Finite Group Databasebeta

← #17993634

Subgroups — #17993634

Order 4736.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#14558110C211yesmaximal, characteristic
2#14557852C211yesmaximal, characteristic, complemented
3#14557849C211yesmaximal, characteristic, complemented
4#14557473C211yesmaximal, characteristic, complemented
5#14557266C211yesmaximal, characteristic, complemented
6#14557258C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9#11924514—21no—
10#11924513—21no—
11#11924510C2211yescharacteristic
12#11924509—21no—
13#11924508—21no—
14#11924508—21no—
15C2×C4⋊Dic37C2211yescharacteristic
16C2×#10596936C2211yescharacteristic
17#11924468—21no—
18#11924467—21no—
19#11924458—21no—
20#11924457—21no—
21C22⋊#64436C2211yescharacteristic
22#11924443—21no—
23#11924443—21no—
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37D411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36C22×Dic37D411yescharacteristic
37C22×Dic37D411yescharacteristic
38#10596964—42no—
39#10596964—42no—
40C2×D148D411yescharacteristic
41C2×C4×D37—21no—
42C2×Dic74—21no—
43C2×C8×C37—21no—
44C4⋊C4×C37D411yescharacteristic
45C22⋊C4×C37—21no—
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37—21no—
50C4⋊Dic37—21no—
51C4⋊Dic37D411yescharacteristic
52#10596936—21no—
53#10596936—21no—
54#10596936—21no—
55C2×#64436—21no—
56C23×C37—21no—
57C23×C37C2×D411yescharacteristic
58C22×D37—21no—
59D4×C37—41no—
60D4×C37—41no—
61D4×C37—41no—
62C2×C4×C37—21no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C22⋊D37—42no—
70C22⋊D37—41no—
71C22⋊D37—41no—
72C22⋊D37—81no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—42no—
78C2×Dic37—41no—
79C2×Dic37—42no—
80C2×Dic37—41no—
81C2×Dic37SD1612yes—
82D148—41no—
83C4×D37—42no—
84Dic74—42no—
85C8×C37—41no—
86#64436—41no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37#12011yescharacteristic
93C22×C37C2×SD1611yescharacteristic
94C22×C37AGL(1,ℤ/8)11yescharacteristic
95C2×D37—41no—
96C2×D37—41no—
97C2×D37—41no—
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—41no—
101C4×C37—81no—
102Dic37—22no—
103Dic37—41no—
104Dic37—41no—
105Dic37—81no—
106#1616—371nomaximal, Sylow
107C2×C37—21no—
108C2×C37—21no—
109C2×C37—81no—
110C2×C37#45011yescharacteristic
111C2×C37#45411yescharacteristic
112C2×C37#45811yescharacteristic
113D37—81no—
114#537—371no—
115#481—371no—
116#481—371no—
117#400—371no—
118#327—371no—
119#327D3711yescharacteristic, complemented
120#324—371no—
121C37#161611yescharacteristic, complemented, Sylow
122C2×#41—741no—
123C22⋊Q8—741no—
124C22⋊Q8—741no—
125#121—371no—
126#121—741no—
127#121—741no—
128#121—741no—
129#121C2×D3711yescharacteristic
130C2×C4⋊C4—371no—
131C2×C4⋊C4—371no—
132#106—741no—
133#106—741no—
134#102—741no—
135#102—741no—
136C22⋊C8—371no—
137C22⋊C8C2×D3711yescharacteristic
138#95—741no—
139#95—741no—
140#95C2×D3711yescharacteristic
141#41—1482no—
142#41—1482no—
143C2×Q8—741no—
144C2×D4—21no—
145C2×D4—371no—
146C2×D4—741no—
147C2×D4—741no—
148C2×D4—741no—
149C2×D4D14811yescharacteristic
150C22×C4—21no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—741no—
154C22×C4—741no—
155C22×C4—741no—
156C22×C4C22×D3711yescharacteristic
157C2×C8—21no—
158C2×C8—741no—
159C4⋊C4—371no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C4⋊C4—741no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4D14811yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—741no—
170C23—21no—
171C23—741no—
172C23D4×D3711yescharacteristic
173Q8—1482no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—2961no—
178D4—1481no—
179D4—1482no—
180D4—1481no—
181D4—1481no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—372no—
188C2×C4—741no—
189C2×C4—741no—
190C2×C4—741no—
191C2×C4—741no—
192C2×C4—1482no—
193C2×C4—1482no—
194C2×C4—1481no—
195C2×C4—1482no—
196C2×C4—1481no—
197C2×C4C2×D14811yescharacteristic
198C2×C4D4×D3711yescharacteristic
199C8—41no—
200C8—1481no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—1481no—
207C22—1481no—
208C22—1481no—
209C22#1192450611yescharacteristic
210C22SD16×D3711yescharacteristic
211C22#1192456011yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—2961no—
217C4—742no—
218C4—1481no—
219C4—1481no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—2961no—
224C2#1455768511yescharacteristic
225C2#1455770711yescharacteristic
226C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37#120
prime radical#14558110C2
hypercenter#327D37
hypocenterC37#1616
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14557852C2semidirect
3. #14557849C2semidirect
4. #14557473C2semidirect
5. #14557266C2semidirect
6. #14557258C2semidirect
7. C37×#327C2semidirect
119. #327D37semidirect
121. C37#1616semidirect

Maximal subgroups

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

subgroupindex
#145581102
#145578522
#145578492
#145574732
#145572662
#145572582
C37×#3272
#161637