Finite Group Databasebeta

← #35318636

Subgroups — #35318636

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#24909718C211yesmaximal, characteristic, complemented
2#24909294C211yesmaximal, characteristic, complemented
3#24906829C211yesmaximal, characteristic, complemented
4#24906815C211yesmaximal, characteristic
5#24905534C211yesmaximal, characteristic, complemented
6#24905513C211yesmaximal, characteristic, complemented
7C83×#1361C211yesmaximal, characteristic, complemented
8C2×#14581736—21no—
9C2×#14581736—21no—
10C2×#14581731—21no—
11#19128081C2211yescharacteristic
12#19127982—21no—
13#19127893—21no—
14C8×D332C2211yescharacteristic
15(C2×D83)⋊C16—21no—
16C4×C83⋊C16C2211yescharacteristic
17#19127454C2211yescharacteristic
18#19127446—21no—
19#19127445—21no—
20#493×C83C2211yescharacteristic
21C4⋊C16×C83C2211yescharacteristic
22#335×C83C2211yescharacteristic
23C2×Dic332—21no—
24C2×Dic332—21no—
25C2×#13050575—41no—
26C2×C8×D83—21no—
27#14581792—21no—
28C4×D332D411yescharacteristic
29#14581736—42no—
30#14581736—42no—
31#14581731—42no—
32C2×C83⋊C16D411yescharacteristic
33C2×C83⋊C16D411yescharacteristic
34#14581726—41no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)D411yescharacteristic
37#14581714—41no—
38#14581713—41no—
39(C2×D83)⋊C8—21no—
40C2×D8×C83—21no—
41C2×D8×C83—21no—
42#127×C83—21no—
43C2×C16×C83—21no—
44C4⋊C8×C83—21no—
45C4×C8×C83C2311yescharacteristic
46C2×Dic166—41no—
47C2×D332D811yescharacteristic
48C2×C4×D83—21no—
49Dic332—41no—
50Dic332—41no—
51Dic332—81no—
52#13050575—82no—
53C2×C83⋊C8—21no—
54C2×C83⋊C8—41no—
55C8×D83—41no—
56C8×D83—41no—
57C4⋊Dic83—41no—
58C4⋊Dic83—41no—
59C4⋊Dic83D811yescharacteristic
60(C2×D83)⋊C4—21no—
61C83⋊C16—21no—
62C83⋊C16D812yescomplemented
63C2×D4×C83—41no—
64C2×D4×C83—41no—
65C2×D4×C83—41no—
66D8×C83—41no—
67D8×C83—41no—
68D8×C83—81no—
69C2×C8×C83—41no—
70C2×C8×C83C2×D411yescharacteristic
71C2×C8×C83#4111yescharacteristic
72C42×C83C2×D411yescharacteristic
73C16×C83—41no—
74C23×C83—81no—
75C22×D83—21no—
76D4×C83—81no—
77D4×C83—81no—
78D4×C83—81no—
79D4×C83—81no—
80D4×C83—161no—
81C2×C4×C83#12111yescharacteristic
82C2×C4×C83C2×D811yescharacteristic
83C2×C4×C83#13511yescharacteristic
84C2×Dic83—21no—
85C2×Dic83—81no—
86D332—21no—
87D332—21no—
88C4×D83—41no—
89C4×D83—41no—
90Dic166—81no—
91Dic166—81no—
92C8×C83—21no—
93C8×C83—81no—
94C8×C83C2×D811yescharacteristic
95C8×C83AGL(1,ℤ/8)11yescharacteristic
96C83⋊C8—41no—
97C83⋊C8—81no—
98C22×C83—161no—
99C22×C83—161no—
100C22×C83—161no—
101C22×C83#46611yescharacteristic
102C2×D83—41no—
103C2×D83—41no—
104C2×D83—41no—
105C4×C83—21no—
106C4×C83#45911yescharacteristic
107C4×C83#47211yescharacteristic
108C4×C83#50911yescharacteristic
109C4×C83#51011yescharacteristic
110Dic83—41no—
111Dic83—161no—
112#12435—831nomaximal, Sylow
113C2×C83—321no—
114C2×C83#166711yescharacteristic
115C2×C83#222011yescharacteristic
116C2×C83#222311yescharacteristic
117D83—81no—
118#2248—831no—
119#2169—831no—
120#1669—831no—
121#1667—831no—
122#1371—831no—
123#1362—831no—
124#1361D8311yescharacteristic, complemented
125C83#1243511yescharacteristic, complemented, Sylow
126C2×SD32—1661no—
127C2×SD32—1661no—
128C2×M32—1661no—
129#494—831no—
130#493C2×D8311yescharacteristic
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—1661no—
142C2×Q16—1661no—
143C2×D8—21no—
144C2×D8—21no—
145C2×D8—3321no—
146C22×C8—1661no—
147C4⋊Q8—1661no—
148#127—21no—
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—3321no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4—831no—
169C22×C4—1661no—
170Q16—3321no—
171Q16—3321no—
172Q16—6641no—
173D8—41no—
174D8—41no—
175D8—81no—
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—3321no—
185C4⋊C4—3321no—
186C4⋊C4—831no—
187C22⋊C4—1661no—
188C42D4×D8311yescharacteristic
189C16—41no—
190C16—832no—
191C16—1661no—
192C23—81no—
193C23—1661no—
194Q8—6641no—
195Q8—6641no—
196D4—81no—
197D4—81no—
198D4—81no—
199D4—81no—
200D4—161no—
201D4—1661no—
202D4—1661no—
203C2×C4—3321no—
204C2×C4—3321no—
205C2×C4—6641no—
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—161no—
217C22—161no—
218C22—161no—
219C22—3321no—
220C22—3321no—
221C22—3321no—
222C22#1912793611yescharacteristic
223C4—21no—
224C4—13281no—
225C4—3321no—
226C4#1912789511yescharacteristic
227C4#1912797011yescharacteristic
228C4#1912813511yescharacteristic
229C4#1912814011yescharacteristic
230C2—321no—
231C2—6641no—
232C2#2490681711yescharacteristic
233C2#2490957511yescharacteristic
234C2#2490959211yescharacteristic
subgroupG/H
centerC22#19127936
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#1361C2
socleC22×C83#466
prime radical#24906815C2
hypercenter#1361D83
hypocenterC83#12435
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #24909718C2semidirect
2. #24909294C2semidirect
3. #24906829C2semidirect
5. #24905534C2semidirect
6. #24905513C2semidirect
7. C83×#1361C2semidirect
62. C83⋊C16D8semidirect
124. #1361D83semidirect
125. C83#12435semidirect

Maximal subgroups

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

subgroupindex
#249097182
#249092942
#249068292
#249068152
#249055342
#249055132
C83×#13612
#1243583