Finite Group Databasebeta

← #17995083

Subgroups — #17995083

Order 4736.

346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#11924562C211yesmaximal, characteristic
2#14557551C211yesmaximal, characteristic, complemented
3#14557538C211yesmaximal, characteristic, complemented
4#14557506C211yesmaximal, characteristic, complemented
5#14557303C211yesmaximal, characteristic, complemented
6#14557289C211yesmaximal, characteristic, complemented
7C37×#518C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924562—22no—
10#11924562—22no—
11C2×#10596940C412yescomplemented
12C2×#10596939C412yescomplemented
13C2×#10596934C2211yescharacteristic
14C2×#10596934C2211yescharacteristic
15#11924495C2211yescharacteristic
16#11924464—22no—
17#11924457—22no—
18#11924450—22no—
19C22×D4×C37C2211yescharacteristic
20C4×D4×C37—22no—
21C4×D4×C37—22no—
22#117×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24C2×C22⋊C4×C37—22no—
25C24×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D4×C37C2×C412yes—
30C2×D4×C37D412yes—
31C2×D4×C37D412yes—
32C22×C4×C37—24no—
33C22×C4×C37C2311yescharacteristic
34C2×C22⋊D37—21no—
35#10596962—21no—
36#10596962—21no—
37#10596962—21no—
38#10596962—21no—
39C2×D148C2×C411yescharacteristic, complemented
40C2×C4×D37—21no—
41C2×Dic74C2×C411yescharacteristic, complemented
42C4⋊C4×C37—21no—
43C4⋊C4×C37—21no—
44C22⋊C4×C37—24no—
45C22⋊C4×C37—21no—
46C22⋊C4×C37D412yes—
47C42×C37—21no—
48C42×C37D412yes—
49C22⋊Dic37—21no—
50#10596940—24no—
51#10596939—24no—
52C4⋊Dic37—21no—
53C4×Dic37—21no—
54#10596934—21no—
55#10596934—21no—
56#10596934—21no—
57#10596934—21no—
58C2×#64436—21no—
59C2×#64436C2×C412yescomplemented
60C23×C37—22no—
61C23×C37—22no—
62C23×C37—22no—
63C23×C37—82no—
64C23×C37C2×D411yescharacteristic
65C22×D37—21no—
66D4×C37—22no—
67D4×C37—22no—
68D4×C37—22no—
69D4×C37C22⋊C414yes—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37—84no—
73C2×C4×C37C22×C411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37#4111yescharacteristic
78C2×C4×C37#4111yescharacteristic
79C22⋊D37—41no—
80C22⋊D37—41no—
81C2×Dic37—21no—
82C2×Dic37—41no—
83D148—21no—
84D148—21no—
85C4×D37—41no—
86C4×D37—41no—
87Dic74—21no—
88Dic74—21no—
89#64436—22no—
90#64436—41no—
91C22×C37—24no—
92C22×C37—41no—
93C22×C37—44no—
94C22×C37—82no—
95C22×C37—82no—
96C22×C37C4×D411yescharacteristic
97C22×C37#12011yescharacteristic
98C22×C37#12111yescharacteristic
99C2×D37—41no—
100C2×D37—81no—
101C4×C37—42no—
102C4×C37—42no—
103C4×C37C2×C22⋊C411yescharacteristic
104C4×C37C4×D411yescharacteristic
105C4×C37#12111yescharacteristic
106C4×C37#12311yescharacteristic
107Dic37—41no—
108Dic37—81no—
109#1904—371nomaximal, Sylow
110C2×C37—21no—
111C2×C37—21no—
112C2×C37—21no—
113C2×C37—44no—
114C2×C37#38611yescharacteristic
115D37—81no—
116C2×AGL(1,ℤ/8)—371no—
117#518D3711yescharacteristic, complemented
118#421—371no—
119#418—371no—
120#410—371no—
121#344—371no—
122H(3,ℤ/4)—371no—
123C37#190411yescharacteristic, complemented, Sylow
124C2×#41—371no—
125C22×D4C2×D3711yescharacteristic
126AGL(1,ℤ/8)—742no—
127AGL(1,ℤ/8)—742no—
128C2×SD16—372no—
129C2×D8—372no—
130C2×M16—371no—
131C2×M16—371no—
132C4×D4—22no—
133C4×D4—22no—
134#117—371no—
135#117C2×D3711yescharacteristic
136#117C2×D3711yescharacteristic
137C2×C22⋊C4—22no—
138#104—742no—
139#102—742no—
140#99—742no—
141C24—21no—
142#41—741no—
143#41—741no—
144#41—741no—
145#41—741no—
146C2×Q8—371no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—371no—
151C2×D4—741no—
152C2×D4C4×D3712yes—
153C2×D4D14812yes—
154C2×D4C22⋊D3712yes—
155C22×C4—24no—
156C22×C4—741no—
157C22×C4C22×D3711yescharacteristic
158SD16—744no—
159D8—744no—
160M16—741no—
161M16—741no—
162M16—741no—
163M16—741no—
164C2×C8—372no—
165C2×C8—741no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—741no—
169C22⋊C4—24no—
170C22⋊C4—21no—
171C22⋊C4—741no—
172C22⋊C4C22⋊D3712yes—
173C42—21no—
174C42—741no—
175C42C22⋊D3712yes—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—82no—
180C23—741no—
181C23C2×C22⋊D3711yescharacteristic
182Q8—741no—
183Q8—741no—
184D4—22no—
185D4—22no—
186D4—22no—
187D4—741no—
188D4—741no—
189D4—1481no—
190D4—1481no—
191D4#1059693814yes—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—84no—
195C2×C4—741no—
196C2×C4—1481no—
197C2×C4—1481no—
198C2×C4—1481no—
199C2×C4C2×C4×D3711yescharacteristic
200C2×C4C2×D14811yescharacteristic
201C2×C4#1059696211yescharacteristic
202C2×C4#1059696211yescharacteristic
203C2×C4C2×C22⋊D3711yescharacteristic
204C2×C4C2×C22⋊D3711yescharacteristic
205C8—742no—
206C8—1481no—
207C22—24no—
208C22—41no—
209C22—44no—
210C22—82no—
211C22—82no—
212C22—2961no—
213C22—1481no—
214C22C4×C22⋊D3711yescharacteristic
215C22#1192450511yescharacteristic
216C22#1192451011yescharacteristic
217C4—42no—
218C4—42no—
219C4—2961no—
220C4—1481no—
221C4C2×#1059693811yescharacteristic
222C4C4×C22⋊D3711yescharacteristic
223C4#1192451011yescharacteristic
224C4#1192451911yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—44no—
229C2—2961no—
230C2#1455741211yescharacteristic
subgroupG/H
centerC2#14557412
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#518C2
socleC2×C37#386
prime radicalC2×#11924562C2
cosocleC22×C4×C37C23
hypercenter#518D37
hypocenterC37#1904
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #14557551C2semidirect
3. #14557538C2semidirect
4. #14557506C2semidirect
5. #14557303C2semidirect
6. #14557289C2semidirect
7. C37×#518C2semidirect
11. C2×#10596940C4semidirect
12. C2×#10596939C4semidirect
39. C2×D148C2×C4semidirect
41. C2×Dic74C2×C4semidirect
59. C2×#64436C2×C4semidirect
117. #518D37semidirect
123. C37#1904semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
#145575512
#145575382
#145575062
#145573032
#145572892
C37×#5182
#190437