Finite Group Databasebeta

← #38768090

Subgroups — #38768090

Order 25472.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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#27164746C211yesmaximal, characteristic
2#27164421C211yesmaximal, characteristic
3#27164300C211yesmaximal, characteristic
4#27163765C211yesmaximal, characteristic
5Q8⋊(C199⋊C8)C211yesmaximal, characteristic
6#27163748C211yesmaximal, characteristic
7#462×C199C211yesmaximal, characteristic
8#20263955C2211yescharacteristic
9#20263953—21no—
10#20263947—21no—
11#20263945—22no—
12C4×Dic398—21no—
13C4×Dic398C2211yescharacteristic
14#20263920—21no—
15#20263888—22no—
16#20263886—21no—
17C4⋊(C199⋊C8)C2211yescharacteristic
18#20263878—21no—
19C4×C199⋊C8C2211yescharacteristic
20C2×Q16×C199—21no—
21C4⋊Q8×C199C2211yescharacteristic
22C4×Q8×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic
24#103×C199—21no—
25C2×Dic398—21no—
26C2×Dic398D411yescharacteristic
27C2×C199⋊C8—21no—
28C2×C199⋊C8—21no—
29C4⋊Dic199—21no—
30C4⋊Dic199D412yes—
31C4⋊Dic199D411yescharacteristic
32Dic199⋊C4—22no—
33Dic199⋊C4—22no—
34Dic199⋊C4—22no—
35Dic199⋊C4—21no—
36C4×Dic199—22no—
37C4×Dic199—21no—
38C2×Q8×C199—21no—
39C2×Q8×C199D411yescharacteristic
40Q16×C199—42no—
41C2×C8×C199—21no—
42C4⋊C4×C199—21no—
43C4⋊C4×C199—21no—
44C4⋊C4×C199—21no—
45C4⋊C4×C199D411yescharacteristic
46C42×C199—21no—
47C42×C199C2311yescharacteristic
48Dic398—21no—
49Dic398—41no—
50Dic398—41no—
51Dic398Q1612yescomplemented
52C2×Dic199—21no—
53C2×Dic199—21no—
54C2×Dic199—22no—
55C199⋊C8—22no—
56C199⋊C8—41no—
57Q8×C199—21no—
58Q8×C199—21no—
59Q8×C199—41no—
60Q8×C199—41no—
61C2×C4×C199—21no—
62C2×C4×C199—21no—
63C2×C4×C199—41no—
64C2×C4×C199C2×D411yescharacteristic
65C2×C4×C199C2×D411yescharacteristic
66C2×C4×C199C2×D411yescharacteristic
67C8×C199—41no—
68C22×C199#12011yescharacteristic
69C4×C199—21no—
70C4×C199—41no—
71C4×C199—41no—
72C4×C199—81no—
73C4×C199C2×Q1611yescharacteristic
74C4×C199#13511yescharacteristic
75C4×C199AGL(1,ℤ/8)11yescharacteristic
76C4×C199#13711yescharacteristic
77Dic199—22no—
78Dic199—42no—
79Dic199—41no—
80C2×C199#44911yescharacteristic
81C2×C199#45111yescharacteristic
82C2×C199#45611yescharacteristic
83C199#164811yescharacteristic, complemented, Sylow
84#1648—1991nomaximal, Sylow
85#557—1991no—
86#500—1991no—
87#475—1991no—
88#462D19911yescharacteristic
89#332—1991no—
90Q8⋊C8—1991no—
91Q8⋊C8—1991no—
92C2×Q16—21no—
93C4⋊Q8—3981no—
94C4⋊Q8—1991no—
95C4⋊Q8C2×D19911yescharacteristic
96#125—3981no—
97#125—3982no—
98C4×Q8—3981no—
99C4×Q8—3981no—
100C4×Q8—1991no—
101C4×Q8C2×D19911yescharacteristic
102#107—3982no—
103#106—3981no—
104C4⋊C8—1991no—
105C4⋊C8C2×D19911yescharacteristic
106#103—21no—
107#103—3981no—
108C4×C8—1991no—
109C2×Q8—21no—
110C2×Q8—3981no—
111C2×Q8—1991no—
112C2×Q8C22⋊D19911yescharacteristic
113Q16—42no—
114C2×C8—21no—
115C2×C8—3981no—
116C2×C8—3981no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—3982no—
121C4⋊C4—3982no—
122C4⋊C4—3982no—
123C4⋊C4—3981no—
124C4⋊C4—3981no—
125C4⋊C4—1991no—
126C4⋊C4—1992no—
127C4⋊C4C22⋊D19911yescharacteristic
128C42—21no—
129C42—3982no—
130C42—3981no—
131C42C22×D19911yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—41no—
135Q8—41no—
136Q8—7961no—
137Q8—7961no—
138Q8—3981no—
139Q8—1992no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—3981no—
144C2×C4—3982no—
145C2×C4—3981no—
146C2×C4D4×D19911yescharacteristic
147C2×C4D4×D19911yescharacteristic
148C2×C4C2×C22⋊D19911yescharacteristic
149C8—41no—
150C8—7961no—
151C8—3982no—
152C22#2026392311yescharacteristic
153C4—21no—
154C4—41no—
155C4—41no—
156C4—81no—
157C4—7962no—
158C4—7961no—
159C4—3982no—
160C4Q16×D19911yescharacteristic
161C4#2026397511yescharacteristic
162C4#2026398111yescharacteristic
163C4#2026398711yescharacteristic
164C2#2716416111yescharacteristic
165C2#2716417211yescharacteristic
166C2#2716419911yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#462×C199C2
socle, prime radicalC22×C199#120
hypercenter#462D199
hypocenterC199#1648
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
51. Dic398Q16semidirect
83. C199#1648semidirect

Maximal subgroups

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

subgroupindex
#271647462
#271644212
#271643002
#271637652
Q8⋊(C199⋊C8)2
#271637482
#462×C1992
#1648199