Finite Group Databasebeta

← #35307544

Subgroups — #35307544

Order 21248.

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

normal subgroups only

This group has 364 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#24908444C211yesmaximal, characteristic
2#24905961C212yesmaximal
3#24905366C212yesmaximal
4#24905292C211yesmaximal, characteristic
5C83×#2402C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7#19127754C2212yes—
8#19127725C2211yescharacteristic
9#19127461—22no—
10#19127437—22no—
11#19127437—22no—
12#400×C83—22no—
13#398×C83—22no—
14C4×C4⋊C4×C83—22no—
15C4×C4⋊C4×C83C2212yes—
16#376×C83C2211yescharacteristic
17C2×#13050574—21no—
18#14581792Q812yes—
19#14581784—21no—
20#14581771—22no—
21C4×Dic166—22no—
22#14581751—21no—
23C4⋊(C83⋊C8)—22no—
24C4⋊(C83⋊C8)—22no—
25C22⋊(C83⋊C8)—22no—
26C4×C83⋊C8—22no—
27C2×C4⋊C4×C83—22no—
28C2×C4⋊C4×C83—22no—
29C2×C4⋊C4×C83—22no—
30C2×C42×C83—22no—
31C2×C42×C83D412yes—
32C2×C42×C83C2311yescharacteristic
33#95×C83—22no—
34#95×C83—22no—
35#95×C83—22no—
36#95×C83D412yes—
37#95×C83D412yes—
38C2×Dic166—22no—
39#13050574—42no—
40C2×C83⋊C8—41no—
41C2×C83⋊C8—42no—
42C4⋊Dic83—22no—
43C4⋊Dic83—22no—
44Dic83⋊C4—42no—
45C22⋊Dic83—41no—
46C4×Dic83—41no—
47C22×C4×C83—22no—
48C22×C4×C83—22no—
49C22×C4×C83—22no—
50C22×C4×C83C2×D412yes—
51C22×C4×C83C2×D411yescharacteristic
52C4⋊C4×C83—44no—
53C4⋊C4×C83—44no—
54C4⋊C4×C83—44no—
55C42×C83—22no—
56C42×C83—22no—
57C42×C83—42no—
58C42×C83—42no—
59C42×C83C2×Q811yescharacteristic
60C42×C83#4111yescharacteristic
61C42×C83#4112yes—
62C23×C83#12011yescharacteristic
63C2×C4×C83—24no—
64C2×C4×C83—42no—
65C2×C4×C83—42no—
66C2×C4×C83—42no—
67C2×C4×C83—42no—
68C2×C4×C83—42no—
69C2×C4×C83—42no—
70C2×C4×C83—42no—
71C2×C4×C83—42no—
72C2×C4×C83—42no—
73C2×C4×C83C22⋊Q812yes—
74C2×C4×C83C22⋊Q811yescharacteristic
75C2×C4×C83#12412yes—
76C2×C4×C83#12411yescharacteristic
77C2×C4×C83#13512yes—
78C2×C4×C83#13712yes—
79C2×Dic83—42no—
80Dic166—82no—
81C83⋊C8—82no—
82C83⋊C8—81no—
83C22×C83—22no—
84C22×C83#39311yescharacteristic
85C22×C83#45212yes—
86C4×C83—22no—
87C4×C83—22no—
88C4×C83—44no—
89C4×C83—82no—
90C4×C83—82no—
91C4×C83#47912yes—
92C4×C83#48811yescharacteristic
93C4×C83#49111yescharacteristic
94Dic83—82no—
95#10373—831nomaximal, Sylow
96C2×C83—22no—
97C2×C83#202611yescharacteristic
98C2×C83#203112yes—
99#2402D8311yescharacteristic
100#1995—831no—
101#1503—832no—
102#1303—832no—
103#1274—831no—
104C83#1037311yescharacteristic, complemented, Sylow
105#533—831no—
106#431—832no—
107#423—831no—
108#400—22no—
109#398—22no—
110C4×C4⋊C4—22no—
111C4×C4⋊C4C2×D8312yes—
112#376C2×D8311yescharacteristic
113#339—1662no—
114#328—1662no—
115#328—1662no—
116C2×M16—1661no—
117C4⋊Q8—832no—
118#125—1661no—
119C22⋊Q8—1662no—
120C4×Q8—1662no—
121#117—1661no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42C22⋊D8312yes—
127C2×C42C22×D8311yescharacteristic
128C4⋊C8—1662no—
129C4⋊C8—1662no—
130C22⋊C8—1662no—
131C4×C8—1662no—
132#95—22no—
133#95—22no—
134#95—22no—
135#95C22⋊D8312yes—
136#95C22⋊D8312yes—
137C2×Q8—1662no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4C2×C22⋊D8312yes—
142C22×C4C2×C22⋊D8311yescharacteristic
143M16—3322no—
144C2×C8—3322no—
145C2×C8—3321no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—44no—
149C4⋊C4—3322no—
150C4⋊C4—1662no—
151C4⋊C4—1662no—
152C22⋊C4—3321no—
153C42—22no—
154C42—22no—
155C42—42no—
156C42—42no—
157C42—3321no—
158C42Q8×D8311yescharacteristic
159C42#1305059111yescharacteristic
160C42#1305059112yes—
161C23#1458176111yescharacteristic
162Q8—6642no—
163C2×C4—24no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—3322no—
174C2×C4#1458176812yes—
175C2×C4#1458176811yescharacteristic
176C2×C4#1458178112yes—
177C2×C4#1458178111yescharacteristic
178C2×C4#1458181212yes—
179C2×C4#1458182212yes—
180C8—6642no—
181C8—6641no—
182C22—22no—
183C22#1912761211yescharacteristic
184C22#1912786312yes—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—82no—
189C4—82no—
190C4—6642no—
191C4#1912800512yes—
192C4#1912805811yescharacteristic
193C4#1912807111yescharacteristic
194C2—22no—
195C2#2490861111yescharacteristic
196C2#2490863212yes—
subgroupG/H
centerC2×C4#14581781
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2402C2
socleC22×C83#393
prime radicalC23×C83#120
hypercenter#2402D83
hypocenterC83#10373
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
104. C83#10373semidirect

Maximal subgroups

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

subgroupindex
#249084442
#249059612
#249053662
#249052922
C83×#24022
#1037383