Finite Group Databasebeta

← #35325229

Subgroups — #35325229

Order 21248.

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

normal subgroups only

This group has 196 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
2#24909781C211yesmaximal, characteristic
3#24909714C211yesmaximal, characteristic, complemented
4#24909343C211yesmaximal, characteristic
5#24905660C211yesmaximal, characteristic, complemented
6#24905655C211yesmaximal, characteristic, complemented
7C83×#1420C211yesmaximal, characteristic, complemented
8#19128133C2211yescharacteristic
9C2×Dic664C2211yescharacteristic
10C2×#14581738—21no—
11#19128079—21no—
12#19127817—21no—
13Dic1328—21no—
14#19127541—21no—
15#19127540—21no—
16#19127538—21no—
17#19127535C2211yescharacteristic
18#19127507—21no—
19C16×Dic83C2211yescharacteristic
20C2×Q32×C83C2211yescharacteristic
21M64×C83C2211yescharacteristic
22#368×C83C2211yescharacteristic
23#14581814—21no—
24C2×Dic332—21no—
25C2×#13050580—41no—
26#14581800—41no—
27#14581790—41no—
28Dic664—21no—
29Dic664—21no—
30Dic664D411yescharacteristic
31#14581738—42no—
32#14581737—21no—
33D1328D411yescharacteristic
34C2×C83⋊C16D411yescharacteristic
35#14581718—41no—
36C8×Dic83D411yescharacteristic
37C83⋊C32—21no—
38C2×Q16×C83—21no—
39Q32×C83—21no—
40Q32×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#13050580—81no—
50#13050580—81no—
51#13050579—41no—
52D664—21no—
53#13050573—81no—
54C2×C83⋊C8D811yescharacteristic
55C8×D83—81no—
56Dic83⋊C4—82no—
57C4×Dic83D811yescharacteristic
58C83⋊C16—21no—
59C2×Q8×C83—41no—
60Q16×C83—41no—
61Q16×C83—41no—
62M16×C83—41no—
63C2×C8×C83C2×D411yescharacteristic
64C16×C83C2×D411yescharacteristic
65C16×C83#4111yescharacteristic
66Q8×C83—81no—
67Q8×C83—81no—
68C2×C4×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#50911yescharacteristic
84C2×D83—81no—
85C4×C83—161no—
86C4×C83#45911yescharacteristic
87C4×C83C2×D1611yescharacteristic
88Dic83—22no—
89Dic83—81no—
90Dic83—161no—
91#13693—831nomaximal, Sylow
92C2×C83—21no—
93C2×C83#220611yescharacteristic
94D83—161no—
95#2264—831no—
96#2264—831no—
97#2247—831no—
98#2178—831no—
99#1422—831no—
100#1420—831no—
101#1420D8311yescharacteristic, complemented
102C83#1369311yescharacteristic, complemented, Sylow
103#508—831no—
104C2×Q32—831no—
105C2×Q32—1661no—
106C2×Q32C2×D8311yescharacteristic
107#494—1661no—
108#443—1661no—
109Q64—1661no—
110Q64—1661no—
111SD64—1661no—
112SD64—1661no—
113M64—831no—
114M64C2×D8311yescharacteristic
115#368C2×D8311yescharacteristic
116#359—1661no—
117C4×C16—831no—
118#135—1661no—
119C2×Q16—21no—
120C2×Q16—3321no—
121C2×Q16—1661no—
122#131—3321no—
123C4⋊Q8—3321no—
124Q32—21no—
125Q32—21no—
126Q32—3322no—
127Q32—831no—
128Q32—1661no—
129Q32—1661no—
130SD32—1661no—
131D16—831no—
132C2×C16—831no—
133C2×C16C22×D8311yescharacteristic
134#108—21no—
135#104—3321no—
136C4×C8—831no—
137C32—21no—
138C32—1661no—
139#41—3321no—
140C2×Q8—41no—
141C2×Q8—3321no—
142Q16—41no—
143Q16—41no—
144Q16—3321no—
145Q16—3321no—
146Q16—6641no—
147Q16—6641no—
148Q16—1661no—
149SD16—3321no—
150D8—1661no—
151M16—41no—
152M16—6641no—
153C2×C8—831no—
154C2×C8—6641no—
155C2×C8D4×D8311yescharacteristic
156C4⋊C4—6642no—
157C42—831no—
158C16—1661no—
159C16D4×D8311yescharacteristic
160C16#1305059011yescharacteristic
161Q8—81no—
162Q8—81no—
163Q8—3321no—
164Q8—6641no—
165Q8—6641no—
166D4—3321no—
167D4—6641no—
168C2×C4—81no—
169C2×C4—6641no—
170C2×C4—6641no—
171C2×C4—1661no—
172C2×C4D8×D8311yescharacteristic
173C8—81no—
174C8—831no—
175C8—831no—
176C8#1458176511yescharacteristic
177C8#1458181911yescharacteristic
178C22—6641no—
179C22#1912813811yescharacteristic
180C4—161no—
181C4—13281no—
182C4—6641no—
183C4—1662no—
184C4#1912789511yescharacteristic
185C4D16×D8311yescharacteristic
186C2—21no—
187C2—13281no—
188C2#2490949711yescharacteristic
subgroupG/H
centerC2#24909497
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1420C2
socleC2×C83#2206
prime radical#19128133C22
hypercenter#1420D83
hypocenterC83#13693
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
3. #24909714C2semidirect
5. #24905660C2semidirect
6. #24905655C2semidirect
7. C83×#1420C2semidirect
101. #1420D83semidirect
102. C83#13693semidirect

Maximal subgroups

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

subgroupindex
#249097832
#249097812
#249097142
#249093432
#249056602
#249056552
C83×#14202
#1369383