Finite Group Databasebeta

← #35309304

Subgroups — #35309304

Order 21248.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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#24906191C211yesmaximal, characteristic
2#24906161C211yesmaximal, characteristic
3#24905937C211yesmaximal, characteristic
4#24905374C211yesmaximal, characteristic
5#24905333C211yesmaximal, characteristic
6#24905325C211yesmaximal, characteristic
7C83×#1570C211yesmaximal, characteristic
8#19128258C2211yescharacteristic
9#19127758C2211yescharacteristic
10#19127758C2211yescharacteristic
11#19127758C2211yescharacteristic
12#19127449—21no—
13#19127448—21no—
14#19127448—21no—
15#19127446—21no—
16#19127433—22no—
17#431×C83C2211yescharacteristic
18#423×C83C2211yescharacteristic
19C2×C4⋊C8×C83C2211yescharacteristic
20#334×C83—22no—
21#14581792D411yescharacteristic
22#14581792D411yescharacteristic
23#14581784—21no—
24#14581771—21no—
25#14581771—21no—
26C4×Dic166—21no—
27C4×Dic166—21no—
28#14581751—21no—
29C4⋊(C83⋊C8)—21no—
30C4⋊(C83⋊C8)—21no—
31C4⋊(C83⋊C8)—21no—
32C22⋊(C83⋊C8)—21no—
33C22⋊(C83⋊C8)—21no—
34C22⋊(C83⋊C8)—21no—
35#14581703—21no—
36#14581703—21no—
37#14581703—21no—
38C2×M16×C83—21no—
39C22×C8×C83—21no—
40C2×C42×C83C2311yescharacteristic
41C4⋊C8×C83—21no—
42C4⋊C8×C83—21no—
43C4⋊C8×C83—21no—
44C4⋊C8×C83—21no—
45C4⋊C8×C83—21no—
46C22⋊C8×C83—21no—
47C4×C8×C83D412yes—
48C2×Dic166—21no—
49C2×Dic166—21no—
50C2×C83⋊C8—41no—
51C2×C83⋊C8—41no—
52C2×C83⋊C8—41no—
53C4⋊Dic83—21no—
54C4⋊Dic83—21no—
55C4⋊Dic83—21no—
56C4⋊Dic83—21no—
57Dic83⋊C4—41no—
58Dic83⋊C4—41no—
59C22⋊Dic83—41no—
60C4×Dic83—41no—
61C22×C4×C83#4111yescharacteristic
62C22×C4×C83#4111yescharacteristic
63C22×C4×C83#4111yescharacteristic
64M16×C83—81no—
65C2×C8×C83—22no—
66C2×C8×C83—41no—
67C2×C8×C83—41no—
68C2×C8×C83—81no—
69C42×C83C2×D411yescharacteristic
70C42×C83C2×D411yescharacteristic
71C42×C83#4111yescharacteristic
72C42×C83#4111yescharacteristic
73C23×C83#12611yescharacteristic
74C2×C4×C83—21no—
75C2×C4×C83—21no—
76C2×C4×C83—41no—
77C2×C4×C83—41no—
78C2×C4×C83#12111yescharacteristic
79C2×C4×C83#12311yescharacteristic
80C2×C4×C83#12311yescharacteristic
81C2×C4×C83#12311yescharacteristic
82C2×C4×C83#12411yescharacteristic
83C2×C4×C83#12611yescharacteristic
84C2×Dic83—41no—
85C2×Dic83—41no—
86Dic166—41no—
87Dic166—41no—
88Dic166—81no—
89C8×C83—42no—
90C8×C83—81no—
91C8×C83—81no—
92C83⋊C8—81no—
93C83⋊C8—81no—
94C83⋊C8—81no—
95C22×C83—21no—
96C22×C83—21no—
97C22×C83—21no—
98C22×C83#39711yescharacteristic
99C4×C83—21no—
100C4×C83—21no—
101C4×C83—21no—
102C4×C83—21no—
103C4×C83—21no—
104C4×C83#47111yescharacteristic
105C4×C83#47111yescharacteristic
106Dic83—81no—
107Dic83—81no—
108#10648—831nomaximal, Sylow
109C2×C83—41no—
110C2×C83#207911yescharacteristic
111C2×C83#208011yescharacteristic
112C2×C83#208211yescharacteristic
113#1570D8311yescharacteristic
114#1559—831no—
115#1552—831no—
116#1497—831no—
117#1307—831no—
118#1290—831no—
119#1287—831no—
120C83#1064811yescharacteristic, complemented, Sylow
121#533—831no—
122#432—831no—
123#432—831no—
124#432—831no—
125#431C2×D8311yescharacteristic
126#423C2×D8311yescharacteristic
127C2×C4⋊C8C2×D8311yescharacteristic
128#334—22no—
129#333—1661no—
130#332—1661no—
131#332—1661no—
132#332—1661no—
133Q8⋊C8—1662no—
134C2×M16—21no—
135C22×C8—21no—
136C4⋊Q8—831no—
137C4⋊Q8—831no—
138#125—1661no—
139C22⋊Q8—1661no—
140C22⋊Q8—1661no—
141C4×Q8—1661no—
142C4×Q8—1661no—
143#117—1661no—
144C2×C42C22×D8311yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—1661no—
151C4⋊C8—1661no—
152C4⋊C8—1661no—
153C22⋊C8—21no—
154C22⋊C8—1661no—
155C22⋊C8—1661no—
156C22⋊C8—1661no—
157#97—1661no—
158#97—1661no—
159#97—1661no—
160C4×C8C22⋊D8312yes—
161C2×Q8—1661no—
162C2×Q8—1661no—
163C22×C4#1305058911yescharacteristic
164C22×C4#1305059011yescharacteristic
165C22×C4#1305059111yescharacteristic
166M16—81no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—81no—
171C2×C8—3321no—
172C2×C8—3321no—
173C2×C8—3321no—
174C4⋊C4—3321no—
175C4⋊C4—3321no—
176C4⋊C4—1661no—
177C4⋊C4—1661no—
178C4⋊C4—1661no—
179C4⋊C4—1661no—
180C22⋊C4—3321no—
181C42—3321no—
182C42D4×D8311yescharacteristic
183C42C2×C22⋊D8311yescharacteristic
184C42#1305059011yescharacteristic
185C42#1305059111yescharacteristic
186C23#1458178711yescharacteristic
187Q8—3321no—
188Q8—3321no—
189Q8—6641no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—3321no—
195C2×C4—3321no—
196C2×C4#1458176311yescharacteristic
197C2×C4#1458177511yescharacteristic
198C2×C4#1458177711yescharacteristic
199C2×C4#1458177711yescharacteristic
200C2×C4#1458178111yescharacteristic
201C2×C4#1458178711yescharacteristic
202C8—42no—
203C8—81no—
204C8—81no—
205C8—6641no—
206C8—6641no—
207C8—6641no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1912762711yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—6641no—
218C4—6641no—
219C4#1912796111yescharacteristic
220C4#1912796111yescharacteristic
221C2—41no—
222C2#2490890911yescharacteristic
223C2#2490891411yescharacteristic
224C2#2490892811yescharacteristic
subgroupG/H
centerC22#19127627
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1570C2
socleC22×C83#397
prime radicalC23×C83#126
hypercenter#1570D83
hypocenterC83#10648
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
120. C83#10648semidirect

Maximal subgroups

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

subgroupindex
#249061912
#249061612
#249059372
#249053742
#249053332
#249053252
C83×#15702
#1064883