Finite Group Databasebeta

← #16821182

Subgroups — #16821182

Order 3712.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271731C211yesmaximal, characteristic
2#14271146C212yesmaximal, complemented
3#14270960C211yesmaximal, characteristic, complemented
4#14270959C212yesmaximal, complemented
5C29×#355C211yesmaximal, characteristic, complemented
6C2×#90809C2211yescharacteristic
7C2×D4×D29C411yescharacteristic
8C29×#124C2211yescharacteristic
9#11745309C2211yescharacteristic
10#11745302C411yescharacteristic
11M16×D29—22no—
12#11745246—22no—
13#11745244—22no—
14#11745236C411yescharacteristic
15#11745234C411yescharacteristic
16C29×#101C2212yescomplemented
17#11745184C2212yescomplemented
18#11745171—22no—
19C23×D29—21no—
20C2×Q8×C29C2311yescharacteristic
21C2×D4×C29C2×C411yescharacteristic
22C2×C22⋊D29—22no—
23C2×C22⋊D29—21no—
24#90809—42no—
25D4×D29—42no—
26C2×D116—22no—
27C2×D116C2×C411yescharacteristic
28C2×D116C2×C411yescharacteristic
29C2×D116D412yes—
30C2×C4×D29C2×C411yescharacteristic
31C2×C4×D29D412yes—
32M16×C29—22no—
33C22⋊C4×C29—22no—
34C42×C29C2×C411yescharacteristic
35#90781—21no—
36#90781—22no—
37#90779—21no—
38C4×Dic29C2×C411yescharacteristic
39#90777—22no—
40#90772—42no—
41C8×D29—42no—
42C23×C29—21no—
43C22×D29—21no—
44C22×D29—42no—
45C22×D29—82no—
46C22×D29C22⋊C411yescharacteristic
47C22×D29C22⋊C412yes—
48Q8×C29—41no—
49D4×C29—41no—
50C2×C4×C29—21no—
51C2×C4×C29C22×C411yescharacteristic
52C2×C4×C29C2×D412yes—
53C22⋊D29—42no—
54C22⋊D29—82no—
55C2×Dic29—21no—
56C2×Dic29C22⋊C411yescharacteristic
57D116—41no—
58D116—42no—
59D116—41no—
60D116—82no—
61C4×D29—22no—
62C4×D29—22no—
63C4×D29—22no—
64C8×C29—42no—
65#6597—42no—
66#2134—291nomaximal, Sylow
67C22×C29—42no—
68C22×C29—41no—
69C22×C29C2×C22⋊C411yescharacteristic
70C2×D29—21no—
71C2×D29—22no—
72C2×D29—42no—
73C2×D29—41no—
74C2×D29—42no—
75C2×D29—41no—
76C2×D29—84no—
77C4×C29—22no—
78C4×C29—21no—
79C4×C29—41no—
80Dic29—41no—
81Dic29#9912yes—
82#535—291no—
83#413—292no—
84#355—291no—
85#355—292no—
86#355D2911yescharacteristic, complemented
87C2×C29—21no—
88C2×C29—81no—
89C2×C29C2×#9911yescharacteristic
90D29—42no—
91D29—41no—
92D29—81no—
93C2×#41—291no—
94C22×D4—291no—
95C2×M16—582no—
96#127—291no—
97#127—291no—
98#124—291no—
99#124C2×D2911yescharacteristic
100#121—582no—
101#120—582no—
102#117—291no—
103#101—292no—
104#101C2×D2912yescomplemented
105#100—582no—
106C29#213411yescharacteristic, complemented, Sylow
107C24—581no—
108#41—1162no—
109C2×Q8C22×D2911yescharacteristic
110C2×D4—291no—
111C2×D4—291no—
112C2×D4—292no—
113C2×D4—582no—
114C2×D4—581no—
115C2×D4—582no—
116C2×D4—1162no—
117C2×D4C4×D2911yescharacteristic
118C22×C4—291no—
119C22×C4—292no—
120M16—22no—
121M16—582no—
122M16—1162no—
123C2×C8—1162no—
124C4⋊C4—581no—
125C22⋊C4—22no—
126C22⋊C4—581no—
127C22⋊C4—582no—
128C42—291no—
129C42C4×D2911yescharacteristic
130C23—21no—
131C23—291no—
132C23—292no—
133C23—581no—
134C23—1162no—
135C23—2322no—
136Q8—41no—
137D4—41no—
138D4—1162no—
139D4—1161no—
140D4—1161no—
141D4—1162no—
142D4—2322no—
143D4—2322no—
144C2×C4—21no—
145C2×C4—291no—
146C2×C4—582no—
147C2×C4—582no—
148C2×C4—582no—
149C2×C4—581no—
150C2×C4C2×C4×D2911yescharacteristic
151C2×C4D4×D2912yes—
152C8—42no—
153C8—1162no—
154C22—42no—
155C22—41no—
156C22—581no—
157C22—582no—
158C22—1162no—
159C22—1161no—
160C22—1162no—
161C22—1161no—
162C22—2324no—
163C22C22⋊C4×D2911yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—292no—
168C4—1161no—
169C2—21no—
170C2—81no—
171C2—1161no—
172C2—1162no—
173C2—2321no—
174C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×Q8C22×D29
FittingC29×#355C2
socleC2×C29C2×#99
prime radical#14271731C2
cosocleC2×Q8×C29C23
hypercenter#355D29
hypocenterC29#2134
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #14271146C2semidirect
3. #14270960C2semidirect
4. #14270959C2semidirect
5. C29×#355C2semidirect
16. C29×#101C22semidirect
17. #11745184C22semidirect
86. #355D29semidirect
104. #101C2×D29semidirect
106. C29#2134semidirect

Maximal subgroups

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

subgroupindex
#142717312
#142711462
#142709602
#142709592
C29×#3552
#213429