Finite Group Databasebeta

← #18006374

Subgroups — #18006374

Order 4736.

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

normal subgroups only

This group has 448 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#14558349C212yesmaximal, complemented
2#14558344C212yesmaximal, complemented
3#14557928C211yesmaximal, characteristic, complemented
4#14557806C212yesmaximal, complemented
5#14557795C212yesmaximal, complemented
6#14557717C212yesmaximal, complemented
7#14557705C211yesmaximal, characteristic, complemented
8#14557652C212yesmaximal, complemented
9C37×#455C211yesmaximal, characteristic, complemented
10#11924584C2211yescharacteristic, complemented
11#11924583C2212yes—
12#11924569C2212yescomplemented
13#11924568—22no—
14#11924566—22no—
15#11924566C2212yes—
16#11924565—22no—
17#11924562—22no—
18#11924562C2212yes—
19#11924557—22no—
20#11924556—22no—
21#11924556C2212yes—
22C2×#10596942C2212yescomplemented
23Q16×D37—22no—
24C2×#10596940—22no—
25C2×#10596940C2212yes—
26#11924544C2212yescomplemented
27#11924543C2212yes—
28#11924536C2211yescharacteristic, complemented
29#11924471C2212yescomplemented
30#11924464C2212yescomplemented
31#11924455C2211yescharacteristic, complemented
32#11924454C2212yescomplemented
33#11924447C2211yescharacteristic, complemented
34H(5,𝔽2)×C37C2211yescharacteristic
35#137×C37C2212yes—
36#124×C37C2211yescharacteristic
37#104×C37C2212yes—
38#100×C37C2211yescharacteristic
39#41×C37—22no—
40#41×C37C2312yes—
41C2×Q8×C37C2311yescharacteristic
42C2×D4×C37—22no—
43C2×D4×C37—41no—
44C2×D4×C37C2311yescharacteristic
45#10596966—22no—
46Q8×D37—22no—
47Q8×D37—22no—
48#10596964—22no—
49#10596964—42no—
50#10596962—22no—
51#10596962—41no—
52#10596962C2312yes—
53C2×Dic74—22no—
54C2×Dic74C2312yes—
55Q16×C37—22no—
56SD16×C37—22no—
57M16×C37C2312yes—
58C22⋊C4×C37—41no—
59C42×C37C2311yescharacteristic
60#10596942—22no—
61#10596942—22no—
62#10596942—22no—
63#10596942D412yes—
64#10596941D412yes—
65#10596940—22no—
66#10596940—22no—
67#10596940—22no—
68#10596940—22no—
69#10596940D412yes—
70#10596939—22no—
71#10596939D412yes—
72C4⋊Dic37—41no—
73#10596934—22no—
74#10596934C2312yes—
75C2×#64436—22no—
76C2×#64436C2312yes—
77Dic148—22no—
78#10596930—22no—
79#10596929—22no—
80C8×D37—22no—
81C23×C37—21no—
82C23×C37—41no—
83Q8×C37—22no—
84Q8×C37C2×D412yes—
85D4×C37—22no—
86D4×C37—22no—
87D4×C37—42no—
88D4×C37C2×D412yes—
89C2×C4×C37—22no—
90C2×C4×C37—21no—
91C2×C4×C37—21no—
92C2×C4×C37—41no—
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—22no—
95C22⋊D37—42no—
96C2×Dic37—22no—
97C2×Dic37—42no—
98D148—41no—
99D148C2×D412yes—
100C4×D37—22no—
101C4×D37—42no—
102C4×D37—42no—
103Dic74—22no—
104Dic74—22no—
105Dic74—41no—
106Dic74—42no—
107Dic74C2×D412yes—
108C8×C37—22no—
109#64436—22no—
110#64436C2×D412yes—
111#64436C2×D412yes—
112C22×C37—22no—
113C22×C37—41no—
114C22×C37—81no—
115C22×C37—161no—
116C22×C37H(5,𝔽2)11yescharacteristic
117C2×D37—22no—
118C4×C37—22no—
119C4×C37—41no—
120C4×C37—41no—
121C4×C37C22×D412yes—
122Dic37—22no—
123Dic37—42no—
124#3289—371nomaximal, Sylow
125C2×C37—21no—
126C2×C37—42no—
127C2×C37—81no—
128C2×C37D4211yescharacteristic
129D37—42no—
130#578—372no—
131#577—372no—
132#497—371no—
133#473—372no—
134#471—372no—
135#456—372no—
136#455D3711yescharacteristic, complemented
137#454—371no—
138#444—372no—
139C37#328911yescharacteristic, complemented, Sylow
1402−1+4—372no—
1412−1+4—371no—
142H(5,𝔽2)C2×D3711yescharacteristic
143#137—372no—
144#137—372no—
145#137—742no—
146#137—742no—
147#137—742no—
148#137C2×D3712yes—
149AGL(1,ℤ/8)—372no—
150AGL(1,ℤ/8)—742no—
151#135—372no—
152#135—742no—
153#135—742no—
154C2×Q16—372no—
155C2×Q16—742no—
156C2×SD16—372no—
157C2×SD16—742no—
158#131—372no—
159#131—372no—
160C4⋊Q8—371no—
161#124C2×D3711yescharacteristic
162#108—372no—
163#104—372no—
164#104C2×D3712yes—
165#101—371no—
166#101—372no—
167#100C2×D3711yescharacteristic
168#97—371no—
169#41—22no—
170#41—372no—
171#41—742no—
172#41—742no—
173#41—742no—
174#41—1481no—
175#41—1482no—
176#41C22×D3712yes—
177C2×Q8—372no—
178C2×Q8—742no—
179C2×Q8—742no—
180C2×Q8—742no—
181C2×Q8C22×D3711yescharacteristic
182C2×D4—22no—
183C2×D4—41no—
184C2×D4C22×D3711yescharacteristic
185Q16—22no—
186Q16—372no—
187Q16—742no—
188Q16—742no—
189Q16—742no—
190Q16—742no—
191SD16—22no—
192SD16—372no—
193SD16—372no—
194SD16—742no—
195SD16—742no—
196SD16—742no—
197SD16—742no—
198SD16—742no—
199D8—372no—
200D8—742no—
201M16—372no—
202M16—742no—
203M16—742no—
204M16C22×D3712yes—
205C2×C8—372no—
206C2×C8—742no—
207C2×C8—742no—
208C4⋊C4—1481no—
209C22⋊C4—41no—
210C42C22×D3711yescharacteristic
211C23—21no—
212C23—41no—
213Q8—22no—
214Q8—372no—
215Q8—742no—
216Q8—742no—
217Q8—1482no—
218Q8—1481no—
219Q8D4×D3712yes—
220D4—22no—
221D4—22no—
222D4—42no—
223D4—372no—
224D4—742no—
225D4—1481no—
226D4—1482no—
227D4D4×D3712yes—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—742no—
233C2×C4—742no—
234C2×C4—1482no—
235C2×C4—1482no—
236C2×C4—1482no—
237C2×C4C23×D3711yescharacteristic
238C8—22no—
239C8—372no—
240C8—372no—
241C8—742no—
242C22—22no—
243C22—41no—
244C22—81no—
245C22—161no—
246C22—742no—
247C22#1192458111yescharacteristic
248C4—22no—
249C4—41no—
250C4—41no—
251C4—742no—
252C4—1482no—
253C4C2×D4×D3712yes—
254C2—21no—
255C2—42no—
256C2—81no—
257C2—1482no—
258C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#455C2
socleC2×C37D42
hypercenter#455D37
hypocenterC37#3289
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14558349C2semidirect
2. #14558344C2semidirect
3. #14557928C2semidirect
4. #14557806C2semidirect
5. #14557795C2semidirect
6. #14557717C2semidirect
7. #14557705C2semidirect
8. #14557652C2semidirect
9. C37×#455C2semidirect
10. #11924584C22semidirect
12. #11924569C22semidirect
22. C2×#10596942C22semidirect
26. #11924544C22semidirect
28. #11924536C22semidirect
29. #11924471C22semidirect
30. #11924464C22semidirect
31. #11924455C22semidirect
32. #11924454C22semidirect
33. #11924447C22semidirect
136. #455D37semidirect
139. C37#3289semidirect

Maximal subgroups

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

subgroupindex
#145583492
#145583442
#145579282
#145578062
#145577952
#145577172
#145577052
#145576522
C37×#4552
#328937