Finite Group Databasebeta

← #35308860

Subgroups — #35308860

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#24908221C212yesmaximal
2#24907619C211yesmaximal, characteristic
3#24905346C211yesmaximal, characteristic
4#24905304C212yesmaximal
5C83×#2571C211yesmaximal, characteristic
6C2×#14581725—22no—
7C2×#14581723—22no—
8C2×C4⋊(C83⋊C8)C2212yes—
9C2×C4×C83⋊C8C2211yescharacteristic
10#19127571C2211yescharacteristic
11#19127463—22no—
12#400×C83—22no—
13#389×C83—22no—
14#384×C83C2211yescharacteristic
15#382×C83—22no—
16C4×C4⋊C4×C83C2212yes—
17C22×C83⋊C8—21no—
18C22×C83⋊C8—22no—
19C2×C4⋊Dic83—22no—
20C2×C4⋊Dic83—21no—
21#14581725—44no—
22#14581723—44no—
23C4⋊(C83⋊C8)—22no—
24C4⋊(C83⋊C8)Q814yes—
25C4×C83⋊C8—21no—
26C4×C83⋊C8Q812yes—
27C2×C4⋊C4×C83—22no—
28C2×C4⋊C4×C83—22no—
29C2×C4⋊C4×C83D412yes—
30C2×C4⋊C4×C83D412yes—
31C2×C4⋊C4×C83D412yes—
32C2×C42×C83—22no—
33C2×C42×C83C2311yescharacteristic
34#95×C83—22no—
35#95×C83—24no—
36#95×C83—22no—
37C22×Dic83—41no—
38C2×C83⋊C8—22no—
39C2×C83⋊C8—22no—
40C2×C83⋊C8—22no—
41C2×C83⋊C8—24no—
42C2×C83⋊C8—42no—
43C2×C83⋊C8—42no—
44C4⋊Dic83—42no—
45C4⋊Dic83—42no—
46C4⋊Dic83—42no—
47C22×C4×C83—22no—
48C22×C4×C83—22no—
49C22×C4×C83—22no—
50C22×C4×C83C2×D411yescharacteristic
51C22×C4×C83C2×D412yes—
52C4⋊C4×C83—22no—
53C4⋊C4×C83—22no—
54C4⋊C4×C83—22no—
55C4⋊C4×C83—22no—
56C4⋊C4×C83—42no—
57C4⋊C4×C83—42no—
58C4⋊C4×C83—42no—
59C4⋊C4×C83—82no—
60C42×C83—42no—
61C42×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—42no—
69C2×C4×C83—42no—
70C2×C4×C83—42no—
71C2×C4×C83—42no—
72C2×C4×C83—44no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83—42no—
76C2×C4×C83C22⋊Q811yescharacteristic
77C2×C4×C83C22⋊Q812yes—
78C2×C4×C83C4⋊Q811yescharacteristic
79C2×C4×C83C4⋊Q812yes—
80C2×C4×C83#13512yes—
81C2×C4×C83#13512yes—
82C2×C4×C83AGL(1,ℤ/8)12yes—
83C2×C4×C83#13712yes—
84C2×Dic83—82no—
85C2×Dic83—81no—
86C83⋊C8—24no—
87C83⋊C8—44no—
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—82no—
97C4×C83—82no—
98C4×C83#47812yes—
99C4×C83#47912yes—
100C4×C83#49912yes—
101C4×C83#50112yes—
102Dic83—161no—
103#10577—831nomaximal, Sylow
104C2×C83#162411yescharacteristic
105C2×C83#163011yescharacteristic
106C2×C83#165212yes—
107C2×C83#205912yes—
108C2×C83#206011yescharacteristic
109#2571D8311yescharacteristic
110#1947—832no—
111#1844—831no—
112#1296—831no—
113#1279—832no—
114C83#1057711yescharacteristic, complemented, Sylow
115C2×#107—1662no—
116C2×#106—1662no—
117C2×C4⋊C8—832no—
118C2×C4×C8—831no—
119#400—22no—
120#389—22no—
121#384—831no—
122#384C2×D8311yescharacteristic
123#382—22no—
124C4×C4⋊C4C2×D8312yes—
125#340—1662no—
126C22×C8—1662no—
127C22×C8—1661no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—1662no—
131C2×C4⋊C4—1661no—
132C2×C4⋊C4C22⋊D8312yes—
133C2×C4⋊C4C22⋊D8312yes—
134C2×C4⋊C4C22⋊D8312yes—
135C2×C42—22no—
136C2×C42C22×D8311yescharacteristic
137#107—3324no—
138#106—3324no—
139C4⋊C8—834no—
140C4⋊C8—1662no—
141C4×C8—832no—
142C4×C8—1661no—
143#95—22no—
144#95—24no—
145#95—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—3321no—
150C22×C4C2×C22⋊D8311yescharacteristic
151C22×C4C2×C22⋊D8312yes—
152C2×C8—3322no—
153C2×C8—3322no—
154C2×C8—1664no—
155C2×C8—1662no—
156C2×C8—1662no—
157C2×C8—1662no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—82no—
166C4⋊C4—3322no—
167C4⋊C4—3322no—
168C4⋊C4—3322no—
169C42—42no—
170C42—42no—
171C42Q8×D8311yescharacteristic
172C42Q8×D8312yes—
173C42#1305059111yescharacteristic
174C23#1458176111yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—6642no—
186C2×C4—6641no—
187C2×C4#1458176811yescharacteristic
188C2×C4#1458176812yes—
189C2×C4#1458179011yescharacteristic
190C2×C4#1458179012yes—
191C2×C4#1458181212yes—
192C2×C4#1458181212yes—
193C2×C4#1458181712yes—
194C2×C4#1458182212yes—
195C8—3324no—
196C8—1664no—
197C22#1912762011yescharacteristic
198C22#1912784612yes—
199C22#1912786312yes—
200C22#1912786911yescharacteristic
201C22#1912788411yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—13281no—
208C4#1912799812yes—
209C4#1912800512yes—
210C4#1912810012yes—
211C4#1912811112yes—
212C2#2490654611yescharacteristic
213C2#2490658411yescharacteristic
214C2#2490673312yes—
215C2#2490879812yes—
216C2#2490880511yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2571C2
socle, prime radicalC23×C83#120
hypercenter#2571D83
hypocenterC83#10577
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

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
#249082212
#249076192
#249053462
#249053042
C83×#25712
#1057783