Finite Group Databasebeta

← #18004248

Subgroups — #18004248

Order 4736.

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

normal subgroups only

This group has 460 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
1C22×#10596942C211yesmaximal, characteristic, complemented
2C2×#11924543C211yesmaximal, characteristic
3#14558104C211yesmaximal, characteristic
4#14557789C214yesmaximal, complemented
5#14557772C214yesmaximal, complemented
6#14557569C211yesmaximal, characteristic, complemented
7#14557542C211yesmaximal, characteristic, complemented
8#14557541C211yesmaximal, characteristic, complemented
9C37×#536C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11C2×#10596942—24no—
12C2×#10596942C2212yes—
13C2×#10596942C2212yes—
14#11924543—24no—
15C2×#10596934C2212yes—
16C2×#10596934C2211yescharacteristic
17C22×#64436C2212yes—
18C22×#64436C2211yescharacteristic
19#11924534—21no—
20#11924523—21no—
21#11924517—22no—
22#11924515C2214yes—
23#11924495C2211yescharacteristic
24#11924469C2212yes—
25#11924467C2212yes—
26#11924460C2214yes—
27#11924459C2214yes—
28C2×#41×C37C2211yescharacteristic
29C22×Q8×C37C2211yescharacteristic
30C4⋊Q8×C37—21no—
31#124×C37—21no—
32#123×C37—22no—
33C22⋊Q8×C37C2214yes—
34#117×C37C2211yescharacteristic
35#41×C37—22no—
36#41×C37—22no—
37C2×Q8×C37—21no—
38C2×Q8×C37—22no—
39C2×Q8×C37—22no—
40C2×Q8×C37D411yescharacteristic
41C2×Q8×C37C2312yes—
42C2×D4×C37D412yes—
43C2×D4×C37D411yescharacteristic
44C22×C4×C37—21no—
45C22×C4×C37C2312yes—
46C22×C4×C37C2311yescharacteristic
47C22×Dic37—21no—
48C2×Dic74—22no—
49C2×Dic74—22no—
50C2×Dic74—21no—
51C2×Dic74C2312yes—
52C4⋊C4×C37—24no—
53C4⋊C4×C37C2312yes—
54C22⋊C4×C37—21no—
55C22⋊C4×C37—24no—
56C42×C37—21no—
57C22⋊Dic37—21no—
58C22⋊Dic37—24no—
59#10596942—24no—
60#10596942—24no—
61C4⋊Dic37C2312yes—
62#10596936—24no—
63C4×Dic37—21no—
64#10596934—22no—
65#10596934—24no—
66C2×#64436—24no—
67C2×#64436D414yes—
68C2×#64436C2312yes—
69C2×#64436C2311yescharacteristic
70C2×#64436C2311yescharacteristic
71C23×C37C2×D412yes—
72C23×C37C2×D411yescharacteristic
73Q8×C37—22no—
74Q8×C37—22no—
75Q8×C37—22no—
76Q8×C37—42no—
77D4×C37—24no—
78D4×C37—22no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—42no—
84C2×C4×C37C2×D412yes—
85C2×C4×C37C2×D412yes—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37#4112yes—
88C2×C4×C37C2411yescharacteristic
89C2×Dic37—22no—
90C2×Dic37—22no—
91C2×Dic37—42no—
92Dic74—22no—
93Dic74—22no—
94Dic74—42no—
95#64436—22no—
96#64436C2×D412yes—
97#64436C2×D412yes—
98C22×C37—22no—
99C22×C37—22no—
100C22×C37—24no—
101C22×C37#12112yes—
102C22×C37C22×D411yescharacteristic
103C4×C37—22no—
104C4×C37—42no—
105C4×C37—42no—
106C4×C37#12112yes—
107C4×C37C22×D411yescharacteristic
108C4×C37C2×#4111yescharacteristic
109Dic37—42no—
110Dic37—42no—
111#3059—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37—42no—
114C2×C37C2×#12111yescharacteristic
115C2×C37#57812yes—
116C22×Q16—371no—
117C2×#131—371no—
118#536—371no—
119#536D3711yescharacteristic
120#470—374no—
121#467—374no—
122#427—371no—
123#419—371no—
124#419—371no—
125C37#305911yescharacteristic, complemented, Sylow
126C2×#41C2×D3711yescharacteristic
127C22×Q8—371no—
128C22×Q8C2×D3711yescharacteristic
129C2×Q16—372no—
130C2×Q16—372no—
131C2×Q16—744no—
132#131—744no—
133C2×M16—371no—
134C2×M16—372no—
135C22×C8—371no—
136C22×C8—372no—
137C4⋊Q8—21no—
138C4⋊Q8—741no—
139#124—21no—
140#124—741no—
141#123—22no—
142#123—742no—
143C22⋊Q8—374no—
144C22⋊Q8C2×D3714yes—
145#117—371no—
146#117C2×D3711yescharacteristic
147#107—372no—
148#106—372no—
149#103—374no—
150#103—374no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—372no—
157C2×Q8—741no—
158C2×Q8—742no—
159C2×Q8—742no—
160C2×Q8C22⋊D3711yescharacteristic
161C2×Q8C22×D3712yes—
162C2×D4C22⋊D3712yes—
163C2×D4C22⋊D3711yescharacteristic
164C22×C4—21no—
165C22×C4—741no—
166C22×C4C22×D3712yes—
167C22×C4C22×D3711yescharacteristic
168Q16—744no—
169Q16—744no—
170M16—744no—
171M16—742no—
172C2×C8—374no—
173C2×C8—371no—
174C2×C8—371no—
175C2×C8—372no—
176C2×C8—744no—
177C4⋊C4—24no—
178C4⋊C4—372no—
179C4⋊C4—744no—
180C4⋊C4C22×D3712yes—
181C22⋊C4—21no—
182C22⋊C4—24no—
183C22⋊C4—741no—
184C22⋊C4—744no—
185C42—21no—
186C42—741no—
187C23C2×C22⋊D3712yes—
188C23C2×C22⋊D3711yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—742no—
194Q8—742no—
195Q8—1482no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—742no—
204C2×C4—742no—
205C2×C4—1482no—
206C2×C4D4×D3712yes—
207C2×C4#1059696412yes—
208C2×C4C2×C22⋊D3712yes—
209C2×C4C2×C22⋊D3711yescharacteristic
210C2×C4C23×D3711yescharacteristic
211C8—372no—
212C8—372no—
213C8—742no—
214C22—22no—
215C22—22no—
216C22—24no—
217C22#1192450812yes—
218C22C22×C22⋊D3711yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—1482no—
223C4—1482no—
224C4#1192450812yes—
225C4C2×D4×D3711yescharacteristic
226C4C2×#1059696411yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#1192450811yescharacteristic
230C2#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#3059
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#10596942C2semidirect
4. #14557789C2semidirect
5. #14557772C2semidirect
6. #14557569C2semidirect
7. #14557542C2semidirect
8. #14557541C2semidirect
125. C37#3059semidirect

Maximal subgroups

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

subgroupindex
C22×#105969422
C2×#119245432
#145581042
#145577892
#145577722
#145575692
#145575422
#145575412
C37×#5362
#305937