Finite Group Databasebeta

← #16821444

Subgroups — #16821444

Order 3712.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#14271960C211yesmaximal, characteristic
2#14271606C211yesmaximal, characteristic, complemented
3#14271603C211yesmaximal, characteristic, complemented
4#14271422C211yesmaximal, characteristic, complemented
5#14270972C211yesmaximal, characteristic, complemented
6#14270944C211yesmaximal, characteristic, complemented
7C29×#360C211yesmaximal, characteristic, complemented
8#41×D29—21no—
9C29×#135C2211yescharacteristic
10#11745312—21no—
11#11745280—21no—
12#11745277—21no—
13#11745276—21no—
14#11745273—21no—
15C2×Dic116C2211yescharacteristic, complemented
16#11745266C2211yescharacteristic
17C2×#90772C2211yescharacteristic
18#11745259—21no—
19C29×M32C2211yescharacteristic, complemented
20C29×#106C2211yescharacteristic, complemented
21#11745177—21no—
22#11745175—21no—
23#11745160C2211yescharacteristic, complemented
24#11745158—21no—
25Dic232—21no—
26#11745148—21no—
27#41×C29—21no—
28#90809—21no—
29Q8×D29—21no—
30#90807—21no—
31#90807—41no—
32D4×D29—21no—
33D4×D29—41no—
34#90805—21no—
35#90805—41no—
36C2×C4×D29—41no—
37C2×C4×D29D411yescharacteristic
38C2×Dic58—21no—
39Q16×C29D411yescharacteristic
40SD16×C29—21no—
41D8×C29D411yescharacteristic
42C2×C8×C29C2311yescharacteristic
43C4⋊C4×C29—21no—
44#90785—21no—
45#90784—21no—
46#90783—21no—
47#90782—21no—
48#90781—41no—
49C4⋊Dic29—41no—
50C2×#6597D411yescharacteristic
51Dic116—21no—
52Dic116—21no—
53Dic116D411yescharacteristic
54D232D411yescharacteristic
55#90773—21no—
56#90772—21no—
57#90772—21no—
58C16×C29—21no—
59#90768—21no—
60C22×D29—41no—
61C22×D29D811yescharacteristic
62Q8×C29—21no—
63D4×C29—21no—
64D4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29C2×D411yescharacteristic
68C22⋊D29—41no—
69C22⋊D29—41no—
70C22⋊D29—41no—
71C2×Dic29—41no—
72C2×Dic29—41no—
73C2×Dic29D811yescharacteristic
74D116—21no—
75D116—41no—
76C4×D29—21no—
77C4×D29—21no—
78C4×D29—41no—
79C4×D29—41no—
80C4×D29—41no—
81Dic58—21no—
82Dic58—41no—
83Dic58—41no—
84Dic58—41no—
85C8×C29C2×D411yescharacteristic
86C8×C29C2×D411yescharacteristic
87#6597—21no—
88#2191—291nomaximal, Sylow
89C22×C29—41no—
90C22×C29C2×D811yescharacteristic
91C2×D29—21no—
92C2×D29—41no—
93C2×D29—41no—
94C2×D29—82no—
95C4×C29—41no—
96C4×C29—81no—
97C4×C29#12011yescharacteristic
98C4×C29AGL(1,ℤ/8)11yescharacteristic
99Dic29—21no—
100Dic29—41no—
101Dic29—81no—
102#575—291no—
103#510—291no—
104#510—291no—
105#470—291no—
106#360—291no—
107#360D2911yescharacteristic, complemented
108#349—291no—
109C2×C29—21no—
110C2×C29—81no—
111C2×C29#44711yescharacteristic
112D29—41no—
113D29—81no—
114C2×#41—581no—
115#137—581no—
116#137—581no—
117AGL(1,ℤ/8)—581no—
118AGL(1,ℤ/8)—581no—
119#135—291no—
120#135—581no—
121#135C2×D2911yescharacteristic
122C2×Q16—291no—
123C2×M16—291no—
124C22⋊Q8—581no—
125Q32—581no—
126Q32—581no—
127SD32—581no—
128SD32—581no—
129M32—291no—
130M32C2×D2911yescharacteristic, complemented
131#106C2×D2911yescharacteristic, complemented
132#103—581no—
133C29#219111yescharacteristic, complemented, Sylow
134#41—21no—
135#41—581no—
136#41—581no—
137#41—581no—
138#41—1161no—
139#41—1161no—
140C2×Q8—581no—
141C2×Q8—581no—
142C2×D4—581no—
143C2×D4—1161no—
144C22×C4—291no—
145C22×C4—1161no—
146Q16—291no—
147Q16—581no—
148Q16—581no—
149Q16—581no—
150Q16D11611yescharacteristic
151SD16—21no—
152SD16—581no—
153SD16—581no—
154SD16—581no—
155D8—291no—
156D8—581no—
157D8D11611yescharacteristic
158M16—581no—
159M16—581no—
160C2×C8—291no—
161C2×C8C22×D2911yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—1161no—
164C22⋊C4—1161no—
165C16—21no—
166C16—581no—
167C23—291no—
168C23—1161no—
169Q8—21no—
170Q8—581no—
171Q8—1161no—
172Q8—1161no—
173Q8—1161no—
174D4—21no—
175D4—41no—
176D4—581no—
177D4—1161no—
178D4—1161no—
179D4—1161no—
180D4—1161no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—291no—
184C2×C4—581no—
185C2×C4—581no—
186C2×C4—1161no—
187C2×C4—1161no—
188C2×C4—1161no—
189C2×C4—1161no—
190C2×C4—1161no—
191C2×C4D4×D2911yescharacteristic
192C8—581no—
193C8C2×D11611yescharacteristic
194C8D4×D2911yescharacteristic
195C22—41no—
196C22—581no—
197C22—1161no—
198C22—1161no—
199C22—2322no—
200C22D8×D2911yescharacteristic
201C4—41no—
202C4—81no—
203C4—581no—
204C4—1161no—
205C4—2321no—
206C4#1174524411yescharacteristic
207C4#1174527611yescharacteristic
208C2—21no—
209C2—81no—
210C2—1161no—
211C2—2321no—
212C2#1427129811yescharacteristic
subgroupG/H
centerC2#14271298
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#360C2
socleC2×C29#447
prime radical#14271960C2
hypercenter#360D29
hypocenterC29#2191
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #14271606C2semidirect
3. #14271603C2semidirect
4. #14271422C2semidirect
5. #14270972C2semidirect
6. #14270944C2semidirect
7. C29×#360C2semidirect
15. C2×Dic116C22semidirect
19. C29×M32C22semidirect
20. C29×#106C22semidirect
23. #11745160C22semidirect
107. #360D29semidirect
130. M32C2×D29semidirect
131. #106C2×D29semidirect
133. C29#2191semidirect

Maximal subgroups

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

subgroupindex
#142719602
#142716062
#142716032
#142714222
#142709722
#142709442
C29×#3602
#219129