Finite Group Databasebeta

← #17996543

Subgroups — #17996543

Order 4736.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#14558330C211yesmaximal, characteristic, complemented
2#14557971C211yesmaximal, characteristic, complemented
3#14557968C211yesmaximal, characteristic, complemented
4#14557787C211yesmaximal, characteristic, complemented
5#14557342C211yesmaximal, characteristic, complemented
6#14557314C211yesmaximal, characteristic, complemented
7C37×#360C211yesmaximal, characteristic, complemented
8#41×D37—21no—
9#11924568—21no—
10#11924565—21no—
11#11924563—21no—
12#11924560—21no—
13#11924558C2211yescharacteristic
14#11924556—21no—
15C2×D296C2211yescharacteristic, complemented
16C2×#10596929C2211yescharacteristic
17#11924511—21no—
18#11924481—21no—
19#11924479—21no—
20D592—21no—
21#11924477—21no—
22#11924476C2211yescharacteristic, complemented
23#11924456—21no—
24#135×C37C2211yescharacteristic
25M32×C37C2211yescharacteristic, complemented
26#106×C37C2211yescharacteristic, complemented
27#41×C37—21no—
28#10596966—21no—
29Q8×D37—21no—
30#10596964—21no—
31#10596964—41no—
32D4×D37—21no—
33D4×D37—41no—
34#10596962—21no—
35#10596962—41no—
36C2×D148—21no—
37C2×D148—41no—
38C2×C4×D37—41no—
39C2×C4×D37D411yescharacteristic
40Q16×C37D411yescharacteristic, complemented
41SD16×C37—21no—
42D8×C37D411yescharacteristic, complemented
43C2×C8×C37C2311yescharacteristic
44C4⋊C4×C37—21no—
45#10596942—21no—
46#10596941—21no—
47#10596940—21no—
48#10596939—21no—
49#10596938—41no—
50C2×#64436D411yescharacteristic
51Dic148D411yescharacteristic, complemented
52D296—21no—
53D296—21no—
54D296D411yescharacteristic, complemented
55#10596930—21no—
56#10596929—21no—
57#10596929—21no—
58C16×C37—21no—
59#10596925—21no—
60C22×D37—41no—
61C22×D37—41no—
62C22×D37D811yescharacteristic
63Q8×C37—21no—
64D4×C37—21no—
65D4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37C2×D411yescharacteristic
69C22⋊D37—41no—
70C22⋊D37—41no—
71C22⋊D37—41no—
72C2×Dic37—41no—
73C2×Dic37D811yescharacteristic
74D148—21no—
75D148—41no—
76D148—41no—
77D148—41no—
78D148—82no—
79C4×D37—21no—
80C4×D37—21no—
81C4×D37—41no—
82C4×D37—41no—
83C4×D37—41no—
84Dic74—21no—
85Dic74—41no—
86C8×C37C2×D411yescharacteristic
87C8×C37C2×D411yescharacteristic
88#64436—21no—
89C22×C37—41no—
90C22×C37C2×D811yescharacteristic
91C2×D37—21no—
92C2×D37—41no—
93C2×D37—41no—
94C2×D37—82no—
95C2×D37—81no—
96C2×D37—81no—
97C2×D37—81no—
98C4×C37—41no—
99C4×C37—81no—
100C4×C37#12011yescharacteristic
101C4×C37AGL(1,ℤ/8)11yescharacteristic
102Dic37—21no—
103Dic37—41no—
104#2190—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—81no—
107C2×C37#44711yescharacteristic
108D37—41no—
109D37—81no—
110D37—161no—
111#575—371no—
112#509—371no—
113#509—371no—
114#469—371no—
115#360—371no—
116#360D3711yescharacteristic, complemented
117#349—371no—
118C37#219011yescharacteristic, complemented, Sylow
119C2×#41—741no—
120#137—741no—
121#137—741no—
122AGL(1,ℤ/8)—741no—
123AGL(1,ℤ/8)—741no—
124#135—371no—
125#135—741no—
126#135C2×D3711yescharacteristic
127C2×D8—371no—
128C2×M16—371no—
129#121—741no—
130SD32—741no—
131SD32—741no—
132D16—741no—
133D16—741no—
134M32—371no—
135M32C2×D3711yescharacteristic, complemented
136#106C2×D3711yescharacteristic, complemented
137#102—741no—
138#41—21no—
139#41—741no—
140#41—741no—
141#41—741no—
142#41—1481no—
143#41—1481no—
144C2×Q8—741no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4—1481no—
148C2×D4—1481no—
149C22×C4—371no—
150C22×C4—1481no—
151Q16—371no—
152Q16—741no—
153Q16D14811yescharacteristic, complemented
154SD16—21no—
155SD16—741no—
156SD16—741no—
157SD16—741no—
158D8—371no—
159D8—741no—
160D8—741no—
161D8—741no—
162D8D14811yescharacteristic, complemented
163M16—741no—
164M16—741no—
165C2×C8—371no—
166C2×C8C22×D3711yescharacteristic
167C4⋊C4—21no—
168C22⋊C4—1481no—
169C16—21no—
170C16—741no—
171C23—371no—
172C23—1481no—
173C23—1481no—
174Q8—21no—
175Q8—741no—
176Q8—1481no—
177D4—21no—
178D4—41no—
179D4—2962no—
180D4—741no—
181D4—1481no—
182D4—1481no—
183D4—1481no—
184D4—1481no—
185D4—1481no—
186D4—1481no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—371no—
190C2×C4—741no—
191C2×C4—741no—
192C2×C4—1481no—
193C2×C4—1481no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4D4×D3711yescharacteristic
197C8—741no—
198C8C2×D14811yescharacteristic
199C8D4×D3711yescharacteristic
200C22—41no—
201C22—2961no—
202C22—2961no—
203C22—2962no—
204C22—2961no—
205C22—741no—
206C22—1481no—
207C22—1481no—
208C22D8×D3711yescharacteristic
209C4—41no—
210C4—81no—
211C4—741no—
212C4—1481no—
213C4#1192450611yescharacteristic
214C4#1192456311yescharacteristic
215C2—21no—
216C2—81no—
217C2—2961no—
218C2—5921no—
219C2—1481no—
220C2#1455766811yescharacteristic
subgroupG/H
centerC2#14557668
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#360C2
socleC2×C37#447
hypercenter#360D37
hypocenterC37#2190
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #14558330C2semidirect
2. #14557971C2semidirect
3. #14557968C2semidirect
4. #14557787C2semidirect
5. #14557342C2semidirect
6. #14557314C2semidirect
7. C37×#360C2semidirect
15. C2×D296C22semidirect
22. #11924476C22semidirect
25. M32×C37C22semidirect
26. #106×C37C22semidirect
40. Q16×C37D4semidirect
42. D8×C37D4semidirect
51. Dic148D4semidirect
54. D296D4semidirect
116. #360D37semidirect
118. C37#2190semidirect
135. M32C2×D37semidirect
136. #106C2×D37semidirect
153. Q16D148semidirect
162. D8D148semidirect

Maximal subgroups

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

subgroupindex
#145583302
#145579712
#145579682
#145577872
#145573422
#145573142
C37×#3602
#219037