Finite Group Databasebeta

← #17993600

Subgroups — #17993600

Order 4736.

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

normal subgroups only

This group has 254 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#14557847C211yesmaximal, characteristic, complemented
3#14557844C211yesmaximal, characteristic, complemented
4#14557465C211yesmaximal, 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⋊Dic37—21no—
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596936C2211yescharacteristic
18#11924470—21no—
19#11924469—21no—
20#11924458—21no—
21#11924457—21no—
22C22⋊#64436C2211yescharacteristic
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⋊Dic37—42no—
52C4⋊Dic37D411yescharacteristic
53#10596936—21no—
54#10596936—21no—
55#10596936—21no—
56C2×#64436—21no—
57C23×C37—21no—
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60D4×C37—41no—
61D4×C37—41no—
62D4×C37—41no—
63C2×C4×C37—22no—
64C2×C4×C37—21no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C22⋊D37—42no—
71C22⋊D37—41no—
72C22⋊D37—41no—
73C22⋊D37—81no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—42no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82C2×Dic37—41no—
83C2×Dic37D812yes—
84D148—41no—
85C4×D37—42no—
86Dic74—42no—
87C8×C37—41no—
88#64436—41no—
89C22×C37—21no—
90C22×C37—21no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37—41no—
94C22×C37#12011yescharacteristic
95C22×C37C2×D811yescharacteristic
96C22×C37AGL(1,ℤ/8)11yescharacteristic
97C2×D37—41no—
98C2×D37—41no—
99C2×D37—41no—
100C4×C37—21no—
101C4×C37—21no—
102C4×C37—42no—
103C4×C37—41no—
104Dic37—22no—
105Dic37—41no—
106Dic37—41no—
107Dic37—81no—
108#1610—371nomaximal, Sylow
109C2×C37—21no—
110C2×C37—21no—
111C2×C37—81no—
112C2×C37#44711yescharacteristic
113C2×C37#45611yescharacteristic
114C2×C37#45811yescharacteristic
115D37—81no—
116#537—371no—
117#480—371no—
118#480—371no—
119#398—371no—
120#327—371no—
121#327D3711yescharacteristic, complemented
122#324—371no—
123C37#161011yescharacteristic, complemented, Sylow
124C2×#41—741no—
125C22⋊Q8—741no—
126C22⋊Q8—741no—
127#121—371no—
128#121—741no—
129#121—741no—
130#121—741no—
131#121C2×D3711yescharacteristic
132C2×C4⋊C4—371no—
133C2×C4⋊C4—371no—
134C2×C4⋊C4—741no—
135#107—741no—
136#107—741no—
137#102—741no—
138#102—741no—
139C22⋊C8—371no—
140C22⋊C8C2×D3711yescharacteristic
141#95—741no—
142#95C2×D3711yescharacteristic
143#41—1482no—
144#41—1482no—
145C2×Q8—741no—
146C2×D4—21no—
147C2×D4—371no—
148C2×D4—741no—
149C2×D4—741no—
150C2×D4—741no—
151C2×D4D14811yescharacteristic
152C22×C4—21no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—741no—
156C22×C4—741no—
157C22×C4—741no—
158C22×C4C22×D3711yescharacteristic
159C2×C8—21no—
160C2×C8—741no—
161C4⋊C4—371no—
162C4⋊C4—741no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4—741no—
166C4⋊C4—741no—
167C4⋊C4—1482no—
168C4⋊C4D14811yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C23—21no—
174C23—741no—
175C23D4×D3711yescharacteristic
176Q8—1482no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—2961no—
181D4—1481no—
182D4—1482no—
183D4—1481no—
184D4—1481no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—372no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—741no—
195C2×C4—1482no—
196C2×C4—1481no—
197C2×C4—1481no—
198C2×C4—1481no—
199C2×C4—1482no—
200C2×C4—1481no—
201C2×C4C2×D14811yescharacteristic
202C2×C4D4×D3711yescharacteristic
203C8—41no—
204C8—1481no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—1481no—
211C22—1481no—
212C22—1481no—
213C22#1192450611yescharacteristic
214C22D8×D3711yescharacteristic
215C22#1192456311yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—2961no—
221C4—742no—
222C4—1481no—
223C4—1481no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—2961no—
228C2#1455766811yescharacteristic
229C2#1455771711yescharacteristic
230C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37#120
prime radical#14558110C2
hypercenter#327D37
hypocenterC37#1610
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. #14557847C2semidirect
3. #14557844C2semidirect
4. #14557465C2semidirect
5. #14557266C2semidirect
6. #14557258C2semidirect
7. C37×#327C2semidirect
121. #327D37semidirect
123. C37#1610semidirect

Maximal subgroups

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

subgroupindex
#145581102
#145578472
#145578442
#145574652
#145572662
#145572582
C37×#3272
#161037