Finite Group Databasebeta

← #17996540

Subgroups — #17996540

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#14557969C211yesmaximal, characteristic, complemented
3#14557783C211yesmaximal, characteristic, complemented
4#14557344C211yesmaximal, characteristic, complemented
5#14557343C211yesmaximal, characteristic, complemented
6#14557314C211yesmaximal, characteristic, complemented
7C37×#509C211yesmaximal, characteristic, complemented
8#41×D37—21no—
9#11924568—21no—
10#11924565—21no—
11#11924563—21no—
12#11924560—21no—
13#11924558C2211yescharacteristic
14#11924556—21no—
15C2×#10596929C2211yescharacteristic
16#11924507—21no—
17#11924480—21no—
18#11924477—21no—
19#11924476C2211yescharacteristic, complemented
20#11924468C2211yescharacteristic, complemented
21#11924457—21no—
22#135×C37C2211yescharacteristic
23C2×D8×C37C2211yescharacteristic, complemented
24SD32×C37—21no—
25D16×C37—21no—
26M32×C37C2211yescharacteristic, complemented
27#41×C37—21no—
28C2×D4×C37—21no—
29C2×C22⋊D37—41no—
30#10596966—21no—
31Q8×D37—21no—
32#10596964—21no—
33#10596964—41no—
34D4×D37—21no—
35D4×D37—41no—
36#10596962—21no—
37#10596962—41no—
38C2×C4×D37—41no—
39C2×C4×D37D411yescharacteristic
40Q16×C37D411yescharacteristic, complemented
41SD16×C37—21no—
42D8×C37—21no—
43D8×C37—21no—
44D8×C37D411yescharacteristic, complemented
45C2×C8×C37C2311yescharacteristic
46C22⋊Dic37—41no—
47#10596942—21no—
48#10596941—21no—
49#10596940—21no—
50#10596939—21no—
51C4⋊Dic37—21no—
52C2×#64436D411yescharacteristic
53Dic148D411yescharacteristic, complemented
54D296D411yescharacteristic, complemented
55#10596930—21no—
56#10596929—21no—
57#10596929—21no—
58C16×C37—21no—
59#10596925—21no—
60C23×C37—41no—
61C22×D37—41no—
62C22×D37D811yescharacteristic
63Q8×C37—21no—
64D4×C37—21no—
65D4×C37—41no—
66D4×C37—41no—
67D4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C2×D411yescharacteristic
70C22⋊D37—41no—
71C22⋊D37—41no—
72C22⋊D37—41no—
73C22⋊D37—82no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37D811yescharacteristic
77D148—21no—
78D148—41no—
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×C37—81no—
91C22×C37—81no—
92C22×C37—81no—
93C22×C37C2×D811yescharacteristic
94C2×D37—21no—
95C2×D37—41no—
96C2×D37—41no—
97C2×D37—82no—
98C4×C37—41no—
99C4×C37#12011yescharacteristic
100C4×C37AGL(1,ℤ/8)11yescharacteristic
101Dic37—21no—
102Dic37—41no—
103Dic37—81no—
104#2190—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—81no—
107C2×C37—161no—
108C2×C37#44711yescharacteristic
109D37—41no—
110D37—81no—
111#575—371no—
112#509—371no—
113#509D3711yescharacteristic, complemented
114#469—371no—
115#360—371no—
116#360—371no—
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×D8C2×D3711yescharacteristic, complemented
128C2×M16—371no—
129#121—741no—
130SD32—21no—
131SD32—741no—
132D16—21no—
133D16—741no—
134M32—371no—
135M32C2×D3711yescharacteristic, complemented
136#106—371no—
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—21no—
146C2×D4—741no—
147C2×D4—1481no—
148C2×D4—1481no—
149C22×C4—371no—
150C22×C4—1481no—
151Q16—371no—
152Q16—741no—
153Q16C22⋊D3711yescharacteristic, complemented
154SD16—21no—
155SD16—741no—
156SD16—741no—
157SD16—741no—
158D8—21no—
159D8—21no—
160D8—371no—
161D8—741no—
162D8C22⋊D3711yescharacteristic, complemented
163M16—741no—
164M16—741no—
165C2×C8—371no—
166C2×C8C22×D3711yescharacteristic
167C4⋊C4—741no—
168C22⋊C4—1481no—
169C16—21no—
170C16—741no—
171C23—41no—
172C23—371no—
173C23—1481no—
174Q8—21no—
175Q8—741no—
176Q8—1481no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—2962no—
182D4—741no—
183D4—1481no—
184D4—1481no—
185D4—1481no—
186D4—1481no—
187C2×C4—41no—
188C2×C4—371no—
189C2×C4—741no—
190C2×C4—741no—
191C2×C4—1481no—
192C2×C4—1481no—
193C2×C4—1481no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4D4×D3711yescharacteristic
197C8—741no—
198C8D4×D3711yescharacteristic
199C8C2×C22⋊D3711yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—2962no—
205C22—741no—
206C22—1481no—
207C22—1481no—
208C22D8×D3711yescharacteristic
209C4—41no—
210C4—2961no—
211C4—741no—
212C4—1481no—
213C4#1192450411yescharacteristic
214C4#1192456011yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—2961no—
219C2—1481no—
220C2#1455766511yescharacteristic
subgroupG/H
centerC2#14557665
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#509C2
socleC2×C37#447
hypercenter#509D37
hypocenterC37#2190
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #14558330C2semidirect
2. #14557969C2semidirect
3. #14557783C2semidirect
4. #14557344C2semidirect
5. #14557343C2semidirect
6. #14557314C2semidirect
7. C37×#509C2semidirect
19. #11924476C22semidirect
20. #11924468C22semidirect
23. C2×D8×C37C22semidirect
26. M32×C37C22semidirect
40. Q16×C37D4semidirect
44. D8×C37D4semidirect
53. Dic148D4semidirect
54. D296D4semidirect
113. #509D37semidirect
118. C37#2190semidirect
127. C2×D8C2×D37semidirect
135. M32C2×D37semidirect
153. Q16C22⋊D37semidirect
162. D8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583302
#145579692
#145577832
#145573442
#145573432
#145573142
C37×#5092
#219037