Finite Group Databasebeta

← #38769917

Subgroups — #38769917

Order 25472.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#27164818C211yesmaximal, characteristic, complemented
2#27164529C212yesmaximal, complemented
3#27164034C212yesmaximal, complemented
4#27163775C211yesmaximal, characteristic, complemented
5#407×C199C211yesmaximal, characteristic, complemented
6C2×#15691886C2212yes—
7#20263988—22no—
8#20263983—22no—
9#20263977—22no—
10#20263938—22no—
11#20263934—22no—
12#20263929—22no—
13#20263924—22no—
14C4×C22⋊D199—24no—
15#20263914C2212yes—
16#20263881—24no—
17C23×C4×C199C2211yescharacteristic
18C2×M16×C199C2211yescharacteristic
19C2×M16×C199C2211yescharacteristic
20C22⋊C8×C199—22no—
21#15691886—22no—
22#15691886—22no—
23#15691886—22no—
24#15691886—22no—
25C2×Dic398D412yescomplemented
26C2×D796D412yescomplemented
27C2×C22⋊D199—24no—
28C2×C22⋊D199—22no—
29C2×C4×D199—22no—
30Dic796—22no—
31#15691875—24no—
32D1592—22no—
33C4⋊Dic199—22no—
34Dic199⋊C4—24no—
35C22⋊Dic199—24no—
36C22⋊Dic199—22no—
37(C2×D199)⋊C4—24no—
38C4×Dic199D414yescomplemented
39C24×C199D411yescharacteristic
40C22×C4×C199—21no—
41C22×C4×C199—22no—
42C22×C4×C199—22no—
43C22×C4×C199—21no—
44C22×C4×C199D411yescharacteristic
45C22×C4×C199C2311yescharacteristic
46M16×C199—22no—
47M16×C199—22no—
48C2×C8×C199—21no—
49C2×C8×C199D412yescomplemented
50C22×D199—22no—
51Dic398—22no—
52Dic398—22no—
53D796—22no—
54D796—22no—
55C22⋊D199—48no—
56C22⋊D199—42no—
57C22⋊D199—42no—
58C2×Dic199—24no—
59C2×Dic199—22no—
60C4×D199—42no—
61C4×D199—42no—
62C23×C199—22no—
63C23×C199—21no—
64C23×C199—42no—
65C23×C199C2×D411yescharacteristic
66C2×C4×C199—22no—
67C2×C4×C199—21no—
68C2×C4×C199—41no—
69C2×C4×C199—42no—
70C2×C4×C199—41no—
71C2×C4×C199C2×D412yes—
72C2×C4×C199C2×D412yes—
73C2×C4×C199C2×D411yescharacteristic
74C2×C4×C199#4111yescharacteristic
75C8×C199—22no—
76C8×C199—41no—
77C22×C199—22no—
78C22×C199—24no—
79C22×C199—41no—
80C22×C199—42no—
81C22×C199—41no—
82C22×C199—41no—
83C22×C199#12012yes—
84C22×C199#12111yescharacteristic
85C2×D199—44no—
86C2×D199—42no—
87C4×C199—41no—
88C4×C199#12011yescharacteristic
89C4×C199#12112yes—
90C4×C199#12711yescharacteristic
91Dic199—44no—
92Dic199—42no—
93C2×C199—22no—
94C2×C199—21no—
95C2×C199—42no—
96C2×C199#39211yescharacteristic
97D199—82no—
98C199#201011yescharacteristic, complemented, Sylow
99#2010—1991nomaximal, Sylow
100#575—1991no—
101#525—1992no—
102#421—1992no—
103#407D19911yescharacteristic, complemented
104H(3,ℤ/4)—1991no—
105C2×#41—1992no—
106C23×C4C2×D19911yescharacteristic
107#137—3982no—
108AGL(1,ℤ/8)—3982no—
109#135—3982no—
110C2×M16C2×D19911yescharacteristic
111C2×M16C2×D19911yescharacteristic
112#123—3982no—
113C22⋊Q8—3982no—
114#121—3982no—
115#120—3982no—
116C4×D4—3984no—
117#117—1992no—
118#104—3984no—
119C22⋊C8—22no—
120C24D79611yescharacteristic
121#41—3982no—
122#41—3982no—
123#41—3982no—
124#41—3982no—
125C2×Q8—1992no—
126C2×D4—3984no—
127C2×D4—3982no—
128C2×D4—1992no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—3982no—
134C22×C4D79611yescharacteristic
135C22×C4C22×D19911yescharacteristic
136Q16—3982no—
137SD16—3984no—
138D8—3982no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D19912yescomplemented
143C4⋊C4—3984no—
144C4⋊C4—3982no—
145C22⋊C4—3984no—
146C22⋊C4—3984no—
147C22⋊C4—3982no—
148C42—1994no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—3982no—
153C23C2×D79611yescharacteristic
154Q8—3982no—
155Q8—3982no—
156D4—7968no—
157D4—7962no—
158D4—7962no—
159D4—3982no—
160D4—3982no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—7962no—
167C2×C4—7962no—
168C2×C4—3984no—
169C2×C4—3982no—
170C2×C4D4×D19912yes—
171C2×C4D4×D19912yes—
172C2×C4C2×C22⋊D19911yescharacteristic
173C2×C4#1569188611yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—7964no—
183C22—7962no—
184C22#2026392512yes—
185C22#2026392911yescharacteristic
186C4—41no—
187C4—7964no—
188C4—7962no—
189C4#2026392311yescharacteristic
190C4#2026392812yes—
191C4#2026395111yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—15922no—
196C2#2716392711yescharacteristic
subgroupG/H
centerC4#20263951
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#407×C199C2
socleC2×C199#392
hypercenter#407D199
hypocenterC199#2010
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #27164818C2semidirect
2. #27164529C2semidirect
3. #27164034C2semidirect
4. #27163775C2semidirect
5. #407×C199C2semidirect
25. C2×Dic398D4semidirect
26. C2×D796D4semidirect
38. C4×Dic199D4semidirect
49. C2×C8×C199D4semidirect
98. C199#2010semidirect
103. #407D199semidirect
142. C2×C8C22⋊D199semidirect

Maximal subgroups

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

subgroupindex
#271648182
#271645292
#271640342
#271637752
#407×C1992
#2010199