Finite Group Databasebeta

← #16821441

Subgroups — #16821441

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#14271604C211yesmaximal, characteristic, complemented
3#14271418C211yesmaximal, characteristic, complemented
4#14270974C211yesmaximal, characteristic, complemented
5#14270973C211yesmaximal, characteristic, complemented
6#14270944C211yesmaximal, characteristic, complemented
7C29×#510C211yesmaximal, characteristic, complemented
8#41×D29—21no—
9C29×#135C2211yescharacteristic
10C2×Q16×C29C2211yescharacteristic, complemented
11#11745312—21no—
12#11745308—21no—
13#11745280—21no—
14#11745277—21no—
15#11745276—21no—
16#11745273—21no—
17#11745266C2211yescharacteristic
18C2×#90772C2211yescharacteristic
19C29×Q32—21no—
20C29×SD32—21no—
21C29×M32C2211yescharacteristic, complemented
22#11745183—21no—
23#11745177—21no—
24#11745176—21no—
25#11745165C2211yescharacteristic, complemented
26#11745160C2211yescharacteristic, complemented
27#41×C29—21no—
28C2×Q8×C29—21no—
29#90809—21no—
30Q8×D29—21no—
31#90807—21no—
32#90807—41no—
33D4×D29—21no—
34D4×D29—41no—
35#90805—21no—
36#90805—41no—
37C2×C4×D29—41no—
38C2×C4×D29D411yescharacteristic
39Q16×C29—21no—
40Q16×C29—21no—
41Q16×C29D411yescharacteristic
42SD16×C29—21no—
43D8×C29D411yescharacteristic
44C2×C8×C29C2311yescharacteristic
45#90785—21no—
46#90784—21no—
47#90783—21no—
48#90782—21no—
49#90781—41no—
50C4⋊Dic29—21no—
51#90779—41no—
52C2×#6597D411yescharacteristic
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—
63Q8×C29—41no—
64Q8×C29—41no—
65D4×C29—21no—
66D4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2×D411yescharacteristic
70C22⋊D29—41no—
71C22⋊D29—41no—
72C22⋊D29—41no—
73C2×Dic29—41no—
74C2×Dic29—41no—
75C2×Dic29D811yescharacteristic
76D116—21no—
77D116—41no—
78C4×D29—21no—
79C4×D29—21no—
80C4×D29—41no—
81C4×D29—41no—
82C4×D29—41no—
83Dic58—21no—
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#510D2911yescharacteristic, complemented
105#470—291no—
106#360—291no—
107#360—291no—
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×Q16C2×D2911yescharacteristic, complemented
123C2×M16—291no—
124C22⋊Q8—581no—
125Q32—21no—
126Q32—581no—
127SD32—21no—
128SD32—581no—
129M32—291no—
130M32C2×D2911yescharacteristic, complemented
131#106—291no—
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—21no—
141C2×Q8—581no—
142C2×D4—581no—
143C2×D4—1161no—
144C22×C4—291no—
145C22×C4—1161no—
146Q16—21no—
147Q16—21no—
148Q16—291no—
149Q16—581no—
150Q16C22⋊D2911yescharacteristic
151SD16—21no—
152SD16—581no—
153SD16—581no—
154SD16—581no—
155D8—291no—
156D8—581no—
157D8C22⋊D2911yescharacteristic
158M16—581no—
159M16—581no—
160C2×C8—291no—
161C2×C8C22×D2911yescharacteristic
162C4⋊C4—581no—
163C4⋊C4—1161no—
164C22⋊C4—1161no—
165C16—21no—
166C16—581no—
167C23—291no—
168C23—1161no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—581no—
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—
193C8D4×D2911yescharacteristic
194C8C2×C22⋊D2911yescharacteristic
195C22—41no—
196C22—581no—
197C22—1161no—
198C22—1161no—
199C22—2322no—
200C22D8×D2911yescharacteristic
201C4—41no—
202C4—81no—
203C4—581no—
204C4—1161no—
205C4—2321no—
206C4#1174527311yescharacteristic
207C4#1174529911yescharacteristic
208C2—21no—
209C2—81no—
210C2—1161no—
211C2—2321no—
212C2#1427129511yescharacteristic
subgroupG/H
centerC2#14271295
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#510C2
socleC2×C29#447
prime radical#14271960C2
hypercenter#510D29
hypocenterC29#2191
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #14271604C2semidirect
3. #14271418C2semidirect
4. #14270974C2semidirect
5. #14270973C2semidirect
6. #14270944C2semidirect
7. C29×#510C2semidirect
10. C2×Q16×C29C22semidirect
21. C29×M32C22semidirect
25. #11745165C22semidirect
26. #11745160C22semidirect
104. #510D29semidirect
122. C2×Q16C2×D29semidirect
130. M32C2×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
#142716042
#142714182
#142709742
#142709732
#142709442
C29×#5102
#219129