Finite Group Databasebeta

← #17995637

Subgroups — #17995637

Order 4736.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#11924562C212yesmaximal, complemented
2#14558114C211yesmaximal, characteristic, complemented
3C2×#11924464C212yesmaximal, complemented
4#14557302C211yesmaximal, characteristic, complemented
5C37×#390C211yesmaximal, characteristic, complemented
6C2×#10596962C2212yes—
7#11924562—24no—
8#11924562—24no—
9C2×#10596940—22no—
10C2×#10596939—22no—
11C2×#10596934C2212yes—
12#11924516—22no—
13#11924511—22no—
14#11924510—22no—
15#11924464—24no—
16C22×D4×C37C2211yescharacteristic
17C2×C4⋊C4×C37C2211yescharacteristic
18C2×C22⋊C4×C37—22no—
19C2×C42×C37C2211yescharacteristic
20C24×C37—21no—
21C2×D4×C37—22no—
22C2×D4×C37—22no—
23C2×D4×C37—21no—
24C2×D4×C37D412yescomplemented
25C22×C4×C37—21no—
26C22×C4×C37D412yes—
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37—22no—
29#10596962—22no—
30#10596962—22no—
31#10596962—22no—
32#10596962—22no—
33C2×D148—22no—
34C2×D148D412yes—
35C2×C4×D37—22no—
36C2×Dic74D412yes—
37C4⋊C4×C37—22no—
38C22⋊C4×C37—44no—
39C42×C37—22no—
40#10596940—28no—
41#10596939—28no—
42#10596938—24no—
43C4⋊Dic37—22no—
44#10596934—22no—
45#10596934D414yescomplemented
46C2×#64436—22no—
47C23×C37—22no—
48C23×C37—42no—
49C23×C37—42no—
50C23×C37—41no—
51C23×C37—41no—
52C23×C37C2×D411yescharacteristic
53C22×D37—22no—
54D4×C37—24no—
55D4×C37—42no—
56C2×C4×C37—22no—
57C2×C4×C37—22no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—42no—
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D412yes—
63C2×C4×C37C2×D412yes—
64C2×C4×C37#4111yescharacteristic
65C22⋊D37—42no—
66C22⋊D37—42no—
67C2×Dic37—22no—
68D148—22no—
69D148—22no—
70D148—82no—
71C4×D37—42no—
72C4×D37—42no—
73Dic74—22no—
74Dic74—22no—
75#64436—24no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—44no—
79C22×C37—42no—
80C22×C37—82no—
81C22×C37—81no—
82C22×C37—81no—
83C22×C37#12011yescharacteristic
84C22×C37#12111yescharacteristic
85C22×C37#12711yescharacteristic
86C2×D37—42no—
87C2×D37—42no—
88C2×D37—42no—
89C4×C37—42no—
90C4×C37—42no—
91C4×C37#12012yes—
92C4×C37#12112yes—
93Dic37—42no—
94#2006—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—21no—
97C2×C37—82no—
98C2×C37#39211yescharacteristic
99C2×C37#45311yescharacteristic
100C2×C37#45411yescharacteristic
101D37—82no—
102C2×AGL(1,ℤ/8)—372no—
103#537—371no—
104C2×#104—372no—
105#390D3711yescharacteristic, complemented
106#343—371no—
107C37#200611yescharacteristic, complemented, Sylow
108C2×#41—372no—
109C22×D4C2×D3711yescharacteristic
110AGL(1,ℤ/8)—744no—
111AGL(1,ℤ/8)—744no—
112C2×SD16—742no—
113C2×D8—742no—
114C2×M16—372no—
115C22⋊Q8—742no—
116#121—742no—
117#121—742no—
118C2×C4⋊C4C2×D3711yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D3711yescharacteristic
121#104—744no—
122C24—21no—
123#41—742no—
124#41—742no—
125#41—742no—
126#41—742no—
127C2×Q8—372no—
128C2×D4—21no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—372no—
132C2×D4—742no—
133C2×D4—742no—
134C2×D4D14812yescomplemented
135C22×C4—21no—
136C22×C4—742no—
137C22×C4C22⋊D3712yes—
138C22×C4C22×D3711yescharacteristic
139SD16—748no—
140D8—748no—
141M16—374no—
142M16—742no—
143C2×C8—742no—
144C4⋊C4—22no—
145C4⋊C4—742no—
146C22⋊C4—44no—
147C22⋊C4—744no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—742no—
155C23C2×C22⋊D3711yescharacteristic
156Q8—742no—
157Q8—742no—
158D4—24no—
159D4—42no—
160D4—2962no—
161D4—742no—
162D4—742no—
163D4—1482no—
164D4—1482no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—742no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4C2×D14811yescharacteristic
174C2×C4#1059696211yescharacteristic
175C2×C4D4×D3712yes—
176C2×C4D4×D3712yes—
177C8—744no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—1482no—
186C22—1482no—
187C22—1482no—
188C22#1192450411yescharacteristic
189C22#1192451011yescharacteristic
190C22#1192453211yescharacteristic
191C4—42no—
192C4—42no—
193C4—1482no—
194C4#1192450612yes—
195C4#1192450912yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—2962no—
200C2#1455744211yescharacteristic
201C2#1455770011yescharacteristic
202C2#1455770511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#390C2
socleC22×C37#120
hypercenter#390D37
hypocenterC37#2006
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. #14558114C2semidirect
3. C2×#11924464C2semidirect
4. #14557302C2semidirect
5. C37×#390C2semidirect
24. C2×D4×C37D4semidirect
45. #10596934D4semidirect
105. #390D37semidirect
107. C37#2006semidirect
134. C2×D4D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
#145581142
C2×#119244642
#145573022
C37×#3902
#200637