Finite Group Databasebeta

← #38770813

Subgroups — #38770813

Order 25472.

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

normal subgroups only

This group has 210 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#27164831C211yesmaximal, characteristic, complemented
2#27164454C211yesmaximal, characteristic, complemented
3#27164285C211yesmaximal, characteristic, complemented
4#27163834C211yesmaximal, characteristic, complemented
5#27163826C211yesmaximal, characteristic, complemented
6#27163801C211yesmaximal, characteristic, complemented
7C2×SD32×C199C211yesmaximal, characteristic, complemented
8#20264003—21no—
9#20263987—22no—
10#20263986—21no—
11#20263981—21no—
12#20263978—21no—
13#20263977C2211yescharacteristic
14Q16×D199—21no—
15#20263961C2211yescharacteristic
16#20263899—21no—
17#20263896—21no—
18#20263895C2211yescharacteristic
19#20263891C2211yescharacteristic
20#20263872—21no—
21C2×Q16×C199C2211yescharacteristic
22C2×D8×C199C2211yescharacteristic
23SD32×C199—22no—
24C2×C16×C199C2211yescharacteristic
25#15691887—22no—
26#15691887—41no—
27#15691886—21no—
28#15691886—42no—
29#15691886D411yescharacteristic
30Q8×D199—22no—
31Q8×D199—41no—
32Dic796D411yescharacteristic
33#15691876—22no—
34#15691875—21no—
35#15691874—41no—
36#15691873—22no—
37D1592D411yescharacteristic
38#15691871—41no—
39#15691870—21no—
40#15691870D411yescharacteristic
41#15691869—21no—
42C8×D199—21no—
43C199⋊C16—21no—
44C2×Q8×C199—21no—
45C2×D4×C199—21no—
46Q16×C199—21no—
47Q16×C199D412yes—
48D8×C199—21no—
49D8×C199—21no—
50C2×C8×C199C2311yescharacteristic
51C16×C199—21no—
52Dic398—21no—
53Dic398—42no—
54Dic398D811yescharacteristic
55D796—21no—
56D796—42no—
57D796D811yescharacteristic
58C22⋊D199—21no—
59C22⋊D199—41no—
60C4×D199—21no—
61C4×D199—42no—
62C4×D199—42no—
63C4×D199—41no—
64C199⋊C8—21no—
65C199⋊C8—41no—
66C23×C199—41no—
67Q8×C199—22no—
68Q8×C199—41no—
69D4×C199—41no—
70D4×C199—41no—
71C2×C4×C199—41no—
72C2×C4×C199C2×D411yescharacteristic
73C8×C199C2×D411yescharacteristic
74C8×C199C2×D411yescharacteristic
75C22×C199—81no—
76C22×C199—161no—
77C22×C199AGL(1,ℤ/8)11yescharacteristic
78C2×D199—21no—
79C2×D199—41no—
80C4×C199—42no—
81C4×C199#12011yescharacteristic
82C4×C199C2×D811yescharacteristic
83Dic199—21no—
84Dic199—41no—
85C2×C199—21no—
86C2×C199—161no—
87C2×C199#44711yescharacteristic
88D199—41no—
89D199—81no—
90C199#219311yescharacteristic, complemented, Sylow
91#2193—1991nomaximal, Sylow
92#578—1991no—
93#509—1991no—
94C2×SD32D19911yescharacteristic, complemented
95#472—1991no—
96#362—1991no—
97#359—1991no—
98#350—1991no—
992−1+4—3981no—
100#137—3982no—
101#137—3981no—
102AGL(1,ℤ/8)—3981no—
103#135—3981no—
104#135—1991no—
105C2×Q16—3981no—
106C2×Q16C2×D19911yescharacteristic
107C2×D8C2×D19911yescharacteristic
108#131—1991no—
109SD32—22no—
110SD32—3981no—
111D16—3981no—
112M32—1991no—
113C2×C16C2×D19911yescharacteristic
114#108—1991no—
115#100—3981no—
116#41—7962no—
117#41—7961no—
118#41—3982no—
119#41—3981no—
120#41—1991no—
121C2×Q8—21no—
122C2×Q8—7961no—
123C2×Q8—3982no—
124C2×D4—21no—
125Q16—21no—
126Q16—3982no—
127Q16—1991no—
128Q16C22⋊D19912yes—
129SD16—7961no—
130SD16—3982no—
131SD16—3981no—
132D8—21no—
133D8—21no—
134D8—7961no—
135D8—1991no—
136M16—3981no—
137M16—3981no—
138M16—1991no—
139C2×C8—3981no—
140C2×C8C22×D19911yescharacteristic
141C16—21no—
142C16—3981no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—7962no—
147Q8—3981no—
148Q8—1991no—
149D4—41no—
150D4—41no—
151D4—7962no—
152D4—7961no—
153D4—3981no—
154D4—3981no—
155D4—1991no—
156C2×C4—41no—
157C2×C4—7962no—
158C2×C4—7962no—
159C2×C4—7961no—
160C2×C4—3981no—
161C2×C4D4×D19911yescharacteristic
162C8—7961no—
163C8—3981no—
164C8D4×D19911yescharacteristic
165C8C2×C22⋊D19911yescharacteristic
166C22—81no—
167C22—161no—
168C22—7961no—
169C22—3981no—
170C22#2026397911yescharacteristic
171C4—42no—
172C4—7961no—
173C4—3981no—
174C4#2026392311yescharacteristic
175C4D8×D19911yescharacteristic
176C2—21no—
177C2—161no—
178C2—7961no—
179C2—15921no—
180C2#2716415011yescharacteristic
subgroupG/H
centerC2#27164150
commutator, cosocleC2×C8×C199C23
FrattiniC2×C8C22×D199
FittingC2×SD32×C199C2
socleC2×C199#447
hypercenterC2×SD32D199
hypocenterC199#2193
LCSG ▷ C2×C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #27164831C2semidirect
2. #27164454C2semidirect
3. #27164285C2semidirect
4. #27163834C2semidirect
5. #27163826C2semidirect
6. #27163801C2semidirect
7. C2×SD32×C199C2semidirect
90. C199#2193semidirect
94. C2×SD32D199semidirect

Maximal subgroups

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

subgroupindex
#271648312
#271644542
#271642852
#271638342
#271638262
#271638012
C2×SD32×C1992
#2193199