Finite Group Databasebeta

← #38767878

Subgroups — #38767878

Order 25472.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#27164613C211yesmaximal, characteristic
2#27164353C211yesmaximal, characteristic, complemented
3#27163956C211yesmaximal, characteristic, complemented
4#27163756C211yesmaximal, characteristic, complemented
5#27163752C211yesmaximal, characteristic
6#27163743C211yesmaximal, characteristic, complemented
7#481×C199C211yesmaximal, characteristic
8#20263948—21no—
9#20263945—21no—
10#20263936—21no—
11#20263936—21no—
12#20263934C2211yescharacteristic
13#20263932—21no—
14D4×Dic199—21no—
15C2×Dic199⋊C4C2211yescharacteristic
16#20263888—21no—
17#20263878—21no—
18C22⋊(C199⋊C8)C2211yescharacteristic
19C199⋊#95—21no—
20C199⋊#95—21no—
21C199⋊#95C2211yescharacteristic
22#121×C199C2211yescharacteristic
23C2×C4⋊C4×C199C2211yescharacteristic
24#106×C199—21no—
25#102×C199—21no—
26C22⋊C8×C199C2211yescharacteristic
27C2×Dic398D411yescharacteristic
28C22×Dic199—21no—
29C22×Dic199—21no—
30C22×Dic199D411yescharacteristic
31C22×Dic199D411yescharacteristic
32C2×C199⋊C8—21no—
33C4⋊Dic199—21no—
34C4⋊Dic199D411yescharacteristic
35Dic199⋊C4—21no—
36Dic199⋊C4—21no—
37Dic199⋊C4—21no—
38Dic199⋊C4—21no—
39Dic199⋊C4—21no—
40C22⋊Dic199—21no—
41C22⋊Dic199—21no—
42C22⋊Dic199—21no—
43C22⋊Dic199—21no—
44C4×Dic199—21no—
45C2×D4×C199—21no—
46C2×D4×C199D411yescharacteristic
47C22×C4×C199—21no—
48C22×C4×C199C2311yescharacteristic
49C2×C8×C199—21no—
50C4⋊C4×C199—21no—
51C4⋊C4×C199—21no—
52C4⋊C4×C199D411yescharacteristic
53C22⋊C4×C199—21no—
54Dic398—41no—
55C2×Dic199—21no—
56C2×Dic199—21no—
57C2×Dic199—21no—
58C2×Dic199—21no—
59C2×Dic199—21no—
60C2×Dic199—21no—
61C2×Dic199—41no—
62C2×Dic199—41no—
63C2×Dic199—41no—
64C2×Dic199—41no—
65C2×Dic199—81no—
66C199⋊C8—41no—
67C23×C199—21no—
68C23×C199C2×D411yescharacteristic
69D4×C199—41no—
70D4×C199—41no—
71D4×C199—41no—
72C2×C4×C199—21no—
73C2×C4×C199—41no—
74C2×C4×C199—42no—
75C2×C4×C199—41no—
76C2×C4×C199C2×D411yescharacteristic
77C2×C4×C199C2×D411yescharacteristic
78C8×C199—41no—
79C22×C199—21no—
80C22×C199—21no—
81C22×C199—41no—
82C22×C199—41no—
83C22×C199—41no—
84C22×C199#12011yescharacteristic
85C22×C199#13511yescharacteristic
86C22×C199#13711yescharacteristic
87C4×C199—21no—
88C4×C199—21no—
89C4×C199—41no—
90C4×C199—81no—
91Dic199—41no—
92Dic199—41no—
93Dic199—41no—
94Dic199—41no—
95Dic199—81no—
96C2×C199—21no—
97C2×C199—21no—
98C2×C199—81no—
99C2×C199#45211yescharacteristic
100C2×C199#45411yescharacteristic
101C2×C199#45811yescharacteristic
102C199#161511yescharacteristic, complemented, Sylow
103#1615—1991nomaximal, Sylow
104#539—1991no—
105#484—1991no—
106#481D19911yescharacteristic
107#400—1991no—
108#328—1991no—
109#327—1991no—
110#324—1991no—
111#126—3981no—
112#125—3981no—
113#123—3981no—
114#123—3981no—
115C22⋊Q8—3981no—
116C22⋊Q8—1991no—
117#121C2×D19911yescharacteristic
118C4×D4—3981no—
119C2×C4⋊C4—1991no—
120C2×C4⋊C4C2×D19911yescharacteristic
121#107—3981no—
122#106—21no—
123#103—3981no—
124#102—21no—
125C22⋊C8—1991no—
126C22⋊C8C2×D19911yescharacteristic
127#95—3981no—
128#95—3981no—
129#95—1991no—
130C2×Q8—1991no—
131C2×D4—21no—
132C2×D4C22⋊D19911yescharacteristic
133C22×C4—21no—
134C22×C4—3981no—
135C22×C4—3981no—
136C22×C4—1991no—
137C22×C4—1991no—
138C22×C4C22×D19911yescharacteristic
139C2×C8—21no—
140C2×C8—3981no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3981no—
144C4⋊C4—3981no—
145C4⋊C4—3981no—
146C4⋊C4—3981no—
147C4⋊C4—3981no—
148C4⋊C4—3981no—
149C4⋊C4—1991no—
150C4⋊C4C22⋊D19911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3981no—
153C22⋊C4—3981no—
154C22⋊C4—3981no—
155C22⋊C4—3981no—
156C42—3981no—
157C23—21no—
158C23D4×D19911yescharacteristic
159Q8—7961no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—7961no—
168C2×C4—7961no—
169C2×C4—7961no—
170C2×C4—7961no—
171C2×C4—15921no—
172C2×C4—3981no—
173C2×C4—3981no—
174C2×C4—3981no—
175C2×C4—3981no—
176C2×C4—3981no—
177C2×C4—3981no—
178C2×C4D4×D19911yescharacteristic
179C2×C4C2×C22⋊D19911yescharacteristic
180C8—41no—
181C8—7961no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#2026392311yescharacteristic
188C22#2026397611yescharacteristic
189C22#2026398411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—7961no—
195C4—7961no—
196C4—7961no—
197C4—7961no—
198C4—15921no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2716417711yescharacteristic
203C2#2716418911yescharacteristic
204C2#2716420711yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#481×C199C2
socleC22×C199#120
prime radical#121×C199C22
hypercenter#481D199
hypocenterC199#1615
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #27164353C2semidirect
3. #27163956C2semidirect
4. #27163756C2semidirect
6. #27163743C2semidirect
102. C199#1615semidirect

Maximal subgroups

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

subgroupindex
#271646132
#271643532
#271639562
#271637562
#271637522
#271637432
#481×C1992
#1615199