Finite Group Databasebeta

← #18004122

Subgroups — #18004122

Order 4736.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10596942C211yesmaximal, characteristic, complemented
3#14558010C211yesmaximal, characteristic, complemented
4#14557752C214yesmaximal, complemented
5#14557740C214yesmaximal, complemented
6#14557560C211yesmaximal, characteristic, complemented
7#14557542C211yesmaximal, characteristic, complemented
8#14557529C211yesmaximal, characteristic
9C37×#536C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11#11924566—24no—
12C2×#10596942—24no—
13C2×#10596942C2212yes—
14C2×#10596942C2214yes—
15C2×#10596940C2212yes—
16C2×#10596934C2211yescharacteristic
17C22×#64436C2211yescharacteristic
18C4×Dic74C2214yes—
19#11924501—22no—
20#11924495C2211yescharacteristic
21#11924492—22no—
22C4⋊#64436C2214yes—
23#11924460C2212yes—
24#11924460C2214yes—
25#11924457C2212yes—
26C2×#41×C37C2211yescharacteristic
27C22×Q8×C37C2211yescharacteristic
28C4⋊Q8×C37C2212yes—
29#124×C37C2212yes—
30#123×C37—22no—
31C22⋊Q8×C37—22no—
32#117×C37C2211yescharacteristic
33#41×C37—22no—
34#41×C37—22no—
35C2×Q8×C37—21no—
36C2×Q8×C37—22no—
37C2×Q8×C37—22no—
38C2×Q8×C37C2312yes—
39C2×Q8×C37C2311yescharacteristic
40C2×D4×C37—21no—
41C2×D4×C37C2311yescharacteristic
42C22×C4×C37—21no—
43C22×C4×C37—21no—
44C22×C4×C37C2311yescharacteristic
45C22×Dic37—21no—
46C2×Dic74—21no—
47C2×Dic74—22no—
48C2×Dic74D414yes—
49C2×Dic74C2312yes—
50C4⋊C4×C37—24no—
51C4⋊C4×C37D412yes—
52C22⋊C4×C37—24no—
53C22⋊C4×C37D412yes—
54C42×C37C2312yes—
55C22⋊Dic37—21no—
56#10596942—28no—
57#10596942—24no—
58#10596940—24no—
59C4⋊Dic37C2312yes—
60#10596936—24no—
61C4×Dic37—24no—
62C4×Dic37—21no—
63#10596934—22no—
64C2×#64436—22no—
65C2×#64436C2312yes—
66C2×#64436C2312yes—
67C23×C37—21no—
68C23×C37C2×D411yescharacteristic
69Q8×C37—22no—
70Q8×C37—21no—
71Q8×C37—22no—
72Q8×C37—21no—
73Q8×C37—42no—
74D4×C37—21no—
75D4×C37—21no—
76D4×C37—42no—
77C2×C4×C37—22no—
78C2×C4×C37—21no—
79C2×C4×C37—42no—
80C2×C4×C37—42no—
81C2×C4×C37C2×D412yes—
82C2×C4×C37C2×D414yes—
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37#4112yes—
85C2×C4×C37C2411yescharacteristic
86C2×Dic37—24no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89Dic74—24no—
90Dic74—22no—
91Dic74C2×D414yes—
92#64436—22no—
93#64436—22no—
94C22×C37—22no—
95C22×C37—41no—
96C22×C37—42no—
97C22×C37#12112yes—
98C22×C37C22×D411yescharacteristic
99C4×C37—24no—
100C4×C37—41no—
101C4×C37—42no—
102C4×C37#12112yes—
103C4×C37C22×D411yescharacteristic
104C4×C37C2×#4111yescharacteristic
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#536D3711yescharacteristic
115#519—371no—
116#464—374no—
117#462—374no—
118#424—371no—
119#419—371no—
120#416—371no—
121C37#304411yescharacteristic, complemented, Sylow
122C2×#41C2×D3711yescharacteristic
123C22×Q8—371no—
124C22×Q8C2×D3711yescharacteristic
125#137—744no—
126C2×Q16—374no—
127C2×Q16—372no—
128C2×Q16—744no—
129C2×SD16—372no—
130C2×M16—371no—
131C22×C8—371no—
132C4⋊Q8C2×D3712yes—
133#124C2×D3712yes—
134#123—22no—
135C22⋊Q8—22no—
136C4×Q8—374no—
137C4×Q8—742no—
138#117—371no—
139#117—742no—
140#117C2×D3711yescharacteristic
141C4⋊C8—374no—
142#103—372no—
143#103—374no—
144#102—372no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—374no—
151C2×Q8—372no—
152C2×Q8—742no—
153C2×Q8—741no—
154C2×Q8C22×D3712yes—
155C2×Q8C22×D3711yescharacteristic
156C2×D4—21no—
157C2×D4C22×D3711yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—741no—
161C22×C4C22×D3711yescharacteristic
162Q16—748no—
163Q16—744no—
164SD16—744no—
165M16—742no—
166C2×C8—372no—
167C2×C8—372no—
168C2×C8—742no—
169C4⋊C4—24no—
170C4⋊C4—372no—
171C4⋊C4—744no—
172C4⋊C4C22⋊D3712yes—
173C22⋊C4—24no—
174C22⋊C4—741no—
175C22⋊C4C22⋊D3712yes—
176C42—741no—
177C42—744no—
178C42C22×D3712yes—
179C23—21no—
180C23C2×C22⋊D3711yescharacteristic
181Q8—22no—
182Q8—21no—
183Q8—22no—
184Q8—21no—
185Q8—42no—
186Q8—374no—
187Q8—744no—
188Q8—742no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—744no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4D4×D3712yes—
200C2×C4#1059696412yes—
201C2×C4C2×C22⋊D3714yes—
202C2×C4C2×C22⋊D3711yescharacteristic
203C2×C4C23×D3711yescharacteristic
204C8—742no—
205C8—742no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#1192450712yes—
210C22C22×C22⋊D3711yescharacteristic
211C4—24no—
212C4—41no—
213C4—42no—
214C4—744no—
215C4—1482no—
216C4#1192450712yes—
217C4C2×D4×D3711yescharacteristic
218C4C2×#1059696411yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1192450711yescharacteristic
222C2#1455834812yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#536C2
socleC22×C37C22×D4
prime radicalC2×#41×C37C22
hypercenter#536D37
hypocenterC37#3044
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C22×#10596942C2semidirect
3. #14558010C2semidirect
4. #14557752C2semidirect
5. #14557740C2semidirect
6. #14557560C2semidirect
7. #14557542C2semidirect
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×#105969422
#145580102
#145577522
#145577402
#145575602
#145575422
#145575292
C37×#5362
#304437