Finite Group Databasebeta

← #35307519

Subgroups — #35307519

Order 21248.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#24908291C211yesmaximal, characteristic
2#24906022C212yesmaximal
3#24905321C212yesmaximal, complemented
4#24905296C211yesmaximal, characteristic, complemented
5C83×#2864C211yesmaximal, characteristic, complemented
6#19128251C2211yescharacteristic
7#19127754C2212yes—
8#19127725C2211yescharacteristic
9C2×#14581720—22no—
10#19127434—24no—
11#389×C83—22no—
12#387×C83—24no—
13#382×C83C2212yes—
14C43×C83C2211yescharacteristic
15C2×#13050590—21no—
16C2×#13050574—21no—
17#14581792Q811yescharacteristic
18#14581789Q811yescharacteristic
19#14581780—21no—
20#14581766—22no—
21C4×D332—22no—
22C4⋊(C83⋊C8)—22no—
23C4⋊(C83⋊C8)—22no—
24#14581720—44no—
25C22⋊(C83⋊C8)—22no—
26C4×C83⋊C8—22no—
27C2×C4⋊C4×C83—24no—
28C2×C4⋊C4×C83—22no—
29C2×C42×C83—22no—
30C2×C42×C83D412yes—
31C2×C42×C83C2311yescharacteristic
32#95×C83—24no—
33#95×C83—22no—
34#95×C83D414yes—
35#13050590—42no—
36#13050590—42no—
37C2×Dic166—21no—
38C2×D332—21no—
39C2×D332—22no—
40C2×C22⋊D83—41no—
41C2×C4×D83—41no—
42#13050574—42no—
43C2×C83⋊C8—41no—
44C2×C83⋊C8—42no—
45C4⋊Dic83—22no—
46(C2×D83)⋊C4—42no—
47C22×C4×C83—22no—
48C22×C4×C83—24no—
49C22×C4×C83C2×D412yes—
50C22×C4×C83C2×D411yescharacteristic
51C4⋊C4×C83—48no—
52C4⋊C4×C83—42no—
53C4⋊C4×C83—42no—
54C42×C83—22no—
55C42×C83—22no—
56C42×C83—44no—
57C42×C83C2×Q811yescharacteristic
58C42×C83#4111yescharacteristic
59C42×C83#4112yes—
60C23×C83#12011yescharacteristic
61C22×D83—41no—
62C2×C4×C83—24no—
63C2×C4×C83—42no—
64C2×C4×C83—42no—
65C2×C4×C83—42no—
66C2×C4×C83—48no—
67C2×C4×C83—44no—
68C2×C4×C83C22⋊Q812yes—
69C2×C4×C83C22⋊Q811yescharacteristic
70C2×C4×C83#12412yes—
71C2×C4×C83#12411yescharacteristic
72C2×C4×C83#13512yes—
73C2×C4×C83AGL(1,ℤ/8)12yes—
74C22⋊D83—82no—
75C2×Dic83—41no—
76D332—42no—
77D332—82no—
78C4×D83—81no—
79C4×D83—81no—
80Dic166—42no—
81C83⋊C8—82no—
82C83⋊C8—81no—
83C22×C83—22no—
84C22×C83#39311yescharacteristic
85C22×C83#44912yes—
86C2×D83—81no—
87C2×D83—82no—
88C4×C83—22no—
89C4×C83—22no—
90C4×C83—44no—
91C4×C83—84no—
92C4×C83#47812yes—
93C4×C83#48811yescharacteristic
94C4×C83#49011yescharacteristic
95Dic83—81no—
96#10368—831nomaximal, Sylow
97C2×C83—22no—
98C2×C83#202511yescharacteristic
99C2×C83#203112yes—
100D83—161no—
101#2864D8311yescharacteristic, complemented
102#1962—831no—
103#1517—832no—
104#1286—832no—
105#1276—831no—
106C83#1036811yescharacteristic, complemented, Sylow
107#532—831no—
108#431—832no—
109#423—831no—
110C2×#104—1662no—
111#389—22no—
112#387—24no—
113#382C2×D8312yes—
114C43C2×D8311yescharacteristic
115#327—1664no—
116C2×#41—1661no—
117C2×M16—1661no—
118C4⋊Q8—831no—
119#127—831no—
120#124—1661no—
121#121—1662no—
122C4×D4—1662no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42C22⋊D8312yes—
127C2×C42C22×D8311yescharacteristic
128C4⋊C8—1662no—
129C4⋊C8—1662no—
130#104—3324no—
131C22⋊C8—1662no—
132C4×C8—1662no—
133#95—24no—
134#95—22no—
135#95C22⋊D8314yes—
136#41—3322no—
137#41—3322no—
138C2×Q8—1661no—
139C2×D4—3321no—
140C2×D4—1661no—
141C2×D4—1662no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—3321no—
145C22×C4C2×C22⋊D8312yes—
146C22×C4C2×C22⋊D8311yescharacteristic
147M16—3322no—
148C2×C8—3322no—
149C2×C8—3321no—
150C4⋊C4—48no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—1662no—
154C22⋊C4—3322no—
155C42—22no—
156C42—22no—
157C42—44no—
158C42Q8×D8311yescharacteristic
159C42#1305059111yescharacteristic
160C42#1305059112yes—
161C23—3321no—
162C23#1458176111yescharacteristic
163Q8—3322no—
164D4—3322no—
165D4—6642no—
166D4—6642no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—3321no—
174C2×C4—6641no—
175C2×C4—6641no—
176C2×C4#1458176812yes—
177C2×C4#1458176811yescharacteristic
178C2×C4#1458178112yes—
179C2×C4#1458178111yescharacteristic
180C2×C4#1458181212yes—
181C2×C4#1458181712yes—
182C8—6642no—
183C8—6641no—
184C22—22no—
185C22—6641no—
186C22—6642no—
187C22#1912761211yescharacteristic
188C22#1912784612yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—6641no—
194C4#1912799812yes—
195C4#1912805811yescharacteristic
196C4#1912806711yescharacteristic
197C2—22no—
198C2—13281no—
199C2#2490860611yescharacteristic
200C2#2490863212yes—
subgroupG/H
centerC22#19127612
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2864C2
socleC22×C83#393
prime radical#19128251C22
hypercenter#2864D83
hypocenterC83#10368
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2864

Complements

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

NH ≅ G/Ntype
3. #24905321C2semidirect
4. #24905296C2semidirect
5. C83×#2864C2semidirect
101. #2864D83semidirect
106. C83#10368semidirect

Maximal subgroups

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

subgroupindex
#249082912
#249060222
#249053212
#249052962
C83×#28642
#1036883