Finite Group Databasebeta

← #16818529

Subgroups — #16818529

Order 3712.

246 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271479C212yesmaximal, complemented
2#14271102C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#537C211yesmaximal, characteristic
6C2×#41×C29—21no—
7C29×C22⋊Q8—22no—
8C29×#121—22no—
9C29×#121—21no—
10C29×#121C2212yes—
11C2×C4⋊C4×C29C2211yescharacteristic
12C2×C4⋊Dic29C2211yescharacteristic
13#11745180—22no—
14#11745179—21no—
15#11745179—21no—
16#11745179C2211yescharacteristic
17C22⋊#6597C2212yes—
18#11745156—22no—
19#41×C29—42no—
20#41×C29—42no—
21C2×Q8×C29—21no—
22C2×D4×C29—21no—
23C2×D4×C29—22no—
24C2×D4×C29—21no—
25C2×D4×C29D412yes—
26C22×C4×C29—22no—
27C22×C4×C29D411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29—22no—
34C4⋊C4×C29D412yes—
35C22⋊C4×C29—22no—
36C22⋊C4×C29—22no—
37C4⋊Dic29—22no—
38C2×#6597—22no—
39C23×C29—22no—
40C23×C29C2×D411yescharacteristic
41Q8×C29—42no—
42D4×C29—42no—
43D4×C29—42no—
44D4×C29—42no—
45D4×C29—42no—
46D4×C29—81no—
47C2×C4×C29—21no—
48C2×C4×C29—21no—
49C2×C4×C29—21no—
50C2×C4×C29—22no—
51C2×C4×C29—41no—
52C2×C4×C29—44no—
53C2×C4×C29—41no—
54C2×C4×C29SD1612yes—
55C2×C4×C29C2×D412yes—
56C2×Dic29—41no—
57C2×Dic29—41no—
58C2×Dic29—42no—
59C2×Dic29—41no—
60C2×Dic29—41no—
61#6597—42no—
62#1616—291nomaximal, Sylow
63C22×C29—21no—
64C22×C29—21no—
65C22×C29—42no—
66C22×C29—42no—
67C22×C29—42no—
68C22×C29#12011yescharacteristic
69C22×C29C2×SD1611yescharacteristic
70C22×C29AGL(1,ℤ/8)11yescharacteristic
71C4×C29—22no—
72C4×C29—22no—
73C4×C29—42no—
74C4×C29—41no—
75Dic29—81no—
76Dic29—81no—
77#537D2911yescharacteristic
78#481—292no—
79#400—291no—
80#327—292no—
81#324—291no—
82C2×C29—21no—
83C2×C29—21no—
84C2×C29—82no—
85C2×C29#45011yescharacteristic
86C2×C29#45411yescharacteristic
87C2×C29#45811yescharacteristic
88C2×#41—21no—
89C22⋊Q8—22no—
90#121—22no—
91#121—21no—
92#121C2×D2912yes—
93C2×C4⋊C4—291no—
94C2×C4⋊C4C2×D2911yescharacteristic
95#106—582no—
96#102—582no—
97C22⋊C8—292no—
98#95—291no—
99#95—581no—
100#95—581no—
101C29#161611yescharacteristic, complemented, Sylow
102#41—42no—
103#41—42no—
104C2×Q8—21no—
105C2×D4—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4C22⋊D2912yes—
109C22×C4—22no—
110C22×C4—581no—
111C22×C4—581no—
112C22×C4C22⋊D2911yescharacteristic
113C22×C4C22⋊D2911yescharacteristic
114C22×C4C22×D2911yescharacteristic
115C2×C8—582no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—582no—
119C4⋊C4C22⋊D2912yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C23—22no—
123C23C2×C22⋊D2911yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—1161no—
138C2×C4—1161no—
139C2×C4—1162no—
140C2×C4—1161no—
141C2×C4—1161no—
142C2×C4#9078312yes—
143C2×C4C2×C22⋊D2912yes—
144C8—1162no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22#1174529411yescharacteristic
151C22C2×#9078311yescharacteristic
152C22#1174531511yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—41no—
157C4—2321no—
158C4—2321no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2#1427131411yescharacteristic
163C2#1427133611yescharacteristic
164C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#537C2
socleC22×C29#120
hypercenter#537D29
hypocenterC29#1616
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14271479C2semidirect
2. #14271102C2semidirect
3. #14270897C2semidirect
4. #14270889C2semidirect
101. C29#1616semidirect

Maximal subgroups

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

subgroupindex
#142714792
#142711022
#142708972
#142708892
C29×#5372
#161629