Finite Group Databasebeta

← #16818525

Subgroups — #16818525

Order 3712.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271760C211yesmaximal, characteristic
2#14271499C211yesmaximal, characteristic, complemented
3#14271482C211yesmaximal, characteristic
4#14271102C211yesmaximal, characteristic, complemented
5#14270901C211yesmaximal, characteristic, complemented
6#14270898C211yesmaximal, characteristic
7C29×#324C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C29C2211yescharacteristic
9#11745292C2211yescharacteristic
10#11745291—21no—
11C4×C22⋊D29—21no—
12C2×C4⋊Dic29C2211yescharacteristic
13#11745286C2211yescharacteristic
14#11745260—21no—
15#11745258—21no—
16#11745256—21no—
17#11745251—21no—
18C29×C22⋊C8C2211yescharacteristic
19C29×C22⋊C8C2211yescharacteristic
20#11745179—21no—
21#11745179—21no—
22#11745179C2211yescharacteristic
23#11745169—21no—
24#11745166—21no—
25#11745165—21no—
26#11745164—21no—
27C22×C4×C29D411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C2×C22⋊D29—21no—
31C22×Dic29—21no—
32C22×Dic29—21no—
33C2×D116D411yescharacteristic
34C2×C4×D29—21no—
35C2×Dic58D411yescharacteristic
36C2×C8×C29—21no—
37C2×C8×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C22⋊Dic29—21no—
41#90781—21no—
42#90781—21no—
43#90781—21no—
44#90781—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29—21no—
47C4⋊Dic29D411yescharacteristic
48C4⋊Dic29D411yescharacteristic
49#90779—21no—
50#90779—21no—
51#90779—21no—
52#90779—21no—
53C4×Dic29—21no—
54C23×C29C2×D411yescharacteristic
55C22×D29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C22⋊D29—41no—
65C22⋊D29—41no—
66C2×Dic29—21no—
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29—41no—
70C2×Dic29—41no—
71C2×Dic29—42no—
72C2×Dic29—41no—
73C2×Dic29—41no—
74D116—41no—
75C4×D29—81no—
76Dic58—41no—
77C8×C29—41no—
78C8×C29—41no—
79#1615—291nomaximal, Sylow
80C22×C29—21no—
81C22×C29—21no—
82C22×C29#12011yescharacteristic
83C22×C29#13511yescharacteristic
84C22×C29#13711yescharacteristic
85C2×D29—41no—
86C2×D29—41no—
87C2×D29—41no—
88C4×C29—21no—
89C4×C29—21no—
90C4×C29—41no—
91C4×C29—41no—
92Dic29—41no—
93Dic29—41no—
94Dic29—41no—
95Dic29—81no—
96Dic29—81no—
97#539—291no—
98#484—291no—
99#481—291no—
100#400—291no—
101#328—291no—
102#327—291no—
103#324D2911yescharacteristic, complemented
104C2×C29—21no—
105C2×C29—21no—
106C2×C29#45211yescharacteristic
107C2×C29#45411yescharacteristic
108C2×C29#45811yescharacteristic
109D29—81no—
110#126—581no—
111#125—581no—
112#123—581no—
113#123—581no—
114C22⋊Q8—291no—
115C22⋊Q8—581no—
116#121—291no—
117C4×D4—581no—
118C2×C4⋊C4—291no—
119C2×C4⋊C4C2×D2911yescharacteristic
120#107—581no—
121#106—581no—
122#103—581no—
123#102—581no—
124C22⋊C8C2×D2911yescharacteristic
125C22⋊C8C2×D2911yescharacteristic
126#95—291no—
127#95—581no—
128#95—581no—
129C29#161511yescharacteristic, complemented, Sylow
130C2×Q8—291no—
131C2×D4—291no—
132C2×D4—581no—
133C22×C4—581no—
134C22×C4—581no—
135C22×C4—581no—
136C22×C4D11611yescharacteristic
137C22×C4D11611yescharacteristic
138C22×C4C22×D2911yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—291no—
144C4⋊C4—291no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C22⋊C4—581no—
152C22⋊C4—581no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C42—581no—
157C23—581no—
158C23C2×D11611yescharacteristic
159Q8—1161no—
160D4—1161no—
161D4—1161no—
162D4—1161no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—581no—
170C2×C4—581no—
171C2×C4—581no—
172C2×C4—1161no—
173C2×C4—1161no—
174C2×C4—1162no—
175C2×C4—1161no—
176C2×C4—1161no—
177C2×C4—2321no—
178C2×C4D4×D2911yescharacteristic
179C2×C4D4×D2911yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—1161no—
185C22—1161no—
186C22—1161no—
187C22#1174524411yescharacteristic
188C22#1174526611yescharacteristic
189C22#1174527111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—1161no—
195C4—1161no—
196C4—1161no—
197C4—2321no—
198C4—2321no—
199C2—21no—
200C2—21no—
201C2—2321no—
202C2#1427132711yescharacteristic
203C2#1427133811yescharacteristic
204C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radical#11745292C22
hypercenter#324D29
hypocenterC29#1615
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14271499C2semidirect
4. #14271102C2semidirect
5. #14270901C2semidirect
7. C29×#324C2semidirect
103. #324D29semidirect
129. C29#1615semidirect

Maximal subgroups

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

subgroupindex
#142717602
#142714992
#142714822
#142711022
#142709012
#142708982
C29×#3242
#161529