Finite Group Databasebeta

← #38767539

Subgroups — #38767539

Order 25472.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#27164573C211yesmaximal, characteristic
2#27164040C211yesmaximal, characteristic
3C4⋊C8×D199C211yesmaximal, characteristic
4#27163766C211yesmaximal, characteristic, complemented
5#27163766C211yesmaximal, characteristic, complemented
6#27163764C211yesmaximal, characteristic, complemented
7#332×C199C211yesmaximal, characteristic, complemented
8C2×#15691869—21no—
9C2×C8×D199—21no—
10#20263955C2211yescharacteristic
11#20263946—21no—
12#20263935C412yes—
13#20263931—21no—
14Q8×Dic199—21no—
15#20263920C412yes—
16#20263913—21no—
17C42×D199C2211yescharacteristic
18C4⋊(C199⋊C8)C2211yescharacteristic
19C4⋊(C199⋊C8)C2211yescharacteristic
20Dic199⋊C8—21no—
21Dic199⋊C8—21no—
22C4⋊Q8×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic
24C4⋊C8×C199C2211yescharacteristic
25C2×Dic398C2×C412yes—
26C2×C4×D199C2×C411yescharacteristic
27C2×C4×D199D411yescharacteristic
28C2×C4×D199D411yescharacteristic
29#15691869—42no—
30C2×C199⋊C8—21no—
31C2×C199⋊C8—21no—
32C8×D199—42no—
33C4⋊Dic199—22no—
34C4⋊Dic199—21no—
35C4⋊Dic199—21no—
36Dic199⋊C4—22no—
37(C2×D199)⋊C4—22no—
38C4×Dic199—22no—
39C4×Dic199C2×C411yescharacteristic
40C4×Dic199D411yescharacteristic
41C4×Dic199D411yescharacteristic
42C2×Q8×C199—21no—
43C2×C8×C199—21no—
44C2×C8×C199—21no—
45C4⋊C4×C199—21no—
46C4⋊C4×C199C2×C412yes—
47C42×C199C2311yescharacteristic
48C22×D199C22⋊C411yescharacteristic
49Dic398—42no—
50C2×Dic199—22no—
51C2×Dic199C22⋊C411yescharacteristic
52C2×Dic199C22⋊C411yescharacteristic
53C2×Dic199C22⋊C411yescharacteristic
54C4×D199—21no—
55C4×D199—21no—
56C4×D199—41no—
57C4×D199SD1612yes—
58C4×D199Q1612yes—
59C199⋊C8—41no—
60C199⋊C8—41no—
61Q8×C199—41no—
62Q8×C199—41no—
63C2×C4×C199—22no—
64C2×C4×C199C22×C411yescharacteristic
65C2×C4×C199C2×D411yescharacteristic
66C2×C4×C199C2×D411yescharacteristic
67C8×C199—41no—
68C8×C199—41no—
69C22×C199C2×C22⋊C411yescharacteristic
70C2×D199—21no—
71C2×D199—21no—
72C2×D199#10312yes—
73C4×C199—21no—
74C4×C199—42no—
75C4×C199C2×SD1611yescharacteristic
76C4×C199C2×Q1611yescharacteristic
77C4×C199AGL(1,ℤ/8)11yescharacteristic
78C4×C199#13711yescharacteristic
79Dic199—21no—
80Dic199—21no—
81Dic199—42no—
82Dic199#10312yes—
83C2×C199#41311yescharacteristic
84C2×C199C2×#10311yescharacteristic
85C2×C199#41711yescharacteristic
86D199—22no—
87C199#155011yescharacteristic, complemented, Sylow
88#1550—1991nomaximal, Sylow
89#533—1991no—
90#423—1991no—
91C2×C4⋊C8—1991no—
92#333—1991no—
93#333—1991no—
94#332—1991no—
95#332D19911yescharacteristic, complemented
96C2×M16—3981no—
97C22×C8—3981no—
98C4⋊Q8—1991no—
99C4⋊Q8C2×D19911yescharacteristic
100#125—3981no—
101C22⋊Q8—3981no—
102C22⋊Q8—1992no—
103C4×Q8—3981no—
104C4×Q8—1992no—
105#117—3981no—
106C2×C42—1991no—
107C4⋊C8—3981no—
108C4⋊C8—3981no—
109C4⋊C8—1991no—
110C4⋊C8—1991no—
111C4⋊C8C2×D19911yescharacteristic
112C4⋊C8C2×D19911yescharacteristic
113C2×Q8—21no—
114C2×Q8—1992no—
115C22×C4—1991no—
116C22×C4—1991no—
117C22×C4—1991no—
118M16—7962no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—7962no—
122C2×C8—3981no—
123C2×C8—3981no—
124C4⋊C4—21no—
125C4⋊C4—3982no—
126C4⋊C4—3982no—
127C4⋊C4—3981no—
128C4⋊C4—3981no—
129C4⋊C4C4×D19912yes—
130C22⋊C4—3982no—
131C42—3982no—
132C42—1991no—
133C42—1991no—
134C42—1991no—
135C42C22×D19911yescharacteristic
136C23—1991no—
137Q8—41no—
138Q8—41no—
139Q8—7962no—
140C2×C4—22no—
141C2×C4—7961no—
142C2×C4—3982no—
143C2×C4—3981no—
144C2×C4—3981no—
145C2×C4—1991no—
146C2×C4—1991no—
147C2×C4—1991no—
148C2×C4—1992no—
149C2×C4—1992no—
150C2×C4C2×C4×D19911yescharacteristic
151C2×C4D4×D19911yescharacteristic
152C2×C4D4×D19911yescharacteristic
153C8—41no—
154C8—41no—
155C8—7961no—
156C8—7961no—
157C22—3981no—
158C22—3981no—
159C22—1992no—
160C22C22⋊C4×D19911yescharacteristic
161C4—21no—
162C4—42no—
163C4—7962no—
164C4—3981no—
165C4—3981no—
166C4—1992no—
167C4SD16×D19911yescharacteristic
168C4Q16×D19911yescharacteristic
169C4#2026397911yescharacteristic
170C4#2026398411yescharacteristic
171C2—3982no—
172C2#2716400111yescharacteristic
173C2#103×D19911yescharacteristic
174C2#2716401611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#332×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC22×D199C22⋊C4
cosocleC42×C199C23
hypercenter#332D199
hypocenterC199#1550
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #27163766C2semidirect
5. #27163766C2semidirect
6. #27163764C2semidirect
7. #332×C199C2semidirect
87. C199#1550semidirect
95. #332D199semidirect

Maximal subgroups

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

subgroupindex
#271645732
#271640402
C4⋊C8×D1992
#271637662
#271637642
#332×C1992
#1550199