Finite Group Databasebeta

← #18010505

Subgroups — #18010505

Order 4736.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#14558519C211yesmaximal, characteristic
2#14558512C211yesmaximal, characteristic
3#14558404C212yesmaximal, complemented
4#14558400C212yesmaximal, complemented
5C4×#10596962C211yesmaximal, characteristic
6D37⋊M16C2212yes—
7#11924615C2212yes—
8#11924597—21no—
9#11924596—21no—
10#11924595—21no—
11#11924594—21no—
12C2×#10596962C2211yescharacteristic
13C4×Dic74—21no—
14C4×D148—21no—
15C4×C22⋊D37—21no—
16C4×C22⋊D37—21no—
17#11924495C411yescharacteristic, complemented
18#11924493C411yescharacteristic, complemented
19#11924493C2211yescharacteristic
20C42×D37C411yescharacteristic, complemented
21C42×D37C2211yescharacteristic
22C2×C42×C37C411yescharacteristic, complemented
23C22×C4×C37—21no—
24C22×C4×C37C2×C411yescharacteristic
25C2×C22⋊D37D411yescharacteristic
26C2×C22⋊D37D411yescharacteristic
27#10596962—22no—
28#10596962—22no—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37—21no—
32C2×C4×D37C2×C411yescharacteristic
33C2×C4×D37C2311yescharacteristic
34C2×Dic74D411yescharacteristic
35C22⋊#3866—22no—
36#10596957—22no—
37C4⋊#3866—22no—
38C4×#3866—22no—
39#10596953—22no—
40D37⋊C8—22no—
41C42×C37—21no—
42C42×C37C2×C411yescharacteristic
43C42×C37C2×C411yescharacteristic
44C22⋊Dic37—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37—21no—
48#10596936—21no—
49#10596936—21no—
50C4×Dic37—21no—
51C4×Dic37—21no—
52C4×Dic37C2×C411yescharacteristic
53C4×Dic37C2×C411yescharacteristic
54C23×C37C22⋊C411yescharacteristic
55C22×D37C22⋊C411yescharacteristic
56C22×D37C2×D411yescharacteristic
57C2×#3866—42no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—42no—
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22×C411yescharacteristic
65C22⋊D37—22no—
66C22⋊D37—22no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C2×D411yescharacteristic
71D148—22no—
72C4×D37—21no—
73C4×D37—21no—
74C4×D37—42no—
75C4×D37—42no—
76C4×D37#4112yes—
77C4×D37#4112yes—
78Dic74—22no—
79#64438—42no—
80C22×C37—21no—
81C22×C37—41no—
82C22×C37C2×C22⋊C411yescharacteristic
83C2×D37—21no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37#12312yes—
87#3866—82no—
88C4×C37—22no—
89C4×C37—21no—
90C4×C37—41no—
91C4×C37#11711yescharacteristic
92C4×C37#11711yescharacteristic
93Dic37—21no—
94Dic37—41no—
95Dic37—41no—
96Dic37#12312yes—
97#1827—371nomaximal, Sylow
98C2×C37—21no—
99C2×C37—41no—
100C2×C37#38111yescharacteristic
101D37—22no—
102D37—41no—
103C4×#41—371no—
104#413—371no—
105#410—371no—
106#339—372no—
107H(3,ℤ/4)—372no—
108C37#182711yescharacteristic, complemented, Sylow
109C2×#41—371no—
110C2×M16—372no—
111C4×Q8—741no—
112C4×D4—741no—
113C4×D4—741no—
114C4×D4—741no—
115#117—371no—
116#117—371no—
117#117—371no—
118#117—372no—
119C2×C42—371no—
120C2×C42—371no—
121C2×C42#386611yescharacteristic, complemented
122#101—741no—
123#100—741no—
124#99—741no—
125#99—741no—
126#41—742no—
127#41—742no—
128C2×Q8—371no—
129C2×D4—371no—
130C2×D4—371no—
131C2×D4—371no—
132C22×C4—21no—
133C22×C4—371no—
134C22×C4—371no—
135C22×C4—741no—
136C22×C4—741no—
137C22×C4C2×#386611yescharacteristic
138M16—742no—
139M16—742no—
140C2×C8—742no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4—742no—
144C4⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C22⋊C4—741no—
148C22⋊C4—742no—
149C42—21no—
150C42—371no—
151C42—371no—
152C42—741no—
153C42—741no—
154C42—742no—
155C42C2×#386611yescharacteristic
156C42C2×#386611yescharacteristic
157C23—371no—
158C23—371no—
159C23C22⋊#386611yescharacteristic
160Q8—742no—
161D4—742no—
162D4—742no—
163D4—742no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—371no—
170C2×C4—372no—
171C2×C4—372no—
172C2×C4—371no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—1482no—
178C2×C4—1482no—
179C2×C4—1482no—
180C2×C4C22⋊#386611yescharacteristic
181C2×C4C22×#386611yescharacteristic
182C8—1482no—
183C22—21no—
184C22—41no—
185C22—372no—
186C22—741no—
187C22—1481no—
188C22—1481no—
189C22C2×C22⋊#386611yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—372no—
194C4—2962no—
195C4—741no—
196C4—1481no—
197C4—1481no—
198C4#1192461511yescharacteristic
199C4#1192461511yescharacteristic
200C2—21no—
201C2—41no—
202C2—742no—
203C2—1481no—
204C2#1455847611yescharacteristic
subgroupG/H
centerC4#11924615
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×C42×C37C4
socleC2×C37#381
prime radicalC2×#10596962C22
cosocleC2×C4×D37C23
hypercenterC2×C42#3866
hypocenterC37#1827
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #14558404C2semidirect
4. #14558400C2semidirect
17. #11924495C4semidirect
18. #11924493C4semidirect
20. C42×D37C4semidirect
22. C2×C42×C37C4semidirect
108. C37#1827semidirect
121. C2×C42#3866semidirect

Maximal subgroups

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

subgroupindex
#145585192
#145585122
#145584042
#145584002
C4×#105969622
#182737