Finite Group Databasebeta

← #35298780

Subgroups — #35298780

Order 21248.

428 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 119 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#24910649C211yesmaximal, characteristic
2#24908433C211yesmaximal, characteristic
3#24907631C212yesmaximal
4#24905345C212yesmaximal
5C2×#330×C83C211yesmaximal, characteristic
6C2×#14581726—22no—
7C2×#14581724—22no—
8C2×#14581703C2211yescharacteristic
9#19127600—22no—
10#19127587—22no—
11#19127587—22no—
12#19127571C2211yescharacteristic
13#19127567C2212yes—
14#19127463—22no—
15C2×#125×C83C2211yescharacteristic
16C2×#97×C83C2212yes—
17#330×C83C414yescomplemented
18C22×C83⋊C8—21no—
19C2×C4⋊Dic83—22no—
20C2×C4⋊Dic83—21no—
21C2×C4⋊Dic83—22no—
22C2×C4⋊Dic83D412yes—
23C2×C4⋊Dic83D412yes—
24C2×C4×Dic83—22no—
25#14581726—44no—
26#14581724—44no—
27#14581703—22no—
28C83⋊#95—22no—
29C83⋊#95—22no—
30C83⋊#95—22no—
31C83⋊#95—22no—
32C22×C8×C83—22no—
33#125×C83—22no—
34#125×C83C2×C412yes—
35#125×C83Q812yes—
36C2×C4⋊C4×C83—22no—
37C2×C4⋊C4×C83D412yes—
38C2×C42×C83C2311yescharacteristic
39#97×C83—22no—
40#97×C83C2×C414yes—
41C22×Dic83—22no—
42C22×Dic83—22no—
43C22×Dic83—41no—
44C2×C83⋊C8—22no—
45C2×C83⋊C8—41no—
46C2×C83⋊C8—41no—
47C4⋊Dic83—42no—
48C4⋊Dic83—42no—
49C4⋊Dic83—42no—
50C4⋊Dic83—42no—
51C4⋊Dic83—42no—
52C4⋊Dic83—82no—
53C4×Dic83—82no—
54C22×C4×C83—22no—
55C22×C4×C83C2×D412yes—
56C22×C4×C83C2×D411yescharacteristic
57C2×C8×C83—24no—
58C2×C8×C83—24no—
59C2×C8×C83—24no—
60C4⋊C4×C83—24no—
61C4⋊C4×C83—24no—
62C4⋊C4×C83—22no—
63C4⋊C4×C83C4⋊C414yes—
64C42×C83C22×C411yescharacteristic
65C42×C83C2×Q811yescharacteristic
66C42×C83#4112yes—
67C23×C83#12011yescharacteristic
68C2×C4×C83—22no—
69C2×C4×C83—21no—
70C2×C4×C83—22no—
71C2×C4×C83—21no—
72C2×C4×C83—24no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83C2×C4⋊C411yescharacteristic
76C2×C4×C83C4×D412yes—
77C2×C4×C83C22⋊Q812yes—
78C2×C4×C83#12311yescharacteristic
79C2×Dic83—42no—
80C2×Dic83—42no—
81C2×Dic83—42no—
82C2×Dic83—42no—
83C2×Dic83—42no—
84C2×Dic83—42no—
85C2×Dic83—82no—
86C2×Dic83—81no—
87C8×C83—28no—
88C83⋊C8—42no—
89C22×C83#38511yescharacteristic
90C22×C83#45312yes—
91C22×C83#45411yescharacteristic
92C22×C83#45612yes—
93C22×C83#45611yescharacteristic
94C4×C83—21no—
95C4×C83—21no—
96C4×C83—22no—
97C4×C83—22no—
98C4×C83—44no—
99Dic83—82no—
100Dic83—82no—
101Dic83—161no—
102#8913—831nomaximal, Sylow
103C2×C83#165611yescharacteristic
104C2×C83#166012yes—
105C2×C83#166311yescharacteristic
106C2×C83#185711yescharacteristic
107C2×C83#185912yes—
108#2382—831no—
109#1992—831no—
110#1847—832no—
111C2×#330D8311yescharacteristic
112#1295—832no—
113C83#891311yescharacteristic, complemented, Sylow
114C2×#125C2×D8311yescharacteristic
115C2×#107—1662no—
116C2×#106—1662no—
117C2×#97—831no—
118C2×#97C2×D8312yes—
119#389—1662no—
120#387—1662no—
121#387—1662no—
122#384—831no—
123#382—832no—
124#340—1662no—
125#330Dic8314yescomplemented
126C22×C8—22no—
127C22×C8—1661no—
128#125—22no—
129#125Dic16612yes—
130#125C2×Dic8312yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—832no—
133C2×C4⋊C4—832no—
134C2×C4⋊C4—1662no—
135C2×C4⋊C4—1661no—
136C2×C4⋊C4—1662no—
137C2×C4⋊C4D33212yes—
138C2×C42—1662no—
139C2×C42C22×D8311yescharacteristic
140#107—3324no—
141#106—3324no—
142#97—22no—
143#97—1662no—
144#97C2×Dic8314yes—
145#95—1662no—
146#95—1662no—
147#95—1662no—
148#95—1662no—
149C22×C4—22no—
150C22×C4—3321no—
151C22×C4—1662no—
152C22×C4—1662no—
153C22×C4D4×D8312yes—
154C22×C4C2×D33211yescharacteristic
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—3321no—
159C2×C8—3321no—
160C2×C8—1662no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—24no—
164C4⋊C4—3322no—
165C4⋊C4—3322no—
166C4⋊C4—3322no—
167C4⋊C4—3322no—
168C4⋊C4—3322no—
169C4⋊C4—6642no—
170C4⋊C4C4⋊Dic8314yes—
171C42—6642no—
172C42C22×Dic8311yescharacteristic
173C42C2×Dic16611yescharacteristic
174C42#1305058912yes—
175C23#1458176211yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—3322no—
184C2×C4—3322no—
185C2×C4—3322no—
186C2×C4—3322no—
187C2×C4—3322no—
188C2×C4—3322no—
189C2×C4—6642no—
190C2×C4—6641no—
191C2×C4C2×C4⋊Dic8311yescharacteristic
192C2×C4D4×Dic8312yes—
193C2×C4#1458176912yes—
194C2×C4#1458177611yescharacteristic
195C8—28no—
196C8—3322no—
197C22#1912757611yescharacteristic
198C22#1912787012yes—
199C22#1912787611yescharacteristic
200C22#1912788512yes—
201C22#1912788611yescharacteristic
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—13281no—
208C4—6642no—
209C4—6642no—
210C2#2490675811yescharacteristic
211C2#2490677612yes—
212C2#2490679211yescharacteristic
213C2#2490768011yescharacteristic
214C2#2490769112yes—
subgroupG/H
centerC23#14581762
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC2×#330×C83C2
socle, prime radicalC23×C83#120
cosocleC2×C42×C83C23
hypercenterC2×#330D83
hypocenterC83#8913
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
17. #330×C83C4semidirect
113. C83#8913semidirect
125. #330Dic83semidirect

Maximal subgroups

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

subgroupindex
#249106492
#249084332
#249076312
#249053452
C2×#330×C832
#891383