Finite Group Databasebeta

← #35308862

Subgroups — #35308862

Order 21248.

406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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#24912705C211yesmaximal, characteristic
2#24908222C212yesmaximal
3#24907619C211yesmaximal, characteristic
4#24905302C212yesmaximal
5C83×#1296C211yesmaximal, characteristic
6C2×#14581726—22no—
7C2×#14581723—22no—
8C2×C4×C83⋊C8C2211yescharacteristic
9#19127640—22no—
10#19127600—22no—
11#19127571C2211yescharacteristic
12#19127566—22no—
13C4×C4⋊Dic83C2212yes—
14#19127464—22no—
15C2×C4⋊C8×C83C2212yes—
16#384×C83C2211yescharacteristic
17C22×C83⋊C8—21no—
18C2×C4⋊Dic83—22no—
19C2×C4⋊Dic83—22no—
20C2×C4⋊Dic83—21no—
21C2×C4⋊Dic83D412yes—
22C2×C4⋊Dic83D412yes—
23C2×C4×Dic83—22no—
24#14581726—44no—
25#14581723—44no—
26C4×C83⋊C8—21no—
27C4×C83⋊C8Q812yes—
28C83⋊#95—22no—
29C83⋊#95—24no—
30C83⋊#95—22no—
31C22×C8×C83—22no—
32C2×C4⋊C4×C83—22no—
33C2×C4⋊C4×C83D412yes—
34C2×C42×C83C2311yescharacteristic
35C4⋊C8×C83—22no—
36C4⋊C8×C83Q814yes—
37C22×Dic83—22no—
38C22×Dic83—22no—
39C22×Dic83—41no—
40C2×C83⋊C8—22no—
41C2×C83⋊C8—22no—
42C2×C83⋊C8—22no—
43C4⋊Dic83—22no—
44C4⋊Dic83—22no—
45C4⋊Dic83—22no—
46C4⋊Dic83—22no—
47C4⋊Dic83—42no—
48C4⋊Dic83—42no—
49C4⋊Dic83—42no—
50C4⋊Dic83—82no—
51C4×Dic83—42no—
52C4×Dic83—42no—
53C22×C4×C83—22no—
54C22×C4×C83C2×D412yes—
55C22×C4×C83C2×D411yescharacteristic
56C2×C8×C83—24no—
57C2×C8×C83—42no—
58C2×C8×C83—42no—
59C4⋊C4×C83—42no—
60C4⋊C4×C83—42no—
61C4⋊C4×C83—42no—
62C42×C83C2×Q811yescharacteristic
63C42×C83C2×Q812yes—
64C42×C83#4111yescharacteristic
65C23×C83#12011yescharacteristic
66C2×C4×C83—21no—
67C2×C4×C83—21no—
68C2×C4×C83—44no—
69C2×C4×C83—42no—
70C2×C4×C83C22⋊Q812yes—
71C2×C4×C83C22⋊Q811yescharacteristic
72C2×C4×C83C4⋊Q812yes—
73C2×C4×C83C4⋊Q811yescharacteristic
74C2×C4×C83#13512yes—
75C2×C4×C83#13512yes—
76C2×C4×C83AGL(1,ℤ/8)12yes—
77C2×C4×C83#13712yes—
78C2×Dic83—42no—
79C2×Dic83—42no—
80C2×Dic83—42no—
81C2×Dic83—42no—
82C2×Dic83—42no—
83C2×Dic83—42no—
84C2×Dic83—82no—
85C2×Dic83—81no—
86C8×C83—44no—
87C83⋊C8—24no—
88C22×C83#39511yescharacteristic
89C22×C83#44912yes—
90C22×C83#45212yes—
91C22×C83#45311yescharacteristic
92C22×C83#45611yescharacteristic
93C4×C83—21no—
94C4×C83—21no—
95C4×C83—82no—
96C4×C83#47812yes—
97C4×C83#47912yes—
98C4×C83#49912yes—
99C4×C83#50112yes—
100Dic83—82no—
101Dic83—82no—
102Dic83—161no—
103#10577—831nomaximal, Sylow
104C2×C83#162411yescharacteristic
105C2×C83#163011yescharacteristic
106C2×C83#165212yes—
107C2×C83#205912yes—
108C2×C83#206011yescharacteristic
109#2571—831no—
110#1947—832no—
111#1844—831no—
112#1296D8311yescharacteristic
113#1279—832no—
114C83#1057711yescharacteristic, complemented, Sylow
115C2×#107—1662no—
116C2×#106—1662no—
117C2×C4⋊C8C2×D8312yes—
118C2×C4×C8—831no—
119#400—1662no—
120#389—1662no—
121#384—831no—
122#384C2×D8311yescharacteristic
123#382—1662no—
124C4×C4⋊C4—832no—
125#340—1662no—
126C22×C8—22no—
127C22×C8—1661no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—832no—
130C2×C4⋊C4—832no—
131C2×C4⋊C4—1662no—
132C2×C4⋊C4—1661no—
133C2×C4⋊C4—1662no—
134C2×C4⋊C4D33212yes—
135C2×C42—1662no—
136C2×C42C22×D8311yescharacteristic
137#107—3324no—
138#106—3324no—
139C4⋊C8—22no—
140C4⋊C8Dic16614yes—
141C4×C8—832no—
142C4×C8—1661no—
143#95—1662no—
144#95—1664no—
145#95—1662no—
146C22×C4—22no—
147C22×C4—3321no—
148C22×C4—1662no—
149C22×C4—1662no—
150C22×C4D4×D8312yes—
151C22×C4C2×D33211yescharacteristic
152C2×C8—24no—
153C2×C8—42no—
154C2×C8—42no—
155C2×C8—1662no—
156C2×C8—1662no—
157C2×C8—1662no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—3322no—
162C4⋊C4—3322no—
163C4⋊C4—3322no—
164C4⋊C4—6642no—
165C4⋊C4—1662no—
166C4⋊C4—1662no—
167C4⋊C4—1662no—
168C4⋊C4—1662no—
169C42—3322no—
170C42—3322no—
171C42Q8×D8311yescharacteristic
172C42C2×Dic16612yes—
173C42#1305058911yescharacteristic
174C23#1458176211yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—44no—
178C2×C4—42no—
179C2×C4—3322no—
180C2×C4—3322no—
181C2×C4—3322no—
182C2×C4—3322no—
183C2×C4—3322no—
184C2×C4—3322no—
185C2×C4—6642no—
186C2×C4—6641no—
187C2×C4#1458176912yes—
188C2×C4#1458177211yescharacteristic
189C2×C4#1458179112yes—
190C2×C4#1458179211yescharacteristic
191C2×C4#1458181112yes—
192C2×C4#1458181512yes—
193C2×C4#1458181912yes—
194C2×C4#1458182112yes—
195C8—44no—
196C8—1664no—
197C22#1912762211yescharacteristic
198C22#1912784912yes—
199C22#1912786412yes—
200C22#1912787111yescharacteristic
201C22#1912788611yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—13281no—
206C4—6642no—
207C4—6642no—
208C4#1912799912yes—
209C4#1912801012yes—
210C4#1912810212yes—
211C4#1912810812yes—
212C2#2490654711yescharacteristic
213C2#2490658511yescharacteristic
214C2#2490673412yes—
215C2#2490880412yes—
216C2#2490880911yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1296C2
socle, prime radicalC23×C83#120
hypercenter#1296D83
hypocenterC83#10577
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
114. C83#10577semidirect

Maximal subgroups

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

subgroupindex
#249127052
#249082222
#249076192
#249053022
C83×#12962
#1057783