Finite Group Databasebeta

← #16818494

Subgroups — #16818494

Order 3712.

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

normal subgroups only

This group has 254 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#14271744C211yesmaximal, characteristic
2#14271476C212yesmaximal, complemented
3#14270896C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#398C211yesmaximal, characteristic, complemented
6C2×#90805—21no—
7C2×C4⋊C4×C29—21no—
8C2×C4⋊C4×C29C2211yescharacteristic
9C2×C4⋊C4×C29C2211yescharacteristic
10#11745292—21no—
11#11745292C2212yes—
12#11745259—22no—
13#11745257—22no—
14C29×#95—21no—
15C29×#95C2211yescharacteristic
16C22⋊#6597C2212yes—
17#11745157—22no—
18#11745155—22no—
19C22×C4×C29—21no—
20C22×C4×C29—21no—
21C22×C4×C29D411yescharacteristic
22C22×C4×C29D411yescharacteristic
23C22×C4×C29C2311yescharacteristic
24C2×C22⋊D29—22no—
25#90805—42no—
26#90805—42no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116D412yes—
30C2×C4×D29—22no—
31C2×Dic58—21no—
32C4⋊C4×C29—22no—
33C4⋊C4×C29—22no—
34C4⋊C4×C29—42no—
35#90781—22no—
36#90781—22no—
37C4⋊Dic29—21no—
38C4⋊Dic29D412yes—
39C2×#6597—22no—
40C23×C29C2×D411yescharacteristic
41C22×D29—22no—
42C2×C4×C29—21no—
43C2×C4×C29—21no—
44C2×C4×C29—22no—
45C2×C4×C29—21no—
46C2×C4×C29—41no—
47C2×C4×C29—41no—
48C2×C4×C29—41no—
49C2×C4×C29—41no—
50C2×C4×C29—41no—
51C2×C4×C29—41no—
52C2×C4×C29—41no—
53C2×C4×C29D812yes—
54C2×C4×C29C2×D412yes—
55C22⋊D29—42no—
56C22⋊D29—42no—
57C2×Dic29—22no—
58D116—42no—
59D116—42no—
60D116—81no—
61C4×D29—44no—
62Dic58—42no—
63#6597—42no—
64#1610—291nomaximal, Sylow
65C22×C29—21no—
66C22×C29—21no—
67C22×C29#12011yescharacteristic
68C22×C29C2×D811yescharacteristic
69C22×C29AGL(1,ℤ/8)11yescharacteristic
70C2×D29—42no—
71C2×D29—42no—
72C2×D29—42no—
73C4×C29—22no—
74C4×C29—22no—
75C4×C29—42no—
76C4×C29—41no—
77C4×C29—81no—
78Dic29—42no—
79#537—291no—
80#480—292no—
81#398D2911yescharacteristic, complemented
82#327—292no—
83#324—291no—
84C2×C29—21no—
85C2×C29—21no—
86C2×C29#44711yescharacteristic
87C2×C29#45611yescharacteristic
88C2×C29#45811yescharacteristic
89D29—82no—
90C2×#41—581no—
91C22⋊Q8—582no—
92#121—292no—
93#121—582no—
94#121—581no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C2×D2911yescharacteristic
97C2×C4⋊C4C2×D2911yescharacteristic
98#107—582no—
99#102—582no—
100C22⋊C8—292no—
101#95—21no—
102#95C2×D2911yescharacteristic
103C29#161011yescharacteristic, complemented, Sylow
104#41—1162no—
105#41—1162no—
106C2×Q8—581no—
107C2×D4—292no—
108C2×D4—581no—
109C2×D4—581no—
110C2×D4—582no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—582no—
114C22×C4C22⋊D2911yescharacteristic
115C22×C4C22⋊D2911yescharacteristic
116C22×C4C22×D2911yescharacteristic
117C2×C8—582no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—42no—
121C4⋊C4—292no—
122C4⋊C4—581no—
123C22⋊C4—582no—
124C22⋊C4—582no—
125C23—582no—
126C23C2×C22⋊D2911yescharacteristic
127Q8—1162no—
128D4—1162no—
129D4—1162no—
130D4—1162no—
131D4—1162no—
132D4—2321no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—582no—
145C2×C4—1164no—
146C2×C4#9078212yes—
147C2×C4D4×D2912yes—
148C8—1162no—
149C22—21no—
150C22—21no—
151C22—1162no—
152C22—1162no—
153C22—1162no—
154C22C2×#9078211yescharacteristic
155C22#1174529911yescharacteristic
156C22#1174531111yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—81no—
162C4—1162no—
163C2—21no—
164C2—21no—
165C2—2322no—
166C2#1427129611yescharacteristic
167C2#1427134511yescharacteristic
168C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#398C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#398D29
hypocenterC29#1610
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #14271476C2semidirect
3. #14270896C2semidirect
4. #14270889C2semidirect
5. C29×#398C2semidirect
81. #398D29semidirect
103. C29#1610semidirect

Maximal subgroups

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

subgroupindex
#142717442
#142714762
#142708962
#142708892
C29×#3982
#161029