Finite Group Databasebeta

← #38767879

Subgroups — #38767879

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#27164615C211yesmaximal, characteristic
2#27164353C211yesmaximal, characteristic, complemented
3#27164336C211yesmaximal, characteristic
4#27163754C211yesmaximal, characteristic, complemented
5#27163751C211yesmaximal, characteristic
6#27163744C211yesmaximal, characteristic, complemented
7#400×C199C211yesmaximal, characteristic, complemented
8#20263950—21no—
9#20263945—21no—
10#20263940—21no—
11#20263938—21no—
12#20263934C2211yescharacteristic
13#20263933—21no—
14#20263929C2211yescharacteristic
15C4×C22⋊D199—21no—
16#20263888—21no—
17#20263886—21no—
18#20263878—21no—
19#20263875—21no—
20C22⋊(C199⋊C8)C2211yescharacteristic
21C22⋊(C199⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C199C2211yescharacteristic
23C2×C4⋊C4×C199C2211yescharacteristic
24#95×C199—21no—
25#95×C199—21no—
26#95×C199C2211yescharacteristic
27C2×Dic398D411yescharacteristic
28C2×D796D411yescharacteristic
29C2×C22⋊D199—21no—
30C2×C4×D199—21no—
31C2×C199⋊C8—21no—
32C2×C199⋊C8—21no—
33C4⋊Dic199D411yescharacteristic
34C4⋊Dic199D411yescharacteristic
35Dic199⋊C4—21no—
36Dic199⋊C4—21no—
37Dic199⋊C4—21no—
38Dic199⋊C4—21no—
39C22⋊Dic199—21no—
40(C2×D199)⋊C4—21no—
41(C2×D199)⋊C4—21no—
42(C2×D199)⋊C4—21no—
43(C2×D199)⋊C4—21no—
44C4×Dic199—21no—
45C22×C4×C199—21no—
46C22×C4×C199—21no—
47C22×C4×C199D411yescharacteristic
48C22×C4×C199D411yescharacteristic
49C22×C4×C199C2311yescharacteristic
50C4⋊C4×C199—21no—
51C4⋊C4×C199—21no—
52C4⋊C4×C199—21no—
53C4⋊C4×C199—21no—
54C22×D199—21no—
55Dic398—41no—
56D796—41no—
57C22⋊D199—41no—
58C22⋊D199—41no—
59C2×Dic199—21no—
60C2×Dic199—21no—
61C2×Dic199—21no—
62C4×D199—81no—
63C199⋊C8—41no—
64C199⋊C8—41no—
65C23×C199C2×D411yescharacteristic
66C2×C4×C199—21no—
67C2×C4×C199—21no—
68C2×C4×C199—21no—
69C2×C4×C199—21no—
70C2×C4×C199—41no—
71C2×C4×C199—41no—
72C2×C4×C199—41no—
73C2×C4×C199—41no—
74C2×C4×C199—42no—
75C2×C4×C199—41no—
76C2×C4×C199—41no—
77C2×C4×C199C2×D411yescharacteristic
78C2×C4×C199C2×D411yescharacteristic
79C22×C199—21no—
80C22×C199—21no—
81C22×C199#12011yescharacteristic
82C22×C199#13511yescharacteristic
83C22×C199#13711yescharacteristic
84C2×D199—41no—
85C2×D199—41no—
86C2×D199—41no—
87C4×C199—21no—
88C4×C199—21no—
89C4×C199—41no—
90C4×C199—41no—
91C4×C199—81no—
92C4×C199—81no—
93Dic199—41no—
94Dic199—41no—
95Dic199—41no—
96C2×C199—21no—
97C2×C199—21no—
98C2×C199#45211yescharacteristic
99C2×C199#45411yescharacteristic
100C2×C199#45811yescharacteristic
101D199—81no—
102C199#161511yescharacteristic, complemented, Sylow
103#1615—1991nomaximal, Sylow
104#539—1991no—
105#484—1991no—
106#481—1991no—
107#400D19911yescharacteristic, complemented
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#121—1991no—
118C4×D4—3981no—
119C2×C4⋊C4C2×D19911yescharacteristic
120C2×C4⋊C4C2×D19911yescharacteristic
121#107—3981no—
122#106—3981no—
123#103—3981no—
124#102—3981no—
125C22⋊C8—1991no—
126C22⋊C8—1991no—
127#95—21no—
128#95—21no—
129#95C2×D19911yescharacteristic
130C2×Q8—1991no—
131C2×D4—3981no—
132C2×D4—1991no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—3981no—
136C22×C4C22⋊D19911yescharacteristic
137C22×C4C22⋊D19911yescharacteristic
138C22×C4C22×D19911yescharacteristic
139C2×C8—3981no—
140C2×C8—3981no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—3981no—
146C4⋊C4—3981no—
147C4⋊C4—3981no—
148C4⋊C4—3981no—
149C4⋊C4—1991no—
150C4⋊C4—1991no—
151C22⋊C4—3981no—
152C22⋊C4—3981no—
153C22⋊C4—3981no—
154C22⋊C4—3981no—
155C22⋊C4—3981no—
156C42—3981no—
157C23—3981no—
158C23C2×C22⋊D19911yescharacteristic
159Q8—7961no—
160D4—7961no—
161D4—7961no—
162D4—7961no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—15921no—
175C2×C4—3981no—
176C2×C4—3981no—
177C2×C4—3981no—
178C2×C4D4×D19911yescharacteristic
179C2×C4D4×D19911yescharacteristic
180C8—7961no—
181C8—7961no—
182C22—21no—
183C22—21no—
184C22—7961no—
185C22—7961no—
186C22—7961no—
187C22#2026392311yescharacteristic
188C22#2026397511yescharacteristic
189C22#2026398611yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—7961no—
197C4—7961no—
198C4—7961no—
199C2—21no—
200C2—21no—
201C2—15921no—
202C2#2716417811yescharacteristic
203C2#2716419011yescharacteristic
204C2#2716420711yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#400×C199C2
socleC22×C199#120
prime radical#20263929C22
hypercenter#400D199
hypocenterC199#1615
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #27164353C2semidirect
4. #27163754C2semidirect
6. #27163744C2semidirect
7. #400×C199C2semidirect
102. C199#1615semidirect
107. #400D199semidirect

Maximal subgroups

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

subgroupindex
#271646152
#271643532
#271643362
#271637542
#271637512
#271637442
#400×C1992
#1615199