Finite Group Databasebeta

← #38767179

Subgroups — #38767179

Order 25472.

312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×Dic199⋊C4C211yesmaximal, characteristic
2#27163982C211yesmaximal, characteristic
3#27163743C214yesmaximal, complemented
4#407×C199C211yesmaximal, characteristic
5C23×Dic199C411yescharacteristic
6C23×Dic199C411yescharacteristic
7C2×#15691870—21no—
8C2×Dic199⋊C4—21no—
9C2×Dic199⋊C4—21no—
10C2×Dic199⋊C4—21no—
11C2×Dic199⋊C4—21no—
12C2×Dic199⋊C4C412yes—
13C2×Dic199⋊C4C2212yes—
14C22⋊(C199⋊C8)—21no—
15C22⋊(C199⋊C8)C2212yes—
16C23×C4×C199C2211yescharacteristic
17C2×M16×C199—21no—
18C22⋊C8×C199—21no—
19C22⋊C8×C199C2212yes—
20C22×Dic199—24no—
21C22×Dic199—21no—
22C22×Dic199—21no—
23C22×Dic199—21no—
24C22×Dic199—21no—
25C22×Dic199—42no—
26C22×Dic199C2×C412yes—
27C22×Dic199C2×C412yes—
28#15691870—42no—
29C2×C199⋊C8—22no—
30Dic199⋊C4—22no—
31Dic199⋊C4—22no—
32Dic199⋊C4—22no—
33Dic199⋊C4—22no—
34C24×C199C2×C411yescharacteristic
35C22×C4×C199—42no—
36C22×C4×C199C2×C411yescharacteristic
37C22×C4×C199D411yescharacteristic
38C22×C4×C199D411yescharacteristic
39C22×C4×C199D411yescharacteristic
40C22×C4×C199D411yescharacteristic
41C22×C4×C199C2311yescharacteristic
42M16×C199—42no—
43C2×C8×C199—22no—
44C2×Dic199—24no—
45C2×Dic199—24no—
46C2×Dic199—22no—
47C2×Dic199—22no—
48C2×Dic199—22no—
49C2×Dic199—42no—
50C2×Dic199—42no—
51C2×Dic199—42no—
52C2×Dic199M1614yescomplemented
53C199⋊C8—42no—
54C23×C199—22no—
55C23×C199—22no—
56C23×C199—22no—
57C23×C199C22⋊C411yescharacteristic
58C23×C199C22⋊C411yescharacteristic
59C23×C199C22×C411yescharacteristic
60C2×C4×C199—22no—
61C2×C4×C199—22no—
62C2×C4×C199—41no—
63C2×C4×C199—41no—
64C2×C4×C199—41no—
65C2×C4×C199—41no—
66C2×C4×C199C22⋊C411yescharacteristic
67C2×C4×C199C22⋊C411yescharacteristic
68C2×C4×C199C2×D411yescharacteristic
69C2×C4×C199C2×D411yescharacteristic
70C8×C199—42no—
71C22×C199—28no—
72C22×C199—21no—
73C22×C199—21no—
74C22×C199—21no—
75C22×C199—21no—
76C22×C199—21no—
77C22×C199—21no—
78C22×C199#9912yes—
79C22×C199#10112yes—
80C22×C199C2×C22⋊C411yescharacteristic
81C22×C199C2×M1612yes—
82C4×C199—21no—
83C4×C199—21no—
84C4×C199—21no—
85C4×C199—21no—
86Dic199—24no—
87Dic199—42no—
88C2×C199—22no—
89C2×C199—22no—
90C2×C199—22no—
91C2×C199#40711yescharacteristic
92C2×C199C2×#9911yescharacteristic
93C2×C199C2×#10111yescharacteristic
94C199#146311yescharacteristic, complemented, Sylow
95#1463—1991nomaximal, Sylow
96C22×C4⋊C4—1991no—
97#407—1991no—
98#407D19911yescharacteristic
99#324—1994no—
100C23×C4—1991no—
101C23×C4—1991no—
102C23×C4C2×D19911yescharacteristic
103C2×M16—21no—
104C2×M16—3981no—
105C2×C4⋊C4—3981no—
106C2×C4⋊C4—3981no—
107C2×C4⋊C4—3981no—
108C2×C4⋊C4—3981no—
109C2×C4⋊C4—1992no—
110C2×C4⋊C4—1992no—
111C22⋊C8—21no—
112C22⋊C8—3981no—
113C22⋊C8—1992no—
114C22⋊C8C2×D19912yes—
115C24C4×D19911yescharacteristic
116C22×C4—42no—
117C22×C4—7962no—
118C22×C4—3981no—
119C22×C4—3981no—
120C22×C4—3981no—
121C22×C4—3981no—
122C22×C4—3984no—
123C22×C4—1992no—
124C22×C4—1992no—
125C22×C4C4×D19911yescharacteristic
126C22×C4C22⋊D19911yescharacteristic
127C22×C4C22⋊D19911yescharacteristic
128C22×C4D79611yescharacteristic
129C22×C4D79611yescharacteristic
130C22×C4C22×D19911yescharacteristic
131M16—42no—
132M16—7962no—
133C2×C8—22no—
134C2×C8—3982no—
135C4⋊C4—3982no—
136C4⋊C4—3982no—
137C4⋊C4—3982no—
138C4⋊C4—3982no—
139C23—22no—
140C23—22no—
141C23—22no—
142C23(C2×D199)⋊C411yescharacteristic
143C23(C2×D199)⋊C411yescharacteristic
144C23C2×C4×D19911yescharacteristic
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—7962no—
152C2×C4—7962no—
153C2×C4—7962no—
154C2×C4—3982no—
155C2×C4—3984no—
156C2×C4—3984no—
157C2×C4—3982no—
158C2×C4—3982no—
159C2×C4—1994no—
160C2×C4(C2×D199)⋊C411yescharacteristic
161C2×C4(C2×D199)⋊C411yescharacteristic
162C2×C4C2×C22⋊D19911yescharacteristic
163C2×C4C2×D79611yescharacteristic
164C8—42no—
165C8—7962no—
166C22—28no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22#2026386912yes—
174C22#2026387312yes—
175C22C2×(C2×D199)⋊C411yescharacteristic
176C22M16×D19912yes—
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—7962no—
182C4—3984no—
183C2—22no—
184C2—22no—
185C2—22no—
186C2#2716398111yescharacteristic
187C2C2×#2026386911yescharacteristic
188C2C2×#2026387311yescharacteristic
subgroupG/H
centerC22C2×(C2×D199)⋊C4
commutatorC23×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#407×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC24×C199C2×C4
cosocleC22×C4×C199C23
hypercenter#407D199
hypocenterC199#1463
LCSG ▷ C23×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #27163743C2semidirect
52. C2×Dic199M16semidirect
94. C199#1463semidirect

Maximal subgroups

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

subgroupindex
C22×Dic199⋊C42
#271639822
#271637432
#407×C1992
#1463199