Finite Group Databasebeta

← #38767410

Subgroups — #38767410

Order 25472.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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#27164071C211yesmaximal, characteristic, complemented
2#27163884C211yesmaximal, characteristic, complemented
3#27163752C214yesmaximal, complemented
4#532×C199C211yesmaximal, characteristic
5C2×C4⋊Dic199—21no—
6C4⋊(C199⋊C8)—21no—
7C22⋊(C199⋊C8)C2212yes—
8C4×C199⋊C8—21no—
9C199⋊#95—21no—
10C199⋊#95C2212yes—
11C2×#41×C199—21no—
12C4⋊Q8×C199C411yescharacteristic, complemented
13#127×C199C411yescharacteristic, complemented
14#124×C199—21no—
15#121×C199—21no—
16#121×C199C2212yes—
17C4×D4×C199—21no—
18C4×D4×C199C412yescomplemented
19C2×C42×C199C2211yescharacteristic
20C22×Dic199—22no—
21C2×C199⋊C8—22no—
22C4⋊Dic199—42no—
23#41×C199—42no—
24#41×C199—42no—
25C2×Q8×C199—21no—
26C2×D4×C199—22no—
27C2×D4×C199—21no—
28C2×D4×C199—21no—
29C2×D4×C199C2×C412yes—
30C22×C4×C199—22no—
31C22×C4×C199D411yescharacteristic
32C22×C4×C199D411yescharacteristic
33C22×C4×C199C2311yescharacteristic
34C4⋊C4×C199—21no—
35C4⋊C4×C199C2×C412yes—
36C22⋊C4×C199—22no—
37C22⋊C4×C199—22no—
38C42×C199C2×C411yescharacteristic
39C42×C199C2×C411yescharacteristic
40C42×C199D411yescharacteristic
41C42×C199D411yescharacteristic
42C2×Dic199—42no—
43C2×Dic199—42no—
44C2×Dic199—42no—
45C199⋊C8—42no—
46C23×C199—22no—
47C23×C199C2×D411yescharacteristic
48Q8×C199—42no—
49D4×C199—42no—
50D4×C199—42no—
51D4×C199—42no—
52D4×C199—42no—
53D4×C199—42no—
54C2×C4×C199—22no—
55C2×C4×C199—41no—
56C2×C4×C199—41no—
57C2×C4×C199—44no—
58C2×C4×C199C22⋊C411yescharacteristic
59C2×C4×C199C22⋊C411yescharacteristic
60C2×C4×C199C22⋊C411yescharacteristic
61C2×C4×C199C22⋊C411yescharacteristic
62C2×C4×C199D812yes—
63C2×C4×C199SD1612yes—
64C2×C4×C199C22×C411yescharacteristic
65C2×C4×C199C2×D411yescharacteristic
66C22×C199—21no—
67C22×C199—21no—
68C22×C199—42no—
69C22×C199—42no—
70C22×C199—42no—
71C22×C199C2×C22⋊C411yescharacteristic
72C22×C199C2×D811yescharacteristic
73C22×C199C2×SD1611yescharacteristic
74C4×C199—21no—
75C4×C199—21no—
76C4×C199—21no—
77C4×C199—21no—
78C4×C199—42no—
79C4×C199#10212yes—
80C4×C199#10212yes—
81Dic199—82no—
82C2×C199—21no—
83C2×C199—21no—
84C2×C199—82no—
85C2×C199#41011yescharacteristic
86C2×C199C2×#10211yescharacteristic
87C2×C199#42111yescharacteristic
88C199#151711yescharacteristic, complemented, Sylow
89#1517—1991nomaximal, Sylow
90#532D19911yescharacteristic
91#431—1991no—
92#382—1991no—
93#327—1994no—
94C2×#41—21no—
95C4⋊Q8Dic19911yescharacteristic, complemented
96#127Dic19911yescharacteristic, complemented
97#124—21no—
98#121—21no—
99#121C2×D19912yes—
100C4×D4—21no—
101C4×D4Dic19912yescomplemented
102C2×C4⋊C4—3981no—
103C2×C42C2×D19911yescharacteristic
104C4⋊C8—3981no—
105C22⋊C8—1992no—
106C4×C8—3981no—
107#95—3981no—
108#95—1992no—
109#41—42no—
110#41—42no—
111C2×Q8—21no—
112C2×D4—22no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4C2×Dic19912yes—
116C22×C4—22no—
117C22×C4—3982no—
118C22×C4C22⋊D19911yescharacteristic
119C22×C4C22⋊D19911yescharacteristic
120C22×C4C22×D19911yescharacteristic
121C2×C8—3982no—
122C4⋊C4—21no—
123C4⋊C4—7962no—
124C4⋊C4C2×Dic19912yes—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C42C2×Dic19911yescharacteristic
128C42C2×Dic19911yescharacteristic
129C42C22⋊D19911yescharacteristic
130C42C22⋊D19911yescharacteristic
131C23—22no—
132C23C2×C22⋊D19911yescharacteristic
133Q8—42no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—44no—
143C2×C4—7962no—
144C2×C4—7962no—
145C2×C4—7962no—
146C2×C4C22⋊Dic19911yescharacteristic
147C2×C4C22⋊Dic19911yescharacteristic
148C2×C4C22⋊Dic19911yescharacteristic
149C2×C4C22⋊Dic19911yescharacteristic
150C2×C4#1569187112yes—
151C2×C4#1569187412yes—
152C2×C4C22×Dic19911yescharacteristic
153C2×C4C2×C22⋊D19911yescharacteristic
154C8—7962no—
155C22—21no—
156C22—21no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22C2×C22⋊Dic19911yescharacteristic
161C22C2×#1569187111yescharacteristic
162C22C2×#1569187411yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—15922no—
169C4#2026387612yes—
170C4#2026387612yes—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#2716399211yescharacteristic
175C2C2×#2026387611yescharacteristic
176C2#2716403511yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic199
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
Fitting, prime radical#532×C199C2
socleC22×C199C2×C22⋊C4
cosocleC22×C4×C199C23
hypercenter#532D199
hypocenterC199#1517
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #27164071C2semidirect
2. #27163884C2semidirect
3. #27163752C2semidirect
12. C4⋊Q8×C199C4semidirect
13. #127×C199C4semidirect
18. C4×D4×C199C4semidirect
88. C199#1517semidirect
95. C4⋊Q8Dic199semidirect
96. #127Dic199semidirect
101. C4×D4Dic199semidirect

Maximal subgroups

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

subgroupindex
#271640712
#271638842
#271637522
#532×C1992
#1517199