Finite Group Databasebeta

← #24909440

Subgroups — #24909440

Order 10624.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#19128514C211yesmaximal, characteristic
2#19128142C211yesmaximal, characteristic, complemented
3#19127973C211yesmaximal, characteristic, complemented
4#19127517C211yesmaximal, characteristic, complemented
5#19127509C211yesmaximal, characteristic, complemented
6#19127484C211yesmaximal, characteristic, complemented
7C2×Q32×C83C211yesmaximal, characteristic, complemented
8#14581840—21no—
9#14581824—22no—
10#14581823—21no—
11#14581823—21no—
12#14581815—21no—
13#14581814C2211yescharacteristic
14Q16×D83—21no—
15#14581798C2211yescharacteristic
16#14581738—21no—
17#14581735—21no—
18#14581732C2211yescharacteristic
19#14581728C2211yescharacteristic
20#14581711—21no—
21C2×Q16×C83C2211yescharacteristic
22C2×Q16×C83C2211yescharacteristic
23Q32×C83—22no—
24C2×C16×C83C2211yescharacteristic
25#13050591—22no—
26#13050591—41no—
27#13050590—21no—
28#13050590—42no—
29#13050590D411yescharacteristic
30Q8×D83—22no—
31Q8×D83—41no—
32Dic332D411yescharacteristic
33#13050580—22no—
34#13050580—41no—
35#13050579—21no—
36#13050577—22no—
37#13050577—41no—
38D664D411yescharacteristic
39#13050574—21no—
40#13050574D411yescharacteristic
41#13050573—21no—
42C8×D83—21no—
43C83⋊C16—21no—
44C2×Q8×C83—21no—
45C2×Q8×C83—21no—
46Q16×C83—21no—
47Q16×C83—21no—
48Q16×C83—21no—
49Q16×C83D412yes—
50C2×C8×C83C2311yescharacteristic
51C16×C83—21no—
52Q8×C83—22no—
53Q8×C83—41no—
54Q8×C83—41no—
55Q8×C83—41no—
56C2×C4×C83—41no—
57C2×C4×C83—41no—
58C2×C4×C83C2×D411yescharacteristic
59C22⋊D83—21no—
60C22⋊D83—41no—
61D332—21no—
62D332—42no—
63D332D811yescharacteristic
64C4×D83—21no—
65C4×D83—42no—
66C4×D83—42no—
67C4×D83—41no—
68Dic166—21no—
69Dic166—42no—
70Dic166D811yescharacteristic
71C8×C83C2×D411yescharacteristic
72C8×C83C2×D411yescharacteristic
73C83⋊C8—21no—
74C83⋊C8—41no—
75C22×C83AGL(1,ℤ/8)11yescharacteristic
76C2×D83—21no—
77C2×D83—41no—
78C4×C83—42no—
79C4×C83—81no—
80C4×C83#12011yescharacteristic
81C4×C83C2×D811yescharacteristic
82Dic83—21no—
83Dic83—41no—
84C2×C83—21no—
85C2×C83#44711yescharacteristic
86D83—41no—
87D83—81no—
88#2195—831nomaximal, Sylow
89C83#219511yescharacteristic, complemented, Sylow
90#578—831no—
91#510—831no—
92C2×Q32D8311yescharacteristic, complemented
93#473—831no—
94#362—831no—
95#359—831no—
96#350—831no—
972−1+4—1661no—
98#137—1661no—
99#137—1661no—
100#137—1662no—
101#135—831no—
102#135—1661no—
103C2×Q16—1661no—
104C2×Q16C2×D8311yescharacteristic
105C2×Q16C2×D8311yescharacteristic
106#131—831no—
107Q32—22no—
108Q32—1661no—
109SD32—1661no—
110M32—831no—
111C2×C16C2×D8311yescharacteristic
112#108—831no—
113#101—1661no—
114#41—3322no—
115#41—3321no—
116#41—831no—
117#41—1662no—
118#41—1661no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—3321no—
122C2×Q8—1662no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—3321no—
127Q16—831no—
128Q16—1662no—
129Q16C22⋊D8312yes—
130SD16—3321no—
131SD16—1662no—
132SD16—1661no—
133D8—831no—
134M16—831no—
135M16—1661no—
136M16—1661no—
137C2×C8—1661no—
138C2×C8C22×D8311yescharacteristic
139C16—21no—
140C16—1661no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—3322no—
146Q8—831no—
147Q8—1661no—
148D4—3322no—
149D4—3321no—
150D4—831no—
151D4—1661no—
152D4—1661no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—3322no—
156C2×C4—3322no—
157C2×C4—3321no—
158C2×C4—1661no—
159C2×C4D4×D8311yescharacteristic
160C8—3321no—
161C8—1661no—
162C8D4×D8311yescharacteristic
163C8C2×C22⋊D8311yescharacteristic
164C22—3321no—
165C22—1661no—
166C22#1458181611yescharacteristic
167C4—42no—
168C4—81no—
169C4—3321no—
170C4—1661no—
171C4#1458176011yescharacteristic
172C4D8×D8311yescharacteristic
173C2—21no—
174C2—3321no—
175C2—6641no—
176C2#1912783311yescharacteristic
subgroupG/H
centerC2#19127833
commutator, cosocleC2×C8×C83C23
FrattiniC2×C8C22×D83
FittingC2×Q32×C83C2
socleC2×C83#447
prime radical#19128514C2
hypercenterC2×Q32D83
hypocenterC83#2195
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #19128142C2semidirect
3. #19127973C2semidirect
4. #19127517C2semidirect
5. #19127509C2semidirect
6. #19127484C2semidirect
7. C2×Q32×C83C2semidirect
89. C83#2195semidirect
92. C2×Q32D83semidirect

Maximal subgroups

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

subgroupindex
#191285142
#191281422
#191279732
#191275172
#191275092
#191274842
C2×Q32×C832
#219583