Finite Group Databasebeta

← #35317402

Subgroups — #35317402

Order 21248.

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

normal subgroups only

This group has 394 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#24908808C211yesmaximal, characteristic
2#24906470C212yesmaximal
3#24905469C212yesmaximal
4#24905409C211yesmaximal, characteristic
5C83×#2582C211yesmaximal, characteristic
6#19128332C2211yescharacteristic
7#19128031—22no—
8#19127741—21no—
9#19127470C2211yescharacteristic
10#19127461—21no—
11#19127437—22no—
12#19127427C2212yes—
13C2×C4×Q8×C83—21no—
14#398×C83—21no—
15#398×C83C2212yes—
16#391×C83—22no—
17#389×C83—22no—
18#384×C83C2211yescharacteristic
19C2×#13050574—21no—
20#14581791—41no—
21#14581783—41no—
22#14581771—22no—
23#14581751—21no—
24#14581725—41no—
25#14581723—41no—
26#14581723—42no—
27#14581715—42no—
28C22⋊(C83⋊C8)—22no—
29C22×Q8×C83—21no—
30C4×Q8×C83—42no—
31C4×Q8×C83—42no—
32C2×C4⋊C4×C83—21no—
33C2×C4⋊C4×C83—22no—
34C2×C4⋊C4×C83—22no—
35C2×C4⋊C4×C83—21no—
36C2×C4⋊C4×C83D411yescharacteristic
37C2×C4⋊C4×C83D412yes—
38C2×C4⋊C4×C83C2311yescharacteristic
39C2×C42×C83—22no—
40C2×C42×C83D411yescharacteristic
41#95×C83—22no—
42#95×C83—21no—
43#95×C83—22no—
44#95×C83D412yes—
45C2×Dic166—22no—
46#13050574—22no—
47#13050574—41no—
48C2×C83⋊C8—41no—
49C2×C83⋊C8—42no—
50C4⋊Dic83—22no—
51C4⋊Dic83—21no—
52C4⋊Dic83—21no—
53Dic83⋊C4—42no—
54C22⋊Dic83—41no—
55C4×Dic83—41no—
56C2×Q8×C83—24no—
57C2×Q8×C83—42no—
58C2×Q8×C83—42no—
59C22×C4×C83—21no—
60C22×C4×C83—22no—
61C22×C4×C83—21no—
62C22×C4×C83—22no—
63C22×C4×C83C2×D411yescharacteristic
64C22×C4×C83C2×D412yes—
65C4⋊C4×C83—41no—
66C4⋊C4×C83—42no—
67C4⋊C4×C83—41no—
68C4⋊C4×C83—44no—
69C4⋊C4×C83—42no—
70C4⋊C4×C83—42no—
71C4⋊C4×C83—42no—
72C4⋊C4×C83—81no—
73C42×C83—21no—
74C42×C83—44no—
75C42×C83SD1612yes—
76C23×C83#12011yescharacteristic
77Q8×C83—48no—
78C2×C4×C83—22no—
79C2×C4×C83—22no—
80C2×C4×C83—22no—
81C2×C4×C83—21no—
82C2×C4×C83—21no—
83C2×C4×C83—24no—
84C2×C4×C83—22no—
85C2×C4×C83—42no—
86C2×C4×C83—42no—
87C2×C4×C83—42no—
88C2×C4×C83—42no—
89C2×C4×C83—42no—
90C2×C4×C83—42no—
91C2×C4×C83—42no—
92C2×C4×C83—41no—
93C2×C4×C83C2×SD1611yescharacteristic
94C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
95C2×Dic83—41no—
96C2×Dic83—41no—
97Dic166—82no—
98C83⋊C8—42no—
99C83⋊C8—82no—
100C22×C83—21no—
101C22×C83—21no—
102C22×C83#45011yescharacteristic
103C22×C83#45611yescharacteristic
104C22×C83B(4,𝔽2)11yescharacteristic
105C4×C83—24no—
106C4×C83—21no—
107C4×C83—21no—
108C4×C83—44no—
109C4×C83—42no—
110C4×C83—82no—
111C4×C83—81no—
112Dic83—81no—
113Dic83—81no—
114#12247—831nomaximal, Sylow
115C2×C83—21no—
116C2×C83—21no—
117C2×C83#160411yescharacteristic
118C2×C83#219811yescharacteristic
119C2×C83#220511yescharacteristic
120#2582D8311yescharacteristic
121#2060—831no—
122#1611—832no—
123#1346—832no—
124#1325—831no—
125C83#1224711yescharacteristic, complemented, Sylow
126#544—831no—
127C2×C4×Q8—21no—
128#483—1662no—
129#428—1661no—
130#398—21no—
131#398C2×D8312yes—
132#391—22no—
133#389—22no—
134#384C2×D8311yescharacteristic
135#343—831no—
136#339—1661no—
137#328—1662no—
138#324—832no—
139C22×Q8—21no—
140C2×M16—1661no—
141C4⋊Q8—3321no—
142#125—3321no—
143C22⋊Q8—1662no—
144C4×Q8—42no—
145C4×Q8—42no—
146#117—1661no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22⋊D8311yescharacteristic
152C2×C4⋊C4C22⋊D8312yes—
153C2×C4⋊C4C22×D8311yescharacteristic
154C2×C42—22no—
155C2×C42C22⋊D8311yescharacteristic
156#107—3321no—
157#106—3321no—
158#106—3322no—
159#103—3322no—
160C22⋊C8—1662no—
161#95—22no—
162#95—21no—
163#95—22no—
164#95C22⋊D8312yes—
165C2×Q8—24no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—1662no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4C2×C22⋊D8311yescharacteristic
174C22×C4C2×C22⋊D8312yes—
175M16—3321no—
176M16—1662no—
177C2×C8—3321no—
178C2×C8—3322no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C4⋊C4—44no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—81no—
187C4⋊C4—3322no—
188C4⋊C4—1661no—
189C4⋊C4—1662no—
190C4⋊C4—1661no—
191C22⋊C4—3321no—
192C42—21no—
193C42—44no—
194C42—3321no—
195C42#1305057812yes—
196C23#1458176111yescharacteristic
197Q8—48no—
198Q8—6642no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—3321no—
215C2×C4—3321no—
216C2×C4C2×#1305057811yescharacteristic
217C2×C4#1458181811yescharacteristic
218C8—3322no—
219C8—6642no—
220C22—21no—
221C22—21no—
222C22#1912785211yescharacteristic
223C22#1912788411yescharacteristic
224C22#1912788811yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4—6641no—
233C4—6641no—
234C2—21no—
235C2—21no—
236C2#2490643211yescharacteristic
237C2#2490945911yescharacteristic
238C2#2490949311yescharacteristic
subgroupG/H
centerC22#19127888
commutator, cosocleC2×C4⋊C4×C83C23
FrattiniC2×C4⋊C4C22×D83
FittingC83×#2582C2
socleC22×C83B(4,𝔽2)
prime radicalC23×C83#120
hypercenter#2582D83
hypocenterC83#12247
LCSG ▷ C2×C4⋊C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2582

Complements

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

NH ≅ G/Ntype
125. C83#12247semidirect

Maximal subgroups

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

subgroupindex
#249088082
#249064702
#249054692
#249054092
C83×#25822
#1224783