Finite Group Databasebeta

← #18005210

Subgroups — #18005210

Order 4736.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#14558152C212yesmaximal, complemented
2#14557931C211yesmaximal, characteristic, complemented
3#14557892C212yesmaximal, complemented
4#14557788C211yesmaximal, characteristic, complemented
5#14557783C211yesmaximal, characteristic
6#14557759C212yesmaximal, complemented
7#14557645C211yesmaximal, characteristic, complemented
8#14557640C211yesmaximal, characteristic, complemented
9SD16×Dic37C212yesmaximal, complemented
10#14557487C211yesmaximal, characteristic, complemented
11C37×#495C211yesmaximal, characteristic, complemented
12C2×#10596929C2211yescharacteristic
13C2×C8×D37C2211yescharacteristic
14#11924536C2212yes—
15#11924529—22no—
16#11924522—22no—
17#11924520—22no—
18#11924513—22no—
19#11924512C2212yes—
20#11924507C2212yes—
21Q8×Dic37C2212yes—
22D4×Dic37C2212yes—
23#11924493C2211yescharacteristic
24#11924468C2212yes—
25#11924468C2211yescharacteristic
26#11924468C2211yescharacteristic
27#11924460C2212yes—
28#11924460C2212yes—
29#11924457C2212yes—
30#11924457C2212yes—
31#11924447C2211yescharacteristic
32#11924446C2211yescharacteristic
33C8×Dic37C2211yescharacteristic
34C2×Q16×C37C2211yescharacteristic
35C2×SD16×C37C2212yes—
36C2×D8×C37C2211yescharacteristic
37#124×C37C2212yes—
38C4×C8×C37C2211yescharacteristic
39C2×Q8×C37C2312yes—
40C2×D4×C37C2312yes—
41C2×C22⋊D37—22no—
42C22×Dic37—22no—
43C2×C4×D37C2311yescharacteristic
44C2×Dic74—22no—
45Q16×C37—22no—
46SD16×C37—24no—
47D8×C37—22no—
48C2×C8×C37C2311yescharacteristic
49C2×C8×C37C2311yescharacteristic
50C22⋊C4×C37—22no—
51C22⋊C4×C37—22no—
52C42×C37C2311yescharacteristic
53C22⋊Dic37—22no—
54C22⋊Dic37—22no—
55#10596938—22no—
56#10596938D412yes—
57C4⋊Dic37—22no—
58C4⋊Dic37—22no—
59C4⋊Dic37C2312yes—
60C4⋊Dic37C2312yes—
61#10596936—22no—
62#10596936D412yes—
63C4×Dic37—22no—
64C4×Dic37C2311yescharacteristic
65C2×#64436C2311yescharacteristic
66C2×#64436C2311yescharacteristic
67#10596929—22no—
68C8×D37—22no—
69C23×C37—22no—
70C22×D37C2×D411yescharacteristic
71Q8×C37—22no—
72Q8×C37—22no—
73D4×C37—22no—
74D4×C37—22no—
75C2×C4×C37—22no—
76C2×C4×C37C2×D412yes—
77C2×C4×C37C2411yescharacteristic
78C22⋊D37—82no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—82no—
82C2×Dic37C2×D412yes—
83C2×Dic37C2×D411yescharacteristic
84C4×D37—21no—
85C4×D37—21no—
86Dic74—82no—
87C8×C37#4112yes—
88C8×C37#4112yes—
89#64436—21no—
90#64436—21no—
91C22×C37—42no—
92C22×C37—42no—
93C22×C37—42no—
94C22×C37C22×D411yescharacteristic
95C2×D37—21no—
96C2×D37—22no—
97C4×C37—22no—
98C4×C37—42no—
99C4×C37C2×#4111yescharacteristic
100C4×C37C2×#4111yescharacteristic
101Dic37—21no—
102Dic37—22no—
103Dic37—42no—
104Dic37—42no—
105#3173—371nomaximal, Sylow
106C2×C37—82no—
107C2×C37#53211yescharacteristic
108C2×C37#57712yes—
109D37—41no—
110#542—372no—
111#498—371no—
112#495D3711yescharacteristic, complemented
113#489—372no—
114#470—371no—
115#469—371no—
116#465—372no—
117#442—371no—
118#441—371no—
119C4×SD16—372no—
120#405—371no—
121C37#317311yescharacteristic, complemented, Sylow
122C2×Q16C2×D3711yescharacteristic
123C2×SD16C2×D3712yes—
124C2×D8C2×D3711yescharacteristic
125C2×M16—371no—
126C22×C8—371no—
127C4⋊Q8—372no—
128#126—742no—
129#124—742no—
130#124C2×D3712yes—
131#123—742no—
132C22⋊Q8—372no—
133C22⋊Q8—742no—
134#121—372no—
135C4×Q8—372no—
136C4×D4—372no—
137#117—371no—
138#106—372no—
139#106—371no—
140#106—371no—
141#103—372no—
142#103—372no—
143#102—372no—
144#102—372no—
145#97—371no—
146#97—371no—
147C4×C8—371no—
148C4×C8C2×D3711yescharacteristic
149C2×Q8—742no—
150C2×Q8C22×D3712yes—
151C2×D4—742no—
152C2×D4C22×D3712yes—
153C22×C4—371no—
154C22×C4—742no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—742no—
159C2×C8—371no—
160C2×C8—371no—
161C2×C8—742no—
162C2×C8C22×D3711yescharacteristic
163C2×C8C22×D3711yescharacteristic
164C4⋊C4—372no—
165C4⋊C4—372no—
166C4⋊C4—372no—
167C4⋊C4—742no—
168C4⋊C4—742no—
169C4⋊C4—742no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—372no—
173C22⋊C4—742no—
174C22⋊C4—742no—
175C22⋊C4—742no—
176C42—371no—
177C42—742no—
178C42C22×D3711yescharacteristic
179C23—22no—
180C23—371no—
181Q8—22no—
182Q8—22no—
183Q8—2962no—
184D4—22no—
185D4—22no—
186D4—2962no—
187C2×C4—22no—
188C2×C4—372no—
189C2×C4—371no—
190C2×C4—2962no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4D4×D3712yes—
196C2×C4C23×D3711yescharacteristic
197C8—741no—
198C8—741no—
199C8#1059696412yes—
200C8#1059696412yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—741no—
205C22—742no—
206C22C2×D4×D3711yescharacteristic
207C4—22no—
208C4—42no—
209C4—741no—
210C4—742no—
211C4—1482no—
212C4—1482no—
213C4C2×#1059696411yescharacteristic
214C4C2×#1059696411yescharacteristic
215C2—82no—
216C2—1481no—
217C2#1455808111yescharacteristic
218C2#1455834012yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#495C2
socleC22×C37C22×D4
prime radical#14557783C2
hypercenter#495D37
hypocenterC37#3173
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14558152C2semidirect
2. #14557931C2semidirect
3. #14557892C2semidirect
4. #14557788C2semidirect
6. #14557759C2semidirect
7. #14557645C2semidirect
8. #14557640C2semidirect
9. SD16×Dic37C2semidirect
10. #14557487C2semidirect
11. C37×#495C2semidirect
112. #495D37semidirect
121. C37#3173semidirect

Maximal subgroups

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

subgroupindex
#145581522
#145579312
#145578922
#145577882
#145577832
#145577592
#145576452
#145576402
SD16×Dic372
#145574872
C37×#4952
#317337