Finite Group Databasebeta

← #18006371

Subgroups — #18006371

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#14558346C212yesmaximal, complemented
2#14558339C212yesmaximal, complemented
3#14557805C212yesmaximal, complemented
4#14557793C212yesmaximal, complemented
5#14557715C212yesmaximal, complemented
6#14557710C211yesmaximal, characteristic, complemented
7#14557705C211yesmaximal, characteristic, complemented
8#14557656C212yesmaximal, complemented
9C37×#497C211yesmaximal, characteristic, complemented
10#11924584C2212yes—
11#11924584C2211yescharacteristic, complemented
12#11924581C2211yescharacteristic
13#11924568—22no—
14#11924568—22no—
15#11924567C2212yes—
16#11924567C2212yes—
17#11924567C2212yescomplemented
18#11924565—22no—
19#11924563—22no—
20#11924562C2212yes—
21#11924559—22no—
22#11924558C2212yes—
23#11924557—22no—
24Q16×D37—22no—
25SD16×D37—22no—
26#11924542C2212yes—
27#11924542C2212yescomplemented
28#11924472C2212yescomplemented
29#11924464C2212yes—
30#11924464C2212yescomplemented
31#11924455C2211yescharacteristic, complemented
32#11924455C2212yescomplemented
33#11924453C2211yescharacteristic
34C2×Q16×C37C2212yescomplemented
35C2×SD16×C37C2212yes—
36C4⋊Q8×C37C2211yescharacteristic, complemented
37#124×C37C2211yescharacteristic
38#97×C37C2211yescharacteristic, complemented
39C2×Q8×C37C2311yescharacteristic
40C2×Q8×C37C2312yes—
41C2×D4×C37C2311yescharacteristic
42C2×C22⋊D37—41no—
43#10596966—22no—
44#10596966—22no—
45#10596966—22no—
46Q8×D37—22no—
47Q8×D37—22no—
48Q8×D37—22no—
49#10596964—22no—
50D4×D37—22no—
51#10596962—42no—
52#10596962—41no—
53#10596962C2312yes—
54#10596962C2312yes—
55Q16×C37—22no—
56Q16×C37—22no—
57SD16×C37—22no—
58SD16×C37—22no—
59C2×C8×C37C2312yes—
60C4⋊C4×C37—41no—
61C22⋊C4×C37—41no—
62C42×C37C2311yescharacteristic
63#10596942—22no—
64#10596942—22no—
65#10596942—22no—
66#10596941—22no—
67#10596941—22no—
68#10596941—22no—
69#10596940—22no—
70#10596939—22no—
71#10596934C2312yes—
72#10596934C2312yes—
73Dic148D412yes—
74D296D412yes—
75#10596930D412yes—
76#10596930D412yes—
77#10596929—22no—
78#10596929—22no—
79C8×D37—22no—
80C8×D37—22no—
81C23×C37—21no—
82C22×D37—41no—
83Q8×C37—22no—
84Q8×C37—22no—
85Q8×C37—22no—
86D4×C37—22no—
87C2×C4×C37—21no—
88C2×C4×C37—21no—
89C2×C4×C37—22no—
90C2×C4×C37C2411yescharacteristic
91C22⋊D37—22no—
92C22⋊D37—22no—
93C22⋊D37—42no—
94C2×Dic37—41no—
95D148—41no—
96D148—42no—
97D148C2×D412yes—
98D148C2×D412yes—
99C4×D37—22no—
100C4×D37—22no—
101C4×D37—42no—
102C4×D37—42no—
103C4×D37—42no—
104Dic74—41no—
105Dic74—42no—
106Dic74C2×D412yes—
107Dic74C2×D412yes—
108C8×C37C2×D412yes—
109C8×C37C2×D412yes—
110#64436—22no—
111#64436—22no—
112C22×C37—41no—
113C22×C37—81no—
114C22×C37H(5,𝔽2)11yescharacteristic
115C2×D37—22no—
116C2×D37—22no—
117C2×D37—161no—
118C4×C37—41no—
119C4×C37—41no—
120C4×C37—42no—
121C4×C37C22×D412yes—
122Dic37—22no—
123Dic37—22no—
124#3289—371nomaximal, Sylow
125C2×C37—21no—
126C2×C37—81no—
127C2×C37D4211yescharacteristic
128D37—42no—
129D37—42no—
130#578—372no—
131#577—372no—
132#497D3711yescharacteristic, complemented
133#473—372no—
134#471—372no—
135#456—372no—
136#455—371no—
137#454—371no—
138#444—372no—
139C37#328911yescharacteristic, complemented, Sylow
1402−1+4—372no—
1412−1+4—371no—
142H(5,𝔽2)—371no—
143#137—372no—
144#137—372no—
145#137—372no—
146#137—742no—
147#137—742no—
148#137—742no—
149AGL(1,ℤ/8)—372no—
150AGL(1,ℤ/8)—742no—
151#135—372no—
152#135—742no—
153#135—742no—
154C2×Q16—742no—
155C2×Q16C2×D3712yescomplemented
156C2×SD16—742no—
157C2×SD16C2×D3712yes—
158#131—372no—
159#131—372no—
160C4⋊Q8C2×D3711yescharacteristic, complemented
161#124C2×D3711yescharacteristic
162#108—372no—
163#104—372no—
164#104—372no—
165#101—371no—
166#101—372no—
167#100—371no—
168#97C2×D3711yescharacteristic, complemented
169#41—372no—
170#41—372no—
171#41—742no—
172#41—742no—
173#41—742no—
174#41—742no—
175#41—1481no—
176#41—1482no—
177C2×Q8—742no—
178C2×Q8—742no—
179C2×Q8—742no—
180C2×Q8C22×D3711yescharacteristic
181C2×Q8C22×D3712yes—
182C2×D4—742no—
183C2×D4—1481no—
184C2×D4C22×D3711yescharacteristic
185Q16—22no—
186Q16—22no—
187Q16—372no—
188Q16—742no—
189Q16—742no—
190Q16—742no—
191SD16—22no—
192SD16—22no—
193SD16—372no—
194SD16—372no—
195SD16—742no—
196SD16—742no—
197SD16—742no—
198SD16—742no—
199D8—372no—
200D8—742no—
201M16—372no—
202M16—372no—
203M16—742no—
204M16—742no—
205C2×C8—742no—
206C2×C8—742no—
207C2×C8C22×D3712yes—
208C4⋊C4—41no—
209C22⋊C4—41no—
210C42C22×D3711yescharacteristic
211C23—21no—
212C23—1481no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—372no—
217Q8—372no—
218Q8—1482no—
219Q8—1481no—
220D4—22no—
221D4—372no—
222D4—372no—
223D4—742no—
224D4—742no—
225D4—1481no—
226D4—1482no—
227D4—1482no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—742no—
232C2×C4—742no—
233C2×C4—1482no—
234C2×C4—1482no—
235C2×C4—1482no—
236C2×C4—1481no—
237C2×C4C23×D3711yescharacteristic
238C8—742no—
239C8—742no—
240C8D4×D3712yes—
241C8D4×D3712yes—
242C22—41no—
243C22—81no—
244C22—742no—
245C22—742no—
246C22—5921no—
247C22#1192458111yescharacteristic
248C4—41no—
249C4—41no—
250C4—42no—
251C4—742no—
252C4—742no—
253C4C2×D4×D3712yes—
254C2—21no—
255C2—81no—
256C2—1482no—
257C2—1482no—
258C2#1455816811yescharacteristic
subgroupG/H
centerC2#14558168
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#497C2
socleC2×C37D42
hypercenter#497D37
hypocenterC37#3289
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14558346C2semidirect
2. #14558339C2semidirect
3. #14557805C2semidirect
4. #14557793C2semidirect
5. #14557715C2semidirect
6. #14557710C2semidirect
7. #14557705C2semidirect
8. #14557656C2semidirect
9. C37×#497C2semidirect
11. #11924584C22semidirect
17. #11924567C22semidirect
27. #11924542C22semidirect
28. #11924472C22semidirect
30. #11924464C22semidirect
31. #11924455C22semidirect
32. #11924455C22semidirect
34. C2×Q16×C37C22semidirect
36. C4⋊Q8×C37C22semidirect
38. #97×C37C22semidirect
132. #497D37semidirect
139. C37#3289semidirect
155. C2×Q16C2×D37semidirect
160. C4⋊Q8C2×D37semidirect
168. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583462
#145583392
#145578052
#145577932
#145577152
#145577102
#145577052
#145576562
C37×#4972
#328937