Finite Group Databasebeta

← #35325224

Subgroups — #35325224

Order 21248.

216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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#24909778C211yesmaximal, characteristic, complemented
2#24909776C211yesmaximal, characteristic, complemented
3#24909711C211yesmaximal, characteristic, complemented
4#24909343C211yesmaximal, characteristic, complemented
5#24905660C211yesmaximal, characteristic, complemented
6#24905652C211yesmaximal, characteristic, complemented
7C83×#1419C211yesmaximal, characteristic, complemented
8#19128133C2211yescharacteristic
9C2×D1328C2211yescharacteristic
10C2×#14581733—21no—
11#19128076—21no—
12#19127817—21no—
13#19127540—21no—
14#19127539—21no—
15D2656—21no—
16#19127536—21no—
17#19127535C2211yescharacteristic
18#19127507—21no—
19C16×Dic83C2211yescharacteristic
20C2×D16×C83C2211yescharacteristic
21M64×C83C2211yescharacteristic
22#368×C83C2211yescharacteristic
23#14581814—21no—
24C2×D664—21no—
25C2×#13050575—41no—
26#14581800—41no—
27#14581788—41no—
28Dic664D411yescharacteristic, complemented
29#14581737—21no—
30D1328—21no—
31D1328—21no—
32D1328D411yescharacteristic, complemented
33#14581733—42no—
34C2×C83⋊C16D411yescharacteristic
35#14581718—41no—
36C8×Dic83D411yescharacteristic
37C83⋊C32—21no—
38C2×D8×C83—21no—
39D16×C83—21no—
40D16×C83—21no—
41C2×C16×C83C2311yescharacteristic
42#108×C83—21no—
43C32×C83—21no—
44#13050590—41no—
45C2×D332—41no—
46C2×C22⋊D83—82no—
47Dic332—21no—
48#13050579—41no—
49D664—21no—
50D664—41no—
51D664—41no—
52#13050575—81no—
53#13050575—81no—
54#13050573—81no—
55C2×C83⋊C8D811yescharacteristic
56C8×D83—81no—
57C4×Dic83D811yescharacteristic
58C83⋊C16—21no—
59C2×D4×C83—41no—
60D8×C83—41no—
61D8×C83—41no—
62M16×C83—41no—
63C2×C8×C83C2×D411yescharacteristic
64C16×C83C2×D411yescharacteristic
65C16×C83#4111yescharacteristic
66C23×C83—81no—
67C22×D83—81no—
68D4×C83—81no—
69D4×C83—81no—
70C2×C4×C83C2×D811yescharacteristic
71C22⋊D83—81no—
72C22⋊D83—164no—
73C2×Dic83—21no—
74D332—41no—
75D332—81no—
76D332—81no—
77C4×D83—81no—
78Dic166—41no—
79C8×C83—81no—
80C8×C83#12111yescharacteristic
81C8×C83AGL(1,ℤ/8)11yescharacteristic
82C83⋊C8D1611yescharacteristic
83C83⋊C8D1611yescharacteristic
84C22×C83—162no—
85C22×C83—161no—
86C22×C83#50911yescharacteristic
87C2×D83—81no—
88C2×D83—162no—
89C2×D83—161no—
90C4×C83#45911yescharacteristic
91C4×C83C2×D1611yescharacteristic
92Dic83—22no—
93Dic83—81no—
94#13692—831nomaximal, Sylow
95C2×C83—21no—
96C2×C83—321no—
97C2×C83#220611yescharacteristic
98D83—161no—
99D83—321no—
100#2263—831no—
101#2263—831no—
102#2246—831no—
103#2178—831no—
104#1422—831no—
105#1419—831no—
106#1419D8311yescharacteristic, complemented
107C83#1369211yescharacteristic, complemented, Sylow
108#508—831no—
109C2×D16—831no—
110C2×D16—1661no—
111C2×D16C2×D8311yescharacteristic
112#493—1661no—
113#443—1661no—
114SD64—1661no—
115SD64—1661no—
116D32—1661no—
117D32—1661no—
118M64—831no—
119M64C2×D8311yescharacteristic
120#368C2×D8311yescharacteristic
121#359—1661no—
122C4×C16—831no—
123#135—1661no—
124C2×D8—21no—
125C2×D8—3321no—
126C2×D8—1661no—
127#131—3321no—
128#127—3321no—
129Q32—831no—
130SD32—1661no—
131D16—21no—
132D16—21no—
133D16—3322no—
134D16—831no—
135D16—1661no—
136D16—1661no—
137C2×C16—831no—
138C2×C16C22×D8311yescharacteristic
139#108—21no—
140#104—3321no—
141C4×C8—831no—
142C32—21no—
143C32—1661no—
144#41—3321no—
145C2×D4—41no—
146C2×D4—3321no—
147C2×D4—6642no—
148Q16—1661no—
149SD16—3321no—
150D8—41no—
151D8—41no—
152D8—3321no—
153D8—3321no—
154D8—6641no—
155D8—6641no—
156D8—1661no—
157M16—41no—
158M16—6641no—
159C2×C8—831no—
160C2×C8—6641no—
161C2×C8D4×D8311yescharacteristic
162C42—831no—
163C16—1661no—
164C16D4×D8311yescharacteristic
165C16#1305059011yescharacteristic
166C23—81no—
167C23—6641no—
168Q8—3321no—
169D4—81no—
170D4—81no—
171D4—13284no—
172D4—3321no—
173D4—6641no—
174D4—6641no—
175D4—6641no—
176C2×C4—6641no—
177C2×C4—1661no—
178C2×C4D8×D8311yescharacteristic
179C8—81no—
180C8—831no—
181C8—831no—
182C8#1458176511yescharacteristic
183C8#1458181911yescharacteristic
184C22—162no—
185C22—161no—
186C22—13282no—
187C22—13281no—
188C22—6641no—
189C22#1912813811yescharacteristic
190C4—6641no—
191C4—1662no—
192C4#1912789511yescharacteristic
193C4D16×D8311yescharacteristic
194C2—21no—
195C2—321no—
196C2—13281no—
197C2—26561no—
198C2#2490949711yescharacteristic
subgroupG/H
centerC2#24909497
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1419C2
socleC2×C83#2206
hypercenter#1419D83
hypocenterC83#13692
LCSG ▷ C2×C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #24909778C2semidirect
2. #24909776C2semidirect
3. #24909711C2semidirect
4. #24909343C2semidirect
5. #24905660C2semidirect
6. #24905652C2semidirect
7. C83×#1419C2semidirect
28. Dic664D4semidirect
32. D1328D4semidirect
106. #1419D83semidirect
107. C83#13692semidirect

Maximal subgroups

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

subgroupindex
#249097782
#249097762
#249097112
#249093432
#249056602
#249056522
C83×#14192
#1369283