Finite Group Databasebeta

← #16818417

Subgroups — #16818417

Order 3712.

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

normal subgroups only

This group has 316 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#14271789C211yesmaximal, characteristic, complemented
2#14271316C212yesmaximal, complemented
3#14271072C211yesmaximal, characteristic
4#14270901C212yesmaximal, complemented
5C29×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D29—21no—
7C22×D116C2211yescharacteristic
8C2×C22⋊C4×C29C2211yescharacteristic
9C2×C22⋊Dic29—21no—
10C2×#90781—21no—
11#11745286—21no—
12#11745286C2212yes—
13C2×#90773—22no—
14#11745240—22no—
15#11745240—22no—
16C29×C22⋊C8C2212yes—
17#11745179C2211yescharacteristic
18#11745169—22no—
19C24×C29D411yescharacteristic
20C23×D29—21no—
21C22×C4×C29D411yescharacteristic
22C22×C4×C29C2311yescharacteristic
23C2×C22⋊D29—42no—
24C2×C22⋊D29—42no—
25C2×C22⋊D29—42no—
26C22×Dic29—21no—
27C22×Dic29—21no—
28C22×Dic29—21no—
29C2×D116—22no—
30C2×D116—42no—
31C2×Dic58—21no—
32C2×Dic58D412yescomplemented
33C2×C8×C29—22no—
34C22⋊C4×C29—22no—
35C22⋊Dic29—22no—
36C22⋊Dic29—22no—
37#90781—42no—
38C4⋊Dic29—21no—
39C4⋊Dic29D412yescomplemented
40#90779—22no—
41#90779—22no—
42#90773—44no—
43C23×C29—21no—
44C23×C29—21no—
45C23×C29—41no—
46C23×C29—41no—
47C23×C29SD1612yescomplemented
48C23×C29C2×D411yescharacteristic
49C22×D29—22no—
50C22×D29—41no—
51C22×D29—41no—
52C22×D29—41no—
53C22×D29—41no—
54C22×D29—41no—
55C22×D29—41no—
56C2×C4×C29—21no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29C2×D412yes—
60C22⋊D29—48no—
61C2×Dic29—22no—
62C2×Dic29—22no—
63C2×Dic29—22no—
64C2×Dic29—41no—
65C2×Dic29—41no—
66C2×Dic29—81no—
67C2×Dic29—81no—
68D116—24no—
69D116—42no—
70Dic58—42no—
71Dic58—81no—
72C8×C29—42no—
73#1596—291nomaximal, Sylow
74C22×C29—21no—
75C22×C29—21no—
76C22×C29—22no—
77C22×C29—42no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29—81no—
81C22×C29#12011yescharacteristic
82C22×C29C2×SD1611yescharacteristic
83C22×C29#13711yescharacteristic
84C2×D29—42no—
85C2×D29—42no—
86C2×D29—42no—
87C2×D29—81no—
88C2×D29—81no—
89C2×D29—81no—
90C2×D29—81no—
91C4×C29—22no—
92C4×C29—41no—
93Dic29—42no—
94Dic29—42no—
95Dic29—42no—
96#543—291no—
97#450—292no—
98#392—291no—
99#328—292no—
100#323D2911yescharacteristic, complemented
101C2×C29—21no—
102C2×C29—21no—
103C2×C29—42no—
104C2×C29#44811yescharacteristic
105C2×C29#45311yescharacteristic
106C2×C29B(4,𝔽2)11yescharacteristic
107D29—82no—
108C22×D4—291no—
109C22×D4—581no—
110C2×SD16—582no—
111C22⋊Q8—292no—
112C22⋊Q8—582no—
113C22⋊Q8—582no—
114C22⋊Q8—581no—
115C2×C22⋊C4—581no—
116C2×C22⋊C4—581no—
117C2×C22⋊C4C2×D2911yescharacteristic
118#102—582no—
119C22⋊C8C2×D2912yes—
120#95—291no—
121C29#159611yescharacteristic, complemented, Sylow
122C24—581no—
123C24D11611yescharacteristic
124C2×Q8—292no—
125C2×Q8—581no—
126C2×D4—582no—
127C2×D4—1162no—
128C2×D4—1162no—
129C2×D4—1162no—
130C2×D4—1162no—
131C22×C4—581no—
132C22×C4—581no—
133C22×C4—581no—
134C22×C4D11611yescharacteristic
135C22×C4C22×D2911yescharacteristic
136SD16—1164no—
137C2×C8—22no—
138C4⋊C4—292no—
139C4⋊C4—582no—
140C4⋊C4—581no—
141C4⋊C4—582no—
142C22⋊C4—22no—
143C22⋊C4—582no—
144C22⋊C4—582no—
145C22⋊C4—1162no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—582no—
151C23—1161no—
152C23—1161no—
153C23—1161no—
154C23—1161no—
155C23—1161no—
156C23—1161no—
157C23#9077312yescomplemented
158C23C2×D11611yescharacteristic
159Q8—1162no—
160Q8—2321no—
161D4—584no—
162D4—1162no—
163D4—1168no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—582no—
168C2×C4—582no—
169C2×C4—582no—
170C2×C4—1161no—
171C2×C4—1161no—
172C2×C4—2321no—
173C2×C4—2321no—
174C2×C4D4×D2912yes—
175C8—42no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—1162no—
184C22—1162no—
185C22—1162no—
186C22—2321no—
187C22—2321no—
188C22—2321no—
189C22—2321no—
190C22#1174524411yescharacteristic
191C22C2×#9077311yescharacteristic
192C22#1174527111yescharacteristic
193C4—22no—
194C4—41no—
195C4—1162no—
196C4—1162no—
197C4—1162no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—2322no—
202C2#1427130411yescharacteristic
203C2#1427133311yescharacteristic
204C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#323C2
socleC22×C29#120
prime radical#14271072C2
hypercenter#323D29
hypocenterC29#1596
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
1. #14271789C2semidirect
2. #14271316C2semidirect
4. #14270901C2semidirect
5. C29×#323C2semidirect
32. C2×Dic58D4semidirect
39. C4⋊Dic29D4semidirect
47. C23×C29SD16semidirect
100. #323D29semidirect
121. C29#1596semidirect
157. C23#90773semidirect

Maximal subgroups

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

subgroupindex
#142717892
#142713162
#142710722
#142709012
C29×#3232
#159629