no—
205C2#2490745411yescharacteristic
206C2#2490751612yes—
subgroupG/H
centerC22#19127560
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1307C2
socleC22×C83#380
prime radical#19128251C22
cosocleC2×C42×C83C23
hypercenter#1307D83
hypocenterC83#8630
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #24906224C2semidirect
4. #24905374C2semidirect
5. C83×#1307C2semidirect
108. #1307D83semidirect
109. C83#8630semidirect

Maximal subgroups

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

subgroupindex
#249161742
#249062242
#249060972
#249053742
C83×#13072
#863083