Finite Group Databasebeta

← #38770796

Subgroups — #38770796

Order 25472.

226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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#27164453C212yesmaximal, complemented
2#27164271C211yesmaximal, characteristic, complemented
3#27163828C212yesmaximal, complemented
4#27163800C211yesmaximal, characteristic, complemented
5#575×C199C211yesmaximal, characteristic, complemented
6C2×D1592C2211yescharacteristic, complemented
7#20263929—21no—
8#20263898—22no—
9#20263896—22no—
10#20263895C2212yescomplemented
11#20263887C2211yescharacteristic, complemented
12#20263877—21no—
13C2×#41×C199—21no—
14#137×C199—22no—
15AGL(1,ℤ/8)×C199—22no—
16#135×C199—21no—
17#135×C199C2212yes—
18C2×M16×C199C2211yescharacteristic
19C2×D796—21no—
20C2×C22⋊D199—41no—
21D1592—22no—
22C4⋊Dic199—21no—
23(C2×D199)⋊C4—41no—
24C199⋊C16—22no—
25#41×C199—22no—
26#41×C199—22no—
27#41×C199—41no—
28#41×C199—41no—
29C2×Q8×C199—21no—
30C2×D4×C199—21no—
31C2×D4×C199—41no—
32C22×C4×C199—41no—
33C22×C4×C199D411yescharacteristic
34Q16×C199—21no—
35Q16×C199D412yescomplemented
36SD16×C199—22no—
37SD16×C199—22no—
38D8×C199—21no—
39D8×C199D412yescomplemented
40M16×C199—22no—
41C2×C8×C199D411yescharacteristic
42C2×C8×C199C2311yescharacteristic
43C22×D199—41no—
44D796—41no—
45D796—41no—
46C22⋊D199—82no—
47C2×Dic199—41no—
48C23×C199—41no—
49C23×C199D811yescharacteristic
50Q8×C199—22no—
51Q8×C199—41no—
52D4×C199—22no—
53D4×C199—41no—
54D4×C199—42no—
55D4×C199—42no—
56C2×C4×C199—21no—
57C2×C4×C199—21no—
58C2×C4×C199—42no—
59C2×C4×C199—41no—
60C2×C4×C199—42no—
61C2×C4×C199D811yescharacteristic
62C2×C4×C199C2×D411yescharacteristic
63C8×C199—21no—
64C8×C199C2×D412yes—
65C22×C199—21no—
66C22×C199—41no—
67C22×C199—42no—
68C22×C199—82no—
69C22×C199C2×D811yescharacteristic
70C2×D199—81no—
71C2×D199—81no—
72C2×D199—81no—
73C4×C199—21no—
74C4×C199—42no—
75C4×C199#12011yescharacteristic
76C4×C199AGL(1,ℤ/8)11yescharacteristic
77Dic199—81no—
78C2×C199—21no—
79C2×C199—41no—
80C2×C199—82no—
81C2×C199#44711yescharacteristic
82D199—161no—
83C199#219011yescharacteristic, complemented, Sylow
84#2190—1991nomaximal, Sylow
85#575D19911yescharacteristic, complemented
86#509—1992no—
87#469—1991no—
88#360—1992no—
89#349—1991no—
90C2×#41—21no—
91#137—22no—
92AGL(1,ℤ/8)—22no—
93#135—21no—
94#135C2×D19912yes—
95C2×D8—1991no—
96C2×M16C2×D19911yescharacteristic
97#121—3981no—
98SD32—3982no—
99D16—3982no—
100M32—1992no—
101#106—1991no—
102#102—3981no—
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—7961no—
111C2×D4—3981no—
112C22×C4—41no—
113C22×C4C22⋊D19911yescharacteristic
114Q16—21no—
115Q16C22⋊D19912yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—3982no—
120D8C22⋊D19912yescomplemented
121M16—22no—
122C2×C8C22⋊D19911yescharacteristic
123C2×C8C22×D19911yescharacteristic
124C4⋊C4—3981no—
125C22⋊C4—7961no—
126C16—3982no—
127C23—41no—
128C23—7961no—
129C23#1569187111yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—7961no—
137D4—7961no—
138D4—15922no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—7961no—
145C2×C4#1569187111yescharacteristic
146C2×C4C2×C22⋊D19911yescharacteristic
147C8—21no—
148C8C2×C22⋊D19912yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—82no—
153C22—15921no—
154C22—15921no—
155C22—15921no—
156C22C2×#1569187111yescharacteristic
157C4—21no—
158C4—42no—
159C4—15921no—
160C4#2026392411yescharacteristic
161C4#2026398111yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—31841no—
166C2#2716415211yescharacteristic
subgroupG/H
centerC2#27164152
commutator, cosocleC2×C8×C199C23
FrattiniC2×C8C22×D199
Fitting#575×C199C2
socleC2×C199#447
hypercenter#575D199
hypocenterC199#2190
LCSG ▷ C2×C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #27164453C2semidirect
2. #27164271C2semidirect
3. #27163828C2semidirect
4. #27163800C2semidirect
5. #575×C199C2semidirect
6. C2×D1592C22semidirect
10. #20263895C22semidirect
11. #20263887C22semidirect
35. Q16×C199D4semidirect
39. D8×C199D4semidirect
83. C199#2190semidirect
85. #575D199semidirect
115. Q16C22⋊D199semidirect
120. D8C22⋊D199semidirect

Maximal subgroups

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

subgroupindex
#271644532
#271642712
#271638282
#271638002
#575×C1992
#2190199