Finite Group Databasebeta

← #16821405

Subgroups — #16821405

Order 3712.

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

normal subgroups only

This group has 266 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
1C2×D8×D29C211yesmaximal, characteristic, complemented
2C2×D464C211yesmaximal, characteristic, complemented
3C2×#11745174C211yesmaximal, characteristic, complemented
4#14271400C211yesmaximal, characteristic, complemented
5#14270963C211yesmaximal, characteristic, complemented
6#14270942C211yesmaximal, characteristic, complemented
7C29×#357C211yesmaximal, characteristic, complemented
8C2×D4×D29—21no—
9C2×D8×C29C2211yescharacteristic
10C2×#90782—21no—
11D8×D29—22no—
12D8×D29—22no—
13C2×D232C2211yescharacteristic
14C2×D232C2211yescharacteristic, complemented
15C2×C8×D29C2211yescharacteristic
16#11745257—21no—
17C2×C16×C29C2211yescharacteristic, complemented
18C29×#107C2211yescharacteristic, complemented
19#11745174—22no—
20C2×#90768C2211yescharacteristic, complemented
21#11745157—21no—
22D464—22no—
23C23×D29—41no—
24C2×D4×C29—21no—
25C2×C22⋊D29—41no—
26D4×D29—24no—
27D4×D29—42no—
28C2×D116—21no—
29C2×D116—21no—
30C2×D116—41no—
31C2×C4×D29D411yescharacteristic
32D8×C29—21no—
33D8×C29D412yescomplemented
34C2×C8×C29C2311yescharacteristic
35C4⋊C4×C29—21no—
36#90782—24no—
37#90781—41no—
38C2×#6597D411yescharacteristic
39D232—21no—
40D232—21no—
41D232—21no—
42D232D412yescomplemented
43C8×D29—21no—
44C8×D29—21no—
45C16×C29—21no—
46#90768—21no—
47C23×C29—41no—
48C22×D29—44no—
49C22×D29—41no—
50C22×D29—41no—
51C22×D29—82no—
52C22×D29—82no—
53C22×D29D811yescharacteristic
54D4×C29—22no—
55D4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29C2×D411yescharacteristic
58C22⋊D29—44no—
59C2×Dic29D811yescharacteristic
60D116—22no—
61D116—41no—
62D116—41no—
63D116—41no—
64D116—82no—
65C4×D29—21no—
66C4×D29—21no—
67C8×C29C2×D411yescharacteristic
68C8×C29C2×D411yescharacteristic
69#6597—21no—
70#2184—291nomaximal, Sylow
71C22×C29—42no—
72C22×C29—81no—
73C22×C29—81no—
74C22×C29C2×D811yescharacteristic
75C2×D29—21no—
76C2×D29—21no—
77C2×D29—42no—
78C2×D29—88no—
79C2×D29—81no—
80C2×D29—81no—
81C2×D29—81no—
82C2×D29—81no—
83C2×D29—81no—
84C2×D29D1612yescomplemented
85C4×C29—81no—
86C4×C29#12011yescharacteristic
87C4×C29AGL(1,ℤ/8)11yescharacteristic
88Dic29—21no—
89C22×D8—291no—
90C2×D16—291no—
91C2×D16—291no—
92#466—291no—
93#357—291no—
94#357D2911yescharacteristic, complemented
95C22⋊C16—291no—
96C2×C29—82no—
97C2×C29#44711yescharacteristic
98C2×C29C2×D1611yescharacteristic
99C2×C29#50911yescharacteristic
100D29—22no—
101D29—82no—
102D29—161no—
103C22×D4—581no—
104C2×D8—291no—
105C2×D8—291no—
106C2×D8—581no—
107C2×D8—582no—
108C2×D8—582no—
109C2×D8C2×D2911yescharacteristic
110C22×C8—291no—
111#121—581no—
112D16—582no—
113D16—582no—
114C2×C16—291no—
115C2×C16C2×D2911yescharacteristic, complemented
116#107C2×D2911yescharacteristic, complemented
117#102—581no—
118C29#218411yescharacteristic, complemented, Sylow
119C24—1161no—
120C2×D4—21no—
121C2×D4—584no—
122C2×D4—581no—
123C2×D4—581no—
124C2×D4—1161no—
125C2×D4—1161no—
126C2×D4—1162no—
127C22×C4—291no—
128D8—21no—
129D8—292no—
130D8—584no—
131D8—581no—
132D8—581no—
133D8—581no—
134D8D11612yescomplemented
135C2×C8—291no—
136C2×C8—581no—
137C2×C8—581no—
138C2×C8C22×D2911yescharacteristic
139C4⋊C4—21no—
140C22⋊C4—1161no—
141C16—21no—
142C16—581no—
143C23—41no—
144C23—291no—
145C23—1164no—
146C23—1161no—
147C23—1161no—
148C23—2322no—
149C23—2322no—
150D4—22no—
151D4—41no—
152D4—582no—
153D4—1164no—
154D4—1161no—
155D4—1161no—
156D4—1161no—
157D4—2322no—
158C2×C4—41no—
159C2×C4—291no—
160C2×C4—581no—
161C2×C4—581no—
162C2×C4D4×D2911yescharacteristic
163C8—581no—
164C8C2×D11611yescharacteristic
165C8D4×D2911yescharacteristic
166C22—42no—
167C22—81no—
168C22—81no—
169C22—292no—
170C22—581no—
171C22—581no—
172C22—1162no—
173C22—2328no—
174C22—2321no—
175C22—2321no—
176C22—2321no—
177C22—2321no—
178C22—2321no—
179C22D8×D2911yescharacteristic
180C4—81no—
181C4—581no—
182C4#1174524411yescharacteristic
183C4#1174527611yescharacteristic
184C2—82no—
185C2—582no—
186C2—4641no—
187C2—2322no—
188C2#1427129811yescharacteristic
189C2D16×D2911yescharacteristic
190C2#1427160011yescharacteristic
subgroupG/H
centerC22D8×D29
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#357C2
socleC22×C29C2×D8
hypercenter#357D29
hypocenterC29#2184
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. C2×D8×D29C2semidirect
2. C2×D464C2semidirect
3. C2×#11745174C2semidirect
4. #14271400C2semidirect
5. #14270963C2semidirect
6. #14270942C2semidirect
7. C29×#357C2semidirect
14. C2×D232C22semidirect
17. C2×C16×C29C22semidirect
18. C29×#107C22semidirect
20. C2×#90768C22semidirect
33. D8×C29D4semidirect
42. D232D4semidirect
84. C2×D29D16semidirect
94. #357D29semidirect
115. C2×C16C2×D29semidirect
116. #107C2×D29semidirect
118. C29#2184semidirect
134. D8D116semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D292
C2×D4642
C2×#117451742
#142714002
#142709632
#142709422
C29×#3572
#218429