Finite Group Databasebeta

← #16821436

Subgroups — #16821436

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#14271599C211yesmaximal, characteristic, complemented
3#14271413C211yesmaximal, characteristic, complemented
4#14270974C211yesmaximal, characteristic, complemented
5#14270973C211yesmaximal, characteristic, complemented
6#14270944C211yesmaximal, characteristic, complemented
7C29×#509C211yesmaximal, characteristic, complemented
8#41×D29—21no—
9C29×#135C2211yescharacteristic
10C2×D8×C29C2211yescharacteristic, complemented
11#11745312—21no—
12#11745300—21no—
13#11745280—21no—
14#11745277—21no—
15#11745276—21no—
16#11745273—21no—
17#11745266C2211yescharacteristic
18C2×#90772C2211yescharacteristic
19C29×SD32—21no—
20C29×D16—21no—
21C29×M32C2211yescharacteristic, complemented
22#11745180—21no—
23#11745175—21no—
24#11745174—21no—
25#11745165C2211yescharacteristic, complemented
26#11745160C2211yescharacteristic, complemented
27#41×C29—21no—
28C2×D4×C29—21no—
29C2×C22⋊D29—41no—
30#90809—21no—
31Q8×D29—21no—
32#90807—21no—
33#90807—41no—
34D4×D29—21no—
35D4×D29—41no—
36#90805—21no—
37#90805—41no—
38C2×C4×D29—41no—
39C2×C4×D29D411yescharacteristic
40Q16×C29D411yescharacteristic, complemented
41SD16×C29—21no—
42D8×C29—21no—
43D8×C29—21no—
44D8×C29D411yescharacteristic, complemented
45C2×C8×C29C2311yescharacteristic
46C22⋊Dic29—41no—
47#90785—21no—
48#90784—21no—
49#90783—21no—
50#90782—21no—
51C4⋊Dic29—21no—
52C2×#6597D411yescharacteristic
53Dic116D411yescharacteristic, complemented
54D232D411yescharacteristic, complemented
55#90773—21no—
56#90772—21no—
57#90772—21no—
58C16×C29—21no—
59#90768—21no—
60C23×C29—41no—
61C22×D29—41no—
62C22×D29D811yescharacteristic
63Q8×C29—21no—
64D4×C29—21no—
65D4×C29—41no—
66D4×C29—41no—
67D4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2×D411yescharacteristic
70C22⋊D29—41no—
71C22⋊D29—41no—
72C22⋊D29—41no—
73C22⋊D29—82no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29D811yescharacteristic
77D116—21no—
78D116—41no—
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×C29—81no—
92C22×C29—81no—
93C22×C29—81no—
94C22×C29C2×D811yescharacteristic
95C2×D29—21no—
96C2×D29—41no—
97C2×D29—41no—
98C2×D29—82no—
99C4×C29—41no—
100C4×C29#12011yescharacteristic
101C4×C29AGL(1,ℤ/8)11yescharacteristic
102Dic29—21no—
103Dic29—41no—
104Dic29—81no—
105#575—291no—
106#509—291no—
107#509D2911yescharacteristic, complemented
108#469—291no—
109#360—291no—
110#360—291no—
111#349—291no—
112C2×C29—21no—
113C2×C29—81no—
114C2×C29—161no—
115C2×C29#44711yescharacteristic
116D29—41no—
117D29—81no—
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×D8C2×D2911yescharacteristic, complemented
127C2×M16—291no—
128#121—581no—
129SD32—21no—
130SD32—581no—
131D16—21no—
132D16—581no—
133M32—291no—
134M32C2×D2911yescharacteristic, complemented
135#106—291no—
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—21no—
146C2×D4—581no—
147C2×D4—1161no—
148C2×D4—1161no—
149C22×C4—291no—
150C22×C4—1161no—
151Q16—291no—
152Q16—581no—
153Q16C22⋊D2911yescharacteristic, complemented
154SD16—21no—
155SD16—581no—
156SD16—581no—
157SD16—581no—
158D8—21no—
159D8—21no—
160D8—291no—
161D8—581no—
162D8C22⋊D2911yescharacteristic, complemented
163M16—581no—
164M16—581no—
165C2×C8—291no—
166C2×C8C22×D2911yescharacteristic
167C4⋊C4—581no—
168C22⋊C4—1161no—
169C16—21no—
170C16—581no—
171C23—41no—
172C23—291no—
173C23—1161no—
174Q8—21no—
175Q8—581no—
176Q8—1161no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—581no—
182D4—1161no—
183D4—1161no—
184D4—1161no—
185D4—1161no—
186D4—2322no—
187C2×C4—41no—
188C2×C4—291no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—1161no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4D4×D2911yescharacteristic
197C8—581no—
198C8D4×D2911yescharacteristic
199C8C2×C22⋊D2911yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—581no—
205C22—1161no—
206C22—1161no—
207C22—2322no—
208C22D8×D2911yescharacteristic
209C4—41no—
210C4—581no—
211C4—1161no—
212C4—2321no—
213C4#1174527311yescharacteristic
214C4#1174529911yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—1161no—
219C2—2321no—
220C2#1427129511yescharacteristic
subgroupG/H
centerC2#14271295
commutator, cosocleC2×C8×C29C23
FrattiniC2×C8C22×D29
FittingC29×#509C2
socleC2×C29#447
hypercenter#509D29
hypocenterC29#2190
LCSG ▷ C2×C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #14271960C2semidirect
2. #14271599C2semidirect
3. #14271413C2semidirect
4. #14270974C2semidirect
5. #14270973C2semidirect
6. #14270944C2semidirect
7. C29×#509C2semidirect
10. C2×D8×C29C22semidirect
21. C29×M32C22semidirect
25. #11745165C22semidirect
26. #11745160C22semidirect
40. Q16×C29D4semidirect
44. D8×C29D4semidirect
53. Dic116D4semidirect
54. D232D4semidirect
107. #509D29semidirect
126. C2×D8C2×D29semidirect
134. M32C2×D29semidirect
137. C29#2190semidirect
153. Q16C22⋊D29semidirect
162. D8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142719602
#142715992
#142714132
#142709742
#142709732
#142709442
C29×#5092
#219029