Finite Group Databasebeta

← #18005320

Subgroups — #18005320

Order 4736.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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#14558064C212yesmaximal, complemented
2#14557933C211yesmaximal, characteristic, complemented
3#14557916C211yesmaximal, characteristic, complemented
4#14557886C212yesmaximal, complemented
5#14557791C211yesmaximal, characteristic, complemented
6#14557777C212yesmaximal, complemented
7#14557645C211yesmaximal, characteristic, complemented
8#14557639C211yesmaximal, characteristic, complemented
9#14557630C212yesmaximal, complemented
10M16×Dic37C211yesmaximal, characteristic, complemented
11C37×#469C211yesmaximal, characteristic
12C2×Dic148C2211yescharacteristic
13C2×#10596940C2212yes—
14C2×#10596934C2211yescharacteristic
15#11924529—22no—
16#11924527C2212yes—
17#11924523C2212yes—
18#11924517—22no—
19#11924515C2212yes—
20#11924501C2212yes—
21D4×Dic37—22no—
22D4×Dic37C2212yes—
23#11924492—22no—
24C2×C4×Dic37C2211yescharacteristic
25#11924469C2212yes—
26#11924468C2211yescharacteristic
27#11924461C2212yes—
28#11924459C2212yes—
29#11924457C2212yes—
30#11924446C2211yescharacteristic
31#11924446C2211yescharacteristic
32C8×Dic37C2211yescharacteristic
33C8×Dic37C2211yescharacteristic
34C2×D8×C37C2211yescharacteristic
35C2×M16×C37C2211yescharacteristic
36#121×C37C2212yes—
37#106×C37C2211yescharacteristic
38#102×C37C2212yes—
39C2×D4×C37—22no—
40C2×D4×C37C2312yes—
41C22×C4×C37C2311yescharacteristic
42C22×Dic37—22no—
43C22×Dic37D412yes—
44C2×Dic74C2312yes—
45D8×C37—22no—
46M16×C37—22no—
47C2×C8×C37C2311yescharacteristic
48C2×C8×C37C2311yescharacteristic
49C4⋊C4×C37C2312yes—
50C22⋊C4×C37—22no—
51C22⋊Dic37—22no—
52C22⋊Dic37—22no—
53C22⋊Dic37—22no—
54C22⋊Dic37—22no—
55#10596940—24no—
56C4⋊Dic37—22no—
57C4⋊Dic37C2312yes—
58#10596936—22no—
59#10596936—22no—
60#10596936—22no—
61C4×Dic37—22no—
62C4×Dic37D412yes—
63C4×Dic37C2311yescharacteristic
64C4×Dic37C2311yescharacteristic
65#10596934—22no—
66C2×#64436C2311yescharacteristic
67C2×#64436C2311yescharacteristic
68Dic148—22no—
69C23×C37—22no—
70C23×C37C2×D411yescharacteristic
71D4×C37—22no—
72D4×C37—22no—
73D4×C37—44no—
74C2×C4×C37—21no—
75C2×C4×C37—21no—
76C2×C4×C37—22no—
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2411yescharacteristic
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—42no—
82C2×Dic37—44no—
83C2×Dic37C2×D412yes—
84C2×Dic37C2×D412yes—
85Dic74—22no—
86Dic74—22no—
87C8×C37—21no—
88C8×C37#4112yes—
89#64436—21no—
90#64436#4112yes—
91C22×C37—21no—
92C22×C37—22no—
93C22×C37—42no—
94C22×C37—42no—
95C22×C37—42no—
96C22×C37C22×D411yescharacteristic
97C4×C37—21no—
98C4×C37—42no—
99C4×C37C2×#4111yescharacteristic
100C4×C37C2×#4111yescharacteristic
101Dic37—22no—
102Dic37—22no—
103Dic37—42no—
104Dic37—42no—
105#3183—371nomaximal, Sylow
106C2×C37—41no—
107C2×C37—82no—
108C2×C37#53211yescharacteristic
109C2×C37#57512yes—
110#529—372no—
111#499—371no—
112#495—371no—
113#488—372no—
114#470—371no—
115#469D3711yescharacteristic
116#468—372no—
117#442—371no—
118#441—371no—
119#440—372no—
120C4×M16—371no—
121C37#318311yescharacteristic, complemented, Sylow
122C2×Q16—371no—
123C2×SD16—372no—
124C2×D8C2×D3711yescharacteristic
125C2×M16—371no—
126C2×M16C2×D3711yescharacteristic
127#126—742no—
128#125—372no—
129#124—372no—
130#123—742no—
131C22⋊Q8—372no—
132#121C2×D3712yes—
133C4×Q8—372no—
134C4×D4—372no—
135C4×D4—742no—
136#117—742no—
137C2×C42—371no—
138#107—372no—
139#106—371no—
140#106C2×D3711yescharacteristic
141#103—372no—
142#103—372no—
143#102—372no—
144#102C2×D3712yes—
145#97—371no—
146#97—371no—
147C4×C8—371no—
148C4×C8—371no—
149C2×Q8—372no—
150C2×D4—22no—
151C2×D4C22×D3712yes—
152C22×C4—372no—
153C22×C4—742no—
154C22×C4C22×D3711yescharacteristic
155Q16—742no—
156SD16—744no—
157D8—22no—
158M16—22no—
159M16—742no—
160C2×C8—371no—
161C2×C8—371no—
162C2×C8C22×D3711yescharacteristic
163C2×C8C22×D3711yescharacteristic
164C4⋊C4—372no—
165C4⋊C4—742no—
166C4⋊C4—742no—
167C4⋊C4—742no—
168C4⋊C4—742no—
169C4⋊C4C22×D3712yes—
170C22⋊C4—22no—
171C22⋊C4—742no—
172C22⋊C4—742no—
173C22⋊C4—742no—
174C22⋊C4—742no—
175C42—372no—
176C42—371no—
177C42—371no—
178C42—742no—
179C23—22no—
180C23D4×D3711yescharacteristic
181Q8—742no—
182Q8—742no—
183D4—22no—
184D4—22no—
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—372no—
190C2×C4—372no—
191C2×C4—742no—
192C2×C4—742no—
193C2×C4—1482no—
194C2×C4—1484no—
195C2×C4D4×D3711yescharacteristic
196C2×C4C23×D3711yescharacteristic
197C8—21no—
198C8—372no—
199C8—741no—
200C8#1059696412yes—
201C22—22no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C2×D4×D3711yescharacteristic
207C4—21no—
208C4—42no—
209C4—742no—
210C4—742no—
211C4—1482no—
212C4—1482no—
213C4#41×D3711yescharacteristic
214C4C2×#1059696411yescharacteristic
215C2—41no—
216C2—82no—
217C2#1455807811yescharacteristic
218C2#1455832912yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37#3183
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14558064C2semidirect
2. #14557933C2semidirect
3. #14557916C2semidirect
4. #14557886C2semidirect
5. #14557791C2semidirect
6. #14557777C2semidirect
7. #14557645C2semidirect
8. #14557639C2semidirect
9. #14557630C2semidirect
10. M16×Dic37C2semidirect
121. C37#3183semidirect

Maximal subgroups

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

subgroupindex
#145580642
#145579332
#145579162
#145578862
#145577912
#145577772
#145576452
#145576392
#145576302
M16×Dic372
C37×#4692
#318337