Finite Group Databasebeta

← #17996545

Subgroups — #17996545

Order 4736.

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

normal subgroups only

This group has 216 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
2#14557974C211yesmaximal, characteristic, complemented
3#14557788C211yesmaximal, characteristic, complemented
4#14557344C211yesmaximal, characteristic, complemented
5#14557343C211yesmaximal, characteristic, complemented
6#14557314C211yesmaximal, characteristic, complemented
7C37×#510C211yesmaximal, 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#11924512—21no—
17#11924482—21no—
18#11924479—21no—
19#11924476C2211yescharacteristic, complemented
20#11924468C2211yescharacteristic, complemented
21#11924460—21no—
22#135×C37C2211yescharacteristic
23C2×Q16×C37C2211yescharacteristic, complemented
24Q32×C37—21no—
25SD32×C37—21no—
26M32×C37C2211yescharacteristic, complemented
27#41×C37—21no—
28C2×Q8×C37—21no—
29#10596966—21no—
30Q8×D37—21no—
31#10596964—21no—
32#10596964—41no—
33D4×D37—21no—
34D4×D37—41no—
35#10596962—21no—
36#10596962—41no—
37C2×C4×D37—41no—
38C2×C4×D37D411yescharacteristic
39Q16×C37—21no—
40Q16×C37—21no—
41Q16×C37D411yescharacteristic
42SD16×C37—21no—
43D8×C37D411yescharacteristic
44C2×C8×C37C2311yescharacteristic
45#10596942—21no—
46#10596941—21no—
47#10596940—21no—
48#10596939—21no—
49#10596938—41no—
50C4⋊Dic37—21no—
51#10596936—41no—
52C2×#64436D411yescharacteristic
53Dic148D411yescharacteristic
54D296D411yescharacteristic
55#10596930—21no—
56#10596929—21no—
57#10596929—21no—
58C16×C37—21no—
59#10596925—21no—
60C22×D37—41no—
61C22×D37D811yescharacteristic
62Q8×C37—21no—
63Q8×C37—41no—
64Q8×C37—41no—
65D4×C37—21no—
66D4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C2×D411yescharacteristic
70C22⋊D37—41no—
71C22⋊D37—41no—
72C22⋊D37—41no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37D811yescharacteristic
76D148—21no—
77D148—41no—
78C4×D37—21no—
79C4×D37—21no—
80C4×D37—41no—
81C4×D37—41no—
82C4×D37—41no—
83Dic74—21no—
84Dic74—41no—
85C8×C37C2×D411yescharacteristic
86C8×C37C2×D411yescharacteristic
87#64436—21no—
88C22×C37—41no—
89C22×C37C2×D811yescharacteristic
90C2×D37—21no—
91C2×D37—41no—
92C2×D37—41no—
93C2×D37—82no—
94C4×C37—41no—
95C4×C37—81no—
96C4×C37#12011yescharacteristic
97C4×C37AGL(1,ℤ/8)11yescharacteristic
98Dic37—21no—
99Dic37—41no—
100Dic37—81no—
101#2191—371nomaximal, Sylow
102C2×C37—21no—
103C2×C37—81no—
104C2×C37#44711yescharacteristic
105D37—41no—
106D37—81no—
107#575—371no—
108#510—371no—
109#510D3711yescharacteristic, complemented
110#470—371no—
111#360—371no—
112#360—371no—
113#349—371no—
114C37#219111yescharacteristic, complemented, Sylow
115C2×#41—741no—
116#137—741no—
117#137—741no—
118AGL(1,ℤ/8)—741no—
119AGL(1,ℤ/8)—741no—
120#135—371no—
121#135—741no—
122#135C2×D3711yescharacteristic
123C2×Q16C2×D3711yescharacteristic, complemented
124C2×M16—371no—
125C22⋊Q8—741no—
126Q32—21no—
127Q32—741no—
128SD32—21no—
129SD32—741no—
130M32—371no—
131M32C2×D3711yescharacteristic, complemented
132#106—371no—
133#103—741no—
134#41—21no—
135#41—741no—
136#41—741no—
137#41—741no—
138#41—1481no—
139#41—1481no—
140C2×Q8—21no—
141C2×Q8—741no—
142C2×D4—741no—
143C2×D4—1481no—
144C22×C4—371no—
145C22×C4—1481no—
146Q16—21no—
147Q16—21no—
148Q16—371no—
149Q16—741no—
150Q16C22⋊D3711yescharacteristic
151SD16—21no—
152SD16—741no—
153SD16—741no—
154SD16—741no—
155D8—371no—
156D8—741no—
157D8C22⋊D3711yescharacteristic
158M16—741no—
159M16—741no—
160C2×C8—371no—
161C2×C8C22×D3711yescharacteristic
162C4⋊C4—741no—
163C4⋊C4—1481no—
164C22⋊C4—1481no—
165C16—21no—
166C16—741no—
167C23—371no—
168C23—1481no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—741no—
173Q8—1481no—
174D4—21no—
175D4—41no—
176D4—741no—
177D4—1481no—
178D4—1481no—
179D4—1481no—
180D4—1481no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—371no—
184C2×C4—741no—
185C2×C4—741no—
186C2×C4—1481no—
187C2×C4—1481no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4—1481no—
191C2×C4D4×D3711yescharacteristic
192C8—741no—
193C8D4×D3711yescharacteristic
194C8C2×C22⋊D3711yescharacteristic
195C22—41no—
196C22—2962no—
197C22—741no—
198C22—1481no—
199C22—1481no—
200C22D8×D3711yescharacteristic
201C4—41no—
202C4—81no—
203C4—2961no—
204C4—741no—
205C4—1481no—
206C4#1192450411yescharacteristic
207C4#1192456011yescharacteristic
208C2—21no—
209C2—81no—
210C2—2961no—
211C2—1481no—
212C2#1455766511yescharacteristic
subgroupG/H
centerC2#14557665
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#510C2
socleC2×C37#447
prime radical#14558330C2
hypercenter#510D37
hypocenterC37#2191
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #14557974C2semidirect
3. #14557788C2semidirect
4. #14557344C2semidirect
5. #14557343C2semidirect
6. #14557314C2semidirect
7. C37×#510C2semidirect
19. #11924476C22semidirect
20. #11924468C22semidirect
23. C2×Q16×C37C22semidirect
26. M32×C37C22semidirect
109. #510D37semidirect
114. C37#2191semidirect
123. C2×Q16C2×D37semidirect
131. M32C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583302
#145579742
#145577882
#145573442
#145573432
#145573142
C37×#5102
#219137