Finite Group Databasebeta

← #35325217

Subgroups — #35325217

Order 21248.

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

normal subgroups only

This group has 200 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#24909783C211yesmaximal, characteristic, complemented
2#24909776C211yesmaximal, characteristic
3#24909721C211yesmaximal, characteristic, complemented
4#24909343C211yesmaximal, characteristic, complemented
5#24905660C211yesmaximal, characteristic, complemented
6#24905655C211yesmaximal, characteristic, complemented
7C83×#1419C211yesmaximal, characteristic, complemented
8#19128133C2211yescharacteristic
9C2×Dic664C2211yescharacteristic
10C2×#14581736—21no—
11#19128084—21no—
12#19127817—21no—
13Dic1328—21no—
14#19127540—21no—
15#19127539—21no—
16#19127536—21no—
17#19127535C2211yescharacteristic
18#19127507—21no—
19C16×Dic83C2211yescharacteristic
20C2×D16×C83C2211yescharacteristic
21M64×C83C2211yescharacteristic
22#368×C83C2211yescharacteristic
23#14581814—21no—
24C2×Dic332—21no—
25C2×#13050578—41no—
26#14581800—41no—
27#14581779—41no—
28Dic664—21no—
29Dic664—21no—
30Dic664D411yescharacteristic
31#14581737—21no—
32#14581736—42no—
33D1328D411yescharacteristic
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×Dic166—41no—
46Dic332—21no—
47Dic332—41no—
48Dic332—41no—
49#13050579—41no—
50#13050578—81no—
51#13050578—81no—
52D664—21no—
53#13050573—81no—
54C2×C83⋊C8D811yescharacteristic
55C8×D83—81no—
56C22⋊Dic83—82no—
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—
67D4×C83—81no—
68D4×C83—81no—
69C2×C4×C83C2×D811yescharacteristic
70C22⋊D83—81no—
71C2×Dic83—21no—
72C2×Dic83—81no—
73D332—41no—
74C4×D83—81no—
75Dic166—41no—
76Dic166—81no—
77Dic166—81no—
78C8×C83—81no—
79C8×C83#12111yescharacteristic
80C8×C83AGL(1,ℤ/8)11yescharacteristic
81C83⋊C8D1611yescharacteristic
82C83⋊C8D1611yescharacteristic
83C22×C83—162no—
84C22×C83—161no—
85C22×C83#50911yescharacteristic
86C2×D83—81no—
87C4×C83#45911yescharacteristic
88C4×C83C2×D1611yescharacteristic
89Dic83—41no—
90Dic83—81no—
91Dic83—161no—
92#13691—831nomaximal, Sylow
93C2×C83—21no—
94C2×C83—321no—
95C2×C83#220611yescharacteristic
96D83—161no—
97#2264—831no—
98#2263—831no—
99#2249—831no—
100#2178—831no—
101#1422—831no—
102#1420—831no—
103#1419D8311yescharacteristic, complemented
104C83#1369111yescharacteristic, complemented, Sylow
105#508—831no—
106C2×Q32—831no—
107C2×SD32—1661no—
108C2×D16C2×D8311yescharacteristic
109#495—1661no—
110#443—1661no—
111Q64—1661no—
112SD64—1661no—
113SD64—1661no—
114D32—1661no—
115M64—831no—
116M64C2×D8311yescharacteristic
117#368C2×D8311yescharacteristic
118#359—1661no—
119C4×C16—831no—
120#135—1661no—
121C2×Q16—1661no—
122C2×SD16—3321no—
123C2×D8—21no—
124#131—3321no—
125#124—3321no—
126Q32—831no—
127Q32—1661no—
128Q32—1661no—
129SD32—3322no—
130SD32—1661no—
131D16—21no—
132D16—21no—
133D16—831no—
134C2×C16—831no—
135C2×C16C22×D8311yescharacteristic
136#108—21no—
137#104—3321no—
138C4×C8—831no—
139C32—21no—
140C32—1661no—
141#41—3321no—
142C2×Q8—3321no—
143C2×D4—41no—
144Q16—3321no—
145Q16—3321no—
146Q16—1661no—
147SD16—3321no—
148SD16—6641no—
149SD16—6641no—
150D8—41no—
151D8—41no—
152D8—1661no—
153M16—41no—
154M16—6641no—
155C2×C8—831no—
156C2×C8—6641no—
157C2×C8D4×D8311yescharacteristic
158C22⋊C4—6642no—
159C42—831no—
160C16—1661no—
161C16D4×D8311yescharacteristic
162C16#1305059011yescharacteristic
163C23—81no—
164Q8—3321no—
165Q8—6641no—
166Q8—6641no—
167D4—81no—
168D4—81no—
169D4—3321no—
170D4—6641no—
171C2×C4—6641no—
172C2×C4—6641no—
173C2×C4—1661no—
174C2×C4D8×D8311yescharacteristic
175C8—81no—
176C8—831no—
177C8—831no—
178C8#1458176511yescharacteristic
179C8#1458181911yescharacteristic
180C22—162no—
181C22—161no—
182C22—6641no—
183C22#1912813811yescharacteristic
184C4—13281no—
185C4—3321no—
186C4—6641no—
187C4#1912789511yescharacteristic
188C4D16×D8311yescharacteristic
189C2—21no—
190C2—321no—
191C2—13281no—
192C2#2490949711yescharacteristic
subgroupG/H
centerC2#24909497
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1419C2
socleC2×C83#2206
prime radical#24909776C2
hypercenter#1419D83
hypocenterC83#13691
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. #24909783C2semidirect
3. #24909721C2semidirect
4. #24909343C2semidirect
5. #24905660C2semidirect
6. #24905655C2semidirect
7. C83×#1419C2semidirect
103. #1419D83semidirect
104. C83#13691semidirect

Maximal subgroups

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

subgroupindex
#249097832
#249097762
#249097212
#249093432
#249056602
#249056552
C83×#14192
#1369183