Finite Group Databasebeta

← #35308904

Subgroups — #35308904

Order 21248.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#24915735C211yesmaximal, characteristic
2#24907598C212yesmaximal
3#24905345C212yesmaximal
4#24905344C211yesmaximal, characteristic
5C83×#1847C211yesmaximal, characteristic
6C2×#14581703C2212yes—
7#19127643—22no—
8#19127640—21no—
9#19127622—22no—
10#19127621—21no—
11#19127567C2212yes—
12#19127463—22no—
13#19127463—22no—
14C2×#107×C83—21no—
15C2×#106×C83—21no—
16C2×#97×C83C2211yescharacteristic
17#384×C83C2211yescharacteristic
18#382×C83C2211yescharacteristic
19C22×Dic166—21no—
20C22×C83⋊C8—22no—
21C2×C4⋊Dic83—21no—
22C2×C4⋊Dic83D412yes—
23C2×C4⋊Dic83D412yes—
24C2×Dic83⋊C4—22no—
25#14581703—22no—
26#14581703Q814yescomplemented
27C83⋊#95—21no—
28C83⋊#95—22no—
29C83⋊#95—21no—
30C83⋊#95—22no—
31C83⋊#95—22no—
32C22×C8×C83—21no—
33C2×C4⋊C4×C83—22no—
34C2×C4⋊C4×C83—21no—
35C2×C4⋊C4×C83D411yescharacteristic
36C2×C4⋊C4×C83D411yescharacteristic
37C2×C42×C83C2311yescharacteristic
38#107×C83—42no—
39#106×C83—42no—
40#97×C83—21no—
41#97×C83Q812yescomplemented
42#95×C83—22no—
43C2×Dic166—81no—
44C2×Dic166—82no—
45C22×Dic83—22no—
46C22×Dic83—22no—
47C2×C83⋊C8—24no—
48C2×C83⋊C8—42no—
49C2×C83⋊C8—42no—
50C4⋊Dic83—42no—
51C4⋊Dic83—42no—
52C4⋊Dic83—81no—
53Dic83⋊C4—82no—
54C22×C4×C83—21no—
55C22×C4×C83—21no—
56C22×C4×C83—41no—
57C22×C4×C83C2×D412yes—
58C22×C4×C83C2×D411yescharacteristic
59C2×C8×C83—22no—
60C2×C8×C83—22no—
61C2×C8×C83—22no—
62C4⋊C4×C83—41no—
63C4⋊C4×C83—41no—
64C4⋊C4×C83—41no—
65C4⋊C4×C83—41no—
66C4⋊C4×C83—44no—
67C42×C83C2×Q812yes—
68C42×C83C2×Q811yescharacteristic
69C42×C83#4111yescharacteristic
70C23×C83#12011yescharacteristic
71C2×C4×C83—21no—
72C2×C4×C83—22no—
73C2×C4×C83—22no—
74C2×C4×C83—21no—
75C2×C4×C83—41no—
76C2×C4×C83—41no—
77C2×C4×C83—42no—
78C2×C4×C83—42no—
79C2×C4×C83—81no—
80C2×C4×C83—82no—
81C2×C4×C83C22⋊Q812yes—
82C2×C4×C83C22⋊Q811yescharacteristic
83C2×C4×C83C4⋊Q811yescharacteristic
84C2×C4×C83C4⋊Q812yes—
85C2×Dic83—42no—
86C2×Dic83—42no—
87C2×Dic83—42no—
88C2×Dic83—42no—
89C2×Dic83—42no—
90C2×Dic83—42no—
91Dic166—84no—
92C8×C83—24no—
93C83⋊C8—44no—
94C22×C83#39511yescharacteristic
95C22×C83#45311yescharacteristic
96C22×C83#45412yes—
97C22×C83#45512yes—
98C22×C83#45611yescharacteristic
99C4×C83—21no—
100C4×C83—21no—
101C4×C83—22no—
102C4×C83—22no—
103C4×C83—81no—
104C4×C83—81no—
105C4×C83—161no—
106Dic83—82no—
107Dic83—82no—
108#10584—831nomaximal, Sylow
109C2×C83#165711yescharacteristic
110C2×C83#165911yescharacteristic
111C2×C83#166412yes—
112C2×C83#206011yescharacteristic
113C2×C83#206112yes—
114#2844—831no—
115#1847D8311yescharacteristic
116#1836—832no—
117#1295—832no—
118#1295—831no—
119C83#1058411yescharacteristic, complemented, Sylow
120C2×#107—21no—
121C2×#106—21no—
122C2×#97—832no—
123C2×#97C2×D8311yescharacteristic
124#400—1662no—
125#400—1661no—
126#395—1662no—
127#395—1661no—
128#384C2×D8311yescharacteristic
129#382—832no—
130#382C2×D8311yescharacteristic
131#340—1662no—
132#340—1662no—
133C22×Q8—1661no—
134C22×C8—21no—
135C22×C8—1662no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—832no—
139C2×C4⋊C4—832no—
140C2×C4⋊C4—1662no—
141C2×C4⋊C4—1661no—
142C2×C4⋊C4C22⋊D8311yescharacteristic
143C2×C4⋊C4C22⋊D8311yescharacteristic
144C2×C42C22×D8311yescharacteristic
145#107—42no—
146#106—42no—
147#97—21no—
148#97—834no—
149#97—1662no—
150#97Dic16612yescomplemented
151#95—22no—
152#95—1662no—
153#95—1661no—
154#95—1661no—
155#95—1662no—
156#95—1662no—
157C2×Q8—6641no—
158C2×Q8—6642no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—41no—
162C22×C4—1662no—
163C22×C4—1662no—
164C22×C4D4×D8312yes—
165C22×C4C2×C22⋊D8311yescharacteristic
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—3322no—
170C2×C8—3322no—
171C2×C8—1664no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—44no—
177C4⋊C4—3322no—
178C4⋊C4—3322no—
179C4⋊C4—6642no—
180C4⋊C4—6641no—
181C42Q8×D8312yes—
182C42C2×Dic16611yescharacteristic
183C42#1305059011yescharacteristic
184C23#1458176011yescharacteristic
185Q8—6644no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—82no—
196C2×C4—3322no—
197C2×C4—3322no—
198C2×C4—3322no—
199C2×C4—3322no—
200C2×C4—3322no—
201C2×C4—3322no—
202C2×C4#1458177012yes—
203C2×C4#1458177111yescharacteristic
204C2×C4#1458179011yescharacteristic
205C2×C4#1458179112yes—
206C8—24no—
207C8—3324no—
208C22#1912762111yescharacteristic
209C22#1912786811yescharacteristic
210C22#1912787212yes—
211C22#1912787712yes—
212C22#1912788311yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—161no—
220C4—6642no—
221C4—6642no—
222C2#2490675911yescharacteristic
223C2#2490676711yescharacteristic
224C2#2490679512yes—
225C2#2490880811yescharacteristic
226C2#2490881112yes—
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1847C2
socle, prime radicalC23×C83#120
hypercenter#1847D83
hypocenterC83#10584
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
26. #14581703Q8semidirect
41. #97×C83Q8semidirect
119. C83#10584semidirect
150. #97Dic166semidirect

Maximal subgroups

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

subgroupindex
#249157352
#249075982
#249053452
#249053442
C83×#18472
#1058483