Finite Group Databasebeta

← #35317488

Subgroups — #35317488

Order 21248.

330 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 63 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#24908813C211yesmaximal, characteristic
2#24906504C212yesmaximal
3#24905490C212yesmaximal
4#24905407C211yesmaximal, characteristic
5C83×#2844C211yesmaximal, characteristic
6#19128332C2211yescharacteristic
7#19128036—22no—
8#19127741—21no—
9#19127470C2211yescharacteristic
10#19127461—21no—
11#19127437—22no—
12#19127427C2212yes—
13#400×C83—22no—
14#400×C83C2212yes—
15#395×C83—22no—
16#395×C83—21no—
17#382×C83—21no—
18#382×C83C2211yescharacteristic
19C2×#13050574—21no—
20#14581791—41no—
21#14581783—41no—
22#14581771—22no—
23#14581751—21no—
24#14581725—41no—
25#14581725—42no—
26#14581723—41no—
27#14581715—42no—
28C22⋊(C83⋊C8)—22no—
29C22×Q8×C83—21no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83—22no—
33C2×C4⋊C4×C83D411yescharacteristic
34C2×C4⋊C4×C83D412yes—
35C2×C4⋊C4×C83C2311yescharacteristic
36C2×C42×C83D411yescharacteristic
37#95×C83—22no—
38#95×C83—21no—
39#95×C83—22no—
40#95×C83—22no—
41#95×C83—22no—
42#95×C83D412yes—
43C2×Dic166—22no—
44#13050574—22no—
45#13050574—41no—
46C2×C83⋊C8—41no—
47C2×C83⋊C8—42no—
48C4⋊Dic83—22no—
49C4⋊Dic83—21no—
50C4⋊Dic83—21no—
51Dic83⋊C4—42no—
52C22⋊Dic83—41no—
53C4×Dic83—41no—
54C2×Q8×C83—82no—
55C2×Q8×C83—81no—
56C22×C4×C83—21no—
57C22×C4×C83—22no—
58C22×C4×C83—22no—
59C22×C4×C83—21no—
60C22×C4×C83C2×D411yescharacteristic
61C22×C4×C83C2×D412yes—
62C4⋊C4×C83—41no—
63C4⋊C4×C83—42no—
64C4⋊C4×C83—41no—
65C4⋊C4×C83—81no—
66C4⋊C4×C83—81no—
67C4⋊C4×C83—82no—
68C42×C83—21no—
69C42×C83Q1612yes—
70C23×C83#12011yescharacteristic
71Q8×C83—84no—
72C2×C4×C83—21no—
73C2×C4×C83—21no—
74C2×C4×C83—22no—
75C2×C4×C83—22no—
76C2×C4×C83—41no—
77C2×C4×C83—41no—
78C2×C4×C83—42no—
79C2×C4×C83—42no—
80C2×C4×C83—42no—
81C2×C4×C83—42no—
82C2×C4×C83—42no—
83C2×C4×C83—42no—
84C2×C4×C83—42no—
85C2×C4×C83—42no—
86C2×C4×C83—41no—
87C2×C4×C83C2×Q1611yescharacteristic
88C2×C4×C83#13711yescharacteristic
89C2×Dic83—41no—
90C2×Dic83—41no—
91Dic166—82no—
92C83⋊C8—42no—
93C83⋊C8—82no—
94C22×C83—21no—
95C22×C83—21no—
96C22×C83#45111yescharacteristic
97C22×C83#45611yescharacteristic
98C22×C83B(4,𝔽2)11yescharacteristic
99C4×C83—21no—
100C4×C83—21no—
101C4×C83—42no—
102C4×C83—42no—
103C4×C83—82no—
104C4×C83—82no—
105C4×C83—81no—
106Dic83—81no—
107Dic83—81no—
108#12261—831nomaximal, Sylow
109C2×C83—21no—
110C2×C83—21no—
111C2×C83#160511yescharacteristic
112C2×C83#220111yescharacteristic
113C2×C83#220211yescharacteristic
114#2844D8311yescharacteristic
115#2061—831no—
116#1617—832no—
117#1353—832no—
118#1324—831no—
119C83#1226111yescharacteristic, complemented, Sylow
120#544—831no—
121#484—1662no—
122#428—1661no—
123#400—22no—
124#400C2×D8312yes—
125#395—22no—
126#395—21no—
127#382—21no—
128#382C2×D8311yescharacteristic
129#343—831no—
130#339—1661no—
131#328—1662no—
132#324—832no—
133C22×Q8—21no—
134C2×M16—1661no—
135C4⋊Q8—3321no—
136#125—3321no—
137C22⋊Q8—1662no—
138#117—1661no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4C22⋊D8311yescharacteristic
143C2×C4⋊C4C22⋊D8312yes—
144C2×C4⋊C4C22×D8311yescharacteristic
145C2×C42C22⋊D8311yescharacteristic
146#107—3321no—
147#107—3322no—
148#106—3321no—
149#103—3322no—
150C22⋊C8—1662no—
151#95—22no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156#95C22⋊D8312yes—
157C2×Q8—82no—
158C2×Q8—81no—
159C2×Q8—1662no—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—21no—
164C22×C4C2×C22⋊D8311yescharacteristic
165C22×C4C2×C22⋊D8312yes—
166M16—3321no—
167M16—1662no—
168C2×C8—3321no—
169C2×C8—3322no—
170C4⋊C4—41no—
171C4⋊C4—42no—
172C4⋊C4—41no—
173C4⋊C4—81no—
174C4⋊C4—81no—
175C4⋊C4—82no—
176C4⋊C4—3322no—
177C4⋊C4—1661no—
178C4⋊C4—1661no—
179C4⋊C4—1662no—
180C22⋊C4—3321no—
181C42—21no—
182C42—3321no—
183C42#1305058012yes—
184C23#1458176111yescharacteristic
185Q8—84no—
186Q8—6642no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—3321no—
203C2×C4—3321no—
204C2×C4C2×#1305058011yescharacteristic
205C2×C4#1458182311yescharacteristic
206C8—3322no—
207C8—6642no—
208C22—21no—
209C22—21no—
210C22#1912785711yescharacteristic
211C22#1912788411yescharacteristic
212C22#1912788811yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—82no—
218C4—82no—
219C4—81no—
220C4—6641no—
221C4—6641no—
222C2—21no—
223C2—21no—
224C2#2490643711yescharacteristic
225C2#2490947611yescharacteristic
226C2#2490948011yescharacteristic
subgroupG/H
centerC22#19127888
commutator, cosocleC2×C4⋊C4×C83C23
FrattiniC2×C4⋊C4C22×D83
FittingC83×#2844C2
socleC22×C83B(4,𝔽2)
prime radicalC23×C83#120
hypercenter#2844D83
hypocenterC83#12261
LCSG ▷ C2×C4⋊C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
119. C83#12261semidirect

Maximal subgroups

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

subgroupindex
#249088132
#249065042
#249054902
#249054072
C83×#28442
#1226183