Finite Group Databasebeta

← #38769309

Subgroups — #38769309

Order 25472.

378 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 97 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×#20263914C211yesmaximal, characteristic, complemented
2C2×#20263870C212yesmaximal
3#27163881C211yesmaximal, characteristic, complemented
4#27163785C212yesmaximal, complemented
5C2×#123×C199C211yesmaximal, characteristic
6#20263914—24no—
7C2×C4⋊Dic199—21no—
8C2×C22⋊Dic199C2212yes—
9C2×C22⋊Dic199C2212yes—
10C2×C4×Dic199—21no—
11#20263870—24no—
12C199⋊#95—22no—
13C22×D4×C199C2211yescharacteristic
14C23×C4×C199C2211yescharacteristic
15#123×C199—22no—
16#123×C199—21no—
17#123×C199—21no—
18C2×C4⋊C4×C199C412yescomplemented
19C2×C22⋊C4×C199C412yescomplemented
20C2×C22⋊C4×C199C2211yescharacteristic
21C22×Dic199—22no—
22C22×Dic199—22no—
23C4⋊Dic199—24no—
24C22⋊Dic199—22no—
25C22⋊Dic199—22no—
26C22⋊Dic199—22no—
27C22⋊Dic199D414yes—
28C4×Dic199—24no—
29C24×C199C2×C411yescharacteristic
30C24×C199C2311yescharacteristic
31C2×D4×C199—21no—
32C2×D4×C199—21no—
33C2×D4×C199—22no—
34C2×D4×C199—22no—
35C22×C4×C199—22no—
36C22×C4×C199—22no—
37C22×C4×C199C2×C411yescharacteristic
38C22×C4×C199C2×C412yes—
39C22×C4×C199C2×C412yes—
40C22×C4×C199D412yes—
41C22×C4×C199D411yescharacteristic
42C22×C4×C199D411yescharacteristic
43C4⋊C4×C199—22no—
44C4⋊C4×C199—22no—
45C22⋊C4×C199—21no—
46C22⋊C4×C199—21no—
47C22⋊C4×C199—22no—
48C22⋊C4×C199—22no—
49C2×Dic199—24no—
50C2×Dic199—44no—
51C2×Dic199—44no—
52C2×Dic199—42no—
53C23×C199—21no—
54C23×C199—22no—
55C23×C199—42no—
56C23×C199—42no—
57C23×C199C22×C411yescharacteristic
58C23×C199C2×D412yes—
59C23×C199C2×D411yescharacteristic
60C23×C199C2×D411yescharacteristic
61C23×C199#4112yes—
62D4×C199—41no—
63D4×C199—42no—
64D4×C199—41no—
65C2×C4×C199—24no—
66C2×C4×C199—21no—
67C2×C4×C199—21no—
68C2×C4×C199—24no—
69C2×C4×C199—21no—
70C2×C4×C199—21no—
71C2×C4×C199—22no—
72C2×C4×C199—21no—
73C2×C4×C199—22no—
74C2×C4×C199—42no—
75C2×C4×C199C22⋊C412yes—
76C2×C4×C199C22⋊C412yes—
77C22×C199—22no—
78C22×C199—22no—
79C22×C199—22no—
80C22×C199—42no—
81C22×C199—42no—
82C22×C199—41no—
83C22×C199—42no—
84C22×C199—82no—
85C22×C199C2×C22⋊C411yescharacteristic
86C22×C199C4×D412yes—
87C22×C199#12011yescharacteristic
88C22×C199#12112yes—
89C22×C199#12311yescharacteristic
90C4×C199—22no—
91C4×C199—22no—
92C4×C199—41no—
93C4×C199—42no—
94Dic199—44no—
95Dic199—82no—
96C2×C199—21no—
97C2×C199—22no—
98C2×C199—22no—
99C2×C199—21no—
100C2×C199—81no—
101C2×C199#38611yescharacteristic
102C2×C199#41012yes—
103C199#189911yescharacteristic, complemented, Sylow
104#1899—1991nomaximal, Sylow
105C2×#123D19911yescharacteristic
106C2×#117—1991no—
107C2×#99—1992no—
108#381—1991no—
109#342—1992no—
110C22×D4C2×D19911yescharacteristic
111C23×C4C2×D19911yescharacteristic
112#123—22no—
113#123—21no—
114#123—21no—
115#117—3984no—
116C2×C4⋊C4—3981no—
117C2×C4⋊C4Dic19912yescomplemented
118C2×C22⋊C4—1992no—
119C2×C22⋊C4—1992no—
120C2×C22⋊C4Dic19912yescomplemented
121C2×C22⋊C4C2×D19911yescharacteristic
122C2×C42—3981no—
123#99—3984no—
124#95—3982no—
125C24C2×Dic19911yescharacteristic
126C24C22×D19911yescharacteristic
127C2×D4—22no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—3982no—
134C22×C4—3982no—
135C22×C4C2×Dic19911yescharacteristic
136C22×C4C2×Dic19912yes—
137C22×C4C2×Dic19912yes—
138C22×C4C22⋊D19912yes—
139C22×C4C22⋊D19911yescharacteristic
140C22×C4C22⋊D19911yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—3984no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—3982no—
149C22⋊C4—3982no—
150C22⋊C4—3982no—
151C22⋊C4—1994no—
152C42—3984no—
153C23—21no—
154C23—22no—
155C23—42no—
156C23—42no—
157C23C22×Dic19911yescharacteristic
158C23D4×D19912yes—
159C23C2×C22⋊D19911yescharacteristic
160C23C2×C22⋊D19911yescharacteristic
161C23#1569188512yes—
162D4—41no—
163D4—41no—
164D4—42no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—7964no—
176C2×C4—7964no—
177C2×C4—7962no—
178C2×C4—3984no—
179C2×C4C22⋊Dic19912yes—
180C2×C4C22⋊Dic19912yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—41no—
188C22—82no—
189C22C2×C22⋊Dic19911yescharacteristic
190C22D4×Dic19912yes—
191C22#2026392311yescharacteristic
192C22#2026392712yes—
193C22#2026393611yescharacteristic
194C4—22no—
195C4—22no—
196C4—42no—
197C4—41no—
198C4—7964no—
199C4—15922no—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2—81no—
205C2#2716389811yescharacteristic
206C2#2716399212yes—
subgroupG/H
centerC22C2×C22⋊Dic199
commutatorC23×C199C22×C4
FrattiniC24C22×D199
FittingC2×#123×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC22×D4×C199C22
cosocleC24×C199C23
hypercenterC2×#123D199
hypocenterC199#1899
LCSG ▷ C23×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#20263914C2semidirect
3. #27163881C2semidirect
4. #27163785C2semidirect
18. C2×C4⋊C4×C199C4semidirect
19. C2×C22⋊C4×C199C4semidirect
103. C199#1899semidirect
117. C2×C4⋊C4Dic199semidirect
120. C2×C22⋊C4Dic199semidirect

Maximal subgroups

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

subgroupindex
C2×#202639142
C2×#202638702
#271638812
#271637852
C2×#123×C1992
#1899199