Finite Group Databasebeta

← #38768923

Subgroups — #38768923

Order 25472.

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

normal subgroups only

This group has 504 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
1C2×C22⋊C4×D199C211yesmaximal, characteristic
2#27163873C212yesmaximal
3#27163785C211yesmaximal, characteristic, complemented
4#27163784C212yesmaximal, complemented
5#342×C199C211yesmaximal, characteristic, complemented
6C24×D199C2211yescharacteristic
7C22×C4×D199C412yescomplemented
8C2×C22⋊Dic199C2212yes—
9C2×C22⋊Dic199C2211yescharacteristic
10C2×(C2×D199)⋊C4—24no—
11C2×(C2×D199)⋊C4C412yescomplemented
12C22⋊C4×D199—24no—
13C2×C22⋊C4×C199C2212yes—
14C2×C22⋊C4×C199C2211yescharacteristic
15C23×D199—21no—
16C23×D199—22no—
17C23×D199—21no—
18C23×D199—44no—
19C23×D199C2×C411yescharacteristic
20C23×D199C2×C411yescharacteristic
21C23×D199D414yes—
22C22×Dic199—22no—
23C22×Dic199C2×C412yes—
24C2×C4×D199—22no—
25C2×C4×D199—22no—
26C2×C4×D199—44no—
27C22⋊Dic199—22no—
28C22⋊Dic199—22no—
29C22⋊Dic199—22no—
30(C2×D199)⋊C4—24no—
31(C2×D199)⋊C4—48no—
32C24×C199C2311yescharacteristic
33C22×C4×C199—22no—
34C22×C4×C199C2×C412yes—
35C22⋊C4×C199—22no—
36C22⋊C4×C199—22no—
37C22⋊C4×C199—22no—
38C22×D199—21no—
39C22×D199—21no—
40C22×D199—24no—
41C22×D199—21no—
42C22×D199—21no—
43C22×D199—24no—
44C22×D199—24no—
45C22×D199—28no—
46C22×D199—42no—
47C22×D199—44no—
48C22×D199—44no—
49C22×D199—48no—
50C22×D199—44no—
51C22×D199C22⋊C412yes—
52C22×D199C22⋊C412yes—
53C2×Dic199—22no—
54C2×Dic199—42no—
55C2×Dic199—44no—
56C2×Dic199—42no—
57C4×D199—44no—
58C4×D199—44no—
59C23×C199—42no—
60C23×C199C22×C411yescharacteristic
61C23×C199C2×D412yes—
62C23×C199#4111yescharacteristic
63C23×C199#4112yes—
64C23×C199#4111yescharacteristic
65C2×C4×C199—22no—
66C2×C4×C199—42no—
67C2×C4×C199—44no—
68C2×C4×C199—42no—
69C22×C199—22no—
70C22×C199—24no—
71C22×C199—41no—
72C22×C199—42no—
73C22×C199—41no—
74C22×C199C2×C22⋊C411yescharacteristic
75C22×C199#11711yescharacteristic
76C22×C199#11711yescharacteristic
77C22×C199#12312yes—
78C22×C199#12312yes—
79C2×D199—24no—
80C2×D199—24no—
81C2×D199—22no—
82C2×D199—22no—
83C2×D199—22no—
84C2×D199—24no—
85C2×D199—48no—
86C2×D199—48no—
87C2×D199—42no—
88C2×D199—42no—
89C2×D199#9914yes—
90C4×C199—42no—
91C4×C199—82no—
92Dic199—42no—
93Dic199—82no—
94C2×C199—22no—
95C2×C199—22no—
96C2×C199—21no—
97C2×C199—21no—
98C2×C199#38111yescharacteristic
99C2×C199C2×#9912yes—
100D199—24no—
101D199—42no—
102C199#181911yescharacteristic, complemented, Sylow
103#1819—1991nomaximal, Sylow
104C22×C22⋊C4—1991no—
105#379—1992no—
106#342—1992no—
107#342—1991no—
108#342D19911yescharacteristic, complemented
109C25—1991no—
110C23×C4—1992no—
111C2×C22⋊C4—3984no—
112C2×C22⋊C4—3984no—
113C2×C22⋊C4—1992no—
114C2×C22⋊C4—1991no—
115C2×C22⋊C4—1992no—
116C2×C22⋊C4C2×D19912yes—
117C2×C22⋊C4C2×D19911yescharacteristic
118C24—7964no—
119C24—3981no—
120C24—3982no—
121C24—3981no—
122C24—1991no—
123C24—1994no—
124C24—1991no—
125C24C22×D19911yescharacteristic
126C22×C4—22no—
127C22×C4—7964no—
128C22×C4—3982no—
129C22×C4—3982no—
130C22×C4—3982no—
131C22×C4—1992no—
132C22×C4C4×D19912yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—7968no—
137C22⋊C4—3984no—
138C22⋊C4—3982no—
139C22⋊C4—3982no—
140C22⋊C4—3982no—
141C23—42no—
142C23—7962no—
143C23—7964no—
144C23—7964no—
145C23—7968no—
146C23—7964no—
147C23—3988no—
148C23—3984no—
149C23—3984no—
150C23—3984no—
151C23—3981no—
152C23—3981no—
153C23—3981no—
154C23—3981no—
155C23—1992no—
156C23—1992no—
157C23C2×C4×D19911yescharacteristic
158C23D4×D19912yes—
159C23#1569188511yescharacteristic
160C23#1569188612yes—
161C23#1569188711yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—7964no—
167C2×C4—7964no—
168C2×C4—7962no—
169C2×C4—7964no—
170C2×C4—7962no—
171C2×C4—3982no—
172C22—22no—
173C22—24no—
174C22—41no—
175C22—42no—
176C22—41no—
177C22—7962no—
178C22—7962no—
179C22—7968no—
180C22—7968no—
181C22—3984no—
182C22—3984no—
183C22—3984no—
184C22—3982no—
185C22—3982no—
186C22—3982no—
187C22—1994no—
188C22C22⋊C4×D19911yescharacteristic
189C22#2026391211yescharacteristic
190C22#2026391311yescharacteristic
191C22#2026393712yes—
192C22#2026394012yes—
193C4—42no—
194C4—82no—
195C4—7962no—
196C4—15922no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—7962no—
202C2—3984no—
203C2#2716388011yescharacteristic
204C2#99×D19912yes—
subgroupG/H
centerC22C22⋊C4×D199
commutatorC23×C199C22×C4
FrattiniC24C22×D199
Fitting#342×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC24×D199C22
cosocleC24×C199C23
hypercenter#342D199
hypocenterC199#1819
LCSG ▷ C23×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #27163785C2semidirect
4. #27163784C2semidirect
5. #342×C199C2semidirect
7. C22×C4×D199C4semidirect
11. C2×(C2×D199)⋊C4C4semidirect
102. C199#1819semidirect
108. #342D199semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D1992
#271638732
#271637852
#271637842
#342×C1992
#1819199