Finite Group Databasebeta

← #17994549

Subgroups — #17994549

Order 4736.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11924581C211yesmaximal, characteristic
2C2×#11924464C212yesmaximal, complemented
3#14557532C212yesmaximal, complemented
4C2×#11924453C211yesmaximal, characteristic, complemented
5C37×#390C211yesmaximal, characteristic, complemented
6#11924581—22no—
7#11924581—24no—
8#11924581C414yescomplemented
9C2×#10596962C2212yes—
10C2×#10596964—22no—
11C22×C22⋊D37—22no—
12C2×D4×D37—22no—
13C2×#10596934C2212yescomplemented
14#11924464—24no—
15#11924459—22no—
16#11924456—22no—
17#11924453—22no—
18C22×D4×C37C2211yescharacteristic
19C2×C4⋊C4×C37C2211yescharacteristic, complemented
20C2×C22⋊C4×C37—22no—
21C2×C42×C37C2211yescharacteristic, complemented
22C24×C37D412yes—
23C23×D37—22no—
24C2×D4×C37—22no—
25C2×D4×C37—22no—
26C2×D4×C37C2×C412yes—
27C2×D4×C37D412yes—
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—24no—
32C2×C22⋊D37—28no—
33C2×C22⋊D37—28no—
34C2×C22⋊D37—22no—
35C22×Dic37—22no—
36#10596964—28no—
37#10596964—28no—
38D4×D37—28no—
39D4×D37—28no—
40#10596962—22no—
41#10596962—22no—
42#10596962C2×C414yes—
43#10596962D414yes—
44C2×D148D412yes—
45C2×C4×D37—22no—
46C2×Dic74D412yes—
47C4⋊C4×C37—22no—
48C22⋊C4×C37—44no—
49C42×C37—22no—
50#10596934—22no—
51#10596934—22no—
52C2×#64436—22no—
53C23×C37—22no—
54C23×C37—22no—
55C23×C37—42no—
56C23×C37—42no—
57C23×C37C22⋊C414yes—
58C23×C37C2×D411yescharacteristic
59C22×D37—22no—
60C22×D37—28no—
61C22×D37—82no—
62C22×D37—82no—
63D4×C37—24no—
64D4×C37—24no—
65C2×C4×C37—22no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37—42no—
69C2×C4×C37—41no—
70C2×C4×C37C22×C411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D412yes—
73C2×C4×C37C2×D412yes—
74C22⋊D37—216no—
75C22⋊D37—24no—
76C22⋊D37—24no—
77C2×Dic37—28no—
78C2×Dic37—22no—
79D148—22no—
80D148C22⋊C414yescomplemented
81C4×D37—24no—
82C4×D37—24no—
83Dic74—22no—
84Dic74C22⋊C414yescomplemented
85#64436—42no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—24no—
89C22×C37—44no—
90C22×C37—42no—
91C22×C37—42no—
92C22×C37—82no—
93C22×C37C2×C22⋊C411yescharacteristic
94C22×C37#12011yescharacteristic
95C22×C37#12011yescharacteristic
96C2×D37—24no—
97C2×D37—42no—
98C2×D37—42no—
99C2×D37—88no—
100C4×C37—42no—
101C4×C37—81no—
102C4×C37C2×C22⋊C412yes—
103C4×C37#12012yes—
104Dic37—24no—
105#1792—371nomaximal, Sylow
106C2×C37—21no—
107C2×C37—21no—
108C2×C37—44no—
109C2×C37#37911yescharacteristic
110C2×C37#45311yescharacteristic
111C2×C37#45511yescharacteristic
112D37—44no—
113C2×H(5,𝔽2)—371no—
114C2×#104—372no—
115#417—372no—
116C2×#100—371no—
117#390D3711yescharacteristic, complemented
118C37#179211yescharacteristic, complemented, Sylow
119H(5,𝔽2)—374no—
120H(5,𝔽2)—744no—
121H(5,𝔽2)—742no—
122C2×#41—372no—
123C2×#41—742no—
124C22×D4—742no—
125C22×D4—742no—
126C22×D4C2×D3711yescharacteristic
127C2×M16—372no—
128C2×C4⋊C4C2×D3711yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D3711yescharacteristic, complemented
131#104—744no—
132#103—742no—
133#102—742no—
134#100—742no—
135C24—742no—
136C24C22⋊D3712yes—
137#41—374no—
138#41—374no—
139#41—748no—
140#41—748no—
141#41—742no—
142#41—742no—
143C2×Q8—372no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—372no—
147C2×D4—748no—
148C2×D4—748no—
149C2×D4—744no—
150C2×D4—748no—
151C2×D4—748no—
152C2×D4—742no—
153C2×D4C4×D3712yes—
154C2×D4D14812yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—742no—
158C22×C4—742no—
159C22×C4C22×D3711yescharacteristic
160M16—742no—
161M16—742no—
162C2×C8—742no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—2962no—
171C23—2962no—
172C23—748no—
173C23—742no—
174C23#1059693814yes—
175C23C2×C22⋊D3711yescharacteristic
176Q8—374no—
177Q8—742no—
178D4—24no—
179D4—24no—
180D4—374no—
181D4—7416no—
182D4—744no—
183D4—744no—
184D4—742no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—748no—
191C2×C4—742no—
192C2×C4—744no—
193C2×C4—744no—
194C2×C4C2×C4×D3711yescharacteristic
195C2×C4C2×D14811yescharacteristic
196C2×C4D4×D3712yes—
197C2×C4D4×D3712yes—
198C8—1482no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—2968no—
207C22—744no—
208C22—1482no—
209C22—1482no—
210C22C2×#1059693811yescharacteristic
211C22#1192450411yescharacteristic
212C22#1192450411yescharacteristic
213C4—42no—
214C4—81no—
215C4—744no—
216C4C22⋊C4×D3712yes—
217C4#1192450612yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—1484no—
222C2#1455738811yescharacteristic
223C2#1455770011yescharacteristic
224C2#1455771011yescharacteristic
subgroupG/H
centerC22#11924504
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#390C2
socleC22×C37#120
prime radicalC2×#11924581C2
cosocleC22×C4×C37C23
hypercenter#390D37
hypocenterC37#1792
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#11924464C2semidirect
3. #14557532C2semidirect
4. C2×#11924453C2semidirect
5. C37×#390C2semidirect
8. #11924581C4semidirect
13. C2×#10596934C22semidirect
19. C2×C4⋊C4×C37C22semidirect
21. C2×C42×C37C22semidirect
80. D148C22⋊C4semidirect
84. Dic74C22⋊C4semidirect
117. #390D37semidirect
118. C37#1792semidirect
128. C2×C4⋊C4C2×D37semidirect
130. C2×C42C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245812
C2×#119244642
#145575322
C2×#119244532
C37×#3902
#179237