Finite Group Databasebeta

← #16818487

Subgroups — #16818487

Order 3712.

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

normal subgroups only

This group has 216 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#14271493C211yesmaximal, characteristic, complemented
3#14271476C211yesmaximal, characteristic
4#14270899C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic
6#14270889C211yesmaximal, characteristic, complemented
7C29×#398C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C29—21no—
9C2×C4⋊C4×C29C2211yescharacteristic
10C2×C4⋊C4×C29C2211yescharacteristic
11#11745292C2211yescharacteristic
12#11745291—21no—
13C4×C22⋊D29—21no—
14#11745286C2211yescharacteristic
15#11745260—21no—
16#11745258—21no—
17#11745256—21no—
18#11745251—21no—
19C29×#95—21no—
20C29×#95C2211yescharacteristic
21C22⋊#6597C2211yescharacteristic
22C22⋊#6597C2211yescharacteristic
23#11745158—21no—
24#11745157—21no—
25#11745156—21no—
26#11745155—21no—
27C22×C4×C29—21no—
28C22×C4×C29—21no—
29C22×C4×C29D411yescharacteristic
30C22×C4×C29D411yescharacteristic
31C22×C4×C29C2311yescharacteristic
32C2×C22⋊D29—21no—
33C2×D116D411yescharacteristic
34C2×C4×D29—21no—
35C2×Dic58D411yescharacteristic
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—42no—
41C22⋊Dic29—21no—
42#90781—21no—
43#90781—21no—
44#90781—21no—
45#90781—21no—
46C4⋊Dic29D411yescharacteristic
47C4⋊Dic29D411yescharacteristic
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52C4×Dic29—21no—
53C2×#6597—21no—
54C2×#6597—21no—
55C23×C29C2×D411yescharacteristic
56C22×D29—21no—
57C2×C4×C29—22no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D411yescharacteristic
71C22⋊D29—41no—
72C22⋊D29—41no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76D116—41no—
77C4×D29—81no—
78Dic58—41no—
79#6597—41no—
80#6597—41no—
81#1609—291nomaximal, Sylow
82C22×C29—21no—
83C22×C29—21no—
84C22×C29#12011yescharacteristic
85C22×C29#13511yescharacteristic
86C22×C29AGL(1,ℤ/8)11yescharacteristic
87C2×D29—41no—
88C2×D29—41no—
89C2×D29—41no—
90C4×C29—21no—
91C4×C29—21no—
92C4×C29—42no—
93C4×C29—41no—
94C4×C29—41no—
95C4×C29—81no—
96Dic29—41no—
97Dic29—41no—
98Dic29—41no—
99#539—291no—
100#483—291no—
101#480—291no—
102#398D2911yescharacteristic, complemented
103#328—291no—
104#327—291no—
105#324—291no—
106C2×C29—21no—
107C2×C29—21no—
108C2×C29#44911yescharacteristic
109C2×C29#45611yescharacteristic
110C2×C29#45811yescharacteristic
111D29—81no—
112#126—581no—
113#125—581no—
114#123—581no—
115#123—581no—
116C22⋊Q8—291no—
117C22⋊Q8—581no—
118#121—291no—
119C4×D4—581no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4C2×D2911yescharacteristic
122C2×C4⋊C4C2×D2911yescharacteristic
123#107—581no—
124#106—581no—
125#103—581no—
126#102—581no—
127C22⋊C8—291no—
128C22⋊C8—291no—
129#95—21no—
130#95C2×D2911yescharacteristic
131C29#160911yescharacteristic, complemented, Sylow
132C2×Q8—291no—
133C2×D4—291no—
134C2×D4—581no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—581no—
138C22×C4C22⋊D2911yescharacteristic
139C22×C4C22⋊D2911yescharacteristic
140C22×C4C22×D2911yescharacteristic
141C2×C8—581no—
142C2×C8—581no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—291no—
149C4⋊C4—291no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4—581no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C22⋊C4—581no—
159C42—581no—
160C23—581no—
161C23C2×C22⋊D2911yescharacteristic
162Q8—1161no—
163D4—1161no—
164D4—1161no—
165D4—1161no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—581no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—2321no—
182C2×C4D4×D2911yescharacteristic
183C2×C4D4×D2911yescharacteristic
184C8—1161no—
185C8—1161no—
186C22—21no—
187C22—21no—
188C22—1161no—
189C22—1161no—
190C22—1161no—
191C22#1174529411yescharacteristic
192C22#1174529911yescharacteristic
193C22#1174531211yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—1161no—
201C4—1161no—
202C4—1161no—
203C2—21no—
204C2—21no—
205C2—2321no—
206C2#1427130611yescharacteristic
207C2#1427134511yescharacteristic
208C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#398C2
socleC22×C29#120
prime radical#11745292C22
hypercenter#398D29
hypocenterC29#1609
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. #14271493C2semidirect
4. #14270899C2semidirect
6. #14270889C2semidirect
7. C29×#398C2semidirect
102. #398D29semidirect
131. C29#1609semidirect

Maximal subgroups

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

subgroupindex
#142717602
#142714932
#142714762
#142708992
#142708962
#142708892
C29×#3982
#160929