Finite Group Databasebeta

← #38768177

Subgroups — #38768177

Order 25472.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C199⋊#564C211yesmaximal, characteristic
2#27164424C211yesmaximal, characteristic
3#27164386C211yesmaximal, characteristic
4#27163760C211yesmaximal, characteristic
5#27163759C211yesmaximal, characteristic
6#27163759C211yesmaximal, characteristic
7#501×C199C211yesmaximal, characteristic
8#20263947C2211yescharacteristic
9#20263947C2211yescharacteristic
10#20263946—21no—
11#20263946—21no—
12#20263945—21no—
13#20263945—21no—
14#20263945—21no—
15#20263945—21no—
16#20263888—21no—
17#20263886—21no—
18#20263879—21no—
19#20263879—21no—
20#20263866C2211yescharacteristic
21#20263866C2211yescharacteristic
22C4⋊Q8×C199C2211yescharacteristic
23#125×C199C2211yescharacteristic
24#107×C199—21no—
25#106×C199—21no—
26#97×C199C2211yescharacteristic
27C2×C199⋊C8—21no—
28C2×C199⋊C8—21no—
29C4⋊Dic199—21no—
30C4⋊Dic199—21no—
31C4⋊Dic199D411yescharacteristic
32C4⋊Dic199D411yescharacteristic
33C4⋊Dic199D411yescharacteristic
34C4⋊Dic199D411yescharacteristic
35Dic199⋊C4—21no—
36Dic199⋊C4—21no—
37Dic199⋊C4—21no—
38Dic199⋊C4—21no—
39Dic199⋊C4—21no—
40Dic199⋊C4—21no—
41Dic199⋊C4—21no—
42Dic199⋊C4—21no—
43C4×Dic199—21no—
44C4×Dic199—21no—
45C2×Q8×C199—21no—
46C2×C8×C199—21no—
47C4⋊C4×C199—21no—
48C4⋊C4×C199—21no—
49C4⋊C4×C199—21no—
50C4⋊C4×C199—21no—
51C4⋊C4×C199D411yescharacteristic
52C4⋊C4×C199D411yescharacteristic
53C42×C199C2311yescharacteristic
54C2×Dic199—21no—
55C2×Dic199—21no—
56C2×Dic199—21no—
57C2×Dic199—21no—
58C199⋊C8—22no—
59C199⋊C8—41no—
60Q8×C199—42no—
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—22no—
68C22×C199#12011yescharacteristic
69C4×C199—21no—
70C4×C199—21no—
71C4×C199—21no—
72C4×C199—41no—
73C4×C199—41no—
74C4×C199—81no—
75Dic199—41no—
76Dic199—41no—
77Dic199—41no—
78Dic199—41no—
79C2×C199#45411yescharacteristic
80C2×C199#45611yescharacteristic
81C2×C199#45611yescharacteristic
82C199#166311yescharacteristic, complemented, Sylow
83#1663—1991nomaximal, Sylow
84#564—1991no—
85#501—1991no—
86#501D19911yescharacteristic
87#491—1991no—
88#330—1991no—
89#330—1991no—
90#330—1991no—
91C4⋊Q8C2×D19911yescharacteristic
92#125—3981no—
93#125—3981no—
94#125—3981no—
95#125—3981no—
96#125—3981no—
97#125—3981no—
98#125—1991no—
99#125—1991no—
100#125C2×D19911yescharacteristic
101#107—21no—
102#107—3981no—
103#106—21no—
104#106—3981no—
105#103—3981no—
106#103—3981no—
107#97—1991no—
108#97—1991no—
109#97C2×D19911yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—3981no—
113C2×C8—3981no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—3981no—
119C4⋊C4—3981no—
120C4⋊C4—3981no—
121C4⋊C4—3981no—
122C4⋊C4—3981no—
123C4⋊C4—3981no—
124C4⋊C4—3981no—
125C4⋊C4—3981no—
126C4⋊C4—3981no—
127C4⋊C4—3981no—
128C4⋊C4—1991no—
129C4⋊C4—1991no—
130C4⋊C4—1991no—
131C4⋊C4—1991no—
132C4⋊C4C22⋊D19911yescharacteristic
133C4⋊C4C22⋊D19911yescharacteristic
134C42—3981no—
135C42—3981no—
136C42C22×D19911yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—3981no—
142C2×C4—3981no—
143C2×C4—3981no—
144C2×C4—3981no—
145C2×C4D4×D19911yescharacteristic
146C2×C4D4×D19911yescharacteristic
147C2×C4C2×C22⋊D19911yescharacteristic
148C8—22no—
149C8—7961no—
150C8—3982no—
151C22#2026392311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—7961no—
159C4—7961no—
160C4—7961no—
161C4—7961no—
162C2#2716418911yescharacteristic
163C2#2716419911yescharacteristic
164C2#2716420011yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#501×C199C2
socle, prime radicalC22×C199#120
hypercenter#501D199
hypocenterC199#1663
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
82. C199#1663semidirect

Maximal subgroups

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

subgroupindex
C199⋊#5642
#271644242
#271643862
#271637602
#271637592
#501×C1992
#1663199