Finite Group Databasebeta

← #38767932

Subgroups — #38767932

Order 25472.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#27164733C211yesmaximal, characteristic, complemented
2#27164390C211yesmaximal, characteristic, complemented
3#27164210C211yesmaximal, characteristic, complemented
4#27163766C211yesmaximal, characteristic, complemented
5D4⋊(C199⋊C8)C211yesmaximal, characteristic, complemented
6#27163745C211yesmaximal, characteristic, complemented
7#459×C199C211yesmaximal, characteristic, complemented
8C2×#15691874—22no—
9C2×#15691871—21no—
10#20263955C2211yescharacteristic
11#20263941—22no—
12#20263929—21no—
13#20263926—21no—
14C4×D796C2211yescharacteristic
15#20263914—21no—
16#20263913—21no—
17C4⋊(C199⋊C8)C2211yescharacteristic
18#20263876—21no—
19C4×C199⋊C8C2211yescharacteristic
20C2×D8×C199—21no—
21#127×C199C2211yescharacteristic
22C4×D4×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic
24#102×C199—21no—
25C2×Dic398D412yes—
26C2×D796D411yescharacteristic
27C2×C22⋊D199—22no—
28C2×C4×D199—21no—
29#15691874—44no—
30#15691871—42no—
31C2×C199⋊C8—21no—
32C2×C199⋊C8—21no—
33C4⋊Dic199—21no—
34C4⋊Dic199—21no—
35C4⋊Dic199D411yescharacteristic
36C22⋊Dic199—22no—
37(C2×D199)⋊C4—22no—
38(C2×D199)⋊C4—21no—
39C4×Dic199—22no—
40C2×D4×C199—21no—
41C2×D4×C199—21no—
42C2×D4×C199—21no—
43C2×D4×C199D411yescharacteristic
44C22×C4×C199—21no—
45D8×C199—42no—
46C2×C8×C199—21no—
47C4⋊C4×C199D411yescharacteristic
48C22⋊C4×C199—21no—
49C42×C199C2311yescharacteristic
50C22×D199—21no—
51Dic398—42no—
52D796—21no—
53D796—21no—
54C22⋊D199—82no—
55C2×Dic199—21no—
56C2×Dic199—22no—
57C4×D199—41no—
58C4×D199—41no—
59C199⋊C8—22no—
60C199⋊C8—41no—
61C23×C199—21no—
62C23×C199—41no—
63D4×C199—21no—
64D4×C199—21no—
65D4×C199—42no—
66D4×C199—41no—
67D4×C199—41no—
68D4×C199—41no—
69D4×C199—41no—
70C2×C4×C199—21no—
71C2×C4×C199—41no—
72C2×C4×C199—41no—
73C2×C4×C199C2×D411yescharacteristic
74C2×C4×C199C2×D411yescharacteristic
75C2×C4×C199C2×D411yescharacteristic
76C8×C199—41no—
77C22×C199—41no—
78C22×C199—41no—
79C22×C199—41no—
80C22×C199—81no—
81C22×C199—81no—
82C22×C199—81no—
83C22×C199#12011yescharacteristic
84C2×D199—41no—
85C2×D199—41no—
86C2×D199—41no—
87C4×C199—21no—
88C4×C199—41no—
89C4×C199#13511yescharacteristic
90C4×C199#13511yescharacteristic
91C4×C199AGL(1,ℤ/8)11yescharacteristic
92C4×C199AGL(1,ℤ/8)11yescharacteristic
93Dic199—41no—
94Dic199—42no—
95C2×C199—81no—
96C2×C199—161no—
97C2×C199#44911yescharacteristic
98C2×C199#44911yescharacteristic
99C2×C199#45311yescharacteristic
100D199—81no—
101C199#162411yescharacteristic, complemented, Sylow
102#1624—1991nomaximal, Sylow
103#555—1991no—
104#492—1991no—
105#459—1991no—
106#459D19911yescharacteristic, complemented
107#333—1991no—
108D4⋊C8—1991no—
109D4⋊C8—1991no—
110C2×SD16—3982no—
111C2×D8—21no—
112C2×D8—3981no—
113C4⋊Q8—1991no—
114#127C2×D19911yescharacteristic
115#124—3982no—
116#121—3981no—
117#121—3981no—
118C4×D4—1991no—
119C4×D4C2×D19911yescharacteristic
120#117—3981no—
121#117—3981no—
122C4⋊C8—1991no—
123C4⋊C8C2×D19911yescharacteristic
124#102—21no—
125#102—3981no—
126C4×C8—1991no—
127C2×Q8—1992no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—3982no—
132C2×D4—1991no—
133C2×D4C22⋊D19911yescharacteristic
134C22×C4—21no—
135C22×C4—3981no—
136SD16—7964no—
137D8—42no—
138D8—7962no—
139C2×C8—21no—
140C2×C8—3981no—
141C2×C8—3981no—
142C4⋊C4—3981no—
143C4⋊C4—3981no—
144C4⋊C4—1991no—
145C4⋊C4C22⋊D19911yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—3982no—
148C22⋊C4—3982no—
149C22⋊C4—3981no—
150C42—3982no—
151C42C22×D19911yescharacteristic
152C23—21no—
153C23—41no—
154C23—3981no—
155Q8—7962no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—15922no—
164D4—3981no—
165D4—3981no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—7961no—
170C2×C4—7961no—
171C2×C4—3981no—
172C2×C4—3982no—
173C2×C4D4×D19911yescharacteristic
174C2×C4D4×D19911yescharacteristic
175C2×C4C2×C22⋊D19911yescharacteristic
176C8—41no—
177C8—7961no—
178C8—3982no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—7961no—
186C22—7961no—
187C22—7961no—
188C22#2026392311yescharacteristic
189C4—21no—
190C4—41no—
191C4—7961no—
192C4—7962no—
193C4#2026397411yescharacteristic
194C4#2026397511yescharacteristic
195C4#2026397911yescharacteristic
196C4#2026398111yescharacteristic
197C2—81no—
198C2—161no—
199C2—15921no—
200C2#2716416011yescharacteristic
201C2#2716416111yescharacteristic
202C2#2716418411yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#459×C199C2
socleC22×C199#120
hypercenter#459D199
hypocenterC199#1624
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #27164733C2semidirect
2. #27164390C2semidirect
3. #27164210C2semidirect
4. #27163766C2semidirect
5. D4⋊(C199⋊C8)C2semidirect
6. #27163745C2semidirect
7. #459×C199C2semidirect
101. C199#1624semidirect
106. #459D199semidirect

Maximal subgroups

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

subgroupindex
#271647332
#271643902
#271642102
#271637662
D4⋊(C199⋊C8)2
#271637452
#459×C1992
#1624199