Finite Group Databasebeta

← #35318642

Subgroups — #35318642

Order 21248.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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#24909712C211yesmaximal, characteristic, complemented
2#24909539C211yesmaximal, characteristic, complemented
3#24909300C211yesmaximal, characteristic, complemented
4#24905538C211yesmaximal, characteristic, complemented
5#24905500C211yesmaximal, characteristic, complemented
6#24905499C211yesmaximal, characteristic, complemented
7C83×#2213C211yesmaximal, characteristic, complemented
8#19128136—21no—
9C2×#14581733—21no—
10C2×#14581733—21no—
11#19128118—21no—
12#19128078C2211yescharacteristic
13#19127522C2211yescharacteristic
14#19127522C2211yescharacteristic
15#19127513—21no—
16#19127485—21no—
17C4×C83⋊C16C2211yescharacteristic
18#509×C83—21no—
19#493×C83C2211yescharacteristic
20#443×C83C2211yescharacteristic
21#364×C83C2211yescharacteristic
22#361×C83—21no—
23C2×D664—21no—
24C2×D664—21no—
25#14581789—21no—
26#14581735—41no—
27#14581733—42no—
28#14581733—41no—
29#14581733—41no—
30#14581733—41no—
31#14581732—21no—
32#14581732—21no—
33#14581732—41no—
34C2×C83⋊C16—41no—
35C2×C83⋊C16D411yescharacteristic
36C2×C83⋊C16D411yescharacteristic
37#135×C83D411yescharacteristic
38C2×D8×C83—21no—
39C2×D8×C83—21no—
40#131×C83—21no—
41#127×C83—21no—
42SD32×C83—41no—
43D16×C83—41no—
44M32×C83—21no—
45#108×C83D411yescharacteristic
46#104×C83—21no—
47C4×C8×C83C2311yescharacteristic
48C2×D332—41no—
49C2×D332—81no—
50D664—41no—
51D664—41no—
52D664—41no—
53D664—41no—
54C83⋊C16—21no—
55C83⋊C16—41no—
56C83⋊C16—41no—
57C83⋊C16D811yescharacteristic
58C83⋊C16D811yescharacteristic
59#41×C83—21no—
60C2×D4×C83—41no—
61C2×D4×C83—81no—
62Q16×C83D811yescharacteristic
63SD16×C83—21no—
64D8×C83—41no—
65D8×C83—41no—
66D8×C83—41no—
67D8×C83—41no—
68D8×C83D811yescharacteristic
69M16×C83—21no—
70M16×C83—41no—
71C2×C8×C83—41no—
72C2×C8×C83C2×D411yescharacteristic
73C2×C8×C83C2×D411yescharacteristic
74C42×C83#4111yescharacteristic
75C16×C83—41no—
76C23×C83—81no—
77C22×D83—81no—
78Q8×C83—21no—
79D4×C83—21no—
80D4×C83—41no—
81D4×C83—81no—
82D4×C83—81no—
83D4×C83—162no—
84C2×C4×C83—21no—
85C2×C4×C83—41no—
86C2×C4×C83#12111yescharacteristic
87D332—81no—
88D332—81no—
89D332—162no—
90C8×C83—41no—
91C8×C83C2×D811yescharacteristic
92C8×C83C2×D811yescharacteristic
93C8×C83#13511yescharacteristic
94C8×C83AGL(1,ℤ/8)11yescharacteristic
95C22×C83—41no—
96C22×C83—162no—
97C22×C83—161no—
98C22×C83#47211yescharacteristic
99C2×D83—162no—
100C2×D83—161no—
101C4×C83—22no—
102C4×C83—41no—
103C4×C83#45911yescharacteristic
104C4×C83#46611yescharacteristic
105#12436—831nomaximal, Sylow
106C2×C83—21no—
107C2×C83—81no—
108C2×C83—321no—
109C2×C83#166711yescharacteristic
110D83—321no—
111#2246—831no—
112#2213—831no—
113#2213D8311yescharacteristic, complemented
114#2170—831no—
115#1373—831no—
116#1357—831no—
117#1357—831no—
118C83#1243611yescharacteristic, complemented, Sylow
119#509—21no—
120#509—1661no—
121C2×D16—1661no—
122C2×D16—1661no—
123#504—1661no—
124#493—831no—
125#493C2×D8311yescharacteristic
126#443C2×D8311yescharacteristic
127#364—831no—
128#364—831no—
129#364C2×D8311yescharacteristic
130#361—21no—
131#361—1661no—
132#350—1661no—
133C4×C16—831no—
134#135C22⋊D8311yescharacteristic
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—1661no—
138C2×D8—1661no—
139#131—21no—
140#127—21no—
141#127—1661no—
142SD32—41no—
143SD32—3321no—
144D16—41no—
145D16—3321no—
146D16—3321no—
147D16—3321no—
148D16—3322no—
149M32—21no—
150M32—3321no—
151M32—1661no—
152M32—1661no—
153C2×C16—3321no—
154C2×C16—831no—
155C2×C16—831no—
156#108C22⋊D8311yescharacteristic
157#104—21no—
158C4×C8C22×D8311yescharacteristic
159#41—21no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—3321no—
163C2×D4—6641no—
164Q16#1305057511yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—3321no—
171D8—3321no—
172D8—3321no—
173D8—3321no—
174D8#1305057511yescharacteristic
175M16—21no—
176M16—41no—
177C2×C8—41no—
178C2×C8D4×D8311yescharacteristic
179C2×C8C2×C22⋊D8311yescharacteristic
180C42#1305058911yescharacteristic
181C16—41no—
182C16—3321no—
183C16—3321no—
184C16—831no—
185C16—831no—
186C16—1661no—
187C23—81no—
188C23—6641no—
189Q8—21no—
190D4—21no—
191D4—41no—
192D4—81no—
193D4—81no—
194D4—162no—
195D4—13282no—
196D4—6641no—
197D4—6641no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4#1458176411yescharacteristic
201C8—41no—
202C8D8×D8311yescharacteristic
203C8C2×#1305057511yescharacteristic
204C8#1458181211yescharacteristic
205C8#1458181611yescharacteristic
206C22—41no—
207C22—162no—
208C22—161no—
209C22—13282no—
210C22—13281no—
211C22#1912796911yescharacteristic
212C4—22no—
213C4—41no—
214C4#1912789411yescharacteristic
215C4#1912793511yescharacteristic
216C2—21no—
217C2—81no—
218C2—321no—
219C2—26561no—
220C2#2490681611yescharacteristic
subgroupG/H
centerC2#24906816
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#2213C2
socleC2×C83#1667
hypercenter#2213D83
hypocenterC83#12436
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #24909712C2semidirect
2. #24909539C2semidirect
3. #24909300C2semidirect
4. #24905538C2semidirect
5. #24905500C2semidirect
6. #24905499C2semidirect
7. C83×#2213C2semidirect
113. #2213D83semidirect
118. C83#12436semidirect

Maximal subgroups

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

subgroupindex
#249097122
#249095392
#249093002
#249055382
#249055002
#249054992
C83×#22132
#1243683