Finite Group Databasebeta

← #38769918

Subgroups — #38769918

Order 25472.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#27164530C212yesmaximal, complemented
3#27164036C212yesmaximal, complemented
4#27163981C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C199C211yesmaximal, characteristic, complemented
6C2×#15691886C2212yes—
7C22×C4×D199C2211yescharacteristic
8#20263988—22no—
9#20263983—22no—
10#20263977—22no—
11C2×#15691870C2211yescharacteristic
12#20263939—22no—
13#20263935—22no—
14#20263930—22no—
15#20263925—22no—
16C4×D796—24no—
17#20263883—24no—
18(C2×D199)⋊C8—22no—
19C2×M16×C199C2211yescharacteristic
20#117×C199C2212yes—
21C23×D199D411yescharacteristic
22#15691886—22no—
23#15691886—22no—
24#15691886—22no—
25#15691886—22no—
26C2×Dic398D412yescomplemented
27C2×D796—24no—
28C2×D796D412yescomplemented
29C2×C22⋊D199—22no—
30C22×Dic199D411yescharacteristic
31C2×C4×D199—21no—
32C2×C4×D199—22no—
33C2×C4×D199—22no—
34C2×C4×D199—22no—
35C2×C4×D199—21no—
36Dic796—22no—
37#15691875—24no—
38D1592—22no—
39#15691870—22no—
40C2×C199⋊C8—21no—
41C4⋊Dic199—24no—
42(C2×D199)⋊C4—24no—
43(C2×D199)⋊C4—24no—
44C22×C4×C199C2311yescharacteristic
45M16×C199—22no—
46C2×C8×C199D412yescomplemented
47C4⋊C4×C199—22no—
48C22⋊C4×C199—22no—
49C42×C199D414yescomplemented
50C22×D199—22no—
51C22×D199—21no—
52C22×D199—22no—
53C22×D199—42no—
54Dic398—22no—
55Dic398—22no—
56D796—22no—
57D796—22no—
58D796—48no—
59C22⋊D199—42no—
60C22⋊D199—42no—
61C2×Dic199—22no—
62C2×Dic199—22no—
63C2×Dic199—21no—
64C4×D199—41no—
65C4×D199—42no—
66C4×D199—42no—
67C4×D199—41no—
68C4×D199—42no—
69C199⋊C8—41no—
70C23×C199C2×D411yescharacteristic
71C2×C4×C199—24no—
72C2×C4×C199C2×D412yes—
73C2×C4×C199C2×D411yescharacteristic
74C2×C4×C199C2×D412yes—
75C2×C4×C199#4111yescharacteristic
76C8×C199—22no—
77C22×C199—41no—
78C22×C199#12012yes—
79C22×C199#12111yescharacteristic
80C2×D199—24no—
81C2×D199—22no—
82C2×D199—42no—
83C2×D199—41no—
84C2×D199—41no—
85C2×D199—44no—
86C2×D199—42no—
87C4×C199—44no—
88C4×C199#12011yescharacteristic
89C4×C199#12112yes—
90C4×C199#12711yescharacteristic
91Dic199—41no—
92Dic199—42no—
93C2×C199—22no—
94C2×C199—21no—
95C2×C199#39211yescharacteristic
96D199—42no—
97D199—82no—
98C199#201011yescharacteristic, complemented, Sylow
99#2010—1991nomaximal, Sylow
100#575—1991no—
101#525—1992no—
102#421—1992no—
103#407—1991no—
104H(3,ℤ/4)D19911yescharacteristic, complemented
105C2×#41—1992no—
106C23×C4—1991no—
107#137—3982no—
108AGL(1,ℤ/8)—3982no—
109#135—3982no—
110C2×M16—1991no—
111C2×M16C2×D19911yescharacteristic
112#123—3982no—
113C22⋊Q8—3982no—
114#121—3982no—
115#120—3982no—
116C4×D4—3984no—
117#117C2×D19912yes—
118#104—3984no—
119C22⋊C8—3982no—
120C24—1991no—
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—3982no—
130C22×C4—3981no—
131C22×C4—3982no—
132C22×C4—3982no—
133C22×C4—3981no—
134C22×C4—1991no—
135C22×C4C22×D19911yescharacteristic
136Q16—3982no—
137SD16—3984no—
138D8—3982no—
139M16—22no—
140M16—3982no—
141C2×C8—3981no—
142C2×C8D79612yescomplemented
143C4⋊C4—22no—
144C4⋊C4—3984no—
145C22⋊C4—22no—
146C22⋊C4—3984no—
147C22⋊C4—3984no—
148C42D79614yescomplemented
149C23—7962no—
150C23—3982no—
151C23—3982no—
152C23—3981no—
153C23D4×D19911yescharacteristic
154Q8—3982no—
155Q8—3982no—
156D4—7968no—
157D4—7962no—
158D4—7962no—
159D4—3982no—
160D4—3982no—
161C2×C4—24no—
162C2×C4—7961no—
163C2×C4—7962no—
164C2×C4—7961no—
165C2×C4—7962no—
166C2×C4—7962no—
167C2×C4—3982no—
168C2×C4—3982no—
169C2×C4—3981no—
170C2×C4D4×D19912yes—
171C2×C4C2×D79611yescharacteristic
172C2×C4C2×D79612yes—
173C2×C4#1569188711yescharacteristic
174C8—22no—
175C8—7961no—
176C22—41no—
177C22—7962no—
178C22—7961no—
179C22—7964no—
180C22—7961no—
181C22—7962no—
182C22—3984no—
183C22—3982no—
184C22#2026392512yes—
185C22#2026393011yescharacteristic
186C4—44no—
187C4—7961no—
188C4—7962no—
189C4#2026392511yescharacteristic
190C4#2026393012yes—
191C4#2026395211yescharacteristic
192C2—22no—
193C2—21no—
194C2—7962no—
195C2—15922no—
196C2#2716392811yescharacteristic
subgroupG/H
centerC4#20263952
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
FittingH(3,ℤ/4)×C199C2
socleC2×C199#392
hypercenterH(3,ℤ/4)D199
hypocenterC199#2010
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #27164818C2semidirect
2. #27164530C2semidirect
3. #27164036C2semidirect
4. #27163981C2semidirect
5. H(3,ℤ/4)×C199C2semidirect
26. C2×Dic398D4semidirect
28. C2×D796D4semidirect
46. C2×C8×C199D4semidirect
49. C42×C199D4semidirect
98. C199#2010semidirect
104. H(3,ℤ/4)D199semidirect
142. C2×C8D796semidirect
148. C42D796semidirect

Maximal subgroups

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

subgroupindex
#271648182
#271645302
#271640362
#271639812
H(3,ℤ/4)×C1992
#2010199