Finite Group Databasebeta

← #38770541

Subgroups — #38770541

Order 25472.

262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 65 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#27164582C211yesmaximal, characteristic
2#27164002C211yesmaximal, characteristic, complemented
3#27163814C214yesmaximal, complemented
4#413×C199C211yesmaximal, characteristic, complemented
5C22×D796C411yescharacteristic
6C2×#15691870—21no—
7#20263951C412yes—
8#20263944C2212yes—
9#20263929—21no—
10#20263929—21no—
11#20263923—21no—
12#20263923—21no—
13#20263914C411yescharacteristic
14#20263874C2212yescomplemented
15#20263872—21no—
16C2×#41×C199C2211yescharacteristic
17C2×M16×C199—21no—
18#101×C199C2212yescomplemented
19#100×C199—21no—
20C23×D199—21no—
21C2×D796—21no—
22C2×D796—41no—
23C2×D796—41no—
24C2×D796C2×C412yes—
25C2×C22⋊D199—22no—
26C2×C22⋊D199—22no—
27#15691870—22no—
28#15691870—41no—
29C2×C199⋊C8—41no—
30C4⋊Dic199—21no—
31C22⋊Dic199—21no—
32(C2×D199)⋊C4—22no—
33(C2×D199)⋊C4—22no—
34C4×Dic199C2×C412yes—
35#41×C199—41no—
36#41×C199—41no—
37C2×Q8×C199C2311yescharacteristic
38C2×D4×C199C2×C411yescharacteristic
39C2×D4×C199D411yescharacteristic
40C2×D4×C199D411yescharacteristic
41C22×C4×C199C2×C411yescharacteristic
42C22×C4×C199D411yescharacteristic
43C22×C4×C199D411yescharacteristic
44M16×C199—22no—
45M16×C199—41no—
46C2×C8×C199—41no—
47C22×D199—22no—
48C22×D199—42no—
49C22×D199—82no—
50D796—42no—
51D796—41no—
52D796—41no—
53C22⋊D199—82no—
54C22⋊D199—82no—
55C2×Dic199—22no—
56C199⋊C8—42no—
57C23×C199C22⋊C411yescharacteristic
58C23×C199C22⋊C411yescharacteristic
59C23×C199C22⋊C411yescharacteristic
60Q8×C199—41no—
61D4×C199—41no—
62D4×C199—41no—
63D4×C199—41no—
64C2×C4×C199—21no—
65C2×C4×C199—21no—
66C2×C4×C199—21no—
67C2×C4×C199—21no—
68C2×C4×C199—21no—
69C2×C4×C199—21no—
70C2×C4×C199C22⋊C411yescharacteristic
71C2×C4×C199C22×C411yescharacteristic
72C2×C4×C199C2×D411yescharacteristic
73C2×C4×C199C2×D411yescharacteristic
74C8×C199—42no—
75C22×C199—21no—
76C22×C199—21no—
77C22×C199—21no—
78C22×C199—41no—
79C22×C199—41no—
80C22×C199—41no—
81C22×C199C2×C22⋊C411yescharacteristic
82C2×D199—42no—
83C2×D199—42no—
84C2×D199—42no—
85C2×D199—84no—
86C4×C199—21no—
87C4×C199—21no—
88C4×C199—21no—
89C4×C199#9911yescharacteristic
90C4×C199#9911yescharacteristic
91Dic199—42no—
92C2×C199—21no—
93C2×C199—41no—
94C2×C199—41no—
95C2×C199—41no—
96C2×C199C2×#9911yescharacteristic
97D199—82no—
98C199#213411yescharacteristic, complemented, Sylow
99#2134—1991nomaximal, Sylow
100#535—1991no—
101#413—1991no—
102#413D19911yescharacteristic, complemented
103#355—1994no—
104C2×#41C2×D19911yescharacteristic
105C22×D4—1991no—
106C2×M16—21no—
107C2×M16—3981no—
108#127—1992no—
109#124—1992no—
110#121—3981no—
111#121—3981no—
112#120—3981no—
113#120—3981no—
114#117—1991no—
115#101—1992no—
116#101C2×D19912yescomplemented
117#100—21no—
118#100—3981no—
119C24—3981no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D19911yescharacteristic
123C2×D4—7961no—
124C2×D4—7961no—
125C2×D4—3982no—
126C2×D4—3982no—
127C2×D4—3981no—
128C2×D4—1992no—
129C2×D4C4×D19911yescharacteristic
130C2×D4C22⋊D19911yescharacteristic
131C2×D4D79611yescharacteristic
132C22×C4C4×D19911yescharacteristic
133C22×C4C22⋊D19911yescharacteristic
134C22×C4D79611yescharacteristic
135M16—22no—
136M16—41no—
137M16—7961no—
138M16—3982no—
139C2×C8—41no—
140C2×C8—7961no—
141C4⋊C4—3981no—
142C22⋊C4—3981no—
143C22⋊C4—3982no—
144C22⋊C4—3982no—
145C42—1992no—
146C23—7962no—
147C23—15922no—
148C23—3982no—
149C23(C2×D199)⋊C411yescharacteristic
150C23(C2×D199)⋊C411yescharacteristic
151C23(C2×D199)⋊C411yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—7962no—
157D4—7961no—
158D4—7961no—
159D4—15922no—
160D4—15922no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—3982no—
168C2×C4(C2×D199)⋊C411yescharacteristic
169C2×C4C2×C4×D19911yescharacteristic
170C2×C4C2×C22⋊D19911yescharacteristic
171C2×C4C2×D79611yescharacteristic
172C8—42no—
173C8—7962no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—7962no—
181C22—7962no—
182C22—7962no—
183C22—15924no—
184C22C2×(C2×D199)⋊C411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—7962no—
189C4#2026386911yescharacteristic
190C4#2026386911yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—15922no—
196C2C2×#2026386911yescharacteristic
subgroupG/H
centerC2C2×#20263869
commutatorC2×C4×C199C22×C4
FrattiniC2×Q8C22×D199
Fitting#413×C199C2
socleC2×C199C2×#99
prime radical#27164582C2
cosocleC2×Q8×C199C23
hypercenter#413D199
hypocenterC199#2134
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #27164002C2semidirect
3. #27163814C2semidirect
4. #413×C199C2semidirect
14. #20263874C22semidirect
18. #101×C199C22semidirect
98. C199#2134semidirect
102. #413D199semidirect
116. #101C2×D199semidirect

Maximal subgroups

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

subgroupindex
#271645822
#271640022
#271638142
#413×C1992
#2134199