Finite Group Databasebeta

← #17994807

Subgroups — #17994807

Order 4736.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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#14558007C211yesmaximal, characteristic
2#14557576C211yesmaximal, characteristic, complemented
3#14557575C211yesmaximal, characteristic, complemented
4C2×#11924452C211yesmaximal, characteristic
5#14557435C211yesmaximal, characteristic
6#14557293C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C22×D148C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10C4×D148—21no—
11C4×D148—21no—
12#11924498—21no—
13#11924498—21no—
14#11924495C2211yescharacteristic
15C2×C4⋊Dic37C2211yescharacteristic
16C2×#10596938—22no—
17C22⋊C4×D37—22no—
18#11924470—21no—
19#11924469—21no—
20#11924468—21no—
21#11924467—21no—
22#11924452C414yescomplemented
23C2×M16×C37C2211yescharacteristic
24#117×C37C2211yescharacteristic
25C2×C42×C37C2211yescharacteristic
26C23×D37D412yes—
27C22×C4×C37—21no—
28C22×C4×C37C2311yescharacteristic
29C22×Dic37—21no—
30C2×D148—21no—
31C2×D148—21no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148C2×C412yes—
35C2×D148Q812yes—
36C2×C4×D37—22no—
37C2×C4×D37—22no—
38M16×C37—21no—
39M16×C37C2×C412yescomplemented
40C2×C8×C37—21no—
41C4⋊C4×C37D411yescharacteristic
42C4⋊C4×C37D411yescharacteristic
43C22⋊C4×C37—21no—
44C42×C37—21no—
45C42×C37—21no—
46C42×C37—21no—
47C22⋊Dic37—21no—
48#10596938—22no—
49#10596938—22no—
50#10596938—44no—
51C4⋊Dic37—21no—
52C4⋊Dic37—21no—
53C4⋊Dic37D411yescharacteristic
54C4⋊Dic37D411yescharacteristic
55C4×Dic37—21no—
56#10596934—21no—
57#10596934C2×C412yescomplemented
58C2×#64436—21no—
59C23×C37C2×D411yescharacteristic
60C22×D37—22no—
61C22×D37—22no—
62C22×D37—42no—
63C22×D37—42no—
64C22×D37C4⋊C414yes—
65C2×C4×C37—22no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37C22×C411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×Q811yescharacteristic
74C2×C4×C37#4111yescharacteristic
75C2×C4×C37#4111yescharacteristic
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—42no—
79C2×Dic37—41no—
80D148—22no—
81D148—22no—
82D148—22no—
83D148—22no—
84C4×D37—82no—
85C4×D37—82no—
86C8×C37—22no—
87#64436—22no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37C2×C4⋊C411yescharacteristic
91C22×C37#12011yescharacteristic
92C22×C37#12311yescharacteristic
93C2×D37—24no—
94C2×D37—42no—
95C2×D37—42no—
96C2×D37—44no—
97C2×D37—82no—
98C4×C37—42no—
99C4×C37—41no—
100C4×C37—41no—
101C4×C37C4×D411yescharacteristic
102C4×C37C4×D411yescharacteristic
103C4×C37C22⋊Q811yescharacteristic
104C4×C37C22⋊Q811yescharacteristic
105Dic37—41no—
106Dic37—41no—
107Dic37—81no—
108#1856—371nomaximal, Sylow
109C2×C37—21no—
110C2×C37—21no—
111C2×C37#38511yescharacteristic
112C2×C37#45311yescharacteristic
113C2×C37#45511yescharacteristic
114D37—44no—
115#518—371no—
116#428—371no—
117#428—371no—
118C2×#100—371no—
119#390—371no—
120#339—371no—
121#339D3711yescharacteristic, complemented
122C37#185611yescharacteristic, complemented, Sylow
123C22×D4—371no—
124C2×M16—371no—
125C2×M16C2×D3711yescharacteristic
126C4×D4—741no—
127C4×D4—741no—
128C4×D4—741no—
129C4×D4—741no—
130#117—371no—
131#117C2×D3711yescharacteristic
132C2×C4⋊C4—371no—
133C2×C22⋊C4—742no—
134C2×C22⋊C4—742no—
135C2×C42C2×D3711yescharacteristic
136#107—741no—
137#107—741no—
138#106—741no—
139#106—741no—
140#100—374no—
141C24—372no—
142C2×D4—372no—
143C2×D4—372no—
144C2×D4—741no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4—741no—
148C22×C4—21no—
149C22×C4—742no—
150C22×C4—742no—
151C22×C4—741no—
152C22×C4C22×D3711yescharacteristic
153M16—21no—
154M16—372no—
155M16—741no—
156M16C4×D3712yescomplemented
157C2×C8—21no—
158C2×C8—741no—
159C4⋊C4—371no—
160C4⋊C4—371no—
161C4⋊C4—741no—
162C4⋊C4—741no—
163C4⋊C4D14811yescharacteristic
164C4⋊C4D14811yescharacteristic
165C22⋊C4—21no—
166C22⋊C4—742no—
167C22⋊C4—742no—
168C22⋊C4—741no—
169C22⋊C4—1484no—
170C42—21no—
171C42—21no—
172C42—21no—
173C42—741no—
174C23—374no—
175C23—742no—
176C23—742no—
177C23—1482no—
178C23—1482no—
179C23D4×D3711yescharacteristic
180D4—742no—
181D4—742no—
182D4—742no—
183D4—742no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2962no—
190C2×C4—2962no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—1482no—
194C2×C4—1481no—
195C2×C4C2×C4×D3711yescharacteristic
196C2×C4C2×D14811yescharacteristic
197C2×C4#1059696211yescharacteristic
198C2×C4D4×D3711yescharacteristic
199C2×C4#1059696411yescharacteristic
200C2×C4Q8×D3711yescharacteristic
201C8—22no—
202C8—742no—
203C22—21no—
204C22—21no—
205C22—2962no—
206C22—744no—
207C22—1484no—
208C22—1482no—
209C22—1482no—
210C22C4⋊C4×D3711yescharacteristic
211C22#1192450611yescharacteristic
212C22#1192451811yescharacteristic
213C4—42no—
214C4—41no—
215C4—41no—
216C4—2961no—
217C4—1481no—
218C4—1481no—
219C4#1192449611yescharacteristic
220C4C4×D14811yescharacteristic
221C4#1192451411yescharacteristic
222C4#1192451611yescharacteristic
223C2—21no—
224C2—21no—
225C2—1484no—
226C2#1455740711yescharacteristic
227C2#1455770211yescharacteristic
228C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radicalC22×D148C22
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1856
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14557576C2semidirect
3. #14557575C2semidirect
6. #14557293C2semidirect
7. C37×#339C2semidirect
22. #11924452C4semidirect
39. M16×C37C2×C4semidirect
57. #10596934C2×C4semidirect
121. #339D37semidirect
122. C37#1856semidirect
156. M16C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145580072
#145575762
#145575752
C2×#119244522
#145574352
#145572932
C37×#3392
#185637