Finite Group Databasebeta

← #17993702

Subgroups — #17993702

Order 4736.

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

normal subgroups only

This group has 250 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×Dic74C211yesmaximal, characteristic, complemented
2#14557880C211yesmaximal, characteristic, complemented
3#14557734C211yesmaximal, characteristic, complemented
4#14557728C211yesmaximal, characteristic
5#14557280C211yesmaximal, characteristic, complemented
6#14557265C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×Dic74—21no—
9C2×#10596930—21no—
10C2×#10596939—21no—
11#11924536C2211yescharacteristic
12#11924535—21no—
13#11924533C2211yescharacteristic
14#11924515—21no—
15#11924513—22no—
16C4×Dic74C2211yescharacteristic
17D4×Dic37—21no—
18C4⋊#64436C2211yescharacteristic
19#11924458—21no—
20#11924458—22no—
21#11924456—21no—
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×D4×C37D411yescharacteristic
26C22×C4×C37—21no—
27C22×Dic37—22no—
28C2×D148—21no—
29C2×D148—21no—
30C2×D148—21no—
31C2×Dic74—22no—
32C2×Dic74—21no—
33C2×Dic74—42no—
34C2×Dic74—42no—
35C2×Dic74D411yescharacteristic
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C4⋊C4×C37D411yescharacteristic
39C22⋊C4×C37—21no—
40C42×C37C2311yescharacteristic
41C22⋊Dic37—22no—
42#10596939—42no—
43C4⋊Dic37—21no—
44C4⋊Dic37D411yescharacteristic
45C4⋊Dic37D412yes—
46#10596936—22no—
47#10596936—21no—
48C4×Dic37—21no—
49C2×#64436—21no—
50#10596930—42no—
51C23×C37—21no—
52C22×D37—41no—
53D4×C37—21no—
54D4×C37SD1612yescomplemented
55C2×C4×C37—21no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37—22no—
64C2×Dic37—44no—
65D148—42no—
66D148—41no—
67D148—41no—
68D148—41no—
69D148—41no—
70Dic74—21no—
71Dic74—44no—
72Dic74—41no—
73Dic74—41no—
74Dic74D812yescomplemented
75C8×C37—41no—
76C8×C37—41no—
77#64436—41no—
78C22×C37—22no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37#12011yescharacteristic
82C2×D37—81no—
83C2×D37—81no—
84C2×D37—81no—
85C4×C37—21no—
86C4×C37—41no—
87C4×C37C2×D811yescharacteristic
88C4×C37C2×SD1611yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90C4×C37#13711yescharacteristic
91Dic37—22no—
92Dic37—42no—
93Dic37—41no—
94#1627—371nomaximal, Sylow
95C2×C37—42no—
96C2×C37#44711yescharacteristic
97C2×C37#44811yescharacteristic
98C2×C37#45411yescharacteristic
99D37—161no—
100D4×Q8—371no—
101#486—371no—
102#460—371no—
103#459—371no—
104#332—371no—
105Q8⋊C8—371no—
106D4⋊C8D3711yescharacteristic, complemented
107C37#162711yescharacteristic, complemented, Sylow
108C22×Q8—741no—
109C2×SD16—741no—
110C2×D8—741no—
111C4⋊Q8—371no—
112C4⋊Q8—741no—
113#127—371no—
114C22⋊Q8—742no—
115C22⋊Q8—741no—
116C4×Q8—371no—
117C4×D4—741no—
118C4×D4C2×D3711yescharacteristic
119C4⋊C8—371no—
120C4⋊C8C2×D3711yescharacteristic
121#102—741no—
122#102—742no—
123#102—741no—
124C4×C8C2×D3711yescharacteristic
125C2×Q8—371no—
126C2×Q8—742no—
127C2×Q8—741no—
128C2×Q8—1482no—
129C2×Q8—1482no—
130C2×D4—741no—
131C2×D4—741no—
132C2×D4—741no—
133C2×D4D14811yescharacteristic
134C22×C4—21no—
135C22×C4—742no—
136SD16—1482no—
137D8—1482no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—741no—
141C4⋊C4—371no—
142C4⋊C4—372no—
143C4⋊C4—742no—
144C4⋊C4—741no—
145C4⋊C4—741no—
146C4⋊C4D14811yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—742no—
149C42—741no—
150C42C22×D3711yescharacteristic
151C23—21no—
152C23—1481no—
153Q8—372no—
154Q8—741no—
155Q8—1484no—
156Q8—1481no—
157Q8—1481no—
158D4—21no—
159D4—1482no—
160D4—1481no—
161D4—1481no—
162D4—1481no—
163D4—1481no—
164D4#1059693012yescomplemented
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—742no—
171C2×C4—1484no—
172C2×C4C2×D14811yescharacteristic
173C2×C4D4×D3711yescharacteristic
174C2×C4D4×D3711yescharacteristic
175C8—41no—
176C8—41no—
177C8—1481no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—2961no—
182C22—2961no—
183C22—2961no—
184C22#1192450611yescharacteristic
185C4—21no—
186C4—41no—
187C4—742no—
188C4—1481no—
189C4—1482no—
190C4D8×D3711yescharacteristic
191C4C2×#1059693011yescharacteristic
192C4#1192456311yescharacteristic
193C4#1192456911yescharacteristic
194C2—42no—
195C2—5921no—
196C2#1455766811yescharacteristic
197C2#1455767411yescharacteristic
198C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37#120
prime radical#14557728C2
hypercenterD4⋊C8D37
hypocenterC37#1627
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. D4×Dic74C2semidirect
2. #14557880C2semidirect
3. #14557734C2semidirect
5. #14557280C2semidirect
6. #14557265C2semidirect
7. C37×D4⋊C8C2semidirect
54. D4×C37SD16semidirect
74. Dic74D8semidirect
106. D4⋊C8D37semidirect
107. C37#1627semidirect
164. D4#10596930semidirect

Maximal subgroups

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

subgroupindex
D4×Dic742
#145578802
#145577342
#145577282
#145572802
#145572652
C37×D4⋊C82
#162737