Finite Group Databasebeta

← #35318654

Subgroups — #35318654

Order 21248.

224 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 63 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#24909719C211yesmaximal, characteristic, complemented
2#24909544C211yesmaximal, characteristic, complemented
3#24909539C211yesmaximal, characteristic
4#24905539C211yesmaximal, characteristic, complemented
5#24905501C211yesmaximal, characteristic, complemented
6#24905499C211yesmaximal, characteristic, complemented
7C83×#2170C211yesmaximal, characteristic, complemented
8#19128141—21no—
9#19128136—21no—
10C2×#14581737—21no—
11C2×#14581737—21no—
12#19128081C2211yescharacteristic
13#19128078C2211yescharacteristic
14#19127522C2211yescharacteristic
15#19127522C2211yescharacteristic
16#19127516—21no—
17#19127513—21no—
18#504×C83—21no—
19#443×C83C2211yescharacteristic
20#364×C83C2211yescharacteristic
21#350×C83—21no—
22C4×C16×C83C2211yescharacteristic
23C2×Dic332—21no—
24C2×Dic332—21no—
25C2×D664—21no—
26C2×D664—21no—
27#14581792—21no—
28#14581789—21no—
29#14581738—41no—
30#14581737—42no—
31#14581737—41no—
32#14581737—41no—
33#14581736—41no—
34#14581735—41no—
35#14581733—41no—
36#14581732—21no—
37#14581732—21no—
38#135×C83D411yescharacteristic
39#131×C83—21no—
40M32×C83—21no—
41M32×C83—41no—
42C2×C16×C83—41no—
43C2×C16×C83D411yescharacteristic
44C2×C16×C83D411yescharacteristic
45#108×C83D411yescharacteristic
46#104×C83—21no—
47C4×C8×C83C2311yescharacteristic
48C2×Dic166—41no—
49C2×D332—41no—
50C2×D332—81no—
51Dic332—41no—
52Dic332—41no—
53Dic332—41no—
54Dic332—41no—
55D664—41no—
56D664—41no—
57D664—41no—
58D664—41no—
59C4⋊Dic83—81no—
60C83⋊C16—41no—
61C83⋊C16—41no—
62#41×C83—21no—
63Q16×C83D811yescharacteristic
64SD16×C83—21no—
65D8×C83D811yescharacteristic
66M16×C83—21no—
67M16×C83—41no—
68C2×C8×C83—41no—
69C2×C8×C83C2×D411yescharacteristic
70C2×C8×C83C2×D411yescharacteristic
71C42×C83#4111yescharacteristic
72C16×C83—21no—
73C16×C83—41no—
74C16×C83D811yescharacteristic
75C16×C83D811yescharacteristic
76C22×D83—81no—
77Q8×C83—21no—
78D4×C83—21no—
79D4×C83—41no—
80C2×C4×C83—21no—
81C2×C4×C83—41no—
82C2×C4×C83#12111yescharacteristic
83C2×Dic83—81no—
84D332—81no—
85D332—81no—
86D332—162no—
87Dic166—81no—
88Dic166—81no—
89C8×C83—41no—
90C8×C83C2×D811yescharacteristic
91C8×C83C2×D811yescharacteristic
92C8×C83#13511yescharacteristic
93C8×C83AGL(1,ℤ/8)11yescharacteristic
94C22×C83—41no—
95C22×C83#47211yescharacteristic
96C2×D83—162no—
97C2×D83—161no—
98C4×C83—22no—
99C4×C83—41no—
100C4×C83#45911yescharacteristic
101C4×C83#46611yescharacteristic
102Dic83—161no—
103#12438—831nomaximal, Sylow
104C2×C83—21no—
105C2×C83—81no—
106C2×C83#166711yescharacteristic
107D83—321no—
108#2248—831no—
109#2214—831no—
110#2213—831no—
111#2170D8311yescharacteristic, complemented
112#1373—831no—
113#1358—831no—
114#1357—831no—
115C83#1243811yescharacteristic, complemented, Sylow
116#510—1661no—
117#509—1661no—
118C2×SD32—1661no—
119C2×SD32—1661no—
120#504—21no—
121#494—831no—
122#493—831no—
123#443C2×D8311yescharacteristic
124#364—831no—
125#364—831no—
126#364C2×D8311yescharacteristic
127#362—1661no—
128#361—1661no—
129#350—21no—
130C4×C16C2×D8311yescharacteristic
131#135D33211yescharacteristic
132C2×Q16—1661no—
133C2×Q16—1661no—
134C2×D8—1661no—
135C2×D8—1661no—
136#131—21no—
137C4⋊Q8—1661no—
138#127—1661no—
139Q32—3321no—
140SD32—3322no—
141SD32—3321no—
142SD32—3321no—
143SD32—3321no—
144SD32—3321no—
145D16—3321no—
146M32—21no—
147M32—41no—
148M32—1661no—
149M32—1661no—
150C2×C16—41no—
151C2×C16C22⋊D8311yescharacteristic
152C2×C16C22⋊D8311yescharacteristic
153#108D33211yescharacteristic
154#104—21no—
155C4×C8C22×D8311yescharacteristic
156#41—21no—
157C2×Q8—3321no—
158C2×D4—3321no—
159C2×D4—6641no—
160Q16—3321no—
161Q16—3321no—
162Q16—3321no—
163Q16—3321no—
164Q16D66411yescharacteristic
165SD16—21no—
166D8—3321no—
167D8—3321no—
168D8—3321no—
169D8—3321no—
170D8D66411yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8C2×C22⋊D8311yescharacteristic
175C2×C8C2×D33211yescharacteristic
176C4⋊C4—6641no—
177C42#1305059011yescharacteristic
178C16—21no—
179C16—41no—
180C16—3321no—
181C16—3321no—
182C16#1305057511yescharacteristic
183C16#1305057511yescharacteristic
184C23—6641no—
185Q8—21no—
186Q8—6641no—
187Q8—6641no—
188D4—21no—
189D4—41no—
190D4—13282no—
191D4—6641no—
192D4—6641no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—6641no—
196C2×C4#1458176611yescharacteristic
197C8—41no—
198C8C2×#1305057511yescharacteristic
199C8C2×D66411yescharacteristic
200C8#1458181411yescharacteristic
201C8#1458181711yescharacteristic
202C22—41no—
203C22—13282no—
204C22—13281no—
205C22#1912797111yescharacteristic
206C4—22no—
207C4—41no—
208C4—13281no—
209C4#1912789611yescharacteristic
210C4#1912793711yescharacteristic
211C2—21no—
212C2—81no—
213C2—26561no—
214C2#2490681811yescharacteristic
subgroupG/H
centerC2#24906818
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#2170C2
socleC2×C83#1667
prime radical#24909539C2
hypercenter#2170D83
hypocenterC83#12438
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #24909719C2semidirect
2. #24909544C2semidirect
4. #24905539C2semidirect
5. #24905501C2semidirect
6. #24905499C2semidirect
7. C83×#2170C2semidirect
111. #2170D83semidirect
115. C83#12438semidirect

Maximal subgroups

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

subgroupindex
#249097192
#249095442
#249095392
#249055392
#249055012
#249054992
C83×#21702
#1243883