Finite Group Databasebeta

← #35318647

Subgroups — #35318647

Order 21248.

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

normal subgroups only

This group has 214 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#24909715C211yesmaximal, characteristic, complemented
2#24909544C211yesmaximal, characteristic
3#24909300C211yesmaximal, characteristic
4#24905538C211yesmaximal, characteristic, complemented
5#24905502C211yesmaximal, characteristic, complemented
6#24905501C211yesmaximal, characteristic, complemented
7C83×#2214C211yesmaximal, characteristic
8#19128141—21no—
9C2×#14581738—21no—
10C2×#14581738—21no—
11#19128118—21no—
12#19128081C2211yescharacteristic
13#19127522C2211yescharacteristic
14#19127522C2211yescharacteristic
15#19127516—21no—
16#19127485—21no—
17C4×C83⋊C16C2211yescharacteristic
18#510×C83—21no—
19#494×C83C2211yescharacteristic
20#443×C83C2211yescharacteristic
21#364×C83C2211yescharacteristic
22#362×C83—21no—
23C2×Dic332—21no—
24C2×Dic332—21no—
25#14581792—21no—
26#14581738—42no—
27#14581738—41no—
28#14581738—41no—
29#14581738—41no—
30#14581736—41no—
31#14581732—21no—
32#14581732—21no—
33#14581732—41no—
34C2×C83⋊C16—41no—
35C2×C83⋊C16D411yescharacteristic
36C2×C83⋊C16D411yescharacteristic
37#135×C83D411yescharacteristic
38C2×Q16×C83—21no—
39C2×Q16×C83—21no—
40#131×C83—21no—
41C4⋊Q8×C83—21no—
42Q32×C83—41no—
43SD32×C83—41no—
44M32×C83—21no—
45#108×C83D411yescharacteristic
46#104×C83—21no—
47C4×C8×C83C2311yescharacteristic
48C2×Dic166—41no—
49Dic332—41no—
50Dic332—41no—
51Dic332—41no—
52Dic332—41no—
53C4⋊Dic83—81no—
54C83⋊C16—21no—
55C83⋊C16—41no—
56C83⋊C16—41no—
57C83⋊C16D811yescharacteristic
58C83⋊C16D811yescharacteristic
59#41×C83—21no—
60C2×Q8×C83—41no—
61Q16×C83—41no—
62Q16×C83—41no—
63Q16×C83—41no—
64Q16×C83—41no—
65Q16×C83D811yescharacteristic
66SD16×C83—21no—
67D8×C83D811yescharacteristic
68M16×C83—21no—
69M16×C83—41no—
70C2×C8×C83—41no—
71C2×C8×C83C2×D411yescharacteristic
72C2×C8×C83C2×D411yescharacteristic
73C4⋊C4×C83—81no—
74C42×C83#4111yescharacteristic
75C16×C83—41no—
76Q8×C83—21no—
77Q8×C83—81no—
78Q8×C83—81no—
79D4×C83—21no—
80D4×C83—41no—
81C2×C4×C83—21no—
82C2×C4×C83—41no—
83C2×C4×C83—81no—
84C2×C4×C83#12111yescharacteristic
85C2×Dic83—81no—
86Dic166—81no—
87Dic166—81no—
88C8×C83—41no—
89C8×C83C2×D811yescharacteristic
90C8×C83C2×D811yescharacteristic
91C8×C83#13511yescharacteristic
92C8×C83AGL(1,ℤ/8)11yescharacteristic
93C22×C83—41no—
94C22×C83#47211yescharacteristic
95C4×C83—22no—
96C4×C83—41no—
97C4×C83—161no—
98C4×C83#45911yescharacteristic
99C4×C83#46611yescharacteristic
100Dic83—161no—
101#12437—831nomaximal, Sylow
102C2×C83—21no—
103C2×C83—81no—
104C2×C83#166711yescharacteristic
105#2247—831no—
106#2214—831no—
107#2214D8311yescharacteristic
108#2170—831no—
109#1373—831no—
110#1358—831no—
111#1358—831no—
112C83#1243711yescharacteristic, complemented, Sylow
113#510—21no—
114#510—1661no—
115C2×Q32—1661no—
116C2×Q32—1661no—
117#504—1661no—
118#494—831no—
119#494C2×D8311yescharacteristic
120#443C2×D8311yescharacteristic
121#364—831no—
122#364—831no—
123#364C2×D8311yescharacteristic
124#362—21no—
125#362—1661no—
126#350—1661no—
127C4×C16—831no—
128#135C22⋊D8311yescharacteristic
129C2×Q16—21no—
130C2×Q16—21no—
131C2×Q16—1661no—
132C2×Q16—1661no—
133#131—21no—
134C4⋊Q8—21no—
135C4⋊Q8—1661no—
136Q32—41no—
137Q32—3321no—
138Q32—3321no—
139Q32—3321no—
140Q32—3322no—
141SD32—41no—
142SD32—3321no—
143M32—21no—
144M32—3321no—
145M32—1661no—
146M32—1661no—
147C2×C16—3321no—
148C2×C16—831no—
149C2×C16—831no—
150#108C22⋊D8311yescharacteristic
151#104—21no—
152C4×C8C22×D8311yescharacteristic
153#41—21no—
154C2×Q8—41no—
155C2×Q8—3321no—
156Q16—41no—
157Q16—41no—
158Q16—41no—
159Q16—41no—
160Q16—3321no—
161Q16—3321no—
162Q16—3321no—
163Q16—3321no—
164Q16#1305057511yescharacteristic
165SD16—21no—
166D8#1305057511yescharacteristic
167M16—21no—
168M16—41no—
169C2×C8—41no—
170C2×C8D4×D8311yescharacteristic
171C2×C8C2×C22⋊D8311yescharacteristic
172C4⋊C4—81no—
173C4⋊C4—6641no—
174C42#1305058911yescharacteristic
175C16—41no—
176C16—3321no—
177C16—3321no—
178C16—831no—
179C16—831no—
180C16—1661no—
181Q8—21no—
182Q8—81no—
183Q8—81no—
184Q8—6641no—
185Q8—6641no—
186D4—21no—
187D4—41no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4—6641no—
192C2×C4#1458176411yescharacteristic
193C8—41no—
194C8D8×D8311yescharacteristic
195C8C2×#1305057511yescharacteristic
196C8#1458181211yescharacteristic
197C8#1458181611yescharacteristic
198C22—41no—
199C22#1912796911yescharacteristic
200C4—22no—
201C4—41no—
202C4—161no—
203C4—13281no—
204C4#1912789411yescharacteristic
205C4#1912793511yescharacteristic
206C2—21no—
207C2—81no—
208C2#2490681611yescharacteristic
subgroupG/H
centerC2#24906816
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#2214C2
socleC2×C83#1667
prime radical#135×C83D4
hypercenter#2214D83
hypocenterC83#12437
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #24909715C2semidirect
4. #24905538C2semidirect
5. #24905502C2semidirect
6. #24905501C2semidirect
112. C83#12437semidirect

Maximal subgroups

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

subgroupindex
#249097152
#249095442
#249093002
#249055382
#249055022
#249055012
C83×#22142
#1243783