Finite Group Databasebeta

← #17993659

Subgroups — #17993659

Order 4736.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558205C211yesmaximal, characteristic, complemented
2#14557909C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic, complemented
4#14557276C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#460C211yesmaximal, characteristic, complemented
8C2×#10596966—21no—
9C2×#10596939—21no—
10C2×#10596939—22no—
11#11924533—21no—
12#11924533C2211yescharacteristic
13#11924511—22no—
14#11924511—21no—
15C4×D148—21no—
16C4×D148C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18#11924457—21no—
19C4×#64436C2211yescharacteristic
20C2×SD16×C37—21no—
21#127×C37C2211yescharacteristic
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×Q8×C37D411yescharacteristic
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29#10596966—42no—
30#10596966—42no—
31C2×D148—22no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148—22no—
35C2×D148D411yescharacteristic
36C2×D148D412yes—
37C2×C4×D37—22no—
38C2×C4×D37—21no—
39SD16×C37—42no—
40C2×C8×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37D411yescharacteristic
43C42×C37—21no—
44C42×C37C2311yescharacteristic
45#10596939—44no—
46#10596939—42no—
47#10596938—22no—
48#10596938—21no—
49C4⋊Dic37D411yescharacteristic
50C2×#64436—21no—
51C2×#64436—21no—
52C23×C37—41no—
53C22×D37—21no—
54C22×D37—22no—
55Q8×C37—21no—
56Q8×C37D812yescomplemented
57D4×C37—42no—
58D4×C37—41no—
59D4×C37—41no—
60D4×C37—41no—
61D4×C37—41no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×Dic37—21no—
68D148—21no—
69D148—21no—
70D148—42no—
71D148—44no—
72D148—41no—
73D148—41no—
74D148—41no—
75D148—41no—
76D148—82no—
77C4×D37—44no—
78C4×D37—41no—
79C4×D37—41no—
80C8×C37—41no—
81#64436—22no—
82#64436—41no—
83C22×C37—81no—
84C22×C37—81no—
85C22×C37—81no—
86C22×C37#12011yescharacteristic
87C2×D37—42no—
88C2×D37—41no—
89C2×D37—41no—
90C2×D37—42no—
91C2×D37—42no—
92C2×D37—41no—
93C4×C37—22no—
94C4×C37—21no—
95C4×C37—41no—
96C4×C37C2×D811yescharacteristic
97C4×C37#13511yescharacteristic
98C4×C37AGL(1,ℤ/8)11yescharacteristic
99C4×C37AGL(1,ℤ/8)11yescharacteristic
100Dic37—41no—
101#1621—371nomaximal, Sylow
102C2×C37—161no—
103C2×C37#44711yescharacteristic
104C2×C37#44911yescharacteristic
105C2×C37#45311yescharacteristic
106D37—81no—
107D37—82no—
108#550—371no—
109#493—371no—
110#460D3711yescharacteristic, complemented
111#459—371no—
112#331—371no—
113Q8⋊C8—371no—
114D4⋊C8—371no—
115C37#162111yescharacteristic, complemented, Sylow
116C2×#41—741no—
117C2×SD16—21no—
118C2×D8—741no—
119C2×D8—742no—
120#127—371no—
121#127—741no—
122#127C2×D3711yescharacteristic
123#121—742no—
124#121—741no—
125C4×Q8C2×D3711yescharacteristic
126C4×D4—371no—
127C4×D4—741no—
128C4⋊C8—371no—
129C4⋊C8C2×D3711yescharacteristic
130#102—21no—
131#102—741no—
132C4×C8—371no—
133#41—1482no—
134#41—1482no—
135C2×Q8C22⋊D3711yescharacteristic
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—371no—
140C2×D4—372no—
141C2×D4—742no—
142C2×D4—742no—
143C2×D4—741no—
144C2×D4—741no—
145C22×C4—742no—
146C22×C4—741no—
147SD16—42no—
148D8—1484no—
149D8—1482no—
150C2×C8—21no—
151C2×C8—741no—
152C2×C8—741no—
153C4⋊C4—21no—
154C4⋊C4—371no—
155C4⋊C4C22⋊D3711yescharacteristic
156C22⋊C4—742no—
157C22⋊C4—741no—
158C42—21no—
159C42C22×D3711yescharacteristic
160C23—41no—
161C23—741no—
162C23—742no—
163Q8—21no—
164Q8#1059693912yescomplemented
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—2962no—
171D4—741no—
172D4—741no—
173D4—1482no—
174D4—1484no—
175D4—1481no—
176D4—1481no—
177D4—1481no—
178D4—1481no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—741no—
182C2×C4—1484no—
183C2×C4—1481no—
184C2×C4—1481no—
185C2×C4D4×D3711yescharacteristic
186C2×C4D4×D3711yescharacteristic
187C2×C4C2×C22⋊D3711yescharacteristic
188C8—41no—
189C8—742no—
190C8—1481no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—1481no—
195C22—1482no—
196C22—1482no—
197C22—1481no—
198C22—1481no—
199C22—1482no—
200C22#1192450411yescharacteristic
201C4—21no—
202C4—22no—
203C4—41no—
204C4—1481no—
205C4C2×#1059693911yescharacteristic
206C4#1192455711yescharacteristic
207C4#1192456111yescharacteristic
208C4#1192456311yescharacteristic
209C2—161no—
210C2—2961no—
211C2—2962no—
212C2#1455766611yescharacteristic
213C2#1455767711yescharacteristic
214C2#1455769911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#460C2
socleC22×C37#120
hypercenter#460D37
hypocenterC37#1621
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14558205C2semidirect
2. #14557909C2semidirect
3. #14557725C2semidirect
4. #14557276C2semidirect
5. Q8⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#460C2semidirect
56. Q8×C37D8semidirect
110. #460D37semidirect
115. C37#1621semidirect
164. Q8#10596939semidirect

Maximal subgroups

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

subgroupindex
#145582052
#145579092
#145577252
#145572762
Q8⋊#644362
#145572602
C37×#4602
#162137