Finite Group Databasebeta

← #35308480

Subgroups — #35308480

Order 21248.

388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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#24907582C211yesmaximal, characteristic, complemented
3#24906159C212yesmaximal, complemented
4#24905972C212yesmaximal, complemented
5C83×#1290C211yesmaximal, characteristic, complemented
6#19128251C2212yes—
7#19127982—22no—
8#19127937—22no—
9#19127897—22no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11#19127547C2211yescharacteristic
12#19127455—22no—
13#19127449—22no—
14#19127444—22no—
15#19127436—24no—
16#432×C83C2212yes—
17C2×C4⋊C8×C83C2211yescharacteristic
18C2×#13050590—22no—
19C2×D664—22no—
20C22×C83⋊C8—21no—
21#14581792D412yes—
22#14581789D412yes—
23#14581780—22no—
24#14581766—22no—
25#14581766—22no—
26C4×D332—22no—
27C4×D332—22no—
28C2×C4×Dic83—21no—
29#14581726—22no—
30C4⋊(C83⋊C8)—22no—
31#14581714—24no—
32C83⋊#95—21no—
33C83⋊#95D412yes—
34C22×C8×C83D412yes—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38C22⋊C8×C83—22no—
39#97×C83—22no—
40#13050590—84no—
41C2×Dic166—22no—
42C2×D332—22no—
43C2×D332—22no—
44C2×D332—22no—
45C2×C22⋊D83—42no—
46C22×Dic83—22no—
47C2×C4×D83—42no—
48D664—82no—
49C2×C83⋊C8—42no—
50C2×C83⋊C8—41no—
51C4⋊Dic83—22no—
52C4⋊Dic83—22no—
53(C2×D83)⋊C4—42no—
54(C2×D83)⋊C4—42no—
55C4×Dic83—41no—
56C4×Dic83—41no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83C2×D411yescharacteristic
59C22×C4×C83#4111yescharacteristic
60C2×C8×C83—22no—
61C2×C8×C83—42no—
62C2×C8×C83—42no—
63C42×C83C2×D412yes—
64C42×C83#4112yes—
65C23×C83#12111yescharacteristic
66C22×D83—42no—
67C2×C4×C83—22no—
68C2×C4×C83—21no—
69C2×C4×C83—21no—
70C2×C4×C83—41no—
71C2×C4×C83#12011yescharacteristic
72C2×C4×C83#12112yes—
73C2×C4×C83#12312yes—
74C2×C4×C83#12411yescharacteristic
75C22⋊D83—84no—
76C2×Dic83—42no—
77C2×Dic83—42no—
78C2×Dic83—42no—
79C2×Dic83—42no—
80D332—42no—
81D332—42no—
82D332—82no—
83D332—82no—
84C4×D83—84no—
85Dic166—82no—
86C8×C83—42no—
87C8×C83—82no—
88C83⋊C8—81no—
89C22×C83—21no—
90C22×C83—21no—
91C22×C83#39411yescharacteristic
92C22×C83#47212yes—
93C2×D83—82no—
94C2×D83—82no—
95C2×D83—82no—
96C4×C83—22no—
97C4×C83—21no—
98C4×C83—22no—
99C4×C83#45411yescharacteristic
100C4×C83#45511yescharacteristic
101Dic83—82no—
102Dic83—82no—
103#10513—831nomaximal, Sylow
104C2×C83—22no—
105C2×C83#204011yescharacteristic
106C2×C83#204511yescharacteristic
107C2×C83#205311yescharacteristic
108D83—162no—
109#3245—831no—
110#1832—831no—
111#1551—832no—
112#1505—832no—
113#1290D8311yescharacteristic, complemented
114C83#1051311yescharacteristic, complemented, Sylow
115#532—832no—
116#474—1662no—
117#466—1662no—
118#459—1662no—
119#432C2×D8312yes—
120C2×C4⋊C8—831no—
121C2×C4⋊C8C2×D8311yescharacteristic
122#376—831no—
123#336—1662no—
124#333—1662no—
125#331—1662no—
126#327—1664no—
127C2×#41—1662no—
128C2×D8—1662no—
129C22×C8—1661no—
130C22×C8D33212yes—
131C4⋊Q8—832no—
132#127—832no—
133#124—1662no—
134#121—1662no—
135#121—1662no—
136C4×D4—1662no—
137C4×D4—1662no—
138C2×C42—1661no—
139C2×C42C22×D8311yescharacteristic
140#107—1662no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—1662no—
144#102—1664no—
145C22⋊C8—22no—
146#97—22no—
147#95—832no—
148#95—1661no—
149#41—6644no—
150C2×Q8—1662no—
151C2×D4—3322no—
152C2×D4—1662no—
153C2×D4—1662no—
154C2×D4—1662no—
155C22×C4—3322no—
156C22×C4—1662no—
157C22×C4D4×D8311yescharacteristic
158C22×C4C2×D33211yescharacteristic
159C22×C4#1305059111yescharacteristic
160D8—6642no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—3322no—
165C2×C8—3321no—
166C4⋊C4—1662no—
167C4⋊C4—1662no—
168C22⋊C4—3322no—
169C22⋊C4—3322no—
170C42—3321no—
171C42—3321no—
172C42D4×D8312yes—
173C42#1305059012yes—
174C23—3322no—
175C23#1458176711yescharacteristic
176Q8—6642no—
177D4—3322no—
178D4—3322no—
179D4—6642no—
180D4—6642no—
181D4—6644no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—3322no—
187C2×C4—3322no—
188C2×C4—3322no—
189C2×C4—3322no—
190C2×C4—6644no—
191C2×C4#1458176211yescharacteristic
192C2×C4#1458176512yes—
193C2×C4#1458177712yes—
194C2×C4#1458178011yescharacteristic
195C8—42no—
196C8—82no—
197C8—6641no—
198C22—21no—
199C22—21no—
200C22—6642no—
201C22—6642no—
202C22—6642no—
203C22#1912761911yescharacteristic
204C22#1912797212yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—6642no—
209C4—6642no—
210C4#1912787611yescharacteristic
211C4#1912788111yescharacteristic
212C2—22no—
213C2—13282no—
214C2#2490869311yescharacteristic
215C2#2490872011yescharacteristic
216C2#2490877011yescharacteristic
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1290C2
socleC22×C83#394
prime radical#24918773C2
hypercenter#1290D83
hypocenterC83#10513
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
2. #24907582C2semidirect
3. #24906159C2semidirect
4. #24905972C2semidirect
5. C83×#1290C2semidirect
113. #1290D83semidirect
114. C83#10513semidirect

Maximal subgroups

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

subgroupindex
#249187732
#249075822
#249061592
#249059722
C83×#12902
#1051383