Finite Group Databasebeta

← #17993711

Subgroups — #17993711

Order 4736.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D148C211yesmaximal, characteristic
2#14557907C211yesmaximal, characteristic, complemented
3#14557820C211yesmaximal, characteristic, complemented
4#14557276C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#476C211yesmaximal, characteristic, complemented
8C22×D148—21no—
9C2×D4×D37—21no—
10C2×#10596941—22no—
11#11924533C2211yescharacteristic
12#11924511—21no—
13#11924510—21no—
14#11924506—22no—
15C4×D148C2211yescharacteristic
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic, complemented
18#11924456—21no—
19C4×#64436C2211yescharacteristic, complemented
20C4⋊Q8×C37C2211yescharacteristic, complemented
21C4×D4×C37C2211yescharacteristic
22#106×C37—21no—
23C4⋊C8×C37C2211yescharacteristic, complemented
24#102×C37—21no—
25C23×D37—22no—
26C2×Q8×C37—21no—
27C2×D4×C37D411yescharacteristic
28C22×C4×C37—21no—
29C2×C22⋊D37—22no—
30D4×D37—42no—
31D4×D37—42no—
32C2×D148—22no—
33C2×D148—21no—
34C2×D148—21no—
35C2×D148—42no—
36C2×D148—42no—
37C2×D148D411yescharacteristic
38C2×D148D412yes—
39C2×C4×D37—21no—
40C2×C8×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37D411yescharacteristic
44C22⋊C4×C37—21no—
45C42×C37C2311yescharacteristic
46#10596941—44no—
47#10596938—22no—
48#10596938—21no—
49C4⋊Dic37D411yescharacteristic
50C2×#64436—21no—
51C2×#64436—21no—
52C23×C37—21no—
53C22×D37—21no—
54C22×D37—22no—
55C22×D37—44no—
56C22×D37—44no—
57C22×D37—82no—
58Q8×C37—42no—
59D4×C37—21no—
60D4×C37SD1612yescomplemented
61C2×C4×C37—21no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C22⋊D37—44no—
69C2×Dic37—21no—
70D148—21no—
71D148—42no—
72D148—44no—
73D148—41no—
74D148—41no—
75D148—41no—
76D148—41no—
77D148SD1612yescomplemented
78C4×D37—41no—
79C4×D37—41no—
80C8×C37—41no—
81#64436—22no—
82#64436—41no—
83C22×C37—22no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37#12011yescharacteristic
87C2×D37—22no—
88C2×D37—41no—
89C2×D37—41no—
90C2×D37—42no—
91C2×D37—42no—
92C2×D37—42no—
93C2×D37—88no—
94C4×C37—21no—
95C4×C37—41no—
96C4×C37—81no—
97C4×C37C2×SD1611yescharacteristic
98C4×C37C2×SD1611yescharacteristic
99C4×C37AGL(1,ℤ/8)11yescharacteristic
100C4×C37AGL(1,ℤ/8)11yescharacteristic
101Dic37—41no—
102#1629—371nomaximal, Sylow
103C2×C37—42no—
104C2×C37#45011yescharacteristic
105C2×C37#45011yescharacteristic
106C2×C37#45311yescharacteristic
107D37—42no—
108D37—82no—
109D42—371no—
110#492—371no—
111#476—371no—
112#476D3711yescharacteristic, complemented
113#331—371no—
114D4⋊C8—371no—
115D4⋊C8—371no—
116C37#162911yescharacteristic, complemented, Sylow
117C22×D4—741no—
118C22×D4—741no—
119C2×SD16—742no—
120C4⋊Q8C2×D3711yescharacteristic, complemented
121#127—371no—
122#121—741no—
123#121—741no—
124#120—742no—
125C4×D4—371no—
126C4×D4C2×D3711yescharacteristic
127#106—21no—
128#106—741no—
129C4⋊C8—371no—
130C4⋊C8C2×D3711yescharacteristic, complemented
131#102—21no—
132#102—741no—
133C4×C8—371no—
134C24—742no—
135C2×Q8—21no—
136C2×D4—371no—
137C2×D4—372no—
138C2×D4—742no—
139C2×D4—742no—
140C2×D4—741no—
141C2×D4—741no—
142C2×D4—1482no—
143C2×D4—1482no—
144C2×D4—1482no—
145C2×D4—1482no—
146C2×D4C22⋊D3711yescharacteristic
147C22×C4—21no—
148C22×C4—741no—
149SD16—1484no—
150C2×C8—21no—
151C2×C8—741no—
152C2×C8—741no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—371no—
156C4⋊C4C22⋊D3711yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—742no—
159C22⋊C4—741no—
160C42C22×D3711yescharacteristic
161C23—21no—
162C23—2962no—
163C23—741no—
164C23—742no—
165C23—1484no—
166C23—1484no—
167Q8—42no—
168D4—21no—
169D4—372no—
170D4—741no—
171D4—1482no—
172D4—1484no—
173D4—1484no—
174D4—1481no—
175D4—1481no—
176D4—1481no—
177D4—1481no—
178D4#1059694112yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—741no—
184C2×C4—1481no—
185C2×C4—1481no—
186C2×C4D4×D3711yescharacteristic
187C2×C4D4×D3711yescharacteristic
188C2×C4C2×C22⋊D3711yescharacteristic
189C8—41no—
190C8—742no—
191C8—1481no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—2968no—
196C22—742no—
197C22—1482no—
198C22—1482no—
199C22—1482no—
200C22—1481no—
201C22—1481no—
202C22#1192450411yescharacteristic
203C4—21no—
204C4—41no—
205C4—81no—
206C4—1481no—
207C4SD16×D3711yescharacteristic
208C4C2×#1059694111yescharacteristic
209C4#1192456111yescharacteristic
210C4#1192456311yescharacteristic
211C2—42no—
212C2—2962no—
213C2—1482no—
214C2#1455768211yescharacteristic
215C2#1455768311yescharacteristic
216C2#1455769911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#476C2
socleC22×C37#120
prime radicalD4×D148C2
hypercenter#476D37
hypocenterC37#1629
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #14557907C2semidirect
3. #14557820C2semidirect
4. #14557276C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#476C2semidirect
17. C4⋊#64436C22semidirect
19. C4×#64436C22semidirect
20. C4⋊Q8×C37C22semidirect
23. C4⋊C8×C37C22semidirect
60. D4×C37SD16semidirect
77. D148SD16semidirect
112. #476D37semidirect
116. C37#1629semidirect
120. C4⋊Q8C2×D37semidirect
130. C4⋊C8C2×D37semidirect
178. D4#10596941semidirect

Maximal subgroups

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

subgroupindex
D4×D1482
#145579072
#145578202
#145572762
D4⋊#644362
#145572602
C37×#4762
#162937