Finite Group Databasebeta

← #35318640

Subgroups — #35318640

Order 21248.

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

normal subgroups only

This group has 246 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#24909720C211yesmaximal, characteristic, complemented
2#24909294C211yesmaximal, characteristic, complemented
3#24906825C211yesmaximal, characteristic, complemented
4#24906819C211yesmaximal, characteristic
5#24905534C211yesmaximal, characteristic, complemented
6#24905510C211yesmaximal, characteristic, complemented
7C83×#1362C211yesmaximal, characteristic, complemented
8C2×#14581735—21no—
9C2×#14581735—21no—
10C2×#14581731—21no—
11#19128078C2211yescharacteristic
12#19127978—21no—
13#19127897—21no—
14C8×D332C2211yescharacteristic
15(C2×D83)⋊C16—21no—
16C4×C83⋊C16C2211yescharacteristic
17#19127454C2211yescharacteristic
18#19127447—21no—
19#19127444—21no—
20#494×C83C2211yescharacteristic
21C4⋊C16×C83C2211yescharacteristic
22#335×C83C2211yescharacteristic
23C2×D664—21no—
24C2×D664—21no—
25C2×D664—41no—
26C2×C8×D83—21no—
27#14581789—21no—
28C4×D332D411yescharacteristic
29#14581735—42no—
30#14581735—42no—
31#14581731—42no—
32C2×C83⋊C16D411yescharacteristic
33C2×C83⋊C16D411yescharacteristic
34#14581725—41no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)D411yescharacteristic
37#14581714—41no—
38#14581712—41no—
39(C2×D83)⋊C8—21no—
40C2×Q16×C83—21no—
41C2×Q16×C83—21no—
42C4⋊Q8×C83—21no—
43C2×C16×C83—21no—
44C4⋊C8×C83—21no—
45C4×C8×C83C2311yescharacteristic
46C2×D332—41no—
47C2×D332—41no—
48C2×D332—41no—
49C2×D332D811yescharacteristic
50C2×C4×D83—21no—
51D664—41no—
52D664—41no—
53D664—81no—
54D664—82no—
55C2×C83⋊C8—21no—
56C2×C83⋊C8—41no—
57C8×D83—41no—
58C8×D83—41no—
59C4⋊Dic83D811yescharacteristic
60(C2×D83)⋊C4—21no—
61C83⋊C16—21no—
62C83⋊C16D812yescomplemented
63C2×Q8×C83—41no—
64Q16×C83—41no—
65Q16×C83—41no—
66Q16×C83—81no—
67C2×C8×C83—41no—
68C2×C8×C83C2×D411yescharacteristic
69C2×C8×C83#4111yescharacteristic
70C4⋊C4×C83—41no—
71C4⋊C4×C83—41no—
72C42×C83C2×D411yescharacteristic
73C16×C83—41no—
74C22×D83—21no—
75C22×D83—81no—
76Q8×C83—81no—
77Q8×C83—81no—
78C2×C4×C83—81no—
79C2×C4×C83#12111yescharacteristic
80C2×C4×C83C2×D811yescharacteristic
81C2×C4×C83#13511yescharacteristic
82C2×Dic83—21no—
83D332—21no—
84D332—21no—
85D332—81no—
86D332—81no—
87D332—81no—
88D332—81no—
89D332—161no—
90C4×D83—41no—
91C4×D83—41no—
92C8×C83—21no—
93C8×C83—81no—
94C8×C83C2×D811yescharacteristic
95C8×C83AGL(1,ℤ/8)11yescharacteristic
96C83⋊C8—41no—
97C83⋊C8—81no—
98C22×C83#46611yescharacteristic
99C2×D83—41no—
100C2×D83—41no—
101C2×D83—41no—
102C2×D83—161no—
103C2×D83—161no—
104C2×D83—161no—
105C4×C83—21no—
106C4×C83—161no—
107C4×C83#45911yescharacteristic
108C4×C83#47211yescharacteristic
109C4×C83#50911yescharacteristic
110C4×C83#51011yescharacteristic
111Dic83—41no—
112#12435—831nomaximal, Sylow
113C2×C83#166711yescharacteristic
114C2×C83#222011yescharacteristic
115C2×C83#222311yescharacteristic
116D83—81no—
117D83—321no—
118#2248—831no—
119#2169—831no—
120#1669—831no—
121#1667—831no—
122#1371—831no—
123#1362D8311yescharacteristic, complemented
124#1361—831no—
125C83#1243511yescharacteristic, complemented, Sylow
126C2×SD32—1661no—
127C2×SD32—1661no—
128C2×M32—1661no—
129#494C2×D8311yescharacteristic
130#493—831no—
131#474—1661no—
132#459—1661no—
133C8×D4—831no—
134C4⋊C16C2×D8311yescharacteristic
135C22⋊C16—1661no—
136C4×C16—831no—
137#335—831no—
138#335C2×D8311yescharacteristic
139#332—1661no—
140#331—1661no—
141C2×Q16—21no—
142C2×Q16—21no—
143C2×D8—3321no—
144C2×D8—1661no—
145C2×D8—1661no—
146C22×C8—1661no—
147C4⋊Q8—21no—
148#127—1661no—
149C4×D4—831no—
150SD32—3322no—
151SD32—3322no—
152M32—3322no—
153C2×C16—21no—
154C2×C16—831no—
155C2×C16—831no—
156#107—3321no—
157C4⋊C8—21no—
158C4⋊C8—831no—
159C4⋊C8—1661no—
160#102—3321no—
161#102—3321no—
162C22⋊C8—1661no—
163C4×C8C22×D8311yescharacteristic
164C2×Q8—41no—
165C2×D4—3321no—
166C2×D4—3321no—
167C2×D4—3321no—
168C2×D4—831no—
169C22×C4—1661no—
170Q16—41no—
171Q16—41no—
172Q16—81no—
173D8—3321no—
174D8—3321no—
175D8—6641no—
176D8—6642no—
177C2×C8—41no—
178C2×C8—3321no—
179C2×C8—3321no—
180C2×C8—3321no—
181C2×C8—1661no—
182C2×C8D4×D8311yescharacteristic
183C2×C8#1305059011yescharacteristic
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—831no—
187C22⋊C4—1661no—
188C42D4×D8311yescharacteristic
189C16—41no—
190C16—832no—
191C16—1661no—
192C23—6641no—
193C23—1661no—
194Q8—81no—
195Q8—81no—
196D4—13281no—
197D4—6641no—
198D4—6641no—
199D4—6641no—
200D4—6641no—
201D4—1661no—
202D4—1661no—
203C2×C4—81no—
204C2×C4—3321no—
205C2×C4—3321no—
206C2×C4—1661no—
207C2×C4#1458176511yescharacteristic
208C2×C4D8×D8311yescharacteristic
209C2×C4#1458181311yescharacteristic
210C8—21no—
211C8—81no—
212C8—3321no—
213C8—6641no—
214C8D8×D8311yescharacteristic
215C8#1458181911yescharacteristic
216C22—13281no—
217C22—13281no—
218C22—13281no—
219C22—3321no—
220C22—3321no—
221C22—3321no—
222C22#1912793611yescharacteristic
223C4—21no—
224C4—161no—
225C4—3321no—
226C4#1912789511yescharacteristic
227C4#1912797011yescharacteristic
228C4#1912813811yescharacteristic
229C4#1912814311yescharacteristic
230C2—26561no—
231C2—6641no—
232C2#2490681711yescharacteristic
233C2#2490957911yescharacteristic
234C2#2490959611yescharacteristic
subgroupG/H
centerC22#19127936
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#1362C2
socleC22×C83#466
prime radical#24906819C2
hypercenter#1362D83
hypocenterC83#12435
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #24909720C2semidirect
2. #24909294C2semidirect
3. #24906825C2semidirect
5. #24905534C2semidirect
6. #24905510C2semidirect
7. C83×#1362C2semidirect
62. C83⋊C16D8semidirect
123. #1362D83semidirect
125. C83#12435semidirect

Maximal subgroups

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

subgroupindex
#249097202
#249092942
#249068252
#249068192
#249055342
#249055102
C83×#13622
#1243583