Finite Group Databasebeta

← #18004129

Subgroups — #18004129

Order 4736.

458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11924566C211yesmaximal, characteristic
2C22×Dic148C211yesmaximal, characteristic, complemented
3#14558104C211yesmaximal, characteristic
4#14558010C211yesmaximal, characteristic, complemented
5#14557754C214yesmaximal, complemented
6#14557742C214yesmaximal, complemented
7#14557559C211yesmaximal, characteristic, complemented
8#14557541C211yesmaximal, characteristic, complemented
9C37×#416C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11C22×Dic74C2211yescharacteristic
12#11924566—24no—
13C2×Dic148—24no—
14C2×Dic148C2214yes—
15C2×#10596942C2212yes—
16C2×#10596940C2212yes—
17C2×#10596934C2211yescharacteristic
18#11924534C2212yes—
19#11924523C2212yes—
20#11924517—22no—
21#11924515—22no—
22C4×Dic74—22no—
23#11924501C2214yes—
24#11924495C2211yescharacteristic
25#11924492—22no—
26#11924465C2214yes—
27#11924459C2214yes—
28C2×#41×C37C2211yescharacteristic
29C22×C8×C37C2211yescharacteristic
30#117×C37C2211yescharacteristic
31#103×C37C2212yes—
32#102×C37C2212yes—
33#41×C37—22no—
34#41×C37—22no—
35C2×Q8×C37C2311yescharacteristic
36C2×D4×C37—21no—
37C2×D4×C37C2311yescharacteristic
38C22×C4×C37—21no—
39C22×C4×C37C2311yescharacteristic
40C22×Dic37—21no—
41C22×Dic37—21no—
42C2×Dic74—21no—
43C2×Dic74—22no—
44C2×Dic74—22no—
45C2×Dic74—22no—
46C2×Dic74—21no—
47C2×Dic74D414yes—
48C2×Dic74C2312yes—
49C2×Dic74C2312yes—
50C2×C8×C37—22no—
51C2×C8×C37C2312yes—
52C4⋊C4×C37C2312yes—
53C22⋊C4×C37—21no—
54C42×C37—21no—
55C22⋊Dic37—24no—
56C22⋊Dic37D412yes—
57#10596942—24no—
58#10596940—24no—
59C4⋊Dic37D412yes—
60#10596936—24no—
61#10596936—24no—
62C4×Dic37—24no—
63C4×Dic37C2312yes—
64#10596934—22no—
65C2×#64436C2312yes—
66Dic148—28no—
67C23×C37—21no—
68C23×C37C2×D411yescharacteristic
69Q8×C37—21no—
70Q8×C37—21no—
71D4×C37—21no—
72D4×C37—21no—
73D4×C37—42no—
74C2×C4×C37—22no—
75C2×C4×C37—21no—
76C2×C4×C37—42no—
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D412yes—
79C2×C4×C37#4112yes—
80C2×C4×C37C2411yescharacteristic
81C2×Dic37—24no—
82C2×Dic37—22no—
83C2×Dic37—22no—
84C2×Dic37—42no—
85C2×Dic37C2×D414yes—
86Dic74—24no—
87Dic74—22no—
88Dic74—22no—
89Dic74—22no—
90Dic74—42no—
91Dic74C2×D414yes—
92C8×C37—22no—
93#64436—22no—
94C22×C37—22no—
95C22×C37—41no—
96C22×C37—42no—
97C22×C37#12112yes—
98C22×C37C22×D411yescharacteristic
99C4×C37—41no—
100C4×C37—42no—
101C4×C37#12112yes—
102C4×C37C22×D411yescharacteristic
103C4×C37C2×#4111yescharacteristic
104Dic37—24no—
105Dic37—24no—
106Dic37—42no—
107#3044—371nomaximal, Sylow
108C2×C37—22no—
109C2×C37—81no—
110C2×C37C2×#12111yescharacteristic
111C2×C37#57812yes—
112C2×#137—371no—
113C22×Q16—371no—
114#536—371no—
115#519—371no—
116#464—374no—
117#462—374no—
118#424—371no—
119#419—371no—
120#416D3711yescharacteristic
121C37#304411yescharacteristic, complemented, Sylow
122C2×#41C2×D3711yescharacteristic
123C22×Q8—371no—
124C22×Q8—371no—
125#137—744no—
126C2×Q16—372no—
127C2×Q16—374no—
128C2×Q16—744no—
129C2×SD16—372no—
130C2×M16—371no—
131C22×C8C2×D3711yescharacteristic
132C4⋊Q8—372no—
133#124—372no—
134#123—742no—
135C22⋊Q8—742no—
136C4×Q8—374no—
137C4×Q8—742no—
138#117—371no—
139#117—742no—
140#117C2×D3711yescharacteristic
141C4⋊C8—374no—
142#103—374no—
143#103C2×D3712yes—
144#102C2×D3712yes—
145#41—22no—
146#41—22no—
147C2×Q8—374no—
148C2×Q8—372no—
149C2×Q8—372no—
150C2×Q8—742no—
151C2×Q8—741no—
152C2×Q8—741no—
153C2×Q8—742no—
154C2×Q8—742no—
155C2×Q8C22×D3711yescharacteristic
156C2×D4—21no—
157C2×D4C22×D3711yescharacteristic
158C22×C4—21no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4C22×D3711yescharacteristic
162Q16—748no—
163Q16—744no—
164SD16—744no—
165M16—742no—
166C2×C8—22no—
167C2×C8—372no—
168C2×C8C22×D3712yes—
169C4⋊C4—372no—
170C4⋊C4—744no—
171C4⋊C4—744no—
172C4⋊C4C22×D3712yes—
173C22⋊C4—21no—
174C22⋊C4—372no—
175C22⋊C4—744no—
176C42—21no—
177C42—372no—
178C42—744no—
179C23—21no—
180C23D4×D3711yescharacteristic
181Q8—21no—
182Q8—21no—
183Q8—374no—
184Q8—744no—
185Q8—742no—
186Q8—742no—
187Q8—742no—
188Q8—1482no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—374no—
196C2×C4—744no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—1482no—
200C2×C4#1059696212yes—
201C2×C4D4×D3711yescharacteristic
202C2×C4D4×D3712yes—
203C2×C4C23×D3711yescharacteristic
204C8—22no—
205C8—742no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#1192450912yes—
210C22C2×D4×D3711yescharacteristic
211C4—41no—
212C4—42no—
213C4—744no—
214C4—744no—
215C4—1482no—
216C4#1192450912yes—
217C4C2×D4×D3711yescharacteristic
218C4C2×#1059696211yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1192450911yescharacteristic
222C2#1455834712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
prime radicalC2×#41×C37C22
hypercenter#416D37
hypocenterC37#3044
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C22×Dic148C2semidirect
4. #14558010C2semidirect
5. #14557754C2semidirect
6. #14557742C2semidirect
7. #14557559C2semidirect
8. #14557541C2semidirect
121. C37#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
C22×Dic1482
#145581042
#145580102
#145577542
#145577422
#145575592
#145575412
C37×#4162
#304437