Finite Group Databasebeta

← #35325273

Subgroups — #35325273

Order 21248.

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

normal subgroups only

This group has 180 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
1C2×#19127541C211yesmaximal, characteristic, complemented
2#24909758C211yesmaximal, characteristic
3#24909589C211yesmaximal, characteristic
4#24909585C211yesmaximal, characteristic
5#24905666C211yesmaximal, characteristic, complemented
6#24905657C211yesmaximal, characteristic, complemented
7C83×#1420C211yesmaximal, characteristic, complemented
8C2×Dic664C2211yescharacteristic
9#19128117C2211yescharacteristic
10#19127977—21no—
11#19127973—21no—
12#19127541—21no—
13#19127541—21no—
14#19127534—21no—
15C2×C83⋊C32C2211yescharacteristic
16C32×D83—21no—
17#19127531C2211yescharacteristic
18#19127517—21no—
19#19127516—21no—
20C2×Q32×C83C2211yescharacteristic
21M64×C83C2211yescharacteristic
22#368×C83C2211yescharacteristic
23#14581825—41no—
24#14581823—41no—
25C2×Dic332—21no—
26#14581798D411yescharacteristic
27Dic664—21no—
28Dic664—21no—
29#14581732D411yescharacteristic
30#14581731—21no—
31C16×D83—21no—
32#14581728—21no—
33#14581711—41no—
34#14581710—41no—
35C83⋊C32D411yescharacteristic
36C83⋊C32D411yescharacteristic
37C2×Q16×C83—21no—
38Q32×C83—21no—
39Q32×C83—21no—
40C2×C16×C83C2311yescharacteristic
41#108×C83—21no—
42C32×C83—21no—
43#13050590D811yescharacteristic
44C2×Dic166—41no—
45Dic332—41no—
46Dic332—41no—
47Dic332—81no—
48#13050580—81no—
49#13050579—81no—
50#13050577—81no—
51#13050574—41no—
52#13050574D811yescharacteristic
53#13050573—21no—
54C8×D83—21no—
55C83⋊C16—21no—
56C2×Q8×C83—41no—
57Q16×C83—41no—
58Q16×C83—41no—
59M16×C83—41no—
60C2×C8×C83C2×D411yescharacteristic
61C16×C83C2×D411yescharacteristic
62C16×C83#4111yescharacteristic
63Q8×C83—81no—
64Q8×C83—81no—
65C2×C4×C83—81no—
66C2×C4×C83C2×D811yescharacteristic
67C22⋊D83—21no—
68C2×Dic83—81no—
69D332D1611yescharacteristic
70C4×D83—21no—
71Dic166—81no—
72Dic166—81no—
73Dic166D1611yescharacteristic
74C8×C83—81no—
75C8×C83#12111yescharacteristic
76C8×C83#13511yescharacteristic
77C83⋊C8—21no—
78C83⋊C8—81no—
79C22×C83#50811yescharacteristic
80C2×D83—21no—
81C4×C83—161no—
82C4×C83#46611yescharacteristic
83C4×C83C2×D1611yescharacteristic
84Dic83—21no—
85Dic83—161no—
86#13701—831nomaximal, Sylow
87C2×C83—21no—
88C2×C83#221511yescharacteristic
89D83—41no—
90C2×Q64—831no—
91#2258—831no—
92#2222—831no—
93#2222—831no—
94#1425—831no—
95#1420—831no—
96#1420D8311yescharacteristic, complemented
97C83#1370111yescharacteristic, complemented, Sylow
98C2×Q32—831no—
99C2×Q32C2×D8311yescharacteristic
100#504—831no—
101#473—1661no—
102#473—1661no—
103Q64—1661no—
104Q64—1661no—
105M64—1661no—
106M64C2×D8311yescharacteristic
107C2×C32—831no—
108C2×C32—1661no—
109#368—831no—
110#368C2×D8311yescharacteristic
111#362—1661no—
112#362—1661no—
113#137—3321no—
114#137—3321no—
115C2×Q16—21no—
116C2×Q16—1661no—
117#131—831no—
118Q32—21no—
119Q32—21no—
120Q32—1661no—
121Q32—1661no—
122M32—831no—
123M32—1661no—
124C2×C16—1661no—
125C2×C16C22×D8311yescharacteristic
126#108—21no—
127#108—1661no—
128#101—3321no—
129#101—3321no—
130C32—21no—
131C32—831no—
132C32—831no—
133#41—831no—
134C2×Q8—41no—
135C2×Q8—3321no—
136Q16—41no—
137Q16—41no—
138Q16—3321no—
139Q16—3321no—
140Q16—6641no—
141Q16—6641no—
142SD16—6641no—
143SD16—6641no—
144M16—41no—
145M16—3321no—
146M16—831no—
147M16—1661no—
148C2×C8—1661no—
149C2×C8D4×D8311yescharacteristic
150C16—1661no—
151C16D4×D8311yescharacteristic
152C16#1305059011yescharacteristic
153Q8—81no—
154Q8—81no—
155Q8—831no—
156Q8—6641no—
157Q8—6641no—
158D4—831no—
159D4—1661no—
160C2×C4—81no—
161C2×C4—6641no—
162C2×C4—1661no—
163C2×C4D8×D8311yescharacteristic
164C8—81no—
165C8—6641no—
166C8—1661no—
167C8#1458176511yescharacteristic
168C8#1458181311yescharacteristic
169C22—1661no—
170C22#1912813211yescharacteristic
171C4—161no—
172C4—13281no—
173C4—1661no—
174C4#1912793611yescharacteristic
175C4D16×D8311yescharacteristic
176C2—21no—
177C2—3321no—
178C2#2490954811yescharacteristic
subgroupG/H
centerC2#24909548
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1420C2
socleC2×C83#2215
prime radical#13050590D8
hypercenter#1420D83
hypocenterC83#13701
LCSG ▷ C2×C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. C2×#19127541C2semidirect
5. #24905666C2semidirect
6. #24905657C2semidirect
7. C83×#1420C2semidirect
96. #1420D83semidirect
97. C83#13701semidirect

Maximal subgroups

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

subgroupindex
C2×#191275412
#249097582
#249095892
#249095852
#249056662
#249056572
C83×#14202
#1370183