Finite Group Databasebeta

← #16821439

Subgroups — #16821439

Order 3712.

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

normal subgroups only

This group has 226 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, complemented
2#14271601C211yesmaximal, characteristic, complemented
3#14271598C211yesmaximal, characteristic, complemented
4#14271417C211yesmaximal, 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—
15#11745266C2211yescharacteristic
16C2×D232C2211yescharacteristic, complemented
17C2×#90772C2211yescharacteristic
18#11745257—21no—
19C29×M32C2211yescharacteristic, complemented
20C29×#106C2211yescharacteristic, complemented
21#11745176—21no—
22#11745174—21no—
23#11745160C2211yescharacteristic, complemented
24#11745157—21no—
25#11745148—21no—
26D464—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×D116—21no—
37C2×D116—41no—
38C2×C4×D29—41no—
39C2×C4×D29D411yescharacteristic
40Q16×C29D411yescharacteristic, complemented
41SD16×C29—21no—
42D8×C29D411yescharacteristic, complemented
43C2×C8×C29C2311yescharacteristic
44C4⋊C4×C29—21no—
45#90785—21no—
46#90784—21no—
47#90783—21no—
48#90782—21no—
49#90781—41no—
50C2×#6597D411yescharacteristic
51Dic116D411yescharacteristic, complemented
52D232—21no—
53D232—21no—
54D232D411yescharacteristic, complemented
55#90773—21no—
56#90772—21no—
57#90772—21no—
58C16×C29—21no—
59#90768—21no—
60C22×D29—41no—
61C22×D29—41no—
62C22×D29D811yescharacteristic
63Q8×C29—21no—
64D4×C29—21no—
65D4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29C2×D411yescharacteristic
69C22⋊D29—41no—
70C22⋊D29—41no—
71C22⋊D29—41no—
72C2×Dic29—41no—
73C2×Dic29D811yescharacteristic
74D116—21no—
75D116—41no—
76D116—41no—
77D116—41no—
78D116—82no—
79C4×D29—21no—
80C4×D29—21no—
81C4×D29—41no—
82C4×D29—41no—
83C4×D29—41no—
84Dic58—21no—
85Dic58—41no—
86C8×C29C2×D411yescharacteristic
87C8×C29C2×D411yescharacteristic
88#6597—21no—
89#2190—291nomaximal, Sylow
90C22×C29—41no—
91C22×C29C2×D811yescharacteristic
92C2×D29—21no—
93C2×D29—41no—
94C2×D29—41no—
95C2×D29—82no—
96C2×D29—81no—
97C2×D29—81no—
98C2×D29—81no—
99C4×C29—41no—
100C4×C29—81no—
101C4×C29#12011yescharacteristic
102C4×C29AGL(1,ℤ/8)11yescharacteristic
103Dic29—21no—
104Dic29—41no—
105#575—291no—
106#509—291no—
107#509—291no—
108#469—291no—
109#360—291no—
110#360D2911yescharacteristic, complemented
111#349—291no—
112C2×C29—21no—
113C2×C29—81no—
114C2×C29#44711yescharacteristic
115D29—41no—
116D29—81no—
117D29—161no—
118C2×#41—581no—
119#137—581no—
120#137—581no—
121AGL(1,ℤ/8)—581no—
122AGL(1,ℤ/8)—581no—
123#135—291no—
124#135—581no—
125#135C2×D2911yescharacteristic
126C2×D8—291no—
127C2×M16—291no—
128#121—581no—
129SD32—581no—
130SD32—581no—
131D16—581no—
132D16—581no—
133M32—291no—
134M32C2×D2911yescharacteristic, complemented
135#106C2×D2911yescharacteristic, complemented
136#102—581no—
137C29#219011yescharacteristic, complemented, Sylow
138#41—21no—
139#41—581no—
140#41—581no—
141#41—581no—
142#41—1161no—
143#41—1161no—
144C2×Q8—581no—
145C2×D4—581no—
146C2×D4—581no—
147C2×D4—1161no—
148C2×D4—1161no—
149C22×C4—291no—
150C22×C4—1161no—
151Q16—291no—
152Q16—581no—
153Q16D11611yescharacteristic, complemented
154SD16—21no—
155SD16—581no—
156SD16—581no—
157SD16—581no—
158D8—291no—
159D8—581no—
160D8—581no—
161D8—581no—
162D8D11611yescharacteristic, complemented
163M16—581no—
164M16—581no—
165C2×C8—291no—
166C2×C8C22×D2911yescharacteristic
167C4⋊C4—21no—
168C22⋊C4—1161no—
169C16—21no—
170C16—581no—
171C23—291no—
172C23—1161no—
173C23—1161no—
174Q8—21no—
175Q8—581no—
176Q8—1161no—
177D4—21no—
178D4—41no—
179D4—581no—
180D4—1161no—
181D4—1161no—
182D4—1161no—
183D4—1161no—
184D4—1161no—
185D4—1161no—
186D4—2322no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—291no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4D4×D2911yescharacteristic
197C8—581no—
198C8C2×D11611yescharacteristic
199C8D4×D2911yescharacteristic
200C22—41no—
201C22—581no—
202C22—1161no—
203C22—1161no—
204C22—2321no—
205C22—2321no—
206C22—2322no—
207C22—2321no—
208C22D8×D2911yescharacteristic
209C4—41no—
210C4—81no—
211C4—581no—
212C4—1161no—
213C4#1174524411yescharacteristic
214C4#1174527611yescharacteristic
215C2—21no—
216C2—81no—
217C2—1161no—
218C2—4641no—
219C2—2321no—
220C2#1427129811yescharacteristic
subgroupG/H
centerC2#14271298
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#360C2
socleC2×C29#447
hypercenter#360D29
hypocenterC29#2190
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
1. #14271960C2semidirect
2. #14271601C2semidirect
3. #14271598C2semidirect
4. #14271417C2semidirect
5. #14270972C2semidirect
6. #14270944C2semidirect
7. C29×#360C2semidirect
16. C2×D232C22semidirect
19. C29×M32C22semidirect
20. C29×#106C22semidirect
23. #11745160C22semidirect
40. Q16×C29D4semidirect
42. D8×C29D4semidirect
51. Dic116D4semidirect
54. D232D4semidirect
110. #360D29semidirect
134. M32C2×D29semidirect
135. #106C2×D29semidirect
137. C29#2190semidirect
153. Q16D116semidirect
162. D8D116semidirect

Maximal subgroups

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

subgroupindex
#142719602
#142716012
#142715982
#142714172
#142709722
#142709442
C29×#3602
#219029