Finite Group Databasebeta

← #35309173

Subgroups — #35309173

Order 21248.

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

normal subgroups only

This group has 330 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#24908295C211yesmaximal, characteristic
2#24906113C212yesmaximal
3#24905360C212yesmaximal, complemented
4#24905292C211yesmaximal, characteristic, complemented
5C83×#1843C211yesmaximal, characteristic, complemented
6#19128251C2211yescharacteristic
7#19127754C2212yes—
8#19127725C2211yescharacteristic
9C2×#14581720—21no—
10C2×#14581720—21no—
11#19127448—22no—
12#19127444—22no—
13C2×C4⋊C8×C83—21no—
14C2×C4⋊C8×C83—21no—
15C2×C4⋊C8×C83C2212yes—
16#376×C83C2211yescharacteristic
17C2×#13050590—21no—
18C2×#13050574—21no—
19#14581792D411yescharacteristic
20#14581789D411yescharacteristic
21#14581780—21no—
22#14581766—22no—
23C4×D332—22no—
24C4⋊(C83⋊C8)—22no—
25C4⋊(C83⋊C8)—22no—
26#14581720—42no—
27#14581720—42no—
28C22⋊(C83⋊C8)—22no—
29C4×C83⋊C8—22no—
30C22×C8×C83—22no—
31C2×C42×C83D411yescharacteristic
32C2×C42×C83D411yescharacteristic
33C2×C42×C83C2311yescharacteristic
34C4⋊C8×C83—22no—
35C4⋊C8×C83—22no—
36C4⋊C8×C83—42no—
37C4⋊C8×C83—42no—
38#95×C83—22no—
39#13050590—41no—
40#13050590—41no—
41#13050590—41no—
42#13050590—41no—
43C2×Dic166—21no—
44C2×D332—21no—
45C2×D332—22no—
46C2×C22⋊D83—41no—
47C2×C4×D83—41no—
48#13050574—41no—
49#13050574—41no—
50C2×C83⋊C8—42no—
51C2×C83⋊C8—41no—
52C4⋊Dic83—22no—
53(C2×D83)⋊C4—42no—
54C22×C4×C83—21no—
55C22×C4×C83—21no—
56C22×C4×C83C2×D411yescharacteristic
57C22×C4×C83#4112yes—
58C2×C8×C83—42no—
59C2×C8×C83—42no—
60C2×C8×C83—42no—
61C42×C83—21no—
62C42×C83—21no—
63C42×C83D812yes—
64C42×C83SD1612yes—
65C42×C83C2×D411yescharacteristic
66C42×C83#4111yescharacteristic
67C42×C83#4112yes—
68C23×C83#12311yescharacteristic
69C22×D83—41no—
70C2×C4×C83—22no—
71C2×C4×C83—22no—
72C2×C4×C83—42no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83#12111yescharacteristic
76C2×C4×C83#12312yes—
77C2×C4×C83#12411yescharacteristic
78C2×C4×C83#12612yes—
79C2×C4×C83C2×D811yescharacteristic
80C2×C4×C83C2×SD1611yescharacteristic
81C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C83#13711yescharacteristic
83C22⋊D83—81no—
84C22⋊D83—81no—
85C2×Dic83—41no—
86D332—41no—
87D332—41no—
88D332—82no—
89C4×D83—81no—
90C4×D83—81no—
91Dic166—41no—
92Dic166—41no—
93C8×C83—82no—
94C83⋊C8—82no—
95C83⋊C8—81no—
96C22×C83—22no—
97C22×C83#39711yescharacteristic
98C22×C83#48011yescharacteristic
99C22×C83#48111yescharacteristic
100C2×D83—81no—
101C2×D83—82no—
102C4×C83—22no—
103C4×C83—22no—
104C4×C83—42no—
105C4×C83—42no—
106C4×C83#45911yescharacteristic
107C4×C83#46111yescharacteristic
108C4×C83#48611yescharacteristic
109C4×C83#48911yescharacteristic
110Dic83—81no—
111#10627—831nomaximal, Sylow
112C2×C83—21no—
113C2×C83—21no—
114C2×C83#207111yescharacteristic
115C2×C83#208012yes—
116D83—161no—
117#1963—831no—
118#1843D8311yescharacteristic, complemented
119#1540—832no—
120#1301—832no—
121#1274—831no—
122C83#1062711yescharacteristic, complemented, Sylow
123#532—831no—
124#431—832no—
125#423—831no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8C2×D8312yes—
129C2×#104—1661no—
130C2×#104—1661no—
131#376C2×D8311yescharacteristic
132#332—1662no—
133#331—1662no—
134C2×#41—1661no—
135C2×M16—1661no—
136C22×C8—22no—
137C4⋊Q8—831no—
138#127—831no—
139#124—1661no—
140#121—1662no—
141C4×D4—1662no—
142C2×C42C22⋊D8311yescharacteristic
143C2×C42C22⋊D8311yescharacteristic
144C2×C42C22×D8311yescharacteristic
145C4⋊C8—22no—
146C4⋊C8—22no—
147C4⋊C8—42no—
148C4⋊C8—42no—
149C4⋊C8—1662no—
150C4⋊C8—1662no—
151#104—3322no—
152#104—3322no—
153C22⋊C8—1662no—
154C4×C8—1662no—
155#95—22no—
156#41—3321no—
157#41—3321no—
158#41—3321no—
159#41—3321no—
160C2×Q8—1661no—
161C2×D4—3321no—
162C2×D4—1661no—
163C2×D4—1662no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—3321no—
167C22×C4C2×C22⋊D8311yescharacteristic
168C22×C4#1305059012yes—
169M16—3321no—
170M16—3321no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—3322no—
175C2×C8—3321no—
176C4⋊C4—1662no—
177C22⋊C4—3322no—
178C42—21no—
179C42—21no—
180C42#1305057512yes—
181C42#1305057712yes—
182C42D4×D8311yescharacteristic
183C42#1305058911yescharacteristic
184C42#1305059112yes—
185C23—3321no—
186C23#1458177511yescharacteristic
187Q8—3321no—
188Q8—3321no—
189D4—3321no—
190D4—3321no—
191D4—6642no—
192D4—6641no—
193D4—6641no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—3321no—
200C2×C4—6641no—
201C2×C4—6641no—
202C2×C4#1458176311yescharacteristic
203C2×C4#1458177712yes—
204C2×C4#1458178111yescharacteristic
205C2×C4#1458178712yes—
206C2×C4C2×#1305057511yescharacteristic
207C2×C4C2×#1305057711yescharacteristic
208C2×C4#1458181811yescharacteristic
209C2×C4#1458182311yescharacteristic
210C8—82no—
211C8—6642no—
212C8—6641no—
213C22—22no—
214C22—6641no—
215C22—6642no—
216C22#1912762711yescharacteristic
217C22#1912801411yescharacteristic
218C22#1912801911yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—6641no—
224C4#1912789311yescharacteristic
225C4#1912790311yescharacteristic
226C4#1912804911yescharacteristic
227C4#1912806311yescharacteristic
228C2—21no—
229C2—21no—
230C2—13281no—
231C2#2490886711yescharacteristic
232C2#2490891412yes—
subgroupG/H
centerC2×C4#14581781
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1843C2
socleC22×C83#397
prime radical#19128251C22
hypercenter#1843D83
hypocenterC83#10627
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
3. #24905360C2semidirect
4. #24905292C2semidirect
5. C83×#1843C2semidirect
118. #1843D83semidirect
122. C83#10627semidirect

Maximal subgroups

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

subgroupindex
#249082952
#249061132
#249053602
#249052922
C83×#18432
#1062783